Linear Transformations

Fully Connected Layer

In a neural network, each layer applies a linear transformation followed by an activation function: $y = Wx + b$. Here, $W$ is a weight matrix, $x$ is the input, and $b$ is the bias vector.
In PHP it can be written as a class LinearTransformation with implementation of linear transformation operations.

Example of use


<?php

// Example usage:
$weightMatrix = [[3, 2], [-1, 4]];  // Weight matrix W
$inputVector = [1, 2];              // Input vector x
$bias = [1, -2];                    // Bias vector b

$linearTransform = new LinearTransformation($weightMatrix);
$resultVector = $linearTransform->linearTransform($weightMatrix, $bias, $inputVector);

echo "Output after Fully Connected Layer: [<span id='output-vector'>" . implode(', ', $resultVector) . '</span>]';

Chart:

Weight Matrix ($W$)

X Component:

Y Component:

Input Vector ($x$)

X Component:

Y Component:

Bias Vector ($b$)

X Component:

Y Component:

Output Vector ($y = Wx + b$)

X Component:

Y Component:

Result: Memory: 0.002 Mb Time running: < 0.001 sec.


                Output after Fully Connected Layer: [8, 5]