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Concepts532

Groups

📐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

Category

🔷All∑Math⚙️Algo🗂️DS📚Theory

Level

AllBeginnerIntermediateAdvanced
📚TheoryIntermediate

Mutual Information

Mutual Information (MI) measures how much knowing one random variable reduces uncertainty about another.

#mutual information#entropy#kl divergence+12
📚TheoryIntermediate

KL Divergence (Kullback-Leibler Divergence)

Kullback–Leibler (KL) divergence measures how one probability distribution P devotes probability mass differently from a reference distribution Q.

#kl divergence
2526272829
#kullback-leibler
#cross-entropy
+12
📚TheoryIntermediate

Shannon Entropy

Shannon entropy quantifies the average uncertainty or information content of a random variable in bits when using base-2 logarithms.

#shannon entropy#information gain#mutual information+12
📚TheoryIntermediate

Information Theory

Information theory quantifies uncertainty and information using measures like entropy, cross-entropy, KL divergence, and mutual information.

#entropy#cross-entropy#kl divergence+12
⚙️AlgorithmAdvanced

DP on Broken Profile - Plug DP

Plug DP (DP on broken profile with plugs) sweeps a grid cell by cell while remembering how partial path segments cross the frontier as labeled “plugs.”

#plug dp#broken profile#hamiltonian path+12
⚙️AlgorithmAdvanced

Matrix Exponentiation - Advanced

Matrix exponentiation turns repeated linear transitions into fast O(n^{3} log k) computation using exponentiation by squaring.

#matrix exponentiation#adjacency matrix#walk counting+12
🗂️Data StructureAdvanced

Top Tree

Top trees are dynamic tree data structures that represent a forest as a hierarchy of clusters, allowing O(log n) amortized time for link, cut, path queries/updates, and many subtree queries.

#top tree#dynamic tree#link cut+12
⚙️AlgorithmAdvanced

Voronoi Diagram and Delaunay

Voronoi diagrams partition the plane so each region contains points closest to one site, while the Delaunay triangulation connects sites whose Voronoi cells touch.

#voronoi diagram#delaunay triangulation#fortune algorithm+12
∑MathIntermediate

Sprague-Grundy Theorem

Sprague–Grundy theory turns every finite impartial game (normal play) into an equivalent Nim heap with a size called the Grundy number.

#sprague-grundy#grundy number#mex+11
∑MathIntermediate

Game Theory - Nim

Nim is a two-player impartial game with several piles where a move removes any positive number of stones from exactly one pile.

#nim#game theory#xor+11
∑MathIntermediate

Game Theory - Calculation Techniques

Sprague–Grundy theory converts any impartial, normal-play game into an equivalent Nim heap using a Grundy number.

#sprague-grundy#grundy numbers#nim-sum+12
∑MathIntermediate

Variance and Covariance

Variance measures how spread out a random variable is around its mean, while covariance measures how two variables move together.

#variance#covariance#standard deviation+12