lectures/Machine_Learning_MOC.md

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

# 🗺️ Machine Learning: Map of Content (MOC)

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

---

## 📅 1. Chronological Lecture Syllabus

| Date | Topic | Note Link |
| :--- | :--- | :--- |
| `2026-08-19` | Curl Test | [[2026-08-19_Machine_Learning_Curl_Test\|Curl Test Note]] |
| `2026-08-19` | Quick Test | [[2026-08-19_Machine_Learning_Quick_Test\|Quick Test Note]] |
| `2026-10-15` | Backpropagation | [[2026-10-15_Machine_Learning_Backpropagation\|Backpropagation Note]] |

---

## 📐 2. Key Derivations & Theorems Index

- **[[2026-10-15_Machine_Learning_Backpropagation#Forward Pass Equations|Forward Pass Equations]]** _(Topic: Backpropagation, Date: `2026-10-15`)_
- **[[2026-10-15_Machine_Learning_Backpropagation#Backward Pass & Gradient Equations|Backward Pass & Gradient Equations]]** _(Topic: Backpropagation, Date: `2026-10-15`)_
- **[[2026-10-15_Machine_Learning_Backpropagation#Section 2: Mathematical Formulation|Section 2: Mathematical Formulation]]** _(Topic: Backpropagation, Date: `2026-10-15`)_

---

## ⚠️ 3. High-Yield Exam Pitfalls Aggregator

### From [[2026-08-19_Machine_Learning_Curl_Test|Curl Test (2026-08-19)]]:
> - Highlight direct warnings, potential exam questions, and common conceptual traps.

### From [[2026-08-19_Machine_Learning_Quick_Test|Quick Test (2026-08-19)]]:
> - **Dimension Mismatch:** Ensure weight matrices and input vectors satisfy inner-dimension equality ($A \in \mathbb{R}^{n \times d}, x \in \mathbb{R}^{d \times 1}$).
> - **Vanishing Gradients:** Pay attention to non-linear activations in deep networks; professors often test on the Sigmoid/ReLU saturation regions.
> - **Notation Trap:** Always define whether your vectors are column vectors or row vectors at the start of the exam paper.

### From [[2026-10-15_Machine_Learning_Backpropagation|Backpropagation (2026-10-15)]]:
> - **Matrix Dimension Verification**: Dimension checks on parameter gradients are guaranteed exam questions. Always explicitly verify that $\operatorname{dim}\left(\frac{\partial L}{\partial W^{(l)}}\right) = \operatorname{dim}\left(W^{(l)}\right) = (n_l \times n_{l-1})$.
> - **Outer Product Order**: A common mistake is swapping the order in the weight gradient formula. Remember: $\frac{\partial L}{\partial W^{(l)}} = \delta^{(l)} (A^{(l-1)})^T$, NOT $A^{(l-1)} (\delta^{(l)})^T$.
> - **Vanishing Gradient Pathology**: Occurs when pre-activations $Z^{(l)}$ enter the saturated regime of activation functions like Sigmoid ($\sigma'(Z^{(l)}) \approx 0$). Multiplying by near-zero terms recursively drives $\delta^{(l)} \to 0$ for early layers.
> - **Memory Caching Necessity**: Intermediate activations $A^{(l-1)}$ MUST be stored in RAM during the forward pass; without caching, computing $\frac{\partial L}{\partial W^{(l)}}$ requires redundant re-computation of the forward pass.