How to Use This Demo:
• Adjust the input values using the sliders or enter custom values
• Click on any node to view and modify its incoming weights
• Use Add Layer and Remove Layer buttons to change network architecture
• Change the number of units in each hidden layer using the controls
• Select different activation functions for each layer to see their effects
• Watch how values propagate through the network in real-time
• Use "Generate Random Inputs" to test with different input combinations

Interactive Features:
• Weight editing: Click any neuron to modify its incoming weights
• Architecture modification: Add/remove layers dynamically
• Layer customization: Change neuron counts and activation functions

Layer Types:
• Input Layer (Blue): 3 input values that you control
• Hidden Layers (Purple): Transform inputs using weights and activation functions
• Output Layer (Green): Single output value representing the network's prediction

Visual Elements:
• Node background intensity represents value magnitudes (brighter = larger values)
• Node colors distinguish positive (cooler hues) vs negative (warmer hues) values
• Node borders are green for positive, red for negative values
• Text color automatically adjusts for readability (white on dark backgrounds)
• Pre-activation labels are green for positive, red for negative values
• Connection thickness represents weight magnitudes
• Values display shows both pre-activation → post-activation for each neuron

Mathematical Foundation:
Each neuron computes a weighted sum of its inputs, then applies an activation function:

$$z_i=\sum _j{w}_{ij}{x}_j+b_i$$ $$a_i=f(z_i)$$

Where $z_i$ is the pre-activation, $a_i$ is the post-activation output, $w_{ij}$ are weights, and $f()$ is the activation function.

Activation Functions:
• Linear: $f(x)=x$ (preserves input)
• ReLU: $f(x)=max(0,x)$ (introduces non-linearity while remaining simple)
• Sigmoid: $f(x)=\frac{1}{1+e^{-x}}$ (squashes to [0,1] range)
• Tanh: $f(x)=\tanh (x)$ (squashes to [-1,1] range, zero-centered)

Non-linear activations enable the network to learn complex patterns.

Architecture Guidelines:
• Start with 1-2 hidden layers for most problems
• Use 10-100 neurons per layer as a starting point
• Deeper networks can model more complex relationships but may be harder to train
• Width vs depth trade-offs: wider layers vs more layers

Activation Function Selection:
• ReLU is most common for hidden layers (fast computation, avoids vanishing gradients)
• Sigmoid for binary classification output layers
• Linear for regression output layers
• Tanh sometimes better than sigmoid in hidden layers (zero-centered)

Practical Considerations:
• Observe how different architectures affect the output for the same inputs
• Notice how activation functions shape the transformation at each layer
• Experiment with weight values to understand their impact
• Real networks require training data and optimization algorithms