MatMul is short for matrix multiplication, which is a mathematical operation that takes two matrices and produces another matrix.

To calculate MatMul, we need to ensure that the number of columns in the first matrix is equal to the number of rows in the second matrix.

Then, we multiply each element of the row in the first matrix by the corresponding element of the column in the second matrix and sum the products.

Refer: https://docs.google.com/spreadsheets/d/1uKK0N86XPEynoN1MpT_0Mm3IId38xzJz3Yptw2FujCo/edit?usp=sharing

In Python, matmul is a function provided by the NumPy library for performing matrix multiplication. Here's an example of how to use matmul in Python:

import numpy as np

# Define input and weight matrices
input_matrix = np.array([[1, 2, 3], [4, 5, 6]])
print ('input matrix:')
print (input_matrix)
print ()


weight_matrix = np.array([[0.1, 0.2], [0.3, 0.4], [0.5, 0.6]])
print ('weight matrix:')
print (weight_matrix)
print ()

# Perform matrix multiplication using matmul
output_matrix = np.matmul(input_matrix, weight_matrix)

# Print the output matrix
print ('output matrix:')
print(output_matrix)

Console output:

input matrix:
[[1 2 3]
 [4 5 6]]

weight matrix:
[[0.1 0.2]
 [0.3 0.4]
 [0.5 0.6]]

output matrix:
[[2.2 2.8]
 [4.9 6.4]]

Refer: https://replit.com/@mahmoodrazzi/using-matmul-for-neural-network

Matmul is a fundamental operation in neural networks that is used to calculate the weighted sum of inputs and weights.

The weighted sum in a neural network allows the network to learn and represent complex relationships between inputs and outputs.

By applying a set of weights to the inputs, the neural network can assign different levels of importance to each input feature, based on how relevant it is to the task at hand.

This allows the network to focus on the most important features and ignore irrelevant or noisy features.

The weighted sum also allows the network to learn non-linear relationships between inputs and outputs.

By applying different weights to different inputs, the network can capture complex interactions between features that would be difficult to model with a simple linear function.

For example, the above output matrix can be represented by a heat map graph as shown below. To generate a heatmap of the output matrix, use the imshow function in Matplotlib. Specify the color map to use (e.g. 'viridis' in this case), and add a color bar to indicate the scale of the values. Different colors indicate different levels of activation for each neuron in the layer.

Refer:

https://replit.com/@mahmoodrazzi/using-matmul-for-neural-network?v=1

Neural Networks Matrix Math and NumPy (https://www.youtube.com/watch?v=P8Xrj70qtyo)

Neural Networks Explained from Scratch using Python (https://www.youtube.com/watch?v=9RN2Wr8xvro)

Why Neural Networks can learn (almost) anything (https://www.youtube.com/watch?v=0QczhVg5HaI)