Dear friends, pls how can I call up the weights and bias of a trained model and write the mathematical expression or equation for it.

% Solve an Input-Output Fitting problem with a Neural Network

% Script generated by Neural Fitting app

% Created 23-Jan-2023 17:53:08

%

% This script assumes these variables are defined:

%

% Input - input data.

% Target - target data.

x = Input;

t = Target;

% Choose a Training Function

% For a list of all training functions type: help nntrain

% 'trainlm' is usually fastest.

% 'trainbr' takes longer but may be better for challenging problems.

% 'trainscg' uses less memory. Suitable in low memory situations.

trainFcn = 'trainbr'; % Bayesian Regularization backpropagation.

% Create a Fitting Network

hiddenLayerSize = 10;

net = fitnet(hiddenLayerSize,trainFcn);

% Choose Input and Output Pre/Post-Processing Functions

% For a list of all processing functions type: help nnprocess

net.input.processFcns = {'removeconstantrows','mapminmax'};

net.output.processFcns = {'removeconstantrows','mapminmax'};

% Setup Division of Data for Training, Validation, Testing

% For a list of all data division functions type: help nndivision

net.divideFcn = 'dividerand'; % Divide data randomly

net.divideMode = 'sample'; % Divide up every sample

net.divideParam.trainRatio = 80/100;

net.divideParam.valRatio = 10/100;

net.divideParam.testRatio = 10/100;

% Choose a Performance Function

% For a list of all performance functions type: help nnperformance

net.performFcn = 'mse'; % Mean Squared Error

% Choose Plot Functions

% For a list of all plot functions type: help nnplot

net.plotFcns = {'plotperform','plottrainstate','ploterrhist', ...

'plotregression', 'plotfit'};

% Train the Network

[net,tr] = train(net,x,t);

% Test the Network

y = net(x);

e = gsubtract(t,y);

performance = perform(net,t,y)

% Recalculate Training, Validation and Test Performance

trainTargets = t .* tr.trainMask{1};

valTargets = t .* tr.valMask{1};

testTargets = t .* tr.testMask{1};

trainPerformance = perform(net,trainTargets,y)

valPerformance = perform(net,valTargets,y)

testPerformance = perform(net,testTargets,y)

% View the Network

view(net)

% Plots

% Uncomment these lines to enable various plots.

%figure, plotperform(tr)

%figure, plottrainstate(tr)

%figure, ploterrhist(e)

%figure, plotregression(t,y)

%figure, plotfit(net,x,t)

% Deployment

% Change the (false) values to (true) to enable the following code blocks.

% See the help for each generation function for more information.

if (false)

% Generate MATLAB function for neural network for application

% deployment in MATLAB scripts or with MATLAB Compiler and Builder

% tools, or simply to examine the calculations your trained neural

% network performs.

genFunction(net,'myNeuralNetworkFunction');

y = myNeuralNetworkFunction(x);

end

if (false)

% Generate a matrix-only MATLAB function for neural network code

% generation with MATLAB Coder tools.

genFunction(net,'myNeuralNetworkFunction','MatrixOnly','yes');

y = myNeuralNetworkFunction(x);

end

if (false)

% Generate a Simulink diagram for simulation or deployment with.

% Simulink Coder tools.

gensim(net);

end

=====================================================================

I have attached the save model, where output (Ra = Y) and inputs X(vc, ap, and f). I want to express the model equation for Ra interms of vc, ap, and f (x1, x2, and x3).

Answer 1

[Avadhoot]

Hi @Ugifada,

I understand that you are trying to express your model mathematically. For that you need the weights and biases of your trained neural network. Your trained neural network is represented by the variable "net". To get the weights and biases for the network, use the following commands:

weights_i = net.LW{i};

This command gives the layer weights of the ith layer in your network.

biases_i = net.b{i};

Similarly the above command gives you the biases for the ith layer in your network.

You can use the commands in a loop to get all the parameters of your network. After that you can represent your model mathematically as per your requirement.

For more information on the "net" object, refer to the below documentation:

https://www.mathworks.com/help/deeplearning/ref/network.html?s_tid=doc_ta#f8-667843

I hope it helps.

[Sam Chak]

Can neural networks truly be transformed into a mathematical model using elementary and transcendental functions? If that's the case, could you please guide me on which built-in MATLAB function allows for such transformations? Thank you.

[Avadhoot]

I don't think neural networks can be transformed into mathematical models using any elementary functions. Only the steps can be traced using the input layer weights and the outputs.

[Sam Chak]

Hi @Avadhoot

I see. Thank you for your clarification. With the steps being traced through the input layer weights and outputs, is it possible for humans to interpret them meaningfully? For instance, if the neural network incorrectly recognizes an object that is evident to humans, can the designers trace back the steps and meaningfully modify the input layer weights and outputs to improve the prediction outcomes for this particular object?

Will the modifications potentially impact the prediction performance of other trained objects? These questions are especially significant when considering the operational safety and risks associated with AI-controlled self-driving vehicles navigating a busy street, particularly if a human is wearing a Panda mascot costume.

[Avadhoot]

I understand your concern here. Even if a human traced back the steps of a neural network, it is still too complex to comprehend which component is causing an error in the final output. The concept of tracing the steps can be somewhat seen in the idea of backpropagation used in neural network where the weights are modified in reverse from the last layer to the first layer. This systematic updation of weights ensures low error rate and thus, better accuracy.

Regarding to your second query, the modifications affect all of the network. Ideally the impact of the modifications should be restricted to the erroneous case but it seldom happens. The network as a whole improves in accuracy. That means the erroneous cases are reduced but it does not guarantee that errors won't be introduced for other predictions.

There are several ways to make neural networks resistant to noise and attacks by data tampering. These are active research fields which are producing newer techniques by the day.

[Ugifada]

@Avadhoot, Thank you so much! This is helpful. My apologies for the late response.

[Sam Chak]

@Avadhoot, Thanks for your explanation.