How to make three-layer perceptron with two inputs and one output in matlab?

Implement one learning cycle of a three-layer perceptron with two inputs and one output

(NS of the form 2-2-2-1, i.e. we have 2 neurons in each hidden layer) of a neural network on one

an example from a training sample. As an activation function for all neurons, select

sigmoid function with coefficient a = 1. Initial values of synaptic link weights

accept equal to 0.4.

Answer 1

[Shubham]

Hi Arturzzaman,

To implement a learning cycle of a three-layer perceptron with the given architecture (2-2-2-1), we will follow these steps:

1. Initialize the weights and the architecture.
2. Perform a forward pass to compute the output.
3. Use the sigmoid activation function.
4. Perform a backward pass to update the weights (backpropagation).

Let's assume we have a single training sample (x1, x2) with a target output t.

Step 1: Initialize the weights

Since all initial weights are 0.4, we'll set up our weight matrices accordingly. We'll have three sets of weights: W1 for the first hidden layer, W2 for the second hidden layer, and W3 for the output layer.

W1 = [0.4, 0.4; 0.4, 0.4]; % Weights from input to first hidden layer (2x2)
W2 = [0.4, 0.4; 0.4, 0.4]; % Weights from first hidden layer to second hidden layer (2x2)
W3 = [0.4, 0.4];           % Weights from second hidden layer to output layer (1x2)

Step 2: Perform a forward pass

Compute the input to each neuron in the first hidden layer (h1), apply the sigmoid activation function, then compute the input to each neuron in the second hidden layer (h2), apply the sigmoid activation function again, and finally compute the input to the output neuron (y), and apply the sigmoid activation function one last time.

sigmoid(x) = 1 / (1 + exp(-a * x))

where a is the coefficient, which is 1 in this case.

% Define the sigmoid activation function
sigmoid = @(x) 1 ./ (1 + exp(-x));

% Input vector
X = [x1; x2];

% Forward pass through the first hidden layer
h1_input = W1 * X;
h1_output = sigmoid(h1_input);

% Forward pass through the second hidden layer
h2_input = W2 * h1_output;
h2_output = sigmoid(h2_input);

% Forward pass through the output layer
y_input = W3 * h2_output;
y_output = sigmoid(y_input);

Step 3: Compute the error

Compute the error at the output neuron.

error = t - y_output;

Step 4: Perform a backward pass

Perform backpropagation to update the weights. This involves computing the gradient of the error with respect to each weight, which requires the derivative of the sigmoid function.

The derivative of the sigmoid function sigmoid'(x) is:

sigmoid'(x) = a * sigmoid(x) * (1 - sigmoid(x))

However, since we are only implementing one learning cycle and not actually updating the weights, we will not perform the full backpropagation algorithm here.

This is the conceptual framework for a single learning cycle of the specified three-layer perceptron.