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Understanding the Hidden Layer

Teaching Point: Understanding the Hidden Layer

What is a Hidden Layer?

Definition: In a neural network, a hidden layer is a layer that is not part of the input or output.

It sits between the input layer and the output layer.

The term "hidden" refers to the fact that this layer's activations (outputs) are not directly visible or used for input/output operations but rather serve as intermediate computations.

Why is it Called "Hidden"?

Visibility: The term "hidden" comes from the fact that this layer's operations are not exposed directly to the outside of the model.

In contrast, the input layer receives raw data, and the output layer produces the final predictions. {next token generation}

Intermediate Processing: Hidden layers are responsible for transforming the input data into more abstract and useful representations through learned weights and activation functions. This transformation is essential for the network to learn complex patterns and features in the data.

What Does a Hidden Layer Do?

Feature Extraction: The hidden layer extracts features from the input data.

Each neuron in the hidden layer applies a weight to the inputs, sums them up, and passes them through an activation function. This process helps the network learn and represent complex patterns in the data.

Non-linearity: Activation functions (like ReLU, Sigmoid, or Tanh) introduce non-linearity into the model, allowing it to learn and represent complex relationships between the input and output.

{Later we will model some math concepts in R to visual how these algorithms process data.}

Learning: During training, the weights in the hidden layers are adjusted through backpropagation to minimize the error in the predictions.

This learning process enables the network to make accurate predictions on new, unseen data.

Example: Simple Neural Network Model with One Hidden Layer

Let's define a simple neural network model with one hidden layer using PyTorch.

We will create a neural network to classify the MNIST dataset (a dataset of handwritten digits).

import torch.nn as nn

# Define the neural network model

class SimpleNN(nn.Module):

def __init__(self):

super(SimpleNN, self).__init__()

# Input layer to hidden layer

self.fc1 = nn.Linear(28 * 28, 128) # 28x28 input image size flattened to 784, 128 hidden units

x = x.view(-1, 28 * 28) # Flatten the input image from (28, 28) to (784,)

x = torch.relu(self.fc1(x)) # Apply ReLU activation function to the first hidden layer

x = self.fc2(x) # Output layer

return x

# Instantiate the model

model = SimpleNN()

print(model)

Explanation:

Input Layer: The input layer takes a 28x28 image, which we flatten into a 784-element vector (28 * 28 = 784).

Hidden Layer (fc1):
The hidden layer (fc1) has 128 neurons. Each neuron computes a weighted sum of the inputs, adds a bias, and applies the ReLU activation function to introduce non-linearity.

Weights and Biases: These are parameters that the network learns during training.

ReLU Activation: ReLU (Rectified Linear Unit) activation function is used to introduce non-linearity, which helps the network learn complex patterns.

Output Layer (fc2): The output layer (fc2) has 10 neurons, corresponding to the 10 classes of digits (0-9). This layer produces the final output of the network.

Activation Function:

The ReLU activation function is used to add non-linearity to the model. Non-linear activation functions are crucial because they allow the network to learn complex patterns and relationships in the data. Without non-linearity, the neural network would behave like a simple linear model, limiting its ability to capture intricate patterns. {This is where we get our Probabilistic Programming. Without this, we would be stuck at the imperative programming model of If This, Then That}

Forward Pass:

Flatten the Input: The input image is flattened into a 784-element vector.

Hidden Layer Computation: The flattened input is passed through the first hidden layer, where each neuron computes a weighted sum of the inputs, adds a bias, and applies the ReLU activation function.

Output Layer Computation: The output of the hidden layer is passed to the output layer, which produces the final predictions.

By understanding the role and functionality of hidden layers, students can appreciate how neural networks transform input data into meaningful predictions through intermediate computations.

This foundational knowledge is crucial for designing and training effective AI models.

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