How to Use This Demo:
• Set input values and target output to define the learning task
• Adjust learning rate to control the step size for weight updates
• Click "Step Optimization" to perform one iteration of backpropagation
• Use "Reset Weights" to start with new random weights
• Hover over table entries to highlight corresponding network connections
• Watch the loss decrease over multiple optimization steps

Network Configuration:
• Architecture: 2 inputs → 3 hidden (ReLU) → 1 output (linear)
• Loss function: Mean Squared Error (MSE)
• Optimization: Gradient descent with adjustable learning rate

Network Visualization:
• Node values: Show current activations after forward pass
• Connection thickness: Represents weight magnitudes

Parameter Tables:
• Weights table: Current weight values for all connections
• Hover highlighting: Shows which connection each table entry represents

Loss History Graph:
• Tracks MSE loss over optimization steps
• Shows learning progress as loss decreases
• Illustrates effect of learning rate on convergence

Learning Rate Guidelines:
• Start with learning rates around 0.01-0.1
• Too high: Loss may oscillate or diverge
• Too low: Very slow convergence
• Observe loss curve to assess if rate is appropriate

Training Observations:
• Watch how gradients propagate backward through layers
• Notice that output layer gradients are typically larger
• Hidden layer gradients depend on both forward activations and backward error signals
• ReLU activation sets gradients to zero for negative inputs (dead neurons)

Practical Insights:
• Multiple steps usually needed to reach good solutions
• Different input-target pairs will produce different gradient patterns
• Weight initialization affects convergence speed and final solution
• Real applications use mini-batches and advanced optimizers (Adam, RMSprop)