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Mathematics,
Algorithms & AI.

Notes on the questions in mathematics, algorithms and AI that are worth understanding more than once: what structure a result depends on, why a method works, and under what conditions it fails.

Structure/Mechanism/Boundary

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Est. 2025Mathematics · Algorithms · AIShanghai

STRUCTURE

Mathematics clarifies structure

Find, among definitions, assumptions and derivations, the part that actually decides the result.

MECHANISM

Algorithms explain process

Follow invariants, information flow and computational steps instead of only stating the outcome.

BOUNDARY

Verification marks the boundary

Use counterexamples, experiments and sources to show when a claim holds and when it breaks.

Latest

Latest notes

All 5 notes →
Learning TheoryFoundation Littlestone Dimension Littlestone dimension, the optimal mistake bound, and the SOA proof, with a comparison to VC dimension. Read → Reinforcement LearningMechanism Policy Gradient from an Optimization Viewpoint One continuous line from the objective to gradient estimation, variance and stepsize choice. Read → Deep LearningPaper Reading LeWorldModel / SIGReg: Why Doesn't It Collapse? Connecting latent prediction, representation collapse and SIGReg, and identifying the conditions the mechanism actually depends on. Read → Information TheoryDerivation Typical Sets: Where Probability Mass Lives in High Dimensions Why does probability mass sit on a thin shell rather than at the point of highest density? Read →

Knowledge map

Knowledge map

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∑ Mathematical Foundations∇ Algorithms & Optimizationψ Learning Systems derives requires extends to applied in requires applied in extends to extends to extends to contrast Law of LargeNumbers Shannon Entropy KL Divergence &Cross Entropy TypicalSet & AEP StochasticGradient Methods MDPs & ValueFunctions Policy Gradient ScaledDot-ProductAttention VAE & ELBO Score Matching ConditionalTechnique ProbabilityFlow ODE LeWorldModel /SIGReg Probability1/4Statistics0/2Information Theory1/4Optimization1/3Reinforcement Learning1/3Learning Theoryno nodes yetDeep Learning3/5Generative Models0/5
Keya coloured region is a subject; concepts where regions overlap belong to each of thembeads on a card: the subjects it belongs torelations appear when you point at or select a concept9 of 13 concepts span more than one subject
NodesConceptTheoremMethodModelPaperwrittenplannedSelect a subject name to open its map; select a concept to read about it4 / 13 written

Select a subject name to open its map; select a concept to read about it4 / 13 written

Probability1/4

Statistics0/2

Information Theory1/4

Optimization1/3

Reinforcement Learning1/3

Deep Learning3/5

Generative Models0/5

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