FedProx.ipynb

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      "metadata": {
        "id": "view-in-github",
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      "source": [
        "<a href=\"https://colab.research.google.com/github/ayushm-agrawal/Federated-Learning-Implementations/blob/master/FedProx.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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        "## How to Navigate through this notebook...\n",
        "\n",
        "  Start by collapsing all the cells in Google Colab. This will allow you to easily navigate through different parts that might be useful for you.\n",
        "\n",
        "The main sections of this notebook are listed below\n",
        "<dl>\n",
        "  <dt><b>Imports</b></dt>\n",
        "  <dd>- Contains all the necessary imports</dd>\n",
        "\n",
        "  <dt><b>Re-Format Time</b></dt>\n",
        "  <dd>- Functions to format time in a readable format.</dd>\n",
        "  <dt><b>Load the MNIST Dataset</b></dt>\n",
        "  <dd>- Load the MNIST Train and Test Dataset from the Torchvision Datasets</dd>\n",
        "  <dt><b>Visualize Data</b></dt>\n",
        "  <dd>- Load the first few images from the train and test dataset as a sanity check.</dd>\n",
        "  <dt><b>Partitioning the Data (IID and non-IID)</b></dt>\n",
        "  <dd>- Two functions defined to replicate data partitioning in real world scenario.</dd>\n",
        "  <dd>- IID: Identical and Independent Dataset, generally provides a uniform distribution to the dataset.</dd>\n",
        "  <dd>- non-IID: This is a pathological implementation where each client in a Federated Learning Scenario gets data from only a subset of classes and not all.</dd>\n",
        "  <dt><b>Models</b></dt>\n",
        "  <dd>- MNIST 2NN: Multi-Layer Perceptron replicated from the FedAvg paper.</dd> \n",
        "  <dd>- MNIST CNN: Two layer CNN model replicated from the FedAvg paper.</dd>\n",
        "  <dt><b>Testing Loop</b></dt>\n",
        "  <dd>- We use this test loop at every epoch to stop our model from overfittin.</dd>\n",
        "  <dt><b>FedProx</b></dt>\n",
        "  <dd>- This block contains the entire implementation of the FedProx algorithm as discussed in the paper.</dd>\n",
        "  <dd>- Different functions are implemented to replicate heterogeneity as mentioned in the FedProx paper</dd>\n",
        "  <dd>- Client Update function is used to train local clients</dd>\n",
        "  <dd>- Server Side Update function takes the local models by clients and updates the global model</dd>\n",
        "\n",
        "  > <b>NOTE: FROM HERE WE START RUNNING DIFFERENT TESTS ON FEDPROX ALGORITHM</b>\n",
        "\n",
        "  > <u>For each experiment, please check the hyperparameters used and update as necessary.</u>\n",
        "\n",
        "  <dt><b>Special Case for FedProx</b></dt>\n",
        "  <dd>- In this case, FedProx acts like FedAvg</dd>\n",
        "  <dt><b>Training with 0% Probability</b></dt>\n",
        "  <dd>- Run tests for CNN and MLP models for IID and non-IID dataset when there are no stragglers.</dd>\n",
        "  <dt><b>Training with 50% Probability</b></dt>\n",
        "  <dd>- Run tests for CNN and MLP models for IID and non-IID dataset when there are 50% stragglers.</dd>\n",
        "  <dt><b>Training with 90% Probability</b></dt>\n",
        "  <dd>- Run tests for CNN and MLP models for IID and non-IID dataset when there are 90% stragglers.</dd>\n",
        "\n",
        "  <dt><b>Comparison of FedAvg and FedProx on IID Dataset Partition</b></dt>\n",
        "  <dd>- Run tests to achieve target accuracy on FedAvg and FedProx under highly heteregeneous system.</dd>\n",
        "  <dt><b>Comparison of FedAvg and FedProx on non-IID Dataset Paritition</b></dt>\n",
        "  <dd>- Run tests to achieve target accuracy on FedAvg and FedProx under highly heteregeneous system.</dd>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1ET8d4SH-g2D",
        "colab_type": "text"
      },
      "source": [
        "## Imports"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "u2iSYH27XY_E",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "d52c0520-b50e-4223-ad1e-10a9ff44f99f"
      },
      "source": [
        "%load_ext tensorboard\n",
        "import os\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import copy\n",
        "import time\n",
        "import random\n",
        "\n",
        "import torch\n",
        "import torch.nn as nn\n",
        "import torch.nn.functional as F\n",
        "\n",
        "from torch.utils.data import Dataset, DataLoader\n",
        "from torch.utils.tensorboard import SummaryWriter\n",
        "from torchvision import transforms, utils, datasets\n",
        "from torchsummary import summary\n",
        "from datetime import datetime, timedelta\n",
        "\n",
        "# Check assigned GPU\n",
        "gpu_info = !nvidia-smi\n",
        "gpu_info = '\\n'.join(gpu_info)\n",
        "if gpu_info.find('failed') >= 0:\n",
        "  print('Select the Runtime > \"Change runtime type\" menu to enable a GPU accelerator, ')\n",
        "  print('and then re-execute this cell.')\n",
        "else:\n",
        "  print(gpu_info)\n",
        "\n",
        "\n",
        "# set manual seed for reproducibility\n",
        "seed = 42\n",
        "\n",
        "# general reproducibility\n",
        "random.seed(seed)\n",
        "np.random.seed(seed)\n",
        "torch.manual_seed(seed)\n",
        "\n",
        "# gpu training specific\n",
        "torch.backends.cudnn.deterministic = True\n",
        "torch.backends.cudnn.benchmark = False"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Wed Aug 12 15:19:47 2020       \n",
            "+-----------------------------------------------------------------------------+\n",
            "| NVIDIA-SMI 450.57       Driver Version: 418.67       CUDA Version: 10.1     |\n",
            "|-------------------------------+----------------------+----------------------+\n",
            "| GPU  Name        Persistence-M| Bus-Id        Disp.A | Volatile Uncorr. ECC |\n",
            "| Fan  Temp  Perf  Pwr:Usage/Cap|         Memory-Usage | GPU-Util  Compute M. |\n",
            "|                               |                      |               MIG M. |\n",
            "|===============================+======================+======================|\n",
            "|   0  Tesla P100-PCIE...  Off  | 00000000:00:04.0 Off |                    0 |\n",
            "| N/A   34C    P0    27W / 250W |      0MiB / 16280MiB |      0%      Default |\n",
            "|                               |                      |                 ERR! |\n",
            "+-------------------------------+----------------------+----------------------+\n",
            "                                                                               \n",
            "+-----------------------------------------------------------------------------+\n",
            "| Processes:                                                                  |\n",
            "|  GPU   GI   CI        PID   Type   Process name                  GPU Memory |\n",
            "|        ID   ID                                                   Usage      |\n",
            "|=============================================================================|\n",
            "|  No running processes found                                                 |\n",
            "+-----------------------------------------------------------------------------+\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "X7MesIL6AAuD",
        "colab_type": "text"
      },
      "source": [
        "## Re-Format Time"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0b0H9UUX__89",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def get_time_format(seconds):\n",
        "    sec = timedelta(seconds=int(seconds))\n",
        "    d = datetime(1, 1, 1) + sec\n",
        "    if d.day-1 == 1:\n",
        "        return \"%.2d:%.2d:%.2d:%.2d\" % (d.day-1, d.hour, d.minute, d.second)\n",
        "    return \"%.2d:%.2d:%.2d\" % (d.hour, d.minute, d.second)\n",
        "\n",
        "\n",
        "def calculate_time(start_time):\n",
        "    return get_time_format(time.time() - start_time)"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NY4eWzGiL6Mj",
        "colab_type": "text"
      },
      "source": [
        "## Load the MNIST Dataset"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "G649tjTXLL8F",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0,
          "referenced_widgets": [
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            "d69518fea14c44c59c53c02457af5495",
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            "0665403511994d82bc8370148f44e070",
            "196969d71b494012b8a52584f9d50201",
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            "3530fc4b65264b61b78e094316877a21",
            "9f47bfb81ffb42d1a943d994ad36cfaf",
            "15d3b624d14a4d3d83726c851c5e21db",
            "0e4e54fdd01a405ba5b80ef1bdd37dea",
            "0b6cac0b1ad14f339bee098ecee86057"
          ]
        },
        "outputId": "735733a1-85a0-46d7-c36a-958264fc99f9"
      },
      "source": [
        "# create transforms\n",
        "# We will just convert to tensor and normalize since no special transforms are mentioned in the paper\n",
        "transforms_mnist = transforms.Compose([\n",
        "                                       transforms.ToTensor(),\n",
        "                                       transforms.Normalize((0.1307,), (0.3081,))\n",
        "                                       ])\n",
        "\n",
        "mnist_data_train = datasets.MNIST('./data/mnist/', train=True, download=True, transform=transforms_mnist)\n",
        "mnist_data_test = datasets.MNIST('../data/mnist/', train=False, download=True, transform=transforms_mnist)"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Downloading http://yann.lecun.com/exdb/mnist/train-images-idx3-ubyte.gz to ./data/mnist/MNIST/raw/train-images-idx3-ubyte.gz\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "98cd9ad523994dda91464699551d2b3b",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=1.0, bar_style='info', max=1.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Extracting ./data/mnist/MNIST/raw/train-images-idx3-ubyte.gz to ./data/mnist/MNIST/raw\n",
            "Downloading http://yann.lecun.com/exdb/mnist/train-labels-idx1-ubyte.gz to ./data/mnist/MNIST/raw/train-labels-idx1-ubyte.gz\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "fd8012fcab0b41b48403689eebd1d2c0",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=1.0, bar_style='info', max=1.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Extracting ./data/mnist/MNIST/raw/train-labels-idx1-ubyte.gz to ./data/mnist/MNIST/raw\n",
            "Downloading http://yann.lecun.com/exdb/mnist/t10k-images-idx3-ubyte.gz to ./data/mnist/MNIST/raw/t10k-images-idx3-ubyte.gz\n",
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "de85728d78694c93b77b6f9695abe15f",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=1.0, bar_style='info', max=1.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Extracting ./data/mnist/MNIST/raw/t10k-images-idx3-ubyte.gz to ./data/mnist/MNIST/raw\n",
            "Downloading http://yann.lecun.com/exdb/mnist/t10k-labels-idx1-ubyte.gz to ./data/mnist/MNIST/raw/t10k-labels-idx1-ubyte.gz\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "ca4959a99d7240f4a839bca8eaab4153",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=1.0, bar_style='info', max=1.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Extracting ./data/mnist/MNIST/raw/t10k-labels-idx1-ubyte.gz to ./data/mnist/MNIST/raw\n",
            "Processing...\n",
            "Done!\n",
            "Downloading http://yann.lecun.com/exdb/mnist/train-images-idx3-ubyte.gz to ../data/mnist/MNIST/raw/train-images-idx3-ubyte.gz\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/torchvision/datasets/mnist.py:469: UserWarning: The given NumPy array is not writeable, and PyTorch does not support non-writeable tensors. This means you can write to the underlying (supposedly non-writeable) NumPy array using the tensor. You may want to copy the array to protect its data or make it writeable before converting it to a tensor. This type of warning will be suppressed for the rest of this program. (Triggered internally at  /pytorch/torch/csrc/utils/tensor_numpy.cpp:141.)\n",
            "  return torch.from_numpy(parsed.astype(m[2], copy=False)).view(*s)\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "b0354cf6272b467f9c1453b30322378e",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=1.0, bar_style='info', max=1.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Extracting ../data/mnist/MNIST/raw/train-images-idx3-ubyte.gz to ../data/mnist/MNIST/raw\n",
            "Downloading http://yann.lecun.com/exdb/mnist/train-labels-idx1-ubyte.gz to ../data/mnist/MNIST/raw/train-labels-idx1-ubyte.gz\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "5d8dbd34b29e422da85886be60567beb",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=1.0, bar_style='info', max=1.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Extracting ../data/mnist/MNIST/raw/train-labels-idx1-ubyte.gz to ../data/mnist/MNIST/raw\n",
            "Downloading http://yann.lecun.com/exdb/mnist/t10k-images-idx3-ubyte.gz to ../data/mnist/MNIST/raw/t10k-images-idx3-ubyte.gz\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "db4543462aa84e3e9f748c3bfcf2a899",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=1.0, bar_style='info', max=1.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Extracting ../data/mnist/MNIST/raw/t10k-images-idx3-ubyte.gz to ../data/mnist/MNIST/raw\n",
            "Downloading http://yann.lecun.com/exdb/mnist/t10k-labels-idx1-ubyte.gz to ../data/mnist/MNIST/raw/t10k-labels-idx1-ubyte.gz\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "196969d71b494012b8a52584f9d50201",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=1.0, bar_style='info', max=1.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Extracting ../data/mnist/MNIST/raw/t10k-labels-idx1-ubyte.gz to ../data/mnist/MNIST/raw\n",
            "Processing...\n",
            "Done!\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dm9usjn2vFkL",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "3b4b2944-71da-41c3-a625-b0bd0cbc7acd"
      },
      "source": [
        "classes = np.array(list(mnist_data_train.class_to_idx.values()))\n",
        "classes_test = np.array(list(mnist_data_test.class_to_idx.values()))\n",
        "num_classes = len(classes_test)\n",
        "print(\"Classes: {} \\tType: {}\".format(classes, type(classes)))\n",
        "print(\"Classes Test: {} \\tType: {}\".format(classes_test, type(classes)))\n"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Classes: [0 1 2 3 4 5 6 7 8 9] \tType: <class 'numpy.ndarray'>\n",
            "Classes Test: [0 1 2 3 4 5 6 7 8 9] \tType: <class 'numpy.ndarray'>\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9lvJt3Ofv2SO",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "ed065a58-369a-44fc-e6c0-4f902b86b8ad"
      },
      "source": [
        "print(\"Image Shape: {}\".format(mnist_data_train.data[0].size()))"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Image Shape: torch.Size([28, 28])\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jCOONkg-zV7Y",
        "colab_type": "text"
      },
      "source": [
        "## Visualize Data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "R9MK03TZw6Qs",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def imshow(img):\n",
        "\timg = img/2 + 0.5 #unnormalize the image\n",
        "\tplt.imshow(img, cmap='gray') # convert from tensor to image"
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gMJ0Kx4Kw-_H",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def visualize(dataset):\n",
        "  figure = plt.figure(figsize=(25,4))\n",
        "  for i in range(20):\n",
        "    axis = figure.add_subplot(2, 20/2, i+1, xticks=[], yticks=[])\n",
        "    data = dataset.data[i]\n",
        "    data = data.numpy()\n",
        "\n",
        "    target = dataset.targets[i]\n",
        "    target = target.numpy()\n",
        "    imshow(data)\n",
        "    axis.set_title(target)\n"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8bPOwKg10Ro7",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "287106dd-9b40-49b3-c0c3-6e86c6113ec2"
      },
      "source": [
        "visualize(mnist_data_train)"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\n",
            "\n",
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 1800x288 with 20 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RKoh5Cf70UYu",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "e0fb725c-046c-403f-d7f6-88dbb80911b6"
      },
      "source": [
        "visualize(mnist_data_test)"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 1800x288 with 20 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ctjRsETiO1qO",
        "colab_type": "text"
      },
      "source": [
        "## Partitioning the Data (IID and non-IID)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3_v8lyrgO5dD",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def iid_partition(dataset, clients):\n",
        "  \"\"\"\n",
        "  I.I.D paritioning of data over clients\n",
        "  Shuffle the data\n",
        "  Split it between clients\n",
        "  \n",
        "  params:\n",
        "    - dataset (torch.utils.Dataset): Dataset containing the MNIST Images\n",
        "    - clients (int): Number of Clients to split the data between\n",
        "\n",
        "  returns:\n",
        "    - Dictionary of image indexes for each client\n",
        "  \"\"\"\n",
        "\n",
        "  num_items_per_client = int(len(dataset)/clients)\n",
        "  client_dict = {}\n",
        "  image_idxs = [i for i in range(len(dataset))]\n",
        "\n",
        "  for i in range(clients):\n",
        "    client_dict[i] = set(np.random.choice(image_idxs, num_items_per_client, replace=False))\n",
        "    image_idxs = list(set(image_idxs) - client_dict[i])\n",
        "\n",
        "  return client_dict"
      ],
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4zMdliGMQoSl",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def non_iid_partition(dataset, clients, total_shards, shards_size, num_shards_per_client):\n",
        "  \"\"\"\n",
        "  non I.I.D parititioning of data over clients\n",
        "  Sort the data by the digit label\n",
        "  Divide the data into N shards of size S\n",
        "  Each of the clients will get X shards\n",
        "\n",
        "  params:\n",
        "    - dataset (torch.utils.Dataset): Dataset containing the MNIST Images\n",
        "    - clients (int): Number of Clients to split the data between\n",
        "    - total_shards (int): Number of shards to partition the data in\n",
        "    - shards_size (int): Size of each shard \n",
        "    - num_shards_per_client (int): Number of shards of size shards_size that each client receives\n",
        "\n",
        "  returns:\n",
        "    - Dictionary of image indexes for each client\n",
        "  \"\"\"\n",
        "  \n",
        "  shard_idxs = [i for i in range(total_shards)]\n",
        "  client_dict = {i: np.array([], dtype='int64') for i in range(clients)}\n",
        "  idxs = np.arange(len(dataset))\n",
        "  data_labels = dataset.targets.numpy()\n",
        "\n",
        "  # sort the labels\n",
        "  label_idxs = np.vstack((idxs, data_labels))\n",
        "  label_idxs = label_idxs[:, label_idxs[1,:].argsort()]\n",
        "  idxs = label_idxs[0,:]\n",
        "\n",
        "  # divide the data into total_shards of size shards_size\n",
        "  # assign num_shards_per_client to each client\n",
        "  for i in range(clients):\n",
        "    rand_set = set(np.random.choice(shard_idxs, num_shards_per_client, replace=False))\n",
        "    shard_idxs = list(set(shard_idxs) - rand_set)\n",
        "\n",
        "    for rand in rand_set:\n",
        "      client_dict[i] = np.concatenate((client_dict[i], idxs[rand*shards_size:(rand+1)*shards_size]), axis=0)\n",
        "  \n",
        "  return client_dict"
      ],
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PTfxv8kFoGAy",
        "colab_type": "text"
      },
      "source": [
        "## Models"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CvoDNFKbZST5",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "class MNIST_2NN(nn.Module):\n",
        "  \"\"\"\n",
        "  A simple multilayer-perceptron with 2-hidden layers with 200 units each\n",
        "  using ReLu activations\n",
        "\n",
        "  Total Expected Params: 199,210\n",
        "  \"\"\"\n",
        "  def __init__(self):\n",
        "    super(MNIST_2NN, self).__init__()\n",
        "\n",
        "    self.fc1 = nn.Linear(28*28, 200)\n",
        "    self.fc2 = nn.Linear(200, 200)\n",
        "    self.fc3 = nn.Linear(200, 10)\n",
        "\n",
        "  def forward(self, x):\n",
        "    x = torch.flatten(x, 1)\n",
        "    x = F.relu(self.fc1(x))\n",
        "    x = F.relu(self.fc2(x))\n",
        "    out = self.fc3(x)\n",
        "\n",
        "    return x"
      ],
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ut1hZ8x3qYPZ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "class MNIST_CNN(nn.Module):\n",
        "  \"\"\"\n",
        "  CNN with two 5x5 convolution lauers(the first with 32 channels, second with 64,\n",
        "  each followed with 2x2 max pooling), a fully connected layer with 512 uunits and \n",
        "  ReLu activation, and the final Softmax output layer\n",
        "\n",
        "  Total Expected Params: 1,663,370\n",
        "  \"\"\"\n",
        "  def __init__(self):\n",
        "    super(MNIST_CNN, self).__init__()\n",
        "\n",
        "    self.conv1 = nn.Conv2d(1, 32, kernel_size=5)\n",
        "    self.conv2 = nn.Conv2d(32, 64, kernel_size=5)\n",
        "    \n",
        "    self.pool = nn.MaxPool2d(2,2)\n",
        "    self.dropout = nn.Dropout(p=0.2)\n",
        "\n",
        "    self.fc1 = nn.Linear(1024, 512)\n",
        "    self.out = nn.Linear(512, 10)\n",
        "\n",
        "  def forward(self, x):\n",
        "    x = self.pool(F.relu(self.conv1(x)))\n",
        "    x = self.pool(F.relu(self.conv2(x)))\n",
        "    x = self.dropout(x)\n",
        "    x = torch.flatten(x, 1)\n",
        "    x = F.relu(self.fc1(x))\n",
        "    x = self.out(x)\n",
        "    out = F.log_softmax(x, dim=1)\n",
        "\n",
        "    return out"
      ],
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uVv4HA9HuLtr",
        "colab_type": "text"
      },
      "source": [
        "### Print Model Summaries"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "I5oTH710sJEt",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "b6061eac-5411-4d76-fa92-cf2aece3341f"
      },
      "source": [
        "mnist_mlp = MNIST_2NN()\n",
        "mnist_cnn = MNIST_CNN()\n",
        "\n",
        "if torch.cuda.is_available():\n",
        "  mnist_mlp.cuda()\n",
        "  mnist_cnn.cuda()\n",
        "\n",
        "print(\"MNIST MLP SUMMARY\")\n",
        "print(summary(mnist_mlp, (28,28)))\n",
        "\n",
        "print(\"\\nMNIST CNN SUMMARY\")\n",
        "print(summary(mnist_cnn, (1, 28,28)))"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "MNIST MLP SUMMARY\n",
            "----------------------------------------------------------------\n",
            "        Layer (type)               Output Shape         Param #\n",
            "================================================================\n",
            "            Linear-1                  [-1, 200]         157,000\n",
            "            Linear-2                  [-1, 200]          40,200\n",
            "            Linear-3                   [-1, 10]           2,010\n",
            "================================================================\n",
            "Total params: 199,210\n",
            "Trainable params: 199,210\n",
            "Non-trainable params: 0\n",
            "----------------------------------------------------------------\n",
            "Input size (MB): 0.00\n",
            "Forward/backward pass size (MB): 0.00\n",
            "Params size (MB): 0.76\n",
            "Estimated Total Size (MB): 0.77\n",
            "----------------------------------------------------------------\n",
            "None\n",
            "\n",
            "MNIST CNN SUMMARY\n",
            "----------------------------------------------------------------\n",
            "        Layer (type)               Output Shape         Param #\n",
            "================================================================\n",
            "            Conv2d-1           [-1, 32, 24, 24]             832\n",
            "         MaxPool2d-2           [-1, 32, 12, 12]               0\n",
            "            Conv2d-3             [-1, 64, 8, 8]          51,264\n",
            "         MaxPool2d-4             [-1, 64, 4, 4]               0\n",
            "           Dropout-5             [-1, 64, 4, 4]               0\n",
            "            Linear-6                  [-1, 512]         524,800\n",
            "            Linear-7                   [-1, 10]           5,130\n",
            "================================================================\n",
            "Total params: 582,026\n",
            "Trainable params: 582,026\n",
            "Non-trainable params: 0\n",
            "----------------------------------------------------------------\n",
            "Input size (MB): 0.00\n",
            "Forward/backward pass size (MB): 0.23\n",
            "Params size (MB): 2.22\n",
            "Estimated Total Size (MB): 2.45\n",
            "----------------------------------------------------------------\n",
            "None\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tUYyb4T-uXmF",
        "colab_type": "text"
      },
      "source": [
        "## Testing Loop"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uCcIZmO5uan9",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def testing(model, dataset, bs, criterion, num_classes, classes):\n",
        "  #test loss \n",
        "  test_loss = 0.0\n",
        "  correct_class = list(0. for i in range(num_classes))\n",
        "  total_class = list(0. for i in range(num_classes))\n",
        "\n",
        "  test_loader = DataLoader(dataset, batch_size=bs)\n",
        "  l = len(test_loader)\n",
        "  model.eval()\n",
        "  for data, labels in test_loader:\n",
        "\n",
        "    if torch.cuda.is_available():\n",
        "      data, labels = data.cuda(), labels.cuda()\n",
        "\n",
        "    output = model(data)\n",
        "    loss = criterion(output, labels)\n",
        "    test_loss += loss.item()*data.size(0)\n",
        "\n",
        "    _, pred = torch.max(output, 1)\n",
        "\n",
        "    correct_tensor = pred.eq(labels.data.view_as(pred))\n",
        "    correct = np.squeeze(correct_tensor.numpy()) if not torch.cuda.is_available() else np.squeeze(correct_tensor.cpu().numpy())\n",
        "\n",
        "    #test accuracy for each object class\n",
        "    for i in range(num_classes):\n",
        "      label = labels.data[i]\n",
        "      correct_class[label] += correct[i].item()\n",
        "      total_class[label] += 1\n",
        "    \n",
        "  # avg test loss\n",
        "  test_loss = test_loss/len(test_loader.dataset)\n",
        "  # print(\"Test Loss: {:.6f}\\n\".format(test_loss))\n",
        "\n",
        "  # print test accuracy\n",
        "  # for i in range(10):\n",
        "  #   if total_class[i]>0:\n",
        "  #     print('Test Accuracy of %5s: %2d%% (%2d/%2d)' % \n",
        "  #           (classes[i], 100 * correct_class[i] / total_class[i],\n",
        "  #           np.sum(correct_class[i]), np.sum(total_class[i])))\n",
        "  #   else:\n",
        "  #     print('Test Accuracy of %5s: N/A (no training examples)' % (classes[i]))\n",
        "\n",
        "  test_accuracy = 100. * np.sum(correct_class) / np.sum(total_class)\n",
        "\n",
        "  # print('\\nFinal Test  Accuracy: {:.3f} ({}/{})'.format(\n",
        "  #       100. * np.sum(correct_class) / np.sum(total_class),\n",
        "  #       np.sum(correct_class), np.sum(total_class)))\n",
        "  return test_loss, test_accuracy"
      ],
      "execution_count": 15,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gf_8XEXa-gZ7",
        "colab_type": "text"
      },
      "source": [
        "## FedProx"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "cjGMTWxAOsf1"
      },
      "source": [
        "### Systems Heterogeneity Simulations\n",
        "\n",
        "Generate epochs for selected clients based on percentage of devices that corresponds to heterogeneity. \n",
        "\n",
        "Assign x number of epochs (chosen unifirmly at random between [1, E]) to 0%, 50% or 90% of the selected devices, respectively. Settings where 0% devices perform fewer than E epochs of work correspond to the environments without system heterogeneity, while 90% of the devices sending their partial solutions corresponds to highly heterogenous system."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "i-WTHuT3OpFD",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def GenerateLocalEpochs(percentage, size, max_epochs):\n",
        "  ''' Method generates list of epochs for selected clients\n",
        "  to replicate system heteroggeneity\n",
        "\n",
        "  Params:\n",
        "    percentage: percentage of clients to have fewer than E epochs\n",
        "    size:       total size of the list\n",
        "    max_epochs: maximum value for local epochs\n",
        "  \n",
        "  Returns:\n",
        "    List of size epochs for each Client Update\n",
        "\n",
        "  '''\n",
        "\n",
        "  # if percentage is 0 then each client runs for E epochs\n",
        "  if percentage == 0:\n",
        "      return np.array([max_epochs]*size)\n",
        "  else:\n",
        "    # get the number of clients to have fewer than E epochs\n",
        "    heterogenous_size = int((percentage/100) * size)\n",
        "\n",
        "    # generate random uniform epochs of heterogenous size between 1 and E\n",
        "    epoch_list = np.random.randint(1, max_epochs, heterogenous_size)\n",
        "\n",
        "    # the rest of the clients will have E epochs\n",
        "    remaining_size = size - heterogenous_size\n",
        "    rem_list = [max_epochs]*remaining_size\n",
        "\n",
        "    epoch_list = np.append(epoch_list, rem_list, axis=0)\n",
        "    \n",
        "    # shuffle the list and return\n",
        "    np.random.shuffle(epoch_list)\n",
        "\n",
        "    return epoch_list"
      ],
      "execution_count": 16,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "L-aNdQsQ-Kvp",
        "colab_type": "text"
      },
      "source": [
        "### Local Training (Client Update)\n",
        "\n",
        "Local training for the model on client side"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oX6OsQyO-Gz7",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "class CustomDataset(Dataset):\n",
        "  def __init__(self, dataset, idxs):\n",
        "      self.dataset = dataset\n",
        "      self.idxs = list(idxs)\n",
        "\n",
        "  def __len__(self):\n",
        "      return len(self.idxs)\n",
        "\n",
        "  def __getitem__(self, item):\n",
        "      image, label = self.dataset[self.idxs[item]]\n",
        "      return image, label\n",
        "\n",
        "class ClientUpdate(object):\n",
        "  def __init__(self, dataset, batchSize, learning_rate, epochs, idxs, mu, algorithm):\n",
        "    self.train_loader = DataLoader(CustomDataset(dataset, idxs), batch_size=batchSize, shuffle=True)\n",
        "    self.algorithm = algorithm\n",
        "    self.learning_rate = learning_rate\n",
        "    self.epochs = epochs\n",
        "\n",
        "  def train(self, model):\n",
        "    # print(\"Client training for {} epochs.\".format(self.epochs))\n",
        "    criterion = nn.CrossEntropyLoss()\n",
        "    proximal_criterion = nn.MSELoss(reduction='mean')\n",
        "    optimizer = torch.optim.SGD(model.parameters(), lr=self.learning_rate, momentum=0.5)\n",
        "\n",
        "    # use the weights of global model for proximal term calculation\n",
        "    global_model = copy.deepcopy(model)\n",
        "\n",
        "    # calculate local training time\n",
        "    start_time = time.time()\n",
        "\n",
        "\n",
        "    e_loss = []\n",
        "    for epoch in range(1, self.epochs+1):\n",
        "\n",
        "      train_loss = 0.0\n",
        "\n",
        "      model.train()\n",
        "      for data, labels in self.train_loader:\n",
        "\n",
        "        if torch.cuda.is_available():\n",
        "          data, labels = data.cuda(), labels.cuda()\n",
        "\n",
        "        # clear the gradients\n",
        "        optimizer.zero_grad()\n",
        "        # make a forward pass\n",
        "        output = model(data)\n",
        "\n",
        "        # calculate the loss + the proximal term\n",
        "        _, pred = torch.max(output, 1)\n",
        "\n",
        "        if self.algorithm == 'fedprox':\n",
        "          proximal_term = 0.0\n",
        "\n",
        "          # iterate through the current and global model parameters\n",
        "          for w, w_t in zip(model.parameters(), global_model.parameters()) :\n",
        "            # update the proximal term \n",
        "            #proximal_term += torch.sum(torch.abs((w-w_t)**2))\n",
        "            proximal_term += (w-w_t).norm(2)\n",
        "\n",
        "          loss = criterion(output, labels) + (mu/2)*proximal_term\n",
        "        else:\n",
        "          loss = criterion(output, labels)\n",
        "    \n",
        "        # do a backwards pass\n",
        "        loss.backward()\n",
        "        # perform a single optimization step\n",
        "        optimizer.step()\n",
        "        # update training loss\n",
        "        train_loss += loss.item()*data.size(0)\n",
        "\n",
        "      # average losses\n",
        "      train_loss = train_loss/len(self.train_loader.dataset)\n",
        "      e_loss.append(train_loss)\n",
        "\n",
        "    total_loss = sum(e_loss)/len(e_loss)\n",
        "\n",
        "    return model.state_dict(), total_loss, (time.time() - start_time)"
      ],
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ukgh1DVHE2Ds",
        "colab_type": "text"
      },
      "source": [
        "### Server Side Training\n",
        "\n",
        "Following Algorithm 1 from the paper"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1NF1e33BgpeL",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def training(model, rounds, batch_size, lr, ds, data_dict, test_data_dict, C, K, E, mu, percentage, plt_title, plt_color, target_test_accuracy, algorithm=\"fedprox\"):\n",
        "  \"\"\"\n",
        "  Function implements the Federated Averaging Algorithm from the FedAvg paper.\n",
        "  Specifically, this function is used for the server side training and weight update\n",
        "\n",
        "  Params:\n",
        "    - model:           PyTorch model to train\n",
        "    - rounds:          Number of communication rounds for the client update\n",
        "    - batch_size:      Batch size for client update training\n",
        "    - lr:              Learning rate used for client update training\n",
        "    - ds:              Dataset used for training\n",
        "    - data_dict:       Type of data partition used for training (IID or non-IID)\n",
        "    - test_data_dict:  Data used for testing the model\n",
        "    - C:               Fraction of clients randomly chosen to perform computation on each round\n",
        "    - K:               Total number of clients\n",
        "    - E:               Number of training passes each client makes over its local dataset per round\n",
        "    - mu:              proximal term constant\n",
        "    - percentage:      percentage of selected client to have fewer than E epochs\n",
        "  Returns:\n",
        "    - model:           Trained model on the server\n",
        "  \"\"\"\n",
        "\n",
        "  # global model weights\n",
        "  global_weights = model.state_dict()\n",
        "\n",
        "  # training loss\n",
        "  train_loss = []\n",
        "\n",
        "  # test accuracy\n",
        "  test_acc = []\n",
        "\n",
        "  # store last loss for convergence\n",
        "  last_loss = 0.0\n",
        "\n",
        "  # total time taken \n",
        "  total_time = 0\n",
        "\n",
        "  print(f\"System heterogeneity set to {percentage}% stragglers.\\n\")\n",
        "  print(f\"Picking {max(int(C*K),1 )} random clients per round.\\n\")\n",
        "\n",
        "  for curr_round in range(1, rounds+1):\n",
        "    w, local_loss, lst_local_train_time = [], [], []\n",
        "\n",
        "    m = max(int(C*K), 1)\n",
        "\n",
        "    heterogenous_epoch_list = GenerateLocalEpochs(percentage, size=m, max_epochs=E)\n",
        "    heterogenous_epoch_list = np.array(heterogenous_epoch_list)\n",
        "\n",
        "    S_t = np.random.choice(range(K), m, replace=False)\n",
        "    S_t = np.array(S_t)\n",
        "    \n",
        "    # For Federated Averaging, drop all the clients that are stragglers\n",
        "    if algorithm == 'fedavg':\n",
        "      stragglers_indices = np.argwhere(heterogenous_epoch_list < E)\n",
        "      heterogenous_epoch_list = np.delete(heterogenous_epoch_list, stragglers_indices)\n",
        "      S_t = np.delete(S_t, stragglers_indices)\n",
        "\n",
        "    for k, epoch in zip(S_t, heterogenous_epoch_list):\n",
        "      local_update = ClientUpdate(dataset=ds, batchSize=batch_size, learning_rate=lr, epochs=epoch, idxs=data_dict[k], mu=mu, algorithm=algorithm)\n",
        "      weights, loss, local_train_time = local_update.train(model=copy.deepcopy(model))\n",
        "\n",
        "      w.append(copy.deepcopy(weights))\n",
        "      local_loss.append(copy.deepcopy(loss))\n",
        "      lst_local_train_time.append(local_train_time)\n",
        "\n",
        "    # calculate time to update the global weights\n",
        "    global_start_time = time.time()\n",
        "\n",
        "    # updating the global weights\n",
        "    weights_avg = copy.deepcopy(w[0])\n",
        "    for k in weights_avg.keys():\n",
        "      for i in range(1, len(w)):\n",
        "        weights_avg[k] += w[i][k]\n",
        "\n",
        "      weights_avg[k] = torch.div(weights_avg[k], len(w))\n",
        "\n",
        "    global_weights = weights_avg\n",
        "\n",
        "    global_end_time = time.time()\n",
        "\n",
        "    # calculate total time \n",
        "    total_time += (global_end_time - global_start_time) + sum(lst_local_train_time)/len(lst_local_train_time)\n",
        "\n",
        "    # move the updated weights to our model state dict\n",
        "    model.load_state_dict(global_weights)\n",
        "\n",
        "    # loss\n",
        "    loss_avg = sum(local_loss) / len(local_loss)\n",
        "\n",
        "    # test accuracy\n",
        "    criterion = nn.CrossEntropyLoss()\n",
        "    test_loss, test_accuracy = testing(model, test_data_dict, 128, criterion, num_classes, classes_test)\n",
        "    \n",
        "\n",
        "\n",
        "    print(f\"Round: {curr_round}... \\tAverage Train Loss: {round(loss_avg, 3)}... \\tTest Loss: {test_loss}... \\tTest Accuracy: {test_accuracy}\")\n",
        "    train_loss.append(loss_avg)\n",
        "\n",
        "    test_acc.append(test_accuracy)\n",
        "    # break if we achieve the target test accuracy\n",
        "    if test_accuracy >= target_test_accuracy:\n",
        "      rounds = curr_round\n",
        "      break\n",
        "\n",
        "    # break if we achieve convergence, i.e., loss between two consecutive rounds is <0.0001\n",
        "    if algorithm == 'fedprox' and abs(loss_avg - last_loss) < 0.0001:\n",
        "      rounds = curr_round\n",
        "      break\n",
        "    \n",
        "    # update the last loss\n",
        "    last_loss = loss_avg\n",
        "\n",
        "  # plot train loss\n",
        "  fig, ax = plt.subplots()\n",
        "  x_axis = np.arange(1, rounds+1)\n",
        "  y_axis = np.array(train_loss)\n",
        "  ax.plot(x_axis, y_axis)\n",
        "\n",
        "  ax.set(xlabel='Number of Rounds', ylabel='Train Loss',\n",
        "       title=plt_title)\n",
        "  ax.grid()\n",
        "  fig.savefig(plt_title+'.jpg', format='jpg')\n",
        "\n",
        "  # plot test accuracy\n",
        "  fig1, ax1 = plt.subplots()\n",
        "  x_axis1 = np.arange(1, rounds+1)\n",
        "  y_axis1 = np.array(test_acc)\n",
        "  ax1.plot(x_axis1, y_axis1)\n",
        "\n",
        "  ax1.set(xlabel='Number of Rounds', ylabel='Test Accuracy', title=plt_title)\n",
        "  ax1.grid()\n",
        "  fig1.savefig(plt_title+'-test.jpg', format='jpg')\n",
        "  \n",
        "  print(\"Training Done!\")\n",
        "  # print(\"Total time taken to Train: {}\".format(get_time_format(total_time)))\n",
        "\n",
        "  return model "
      ],
      "execution_count": 18,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4hO5oV6aXqeh",
        "colab_type": "text"
      },
      "source": [
        "## Special Case of FedProx with mu = 0 where it is Federated Averaging"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "flSQv_P4zCfx",
        "colab_type": "text"
      },
      "source": [
        "### Train\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0ZalcKZtEseA",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "35adcc5f-5210-45f5-d2c1-817421fcb5d0"
      },
      "source": [
        "# number of training rounds\n",
        "rounds = 100\n",
        "# client fraction\n",
        "C = 0.1\n",
        "# number of clients\n",
        "K = 100\n",
        "# number of training passes on local dataset for each roung\n",
        "E = 20\n",
        "# batch size\n",
        "batch_size = 10\n",
        "# learning Rate\n",
        "lr=0.01\n",
        "# proximal term constant\n",
        "mu = 0.0\n",
        "# percentage of clients to have fewer than E epochs\n",
        "percentage = 0\n",
        "# target test accuracy\n",
        "target_test_accuracy=99.0\n",
        "# data partition dictionary\n",
        "iid_dict = iid_partition(mnist_data_train, 100)\n",
        "# load model\n",
        "mnist_cnn = MNIST_CNN()\n",
        "\n",
        "if torch.cuda.is_available():\n",
        "  mnist_cnn.cuda()\n",
        "\n",
        "mnist_cnn_iid_trained = training(mnist_cnn, rounds, batch_size, lr, mnist_data_train, iid_dict, mnist_data_test, C, K, E, mu, percentage, \"FedProx MNIST CNN Special Case (FedAvg)\", \"orange\", target_test_accuracy)"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "System heterogeneity set to 0% stragglers.\n",
            "\n",
            "Picking 10 random clients per round.\n",
            "\n",
            "Round: 1... \tAverage Train Loss: 0.255... \tTest Loss: 0.1682491548925638... \tTest Accuracy: 95.69620253164557\n",
            "Round: 2... \tAverage Train Loss: 0.041... \tTest Loss: 0.1270620659807697... \tTest Accuracy: 97.34177215189874\n",
            "Round: 3... \tAverage Train Loss: 0.03... \tTest Loss: 0.1009558584760176... \tTest Accuracy: 97.59493670886076\n",
            "Round: 4... \tAverage Train Loss: 0.021... \tTest Loss: 0.08788339576094877... \tTest Accuracy: 97.84810126582279\n",
            "Round: 5... \tAverage Train Loss: 0.017... \tTest Loss: 0.0806972319102846... \tTest Accuracy: 97.9746835443038\n",
            "Round: 6... \tAverage Train Loss: 0.015... \tTest Loss: 0.07215070306889247... \tTest Accuracy: 97.84810126582279\n",
            "Round: 7... \tAverage Train Loss: 0.015... \tTest Loss: 0.06769896842179877... \tTest Accuracy: 98.48101265822785\n",
            "Round: 8... \tAverage Train Loss: 0.014... \tTest Loss: 0.05974470126784727... \tTest Accuracy: 98.60759493670886\n",
            "Round: 9... \tAverage Train Loss: 0.012... \tTest Loss: 0.05936614667915564... \tTest Accuracy: 98.60759493670886\n",
            "Round: 10... \tAverage Train Loss: 0.01... \tTest Loss: 0.05457464850716351... \tTest Accuracy: 98.35443037974683\n",
            "Round: 11... \tAverage Train Loss: 0.01... \tTest Loss: 0.051049984900304116... \tTest Accuracy: 98.73417721518987\n",
            "Round: 12... \tAverage Train Loss: 0.01... \tTest Loss: 0.048485785214540375... \tTest Accuracy: 98.86075949367088\n",
            "Round: 13... \tAverage Train Loss: 0.008... \tTest Loss: 0.04938509133536718... \tTest Accuracy: 98.86075949367088\n",
            "Round: 14... \tAverage Train Loss: 0.01... \tTest Loss: 0.0464438995219316... \tTest Accuracy: 98.60759493670886\n",
            "Round: 15... \tAverage Train Loss: 0.008... \tTest Loss: 0.04637975217253479... \tTest Accuracy: 98.86075949367088\n",
            "Round: 16... \tAverage Train Loss: 0.008... \tTest Loss: 0.04825396521651491... \tTest Accuracy: 98.73417721518987\n",
            "Round: 17... \tAverage Train Loss: 0.007... \tTest Loss: 0.04468643943851785... \tTest Accuracy: 98.9873417721519\n",
            "Round: 18... \tAverage Train Loss: 0.007... \tTest Loss: 0.04434340585159698... \tTest Accuracy: 98.9873417721519\n",
            "Training Done!\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "b4btCseB0MtI",
        "colab_type": "text"
      },
      "source": [
        " # Training with 0% probability of system heterogeneity"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "ewgOl5Va6DQs"
      },
      "source": [
        "## MNIST CNN on IID"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "Q-NXHBgy6DQ1"
      },
      "source": [
        "### Train\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "CuPEOShG6DQ2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 947
        },
        "outputId": "40d6c431-cc48-4938-e563-56cd1471dcda"
      },
      "source": [
        "# number of training rounds\n",
        "rounds = 100\n",
        "# client fraction\n",
        "C = 0.1\n",
        "# number of clients\n",
        "K = 100\n",
        "# number of training passes on local dataset for each roung\n",
        "E = 20\n",
        "# batch size\n",
        "batch_size = 10\n",
        "# learning Rate\n",
        "lr=0.01\n",
        "# proximal term constant\n",
        "mu = 0.01\n",
        "# percentage of clients to have fewer than E epochs\n",
        "percentage = 0\n",
        "# target_test_accuracy\n",
        "target_test_accuracy=99.0\n",
        "# data partition dictionary\n",
        "iid_dict = iid_partition(mnist_data_train, 100)\n",
        "# load model\n",
        "mnist_cnn = MNIST_CNN()\n",
        "\n",
        "if torch.cuda.is_available():\n",
        "  mnist_cnn.cuda()\n",
        "\n",
        "mnist_cnn_iid_trained = training(mnist_cnn, rounds, batch_size, lr, mnist_data_train, iid_dict, mnist_data_test, C, K, E, mu, percentage, \"FedProx MNIST CNN on IID Dataset (0%)\", \"orange\", target_test_accuracy)"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "System heterogeneity set to 0% stragglers.\n",
            "\n",
            "Picking 10 random clients per round.\n",
            "\n",
            "Round: 1... \tAverage Train Loss: 0.286... \tTest Loss: 0.15677423682063818... \tTest Accuracy: 96.07594936708861\n",
            "Round: 2... \tAverage Train Loss: 0.054... \tTest Loss: 0.12309533291310072... \tTest Accuracy: 97.46835443037975\n",
            "Round: 3... \tAverage Train Loss: 0.034... \tTest Loss: 0.10244630348230713... \tTest Accuracy: 97.72151898734177\n",
            "Round: 4... \tAverage Train Loss: 0.035... \tTest Loss: 0.08234688316583634... \tTest Accuracy: 97.59493670886076\n",
            "Round: 5... \tAverage Train Loss: 0.031... \tTest Loss: 0.07274353896492394... \tTest Accuracy: 97.9746835443038\n",
            "Round: 6... \tAverage Train Loss: 0.025... \tTest Loss: 0.07058423596122303... \tTest Accuracy: 98.22784810126582\n",
            "Round: 7... \tAverage Train Loss: 0.021... \tTest Loss: 0.06626725818404229... \tTest Accuracy: 98.10126582278481\n",
            "Round: 8... \tAverage Train Loss: 0.023... \tTest Loss: 0.06061577648965758... \tTest Accuracy: 98.48101265822785\n",
            "Round: 9... \tAverage Train Loss: 0.019... \tTest Loss: 0.06015368863070034... \tTest Accuracy: 98.22784810126582\n",
            "Round: 10... \tAverage Train Loss: 0.018... \tTest Loss: 0.05828004782385833... \tTest Accuracy: 98.35443037974683\n",
            "Round: 11... \tAverage Train Loss: 0.017... \tTest Loss: 0.05647912394453888... \tTest Accuracy: 98.48101265822785\n",
            "Round: 12... \tAverage Train Loss: 0.017... \tTest Loss: 0.055933697147374915... \tTest Accuracy: 98.60759493670886\n",
            "Round: 13... \tAverage Train Loss: 0.015... \tTest Loss: 0.054436346307488566... \tTest Accuracy: 98.48101265822785\n",
            "Round: 14... \tAverage Train Loss: 0.018... \tTest Loss: 0.05242677895735324... \tTest Accuracy: 98.9873417721519\n",
            "Round: 15... \tAverage Train Loss: 0.017... \tTest Loss: 0.04702896563633403... \tTest Accuracy: 98.9873417721519\n",
            "Round: 16... \tAverage Train Loss: 0.014... \tTest Loss: 0.048616405076737285... \tTest Accuracy: 98.86075949367088\n",
            "Round: 17... \tAverage Train Loss: 0.015... \tTest Loss: 0.04623190985184047... \tTest Accuracy: 99.24050632911393\n",
            "Training Done!\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uF8MdSIUYcnl",
        "colab_type": "text"
      },
      "source": [
        "## MNIST CNN on Non IID"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "a6wXX7JW11bx",
        "colab_type": "text"
      },
      "source": [
        "### Train\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fCD3kBCKYfBK",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 811
        },
        "outputId": "9cb5f594-1191-4900-e5a8-b715bb330a89"
      },
      "source": [
        "# number of training rounds\n",
        "rounds = 100\n",
        "# client fraction\n",
        "C = 0.1\n",
        "# number of clients\n",
        "K = 100\n",
        "# number of training passes on local dataset for each roung\n",
        "E = 20\n",
        "# batch size\n",
        "batch_size = 10\n",
        "# learning Rate\n",
        "lr=0.01\n",
        "# proximal term constant\n",
        "mu = 0.01\n",
        "# percentage of clients to have fewer than E epochs\n",
        "percentage = 0\n",
        "\n",
        "# target_test_accuracy\n",
        "target_test_accuracy=99.0\n",
        "# dict containing different type of data partition\n",
        "data_dict = non_iid_partition(mnist_data_train, 100, 200, 300, 2)\n",
        "# load model\n",
        "mnist_cnn = MNIST_CNN()\n",
        "\n",
        "if torch.cuda.is_available():\n",
        "  mnist_cnn.cuda()\n",
        "\n",
        "mnist_cnn_non_iid_trained = training(mnist_cnn, rounds, batch_size, lr, mnist_data_train, data_dict, mnist_data_test, C, K, E, mu, percentage, \"FedProx MNIST CNN on non-IID Dataset (0%)\", \"green\", target_test_accuracy)\n"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "System heterogeneity set to 0% stragglers.\n",
            "\n",
            "Picking 10 random clients per round.\n",
            "\n",
            "Round: 1... \tAverage Train Loss: 0.049... \tTest Loss: 2.9775880100250243... \tTest Accuracy: 26.075949367088608\n",
            "Round: 2... \tAverage Train Loss: 0.032... \tTest Loss: 2.091098132324219... \tTest Accuracy: 27.59493670886076\n",
            "Round: 3... \tAverage Train Loss: 0.03... \tTest Loss: 1.4389735929489136... \tTest Accuracy: 50.63291139240506\n",
            "Round: 4... \tAverage Train Loss: 0.024... \tTest Loss: 1.5055664682388306... \tTest Accuracy: 55.31645569620253\n",
            "Round: 5... \tAverage Train Loss: 0.017... \tTest Loss: 1.0132979842185974... \tTest Accuracy: 63.79746835443038\n",
            "Round: 6... \tAverage Train Loss: 0.015... \tTest Loss: 0.589519287443161... \tTest Accuracy: 80.12658227848101\n",
            "Round: 7... \tAverage Train Loss: 0.012... \tTest Loss: 0.5778641642093658... \tTest Accuracy: 80.88607594936708\n",
            "Round: 8... \tAverage Train Loss: 0.014... \tTest Loss: 0.4602468936443329... \tTest Accuracy: 84.68354430379746\n",
            "Round: 9... \tAverage Train Loss: 0.014... \tTest Loss: 0.6028336941242218... \tTest Accuracy: 76.58227848101266\n",
            "Training Done!\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "z_jifdzniuhm",
        "colab_type": "text"
      },
      "source": [
        "## MNIST MLP on IID"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uh-te0Od2XGO",
        "colab_type": "text"
      },
      "source": [
        "### Train"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UmpWmKOQixVV",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 777
        },
        "outputId": "5589d55e-6803-4961-cf94-35a0c3d45799"
      },
      "source": [
        "# number of training rounds\n",
        "rounds = 100\n",
        "# client fraction\n",
        "C = 0.1\n",
        "# number of clients\n",
        "K = 100\n",
        "# number of training passes on local dataset for each round\n",
        "E = 20\n",
        "# batch size\n",
        "batch_size = 10\n",
        "# learning Rate\n",
        "lr=0.01\n",
        "# proximal term constant\n",
        "mu = 0.01\n",
        "# percentage of clients to have fewer than E epochs\n",
        "percentage = 90\n",
        "# target_test_accuracy\n",
        "target_test_accuracy=94.0\n",
        "# dict containing different type of data partition\n",
        "data_dict = iid_partition(mnist_data_train, 100)\n",
        "# load model\n",
        "mnist_mlp = MNIST_2NN()\n",
        "\n",
        "if torch.cuda.is_available():\n",
        "  mnist_mlp.cuda()\n",
        "\n",
        "mnist_mlp_iid_trained = training(mnist_mlp, rounds, batch_size, lr, mnist_data_train, data_dict, mnist_data_test, C, K, E, mu, percentage, \"FedProx MNIST MLP on IID Dataset (90%)\", \"orange\", target_test_accuracy)\n"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "System heterogeneity set to 90% stragglers.\n",
            "\n",
            "Picking 10 random clients per round.\n",
            "\n",
            "Round: 1... \tAverage Train Loss: 0.597... \tTest Loss: 0.33981159615516665... \tTest Accuracy: 90.50632911392405\n",
            "Round: 2... \tAverage Train Loss: 0.19... \tTest Loss: 0.295352877998352... \tTest Accuracy: 92.65822784810126\n",
            "Round: 3... \tAverage Train Loss: 0.165... \tTest Loss: 0.2759601198077202... \tTest Accuracy: 93.16455696202532\n",
            "Round: 4... \tAverage Train Loss: 0.152... \tTest Loss: 0.25294016422331334... \tTest Accuracy: 92.9113924050633\n",
            "Round: 5... \tAverage Train Loss: 0.112... \tTest Loss: 0.23895647785663604... \tTest Accuracy: 93.29113924050633\n",
            "Round: 6... \tAverage Train Loss: 0.072... \tTest Loss: 0.2299989909812808... \tTest Accuracy: 93.92405063291139\n",
            "Round: 7... \tAverage Train Loss: 0.135... \tTest Loss: 0.21545796639323234... \tTest Accuracy: 94.0506329113924\n",
            "Training Done!\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "J8jzEyO0iywz",
        "colab_type": "text"
      },
      "source": [
        "## MNIST MLP on Non IID"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pJFepr3y2bF-",
        "colab_type": "text"
      },
      "source": [
        "### Train"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EBKO44Hgi1Uh",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "0842559f-da96-4efd-c965-9d27cc5bcba2"
      },
      "source": [
        "# number of training rounds\n",
        "rounds = 100\n",
        "# client fraction\n",
        "C = 0.1\n",
        "# number of clients\n",
        "K = 100\n",
        "# number of training passes on local dataset for each roung\n",
        "E = 20\n",
        "# batch size\n",
        "batch_size = 10\n",
        "# learning Rate\n",
        "lr=0.01\n",
        "# proximal term constant\n",
        "mu = 0.01\n",
        "# percentage of clients to have fewer than E epochs\n",
        "percentage = 90\n",
        "# target_test_accuracy\n",
        "target_test_accuracy=94.0\n",
        "# dict containing different type of data partition\n",
        "data_dict = non_iid_partition(mnist_data_train, 100, 200, 300, 2)\n",
        "# load model\n",
        "mnist_mlp = MNIST_2NN()\n",
        "\n",
        "if torch.cuda.is_available():\n",
        "  mnist_mlp.cuda()\n",
        "\n",
        "mnist_mlp_non_iid_trained = training(mnist_mlp, rounds, batch_size, lr, mnist_data_train, data_dict, mnist_data_test, C, K, E, mu, percentage, \"FedProx MNIST MLP on non-IID Dataset (90%)\", \"green\", target_test_accuracy)"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "System heterogeneity set to 90% stragglers.\n",
            "\n",
            "Picking 10 random clients per round.\n",
            "\n",
            "Round: 1... \tAverage Train Loss: 0.248... \tTest Loss: 3.7023820693969727... \tTest Accuracy: 20.759493670886076\n",
            "Round: 2... \tAverage Train Loss: 0.115... \tTest Loss: 3.390885832977295... \tTest Accuracy: 23.29113924050633\n",
            "Round: 3... \tAverage Train Loss: 0.034... \tTest Loss: 2.566848978805542... \tTest Accuracy: 36.70886075949367\n",
            "Round: 4... \tAverage Train Loss: 0.054... \tTest Loss: 1.6602831937789917... \tTest Accuracy: 54.68354430379747\n",
            "Round: 5... \tAverage Train Loss: 0.039... \tTest Loss: 1.1001135723114013... \tTest Accuracy: 57.721518987341774\n",
            "Round: 6... \tAverage Train Loss: 0.042... \tTest Loss: 1.0657608781814576... \tTest Accuracy: 62.151898734177216\n",
            "Round: 7... \tAverage Train Loss: 0.035... \tTest Loss: 0.8269805119514465... \tTest Accuracy: 71.13924050632912\n",
            "Round: 8... \tAverage Train Loss: 0.037... \tTest Loss: 0.9334937385559082... \tTest Accuracy: 63.54430379746835\n",
            "Round: 9... \tAverage Train Loss: 0.042... \tTest Loss: 0.5764040384292602... \tTest Accuracy: 82.78481012658227\n",
            "Round: 10... \tAverage Train Loss: 0.042... \tTest Loss: 0.6891395734786987... \tTest Accuracy: 74.9367088607595\n",
            "Round: 11... \tAverage Train Loss: 0.035... \tTest Loss: 0.6642351544857025... \tTest Accuracy: 74.9367088607595\n",
            "Round: 12... \tAverage Train Loss: 0.038... \tTest Loss: 0.4835863648176193... \tTest Accuracy: 85.0632911392405\n",
            "Round: 13... \tAverage Train Loss: 0.043... \tTest Loss: 0.5634748459815979... \tTest Accuracy: 80.75949367088607\n",
            "Round: 14... \tAverage Train Loss: 0.02... \tTest Loss: 0.5312457490444183... \tTest Accuracy: 81.77215189873418\n",
            "Round: 15... \tAverage Train Loss: 0.037... \tTest Loss: 0.46458884143829343... \tTest Accuracy: 84.55696202531645\n",
            "Round: 16... \tAverage Train Loss: 0.021... \tTest Loss: 0.4160654675006866... \tTest Accuracy: 86.70886075949367\n",
            "Round: 17... \tAverage Train Loss: 0.031... \tTest Loss: 0.362162854719162... \tTest Accuracy: 88.9873417721519\n",
            "Round: 18... \tAverage Train Loss: 0.018... \tTest Loss: 0.3884798283576965... \tTest Accuracy: 87.72151898734177\n",
            "Round: 19... \tAverage Train Loss: 0.032... \tTest Loss: 0.3784920303583145... \tTest Accuracy: 89.49367088607595\n",
            "Round: 20... \tAverage Train Loss: 0.024... \tTest Loss: 0.5141837775707245... \tTest Accuracy: 80.50632911392405\n",
            "Round: 21... \tAverage Train Loss: 0.026... \tTest Loss: 0.5856140151977539... \tTest Accuracy: 79.62025316455696\n",
            "Round: 22... \tAverage Train Loss: 0.02... \tTest Loss: 0.3913197860240936... \tTest Accuracy: 87.72151898734177\n",
            "Round: 23... \tAverage Train Loss: 0.028... \tTest Loss: 0.3469475873947144... \tTest Accuracy: 90.37974683544304\n",
            "Round: 24... \tAverage Train Loss: 0.027... \tTest Loss: 0.5006078257083892... \tTest Accuracy: 82.9113924050633\n",
            "Round: 25... \tAverage Train Loss: 0.026... \tTest Loss: 0.35817418155670167... \tTest Accuracy: 89.24050632911393\n",
            "Round: 26... \tAverage Train Loss: 0.018... \tTest Loss: 0.34393176753520965... \tTest Accuracy: 90.0\n",
            "Round: 27... \tAverage Train Loss: 0.019... \tTest Loss: 0.3468616493582726... \tTest Accuracy: 88.48101265822785\n",
            "Round: 28... \tAverage Train Loss: 0.028... \tTest Loss: 0.41982631006240845... \tTest Accuracy: 85.0632911392405\n",
            "Round: 29... \tAverage Train Loss: 0.013... \tTest Loss: 0.41776658992767335... \tTest Accuracy: 85.9493670886076\n",
            "Round: 30... \tAverage Train Loss: 0.025... \tTest Loss: 0.5076148697853088... \tTest Accuracy: 82.53164556962025\n",
            "Round: 31... \tAverage Train Loss: 0.029... \tTest Loss: 0.3386457708120346... \tTest Accuracy: 88.48101265822785\n",
            "Round: 32... \tAverage Train Loss: 0.014... \tTest Loss: 0.2802073529958725... \tTest Accuracy: 92.9113924050633\n",
            "Round: 33... \tAverage Train Loss: 0.02... \tTest Loss: 0.36802913465499876... \tTest Accuracy: 87.9746835443038\n",
            "Round: 34... \tAverage Train Loss: 0.032... \tTest Loss: 0.37174051542282105... \tTest Accuracy: 86.58227848101266\n",
            "Round: 35... \tAverage Train Loss: 0.016... \tTest Loss: 0.490978952217102... \tTest Accuracy: 81.0126582278481\n",
            "Round: 36... \tAverage Train Loss: 0.017... \tTest Loss: 0.4706635729312897... \tTest Accuracy: 85.0632911392405\n",
            "Round: 37... \tAverage Train Loss: 0.015... \tTest Loss: 0.36995785894393923... \tTest Accuracy: 87.34177215189874\n",
            "Round: 38... \tAverage Train Loss: 0.016... \tTest Loss: 0.3481424806833267... \tTest Accuracy: 90.0\n",
            "Round: 39... \tAverage Train Loss: 0.021... \tTest Loss: 0.31573468372821806... \tTest Accuracy: 89.74683544303798\n",
            "Round: 40... \tAverage Train Loss: 0.022... \tTest Loss: 0.37245381324291227... \tTest Accuracy: 88.35443037974683\n",
            "Round: 41... \tAverage Train Loss: 0.019... \tTest Loss: 0.3420349896669388... \tTest Accuracy: 90.0\n",
            "Round: 42... \tAverage Train Loss: 0.012... \tTest Loss: 0.32709026992321016... \tTest Accuracy: 88.10126582278481\n",
            "Round: 43... \tAverage Train Loss: 0.016... \tTest Loss: 0.3146715807914734... \tTest Accuracy: 89.49367088607595\n",
            "Round: 44... \tAverage Train Loss: 0.029... \tTest Loss: 0.30998296179771423... \tTest Accuracy: 90.75949367088607\n",
            "Round: 45... \tAverage Train Loss: 0.015... \tTest Loss: 0.26676477961540224... \tTest Accuracy: 91.39240506329114\n",
            "Round: 46... \tAverage Train Loss: 0.016... \tTest Loss: 0.2721325135707855... \tTest Accuracy: 91.64556962025317\n",
            "Round: 47... \tAverage Train Loss: 0.021... \tTest Loss: 0.25114502583742143... \tTest Accuracy: 92.40506329113924\n",
            "Round: 48... \tAverage Train Loss: 0.01... \tTest Loss: 0.24566636035442352... \tTest Accuracy: 91.39240506329114\n",
            "Round: 49... \tAverage Train Loss: 0.022... \tTest Loss: 0.2732821732521057... \tTest Accuracy: 90.37974683544304\n",
            "Round: 50... \tAverage Train Loss: 0.015... \tTest Loss: 0.4563986262798309... \tTest Accuracy: 83.29113924050633\n",
            "Round: 51... \tAverage Train Loss: 0.018... \tTest Loss: 0.30525658054351806... \tTest Accuracy: 91.77215189873418\n",
            "Round: 52... \tAverage Train Loss: 0.018... \tTest Loss: 0.27566762311458587... \tTest Accuracy: 91.26582278481013\n",
            "Training Done!\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HdOmGsJLC5OD",
        "colab_type": "text"
      },
      "source": [
        "# Training with 50% probability of system heterogeneity"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "gnlxH6QdDGzc"
      },
      "source": [
        "## MNIST CNN on IID"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "8fiWKhiKDGze"
      },
      "source": [
        "### Train\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "bmHjsXHeDGzg",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "c3ebacb5-a135-4136-db5f-1d8d1b26ad3d"
      },
      "source": [
        "# number of training rounds\n",
        "rounds = 100\n",
        "# client fraction\n",
        "C = 0.1\n",
        "# number of clients\n",
        "K = 100\n",
        "# number of training passes on local dataset for each roung\n",
        "E = 20\n",
        "# batch size\n",
        "batch_size = 10\n",
        "# learning Rate\n",
        "lr=0.01\n",
        "# proximal term constant\n",
        "mu = 0.01\n",
        "# percentage of clients to have fewer than E epochs\n",
        "percentage = 50\n",
        "# target_test_accuracy\n",
        "target_test_accuracy=99.0\n",
        "# data partition dictionary\n",
        "iid_dict = iid_partition(mnist_data_train, 100)\n",
        "# load model\n",
        "mnist_cnn = MNIST_CNN()\n",
        "\n",
        "if torch.cuda.is_available():\n",
        "  mnist_cnn.cuda()\n",
        "\n",
        "mnist_cnn_iid_trained = training(mnist_cnn, rounds, batch_size, lr, mnist_data_train, iid_dict, mnist_data_test, C, K, E, mu, percentage, \"FedProx MNIST CNN on IID Dataset (50%)\", \"orange\", target_test_accuracy)"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "System heterogeneity set to 50% stragglers.\n",
            "\n",
            "Picking 10 random clients per round.\n",
            "\n",
            "Round: 1... \tAverage Train Loss: 0.447... \tTest Loss: 0.17414842083454132... \tTest Accuracy: 95.0632911392405\n",
            "Round: 2... \tAverage Train Loss: 0.106... \tTest Loss: 0.11909288570284843... \tTest Accuracy: 96.83544303797468\n",
            "Round: 3... \tAverage Train Loss: 0.066... \tTest Loss: 0.09787474223300814... \tTest Accuracy: 97.21518987341773\n",
            "Round: 4... \tAverage Train Loss: 0.044... \tTest Loss: 0.0854887622129987... \tTest Accuracy: 97.59493670886076\n",
            "Round: 5... \tAverage Train Loss: 0.057... \tTest Loss: 0.07197073401981033... \tTest Accuracy: 98.10126582278481\n",
            "Round: 6... \tAverage Train Loss: 0.03... \tTest Loss: 0.06523324645482353... \tTest Accuracy: 98.22784810126582\n",
            "Round: 7... \tAverage Train Loss: 0.027... \tTest Loss: 0.06482798097054474... \tTest Accuracy: 98.60759493670886\n",
            "Round: 8... \tAverage Train Loss: 0.04... \tTest Loss: 0.058713185988122134... \tTest Accuracy: 98.73417721518987\n",
            "Round: 9... \tAverage Train Loss: 0.048... \tTest Loss: 0.05702155717918067... \tTest Accuracy: 98.86075949367088\n",
            "Round: 10... \tAverage Train Loss: 0.035... \tTest Loss: 0.05551980754535762... \tTest Accuracy: 99.11392405063292\n",
            "Training Done!\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "3C1o99ZODOH8"
      },
      "source": [
        "## MNIST CNN on Non IID"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "MxLku0pEDOH9"
      },
      "source": [
        "### Train\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "jzQZEeOeDOH-",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 964
        },
        "outputId": "feb5328f-75fc-459e-d070-546261985d59"
      },
      "source": [
        "# number of training rounds\n",
        "rounds = 100\n",
        "# client fraction\n",
        "C = 0.1\n",
        "# number of clients\n",
        "K = 100\n",
        "# number of training passes on local dataset for each roung\n",
        "E = 20\n",
        "# batch size\n",
        "batch_size = 10\n",
        "# learning Rate\n",
        "lr=0.01\n",
        "# proximal term constant\n",
        "mu = 0.01\n",
        "# percentage of clients to have fewer than E epochs\n",
        "percentage = 50\n",
        "# target_test_accuracy\n",
        "target_test_accuracy=96.0\n",
        "# dict containing different type of data partition\n",
        "data_dict = non_iid_partition(mnist_data_train, 100, 200, 300, 2)\n",
        "# load model\n",
        "mnist_cnn = MNIST_CNN()\n",
        "\n",
        "if torch.cuda.is_available():\n",
        "  mnist_cnn.cuda()\n",
        "\n",
        "mnist_cnn_non_iid_trained = training(mnist_cnn, rounds, batch_size, lr, mnist_data_train, data_dict, mnist_data_test, C, K, E, mu, percentage, \"FedProx MNIST CNN on non-IID Dataset (50%)\", \"green\", target_test_accuracy)\n"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "System heterogeneity set to 50% stragglers.\n",
            "\n",
            "Picking 10 random clients per round.\n",
            "\n",
            "Round: 1... \tAverage Train Loss: 0.063... \tTest Loss: 2.104177982711792... \tTest Accuracy: 28.10126582278481\n",
            "Round: 2... \tAverage Train Loss: 0.035... \tTest Loss: 2.0645568244934083... \tTest Accuracy: 40.25316455696203\n",
            "Round: 3... \tAverage Train Loss: 0.031... \tTest Loss: 1.3013924940109254... \tTest Accuracy: 60.50632911392405\n",
            "Round: 4... \tAverage Train Loss: 0.02... \tTest Loss: 2.260540909194946... \tTest Accuracy: 29.873417721518987\n",
            "Round: 5... \tAverage Train Loss: 0.014... \tTest Loss: 1.1929788646697999... \tTest Accuracy: 59.36708860759494\n",
            "Round: 6... \tAverage Train Loss: 0.021... \tTest Loss: 0.6739433184623719... \tTest Accuracy: 78.22784810126582\n",
            "Round: 7... \tAverage Train Loss: 0.024... \tTest Loss: 0.7578722602844238... \tTest Accuracy: 74.17721518987342\n",
            "Round: 8... \tAverage Train Loss: 0.029... \tTest Loss: 0.622692104101181... \tTest Accuracy: 76.45569620253164\n",
            "Round: 9... \tAverage Train Loss: 0.022... \tTest Loss: 0.38677294392585754... \tTest Accuracy: 86.83544303797468\n",
            "Round: 10... \tAverage Train Loss: 0.017... \tTest Loss: 0.44535790510177614... \tTest Accuracy: 82.65822784810126\n",
            "Round: 11... \tAverage Train Loss: 0.031... \tTest Loss: 0.3308607350349426... \tTest Accuracy: 87.9746835443038\n",
            "Round: 12... \tAverage Train Loss: 0.015... \tTest Loss: 0.2328262808084488... \tTest Accuracy: 92.27848101265823\n",
            "Round: 13... \tAverage Train Loss: 0.017... \tTest Loss: 0.2151803363442421... \tTest Accuracy: 92.65822784810126\n",
            "Round: 14... \tAverage Train Loss: 0.011... \tTest Loss: 0.22158964908123016... \tTest Accuracy: 93.16455696202532\n",
            "Round: 15... \tAverage Train Loss: 0.013... \tTest Loss: 0.18977326508760453... \tTest Accuracy: 94.0506329113924\n",
            "Round: 16... \tAverage Train Loss: 0.019... \tTest Loss: 0.15102728889137507... \tTest Accuracy: 95.44303797468355\n",
            "Round: 17... \tAverage Train Loss: 0.008... \tTest Loss: 0.24310468459129334... \tTest Accuracy: 91.26582278481013\n",
            "Round: 18... \tAverage Train Loss: 0.018... \tTest Loss: 0.13855979530513288... \tTest Accuracy: 96.07594936708861\n",
            "Training Done!\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "Mgspmmb1DSgu"
      },
      "source": [
        "## MNIST MLP on IID"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "t1AlbPY7DSgv"
      },
      "source": [
        "### Train"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "a1nUItg3DSgv",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 794
        },
        "outputId": "cdc55651-aba5-41d9-fe0c-e24d9b524ac1"
      },
      "source": [
        "# number of training rounds\n",
        "rounds = 100\n",
        "# client fraction\n",
        "C = 0.1\n",
        "# number of clients\n",
        "K = 100\n",
        "# number of training passes on local dataset for each round\n",
        "E = 20\n",
        "# batch size\n",
        "batch_size = 10\n",
        "# learning Rate\n",
        "lr=0.01\n",
        "# proximal term constant\n",
        "mu = 0.01\n",
        "# percentage of clients to have fewer than E epochs\n",
        "percentage = 50\n",
        "# target_test_accuracy\n",
        "target_test_accuracy=94.0\n",
        "# dict containing different type of data partition\n",
        "data_dict = iid_partition(mnist_data_train, 100)\n",
        "# load model\n",
        "mnist_mlp = MNIST_2NN()\n",
        "\n",
        "if torch.cuda.is_available():\n",
        "  mnist_mlp.cuda()\n",
        "\n",
        "mnist_mlp_iid_trained = training(mnist_mlp, rounds, batch_size, lr, mnist_data_train, data_dict, mnist_data_test, C, K, E, mu, percentage, \"FedProx MNIST MLP on IID Dataset (50%)\", \"orange\", target_test_accuracy)\n"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "System heterogeneity set to 50% stragglers.\n",
            "\n",
            "Picking 10 random clients per round.\n",
            "\n",
            "Round: 1... \tAverage Train Loss: 1.023... \tTest Loss: 0.674980073261261... \tTest Accuracy: 83.29113924050633\n",
            "Round: 2... \tAverage Train Loss: 0.155... \tTest Loss: 0.3039632867515087... \tTest Accuracy: 92.15189873417721\n",
            "Round: 3... \tAverage Train Loss: 0.085... \tTest Loss: 0.2791133965432644... \tTest Accuracy: 93.29113924050633\n",
            "Round: 4... \tAverage Train Loss: 0.098... \tTest Loss: 0.26072224661409854... \tTest Accuracy: 93.41772151898734\n",
            "Round: 5... \tAverage Train Loss: 0.086... \tTest Loss: 0.24342278826087713... \tTest Accuracy: 93.29113924050633\n",
            "Round: 6... \tAverage Train Loss: 0.091... \tTest Loss: 0.22526649805903434... \tTest Accuracy: 93.67088607594937\n",
            "Round: 7... \tAverage Train Loss: 0.113... \tTest Loss: 0.21335024886131287... \tTest Accuracy: 93.67088607594937\n",
            "Round: 8... \tAverage Train Loss: 0.054... \tTest Loss: 0.20204983824044467... \tTest Accuracy: 94.68354430379746\n",
            "Training Done!\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "PrWMRFBCDWu-"
      },
      "source": [
        "## MNIST MLP on Non IID"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "joc_YdwDDWu-"
      },
      "source": [
        "### Train"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "JEhvU3V1DWu_",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "eaf7b331-5baf-467d-dcae-442251a4c79a"
      },
      "source": [
        "# number of training rounds\n",
        "rounds = 100\n",
        "# client fraction\n",
        "C = 0.1\n",
        "# number of clients\n",
        "K = 100\n",
        "# number of training passes on local dataset for each roung\n",
        "E = 20\n",
        "# batch size\n",
        "batch_size = 10\n",
        "# learning Rate\n",
        "lr=0.01\n",
        "# proximal term constant\n",
        "mu = 0.01\n",
        "# percentage of clients to have fewer than E epochs\n",
        "percentage = 50\n",
        "# target_test_accuracy\n",
        "target_test_accuracy=94.0\n",
        "# dict containing different type of data partition\n",
        "data_dict = non_iid_partition(mnist_data_train, 100, 200, 300, 2)\n",
        "# load model\n",
        "mnist_mlp = MNIST_2NN()\n",
        "\n",
        "if torch.cuda.is_available():\n",
        "  mnist_mlp.cuda()\n",
        "\n",
        "mnist_mlp_non_iid_trained = training(mnist_mlp, rounds, batch_size, lr, mnist_data_train, data_dict, mnist_data_test, C, K, E, mu, percentage, \"FedProx MNIST MLP on non-IID Dataset (50%)\", \"green\", target_test_accuracy)"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "System heterogeneity set to 50% stragglers.\n",
            "\n",
            "Picking 10 random clients per round.\n",
            "\n",
            "Round: 1... \tAverage Train Loss: 0.168... \tTest Loss: 3.712359524536133... \tTest Accuracy: 18.9873417721519\n",
            "Round: 2... \tAverage Train Loss: 0.036... \tTest Loss: 3.0823422039031985... \tTest Accuracy: 31.772151898734176\n",
            "Round: 3... \tAverage Train Loss: 0.046... \tTest Loss: 1.894597993659973... \tTest Accuracy: 57.848101265822784\n",
            "Round: 4... \tAverage Train Loss: 0.031... \tTest Loss: 2.049077114868164... \tTest Accuracy: 34.050632911392405\n",
            "Round: 5... \tAverage Train Loss: 0.022... \tTest Loss: 1.3539307416915893... \tTest Accuracy: 66.07594936708861\n",
            "Round: 6... \tAverage Train Loss: 0.03... \tTest Loss: 1.1763375792503357... \tTest Accuracy: 56.58227848101266\n",
            "Round: 7... \tAverage Train Loss: 0.017... \tTest Loss: 0.887056803894043... \tTest Accuracy: 66.20253164556962\n",
            "Round: 8... \tAverage Train Loss: 0.024... \tTest Loss: 0.553860544538498... \tTest Accuracy: 82.27848101265823\n",
            "Round: 9... \tAverage Train Loss: 0.039... \tTest Loss: 0.6307606659889221... \tTest Accuracy: 80.37974683544304\n",
            "Round: 10... \tAverage Train Loss: 0.033... \tTest Loss: 0.48894611897468565... \tTest Accuracy: 81.13924050632912\n",
            "Round: 11... \tAverage Train Loss: 0.019... \tTest Loss: 0.5755590933799744... \tTest Accuracy: 78.60759493670886\n",
            "Round: 12... \tAverage Train Loss: 0.014... \tTest Loss: 0.5769807983398437... \tTest Accuracy: 79.49367088607595\n",
            "Round: 13... \tAverage Train Loss: 0.027... \tTest Loss: 0.5950492193222046... \tTest Accuracy: 78.22784810126582\n",
            "Round: 14... \tAverage Train Loss: 0.017... \tTest Loss: 0.5461740189552308... \tTest Accuracy: 80.0\n",
            "Round: 15... \tAverage Train Loss: 0.021... \tTest Loss: 0.4674934203147888... \tTest Accuracy: 85.82278481012658\n",
            "Round: 16... \tAverage Train Loss: 0.02... \tTest Loss: 0.44554568395614624... \tTest Accuracy: 86.32911392405063\n",
            "Round: 17... \tAverage Train Loss: 0.019... \tTest Loss: 0.42749431185722353... \tTest Accuracy: 86.58227848101266\n",
            "Round: 18... \tAverage Train Loss: 0.011... \tTest Loss: 0.6225334002017975... \tTest Accuracy: 78.9873417721519\n",
            "Round: 19... \tAverage Train Loss: 0.023... \tTest Loss: 0.4199196865558624... \tTest Accuracy: 84.55696202531645\n",
            "Round: 20... \tAverage Train Loss: 0.014... \tTest Loss: 0.46552779784202575... \tTest Accuracy: 85.44303797468355\n",
            "Round: 21... \tAverage Train Loss: 0.02... \tTest Loss: 0.46814559607505796... \tTest Accuracy: 84.43037974683544\n",
            "Round: 22... \tAverage Train Loss: 0.011... \tTest Loss: 0.6211625374794006... \tTest Accuracy: 80.0\n",
            "Round: 23... \tAverage Train Loss: 0.012... \tTest Loss: 0.6092605542182923... \tTest Accuracy: 76.58227848101266\n",
            "Round: 24... \tAverage Train Loss: 0.018... \tTest Loss: 0.4168277244567871... \tTest Accuracy: 85.18987341772151\n",
            "Round: 25... \tAverage Train Loss: 0.017... \tTest Loss: 0.5787598196983338... \tTest Accuracy: 79.62025316455696\n",
            "Round: 26... \tAverage Train Loss: 0.016... \tTest Loss: 0.49027401239871976... \tTest Accuracy: 81.51898734177215\n",
            "Round: 27... \tAverage Train Loss: 0.021... \tTest Loss: 0.4492709177017212... \tTest Accuracy: 84.81012658227849\n",
            "Round: 28... \tAverage Train Loss: 0.02... \tTest Loss: 0.5018049314260483... \tTest Accuracy: 83.0379746835443\n",
            "Round: 29... \tAverage Train Loss: 0.016... \tTest Loss: 0.45934252438545226... \tTest Accuracy: 83.79746835443038\n",
            "Round: 30... \tAverage Train Loss: 0.021... \tTest Loss: 0.36482482808828354... \tTest Accuracy: 87.84810126582279\n",
            "Round: 31... \tAverage Train Loss: 0.013... \tTest Loss: 0.3577007220029831... \tTest Accuracy: 88.60759493670886\n",
            "Round: 32... \tAverage Train Loss: 0.017... \tTest Loss: 0.42515288686752317... \tTest Accuracy: 84.17721518987342\n",
            "Round: 33... \tAverage Train Loss: 0.016... \tTest Loss: 0.43408172798156736... \tTest Accuracy: 83.16455696202532\n",
            "Round: 34... \tAverage Train Loss: 0.011... \tTest Loss: 0.34626503009796145... \tTest Accuracy: 88.9873417721519\n",
            "Round: 35... \tAverage Train Loss: 0.013... \tTest Loss: 0.3244288304805756... \tTest Accuracy: 89.62025316455696\n",
            "Round: 36... \tAverage Train Loss: 0.014... \tTest Loss: 0.479108500957489... \tTest Accuracy: 82.53164556962025\n",
            "Round: 37... \tAverage Train Loss: 0.011... \tTest Loss: 0.3277515441894531... \tTest Accuracy: 90.12658227848101\n",
            "Round: 38... \tAverage Train Loss: 0.009... \tTest Loss: 0.3794738531112671... \tTest Accuracy: 87.72151898734177\n",
            "Round: 39... \tAverage Train Loss: 0.015... \tTest Loss: 0.3945027299404144... \tTest Accuracy: 85.69620253164557\n",
            "Round: 40... \tAverage Train Loss: 0.017... \tTest Loss: 0.4103739624977112... \tTest Accuracy: 83.29113924050633\n",
            "Round: 41... \tAverage Train Loss: 0.011... \tTest Loss: 0.3115645267724991... \tTest Accuracy: 89.74683544303798\n",
            "Round: 42... \tAverage Train Loss: 0.013... \tTest Loss: 0.304384935259819... \tTest Accuracy: 90.25316455696202\n",
            "Round: 43... \tAverage Train Loss: 0.016... \tTest Loss: 0.28238093602657316... \tTest Accuracy: 90.63291139240506\n",
            "Round: 44... \tAverage Train Loss: 0.012... \tTest Loss: 0.3129753303050995... \tTest Accuracy: 89.87341772151899\n",
            "Round: 45... \tAverage Train Loss: 0.025... \tTest Loss: 0.4989635131835938... \tTest Accuracy: 81.39240506329114\n",
            "Round: 46... \tAverage Train Loss: 0.016... \tTest Loss: 0.31308250200748444... \tTest Accuracy: 88.86075949367088\n",
            "Round: 47... \tAverage Train Loss: 0.02... \tTest Loss: 0.44739756410121917... \tTest Accuracy: 84.68354430379746\n",
            "Round: 48... \tAverage Train Loss: 0.011... \tTest Loss: 0.4023991818189621... \tTest Accuracy: 86.58227848101266\n",
            "Round: 49... \tAverage Train Loss: 0.012... \tTest Loss: 0.3534633935213089... \tTest Accuracy: 87.72151898734177\n",
            "Round: 50... \tAverage Train Loss: 0.008... \tTest Loss: 0.3188331545829773... \tTest Accuracy: 87.9746835443038\n",
            "Round: 51... \tAverage Train Loss: 0.018... \tTest Loss: 0.4066601775407791... \tTest Accuracy: 86.45569620253164\n",
            "Round: 52... \tAverage Train Loss: 0.011... \tTest Loss: 0.32738818068504333... \tTest Accuracy: 88.86075949367088\n",
            "Round: 53... \tAverage Train Loss: 0.008... \tTest Loss: 0.36789972696304324... \tTest Accuracy: 88.22784810126582\n",
            "Round: 54... \tAverage Train Loss: 0.01... \tTest Loss: 0.31198189861774445... \tTest Accuracy: 91.51898734177215\n",
            "Round: 55... \tAverage Train Loss: 0.007... \tTest Loss: 0.2983414428472519... \tTest Accuracy: 91.77215189873418\n",
            "Round: 56... \tAverage Train Loss: 0.011... \tTest Loss: 0.5782404295921326... \tTest Accuracy: 81.39240506329114\n",
            "Round: 57... \tAverage Train Loss: 0.012... \tTest Loss: 0.2579221390128136... \tTest Accuracy: 92.15189873417721\n",
            "Round: 58... \tAverage Train Loss: 0.012... \tTest Loss: 0.33104815764427187... \tTest Accuracy: 90.12658227848101\n",
            "Round: 59... \tAverage Train Loss: 0.013... \tTest Loss: 0.4332024688720703... \tTest Accuracy: 87.21518987341773\n",
            "Round: 60... \tAverage Train Loss: 0.02... \tTest Loss: 0.3304830419063568... \tTest Accuracy: 89.87341772151899\n",
            "Round: 61... \tAverage Train Loss: 0.011... \tTest Loss: 0.25218432602882385... \tTest Accuracy: 92.9113924050633\n",
            "Round: 62... \tAverage Train Loss: 0.008... \tTest Loss: 0.2761925098657608... \tTest Accuracy: 91.13924050632912\n",
            "Round: 63... \tAverage Train Loss: 0.014... \tTest Loss: 0.36150813374519347... \tTest Accuracy: 87.9746835443038\n",
            "Round: 64... \tAverage Train Loss: 0.011... \tTest Loss: 0.2465945352911949... \tTest Accuracy: 92.15189873417721\n",
            "Round: 65... \tAverage Train Loss: 0.009... \tTest Loss: 0.24669755659103393... \tTest Accuracy: 92.0253164556962\n",
            "Round: 66... \tAverage Train Loss: 0.013... \tTest Loss: 0.3185893979072571... \tTest Accuracy: 88.86075949367088\n",
            "Round: 67... \tAverage Train Loss: 0.015... \tTest Loss: 0.2294766831576824... \tTest Accuracy: 92.40506329113924\n",
            "Round: 68... \tAverage Train Loss: 0.011... \tTest Loss: 0.2675137812972069... \tTest Accuracy: 90.75949367088607\n",
            "Round: 69... \tAverage Train Loss: 0.01... \tTest Loss: 0.2521141835808754... \tTest Accuracy: 92.0253164556962\n",
            "Round: 70... \tAverage Train Loss: 0.013... \tTest Loss: 0.2870825134158134... \tTest Accuracy: 91.64556962025317\n",
            "Round: 71... \tAverage Train Loss: 0.009... \tTest Loss: 0.30741090087890627... \tTest Accuracy: 90.63291139240506\n",
            "Round: 72... \tAverage Train Loss: 0.007... \tTest Loss: 0.307523491692543... \tTest Accuracy: 90.50632911392405\n",
            "Round: 73... \tAverage Train Loss: 0.01... \tTest Loss: 0.3134946197509766... \tTest Accuracy: 89.24050632911393\n",
            "Round: 74... \tAverage Train Loss: 0.009... \tTest Loss: 0.28998068840503693... \tTest Accuracy: 90.37974683544304\n",
            "Round: 75... \tAverage Train Loss: 0.011... \tTest Loss: 0.24057366160154342... \tTest Accuracy: 92.27848101265823\n",
            "Round: 76... \tAverage Train Loss: 0.014... \tTest Loss: 0.29875920128822325... \tTest Accuracy: 90.75949367088607\n",
            "Round: 77... \tAverage Train Loss: 0.01... \tTest Loss: 0.33231127648353576... \tTest Accuracy: 91.0126582278481\n",
            "Round: 78... \tAverage Train Loss: 0.011... \tTest Loss: 0.3551373977661133... \tTest Accuracy: 90.0\n",
            "Round: 79... \tAverage Train Loss: 0.008... \tTest Loss: 0.32229498162269593... \tTest Accuracy: 90.0\n",
            "Round: 80... \tAverage Train Loss: 0.01... \tTest Loss: 0.28012086093425753... \tTest Accuracy: 91.77215189873418\n",
            "Round: 81... \tAverage Train Loss: 0.015... \tTest Loss: 0.23681907840967178... \tTest Accuracy: 92.9113924050633\n",
            "Round: 82... \tAverage Train Loss: 0.008... \tTest Loss: 0.26085984666347506... \tTest Accuracy: 91.13924050632912\n",
            "Round: 83... \tAverage Train Loss: 0.006... \tTest Loss: 0.21511643544435502... \tTest Accuracy: 94.0506329113924\n",
            "Training Done!\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "ORHykPm3Fv_8"
      },
      "source": [
        "# Training with 90% probability of system heterogeneity"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "TXqBlMtHFwAN"
      },
      "source": [
        "## MNIST CNN on IID"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "BXstm_BVFwAO"
      },
      "source": [
        "### Train\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "gmPH7ly3FwAP",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "ecbc768b-5e40-46dc-863e-87bb8eee5cc6"
      },
      "source": [
        "# number of training rounds\n",
        "rounds = 100\n",
        "# client fraction\n",
        "C = 0.1\n",
        "# number of clients\n",
        "K = 100\n",
        "# number of training passes on local dataset for each roung\n",
        "E = 20\n",
        "# batch size\n",
        "batch_size = 10\n",
        "# learning Rate\n",
        "lr=0.01\n",
        "# proximal term constant\n",
        "mu = 0.01\n",
        "# percentage of clients to have fewer than E epochs\n",
        "percentage = 90\n",
        "# target_test_accuracy\n",
        "target_test_accuracy=97.0\n",
        "# data partition dictionary\n",
        "iid_dict = iid_partition(mnist_data_train, 100)\n",
        "# load model\n",
        "mnist_cnn = MNIST_CNN()\n",
        "\n",
        "if torch.cuda.is_available():\n",
        "  mnist_cnn.cuda()\n",
        "\n",
        "mnist_cnn_iid_trained = training(mnist_cnn, rounds, batch_size, lr, mnist_data_train, iid_dict, mnist_data_test, C, K, E, mu, percentage, \"FedProx MNIST CNN on IID Dataset (90%)\", \"orange\", target_test_accuracy)"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "System heterogeneity set to 90% stragglers.\n",
            "\n",
            "Picking 10 random clients per round.\n",
            "\n",
            "Round: 1... \tAverage Train Loss: 0.458... \tTest Loss: 0.17735546071380376... \tTest Accuracy: 94.9367088607595\n",
            "Round: 2... \tAverage Train Loss: 0.13... \tTest Loss: 0.12703009561747314... \tTest Accuracy: 96.70886075949367\n",
            "Round: 3... \tAverage Train Loss: 0.095... \tTest Loss: 0.10612152363434434... \tTest Accuracy: 96.83544303797468\n",
            "Round: 4... \tAverage Train Loss: 0.075... \tTest Loss: 0.08663514154180885... \tTest Accuracy: 97.72151898734177\n",
            "Training Done!\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "RnBEDxmwFwAb"
      },
      "source": [
        "## MNIST CNN on Non IID"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "Gkgaorx7FwAb"
      },
      "source": [
        "### Train\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "8FB_3VV4FwAc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "1b08fdff-7da5-4145-e426-880e7f9a137a"
      },
      "source": [
        "# number of training rounds\n",
        "rounds = 1000\n",
        "# client fraction\n",
        "C = 0.1\n",
        "# number of clients\n",
        "K = 100\n",
        "# number of training passes on local dataset for each roung\n",
        "E = 20\n",
        "# batch size\n",
        "batch_size = 10\n",
        "# learning Rate\n",
        "lr=0.01\n",
        "# target test accuracy\n",
        "target_test_accuracy = 97.0\n",
        "# proximal term constant\n",
        "mu = 0.01\n",
        "# percentage of clients to have fewer than E epochs\n",
        "percentage = 90\n",
        "# dict containing different type of data partition\n",
        "data_dict = non_iid_partition(mnist_data_train, 100, 200, 300, 2)\n",
        "# load model\n",
        "mnist_cnn = MNIST_CNN()\n",
        "\n",
        "if torch.cuda.is_available():\n",
        "  mnist_cnn.cuda()\n",
        "\n",
        "mnist_cnn_non_iid_trained = training(mnist_cnn, rounds, batch_size, lr, mnist_data_train, data_dict, mnist_data_test, C, K, E, mu, percentage, \"FedProx MNIST CNN on non-IID Dataset (90%)\", \"green\", target_test_accuracy)\n"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "System heterogeneity set to 90% stragglers.\n",
            "\n",
            "Picking 10 random clients per round.\n",
            "\n",
            "Round: 1... \tAverage Train Loss: 0.126... \tTest Loss: 2.171712088394165... \tTest Accuracy: 39.24050632911393\n",
            "Round: 2... \tAverage Train Loss: 0.053... \tTest Loss: 1.7844791311264039... \tTest Accuracy: 42.78481012658228\n",
            "Round: 3... \tAverage Train Loss: 0.05... \tTest Loss: 1.2232531314849853... \tTest Accuracy: 60.25316455696203\n",
            "Round: 4... \tAverage Train Loss: 0.042... \tTest Loss: 1.2373505483627318... \tTest Accuracy: 56.075949367088604\n",
            "Round: 5... \tAverage Train Loss: 0.04... \tTest Loss: 0.7091968745231628... \tTest Accuracy: 71.89873417721519\n",
            "Round: 6... \tAverage Train Loss: 0.034... \tTest Loss: 1.042835661125183... \tTest Accuracy: 65.18987341772151\n",
            "Round: 7... \tAverage Train Loss: 0.027... \tTest Loss: 0.5256869955539704... \tTest Accuracy: 83.92405063291139\n",
            "Round: 8... \tAverage Train Loss: 0.032... \tTest Loss: 0.3803427419185638... \tTest Accuracy: 88.48101265822785\n",
            "Round: 9... \tAverage Train Loss: 0.02... \tTest Loss: 0.3421232057571411... \tTest Accuracy: 89.36708860759494\n",
            "Round: 10... \tAverage Train Loss: 0.023... \tTest Loss: 0.3510353028535843... \tTest Accuracy: 87.84810126582279\n",
            "Round: 11... \tAverage Train Loss: 0.011... \tTest Loss: 0.26592333443164823... \tTest Accuracy: 92.0253164556962\n",
            "Round: 12... \tAverage Train Loss: 0.015... \tTest Loss: 0.2652596974849701... \tTest Accuracy: 92.27848101265823\n",
            "Round: 13... \tAverage Train Loss: 0.016... \tTest Loss: 0.19301029484868049... \tTest Accuracy: 95.31645569620254\n",
            "Round: 14... \tAverage Train Loss: 0.012... \tTest Loss: 0.20750539259314538... \tTest Accuracy: 93.16455696202532\n",
            "Round: 15... \tAverage Train Loss: 0.014... \tTest Loss: 0.2229753757238388... \tTest Accuracy: 92.78481012658227\n",
            "Round: 16... \tAverage Train Loss: 0.025... \tTest Loss: 0.21755059767961502... \tTest Accuracy: 93.16455696202532\n",
            "Round: 17... \tAverage Train Loss: 0.011... \tTest Loss: 0.18018130711317062... \tTest Accuracy: 94.55696202531645\n",
            "Round: 18... \tAverage Train Loss: 0.02... \tTest Loss: 0.18440087473392486... \tTest Accuracy: 94.0506329113924\n",
            "Round: 19... \tAverage Train Loss: 0.016... \tTest Loss: 0.3172649812221527... \tTest Accuracy: 89.87341772151899\n",
            "Round: 20... \tAverage Train Loss: 0.009... \tTest Loss: 0.2875223340272903... \tTest Accuracy: 90.25316455696202\n",
            "Round: 21... \tAverage Train Loss: 0.013... \tTest Loss: 0.16778272593021393... \tTest Accuracy: 94.17721518987342\n",
            "Round: 22... \tAverage Train Loss: 0.012... \tTest Loss: 0.15535783529877661... \tTest Accuracy: 95.0632911392405\n",
            "Round: 23... \tAverage Train Loss: 0.018... \tTest Loss: 0.13569255689233542... \tTest Accuracy: 96.20253164556962\n",
            "Round: 24... \tAverage Train Loss: 0.012... \tTest Loss: 0.1338956009477377... \tTest Accuracy: 96.83544303797468\n",
            "Round: 25... \tAverage Train Loss: 0.013... \tTest Loss: 0.1068490229614079... \tTest Accuracy: 96.45569620253164\n",
            "Round: 26... \tAverage Train Loss: 0.019... \tTest Loss: 0.1286315556704998... \tTest Accuracy: 96.20253164556962\n",
            "Round: 27... \tAverage Train Loss: 0.012... \tTest Loss: 0.15570870715379714... \tTest Accuracy: 94.68354430379746\n",
            "Round: 28... \tAverage Train Loss: 0.009... \tTest Loss: 0.10583425091058016... \tTest Accuracy: 96.45569620253164\n",
            "Round: 29... \tAverage Train Loss: 0.013... \tTest Loss: 0.14693712473511697... \tTest Accuracy: 94.68354430379746\n",
            "Round: 30... \tAverage Train Loss: 0.01... \tTest Loss: 0.14156909843683244... \tTest Accuracy: 95.82278481012658\n",
            "Round: 31... \tAverage Train Loss: 0.011... \tTest Loss: 0.11410330241620541... \tTest Accuracy: 96.9620253164557\n",
            "Round: 32... \tAverage Train Loss: 0.012... \tTest Loss: 0.08553478383794427... \tTest Accuracy: 97.59493670886076\n",
            "Training Done!\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "DwwgVhnzFwAg"
      },
      "source": [
        "## MNIST MLP on IID"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "JVs0NLz6FwAh"
      },
      "source": [
        "### Train"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "9MuSeGADFwAh",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "9bcf2d5e-321f-4a29-8ea3-19dfc4864d3b"
      },
      "source": [
        "# number of training rounds\n",
        "rounds = 100\n",
        "# client fraction\n",
        "C = 0.1\n",
        "# number of clients\n",
        "K = 100\n",
        "# number of training passes on local dataset for each round\n",
        "E = 20\n",
        "# batch size\n",
        "batch_size = 10\n",
        "# learning Rate\n",
        "lr=0.01\n",
        "# proximal term constant\n",
        "mu = 0.01\n",
        "# percentage of clients to have fewer than E epochs\n",
        "percentage = 90\n",
        "# target_test_accuracy\n",
        "target_test_accuracy=94.0\n",
        "# dict containing different type of data partition\n",
        "data_dict = iid_partition(mnist_data_train, 100)\n",
        "# load model\n",
        "mnist_mlp = MNIST_2NN()\n",
        "\n",
        "if torch.cuda.is_available():\n",
        "  mnist_mlp.cuda()\n",
        "\n",
        "mnist_mlp_iid_trained = training(mnist_mlp, rounds, batch_size, lr, mnist_data_train, data_dict, mnist_data_test, C, K, E, mu, percentage, \"FedProx MNIST MLP on IID Dataset (90%)\", \"orange\", target_test_accuracy)\n"
      ],
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "System heterogeneity set to 90% stragglers.\n",
            "\n",
            "Picking 10 random clients per round.\n",
            "\n",
            "Round: 1... \tAverage Train Loss: 0.833... \tTest Loss: 0.3505539712905884... \tTest Accuracy: 89.87341772151899\n",
            "Round: 2... \tAverage Train Loss: 0.185... \tTest Loss: 0.2982291683673859... \tTest Accuracy: 91.77215189873418\n",
            "Round: 3... \tAverage Train Loss: 0.114... \tTest Loss: 0.27757849668860435... \tTest Accuracy: 92.9113924050633\n",
            "Round: 4... \tAverage Train Loss: 0.141... \tTest Loss: 0.25468652298152444... \tTest Accuracy: 93.67088607594937\n",
            "Round: 5... \tAverage Train Loss: 0.098... \tTest Loss: 0.24234317042678594... \tTest Accuracy: 93.41772151898734\n",
            "Round: 6... \tAverage Train Loss: 0.117... \tTest Loss: 0.23247412038445472... \tTest Accuracy: 93.79746835443038\n",
            "Round: 7... \tAverage Train Loss: 0.105... \tTest Loss: 0.20959458766281605... \tTest Accuracy: 94.17721518987342\n",
            "Training Done!\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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3HWbltv2JDsU554aNJ4II9TXlAN495JzLKHFNBJKukLRK0lpJd/Qx/f9JejF8rZa0J57xHE/FyAJOnzDSrydwzmWUuCUCSdnAPcCVwAzgZkkzIsuY2afN7CwzOwv4V+CReMUTrdk1FSzd1ErrgSOJDsU554ZFPFsE5wFrzWydmR0B5gPXDVD+ZuDBOMYTlfraCroNnl7j9x5yzmUGxesMGUlzgCvM7KPh8C3A+WY2r4+y1cBzQJWZveXBAJLmAnMBKisr6+bPnx9TTG1tbRQXFw9YptuM2588yOll2Xz8zIKY1jMcoqlLqkiXuqRLPcDrkqwGU5eGhoZmM5vV17ScQUU1dG4CFvSVBADM7F7gXoBZs2ZZfX19TCtpamoimnnfvv1FmlZt55JLLyM7SzGtK96irUsqSJe6pEs9wOuSrOJVl3h2DW0BJkYMV4Xj+nITSdAt1KOhtoLWgx28uDmhx66dc25YxDMRLAamSZoiKY9gY7+wdyFJtcBo4C9xjOWEXDatnCz53Uidc5khbonAzDqBecATwErgITNbLuluSddGFL0JmG9JdDnvqMJc6qpH+/UEzrmMENdjBGa2CFjUa9ydvYa/Es8YYtVQW8HXf7uKN/YdpnJk8h40ds65wfIri/vhD6txzmUKTwT9qD2phHGjCrx7yDmX9jwR9EMSDbUVPLtmJ+2dfZ7V6pxzacETwQAaaio4cKSLJRtaEx2Kc87FjSeCAVx0yljysrN40o8TOOfSmCeCARTm5XD+yWP8OIFzLq15IjiO2bUVrNtxgI27DiQ6FOeciwtPBMfRcxqpdw8559KVJ4LjmFxWxMllRTSu8ttSO+fSkyeCKDTUVvDcul0cPNKZ6FCcc27IeSKIQkNNBUc6u/nz2l2JDsU554acJ4IonDdlDEV52TzpZw8559KQJ4Io5OVkcfG0Mhpf3U4S3STVOeeGhCeCKDXUVLBt72FWvbE/0aE459yQ8kQQpYZaP43UOZeePBFEqXJkATPGjaTpVT+N1DmXXjwRnIDZtRU0b2pl78GORIfinHNDxhPBCWioraCr23hqjbcKnHPpI66JQNIVklZJWivpjn7KvFfSCknLJf0invEM1lkTSxldmEuTHydwzqWRuD2zWFI2cA/wDqAFWCxpoZmtiCgzDfg8cJGZtUqqiFc8QyE7S1w2vZym1Tvo6jays5TokJxzbtDi2SI4D1hrZuvM7AgwH7iuV5mPAfeYWSuAmSX9rnZDbQW7DxxhWcueRIfinHNDQvG6QErSHOAKM/toOHwLcL6ZzYso82tgNXARkA18xcx+28ey5gJzASorK+vmz58fU0xtbW0UFxfHNO/RZRwxPvnkQa6Zmst7puUNalmDimMI6pIs0qUu6VIP8Lokq8HUpaGhodnMZvU1LW5dQ1HKAaYB9UAV8LSkM8zsmN1tM7sXuBdg1qxZVl9fH9PKmpqaiHXeSPe/9mfWHe6ivv6SQS8rVkNVl2SQLnVJl3qA1yVZxasu8ewa2gJMjBiuCsdFagEWmlmHma0naB1Mi2NMQ6KhtoJXtuxj+77DiQ7FOecGLZ6JYDEwTdIUSXnATcDCXmV+TdAaQFIZMB1YF8eYhkTPw2qa/BkFzrk0ELdEYGadwDzgCWAl8JCZLZd0t6Rrw2JPALskrQAagf9tZkl/r+dTx5Vw0sgCf5axcy4txPUYgZktAhb1GndnxHsDPhO+UoYkGmrL+c1L2zjS2U1ejl+X55xLXb4Fi1FDTQVt7Z0s2bA70aE459ygeCKI0UWnlJGXneXdQ865lOeJIEZF+Tmcf/IYvy21cy7leSIYhPqaCl7bcYBNuw4mOhTnnIuZJ4JBmB0+rMa7h5xzqcwTwSBMKStiSlmRdw8551KaJ4JBqq8p5y/rdnHoSFeiQ3HOuZgcNxFImiopP3xfL+k2SaXxDy01zK6t4EhnN39+bWeiQ3HOuZhE0yL4JdAl6RSCG79NBJL6ATLD6bwpYyjMy/bjBM65lBVNIugObxfxbuBfzex/A+PiG1bqyM/J5qJTymh8dQfxuqW3c87FUzSJoEPSzcCtwGPhuNz4hZR6ZtdWsGXPIVa/0ZboUJxz7oRFkwg+DFwA/LOZrZc0BXggvmGllvqacsBPI3XOpabjJgIzW2Fmt5nZg5JGAyVm9rVhiC1ljBs1glPHjfTTSJ1zKSmas4aaJI2UNAZYCvxI0rfjH1pqaagpp3ljK3sPdSQ6FOecOyHRdA2NMrN9wHuAn5nZ+cDb4xtW6pldW0FXt/HMGn9YjXMutUSTCHIkjQPey5sHi10vZ08aTWlhrncPOedSTjSJ4G6CJ4m9ZmaLJZ0MrIlvWKknO0tcOq2cp1btoLvbTyN1zqWOaA4WP2xmM83sE+HwOjO7If6hpZ7ZtRXsOnCEZVv2JjoU55yLWjQHi6sk/UrS9vD1S0lV0Sxc0hWSVklaK+mOPqZ/SNIOSS+Gr4/GUolkcen0ciRo9O4h51wKiaZr6KfAQmB8+PpNOG5AkrKBe4ArgRnAzZJm9FH0v8zsrPB1X9SRJ6ExRXmcPbHUrydwzqWUaBJBuZn91Mw6w9f9QHkU850HrA27ko4A84HrBhFrSphdW8Gylr1s33840aE451xUcqIos0vSB4AHw+GbgV1RzDcB2Bwx3AKc30e5GyRdCqwGPm1mm3sXkDQXmAtQWVlJU1NTFKt/q7a2tpjnjVZJW3A76h8++gyXVMXvThzDUZfhki51SZd6gNclWcWtLmY24AuoJuga2gFsB34NTIxivjnAfRHDtwDf71VmLJAfvv848OTxlltXV2examxsjHneaHV3d9u5X/29feLnS+K6nuGoy3BJl7qkSz3MvC7JajB1AZZYP9vVaM4a2mhm15pZuZlVmNn1wO1R5JgtBLes7lEVjotc9i4zaw8H7wPqolhuUpNEQ00Fz6zeSUdXd6LDcc6544r1CWXvjaLMYmCapCmS8oCbCFoWR4UXqvW4FlgZYzxJpaG2gv3tnSzZ0JroUJxz7rhiTQQ6XgELnmEwj+BitJXAQ2a2XNLdkq4Ni90mabmkl4DbgA/FGE9SuXhaGbnZ8rOHnHMpod+DxeFN5vqcRBSJAMDMFgGLeo27M+L954HPR7OsVFKcn8N5U8bQ+Op2vvCuUxMdjnPODWigs4aaAaPvjf6R+ISTPhpqKvjq4yvZvPsgE8cUJjoc55zrV79dQ2Y2xcxODv/2fp08nEGmoobaCgCavHvIOZfkYj1G4I7j5LIiqscW+t1InXNJzxNBnPScRvrn13Zx6EhXosNxzrl+eSKIo4baCto7u3luXTQXYjvnXGJElQgkZUsaL2lSzyvegaWD86eMYURutncPOeeS2nHvNSTpk8CXgTeAnktlDZgZx7jSQkFuNhedMpbGVdsxM6Sozrp1zrlhFc1N524HaszM+zdi0FBbwR9Wbmft9jamVZYkOhznnHuLaLqGNgP+yK0YNdQEp5F695BzLllF0yJYBzRJehzouUEcZvbtuEWVRsaXjqD2pBIaV23n45dNTXQ4zjn3FtG0CDYBvwfygJKIl4tSQ20FSza0su9wR6JDcc65tzhui8DM7hqOQNJZQ00FP2h6jWfX7ORdZ4w7/gzOOTeMBrrp3HfM7FOSfkNwltAxzOzaPmZzfThnUimjRuTy5KvbPRE455LOQC2CB8K/3xyOQNJZTnYWl04vp2nVdrq7jawsP43UOZc8+k0EZtYc/n1q+MJJXw015fzmpa28snUvM6tKEx2Oc84dddyDxZKmSVogaYWkdT2v4QgunVw2vRzJTyN1ziWfaM4a+inwA6ATaAB+Bvw8nkGlo7HF+ZxZVUrjqh2JDsU5544RTSIYYWZ/BBQ+yP4rwFXRLFzSFZJWSVor6Y4Byt0gySTNii7s1DS7toJlLXvY2dZ+/MLOOTdMokkE7ZKygDWS5kl6N1B8vJkkZQP3AFcCM4CbJc3oo1wJwW0s/npCkaeg2bUVmEGTtwqcc0kkmkRwO1BI8HD5OuADwK1RzHcesNbM1pnZEWA+cF0f5f4J+BpwOKqIU9iMcSMpL8n3h9o755LKgIkg3Kt/n5m1mVmLmX3YzG4ws+eiWPYEgvsU9WgJx0Uu/xxgopk9fqKBp6KsLNFQU87Tq3fQ0dV9/Bmcc24YDHRBWY6ZdUq6OB4rDrubvg18KIqyc4G5AJWVlTQ1NcW0zra2tpjnHSrlnZ3sP9zJTx5tpGZMdszLSYa6DJV0qUu61AO8LskqbnUxsz5fwNLw7w+AhcAtwHt6Xv3NFzH/BcATEcOfBz4fMTwK2AlsCF+Hga3ArIGWW1dXZ7FqbGyMed6hsu/QETvlC4/b/1m0YlDLSYa6DJV0qUu61MPM65KsBlMXYIn1s12N5hhBAbALmA1cDVwT/j2excA0SVMk5QE3hQmlJwHtNbMyM5tsZpOB54BrzWxJFMtOWSUFuZw7eQyNfj2Bcy5JDJQIKiR9BngFeDn8uzz8+8rxFmxmncA84AlgJfCQmS2XdLekjL5PUUNNBavfaKOl9WCiQ3HOuQETQTbBaaLFBLedLu71Oi4zW2Rm081sqpn9czjuTjNb2EfZ+nRvDfRoqA0eVuMXlznnksFAN53bZmZ3D1skGWRqeRETx4yg6dXt3PK26kSH45zLcAO1CPwWmXEiidk1FfzptZ0c7uhKdDjOuQw3UCK4fNiiyEANtRUc7ujmL+t2JToU51yG6zcRmNnu4Qwk07zt5LEU5GbR5GcPOecSLJrTR10cFORmc9HUMp5ctb3nugrnnEsITwQJVF9bwebdh3htx4FEh+Kcy2CeCBJods9ppN495JxLIE8ECTShdAQ1lSX+1DLnXEJ5Ikiw+tpyFm/Yzf7DHYkOxTmXoTwRJNjsmgo6u41n1+xMdCjOuQzliSDBzqkeTUlBjj+sxjmXMJ4IEiw3O4tLp5fTuGoH3d1+Gqlzbvh5IkgCs2sq2LG/neVb9yU6FOdcBvJEkAQuqylHwruHnHMJ4YkgCZQV5zOzqtRPI3XOJYQngiTRUFPOSy172NXWnuhQnHMZxhNBkphdW4EZPLXaH1bjnBtengiSxOnjR1FWnO/dQ865YRfXRCDpCkmrJK2VdEcf0/9W0suSXpT0rKQZ8YwnmWVlifqacp5evYPOru5Eh+OcyyBxSwSSsoF7gCuBGcDNfWzof2FmZ5jZWcDXgW/HK55UMLu2gn2HO1m6aU+iQ3HOZZB4tgjOA9aa2TozOwLMB66LLGBmkSfOFwEZfUXVxdPKyMmSn0bqnBtWitdDUSTNAa4ws4+Gw7cA55vZvF7l/hfwGSAPmG1ma/pY1lxgLkBlZWXd/PnzY4qpra2N4uLimOYdLv/y/CHajhhfvbhwwHKpUJdopUtd0qUe4HVJVoOpS0NDQ7OZzepzopnF5QXMAe6LGL4F+P4A5d8P/MfxlltXV2examxsjHne4fLDp9Za9T88Zi2tBwcslwp1iVa61CVd6mHmdUlWg6kLsMT62a7Gs2toCzAxYrgqHNef+cD1cYwnJTTUBA+rafLuIefcMIlnIlgMTJM0RVIecBOwMLKApGkRg1cBb+kWyjSnVBRTNXqEP7XMOTdscuK1YDPrlDQPeALIBn5iZssl3U3QRFkIzJP0dqADaAVujVc8qUISDTUVLGhu4XBHFwW52YkOyTmX5uKWCADMbBGwqNe4OyPe3x7P9aeq2bUVPPDcRv66fjeXTS9PdDjOuTTnVxYnoQumjiU/J8u7h5xzw8ITQRIqyM3mwqljefLV7T1nVDnnXNx4IkhSs2sr2LT7IOt2Hkh0KM65NOeJIEnVh6eReveQcy7ePBEkqYljCplWUey3m3DOxZ0ngiQ2u7aC59fvpq29M9GhOOfSmCeCJFZfU0FHl/Hsmp2JDsU5l8Y8ESSxWZNHU5Kf48cJnHNx5YkgieVmZ3HJ9DIaV/lppM65+PFEkOQaairYvr+d5Vv3Hb+wc87FwBNBkqv3u5E65+LME0GSKy/JZ2bVKH+ovXMubjwRpICGmgpe2LyH3QeOJDoU51wa8kSQAhpqKzCDp1fvSHQozrk05IkgBcycMIqy4jzvHnLOxYUnghSQlSUum17BU6t30NXtp5E654aWJ4IU0VBbzt5DHbywqfAU+1sAABN0SURBVDXRoTjn0ownghRxybRysrPk3UPOuSEX10Qg6QpJqyStlXRHH9M/I2mFpGWS/iipOp7xpLJRI3Kpqx5N4yo/YOycG1pxSwSSsoF7gCuBGcDNkmb0KvYCMMvMZgILgK/HK550MLu2gpXb9rFt76FEh+KcSyPxbBGcB6w1s3VmdgSYD1wXWcDMGs3sYDj4HFAVx3hS3uzanquMvVXgnBs6itfNzCTNAa4ws4+Gw7cA55vZvH7Kfx943cy+2se0ucBcgMrKyrr58+fHFFNbWxvFxcUxzZsMzIzPPXWISSOz+Mj0zpSuS6RU/7/0SJd6gNclWQ2mLg0NDc1mNquvaTmDimqISPoAMAu4rK/pZnYvcC/ArFmzrL6+Pqb1NDU1Eeu8yeLKvS/zyNIt5BcWpXxdeqTD/wXSpx7gdUlW8apLPLuGtgATI4arwnHHkPR24IvAtWbWHsd40kJDTQUHj3Sxand3okNxzqWJeCaCxcA0SVMk5QE3AQsjC0g6G/ghQRLw8yKjcOHUMvJzsnhuWycdXZ4MnHODF7dEYGadwDzgCWAl8JCZLZd0t6Rrw2LfAIqBhyW9KGlhP4tzoRF52Vxx+kk8u6WTC/7vk/zz4ytY/cb+RIflnEthcT1GYGaLgEW9xt0Z8f7t8Vx/uvrmjWcyOWsXKw+X8tM/beBHz6xnZtUobqyr4pozx1NamJfoEJ1zKSQpDha7E5ObncXZFTl8un4WO9vaefTFrTy8ZDP/+Ohy/umxlbzjtErm1FVxaXg1snPODcQTQYorK87nIxdP4X9eNJnlW/exoLmFX7+4hceXbaNyZD7vPruKOXVVnFKRHqfPOeeGnieCNCGJ0yeM4vQJo/j8u2p5cuV2FjS38KNn1vHvT73G2ZNKubFuIlefOY6RBbmJDtc5l0Q8EaSh/JxsrjxjHFeeMY7t+w/z6xe28PCSFr7wq5e56zfLueL0k5hTV8WFU8u868g554kg3VWUFDD30ql87JKTWdaylwXNLTz64hYefXEr40cV8J5zgq6jyWVFiQ7VOZcgnggyhCTOnFjKmRNL+eJVp/KHlW/w8JIW/q1pLd9vXMu5k0dzY91E3jVzHMX5/rVwLpP4Lz4DFeRmc/XM8Vw9czyv7z3MIy+0sGBJC3//y2V8eeFyrjwj6Dp625SxZHnXkXNpzxNBhjtpVAF/V38Kn7hsKks37WFB82Yee2kbjyzdQtXoEdwQdh1NHFOY6FCdc3HiicABQddRXfVo6qpHc+fVp/HE8tdZ0NzC955cw3f/uIa3nTyGG+smcuUZJ1GY518b59KJ/6LdW4zIy+b6sydw/dkT2LLnEI80t7BgaQufffgl7nz0Fa6aOY45dRM5d/JopMzuOuro6mZL6yE27j7Is1s6KNuyl9qTSsjJ9qfAutThicANaELpCD55+TTmzT6FxRtaWdC8mceXbeOhJS1Ujy1kzjlVvKeuigmlIxIdatwc7uiipfUgG3YeZOPug2zcdYANu4K/La2H6Op+85ke9738LIV52Zw1sZRZ1aM5p3o0Z08azagRfu2GS16eCFxUJHHelDGcN2UMX77mNH77yus83LyZb/1+Nd/+w2oumlrGjbOqeOdpJ1GQm53ocE/YwSOdbNwVuZEP3m/cdZCtew8R+fymkoIcJo8t4owJo7hm5niqxxYyuayINa+8SFFVDUs3ttK8qZXvN66l20CC6RUlnFM9mllh91v12MKMb0255OGJwJ2wovwcbqir4oa6KjbvPsiC5hYWNLdw+/wXKcnP4eozxzOnropzJpUm1cZu76EONu06yIZdB45u8HuGt+8/9lEYY4vyqB5byHlTxgQb+rFFR/+WFub2Wa8DG7KoP2sC1501IRhu7+SlzXtYsrGV5o2tPLZsKw8+vwmAsuI8zpkUJIVZk0dz2vhRKZlAXXrwROAGZeKYQj79juncfvk0nlu/iwVLWvjVCy08+PwmTi4vYk5dFTecU0XlyIK4x2JmtB7seHNDv/PNPfxNuw+y+8CRY8pXjsynemwR9TXlVEds6CeNLRyS23AU5edw4SllXHhKGQDd3caa7W00b2xlycbdLN3Yyu9WvAFAXnYWp08YyazJY44miPKS/EHH4Fw0PBG4IZGVJS6cWsaFU8u467rTWPTyNhY0t/D1367im0+s4tLp5cypq+Ltp1YOas/XzNi+v52NvfbsN+46wMadB9nf3nm0rATjR41gclkhV5x+EtVjCqkeW8TkskImjSkc9rOfsrJEzUkl1JxUwvvPnwTAjv3tLN3UytKNrSzZ2Mr9f9rAvU+vA6B6bCF1k0ZTNzlIDNMqSvyWIC4uPBG4IVdSkMv7zp3E+86dxPqdB/hlcwu/XNrCvF+8wKgRuVwbdh3NrBrVZxdLV7exbe+hsJ++Z6/+wNHhQx1dR8tmZ4mJo0dQPbaIukmjj+7ZV48tYuKYEeTnJHd3S3lJPu887STeedpJALR3dvHKlr00h91JT6/ZwSMvBE94LcnP4ezq0dRNCrqTzpxY6leBuyHh3yIXV1PKivjcO2v49Dum8+fXdrKguYWHlmzmgec2Mr2ymPecU0XLxg6e/s2Koxv8zbsPcSTiMZx5OVlMGlPI5LGFXHRKGZPDDX312ELGl44gN41O1czPyaauegx11WOAoAW0afdBlmwIDkAv3djKd/64GjPIEtSeNJJZYYuhrno0E0pHJNVxmXg6dKSLN/YdDl7729ne835fO2/sO8z2/cHfjs4uSv/0B0oKchhZkBv8HZHLyIJcRobve0+LHC7Ky0n7K+w9EbhhkZ0lLplWziXTytl7qIPHl23j4ebN/Mt/vwpAYd4mJo0pZFpFCW+fUXnMwdmTRhak/Q+xP5LCpFfEDXVVQHDQ+8XNe2jesJvmTa0saG7hZ3/ZCATHPYKkMIa66tGcNn5kyiXK9s4utu9rZ/v+Nzfqb+wLN/QR4/Yf7nzLvPk5WZw0qoDKkgJOGz+ShpoKtm5pobS8gv2HO9l3uIN9hzvZ0nqIfeHwkc6Bn/2dJSjO70kQQfIoKchl5IicfpJJMC2ybF5Ocv8P4poIJF0BfBfIBu4zs3/pNf1S4DvATOAmM1sQz3hcchg1Ipf3nz+J958/iS17DrH4r3/hur9pyJg92cEaNSKXy6aXc9n0cgA6u7p59fX9LN3UGrQcNray6OXXASjIzWJmVWlwdlL1aM6ZNJrRRYl5lGlHVzc729rf3GOP2HuP3KNvPdjxlnlzs0VFSQGVI/OZVlHMxaeUUTEyn8qSAipHBuMrRhYwsiDnLd+jpqbt1NfP7Deuwx1d7D/cyf4wSew/3MG+Qz3DHUECOdRxTCJpaT3I/m3BcFt75zGnF/elIDerVxJ5M3Ecr1UyckQuRXnZcf19xC0RSMoG7gHeAbQAiyUtNLMVEcU2AR8CPhevOFxym1A6gjX5WZ4EBiEnO+voQ4k+eMFkAF7fe/jocYbmjbv50dPr+EF44dvU8qKjXUl11WOYWl40qM+/u9vYdeBI2B0TuRd/7B79rgPtb9lgZik4TlI5soCq0YXUVY8+ZsNeGW78Rxfmxa1VWJCbTUFudsxnaXV3G21HOo9NGIc62N8emVDeTDD7Dnew91AHLa0Hj05vj6JVUlKQy5ypoj6mKAcWzxbBecBaM1sHIGk+cB1wNBGY2YZw2sCfgnPuhJw0qoCrZo7jqpnjgKA/fVlLcE1Dz2mrDy1pAaC0MPfoKat11aM5s6oUCI5P7DnYcUx3TF978dv3tx9zdXWPsuK8o3vxZ0wYFWzYe+3Fjy3OT/kzobKyFO7Z58Z8hX17Z9dbWh59DVd2vT7E0Qdkx2vTxLpgaQ5whZl9NBy+BTjfzOb1UfZ+4LH+uoYkzQXmAlRWVtbNnz8/ppja2tooLk6PZ/d6XZJPKtWj24zXDxhr9nSxtrWbtXu62HYg2BZkC0bmGfuPiM4+Ng9FuTA6X5TmZ1FaIErzg9foiPej8kVOkmzgU+n/cjyDqUtDQ0Ozmc3qa1pKHCw2s3uBewFmzZpl9fX1MS2nqamJWOdNNl6X5JPq9dh94AgvbAq6k15YvYGZp1S/uRcfdtNUjMxPuSugU/3/EiledYlnItgCTIwYrgrHOeeS0JiiPC4/tZLLT62kqeB16utPTXRIbpjE85ymxcA0SVMk5QE3AQvjuD7nnHMxiFsiMLNOYB7wBLASeMjMlku6W9K1AJLOldQC3Aj8UNLyeMXjnHOub3E9RmBmi4BFvcbdGfF+MUGXkXPOuQRJ7svdnHPOxZ0nAuecy3CeCJxzLsN5InDOuQznicA55zJc3G4xES+SdgAbY5y9DNg5hOEkktcl+aRLPcDrkqwGU5dqMyvva0LKJYLBkLSkv3ttpBqvS/JJl3qA1yVZxasu3jXknHMZzhOBc85luExLBPcmOoAh5HVJPulSD/C6JKu41CWjjhE455x7q0xrETjnnOvFE4FzzmW4jEgEkn4iabukVxIdy2BJmiipUdIKScsl3Z7omGIhqUDS85JeCutxV6JjGixJ2ZJekPRYomMZDEkbJL0s6UVJSxIdT6wklUpaIOlVSSslXZDomGIhqSb8X/S89kn61JCuIxOOEUi6FGgDfmZmpyc6nsGQNA4YZ2ZLJZUAzcD1ZrYiwaGdEEkCisysTVIu8Cxwu5k9l+DQYibpM8AsYKSZXZ3oeGIlaQMwy8xS+iIsSf8BPGNm94UPxyo0sz2JjmswJGUTPOnxfDOL9cLat8iIFoGZPQ3sTnQcQ8HMtpnZ0vD9foKH/kxIbFQnzgJt4WBu+ErZvRJJVcBVwH2JjsWBpFHApcCPAczsSKongdDlwGtDmQQgQxJBupI0GTgb+GtiI4lN2JXyIrAd+L2ZpWQ9Qt8B/h7oTnQgQ8CA30lqljQ30cHEaAqwA/hp2F13n6SiRAc1BG4CHhzqhXoiSFGSioFfAp8ys32JjicWZtZlZmcRPKXuPEkp2W0n6Wpgu5k1JzqWIXKxmZ0DXAn8r7BrNdXkAOcAPzCzs4EDwB2JDWlwwu6ta4GHh3rZnghSUNin/kvgP83skUTHM1hhk70RuCLRscToIuDasG99PjBb0s8TG1LszGxL+Hc78CvgvMRGFJMWoCWilbmAIDGksiuBpWb2xlAv2BNBigkPsv4YWGlm3050PLGSVC6pNHw/AngH8Gpio4qNmX3ezKrMbDJB0/1JM/tAgsOKiaSi8CQEwq6UvwFS7mw7M3sd2CypJhx1OZBSJ1T04Wbi0C0EcX54fbKQ9CBQD5RJagG+bGY/TmxUMbsIuAV4OexfB/iCmS1KYEyxGAf8R3gWRBbwkJml9GmXaaIS+FWwv0EO8Asz+21iQ4rZJ4H/DLtU1gEfTnA8MQuT8juAj8dl+Zlw+qhzzrn+edeQc85lOE8EzjmX4TwROOdchvNE4JxzGc4TgXPOZThPBC4pSTJJ34oY/pykrwzRsu+XNGcolnWc9dwY3vWysdf4yZIOhXeSXCHpZ+FFgvGM5SuSPhfPdbjU5YnAJat24D2SyhIdSCRJJ3LtzUeAj5lZQx/TXgtvr3EGwS023jsU8TkXC08ELll1Ejyf9dO9J/Teo5fUFv6tl/SUpEclrZP0L5L+R/jcg5clTY1YzNslLZG0OrxXUM9N8L4habGkZZI+HrHcZyQtpI+rUyXdHC7/FUlfC8fdCVwM/FjSN/qrpJl1Ac8T3kFW0uXhTdJeVvAcjfxw/IaepChplqSm8P1XwnJNYZ1vi4jri2H9ngVqIsbfFrZElkmaP9A/wWWGjLiy2KWse4Blkr5+AvOcCZxKcNvxdcB9Znaeggf4fBLoeaDHZIJ76EwFGiWdAnwQ2Gtm54Yb4D9J+l1Y/hzgdDNbH7kySeOBrwF1QCvBXTuvN7O7Jc0GPmdm/T7cRVIBcD5we/j+fuByM1st6WfAJwjubDqQWqABKAFWSfoBMJPgdhdnEfzOlxI8uwKCm69NMbP2ntt8uMzmLQKXtMK7qv4MuO14ZSMsDp/Z0A68BvRsyF8m2Pj3eMjMus1sDUHCqCW4r84Hw1t3/BUYC0wLyz/fOwmEzgWazGyHmXUC/0lwH/zjmRqu5w1gm5ktI9hrX29mq8My/xHlsh43s/bwQTLbCW4TcQnwKzM7GH6OCyPKLyO49cIHCFpeLsN5InDJ7jsEfe2R95LvJPzuSsoC8iKmtUe8744Y7ubYFnDve6sYIOCTZnZW+JpiZj2J5MCgavFWPccIpgJ1kq49TvmjdQYKek2LrHMXx2/pX0XQ2joHWHyCxz1cGvJE4JKame0GHiJIBj02EHTFQHB/9ljOuLlRUlZ43OBkYBXwBPCJnjN4JE2P4mEmzwOXSSoLb6B3M/BUtEGEe/F3AJ8PY5gcdlNBcHPBnmVt4M063xDFop8Grpc0Iryb6DVwNHFONLNG4B+AUUBxtPG69OSJwKWCbwGRZw/9iGDj+xJwAbHtrW8i2Ij/N/C3ZnaY4DGTK4Clkl4Bfshx9q7NbBvBhrwReAloNrNHTzCWXwOFBN1MHwYelvQyQSvm38MydwHfVfAw+a7jLTB8nOl/hTH9N7A4nJQN/Dxc/gvA99LkEY5uEPzuo845l+G8ReCccxnOE4FzzmU4TwTOOZfhPBE451yG80TgnHMZzhOBc85lOE8EzjmX4f4/ohTzbEKisJ8AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "0HlS1DmnFwAm"
      },
      "source": [
        "## MNIST MLP on Non IID"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "m3gm47fHFwAn"
      },
      "source": [
        "### Train"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "Z0XLVPfNFwAn",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "67e293da-60ad-4b4d-934d-1e4a5ee11831"
      },
      "source": [
        "# number of training rounds\n",
        "rounds = 100\n",
        "# client fraction\n",
        "C = 0.1\n",
        "# number of clients\n",
        "K = 100\n",
        "# number of training passes on local dataset for each roung\n",
        "E = 20\n",
        "# batch size\n",
        "batch_size = 10\n",
        "# learning Rate\n",
        "lr=0.05\n",
        "# proximal term constant\n",
        "mu = 0.01\n",
        "# percentage of clients to have fewer than E epochs\n",
        "percentage = 90\n",
        "# target_test_accuracy\n",
        "target_test_accuracy=94.0\n",
        "# dict containing different type of data partition\n",
        "data_dict = non_iid_partition(mnist_data_train, 100, 200, 300, 2)\n",
        "# load model\n",
        "mnist_mlp = MNIST_2NN()\n",
        "\n",
        "if torch.cuda.is_available():\n",
        "  mnist_mlp.cuda()\n",
        "\n",
        "mnist_mlp_non_iid_trained = training(mnist_mlp, rounds, batch_size, lr, mnist_data_train, data_dict, mnist_data_test, C, K, E, mu, percentage, \"FedProx MNIST MLP on non-IID Dataset (90%)\", \"green\", target_test_accuracy)"
      ],
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "System heterogeneity set to 90% stragglers.\n",
            "\n",
            "Picking 10 random clients per round.\n",
            "\n",
            "Round: 1... \tAverage Train Loss: 0.072... \tTest Loss: 3.5024506057739258... \tTest Accuracy: 30.632911392405063\n",
            "Round: 2... \tAverage Train Loss: 0.074... \tTest Loss: 2.408240445327759... \tTest Accuracy: 32.53164556962025\n",
            "Round: 3... \tAverage Train Loss: 0.033... \tTest Loss: 1.5212392637252807... \tTest Accuracy: 56.835443037974684\n",
            "Round: 4... \tAverage Train Loss: 0.049... \tTest Loss: 1.2721297611236573... \tTest Accuracy: 59.620253164556964\n",
            "Round: 5... \tAverage Train Loss: 0.04... \tTest Loss: 1.049706690788269... \tTest Accuracy: 63.037974683544306\n",
            "Round: 6... \tAverage Train Loss: 0.035... \tTest Loss: 0.7717835886955261... \tTest Accuracy: 70.25316455696202\n",
            "Round: 7... \tAverage Train Loss: 0.024... \tTest Loss: 0.9928293849945068... \tTest Accuracy: 68.22784810126582\n",
            "Round: 8... \tAverage Train Loss: 0.03... \tTest Loss: 0.8056202705383301... \tTest Accuracy: 74.55696202531645\n",
            "Round: 9... \tAverage Train Loss: 0.027... \tTest Loss: 0.5444605065345764... \tTest Accuracy: 83.0379746835443\n",
            "Round: 10... \tAverage Train Loss: 0.029... \tTest Loss: 0.5914243157386779... \tTest Accuracy: 81.51898734177215\n",
            "Round: 11... \tAverage Train Loss: 0.027... \tTest Loss: 0.4415578445911407... \tTest Accuracy: 85.31645569620254\n",
            "Round: 12... \tAverage Train Loss: 0.023... \tTest Loss: 0.5952076082229614... \tTest Accuracy: 78.48101265822785\n",
            "Round: 13... \tAverage Train Loss: 0.056... \tTest Loss: 0.47486790461540224... \tTest Accuracy: 84.0506329113924\n",
            "Round: 14... \tAverage Train Loss: 0.017... \tTest Loss: 0.4699278622150421... \tTest Accuracy: 82.65822784810126\n",
            "Round: 15... \tAverage Train Loss: 0.017... \tTest Loss: 0.3987764518737793... \tTest Accuracy: 86.83544303797468\n",
            "Round: 16... \tAverage Train Loss: 0.023... \tTest Loss: 0.3550555797576904... \tTest Accuracy: 89.11392405063292\n",
            "Round: 17... \tAverage Train Loss: 0.028... \tTest Loss: 0.29444893481731416... \tTest Accuracy: 91.39240506329114\n",
            "Round: 18... \tAverage Train Loss: 0.015... \tTest Loss: 0.3303351098060608... \tTest Accuracy: 89.49367088607595\n",
            "Round: 19... \tAverage Train Loss: 0.027... \tTest Loss: 0.2830175088882446... \tTest Accuracy: 91.39240506329114\n",
            "Round: 20... \tAverage Train Loss: 0.02... \tTest Loss: 0.25165053198337556... \tTest Accuracy: 92.27848101265823\n",
            "Round: 21... \tAverage Train Loss: 0.014... \tTest Loss: 0.2876241144895554... \tTest Accuracy: 91.39240506329114\n",
            "Round: 22... \tAverage Train Loss: 0.019... \tTest Loss: 0.2692352819919586... \tTest Accuracy: 92.15189873417721\n",
            "Round: 23... \tAverage Train Loss: 0.025... \tTest Loss: 0.2940206934928894... \tTest Accuracy: 91.13924050632912\n",
            "Round: 24... \tAverage Train Loss: 0.019... \tTest Loss: 0.3795086560487747... \tTest Accuracy: 88.48101265822785\n",
            "Round: 25... \tAverage Train Loss: 0.021... \tTest Loss: 0.29102097009420397... \tTest Accuracy: 90.50632911392405\n",
            "Round: 26... \tAverage Train Loss: 0.02... \tTest Loss: 0.2608605251789093... \tTest Accuracy: 92.53164556962025\n",
            "Round: 27... \tAverage Train Loss: 0.015... \tTest Loss: 0.20730138581991195... \tTest Accuracy: 94.30379746835443\n",
            "Training Done!\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ifWreXVkYctp",
        "colab_type": "text"
      },
      "source": [
        "# Comparison with Federated Averaging IID Partition\n",
        "\n",
        "> In a highly heterogenous system (90%) stragglers, authors of FedProx have claimed that FedProx achieves on average **22%** improvement in testing accuracy compared to Federated Averaging\n",
        "\n",
        "With our first test above, we know that the special case where **mu=0**, FedProx matches the results of FedAvg. \n",
        "\n",
        "We will use the same idea but increase our stragglers this time. We will run the same experiment with **mu > 0** to compare results of FedProx."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "O8ydCcIaZwP3",
        "colab_type": "text"
      },
      "source": [
        "### Training Federated Averaging with 90% stragglers (IID Partition)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "s07MAIAiZhky",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "7d76d908-c24a-410f-a1ed-ecbb235cb2b7"
      },
      "source": [
        "# number of training rounds\n",
        "rounds = 100\n",
        "# client fraction\n",
        "C = 0.1\n",
        "# number of clients\n",
        "K = 100\n",
        "# number of training passes on local dataset for each roung\n",
        "E = 20\n",
        "# batch size\n",
        "batch_size = 10\n",
        "# learning Rate\n",
        "lr=0.01\n",
        "# proximal term constant\n",
        "mu = 0.0\n",
        "# percentage of clients to have fewer than E epochs\n",
        "percentage = 90\n",
        "# target test accuracy\n",
        "target_test_accuracy = 99.0\n",
        "# data partition dictionary\n",
        "iid_dict = iid_partition(mnist_data_train, 100)\n",
        "# load model\n",
        "mnist_cnn = MNIST_CNN()\n",
        "\n",
        "if torch.cuda.is_available():\n",
        "  mnist_cnn.cuda()\n",
        "\n",
        "mnist_cnn_iid_trained_fedavg = training(mnist_cnn, rounds, batch_size, lr, mnist_data_train, iid_dict, mnist_data_test, C, K, E, mu, percentage, \"FedAvg MNIST CNN (90% Stragglers)\", \"orange\", target_test_accuracy, algorithm='fedavg')"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "System heterogeneity set to 90% stragglers.\n",
            "\n",
            "Picking 10 random clients per round.\n",
            "\n",
            "Round: 1... \tAverage Train Loss: 0.243... \tTest Loss: 0.1800511596955359... \tTest Accuracy: 94.55696202531645\n",
            "Round: 2... \tAverage Train Loss: 0.035... \tTest Loss: 0.14766051300512628... \tTest Accuracy: 96.45569620253164\n",
            "Round: 3... \tAverage Train Loss: 0.035... \tTest Loss: 0.10738021533368156... \tTest Accuracy: 97.21518987341773\n",
            "Round: 4... \tAverage Train Loss: 0.024... \tTest Loss: 0.10633101256506051... \tTest Accuracy: 97.21518987341773\n",
            "Round: 5... \tAverage Train Loss: 0.018... \tTest Loss: 0.10073894104869105... \tTest Accuracy: 97.0886075949367\n",
            "Round: 6... \tAverage Train Loss: 0.016... \tTest Loss: 0.0966373064121406... \tTest Accuracy: 97.34177215189874\n",
            "Round: 7... \tAverage Train Loss: 0.016... \tTest Loss: 0.09341529543192592... \tTest Accuracy: 97.72151898734177\n",
            "Round: 8... \tAverage Train Loss: 0.015... \tTest Loss: 0.0747657953685848... \tTest Accuracy: 97.59493670886076\n",
            "Round: 9... \tAverage Train Loss: 0.018... \tTest Loss: 0.07796002008811338... \tTest Accuracy: 98.10126582278481\n",
            "Round: 10... \tAverage Train Loss: 0.023... \tTest Loss: 0.0748558697888744... \tTest Accuracy: 98.60759493670886\n",
            "Round: 11... \tAverage Train Loss: 0.019... \tTest Loss: 0.07428643092515412... \tTest Accuracy: 97.84810126582279\n",
            "Round: 12... \tAverage Train Loss: 0.011... \tTest Loss: 0.08080420969499537... \tTest Accuracy: 97.9746835443038\n",
            "Round: 13... \tAverage Train Loss: 0.004... \tTest Loss: 0.08317136647805383... \tTest Accuracy: 97.9746835443038\n",
            "Round: 14... \tAverage Train Loss: 0.008... \tTest Loss: 0.06960385034091306... \tTest Accuracy: 98.22784810126582\n",
            "Round: 15... \tAverage Train Loss: 0.011... \tTest Loss: 0.07245368560309508... \tTest Accuracy: 99.24050632911393\n",
            "Training Done!\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xVjIEgHPaClX",
        "colab_type": "text"
      },
      "source": [
        "### Training FedProx with 90% Stragglers (IID Parition)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jn9WLZTHaBnq",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "01b38dab-4805-4351-fd4a-cf07e087ddfa"
      },
      "source": [
        "# number of training rounds\n",
        "rounds = 300\n",
        "# client fraction\n",
        "C = 0.1\n",
        "# number of clients\n",
        "K = 100\n",
        "# number of training passes on local dataset for each roung\n",
        "E = 20\n",
        "# batch size\n",
        "batch_size = 10\n",
        "# learning Rate\n",
        "lr=0.01\n",
        "# proximal term constant\n",
        "mu = 0.01\n",
        "# percentage of clients to have fewer than E epochs\n",
        "percentage = 90\n",
        "# target test accuracy\n",
        "target_test_accuracy = 99.0\n",
        "\n",
        "# data partition dictionary\n",
        "iid_dict = iid_partition(mnist_data_train, 100)\n",
        "# load model\n",
        "mnist_cnn = MNIST_CNN()\n",
        "\n",
        "if torch.cuda.is_available():\n",
        "  mnist_cnn.cuda()\n",
        "\n",
        "mnist_cnn_iid_trained_fedprox = training(mnist_cnn, rounds, batch_size, lr, mnist_data_train, iid_dict, mnist_data_test, C, K, E, mu, percentage, \"FedProx MNIST CNN (90% Stragglers)\", \"green\", target_test_accuracy)"
      ],
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "System heterogeneity set to 90% stragglers.\n",
            "\n",
            "Picking 10 random clients per round.\n",
            "\n",
            "Round: 1... \tAverage Train Loss: 0.841... \tTest Loss: 0.23637543864250182... \tTest Accuracy: 92.9113924050633\n",
            "Round: 2... \tAverage Train Loss: 0.114... \tTest Loss: 0.1387696297518909... \tTest Accuracy: 96.70886075949367\n",
            "Round: 3... \tAverage Train Loss: 0.09... \tTest Loss: 0.10665031041502952... \tTest Accuracy: 97.21518987341773\n",
            "Round: 4... \tAverage Train Loss: 0.065... \tTest Loss: 0.091045677876845... \tTest Accuracy: 97.46835443037975\n",
            "Round: 5... \tAverage Train Loss: 0.035... \tTest Loss: 0.08589293542765081... \tTest Accuracy: 97.84810126582279\n",
            "Round: 6... \tAverage Train Loss: 0.065... \tTest Loss: 0.06773719151284313... \tTest Accuracy: 98.10126582278481\n",
            "Round: 7... \tAverage Train Loss: 0.047... \tTest Loss: 0.06703249160738778... \tTest Accuracy: 98.22784810126582\n",
            "Round: 8... \tAverage Train Loss: 0.034... \tTest Loss: 0.06355271759871975... \tTest Accuracy: 98.35443037974683\n",
            "Round: 9... \tAverage Train Loss: 0.065... \tTest Loss: 0.056771527897077616... \tTest Accuracy: 98.35443037974683\n",
            "Round: 10... \tAverage Train Loss: 0.036... \tTest Loss: 0.05375445580886444... \tTest Accuracy: 98.35443037974683\n",
            "Round: 11... \tAverage Train Loss: 0.04... \tTest Loss: 0.050227536917018006... \tTest Accuracy: 98.35443037974683\n",
            "Round: 12... \tAverage Train Loss: 0.037... \tTest Loss: 0.04918937638697098... \tTest Accuracy: 98.60759493670886\n",
            "Round: 13... \tAverage Train Loss: 0.034... \tTest Loss: 0.05199227368285064... \tTest Accuracy: 98.73417721518987\n",
            "Round: 14... \tAverage Train Loss: 0.027... \tTest Loss: 0.04749983308834635... \tTest Accuracy: 98.60759493670886\n",
            "Round: 15... \tAverage Train Loss: 0.034... \tTest Loss: 0.04527120476504206... \tTest Accuracy: 98.60759493670886\n",
            "Round: 16... \tAverage Train Loss: 0.028... \tTest Loss: 0.044824296839606544... \tTest Accuracy: 98.60759493670886\n",
            "Round: 17... \tAverage Train Loss: 0.021... \tTest Loss: 0.04425865141105169... \tTest Accuracy: 98.86075949367088\n",
            "Round: 18... \tAverage Train Loss: 0.027... \tTest Loss: 0.04344631481611577... \tTest Accuracy: 98.60759493670886\n",
            "Round: 19... \tAverage Train Loss: 0.016... \tTest Loss: 0.043170642897550716... \tTest Accuracy: 98.86075949367088\n",
            "Round: 20... \tAverage Train Loss: 0.033... \tTest Loss: 0.04040271607170289... \tTest Accuracy: 98.86075949367088\n",
            "Round: 21... \tAverage Train Loss: 0.033... \tTest Loss: 0.039728041275564466... \tTest Accuracy: 99.11392405063292\n",
            "Training Done!\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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q7nhtEX+d9QVZElMOG8bFhw+nV9eOO7TdDlkt21KnJXjid24ns2pjJbOWriM3uxP7D+5Nx/Zto8ut978o4cYXPuXdJesY2LsLt0wew0n77Ua7BolzeG42d54xlguLS7npxQX8+l+fcP+bSzl2UB2H1tbRPsmS+YbKav48Ywn3v7WUqpo6TjtgEJd9YyS79uzcki8vo3jidy7DlVXVMHPJWt5cvIa3Fq9h4cqyLfO6dGjHgcP6MHF4DhNH5LDHrt3JysASZlMWrtzITS8u4OWPV5KT3ZEbTtyL0ycMolP7pi+A7juwF38570DeXryG37+4gPvnlTJj6htcdcwojtlr12bbxFdW1/LwO8v4v9c/o7S8mhP27c+VR49i95xuLfjqMpMnfucyTHVtHXOKSnly0Wbu+ORt5hSVUlNndGqfxYTd+3DK2IEcNKwvqzZU8tbiNby5eA2/WfAJAH27deSQETkcOqIvE0fktHoLmGQUrStn6iuLeOKDYrI7tufKb+bxn4fuTrdOyaWlQ0bk8NTwvtwy7VWeXy4ueuR9xgzsyU+P3YOJI3K2Wb6mto5/FhYzNbxgfHheLlcdM4q9d+vZUi8t43nidy7NzIwFKzfy5qKgRD9r6To2ba5FwL6DjAsPH8bEETmMHdybzh22LgUfvdeuAKxYX8Fbi9fyVnhW8OyHXwIwtG/X8Icgh4OH9aV3tx2rr24Ja8qquOO1xTw683Mkcf6hu3PxESPoswOxSWJcv/ZcfuoknvhgOVNfXsgZ987k0BE5XHXMKMYM6kVdnfH8vK+4+aUFLFmzif0H9+LW0/bj4OF9W/DV7Rw88TuXBlU1tUz/cAVvLFrNW4vXsqasCoBhud04ZexAJo7IoXbFJxz/zYkJba9/zy6cOm4gp44biJmxeFXZlqqhZ+Z8yV9nfoEEew/oycQROQzP7bbd3QN8uryaNYXF27XuktVlPPj2Miqra5k8fhCXHTmSAb26bNe24mnfLovJ4wdx4pgBPDrzC+4sWMxJd77FMXv148vSSj5avp68ftn8+T/G8c09+7V4Fwk7C0/8zrWi2jrjifeDaoblpRXkZHfaUi0zcUTOVknw9TWfbtc+JDGyX3dG9uvOuRN3p7q2jrnFpby5KDgjuO/NJVTX7mAfXR99uN2rHr9Pf358dB7Dc1PXr07nDu0479DdmTx+IPe9uZR73lhCr64dufl7Yzh5/20vGEeNJ37nWoGZ8dLHK/nDiwtYtKqMfQf25H+/uw+HjshJeamzQ7ssxg3pw7ghfbj8qJGUb65hbdnm7d7eu+++y0EHHbRd63bu0I7c7qm98SpW984duOKoPC45YgTtshT5hF/PE79zKfb2Z2u48YUFzCkqZXhuN+4+c2xCrU5SpWvH9nTts/1f/c+6ZjGoT+ZeNI6nrTR5bSme+J1LkY+K13Pji5/y70Vr6N+zMzd+d19OGbtb0u3MnWtpnvida2GfrS7jlpcW8q+PVtC7aweuO340Zx40ZJsWOc6liyd+51rIivUV3P7qIqbNLqZT+ywuO3JkSvqScW5HeeJ3bgeVbNrMXTM+48G3l4HBWQcPaZXeI53bXp74XdqVb65hTlEp5VW1adn/R6tqqPl45Xat+/GKDdzzxhI2ba7hO/sP5IqjRu50Fz5d9Hjid62upraOucvX89aioLuBD74oZXNtXXqDen/2dq969J79+Mkxo8jrt83Q0c5lJE/8LuXMjM9Wb+KVz6t59OHZvPvZWjZW1QCw14AenDtxKAcN70tOt/RUjRQWzmbcuG3Ho05Ejy7tGdK37Xfq5doWT/wuJVbGdCD29uK1fLWhEoDBfTZywpj+TAz7jumbAfXgaxe3Y5+B0emgyzlP/K5FbKysZuaSdVv6h1m0Kug6uHfXDls6CWu3ZjGTj8tPc6TOOU/8brtsrqnjgy9KtpTqPyxeT22d0blDFhN278v3xg/kkOE57Nm/x5b+4V9/fUmao3bOgSd+l6C6uqDr4PpEP3PJOiqqa8lSMCDGxYcP55ARfRk3pHezA2g459LLE79rVHFJedi/+1re/mwNa8KOvYbndmPy+KDr4AOH9aVnF79BybmdiSd+t0VldS0Fn67aUk+/bG05ALt078Skkblh18F96d+z5fpPd861Pk/8juraOqbNLuK2VxaxamMV2Z3ac9CwPpx9yFAOHZHDiF2yIztghXNtUUoTv6TLgQsAAfeY2VRJ+wF3A52BGuASM5uVyjhcfHV1xvSPVnDLSwtYtrac8UN6c8vk/ThwWB86eA+SzrVZKUv8kvYmSPoTgM3AC5KmAzcCN5jZ85KOC58fkao43LbMjBkLV3PjCwv4eMUG9ti1O/efM578Ubt4yd65CEhliX80MNPMygEkzQBOAQzoES7TE/gyhTG4Bgo/X8fvX1jArKXrGNSnC1NP248TxwzY0uTSOdf2yWwHx95sbMPSaOBp4GCgAngVmA38H/AiQfVPFnCImX0eZ/0pwBSA3NzccdOmTUtJnDuirKyM7OzUjRu6veLFVbyxjscXbeaDVbX06ChOHN6BIwa1p30rJvyd6XhlAo8rOR7XtvLz8wvNbNv+SMwsZQ/gPKAQeAO4C5gK3A58N5w/GXilue3k5eVZJiooKEh3CHHFxvXF2k32o8c+sKHXTLe9f/6C3fHaIttUVZ32uDKJx5Ucjys56YwLmG1xcmpKL+6a2X3AfQCSfgsUA78DLg8X+QdwbypjiKrVG6u4s2Axj878nCyJKYcN4+LDh9Ora8d0h+acS7NUt+rZxcxWSRpMUL9/EPBD4HDgdeAbwKJUxhA1GyureWLRZi55rYCqmjomjx/E5UeOZNeendMdmnMuQ6S6Hf/jkvoC1cClZlYq6QLgNkntgUrCeny34+YtX8+FfylkeWk1J+zbnx9/M49huZlX5+mcS69UV/VMijPtTWBcKvcbRU9+UMw1j39En24due7Azpz/nbHpDsk5l6H8Lp2dXHVtHTc8O58fPfYh+w3qxbM/PJQRvb2TNOdc47zLhp3YmrIqLn30fWYuXce5E4fyP8eN9jtunXPN8sS/k/qwqJSLHilk3abN3HraGL6z/8B0h+Sc20l44t8JTXuviOuenkdudicev/gQ9t7Nhw10ziXOE/9OZHNNHb+cPp9H3v2CQ0fkcPv396dPN2+X75xLjif+ncSqDZVc/Oj7FH5ewoWHD+Oqo0fR3uvznXPbwRP/TqDw8xIufqSQjZU13PGD/Tlh3wHpDsk5txPzxJ/BzIy/zvqC65+Zz4BeXXj4vAnssWuP5ld0zrkmeOLPUJXVtfzi6fk8NruII0blcttp+9Ozq49t65zbcZ74M9CK9RVc9Mj7fFhUyg+/MYIrjsqjnfeX75xrIZ74M0jF5loeemcZ/1ewmNo64+4zx3Hs3rumOyznXBvjiT8DNBzsPH9ULtedsCfDvYM151wKeOJPo3iDnd/xg7FM2L1PukNzzrVhnvjTwOIMdn7f2eP5xh4+2LlzLvU88beyeIOdf3vMAL9465xrNZ74W8mCrzZy04sLeOWTleRkd+KXJ+3F6QcMpmN7v/vWOde6PPGnWNG6cm59ZSFPfrCc7I7tueqYUZw7cShdO/qhd86lh2efFPHBzp1zmcoTfwrMXraOcx54j4rqWh/s3DmXcTzxt7B5y9dz7gPvsUv3Ttx79ngf7Nw5l3E88begxas2ctb9s+jRpQOPnH8gA3p1SXdIzjm3DW9S0kKK1pVz5r2zyJI86TvnMlpKE7+kyyXNkzRf0hXhtMckzQkfyyTNSWUMrWHlhkrOuHcmFdW1PHL+BHbP6ZbukJxzrlEpq+qRtDdwATAB2Ay8IGm6mZ0Ws8zNwPpUxdAa1m3azJn3zmRtWRWPnH+g95fvnMt4zZb4JbXbzm2PBmaaWbmZ1QAzgFNititgMvC37dx+2lXUGGffP4vP15Vz79kHsP/g3ukOyTnnmpVIVc8iSTdJ2jPJbc8DJknqK6krcBwwKGb+JGClmS1KcrsZoWJzLVMLK/lkxQbuOmMsBw/vm+6QnHMuITKzpheQugOnA+cS/FDcD/zdzDY0u3HpPOASYBMwH6gys/q6/ruAxWZ2cyPrTgGmAOTm5o6bNm1aoq8p5WrqjNver2LemhouHNOZg/pnVuOosrIysrMzrxmpx5Ucjys5Hte28vPzC81s/DYzzCzhB3A4sJwgkT8EjEhi3d8Cl4T/twdWAgMTWTcvL88yRU1tnV3ySKENuXq6/eLhl9IdTlwFBQXpDiEujys5HldyPK5tAbMtTk5ttqga1vEfT1DiHwrcDDxKUFXzHJDXxLq7mNkqSYMJ6vcPCmcdBXxqZsXN7T+T1NUZ1zw+l399tILrjh/NiNov0h2Sc84lLZE6ikVAAXCTmb0dM/2fkg5rZt3HJfUFqoFLzaw0nH46O9lFXTPjV//6mH8UFnPZkSM5f9IwXn/dE79zbueTSOLf18zK4s0ws8uaWtHMJjUy/ZwE9ptRbn1lEQ+8tYxzJw7lR0eNTHc4zjm33RJp1XOnpF71TyT1lnR/CmPKOPe8sYTbX13E5PED+dnxe/ooWc65nVoiiX/fmCoazKwE2D91IWWWv878gt889wnH79Of352yL1k+UpZzbieXSOLPkrTlziRJfYhI525Pz1nOtU99xBGjcrn1tP18eETnXJuQSAK/GXhH0j8AAacCv0lpVBngo+L1XDntQw4Y2oe7zhjnQyQ659qMZhO/mT0sqRDIDyedYmYfpzas9Ht3yVpq6ow7fzCWLh23t9cK55zLPAlV2ZjZfEmrgc4AkgabWZtuy1hcUk73Tu3JyfahEp1zbUsinbSdKGkRsJSgo7VlwPMpjivtikoq2K13F2/B45xrcxKpuP4VwR23C81sd+BI4N2URpUBikvKGdSna7rDcM65FpdI4q82s7UErXuyzKwA2LbTnzbEzCguqWBgbx9FyznX9iRSx18qKRt4A3hU0iqCTtrarJLyaso31zKwt5f4nXNtTyIl/pOAcuBHwAvAZ8C3UxlUuhWXlAN4id851yY1WeIPe+acbmb5QB1BV8xtXtG6CsATv3OubWqyxG9mtUCdpJ6tFE9G+LrE71U9zrm2J5E6/jLgI0kvE1O331zPnDuz4pIKenRuT88uHdIdinPOtbhEEv8T4SMyikvKvbTvnGuzEumyIRL1+rGKSyrYPadbusNwzrmUSGToxaXANiOym9mwlESUZvVt+CeNzE13KM45lxKJVPXE3qzVGfge0Cc14aTf2k2bqaiuZVAfb9HjnGubmm3Hb2ZrYx7LzWwqweDrbVJxSX1TTq/jd861TYlU9YyNeZpFcAbQZgdi8Zu3nHNtXaIDsdSrIeilc3Jqwkm/+hL/bp74nXNtVCKtevKbW6YtKS4pp2eXDvTo7G34nXNtUyL98f9WUq+Y570l/Tq1YaVP0boKv7DrnGvTEumk7VtmVlr/xMxKgOMS2bikyyXNkzRf0hUx038o6dNw+o3Jh506xSXlDOzlF3adc21XInX87SR1MrMqAEldgE7NrSRpb+ACYAKwGXhB0nRgEEGPn2PMrErSLtsdfQurb8OfPypjQnLOuRaXSOJ/FHhV0gPh83NJrJfO0cBMMysHkDQDOIWgVdD/1v+QmNmqpKNOkTVlm6mqqfMWPc65Nk1m29yUu+1C0rHAUeHTl83sxQTWGQ08DRwMVACvArOBSeH0Y4FK4Cdm9l6c9acAUwByc3PHTZs2LZHXs0M+K63lV+9WcvnYTuy/S/O/iWVlZWRnZ6c8rmR5XMnxuJLjcSUnnXHl5+cXmtm2IyaaWZMPYHegc8zzLsDQ5tYLlz0PKCQYvesuYCowD/gjIIJqoKWEP0CNPfLy8qw1PDNnuQ25erp9smJ9QssXFBSkNqDt5HElx+NKjseVnHTGBcy2ODk1kYu7/yAYhKVebTitWWZ2n5mNM7PDgBJgIVAMPBHGNSvcdk4i20u1Iu+H3zkXAYnU8bc3s831T8xss6SOiWxc0i5mtkrSYIL6/YMIEn0+UCApD+gIrEk+9JZXXFJB764dyO7UZm9Mds65hBL/akknmtkzAJJOIvFE/bikvkA1cKmZlUq6H7hf0jyC1j5nh6ckaVdcUuGlfedcm5dI4uJQ+koAABMcSURBVL8IeFTSHQT18kXAfySycTObFGfaZuDMZIJsLcUl5Yzq1z3dYTjnXEol0jvnZ2Z2ELAnMNrMDqENdstsZiwvqfCmnM65Ni+ZyuzBwPclnQ6sZ+t++nd6qzdWUVVTx6A+XtXjnGvbmkz8koYC3w8f1cAQYLyZLUt1YK2taEs//F7id861bY1W9Uh6B/gXwY/Dd81sHLCxLSZ9iO2H30v8zrm2rak6/pVAd6AfUD8AbUa0vkmFLf3w9/ISv3OubWs08ZvZycA+BHfeXh8Out5b0oTWCq41FZdU0KdbR7p5G37nXBvXZJYzs/XAA8ADYS+ak4FbJQ02s0GtEWBrKS4pZ5DX7zvnIiCRLhuAoBdNM7vDzCYCh6YwprTwm7ecc1GRcOKPZWaft3Qg6VRX5234nXPRsV2Jv61ZXVbF5lrvh985Fw2JjLk7MZFpOzNvyumci5JESvx/THDaTqu+KacPsu6ci4JGW/VIOhg4BMiV9OOYWT2AdqkOrDUVrQtK/Lv5IOvOuQhoqjlnRyA7XCa2y8oNwKmpDKq1FZdUkJPdkS4d29TvmXPOxdVo4jezGcAMSQ/Wt+KRlAVkm9mG1gqwNRSXVLCb1+875yIikTr+30nqIakbwXi5H0u6KsVxtariknJv0eOci4xEEv+eYQn/ZOB5gsHXExqIZWdQV2csL/U2/M656Egk8XeQ1IEg8T9jZtW0oc7aVm2sorrWGORVPc65iEgk8f8JWAZ0A96QNITgAm+bULSlDb+X+J1z0dBsV5Rmdjtwe8ykzyXlpy6k1uU3bznnoiaRO3f7SbpP0vPh8z2Bs1MeWSspXucjbznnoiWRqp4HgReBAeHzhcAVqQqotQVt+DvRuYO34XfORUNTQy/WVwPlmNk0oA7AzGqA2laIrVUUl5Z7Vw3OuUhpqsQ/K/y7SVJfwpY8kg4C1ieycUmXS5onab6kK8Jp10taLmlO+DhuR17Ajipa5/3wO+eipamLuwr//hh4Bhgu6S2C8Xeb7bJB0t7ABcAEYDPwgqTp4exbzewP2x11C6mtM74sreD4ffunOxTnnGs1TSX+2M7ZngSeI/gxqAKOAuY2s+3RwEwzKweQNAM4ZcfCbVkrN1RSU2d+Ydc5Fykyi38vlqQVwF18XfLfipnd0OSGpdHA08DBQAXwKjAbWAucQ3AvwGzgSjMribP+FGAKQG5u7rhp06Yl9IKSsWBdLb+bVcmV4zqxT27yg6yXlZWRnZ3d4nHtKI8rOR5Xcjyu5KQzrvz8/EIzG7/NDDOL+wDeb2xeog/gPKAQeIPgR2Qq0I+gW+cs4DfA/c1tJy8vz1Lh8cIiG3L1dPts1cbtWr+goKBlA2ohHldyPK7keFzJSWdcwGyLk1Oburgbt6SfDDO7z8zGmdlhQAmw0MxWmlmtmdUB9xBcA0iLorAN/4BeXtXjnIuOphL/kTu6cUm7hH8HE9Tv/1VS7JXU7xD0+JkWxSXl7NLd2/A756Klqf7417XA9h8Pm4JWA5eaWamkP0raj6B56DLgwhbYz3YpLvFeOZ1z0ZP8Fc0kmNmkONMypkvn4tJy9h/UO91hOOdcq0qky4Y2qaa2jhWllX7XrnMuciKb+FdurArb8Ptdu865aIls4i9a5/3wO+eiKbKJv7ikvjtmL/E756Ilwom/HAkG9Oqc7lCcc65VRTjxV9Cve2c6tfc2/M65aIlw4i/3+n3nXCRFNvEH/fB74nfORU8kE39NbR1fbaj0C7vOuUiKZOJfsb6SWu+H3zkXUZFM/N6U0zkXZRFN/MHNW95dg3MuiiKa+CuQoH9PT/zOueiJZOIvKiln1x6d6dg+ki/fORdxkcx83g+/cy7KIpn4l5dU+IVd51xkRS7xV9fWsWJ9BYO8xO+ci6jIJf6v1ldSZ96U0zkXXZFL/N4Pv3Mu6iKX+P3mLedc1EUw8ZeTJejv/fA75yIqgom/gv49u9ChXeReunPOARFN/Lt5/b5zLsJSmvglXS5pnqT5kq5oMO9KSSYpJ5UxNOQDsDjnoi5liV/S3sAFwARgDHCCpBHhvEHA0cAXqdp/PJtr6ljh/fA75yIulSX+0cBMMys3sxpgBnBKOO9W4KeApXD/21ixvgIzb8rpnIs2maUm90oaDTwNHAxUAK8Cs4FXgG+Y2eWSlgHjzWxNnPWnAFMAcnNzx02bNm2HY/p4bS03vlfJ1Qd0ZnTfHR9kvaysjOzs7B3eTkvzuJLjcSXH40pOOuPKz88vNLPx28wws5Q9gPOAQuAN4C7gz8BMoGc4fxmQ09x28vLyrCX8fdbnNuTq6fbF2k0tsr2CgoIW2U5L87iS43Elx+NKTjrjAmZbnJya0ou7ZnafmY0zs8OAEmA+sDvwYVjaHwi8L2nXVMZRr7ikgnZZon9Pb8PvnIuuVLfq2SX8O5igfv8hM9vFzIaa2VCgGBhrZl+lMo56ReuCfvjbext+51yEtU/x9h+X1BeoBi41s9IU769J3g+/c86lOPGb2aRm5g9N5f4bKi6pYOKIVr1twDnnMk5k6jyqampZubHSB1h3zkVeZBL/itLKsA2/37zlnIu2yCT+r7tj9hK/cy7aIpP4i0p8ABbnnIMIJf7iknLaZYlde3gbfudctEUo8VcwoJe34XfOuchkweKSCgb28gu7zjkXocTv/fA75xxEJPFXVteyckOVN+V0zjkikvi/LPWmnM45Vy8Sib++Df+gPl7id865SCV+L/E751xkEn857bNEP2/D75xz0Uj8RSUVDOjVhXZZSncozjmXdpFI/N6U0znnvhaRxF/BIG/K6ZxzQAQSf2V1Las3VnmJ3znnQm0+8S+vb8PvA7A45xwQgcT/dVNOr+pxzjmIQOIvWuf98DvnXKw2n/iLSyro0E706+5t+J1zDiKR+MvZrVcXsrwNv3POAZFI/BVev++cczFSmvglXS5pnqT5kq4Ip/1K0lxJcyS9JGlAKmMIEr/X7zvnXL2UJX5JewMXABOAMcAJkkYAN5nZvma2HzAd+HmqYqjYXMuaMm/D75xzsVJZ4h8NzDSzcjOrAWYAp5jZhphlugGWqgCWl9a36PGqHuecqyez1ORdSaOBp4GDgQrgVWC2mf1Q0m+As4D1QL6ZrY6z/hRgCkBubu64adOmJR3D3NU13FJYxbUHdmZk73bb/2IaUVZWRnZ2dotvd0d5XMnxuJLjcSUnnXHl5+cXmtn4bWaYWcoewHlAIfAGcBcwtcH8/wZuaG47eXl5tj0efmeZDbl6un21vmK71m9OQUFBSra7ozyu5HhcyfG4kpPOuAgK29vk1JRe3DWz+8xsnJkdBpQACxss8ijw3VTtv7iknI7tssjN7pSqXTjn3E4n1a16dgn/DgZOAf4qaWTMIicBn6Zq/8NyunHy/gO8Db9zzsVon+LtPy6pL1ANXGpmpZLukzQKqAM+By5K1c5PO2Awpx0wOFWbd865nVJKE7+ZTYozLWVVO84555rX5u/cdc45tzVP/M45FzGe+J1zLmI88TvnXMR44nfOuYjxxO+ccxHjid855yImZZ20tSRJG4EF6Y4jjhxgTbqDiMPjSo7HlRyPKznpjGuImeU2nJjqO3dbygKL18Ncmkma7XElzuNKjseVHI8rcV7V45xzEeOJ3znnImZnSfx/TncAjfC4kuNxJcfjSo7HlaCd4uKuc865lrOzlPidc861EE/8zjkXMRmV+CUdK2mBpMWSrokzv5Okx8L5MyUNbYWYBkkqkPSxpPmSLo+zzBGS1kuaEz5+nuq4wv0uk/RRuM/ZceZL0u3h8ZoraWwrxDQq5jjMkbRB0hUNlmmV4yXpfkmrJM2LmdZH0suSFoV/ezey7tnhMosknd0Kcd0k6dPwfXpSUq9G1m3yPU9BXNdLWh7zXh3XyLpNfndTENdjMTEtkzSnkXVTebzi5oZM+Iw1K95AvOl4AO2Az4BhQEfgQ2DPBstcAtwd/n868FgrxNUfGBv+351g3OCGcR0BTE/DMVsG5DQx/zjgeUDAQcDMNLynXxHcRNLqxws4DBgLzIuZdiNwTfj/NcDv46zXB1gS/u0d/t87xXEdDbQP//99vLgSec9TENf1wE8SeJ+b/O62dFwN5t8M/DwNxytubsiEz1hzj0wq8U8AFpvZEjPbDPydYEzeWCcBD4X//xM4UlJKB9Q1sxVm9n74/0bgE2C3VO6zBZ0EPGyBd4Fekvq34v6PBD4zs89bcZ9bmNkbwLoGk2M/Qw8BJ8dZ9RjgZTNbZ2YlwMvAsamMy8xeMrOa8Om7wMCW2t+OxJWgRL67KYkr/P5PBv7WUvtLVBO5Ie2fseZkUuLfDSiKeV7Mtgl2yzLhl2Q90LdVogPCqqX9gZlxZh8s6UNJz0vaq5VCMuAlSYWSpsSZn8gxTaXTafwLmY7jBdDPzFaE/38F9IuzTLqP238SnKnF09x7ngr/FVZB3d9ItUU6j9ckYKWZLWpkfqscrwa5IeM/Y5mU+DOapGzgceAKM9vQYPb7BNUZY4A/Ak+1UliHmtlY4FvApZIOa6X9NktSR+BE4B9xZqfreG3FgnPujGrPLOlaoAZ4tJFFWvs9vwsYDuwHrCCoVskk36fp0n7Kj1dTuSETP2OQWYl/OTAo5vnAcFrcZSS1B3oCa1MdmKQOBG/so2b2RMP5ZrbBzMrC/58DOkjKSXVcZrY8/LsKeJLglDtWIsc0Vb4FvG9mKxvOSNfxCq2sr+4K/66Ks0xajpukc4ATgDPChLGNBN7zFmVmK82s1szqgHsa2V+6jld74BTgscaWSfXxaiQ3ZOxnrF4mJf73gJGSdg9Li6cDzzRY5hmg/ur3qcBrjX1BWkpYh3gf8ImZ3dLIMrvWX2uQNIHguKb0B0lSN0nd6/8nuDg4r8FizwBnKXAQsD7mFDTVGi2JpeN4xYj9DJ0NPB1nmReBoyX1Dqs2jg6npYykY4GfAieaWXkjyyTynrd0XLHXhL7TyP4S+e6mwlHAp2ZWHG9mqo9XE7khIz9jW2mtq8iJPAhaoSwkaCFwbTjtlwRfBoDOBFUHi4FZwLBWiOlQglO1ucCc8HEccBFwUbjMfwHzCVozvAsc0gpxDQv392G47/rjFRuXgDvD4/kRML6V3sduBIm8Z8y0Vj9eBD88K4BqgjrU8wiuCb0KLAJeAfqEy44H7o1Z9z/Dz9li4NxWiGsxQZ1v/WesvvXaAOC5pt7zFMf1l/CzM5cgofVvGFf4fJvvbirjCqc/WP+Zilm2NY9XY7kh7Z+x5h7eZYNzzkVMJlX1OOecawWe+J1zLmI88TvnXMR44nfOuYjxxO+ccxHjid9lDEkm6eaY5z+RdH0LbftBSae2xLaa2c/3JH0iqaDB9KGSKsJeIj+W9HB4808qY7le0k9SuQ+3c/LE7zJJFXBKK97Fm5DwDtFEnQdcYGb5ceZ9Zmb7AfsQ3Kk5uSXicy5ZnvhdJqkhGJ/0Rw1nNCyxSyoL/x4haYakpyUtkfS/ks6QNCvsh314zGaOkjRb0kJJJ4Trt1PQF/57YUdkF8Zs99+SngE+jhPP98Ptz5P0+3Dazwlu6rlP0k2NvUgzqyW4AXG3cL0jJX0Qbu9+SZ3C6cvqfwQljZf0evj/9eFyr4ev+bKYuK4NX9+bwKiY6ZeFZxpzJf29qTfBtX3JlGScaw13AnMl3ZjEOmOA0QRd9y4huDtygoKBMX4I1A8EM5Sgr5bhQIGkEcBZBF1ZHBAm3LckvRQuPxbY28yWxu5M0gCCPvPHASUEvT+ebGa/lPQNgv7rGx30Q1Jn4EDg8vD/B4EjzWyhpIeBi4GpzbzmPYB8gn7gF0i6C9iXoLuE/Qi+2+8DheHy1wC7m1mVGhnkxUWHl/hdRrGgd8OHgcuaWzbGexb0jV5F0GVAfeL+iCDZ15tmZnUWdOG7hCB5Hk3Qn9Ecgi51+wIjw+VnNUz6oQOA181stQXdgz9KMFhIc4aH+1kJrDCzuQSl8qVmtjBc5qEEt/UvM6syszUEnYD1I+ii+EkzKw+PY2x/OXOBRyWdSXBm5SLME7/LRFMJ6sq7xUyrIfy8SsoiGOmpXlXM/3Uxz+vY+qy2Yf8kRtCf0Q/NbL/wsbuZ1f9wbNqhV7Gt+jr+4cA4SSc2s/yW10zQT1Ws2NdcS/Nn78cTnE2NBd5L8rqFa2M88buMY2brgGkEyb/eMoKqFQj6+d+eFjHfk5QV1vsPAxYQ9Ih4cX0LG0l5YU+OTZkFHC4pR1I7gp5IZyQaRFhKvwb47zCGoWG1E8B/xGxrGV+/5u8msOk3gJMldQl7pfw2bPmhHGRmBcDVBN2ZZycar2t7PPG7THUzENu65x6CZPshcDDbVxr/giBpP0/Qq2MlcC/Bxdv3FQzm/SeaKT1b0LX1NUABQc+PhWYWr+vdpjwFdCWoNjoX+IekjwjOUu4Ol7kBuE3BIOG1zW3QgmEAHwtjep6gu2QIxsR9JNz+B8DtZlaaZLyuDfHeOZ1zLmK8xO+ccxHjid855yLGE79zzkWMJ37nnIsYT/zOORcxnvidcy5iPPE751zE/D9BkEfun2zr/QAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "ha1hFkm7pJr9"
      },
      "source": [
        "# Comparison with Federated Averaging non-IID Partition\n",
        "\n",
        "> In a highly heterogenous system (90%) stragglers, authors of FedProx have claimed that FedProx achieves on average **22%** improvement in testing accuracy compared to Federated Averaging\n",
        "\n",
        "With our first test above, we know that the special case where **mu=0**, FedProx matches the results of FedAvg. \n",
        "\n",
        "We will use the same idea but increase our stragglers this time. We will run the same experiment with **mu > 0** to compare results of FedProx."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "UZYw192zpJsL"
      },
      "source": [
        "### Training Federated Averaging with 90% stragglers (non-IID Partition)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "HHCqV3f-pJsM",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "01c34ee6-6442-4368-999e-834d25a2355e"
      },
      "source": [
        "# number of training rounds\n",
        "rounds = 100\n",
        "# client fraction\n",
        "C = 0.1\n",
        "# number of clients\n",
        "K = 100\n",
        "# number of training passes on local dataset for each roung\n",
        "E = 20\n",
        "# batch size\n",
        "batch_size = 10\n",
        "# learning Rate\n",
        "lr=0.01\n",
        "# proximal term constant\n",
        "mu = 0.0\n",
        "# percentage of clients to have fewer than E epochs\n",
        "percentage = 90\n",
        "# target test accuracy\n",
        "target_test_accuracy = 90.0\n",
        "# data partition dictionary\n",
        "non_iid_dict = non_iid_partition(mnist_data_train, 100, 200, 300, 2)\n",
        "# load model\n",
        "mnist_cnn = MNIST_CNN()\n",
        "\n",
        "if torch.cuda.is_available():\n",
        "  mnist_cnn.cuda()\n",
        "\n",
        "mnist_cnn_non_iid_trained_fedavg = training(mnist_cnn, rounds, batch_size, lr, mnist_data_train, non_iid_dict, mnist_data_test, C, K, E, mu, percentage, \"FedAvg MNIST CNN (90% Stragglers) non-IID\", \"orange\", target_test_accuracy, algorithm='fedavg')"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "System heterogeneity set to 90% stragglers.\n",
            "\n",
            "Picking 10 random clients per round.\n",
            "\n",
            "Round: 1... \tAverage Train Loss: 0.027... \tTest Loss: 10.416439100646972... \tTest Accuracy: 17.59493670886076\n",
            "Round: 2... \tAverage Train Loss: 0.041... \tTest Loss: 7.65616241607666... \tTest Accuracy: 21.772151898734176\n",
            "Round: 3... \tAverage Train Loss: 0.026... \tTest Loss: 7.248042140960694... \tTest Accuracy: 20.759493670886076\n",
            "Round: 4... \tAverage Train Loss: 0.013... \tTest Loss: 7.772884909057617... \tTest Accuracy: 18.10126582278481\n",
            "Round: 5... \tAverage Train Loss: 0.034... \tTest Loss: 8.889501936340332... \tTest Accuracy: 18.354430379746834\n",
            "Round: 6... \tAverage Train Loss: 0.025... \tTest Loss: 10.150454154968262... \tTest Accuracy: 21.0126582278481\n",
            "Round: 7... \tAverage Train Loss: 0.038... \tTest Loss: 7.200136389923096... \tTest Accuracy: 17.59493670886076\n",
            "Round: 8... \tAverage Train Loss: 0.01... \tTest Loss: 6.309183881378174... \tTest Accuracy: 12.025316455696203\n",
            "Round: 9... \tAverage Train Loss: 0.027... \tTest Loss: 6.458654864501953... \tTest Accuracy: 21.89873417721519\n",
            "Round: 10... \tAverage Train Loss: 0.017... \tTest Loss: 6.368773694610596... \tTest Accuracy: 28.227848101265824\n",
            "Round: 11... \tAverage Train Loss: 0.012... \tTest Loss: 5.433362548065186... \tTest Accuracy: 36.58227848101266\n",
            "Round: 12... \tAverage Train Loss: 0.03... \tTest Loss: 5.71662806930542... \tTest Accuracy: 23.924050632911392\n",
            "Round: 13... \tAverage Train Loss: 0.013... \tTest Loss: 4.610236717224121... \tTest Accuracy: 24.050632911392405\n",
            "Round: 14... \tAverage Train Loss: 0.01... \tTest Loss: 4.024276881408691... \tTest Accuracy: 34.81012658227848\n",
            "Round: 15... \tAverage Train Loss: 0.006... \tTest Loss: 4.228279295349121... \tTest Accuracy: 39.620253164556964\n",
            "Round: 16... \tAverage Train Loss: 0.001... \tTest Loss: 4.114131257247925... \tTest Accuracy: 43.164556962025316\n",
            "Round: 17... \tAverage Train Loss: 0.01... \tTest Loss: 3.607116030883789... \tTest Accuracy: 39.620253164556964\n",
            "Round: 18... \tAverage Train Loss: 0.004... \tTest Loss: 4.037928153991699... \tTest Accuracy: 31.89873417721519\n",
            "Round: 19... \tAverage Train Loss: 0.011... \tTest Loss: 3.5925017517089843... \tTest Accuracy: 34.177215189873415\n",
            "Round: 20... \tAverage Train Loss: 0.004... \tTest Loss: 3.075060792541504... \tTest Accuracy: 30.759493670886076\n",
            "Round: 21... \tAverage Train Loss: 0.01... \tTest Loss: 3.7690964637756346... \tTest Accuracy: 40.0\n",
            "Round: 22... \tAverage Train Loss: 0.004... \tTest Loss: 3.579914125442505... \tTest Accuracy: 38.860759493670884\n",
            "Round: 23... \tAverage Train Loss: 0.006... \tTest Loss: 3.158122076416016... \tTest Accuracy: 39.74683544303797\n",
            "Round: 24... \tAverage Train Loss: 0.016... \tTest Loss: 2.3384339977264403... \tTest Accuracy: 48.35443037974684\n",
            "Round: 25... \tAverage Train Loss: 0.005... \tTest Loss: 2.05525118560791... \tTest Accuracy: 55.69620253164557\n",
            "Round: 26... \tAverage Train Loss: 0.007... \tTest Loss: 2.335457943725586... \tTest Accuracy: 45.949367088607595\n",
            "Round: 27... \tAverage Train Loss: 0.006... \tTest Loss: 2.4595235877990724... \tTest Accuracy: 58.734177215189874\n",
            "Round: 28... \tAverage Train Loss: 0.001... \tTest Loss: 1.4843696899414063... \tTest Accuracy: 65.82278481012658\n",
            "Round: 29... \tAverage Train Loss: 0.012... \tTest Loss: 1.7415517560958862... \tTest Accuracy: 56.32911392405063\n",
            "Round: 30... \tAverage Train Loss: 0.001... \tTest Loss: 2.055044277000427... \tTest Accuracy: 52.53164556962025\n",
            "Round: 31... \tAverage Train Loss: 0.009... \tTest Loss: 2.469910019302368... \tTest Accuracy: 51.0126582278481\n",
            "Round: 32... \tAverage Train Loss: 0.006... \tTest Loss: 2.1080510366439817... \tTest Accuracy: 52.65822784810127\n",
            "Round: 33... \tAverage Train Loss: 0.011... \tTest Loss: 2.5632187868118286... \tTest Accuracy: 53.79746835443038\n",
            "Round: 34... \tAverage Train Loss: 0.003... \tTest Loss: 2.1894981121063233... \tTest Accuracy: 55.822784810126585\n",
            "Round: 35... \tAverage Train Loss: 0.004... \tTest Loss: 2.6327213523864748... \tTest Accuracy: 56.32911392405063\n",
            "Round: 36... \tAverage Train Loss: 0.0... \tTest Loss: 3.707807012939453... \tTest Accuracy: 45.44303797468354\n",
            "Round: 37... \tAverage Train Loss: 0.005... \tTest Loss: 1.914140502357483... \tTest Accuracy: 59.74683544303797\n",
            "Round: 38... \tAverage Train Loss: 0.001... \tTest Loss: 2.119851525115967... \tTest Accuracy: 62.151898734177216\n",
            "Round: 39... \tAverage Train Loss: 0.005... \tTest Loss: 1.1461019533157348... \tTest Accuracy: 71.77215189873418\n",
            "Round: 40... \tAverage Train Loss: 0.003... \tTest Loss: 1.5714190985679626... \tTest Accuracy: 77.21518987341773\n",
            "Round: 41... \tAverage Train Loss: 0.014... \tTest Loss: 1.8057931926727295... \tTest Accuracy: 66.45569620253164\n",
            "Round: 42... \tAverage Train Loss: 0.002... \tTest Loss: 1.2847724424362184... \tTest Accuracy: 68.22784810126582\n",
            "Round: 43... \tAverage Train Loss: 0.005... \tTest Loss: 1.85410186958313... \tTest Accuracy: 64.55696202531645\n",
            "Round: 44... \tAverage Train Loss: 0.005... \tTest Loss: 1.4541222661972046... \tTest Accuracy: 74.9367088607595\n",
            "Round: 45... \tAverage Train Loss: 0.003... \tTest Loss: 1.244193748474121... \tTest Accuracy: 70.0\n",
            "Round: 46... \tAverage Train Loss: 0.003... \tTest Loss: 1.777280459213257... \tTest Accuracy: 70.50632911392405\n",
            "Round: 47... \tAverage Train Loss: 0.011... \tTest Loss: 1.4940792452812195... \tTest Accuracy: 72.78481012658227\n",
            "Round: 48... \tAverage Train Loss: 0.002... \tTest Loss: 1.1234139110565184... \tTest Accuracy: 73.79746835443038\n",
            "Round: 49... \tAverage Train Loss: 0.004... \tTest Loss: 0.9072204474449158... \tTest Accuracy: 82.0253164556962\n",
            "Round: 50... \tAverage Train Loss: 0.0... \tTest Loss: 0.8194513652324676... \tTest Accuracy: 79.24050632911393\n",
            "Round: 51... \tAverage Train Loss: 0.021... \tTest Loss: 0.8989478851795196... \tTest Accuracy: 82.27848101265823\n",
            "Round: 52... \tAverage Train Loss: 0.004... \tTest Loss: 1.1444910806655884... \tTest Accuracy: 76.45569620253164\n",
            "Round: 53... \tAverage Train Loss: 0.003... \tTest Loss: 0.6612476860523224... \tTest Accuracy: 82.65822784810126\n",
            "Round: 54... \tAverage Train Loss: 0.003... \tTest Loss: 0.7879238713264465... \tTest Accuracy: 80.63291139240506\n",
            "Round: 55... \tAverage Train Loss: 0.013... \tTest Loss: 0.915136074924469... \tTest Accuracy: 79.87341772151899\n",
            "Round: 56... \tAverage Train Loss: 0.002... \tTest Loss: 1.5109243631362914... \tTest Accuracy: 65.9493670886076\n",
            "Round: 57... \tAverage Train Loss: 0.005... \tTest Loss: 0.7610169510841369... \tTest Accuracy: 81.39240506329114\n",
            "Round: 58... \tAverage Train Loss: 0.005... \tTest Loss: 0.832780695438385... \tTest Accuracy: 78.86075949367088\n",
            "Round: 59... \tAverage Train Loss: 0.002... \tTest Loss: 0.8553040595054626... \tTest Accuracy: 78.73417721518987\n",
            "Round: 60... \tAverage Train Loss: 0.009... \tTest Loss: 1.0215564136505126... \tTest Accuracy: 75.31645569620254\n",
            "Round: 61... \tAverage Train Loss: 0.002... \tTest Loss: 0.38131789014339446... \tTest Accuracy: 88.86075949367088\n",
            "Round: 62... \tAverage Train Loss: 0.003... \tTest Loss: 1.177911737728119... \tTest Accuracy: 74.81012658227849\n",
            "Round: 63... \tAverage Train Loss: 0.003... \tTest Loss: 0.7632400828361511... \tTest Accuracy: 79.62025316455696\n",
            "Round: 64... \tAverage Train Loss: 0.009... \tTest Loss: 0.9632815877914429... \tTest Accuracy: 78.10126582278481\n",
            "Round: 65... \tAverage Train Loss: 0.007... \tTest Loss: 0.6057459532618522... \tTest Accuracy: 84.43037974683544\n",
            "Round: 66... \tAverage Train Loss: 0.002... \tTest Loss: 0.451424348950386... \tTest Accuracy: 88.60759493670886\n",
            "Round: 67... \tAverage Train Loss: 0.005... \tTest Loss: 0.7070705275535584... \tTest Accuracy: 82.9113924050633\n",
            "Round: 68... \tAverage Train Loss: 0.009... \tTest Loss: 1.091169603061676... \tTest Accuracy: 76.58227848101266\n",
            "Round: 69... \tAverage Train Loss: 0.008... \tTest Loss: 0.6087208345890045... \tTest Accuracy: 84.55696202531645\n",
            "Round: 70... \tAverage Train Loss: 0.007... \tTest Loss: 0.8813691374778747... \tTest Accuracy: 78.48101265822785\n",
            "Round: 71... \tAverage Train Loss: 0.004... \tTest Loss: 1.4853597324371337... \tTest Accuracy: 68.22784810126582\n",
            "Round: 72... \tAverage Train Loss: 0.009... \tTest Loss: 1.1539276893615722... \tTest Accuracy: 72.9113924050633\n",
            "Round: 73... \tAverage Train Loss: 0.003... \tTest Loss: 0.6346582508087159... \tTest Accuracy: 83.67088607594937\n",
            "Round: 74... \tAverage Train Loss: 0.003... \tTest Loss: 0.4766974732875824... \tTest Accuracy: 86.58227848101266\n",
            "Round: 75... \tAverage Train Loss: 0.003... \tTest Loss: 1.1649490303039551... \tTest Accuracy: 71.39240506329114\n",
            "Round: 76... \tAverage Train Loss: 0.002... \tTest Loss: 0.8328578180789947... \tTest Accuracy: 80.37974683544304\n",
            "Round: 77... \tAverage Train Loss: 0.007... \tTest Loss: 0.9089833057880402... \tTest Accuracy: 78.48101265822785\n",
            "Round: 78... \tAverage Train Loss: 0.005... \tTest Loss: 0.9853737588882446... \tTest Accuracy: 76.83544303797468\n",
            "Round: 79... \tAverage Train Loss: 0.002... \tTest Loss: 0.7328842282295227... \tTest Accuracy: 80.63291139240506\n",
            "Round: 80... \tAverage Train Loss: 0.005... \tTest Loss: 0.732815515947342... \tTest Accuracy: 83.54430379746836\n",
            "Round: 81... \tAverage Train Loss: 0.002... \tTest Loss: 0.6664907504081726... \tTest Accuracy: 83.67088607594937\n",
            "Round: 82... \tAverage Train Loss: 0.004... \tTest Loss: 0.5302086965560913... \tTest Accuracy: 86.32911392405063\n",
            "Round: 83... \tAverage Train Loss: 0.001... \tTest Loss: 0.9882855861663818... \tTest Accuracy: 77.9746835443038\n",
            "Round: 84... \tAverage Train Loss: 0.004... \tTest Loss: 0.33703032514452935... \tTest Accuracy: 92.0253164556962\n",
            "Training Done!\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "YAEZ4zjopJsS"
      },
      "source": [
        "### Training FedProx with 90% Stragglers (non-IID Parition)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "4d3AH4IgpJsT",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "631e3d15-a87a-4a0e-dc16-81e4637d7103"
      },
      "source": [
        "# number of training rounds\n",
        "rounds = 100\n",
        "# client fraction\n",
        "C = 0.1\n",
        "# number of clients\n",
        "K = 100\n",
        "# number of training passes on local dataset for each roung\n",
        "E = 20\n",
        "# batch size\n",
        "batch_size = 10\n",
        "# learning Rate\n",
        "lr=0.01\n",
        "# proximal term constant\n",
        "mu = 0.01\n",
        "# percentage of clients to have fewer than E epochs\n",
        "percentage = 90\n",
        "# target test accuracy\n",
        "target_test_accuracy = 90.0\n",
        "\n",
        "# data partition dictionary\n",
        "non_iid_dict = non_iid_partition(mnist_data_train, 100, 200, 300, 2)\n",
        "# load model\n",
        "mnist_cnn = MNIST_CNN()\n",
        "\n",
        "if torch.cuda.is_available():\n",
        "  mnist_cnn.cuda()\n",
        "\n",
        "mnist_cnn_non_iid_trained_fedprox = training(mnist_cnn, rounds, batch_size, lr, mnist_data_train, non_iid_dict, mnist_data_test, C, K, E, mu, percentage, \"FedProx MNIST CNN (90% Stragglers) non-IID\", \"green\", target_test_accuracy)"
      ],
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "System heterogeneity set to 90% stragglers.\n",
            "\n",
            "Picking 10 random clients per round.\n",
            "\n",
            "Round: 1... \tAverage Train Loss: 0.074... \tTest Loss: 2.3928937355041504... \tTest Accuracy: 15.063291139240507\n",
            "Round: 2... \tAverage Train Loss: 0.049... \tTest Loss: 2.1259401973724366... \tTest Accuracy: 39.49367088607595\n",
            "Round: 3... \tAverage Train Loss: 0.05... \tTest Loss: 1.7753675369262696... \tTest Accuracy: 46.962025316455694\n",
            "Round: 4... \tAverage Train Loss: 0.038... \tTest Loss: 1.0632993242263793... \tTest Accuracy: 63.29113924050633\n",
            "Round: 5... \tAverage Train Loss: 0.025... \tTest Loss: 0.6285026379585266... \tTest Accuracy: 78.86075949367088\n",
            "Round: 6... \tAverage Train Loss: 0.02... \tTest Loss: 0.6191626049041749... \tTest Accuracy: 81.26582278481013\n",
            "Round: 7... \tAverage Train Loss: 0.024... \tTest Loss: 0.6317765829563141... \tTest Accuracy: 76.20253164556962\n",
            "Round: 8... \tAverage Train Loss: 0.033... \tTest Loss: 0.4101809196472168... \tTest Accuracy: 87.72151898734177\n",
            "Round: 9... \tAverage Train Loss: 0.014... \tTest Loss: 0.5674488192558289... \tTest Accuracy: 75.82278481012658\n",
            "Round: 10... \tAverage Train Loss: 0.041... \tTest Loss: 0.48969893345832827... \tTest Accuracy: 78.86075949367088\n",
            "Round: 11... \tAverage Train Loss: 0.016... \tTest Loss: 0.4055392473220825... \tTest Accuracy: 83.54430379746836\n",
            "Round: 12... \tAverage Train Loss: 0.011... \tTest Loss: 0.5501030151367188... \tTest Accuracy: 82.78481012658227\n",
            "Round: 13... \tAverage Train Loss: 0.025... \tTest Loss: 0.27688889338970185... \tTest Accuracy: 91.26582278481013\n",
            "Training Done!\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}