Great question! Neural networks learn through a process called backpropagation, which is essentially a way for the network to adjust its internal parameters based on the errors it makes. Here is how it works at a high level:

• Forward Pass: Input data flows through the network layer by layer, with each neuron applying weights, biases, and an activation function to produce an output.
• Loss Calculation: The network's output is compared to the expected result using a loss function (e.g., Mean Squared Error), which quantifies how wrong the prediction is.
• Backward Pass: The gradient of the loss with respect to each weight is computed using the chain rule of calculus. These gradients indicate how much each weight contributed to the error.

The weights are then updated in the direction that reduces the loss, typically using an optimizer like Stochastic Gradient Descent (SGD). This cycle repeats over many iterations until the network converges on accurate predictions.

Here is a minimal neural network implementation using NumPy that demonstrates the core concepts:

import numpy as np

class SimpleNeuralNetwork:
    def __init__(self, input_size, hidden_size, output_size):
        self.weights1 = np.random.randn(input_size, hidden_size) * 0.01
        self.weights2 = np.random.randn(hidden_size, output_size) * 0.01

    def forward(self, X):
        self.hidden = np.tanh(np.dot(X, self.weights1))
        return np.dot(self.hidden, self.weights2)

This class initializes random weights and implements a forward pass with a tanh activation in the hidden layer. You would extend this with a loss function and backward pass to complete the training loop.

The tanh (hyperbolic tangent) activation function is a popular choice for hidden layers because it maps input values to a range of [-1, 1], making it zero-centered. This helps with gradient flow during backpropagation compared to sigmoid, which outputs values between 0 and 1 and can cause gradients to shift in one direction.

Step 1: Consider activation function requirements
Step 2: Compare sigmoid vs tanh vs ReLU
Step 3: tanh maps to [-1, 1] — zero-centered
Step 4: Better gradient flow than sigmoid
Conclusion: tanh is good for hidden layers

Absolutely! Here are some excellent resources for learning about neural networks and deep learning:

1. Neural Networks and Deep Learning by Michael Nielsen -- A free online book that provides an intuitive, visual explanation of backpropagation and gradient descent with interactive examples.
2. Deep Learning Specialization by Andrew Ng (Coursera) -- A comprehensive 5-course series covering everything from basic neural networks to sequence models and convolutional networks.
3. PyTorch Tutorials (pytorch.org) -- Hands-on, code-first tutorials that let you build and train neural networks from scratch using one of the most popular frameworks.
4. 3Blue1Brown Neural Network Series (YouTube) -- Beautifully animated videos that visually explain the math behind neural networks, including an outstanding episode on backpropagation.