Add neural network

shard.lock

@@ -0,0 +1,6 @@
+version: 1.0
+shards:
+  linalg:
+    github: konovod/linalg
+    commit: 3467699ad720d5f4c2e55cbfe925bec5addce227
+

shard.yml

@@ -11,3 +11,7 @@ targets:
 crystal: 0.26.1
 
 license: MIT
+
+dependencies:
+  linalg:
+    github: konovod/linalg

src/deep_learning.cr

@@ -1,4 +1,7 @@
+require "linalg"
+
 require "./mnist/**"
+require "./neural/**"
 
 module DeepLearning
   VERSION = "0.1.0"
@@ -11,3 +14,7 @@ labels = File.open("./data/train-labels.idx1-ubyte")
 
 loader = Mnist::Loader.new(images, labels)
 data = loader.call
+
+network = Neural::Builder.new([28 * 28, 16, 16, 10]).call(Neural::Builder::RANDOM_VALUE)
+image = LA::GMat.new(28 * 28, 1) { |i, _| data.first.image[i] }
+pp network.call(image)

src/neural/builder.cr

@@ -0,0 +1,23 @@
+require "./network"
+
+module Neural
+  class Builder
+    DEFAULT_VALUE = Proc(Float64).new { 0.0 }
+    RANDOM_VALUE  = Proc(Float64).new { rand(-1.0..1.0) }
+
+    def initialize(@levels : Array(Int32))
+    end
+
+    def call(default_value = DEFAULT_VALUE) : Network
+      nodes = Array.new(@levels.size) do |i|
+        LA::GMat.new(@levels[i], 1) { default_value.call }
+      end
+
+      links = Array.new(@levels.size - 1) do |i|
+        LA::GMat.new(@levels[i + 1], @levels[i]) { default_value.call }
+      end
+
+      Network.new(nodes, links)
+    end
+  end
+end

src/neural/network.cr

@@ -1,4 +1,38 @@
 module Neural
   class Network
+    getter nodes, links
+
+    def initialize(@nodes : Array(LA::GMat), @links : Array(LA::GMat))
+    end
+
+    def call(image : LA::GMat)
+      vector_for(@nodes.size - 1, image)
+    end
+
+    private def vector_for(x : Int32, image : LA::GMat)
+      if x == 0
+        bias = @nodes[x]
+        matrix = image
+        matrix_sigmoid(matrix + bias)
+      else
+        matrix = @links[x - 1]
+        bias = @nodes[x]
+
+        matrix_sigmoid(matrix * vector_for(x - 1, image) + bias)
+      end
+    end
+
+    private def sigmoid(x)
+      1 / (1 + Math.exp(-x))
+    end
+
+    private def matrix_sigmoid(matrix)
+      matrix.map { |val| sigmoid(val) }
+    end
+
+    private def matrix_sigmoid_derivative(matrix)
+      ones = Matrix.build(matrix.column_size, matrix.row_size) { 1 }
+      matrix_sigmoid(matrix) * (ones - matrix_sigmoid(matrix))
+    end
   end
 end