diff --git a/code/nnv/engine/nn/layers/MaxPooling2DLayer.m b/code/nnv/engine/nn/layers/MaxPooling2DLayer.m
index 1317c17372..b8dd039414 100644
--- a/code/nnv/engine/nn/layers/MaxPooling2DLayer.m
+++ b/code/nnv/engine/nn/layers/MaxPooling2DLayer.m
@@ -580,7 +580,7 @@ function set_padding(obj, padding)
             if n > 0         
                 for i=1:n
                     m1 = length(images);           
-                    images = obj.stepSplitMultipleInputs(images, pad_image, split_pos(i, :, :), max_index{split_pos(i, 1), split_pos(i, 2), split_pos(i, 3)}, []);
+                    images = obj.stepSplitMultipleInputs(images, pad_image, split_pos(i, :, :), max_index{split_pos(i, 1), split_pos(i, 2), split_pos(i, 3)}, [], lp_solver);
                     m2 = length(images);
                     if strcmp(dis_opt, 'display')
                         fprintf('\nSplit %d images into %d images', m1, m2);
diff --git a/code/nnv/engine/utils/lpsolver.m b/code/nnv/engine/utils/lpsolver.m
index bf419da5ea..ccde224ead 100644
--- a/code/nnv/engine/utils/lpsolver.m
+++ b/code/nnv/engine/utils/lpsolver.m
@@ -49,6 +49,8 @@
         % Define solver parameters
         params = struct; % for now, leave default options/params
         params.OutputFlag = 0; % no display
+        params.OptimalityTol = 1e-09;
+        params.FeasibilityTol = 1e-09;
         result = gurobi(model, params);
         fval = result.objval; % get fval value from results
         % get exitflag and match those of linprog for easier parsing
diff --git a/code/nnv/examples/Submission/WiP_3d/functions/add_voxels.m b/code/nnv/examples/Submission/WiP_3d/functions/add_voxels.m
index 8b97e67dde..2c50ed1c99 100644
--- a/code/nnv/examples/Submission/WiP_3d/functions/add_voxels.m
+++ b/code/nnv/examples/Submission/WiP_3d/functions/add_voxels.m
@@ -5,32 +5,18 @@
     % Return a VolumeStar of a brightening attack on a few pixels
 
     % Initialize vars
-    ct = 0; % keep track of pixels modified
-    flag = 0; % determine when to stop modifying pixels
     vol = single(vol);
     at_vol = vol;
 
-    % Create brightening attack
-    for i=1:size(vol,1)
-        for j=1:size(vol,2)
-            for k=1:size(vol,3)
-                if vol(i,j,k) < threshold
-                    at_vol(i,j,k) = 255;
-                    ct = ct + 1;
-                    if ct >= max_pixels
-                        flag = 1;
-                        break;
-                    end
-                end
-            end
-            if flag == 1
-                break
-            end
-        end
-        if flag == 1
-            break;
-        end
-    end
+    % we can find the edge of the shape
+    shape = edge3(vol,'approxcanny',0.6); % this should be okay for this data, but let's test it
+
+    % select a random pixel
+    idxs = setdiff(find(shape), find(vol));
+    voxels = min(voxels,length(idxs));
+
+    % For now, we can select the first ones
+    at_vol(idxs(1:voxels)) = 255;
 
     % Define input set as VolumeStar
     dif_vol = -vol + at_vol;
diff --git a/code/nnv/examples/Submission/WiP_3d/functions/remove_voxels.m b/code/nnv/examples/Submission/WiP_3d/functions/remove_voxels.m
index e69de29bb2..dc5703098a 100644
--- a/code/nnv/examples/Submission/WiP_3d/functions/remove_voxels.m
+++ b/code/nnv/examples/Submission/WiP_3d/functions/remove_voxels.m
@@ -0,0 +1,31 @@
+function I = remove_voxels(vol, voxels, noise_disturbance)
+    % noise_disturnamce can be kept fixed here, more interesting on number
+    % of voxels changed
+
+    % Return a VolumeStar of a brightening attack on a few pixels
+
+    % Initialize vars
+    vol = single(vol);
+    at_vol = vol;
+
+    % we can find the edge of the shape
+    shape = edge3(vol,'approxcanny',0.6); % this should be okay for this data, but let's test it
+
+    % select a random pixel
+    idxs = intersect(find(shape),find(vol));
+    voxels = min(voxels,length(idxs));
+
+    % For now, we can select the first ones
+    at_vol(idxs(1:voxels)) = 0;
+
+    % Define input set as VolumeStar
+    dif_vol = -vol + at_vol;
+    noise = dif_vol;
+    V(:,:,:,:,1) = vol;   % center of set
+    V(:,:,:,:,2) = noise; % basis vectors
+    C = [1; -1];          % constraints
+    d = [1; noise_disturbance-1];          % constraints
+    I = VolumeStar(V, C, d, 1-noise_disturbance, 1); % input set
+
+    
+end
\ No newline at end of file
diff --git a/code/nnv/examples/Submission/WiP_3d/functions/summarize_results.m b/code/nnv/examples/Submission/WiP_3d/functions/summarize_results.m
deleted file mode 100644
index 139597f9cb..0000000000
--- a/code/nnv/examples/Submission/WiP_3d/functions/summarize_results.m
+++ /dev/null
@@ -1,2 +0,0 @@
-
-
diff --git a/code/nnv/examples/Submission/WiP_3d/functions/verify_instance_shape.m b/code/nnv/examples/Submission/WiP_3d/functions/verify_instance_shape.m
index 0b8e0b66e5..784a01c3af 100644
--- a/code/nnv/examples/Submission/WiP_3d/functions/verify_instance_shape.m
+++ b/code/nnv/examples/Submission/WiP_3d/functions/verify_instance_shape.m
@@ -6,7 +6,6 @@
     % Check what type of attack to consider
     if strcmp(attack.Name, 'add') || strcmp(attack.Name, 'remove')
         max_pixels = attack.max_pixels;
-        threshold = attack.threshold;
         noise_disturbance = attack.noise_de;
     else
         error("Adversarial attack not supported.");
@@ -14,9 +13,9 @@
 
     % Choose attack
     if strcmp(attack.Name, 'add')
-        I = add_voxels(vol, max_pixels, threshold, noise_disturbance);
+        I = add_voxels(vol, max_pixels, noise_disturbance);
     elseif strcmp(attack.Name, 'remove')
-        I = remove_voxels(vol, max_pixels, threshold, noise_disturbance);
+        I = remove_voxels(vol, max_pixels, noise_disturbance);
     end
 
     % Begin analysis
diff --git a/code/nnv/examples/Submission/WiP_3d/other/NAV/README.md b/code/nnv/examples/Submission/WiP_3d/other/NAV/README.md
new file mode 100644
index 0000000000..ce27712094
--- /dev/null
+++ b/code/nnv/examples/Submission/WiP_3d/other/NAV/README.md
@@ -0,0 +1,39 @@
+
+# NAV Benchmark
+
+## Property:
+The control goal is to navigate a robot to a goal region while avoiding an obstacle.
+Time horizon: `t = 6s`. Control period: `0.2s`.
+
+Initial states:
+
+    x1 = [2.9, 3.1]
+    x2 = [2.9, 3.1]
+    x3 = [0, 0]
+    x4 = [0, 0]
+
+Dynamic system: [dynamics.m](./dynamics.m)
+
+Goal region ( t=6 ):
+
+    x1 = [-0.5, 0.5]
+    x2 = [-0.5, 0.5]
+    x3 = [-Inf, Inf]
+    x4 = [-Inf, Inf]
+
+Obstacle ( always ):
+
+    x1 = [1, 2]
+    x2 = [1, 2]
+    x3 = [-Inf, Inf]
+    x4 = [-Inf, Inf]
+
+## Networks:
+
+We provide two networks:
+- The first network is trained with standard (point-based) reinforcement learning: `nn-nav-point.onnx`
+- The second network is trained set-based to improve its verifiable robustness by integrating reachability analysis into the training process: `nn-nav-set.onnx`
+
+Reference set-based training: https://arxiv.org/abs/2401.14961
+
+
diff --git a/code/nnv/examples/Submission/WiP_3d/other/NAV/dynamics.m b/code/nnv/examples/Submission/WiP_3d/other/NAV/dynamics.m
new file mode 100644
index 0000000000..632c28d9ff
--- /dev/null
+++ b/code/nnv/examples/Submission/WiP_3d/other/NAV/dynamics.m
@@ -0,0 +1,11 @@
+function dx = dynamics(x,u)
+
+dx = [
+    x(3)*cos(x(4));
+    x(3)*sin(x(4));
+    u(1);
+    u(2)
+];
+
+end
+
diff --git a/code/nnv/examples/Submission/WiP_3d/other/NAV/figs/nav_point.png b/code/nnv/examples/Submission/WiP_3d/other/NAV/figs/nav_point.png
new file mode 100644
index 0000000000..3aa4b19bfb
Binary files /dev/null and b/code/nnv/examples/Submission/WiP_3d/other/NAV/figs/nav_point.png differ
diff --git a/code/nnv/examples/Submission/WiP_3d/other/NAV/figs/nav_set.png b/code/nnv/examples/Submission/WiP_3d/other/NAV/figs/nav_set.png
new file mode 100644
index 0000000000..623418b6c5
Binary files /dev/null and b/code/nnv/examples/Submission/WiP_3d/other/NAV/figs/nav_set.png differ
diff --git a/code/nnv/examples/Submission/WiP_3d/other/NAV/nav_point.mat b/code/nnv/examples/Submission/WiP_3d/other/NAV/nav_point.mat
new file mode 100644
index 0000000000..b33cbd44f2
Binary files /dev/null and b/code/nnv/examples/Submission/WiP_3d/other/NAV/nav_point.mat differ
diff --git a/code/nnv/examples/Submission/WiP_3d/other/NAV/nav_point.png b/code/nnv/examples/Submission/WiP_3d/other/NAV/nav_point.png
new file mode 100644
index 0000000000..f7660557ae
Binary files /dev/null and b/code/nnv/examples/Submission/WiP_3d/other/NAV/nav_point.png differ
diff --git a/code/nnv/examples/Submission/WiP_3d/other/NAV/nav_point_21.png b/code/nnv/examples/Submission/WiP_3d/other/NAV/nav_point_21.png
new file mode 100644
index 0000000000..4f0543e91b
Binary files /dev/null and b/code/nnv/examples/Submission/WiP_3d/other/NAV/nav_point_21.png differ
diff --git a/code/nnv/examples/Submission/WiP_3d/other/NAV/nav_set.mat b/code/nnv/examples/Submission/WiP_3d/other/NAV/nav_set.mat
new file mode 100644
index 0000000000..da3ba0f19f
Binary files /dev/null and b/code/nnv/examples/Submission/WiP_3d/other/NAV/nav_set.mat differ
diff --git a/code/nnv/examples/Submission/WiP_3d/other/NAV/networks/nn-nav-point.onnx b/code/nnv/examples/Submission/WiP_3d/other/NAV/networks/nn-nav-point.onnx
new file mode 100644
index 0000000000..3b4a1c4dbb
Binary files /dev/null and b/code/nnv/examples/Submission/WiP_3d/other/NAV/networks/nn-nav-point.onnx differ
diff --git a/code/nnv/examples/Submission/WiP_3d/other/NAV/networks/nn-nav-set.onnx b/code/nnv/examples/Submission/WiP_3d/other/NAV/networks/nn-nav-set.onnx
new file mode 100644
index 0000000000..7ca29df9db
Binary files /dev/null and b/code/nnv/examples/Submission/WiP_3d/other/NAV/networks/nn-nav-set.onnx differ
diff --git a/code/nnv/examples/Submission/WiP_3d/other/NAV/reach_point.m b/code/nnv/examples/Submission/WiP_3d/other/NAV/reach_point.m
new file mode 100644
index 0000000000..0abc4e3d0b
--- /dev/null
+++ b/code/nnv/examples/Submission/WiP_3d/other/NAV/reach_point.m
@@ -0,0 +1,135 @@
+function rT = reach_point()
+
+    %% Reachability analysis of NAV Benchmark
+    
+    %% Load Components 
+
+    % Load the controller
+    %netonnx = importNetworkFromONNX('networks/nn-nav-point.onnx', "InputDataFormats", "BC");
+    netonnx = importONNXNetwork('networks/nn-nav-point.onnx', "InputDataFormats", "BC");
+    
+    % Load plant
+    reachStep = 0.02;
+    controlPeriod = 0.2;
+    % plant = NonLinearODE(4, 2, @dynamics, reachStep, controlPeriod, eye(4));
+    % plant.set_tensorOrder(2);
+    % plant.set_taylorTerms(3);
+    % plant.set_zonotopeOrder(100);
+    % plant.set_intermediateOrder(50);
+
+    %% Reachability analysis
+
+    % Initial set
+    lb = [2.9; 2.9; 0; 0];
+    ub = [3.1; 3.1; 0; 0];
+    init_set = Box(lb,ub);
+    init = init_set.partition([1 2],[50 50]);
+
+    % Reachability options
+    num_steps = 20;
+    reachOptions.reachMethod = 'approx-star';
+    
+    N = length(init);
+    disp("Verifying "+string(N)+" samples...")
+    
+    mkdir('tmp');
+    parpool("Processes"); % initialize parallel process
+    
+    % Execute reachabilty analysis
+    t = tic;
+    parfor j = 1:length(init)
+        % Get NNV network
+        net = matlab2nnv(netonnx);
+        % Create plant
+        plant = NonLinearODE(4, 2, @dynamics, reachStep, controlPeriod, eye(4));
+        plant.set_tensorOrder(2);
+        plant.set_taylorTerms(3);
+        plant.set_zonotopeOrder(100);
+        plant.set_intermediateOrder(50);
+        % Get initial conditions
+        init_set = init(j).toStar;
+        %reachSub = init_set;
+        for i = 1:num_steps
+            % Compute controller output set
+            input_set = net.reach(init_set,reachOptions);
+
+            % Compute plant reachable set
+            init_set = plantReach(plant, init_set, input_set,'lin');
+        end
+        toc(t);
+        parsave("tmp/reachSet"+string(j)+".mat",plant);
+    end
+    rT = toc(t); % get reach time
+    disp("Finished reachability...")
+
+    % Shut Down Current Parallel Pool
+    poolobj = gcp('nocreate');
+    delete(poolobj);
+
+    % Save results
+    if is_codeocean
+        save('/results/logs/nav_point.mat', 'rT','-v7.3');
+    else
+        save('nav_point.mat', 'rT','-v7.3');
+    end
+
+
+    %% Visualize results
+    setFiles = dir('tmp/*.mat');
+
+    t = tic;
+    
+    f = figure;
+    rectangle('Position',[-0.5,-0.5,1,1],'FaceColor',[0 0.5 0 0.5],'EdgeColor','y', 'LineWidth', 0.1); % goal region
+    hold on;
+    rectangle('Position',[1,1,1,1],'FaceColor',[0.7 0 0 0.8], 'EdgeColor','r', 'LineWidth', 0.1); % obstacle
+    grid;
+    for K = 1 : length(setFiles)
+        if ~mod(K,50)
+            disp("Plotting partition "+string(K)+" ...");
+            toc(t)
+            pause(0.01); % to ensure it prints
+        end
+        res = load("tmp/"+setFiles(K).name);
+        plant = res.plant;
+        for k=1:length(plant.cora_set)
+            plot(plant.cora_set{k}, [1,2], 'b', 'Unify', true);
+        end
+    end
+    hold on;
+    xlabel('x1');
+    ylabel('x2');
+
+    disp("Finished plotting all reach sets");
+
+    %% Save figure
+    if is_codeocean
+        saveas(f,'/results/logs/nav_point.png');
+        % exportgraphics(f,'/results/logs/nav-set.pdf', 'ContentType', 'vector');
+    else
+        saveas(f,'nav_point_21.png');
+        % exportgraphics(f,'nav-set.pdf','ContentType', 'vector');
+    end
+
+    % Save results
+    if is_codeocean
+        save('/results/logs/nav_point.mat','rT','-v7.3');
+    else
+        save('nav_point.mat', 'rT','-v7.3');
+    end
+
+end
+
+%% Helper function
+function init_set = plantReach(plant,init_set,input_set,algoC)
+    nS = length(init_set); % based on approx-star, number of sets should be equal
+    ss = [];
+    for k=1:nS
+            ss =[ss plant.stepReachStar(init_set(k), input_set(k),algoC)];
+    end
+    init_set = ss;
+end
+
+function parsave(fname, plant) % trick to save while on parpool
+  save(fname, 'plant')
+end
\ No newline at end of file
diff --git a/code/nnv/examples/Submission/WiP_3d/other/NAV/reach_set.m b/code/nnv/examples/Submission/WiP_3d/other/NAV/reach_set.m
new file mode 100644
index 0000000000..0bc987ae97
--- /dev/null
+++ b/code/nnv/examples/Submission/WiP_3d/other/NAV/reach_set.m
@@ -0,0 +1,129 @@
+function rT = reach_set()
+
+    %% Reachability analysis of NAV Benchmark
+    
+    %% Load Components 
+
+    % Load the controller
+    % net = importNetworkFromONNX('networks/nn-nav-set.onnx', "InputDataFormats", "BC");
+    netonnx = importONNXNetwork('networks/nn-nav-set.onnx', "InputDataFormats", "BC");
+    % Load plant
+    reachStep = 0.02;
+    controlPeriod = 0.2;
+    % plant = NonLinearODE(4, 2, @dynamics, reachStep, controlPeriod, eye(4));
+    % plant.set_tensorOrder(2);
+    % plant.set_taylorTerms(3);
+    % plant.set_zonotopeOrder(100);
+    % plant.set_intermediateOrder(50);
+
+
+    %% Reachability analysis
+
+    % Initial set
+    lb = [2.9; 2.9; 0; 0];
+    ub = [3.1; 3.1; 0; 0];
+    init_set = Box(lb,ub);
+    init = init_set.partition([1 2],[50 50]);
+
+    % Reachability options
+    num_steps = 21;
+    reachOptions.reachMethod = 'approx-star';
+
+    N = length(init);
+    disp("Verifying "+string(N)+" samples...")
+    
+    mkdir('temp');
+    parpool("Processes"); % initialize parallel process
+    
+    % Execute reachabilty analysis
+    t = tic;
+    parfor j = 1:length(init)
+        % Get NNV network
+        net = matlab2nnv(netonnx);
+        % Create plant
+        plant = NonLinearODE(4, 2, @dynamics, reachStep, controlPeriod, eye(4));
+        plant.set_tensorOrder(2);
+        plant.set_taylorTerms(3);
+        plant.set_zonotopeOrder(100);
+        plant.set_intermediateOrder(50);
+        % Get initial conditions
+        init_set = init(j).toStar;
+        %reachSub = init_set;
+        for i = 1:num_steps
+            % Compute controller output set
+            input_set = net.reach(init_set,reachOptions);
+
+            % Compute plant reachable set
+            init_set = plantReach(plant, init_set, input_set,'lin');
+        end
+        toc(t);
+        parsave("temp/reachSet"+string(j)+".mat",plant);
+    end
+    rT = toc(t); % get reach time
+    disp("Finished reachability...")
+
+    % Shut Down Current Parallel Pool
+    poolobj = gcp('nocreate');
+    delete(poolobj);
+
+    %% Visualize results
+    setFiles = dir('temp/*.mat');
+    
+    f = figure;
+    rectangle('Position',[-0.5,-0.5,1,1],'FaceColor',[0 0.5 0 0.5],'EdgeColor','y', 'LineWidth', 0.1); % goal region
+    hold on;
+    rectangle('Position',[1,1,1,1],'FaceColor',[0.7 0 0 0.8], 'EdgeColor','r', 'LineWidth', 0.1); % obstacle
+    grid;
+    t = tic;
+    for K = 1 : length(setFiles)
+        if ~mod(K,50)
+            disp("Plotting partition "+string(K)+" ...");
+            toc(t)
+            pause(0.01); % to ensure it prints
+        end
+        res = load("temp/"+setFiles(K).name);
+        plant = res.plant;
+        % plant.get_interval_sets;
+        % Star.plotBoxes_2D_noFill(plant.intermediate_reachSet, 1,2,'b');
+        for k=1:(length(plant.cora_set))
+            plot(plant.cora_set{k}, [1,2], 'b', 'Unify', true);
+        end
+    end
+    hold on;
+    xlabel('x1');
+    ylabel('x2');
+
+    disp("Finished plotting all reach sets");
+
+
+    %% Save figure
+    if is_codeocean
+        saveas(f,'/results/logs/nav_set.png');
+        % exportgraphics(f,'/results/logs/nav-set.pdf', 'ContentType', 'vector');
+    else
+        saveas(f,'nav_set.png');
+        % exportgraphics(f,'nav-set.pdf','ContentType', 'vector');
+    end
+
+    % Save results
+    if is_codeocean
+        save('/results/logs/nav_set.mat','rT','-v7.3');
+    else
+        save('nav_set.mat', 'rT','-v7.3');
+    end
+
+end
+
+%% Helper function
+function init_set = plantReach(plant,init_set,input_set,algoC)
+    nS = length(init_set); % based on approx-star, number of sets should be equal
+    ss = [];
+    for k=1:nS
+            ss =[ss plant.stepReachStar(init_set(k), input_set(k),algoC)];
+    end
+    init_set = ss;
+end
+
+function parsave(fname, plant) % trick to save while on parpool
+  save(fname, 'plant')
+end
diff --git a/code/nnv/examples/Submission/WiP_3d/other/Single_Pendulum/controller_single_pendulum.h5 b/code/nnv/examples/Submission/WiP_3d/other/Single_Pendulum/controller_single_pendulum.h5
new file mode 100644
index 0000000000..6aa242509b
Binary files /dev/null and b/code/nnv/examples/Submission/WiP_3d/other/Single_Pendulum/controller_single_pendulum.h5 differ
diff --git a/code/nnv/examples/Submission/WiP_3d/other/Single_Pendulum/controller_single_pendulum.mat b/code/nnv/examples/Submission/WiP_3d/other/Single_Pendulum/controller_single_pendulum.mat
new file mode 100644
index 0000000000..1984b024c2
Binary files /dev/null and b/code/nnv/examples/Submission/WiP_3d/other/Single_Pendulum/controller_single_pendulum.mat differ
diff --git a/code/nnv/examples/Submission/WiP_3d/other/Single_Pendulum/controller_single_pendulum.nnet b/code/nnv/examples/Submission/WiP_3d/other/Single_Pendulum/controller_single_pendulum.nnet
new file mode 100644
index 0000000000..5f9e900a87
--- /dev/null
+++ b/code/nnv/examples/Submission/WiP_3d/other/Single_Pendulum/controller_single_pendulum.nnet
@@ -0,0 +1,112 @@
+// The contents of this file are licensed under the Creative Commons
+// Attribution 4.0 International License: https://creativecommons.org/licenses/by/4.0/
+// Neural Network File Format by Kyle Julian, Stanford 2016
+3, 2, 1, 25 
+2, 25, 25,1, 1 
+0
+0
+0
+0
+0
+-0.24301, -0.18771 
+-0.26350, -0.30369 
+0.14823, -0.35473 
+-0.32726, 0.23397 
+-0.03466, -0.19298 
+0.37591, 0.46209 
+0.72291, 0.69352 
+0.03561, 0.26642 
+-0.12026, 0.21470 
+-0.16872, -0.30651 
+-0.43472, -0.18382 
+-0.13991, -0.16939 
+-0.40639, 0.06983 
+0.27941, -0.20360 
+-0.40475, -0.43684 
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diff --git a/code/nnv/examples/Submission/WiP_3d/other/Single_Pendulum/controller_single_pendulum.onnx b/code/nnv/examples/Submission/WiP_3d/other/Single_Pendulum/controller_single_pendulum.onnx
new file mode 100644
index 0000000000..25837086f4
Binary files /dev/null and b/code/nnv/examples/Submission/WiP_3d/other/Single_Pendulum/controller_single_pendulum.onnx differ
diff --git a/code/nnv/examples/Submission/WiP_3d/other/Single_Pendulum/dynamics_sp.m b/code/nnv/examples/Submission/WiP_3d/other/Single_Pendulum/dynamics_sp.m
new file mode 100644
index 0000000000..073d2b6749
--- /dev/null
+++ b/code/nnv/examples/Submission/WiP_3d/other/Single_Pendulum/dynamics_sp.m
@@ -0,0 +1,12 @@
+function [dx] = dynamics_sp(x,a)
+% Ex_single_pendulum
+% constants as per the documentation l=0.5, m=0.5; g= 1; c=0;
+% description of the pararameters in these equations can be found here
+% https://github.com/amaleki2/benchmark_closedloop_verification/blob/master/AINNC_benchmark.pdf
+
+l=0.5; m=0.5; g= 1; c= 0;
+
+dx(1,1) = x(2);
+dx(2,1) = g/l * sin(x(1)) + (a - c*x(2))/(m*l^2);
+% dx(3,1) = 20;
+dx(3,1) = 1;
\ No newline at end of file
diff --git a/code/nnv/examples/Submission/WiP_3d/other/Single_Pendulum/figs/singlePendulum.png b/code/nnv/examples/Submission/WiP_3d/other/Single_Pendulum/figs/singlePendulum.png
new file mode 100644
index 0000000000..a20c8467f5
Binary files /dev/null and b/code/nnv/examples/Submission/WiP_3d/other/Single_Pendulum/figs/singlePendulum.png differ
diff --git a/code/nnv/examples/Submission/WiP_3d/other/Single_Pendulum/reach.m b/code/nnv/examples/Submission/WiP_3d/other/Single_Pendulum/reach.m
new file mode 100644
index 0000000000..5380da5ed1
--- /dev/null
+++ b/code/nnv/examples/Submission/WiP_3d/other/Single_Pendulum/reach.m
@@ -0,0 +1,117 @@
+% function rT = reach()
+
+    %% Reachability analysis of Single Pendulum Benchmark
+    
+    %% Load Components 
+
+    % Load the controller
+    % net = load_NN_from_mat('controller_single_pendulum.mat');
+    % Load plant
+    reachStep = 0.01;
+    controlPeriod = 0.05;
+    % plant = NonLinearODE(3,1,@dynamics_sp, reachStep, controlPeriod, eye(3));
+    % plant.set_tensorOrder(2);
+    
+
+    %% Reachability analysis
+
+    % Initial set 
+    lb = [1.0; 0.0; 0];
+    ub = [1.175; 0.2; 0]; % original bounds
+    init_set = Box(lb,ub);
+    init = init_set.partition([1 2],[35 40]);
+    % init_set = Star(lb,ub);
+    
+    num_steps = 13;
+    reachOptions.reachMethod = 'approx-star';
+
+    N = length(init);
+    disp("Verifying "+string(N)+" samples...")
+
+    mkdir('temp');
+    parpool("Processes"); % initialize parallel process
+    
+    % Execute reachabilty analysis
+    t = tic;
+    parfor j = 1:length(init)
+        % Create NNCS for each process 
+        net = load_NN_from_mat('controller_single_pendulum.mat');
+        plant = NonLinearODE(3,1,@dynamics_sp, reachStep, controlPeriod, eye(3));
+        plant.set_tensorOrder(2);
+        % Get initial conditions
+        init_set = init(j).toStar;
+        for i = 1:num_steps
+            % Compute controller output set
+            init_set_s = init_set.affineMap([1 0 0;0 1 0],[]);
+            input_set = net.reach(init_set_s,reachOptions);
+
+            % Compute plant reachable set
+            init_set = plantReach(plant, init_set, input_set,'lin');
+        end
+        toc(t);
+        parsave("temp/reachSet"+string(j)+".mat",plant);
+    end
+    rT = toc(t); % get reach time
+    disp("Finished reachability...")
+
+    % Shut Down Current Parallel Pool
+    poolobj = gcp('nocreate');
+    delete(poolobj);
+
+    %% Visualize results
+    setFiles = dir('temp/*.mat');
+    
+    t = tic;
+    f = figure;
+    hold on;
+    rectangle('Position',[0.5,1,1,1],'FaceColor',[1 0 0 0.5],'EdgeColor','r', 'LineWidth',0.1)
+    grid;
+    for K = 1 : length(setFiles)
+        if ~mod(K,50)
+            disp("Plotting partition "+string(K)+" ...");
+        end
+        res = load("temp/"+setFiles(K).name);
+        plant = res.plant;
+        for k=1:length(plant.cora_set)
+            plot(plant.cora_set{k}, [3,1], 'b', 'Unify', true); % this seems to be faster
+        end
+    end
+    xlim([0.1 0.6])
+    ylim([0.85 1.25])
+    xlabel('Time (s)');
+    ylabel('\theta');
+    toc(t);
+
+    disp("Finished plotting all reach sets");
+    
+    %% Save figure
+    if is_codeocean
+        % exportgraphics(f,'/results/logs/singlePendulum.pdf', 'ContentType', 'vector'); % takes too long
+        saveas(f,'/results/logs/singlePendulum.png');
+    else
+        saveas(f,'singlePendulum.png');
+        % exportgraphics(f,'singlePendulum.pdf','ContentType', 'vector');
+    end
+
+    % Save results
+    if is_codeocean
+        save('/results/logs/single_pendulum.mat', 'rT','-v7.3');
+    else
+        save('single_pendulum.mat', 'rT', '-v7.3');
+    end
+   
+% end
+
+%% Helper function
+function init_set = plantReach(plant,init_set,input_set,algoC)
+    nS = length(init_set); % based on approx-star, number of sets should be equal
+    ss = [];
+    for k=1:nS
+            ss =[ss plant.stepReachStar(init_set(k), input_set(k),algoC)];
+    end
+    init_set = ss;
+end
+
+function parsave(fname, plant) % trick to save while on parpool
+  save(fname, 'plant')
+end
diff --git a/code/nnv/examples/Submission/WiP_3d/other/Single_Pendulum/singlePendulum.png b/code/nnv/examples/Submission/WiP_3d/other/Single_Pendulum/singlePendulum.png
new file mode 100644
index 0000000000..0d60b0ca40
Binary files /dev/null and b/code/nnv/examples/Submission/WiP_3d/other/Single_Pendulum/singlePendulum.png differ
diff --git a/code/nnv/examples/Submission/WiP_3d/other/Single_Pendulum/single_pendulum.mat b/code/nnv/examples/Submission/WiP_3d/other/Single_Pendulum/single_pendulum.mat
new file mode 100644
index 0000000000..cacc0d90f1
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diff --git a/code/nnv/examples/Submission/WiP_3d/other/Single_Pendulum/specifications.txt b/code/nnv/examples/Submission/WiP_3d/other/Single_Pendulum/specifications.txt
new file mode 100644
index 0000000000..4d962f99ca
--- /dev/null
+++ b/code/nnv/examples/Submission/WiP_3d/other/Single_Pendulum/specifications.txt
@@ -0,0 +1,12 @@
+Initial states:
+
+x1 = [1.0, 1.2]
+x2 = [0.0, 0.2]
+
+The controller timestep (control period) = 0.05 (seconds).
+
+Property:
+
+x1 in [0.0,1.0] for 0.5 <= t <=1
+
+Refer to this for more details: https://github.com/amaleki2/benchmark_closedloop_verification/blob/master/AINNC_benchmark.pdf
diff --git a/code/nnv/examples/Submission/WiP_3d/plots/fracture/avgTime_bright_10.png b/code/nnv/examples/Submission/WiP_3d/plots/fracture/avgTime_bright_10.png
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diff --git a/code/nnv/examples/Submission/WiP_3d/results/verification_vessel_remove_1_500.mat b/code/nnv/examples/Submission/WiP_3d/results/verification_vessel_remove_1_500.mat
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diff --git a/code/nnv/examples/Submission/WiP_3d/run_all.m b/code/nnv/examples/Submission/WiP_3d/run_all.m
index e87c0011fa..6ff562bd3b 100644
--- a/code/nnv/examples/Submission/WiP_3d/run_all.m
+++ b/code/nnv/examples/Submission/WiP_3d/run_all.m
@@ -1,9 +1,12 @@
 %% Shape only data (3d)
 
+disp("... adrenal ...");
 verify_adrenal;
 
+disp("... vessel ...");
 verify_vessel;
 
+
 %% Volume data (general 3D)
 
 
@@ -21,3 +24,8 @@
 
 disp("... synapse ...")
 verify_synapse;
+
+
+disp("... Creating plots...");
+visualize_results_gen;
+visualize_results_shape;
diff --git a/code/nnv/examples/Submission/WiP_3d/verify_adrenal.m b/code/nnv/examples/Submission/WiP_3d/verify_adrenal.m
index f5061dd62c..de5e9f0fd5 100644
--- a/code/nnv/examples/Submission/WiP_3d/verify_adrenal.m
+++ b/code/nnv/examples/Submission/WiP_3d/verify_adrenal.m
@@ -20,7 +20,7 @@
 net = matlab2nnv(net);
 
 % select volumes to verify
-N = 24; % even for numCores
+N = 50;
 inputs = single(test_images(:,:,:,:,1:N));
 targets = single(test_labels(1:N));
 
@@ -31,6 +31,13 @@
 reachOptions.lp_solver = "gurobi";
 
 
+% Study variables
+advType = ["add", "remove"];
+maxpixels = [50, 100, 500, 1000]; %out of 28x28x28 pixels
+% maxpixels = 1000;
+epsilon = 1; % ep / 255
+
+
 %% Verification analysis
 for a=advType
     for mp=maxpixels
@@ -41,12 +48,7 @@
             
             % 2) Create adversarial attack
             adv_attack = struct;
-            adv_attack.Name = a; % bright or dark
-            if strcmp(a, "bright") 
-                adv_attack.threshold = threshold(1); % perturb pixels below this value
-            else 
-                adv_attack.threshold = threshold(2); % perturb pixels below this value
-            end 
+            adv_attack.Name = a; % add or remove
             adv_attack.max_pixels = mp; % Max number of pixels to modify from input image
             adv_attack.noise_de = ep/255; % disturbance (noise) on pixels
             
@@ -54,7 +56,7 @@
             for i=1:N
                 img = squeeze(inputs(:,:,:,:,i));
                 target = targets(i);
-                results(i,:) = verify_instance_3d(net, img, target, adv_attack, reachOptions);
+                results(i,:) = verify_instance_shape(net, img, target, adv_attack, reachOptions);
             end
             
             % 4) % save results
diff --git a/code/nnv/examples/Submission/WiP_3d/verify_fracture.m b/code/nnv/examples/Submission/WiP_3d/verify_fracture.m
index c66a8c60f3..d629615012 100644
--- a/code/nnv/examples/Submission/WiP_3d/verify_fracture.m
+++ b/code/nnv/examples/Submission/WiP_3d/verify_fracture.m
@@ -20,7 +20,7 @@
 net = matlab2nnv(net);
 
 % select volumes to verify
-N = 24; % even for numCores
+N = 50; % even for numCores
 inputs = single(test_images(:,:,:,:,1:N));
 targets = single(test_labels(1:N));
 
@@ -33,7 +33,7 @@
 % Study variables
 advType = ["bright", "dark"];
 maxpixels = [50, 100, 500, 1000]; %out of 28x28x28 pixels
-epsilon = [2, 4, 10]; % ep / 255
+epsilon = [2, 5, 10, 25]; % ep / 255
 threshold = [100; 150]; % bright ; dark
 
 %% Verification analysis
diff --git a/code/nnv/examples/Submission/WiP_3d/verify_nodule.m b/code/nnv/examples/Submission/WiP_3d/verify_nodule.m
index d2b09d0778..0e6e7f6af0 100644
--- a/code/nnv/examples/Submission/WiP_3d/verify_nodule.m
+++ b/code/nnv/examples/Submission/WiP_3d/verify_nodule.m
@@ -20,7 +20,7 @@
 net = matlab2nnv(net);
 
 % select volumes to verify
-N = 24; % even for numCores
+N = 50; % even for numCores
 inputs = single(test_images(:,:,:,:,1:N));
 targets = single(test_labels(1:N));
 
@@ -34,7 +34,7 @@
 % Study variables
 advType = ["bright", "dark"];
 maxpixels = [50, 100, 500, 1000]; %out of 28x28x28 pixels
-epsilon = [2, 4, 10]; % ep / 255
+epsilon = [2, 5, 10, 25]; % ep / 255
 threshold = [100; 150]; % bright ; dark
 
 %% Verification analysis
diff --git a/code/nnv/examples/Submission/WiP_3d/verify_organ.m b/code/nnv/examples/Submission/WiP_3d/verify_organ.m
index c05164bf48..563f5ca2c4 100644
--- a/code/nnv/examples/Submission/WiP_3d/verify_organ.m
+++ b/code/nnv/examples/Submission/WiP_3d/verify_organ.m
@@ -20,7 +20,7 @@
 net = matlab2nnv(net);
 
 % select volumes to verify
-N = 24;
+N = 50;
 inputs = single(test_images(:,:,:,:,1:N));
 targets = single(test_labels(1:N));
 
@@ -33,7 +33,7 @@
 % Study variables
 advType = ["bright", "dark"];
 maxpixels = [50, 100, 500, 1000]; %out of 28x28x28 pixels
-epsilon = [2, 4, 10]; % ep / 255
+epsilon = [2, 5, 10, 25]; % ep / 255
 threshold = [100; 150]; % bright ; dark
 
 %% Verification analysis
diff --git a/code/nnv/examples/Submission/WiP_3d/verify_synapse.m b/code/nnv/examples/Submission/WiP_3d/verify_synapse.m
index 76d0160cdd..e09474ffb5 100644
--- a/code/nnv/examples/Submission/WiP_3d/verify_synapse.m
+++ b/code/nnv/examples/Submission/WiP_3d/verify_synapse.m
@@ -20,7 +20,7 @@
 net = matlab2nnv(net);
 
 % select volumes to verify
-N = 24; % even for numCores
+N = 50; % even for numCores
 inputs = single(test_images(:,:,:,:,1:N));
 targets = single(test_labels(1:N));
 
@@ -33,7 +33,7 @@
 % Study variables
 advType = ["bright", "dark"];
 maxpixels = [50, 100, 500, 1000]; %out of 28x28x28 pixels
-epsilon = [2, 4, 10]; % ep / 255
+epsilon = [2, 5, 10, 25]; % ep / 255
 threshold = [100; 150]; % bright ; dark
 
 %% Verification analysis
diff --git a/code/nnv/examples/Submission/WiP_3d/verify_vessel.m b/code/nnv/examples/Submission/WiP_3d/verify_vessel.m
index d8775e01e2..738fa2cf45 100644
--- a/code/nnv/examples/Submission/WiP_3d/verify_vessel.m
+++ b/code/nnv/examples/Submission/WiP_3d/verify_vessel.m
@@ -20,7 +20,7 @@
 net = matlab2nnv(net);
 
 % select volumes to verify
-N = 24; % even for numCores
+N = 50; % even for numCores
 inputs = single(test_images(:,:,:,:,1:N));
 targets = single(test_labels(1:N));
 
@@ -30,139 +30,37 @@
 reachOptions.relaxFactor = 0.95;
 reachOptions.lp_solver = "gurobi";
 
-%% Attack 1
-
-% adv_attack = struct;
-%???????
-
-% results = zeros(N,2); % verification result, time
-
-% verify volumes
-% parfor i=1:N
-%     img = squeeze(inputs(:,:,:,:,i));
-%     target = targets(i);
-%     results(i,:) = verify_instance_3d(net, img, target, adv_attack, reachOptions);
-% end
-
-% save results
-% save("results/verification_vessel_"+adv_attack.Name+"_" +adv_attack.noise_de +"_" +adv_attack.max_pixels + ".mat", "results");
-
-
-%% Attack 2
-
-adv_attack = struct;
-
-% results = zeros(N,2); % verification result, time
-% 
-% % verify volumes
-% parfor i=1:N
-%     img = squeeze(inputs(:,:,:,:,i));
-%     target = targets(i);
-%     results(i,:) = verify_instance_3d(net, img, target, adv_attack, reachOptions);
-% end
-% 
-% % save results
-% save("results/verification_vessel_"+adv_attack.Name+"_" +adv_attack.noise_de +"_" +adv_attack.max_pixels + ".mat", "results");
-
-
-%% Attack 3
-
-% adv_attack = struct;
-% 
-% results = zeros(N,2); % verification result, time
-% 
-% % verify volumes
-% parfor i=1:N
-%     img = squeeze(inputs(:,:,:,:,i));
-%     target = targets(i);
-%     results(i,:) = verify_instance_3d(net, img, target, adv_attack, reachOptions);
-% end
-% 
-% % save results
-% save("results/verification_vessel_"+adv_attack.Name+"_" +adv_attack.noise_de +"_" +adv_attack.max_pixels + ".mat", "results");
-
-
-%% Attack 4
-
-% adv_attack = struct;
-%
-% results = zeros(N,2); % verification result, time
-% 
-% % verify volumes
-% parfor i=1:N
-%     img = squeeze(inputs(:,:,:,:,i));
-%     target = targets(i);
-%     results(i,:) = verify_instance_3d(net, img, target, adv_attack, reachOptions);
-% end
-% 
-% % save results
-% save("results/verification_vessel_"+adv_attack.Name+"_" +adv_attack.noise_de +"_" +adv_attack.max_pixels + ".mat", "results");
-
-
-%% Attack 5
-
-% adv_attack = struct;
-% 
-% results = zeros(N,2); % verification result, time
-% 
-% % verify volumes
-% parfor i=1:N
-%     img = squeeze(inputs(:,:,:,:,i));
-%     target = targets(i);
-%     results(i,:) = verify_instance_3d(net, img, target, adv_attack, reachOptions);
-% end
-% 
-% % save results
-% save("results/verification_vessel_"+adv_attack.Name+"_" +adv_attack.noise_de +"_" +adv_attack.max_pixels + ".mat", "results");
-
-
-%% Attack 6
-
-% adv_attack = struct;
-%
-% results = zeros(N,2); % verification result, time
-% 
-% % verify volumes
-% parfor i=1:N
-%     img = squeeze(inputs(:,:,:,:,i));
-%     target = targets(i);
-%     results(i,:) = verify_instance_3d(net, img, target, adv_attack, reachOptions);
-% end
-% 
-% % save results
-% save("results/verification_vessel_"+adv_attack.Name+"_" +adv_attack.noise_de +"_" +adv_attack.max_pixels + ".mat", "results");
-
-
-%% Attack 7
-
-% adv_attack = struct;
-% 
-% results = zeros(N,2); % verification result, time
-% 
-% % verify volumes
-% parfor i=1:N
-%     img = squeeze(inputs(:,:,:,:,i));
-%     target = targets(i);
-%     results(i,:) = verify_instance_3d(net, img, target, adv_attack, reachOptions);
-% end
-% 
-% % save results
-% save("results/verification_vessel_"+adv_attack.Name+"_" +adv_attack.noise_de +"_" +adv_attack.max_pixels + ".mat", "results");
-
-
-%% Attack 8
-
-% adv_attack = struct;
-% 
-% results = zeros(N,2); % verification result, time
-% 
-% % verify volumes
-% parfor i=1:N
-%     img = squeeze(inputs(:,:,:,:,i));
-%     target = targets(i);
-%     results(i,:) = verify_instance_3d(net, img, target, adv_attack, reachOptions);
-% end
-% 
-% % save results
-% save("results/verification_vessel_"+adv_attack.Name+"_" +adv_attack.noise_de +"_" +adv_attack.max_pixels + ".mat", "results");
+% Study variables
+advType = ["add", "remove"];
+maxpixels = [50, 100, 500, 1000]; %out of 28x28x28 pixels
+epsilon = 1; % ep / 255
+
+
+%% Verification analysis
+for a=advType
+    for mp=maxpixels
+        for ep=epsilon
+            
+            % 1) Initialize results var
+            results = zeros(N,2);
+            
+            % 2) Create adversarial attack
+            adv_attack = struct;
+            adv_attack.Name = a; % add or remove
+            adv_attack.max_pixels = mp; % Max number of pixels to modify from input image
+            adv_attack.noise_de = ep/255; % disturbance (noise) on pixels
+            
+            % 3) Begin verification analysis
+            for i=1:N
+                img = squeeze(inputs(:,:,:,:,i));
+                target = targets(i);
+                results(i,:) = verify_instance_shape(net, img, target, adv_attack, reachOptions);
+            end
+            
+            % 4) % save results
+            save("results/verification_vessel_"+ a +"_" + ep +"_" + mp + ".mat", "results");
+
+        end
+    end
+end
 
diff --git a/code/nnv/examples/Submission/WiP_3d/visualize_results_gen.m b/code/nnv/examples/Submission/WiP_3d/visualize_results_gen.m
new file mode 100644
index 0000000000..f0e14d02ad
--- /dev/null
+++ b/code/nnv/examples/Submission/WiP_3d/visualize_results_gen.m
@@ -0,0 +1,196 @@
+%% Get all results, one dataset at a time
+
+results = dir('results');
+
+% Variable in the study
+datasets = ["fracture", "nodule", "organ", "synapse"]; 
+attackType = ["bright", "dark"];
+maxpixels = ["50", "100", "500", "1000"];
+epsilon = ["2", "5", "10", "25"]; % epsilon/255
+
+% Initialize directories
+% mkdir('plots');
+% for i=datasets
+%     mkdir("plots/"+i);
+% end
+
+%% Visualize verification results/trends
+
+% What do we want to show?
+
+% 1) Trends
+%  - Time: How does the time increases as the input set gets larger?
+%     - Epsilon increasing
+%     - Number of pixels increasing
+%  - results: How robust are the models as we increase the size of the attack? more unknowns? more sats?
+%     - Epsilon increasing
+%     - Number of pixels increasing
+% 2) Certified robust accuracy
+%  - Is it much worse than the accuracy of the model? 
+%  - Do we need more samples?
+ 
+
+% Time for plots (maxpixels variable)
+for ds = datasets
+    for adv = attackType
+        for ep = epsilon
+            
+            % Initialize vars to plot
+            sat   = [];
+            unsat = [];
+            unk   = [];
+            miss  = [];
+            avgVT = [];
+            avgRT = [];
+            
+            % Get data
+            for mp = maxpixels
+                resFile = "results/verification_" + ds + "_" + adv + "_" + ep + "_" + mp +".mat";
+                res = summarize_results(resFile);
+                sat = [sat, res.sat];
+                unsat = [unsat, res.unsat];
+                unk = [unk, res.unknown];
+                miss = [miss, res.misclassified];
+                avgVT = [avgVT, res.avgTime]; % average computation time to verify one instance
+                avgRT = [avgRT, res.avgRT]; % average computation time to compute the reachable sets (miss and sat do not count here)
+            end
+            counts = [unsat; sat; unk; miss];
+            
+            
+            % Create figure (results)
+            f = figure('visible','off');
+            bar(1:4, counts','stacked') % plot verification results
+            grid;
+            % set values for x-axis
+            xticks([1 2 3 4]);
+            xticklabels(maxpixels);
+            % axis labels
+            xlabel('Max pixels perturbed');
+            ylabel('# instances')
+            % legend
+            leg = {"unsat", "sat", "unknown", "missclass"};
+            legend(leg, 'Location', 'best');
+            % save figure
+            saveas(f, "plots/" + ds + "/verification_" + adv + "_" + ep + ".png");
+            
+            % create figure (time)
+            f = figure('visible','off');
+            % plot computation time results
+            plot(1:4, avgVT, 'r--o');
+            hold on;
+            plot(1:4, avgRT, 'b--v');
+            % set values for x-axis
+            xticks([1 2 3 4]);
+            xticklabels(maxpixels)
+            % axis labels
+            xlabel('Max pixels perturbed');
+            ylabel("Average Time (s)")
+            % legend
+            leg = {"all", "unsat & unknown"};
+            legend(leg, 'Location', 'best');
+            % save figure
+            saveas(f, "plots/" + ds + "/avgTime_" + adv + "_" + ep + ".png");
+
+        end
+    end
+end
+
+% Time for plots (epsilon variable)
+for ds = datasets
+    for adv = attackType
+        for mp = maxpixels
+            
+            % Initialize vars to plot
+            sat   = [];
+            unsat = [];
+            unk   = [];
+            miss  = [];
+            avgVT = [];
+            avgRT = [];
+            
+            % Get data
+            for ep = epsilon
+                resFile = "results/verification_" + ds + "_" + adv + "_" + ep + "_" + mp +".mat";
+                res = summarize_results(resFile);
+                sat = [sat, res.sat];
+                unsat = [unsat, res.unsat];
+                unk = [unk, res.unknown];
+                miss = [miss, res.misclassified];
+                avgVT = [avgVT, res.avgTime]; % average computation time to verify one instance
+                avgRT = [avgRT, res.avgRT]; % average computation time to compute the reachable sets (miss and sat do not count here)
+            end
+            counts = [unsat; sat; unk; miss];
+            
+            % Create figure (results)
+            f = figure('visible','off');
+            bar(1:3, counts','stacked'); % plot results
+            grid;
+            % set values for x-axis
+            xticks([1 2 3]);
+            xticklabels(epsilon)
+            % axis labels
+            xlabel('epsilon (\epsilon)');
+            ylabel('# instances')
+            % legend
+            leg = {"unsat", "sat", "unknown", "missclass"};
+            legend(leg, 'Location', 'best');
+            % save figure
+            saveas(f, "plots/" + ds + "/verification_" + adv + "_" + mp + ".png");
+            
+            % create figure (time)
+            f = figure('visible','off');
+            % plot timing results
+            plot(1:3, avgVT, 'r--o');
+            hold on;
+            plot(1:3, avgRT, 'b--v');
+            % set values for x-axis
+            xticks([1 2 3]);
+            xticklabels(epsilon)
+            % axis labels
+            xlabel('epsilon (\epsilon)');
+            ylabel("Average Time (s)")
+            % legend
+            leg = {"all", "unsat & unknown"};
+            legend(leg, 'Location', 'best');
+            % save figure
+            saveas(f, "plots/" + ds + "/avgTime_" + adv + "_" + mp + ".png");
+
+        end
+    end
+end
+
+
+%% Helper functions
+
+function summary = summarize_results(resFile)
+    
+    % Provide details from results file
+    summary = struct;
+    data = load(resFile);
+    results = data.results;
+    
+    % Total number of samples examined
+    summary.N = length(results);
+    
+    % Verified (unsat)
+    summary.unsat = sum(results(:,1) == 1);
+    
+    % Falsified (sat) from input set
+    summary.sat = sum(results(:,1) == 0);
+    
+    % Unknown (not using exact)
+    summary.unknown = sum(results(:,1) == 2);
+    
+    % Misclasified (sat) of original image
+    summary.misclassified = sum(results(:,1) == -1);
+    
+    % Also possible -2 (error), which may be out of memory (most common here)
+    summary.avgTime = sum(results(:,2))/summary.N;
+    
+    % Find instances where reachability is needed
+    x = [find(results(:,1)==2); find(results(:,1)==1)];
+    nx = length(x); % how many instances reachability is computed for
+
+    % Average time only for unknown and unsat properties (reachsets computed)
+    summary.avgRT = sum(results(x,2))/nx;
+end
\ No newline at end of file
diff --git a/code/nnv/examples/Submission/WiP_3d/visualize_results.m b/code/nnv/examples/Submission/WiP_3d/visualize_results_shape.m
similarity index 93%
rename from code/nnv/examples/Submission/WiP_3d/visualize_results.m
rename to code/nnv/examples/Submission/WiP_3d/visualize_results_shape.m
index 4b273482d1..09c8c60370 100644
--- a/code/nnv/examples/Submission/WiP_3d/visualize_results.m
+++ b/code/nnv/examples/Submission/WiP_3d/visualize_results_shape.m
@@ -3,17 +3,16 @@
 results = dir('results');
 
 % Variable in the study
-% datasets = ["adrenal", "fracture", "nodule", "organ", "synapse", "vessel"];
-datasets = ["fracture", "nodule", "organ", "synapse"]; 
+datasets = ["adrenal", "vessel"];
 attackType = ["bright", "dark"];
 maxpixels = ["50", "100", "500", "1000"];
-epsilon = ["2", "4", "10"]; % epsilon/255
+epsilon = ["1"]; % epsilon/255
 
 % Initialize directories
-mkdir('plots');
-for i=datasets
-    mkdir("plots/"+i);
-end
+% mkdir('plots');
+% for i=datasets
+%     mkdir("plots/"+i);
+% end
 
 %% Visualize verification results/trends
 
@@ -46,7 +45,7 @@
             
             % Get data
             for mp = maxpixels
-                resFile = "verification_" + ds + "_" + adv + "_" + ep + "_" + mp +".mat";
+                resFile = "results/verification_" + ds + "_" + adv + "_" + ep + "_" + mp +".mat";
                 res = summarize_results(resFile);
                 sat = [sat, res.sat];
                 unsat = [unsat, res.unsat];
@@ -111,7 +110,7 @@
             
             % Get data
             for ep = epsilon
-                resFile = "verification_" + ds + "_" + adv + "_" + ep + "_" + mp +".mat";
+                resFile = "results/verification_" + ds + "_" + adv + "_" + ep + "_" + mp +".mat";
                 res = summarize_results(resFile);
                 sat = [sat, res.sat];
                 unsat = [unsat, res.unsat];