You hated matrix multiplication in school right?

In Deep learning, matrix multiplication is one of the most fundamental mathematical operations used in training neural networks.

Here's why it's so important:

• Inputs and Weights : In a neural network, you start with inputs (x1, x2, x3). These inputs can be anything- like pixel values in an image, sound waves in audio, or even words in a sentence.

The network also has weights (w1, w2, w3) assigned to each input. These weights are adjusted by the model during training to learn patterns from the data.

• Matrix Multiplication : Matrix multiplication is a process where each input is multiplied by its corresponding weight.

For example, if you have three inputs and three weights, they are combined into a matrix. When you multiply them, you're essentially combining the information from the inputs and their learned importance (weights).

[ x₁ ] [ w₁ ] [ x₂ ] . [ w₂ ] = [ x₁ * w₁ + x₂ * w₂ + x₃ * w₃ ] [ x₃ ] [ w₃ ]

• Learning in Neural Networks : The network uses this multiplication to calculate an output, like whether an image contains a cat or a dog.

During training, the weights are updated based on how far the prediction is from the actual result. This process is called backpropagation.

The goal is to adjust the weights so that the network gets better at making accurate predictions.

• Why It Matters : Matrix multiplication allows the neural network to combine input features in a way that helps it detect patterns. Whether it's finding edges in an image or understanding the sentiment of a sentence, this operation helps the network make sense of the data.

As you stack multiple layers of neurons (each with their own matrices), the network can capture increasingly complex patterns, which is why deep learning is so powerful 💪

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