lectures/Machine_MOC.md

---
title: "Machine Map of Content (MOC)"
course: "[[Machine]]"
type: "moc"
updated: "2026-08-20"
tags:
  - moc
  - course/Machine
---

# 🗺️ Machine: Map of Content (MOC)

> [!NOTE] Master Course Knowledge Hub
> This hub connects all lecture notes, derivations, and exam warnings for **Machine**.

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## 📅 1. Chronological Lecture Syllabus

| Date | Topic | Note Link |
| :--- | :--- | :--- |
| `2026-08-19` | Learning Backpropagation 2026 08 19 | [[2026-08-19_Machine_Learning_Backpropagation_2026_08_19\|Learning Backpropagation 2026 08 19 Note]] |

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## 📐 2. Key Derivations & Theorems Index

- **[[2026-08-19_Machine_Learning_Backpropagation_2026_08_19#Forward Pass Formulation|Forward Pass Formulation]]** _(Topic: Learning Backpropagation 2026 08 19, Date: `2026-08-19`)_
- **[[2026-08-19_Machine_Learning_Backpropagation_2026_08_19#Backward Pass Derivations|Backward Pass Derivations]]** _(Topic: Learning Backpropagation 2026 08 19, Date: `2026-08-19`)_
- **[[2026-08-19_Machine_Learning_Backpropagation_2026_08_19#Section 2: Mathematical Formulation|Section 2: Mathematical Formulation]]** _(Topic: Learning Backpropagation 2026 08 19, Date: `2026-08-19`)_

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## ⚠️ 3. High-Yield Exam Pitfalls Aggregator

### From [[2026-08-19_Machine_Learning_Backpropagation_2026_08_19|Learning Backpropagation 2026 08 19 (2026-08-19)]]:
> - **Dimension Verification Mandatory**: Always verify that $\dim\left(\frac{\partial L}{\partial W^{(l)}}\right) = \dim\left(W^{(l)}\right)$. A common exam trap is mixing up the order of the outer product ($\delta^{(l)} (A^{(l-1)})^T$ vs $(A^{(l-1)})^T \delta^{(l)}$).
> - **Activation Caching Requirement**: Remember that intermediate activations $A^{(l-1)}$ are required to compute weight updates during backpropagation. Failing to cache $A^{(l-1)}$ in memory during the forward pass forces redundant recomputations.
> - **Vanishing Gradient Mechanics**: Saturated activations such as Sigmoid $\sigma(z) = \frac{1}{1 + e^{-z}}$ have derivatives bounded by $\sigma'(z) \le 0.25$. As gradients are multiplied across deep layers ($l \ll L$), $\prod \sigma'(Z^{(k)}) \to 0$, causing deep layers to stop updating.