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How I Study AI - Learn AI Papers & Lectures the Easy Way

Concepts172

Groups

๐Ÿ“Linear Algebra15๐Ÿ“ˆCalculus & Differentiation10๐ŸŽฏOptimization14๐ŸŽฒProbability Theory12๐Ÿ“ŠStatistics for ML9๐Ÿ“กInformation Theory10๐Ÿ”บConvex Optimization7๐Ÿ”ขNumerical Methods6๐Ÿ•ธGraph Theory for Deep Learning6๐Ÿ”ตTopology for ML5๐ŸŒDifferential Geometry6โˆžMeasure Theory & Functional Analysis6๐ŸŽฐRandom Matrix Theory5๐ŸŒŠFourier Analysis & Signal Processing9๐ŸŽฐSampling & Monte Carlo Methods10๐Ÿง Deep Learning Theory12๐Ÿ›ก๏ธRegularization Theory11๐Ÿ‘๏ธAttention & Transformer Theory10๐ŸŽจGenerative Model Theory11๐Ÿ”ฎRepresentation Learning10๐ŸŽฎReinforcement Learning Mathematics9๐Ÿ”„Variational Methods8๐Ÿ“‰Loss Functions & Objectives10โฑ๏ธSequence & Temporal Models8๐Ÿ’ŽGeometric Deep Learning8

Category

๐Ÿ”ทAllโˆ‘Mathโš™๏ธAlgo๐Ÿ—‚๏ธDS๐Ÿ“šTheory

Level

AllBeginnerIntermediate
โˆ‘MathAdvanced

Betti Numbers

Betti numbers count independent k-dimensional holes: ฮฒโ‚€ counts connected components, ฮฒโ‚ counts independent loops/tunnels, and ฮฒโ‚‚ counts voids.

#betti numbers#homology#simplicial complex+12
โˆ‘MathAdvanced

Persistent Homology

Persistent homology tracks how topological features (components, loops, voids) appear and disappear as you grow a scale parameter over a filtered simplicial complex.

#persistent homology
34567
Advanced
#filtration
#vietoris-rips
+12
โˆ‘MathAdvanced

Manifolds & Manifold Hypothesis

A manifold is a space that locally looks like Euclidean space, stitched together by coordinate charts and smooth transition maps.

#manifold#topological manifold#smooth manifold+12
โˆ‘MathAdvanced

Topological Spaces & Continuity

A topological space abstracts the idea of โ€œclosenessโ€ using open sets instead of distances, allowing geometry without measuring lengths.

#topological space#open set#continuity+12
โš™๏ธAlgorithmAdvanced

Interior Point Methods

Interior point methods solve constrained optimization by replacing hard constraints with a smooth barrier that becomes infinite at the boundary, keeping iterates strictly inside the feasible region.

#interior point method#logarithmic barrier#central path+12
โš™๏ธAlgorithmAdvanced

ADMM (Alternating Direction Method of Multipliers)

ADMM splits a hard optimization problem into two easier subproblems that communicate through simple averaging-like steps.

#admm#alternating direction method of multipliers#augmented lagrangian+11
โˆ‘MathAdvanced

KKT Conditions

KKT conditions generalize Lagrange multipliers to handle inequality constraints in constrained optimization problems.

#kkt conditions#lagrangian#complementary slackness+12
๐Ÿ“šTheoryAdvanced

Maximum Entropy Principle

The Maximum Entropy Principle picks the probability distribution with the greatest uncertainty (entropy) that still satisfies the facts you know (constraints).

#maximum entropy principle#jaynes#exponential family+12
๐Ÿ“šTheoryAdvanced

Rate-Distortion Theory

Rateโ€“distortion theory tells you the minimum number of bits per symbol needed to represent data while keeping average distortion below a target D.

#rate-distortion#mutual information#blahut-arimoto+12
๐Ÿ“šTheoryAdvanced

Information Bottleneck

The Information Bottleneck (IB) principle formalizes the tradeoff between compressing an input X and preserving information about a target Y using the objective min_{p(t|x)} I(X;T) - \beta I(T;Y).

#information bottleneck#mutual information#kl divergence+12
โš™๏ธAlgorithmAdvanced

Newton's Method & Second-Order Optimization

Newton's method uses both the gradient and the Hessian to take steps that aim directly at the local optimum by fitting a quadratic model of the loss around the current point.

#newton's method#second-order optimization#hessian+12
๐Ÿ—‚๏ธData StructureAdvanced

Sqrt Tree

A sqrt tree is a layered block-decomposition data structure that answers range queries in O(1) time after O(n \log \log n) preprocessing.

#sqrt tree#range query#associative operation+11