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Concepts172

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📐Linear Algebra15📈Calculus & Differentiation10🎯Optimization14🎲Probability Theory12📊Statistics for ML9📡Information Theory10🔺Convex Optimization7🔢Numerical Methods6🕸Graph Theory for Deep Learning6🔵Topology for ML5🌐Differential Geometry6∞Measure Theory & Functional Analysis6🎰Random Matrix Theory5🌊Fourier Analysis & Signal Processing9🎰Sampling & Monte Carlo Methods10🧠Deep Learning Theory12🛡️Regularization Theory11👁️Attention & Transformer Theory10🎨Generative Model Theory11🔮Representation Learning10🎮Reinforcement Learning Mathematics9🔄Variational Methods8📉Loss Functions & Objectives10⏱️Sequence & Temporal Models8💎Geometric Deep Learning8

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🔷All∑Math⚙️Algo🗂️DS📚Theory

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🗂️Data StructureAdvanced

Dominator Tree

A dominator tree summarizes “must-pass” relationships in a directed graph from a chosen root r: u dominates v if every path from r to v goes through u.

#dominator tree#lengauer tarjan#semidominator+10
🗂️Data StructureAdvanced

Chtholly Tree (ODT - Old Driver Tree)

Chtholly Tree (ODT) stores an array as a set of non-overlapping value-constant intervals and updates by cutting and replacing whole ranges.

#odt
45678
Advanced
#chtholly tree
#range assign
+9
⚙️AlgorithmAdvanced

3D Geometry Basics

3D geometry relies on a small toolkit: vectors, dot products, cross products, and planes; mastering these unlocks most 3D problem-solving.

#3d geometry#dot product#cross product+12
🗂️Data StructureAdvanced

Segment Tree with Range Affine Transformation

A segment tree with lazy propagation can support range updates of the form x → a·x + b (affine transformations) and range-sum queries in O(log n) per operation.

#segment tree#lazy propagation#affine update+12
🗂️Data StructureAdvanced

Persistent DSU (Fully Persistent Union-Find)

A persistent DSU (Union-Find) keeps all historical versions so you can query connectivity at any past version and even branch new futures from old states.

#persistent dsu#fully persistent union-find#union by rank+12
⚙️AlgorithmAdvanced

Directed MST (Edmonds/Chu-Liu Algorithm)

A directed minimum spanning arborescence (MSA) is a minimum-cost set of edges that makes every vertex reachable from a chosen root with exactly one incoming edge per non-root vertex.

#directed mst#edmonds algorithm#chu-liu+11
∑MathAdvanced

Floor Sum Formula

The floor sum computes S(n,m,a,b) = sum_{i=0}^{n-1} floor((a i + b)/m) efficiently in O(log(min(a,m))) time.

#floor sum#atcoder library#euclidean algorithm+12
📚TheoryAdvanced

PAC-Bayes Theory

PAC-Bayes provides high-probability generalization bounds for randomized predictors by comparing a data-dependent posterior Q to a fixed, data-independent prior P through KL(Q||P).

#pac-bayes#generalization bound#kl divergence+12
📚TheoryAdvanced

MCMC Theory

MCMC simulates a Markov chain whose long-run behavior matches a target distribution, letting us sample from complex posteriors without knowing the normalization constant.

#mcmc#metropolis-hastings#gibbs sampling+11
📚TheoryAdvanced

Graph Neural Network Theory

Graph Neural Networks (GNNs) learn on graphs by repeatedly letting each node aggregate messages from its neighbors and update its representation.

#graph neural networks#message passing#weisfeiler-leman+12
📚TheoryAdvanced

Differential Privacy Theory

Differential privacy (DP) guarantees that the output of a randomized algorithm does not change much when one person’s data is added or removed.

#differential privacy#epsilon delta dp#laplace mechanism+12
📚TheoryAdvanced

Information-Theoretic Lower Bounds

Information-theoretic lower bounds tell you the best possible performance any learning algorithm can achieve, regardless of cleverness or compute.

#information-theoretic lower bounds#fano inequality#le cam method+12