Backpropagation — Gradient Flow

Description

Demonstrates backpropagation in a 3-layer neural network. A forward pass first computes activations left to right, then a loss is computed. Gradients flow backward through the network as a glowing wave, with the chain rule applied at each layer. The key partial derivative formula is displayed.

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Phases

#	Phase Name	Duration	Description
1	Intro	3s	Title and network displayed
2	Forward Pass	10s	Activations flow left to right with values shown
3	Loss Computation	5s	Loss function displayed; error value shown in red
4	Backward Pass	16s	Gradient glow travels right to left through layers
5	Chain Rule	8s	Chain rule formula displayed layer by layer
6	Weight Update	6s	Show w ← w - lr * ∂L/∂w update
7	Outro	4s	Training loop concept shown

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Layout

+--------------------------------------------------+
|  Title: Backpropagation — Gradient Flow          |
+--------------------------------------------------+
|                                                  |
|  [Input]→→→[Hidden]→→→[Output]→→→[Loss L]       |
|                                                  |
|  Forward: activations flow →                     |
|  Backward: gradients flow ←  (orange glow)       |
|                                                  |
|  Chain rule:                                     |
|  ∂L/∂w = (∂L/∂a)(∂a/∂z)(∂z/∂w)                 |
|                                                  |
|  Weight update:                                  |
|  w ← w - η * ∂L/∂w                              |
+--------------------------------------------------+

Area Descriptions

• Center: 3-layer network with forward (cyan) and backward (orange) flow
• Right: Loss computation box
• Bottom: Chain rule formula panel

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Assets & Dependencies

• Fonts: LaTeX / sans-serif
• Manim version: ManimCE 0.19.1

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Notes

• Forward pass shown as cyan flowing wave
• Backward pass shown as orange/red glowing wave moving in reverse
• Gradient values shown as small floating numbers near weights
• Chain rule decomposed into three factors with color coding