Linear Transformations

Simple Linear Layer

In neural networks, linear transformations are represented as: $y = Wx + b$. 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 = [[2, -1], [1, 3]];  // Weight matrix W
$inputVector = [1, 2];              // Input vector x
$bias = [1, 0];                     // Bias vector b

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

echo "Output after Linear 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 Linear Layer: [1, 7]