If you want to express that output as a single equation, it would look extremely complex due to the nested nature of the computations, especially with 25 neurons in the hidden layer. The equation would be a large summation of the products of inputs and weights, passed through an activation function, and then summed again with another set of weights to produce the output.
To manually generate the output based on the input variables, you can refer to this example code snippet:
% Assuming 'net' is your trained neural network and 'X' is your input matrix
% Let's say X is of size [10 x 3], where 10 is the number of examples and 3 is the number of features
% Retrieve the network parameters
IW = net.IW{1,1}; % Input weights for the hidden layer [25 x 3]
LW = net.LW{2,1}; % Weights from hidden layer to output layer [1 x 25]
b1 = net.b{1}; % Biases for the hidden layer [25 x 1]
b2 = net.b{2}; % Bias for the output layer [1 x 1]
% Compute the hidden layer outputs in a vectorized way
% Each row of X is multiplied by IW' and the bias b1 is added to each row
hiddenLayerInput = X * IW' + repmat(b1', size(X, 1), 1);
hiddenLayerOutput = myActivationFunction(hiddenLayerInput); % Apply the activation function
% Compute the output layer
% Multiply each row of the hiddenLayerOutput by LW' and add the bias b2
output = hiddenLayerOutput * LW' + b2;
This code performs vectorized operations over each row of inputs. I used "repmat" function here to replicate the bias vector to match the number of examples in the input matrix.
You can refer to below documentation regarding retrieving network parameters:
If you still want to go ahead and generate a symbolic equation for the entire process, you can use MATLAB's Symbolic Math Toolbox to handle the symbolic representation of the equation. This allows you to express the network's operations in terms of algebraic expressions rather than numerical computations and extract a mathematical equation explicitly that represents the network's computation. Below is an example code snippet for using this: (this is assumed for only 2 neurons in hidden layer, for 25 neurons the equation would be much more bigger and complicated)
% Initialize the MATLAB symbolic toolbox
syms x1 x2 x3 real
% Define symbolic variables for weights and biases
% Input weights and biases for the hidden layer
syms iw11 iw12 iw13 iw21 iw22 iw23 real
syms b1_1 b1_2 real
% Weights and bias for the output layer
syms lw11 lw12 real
syms b2 real
% Define symbolic variables for activation functions
syms activationFunction1(x) activationFunction2(x)
% Write the equations for the outputs of the hidden layer neurons
h1 = activationFunction1(iw11*x1 + iw12*x2 + iw13*x3 + b1_1);
h2 = activationFunction2(iw21*x1 + iw22*x2 + iw23*x3 + b1_2);
% Write the equation for the output neuron
% Assuming a linear activation function for the output layer
Y = lw11*h1 + lw12*h2 + b2;
% Now Y is a symbolic expression representing the output of the network
% in terms of the inputs (x1, x2, x3) and the network parameters (weights and biases)
% You can use this expression to create a function handle or to perform further symbolic manipulation
Find these documentations related to Symbolic math toolbox for your reference:
Hope this helps to a certain extent!
