Animation Specification: Simple Feedforward Neural Network Flow

Animation Description and Purpose

This animation demonstrates the flow of data through a simple feedforward neural network with 3 layers (input, hidden, output) and 3 neurons per layer. The animation will show numerical input propagating through the network, weighted sums being calculated, and the Sigmoid activation function being applied. The purpose is to visually explain the basic mechanics of a neural network.

Mathematical Elements and Formulas

1. Weighted Sum Calculation: For each neuron, the weighted sum $z$ is calculated as:
   $$z = w_1x_1 + w_2x_2 + w_3x_3 + b$$
   where $w_i$ are weights, $x_i$ are inputs, and $b$ is the bias.

2. Sigmoid Activation Function: The activation $a$ is computed as:
   $$a = \sigma(z) = \frac{1}{1 + e^{-z}}$$

3. Input Values: Generic numerical inputs (e.g., $x_1 = 0.5$, $x_2 = 1.0$, $x_3 = 0.8$).

Visual Elements

1. Neurons: Represented as circles with labels (e.g., $x_1, x_2, x_3$ for input layer, $h_1, h_2, h_3$ for hidden layer, $o_1, o_2, o_3$ for output layer).

   • Input layer: Light blue fill.
   • Hidden layer: Light green fill.
   • Output layer: Light orange fill.

2. Connections: Lines connecting neurons between layers, with small text labels for weights (e.g., $w_{11}$ for the weight from $x_1$ to $h_1$).

3. Activation Function Visualization: A small inset graph showing the Sigmoid function $\sigma(z)$ when a neuron is activated.

4. Mathematical Operations: Temporary text boxes showing the weighted sum and activation calculations as data flows through the network.

5. Input/Output Values: Numerical values displayed near neurons as they are processed.

Animation Timing and Transitions

1. Total Duration: ~25 seconds.

2. Sequence:

   • 0-2s: Introduce the neural network structure (layers and neurons).
   • 2-5s: Show input values appearing at the input layer neurons.
   • 5-10s: Animate the flow of data from input to hidden layer:
     • Highlight connections and show weighted sum calculations.
     • Display the Sigmoid activation function graph and apply it to the weighted sum.
   • 10-15s: Show the activated values flowing to the output layer.
   • 15-20s: Repeat the weighted sum and activation process for the output layer.
   • 20-25s: Display the final output values and summarize the flow.

3. Transitions: Smooth fading and scaling for text/equations. Data flow represented as small animated dots moving along connections.

Camera Angles and Perspectives

• Static camera angle centered on the neural network.
• Zoom in slightly on the hidden layer during the activation function explanation.

Additional Details

• Text Backgrounds: All text (equations, values, labels) will have an opaque white background with black text for readability.
• Color Scheme:
  • Neurons: Light blue (input), light green (hidden), light orange (output).
  • Connections: Gray lines with black weight labels.
  • Activation graph: Purple curve on a light gray background.
• Animation Style: Clean and minimalistic, focusing on clarity and educational value.