lectures/Machine_MOC.md

metadata

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

🗺️ Machine: Map of Content (MOC)

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.