๐ŸŽ“How I Study AIHISA
๐Ÿ“–Read
๐Ÿ“„Papers๐Ÿ“ฐBlogs๐ŸŽฌCourses
๐Ÿ’กLearn
๐Ÿ›ค๏ธPaths๐Ÿ“šTopics๐Ÿ’กConcepts๐ŸŽดShorts
๐ŸŽฏPractice
๐Ÿ“Daily Log๐ŸŽฏPrompts๐Ÿง Review
SearchSettings
How I Study AI - Learn AI Papers & Lectures the Easy Way

Concepts39

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

f-Divergences

An f-divergence measures how different two probability distributions P and Q are by averaging a convex function f of the density ratio p(x)/q(x) under Q.

#f-divergence#csiszar divergence#kullbackโ€“leibler+11
โˆ‘MathAdvanced

Copulas & Dependency Structures

A copula is a function that glues together marginal distributions to form a multivariate joint distribution while isolating dependence from the margins.

#copula
1234
Advanced
#sklar's theorem
#gaussian copula
+12
โˆ‘MathAdvanced

Spherical Harmonics & SO(3) Representations

Spherical harmonics are smooth wave patterns on the sphere that form an orthonormal basis, much like sine and cosine form a basis on the circle.

#spherical harmonics#so(3)#wigner d-matrix+12
โˆ‘MathAdvanced

Evidence Lower Bound (ELBO)

The Evidence Lower Bound (ELBO) is a tractable lower bound on the log evidence log p(x) used to perform approximate Bayesian inference.

#elbo#variational inference#vae+12
โˆ‘MathAdvanced

Stochastic Differential Equations for Generation

A forward stochastic differential equation (SDE) models a state that drifts deterministically and is shaken by random Brownian noise over time.

#stochastic differential equation#diffusion model#euler maruyama+12
โˆ‘MathAdvanced

Free Probability Theory

Free probability studies "random variables" that do not commute, where independence is replaced by freeness and noncrossing combinatorics replaces classical partitions.

#free probability#freeness#r-transform+11
โˆ‘MathAdvanced

Marchenko-Pastur Distribution

The Marchenkoโ€“Pastur (MP) distribution describes the limiting eigenvalue distribution of sample covariance matrices S = (1/n) XX^{\top} when both the dimension p and the sample size n grow with p/n \to \gamma.

#marchenko-pastur#random matrix theory#sample covariance+10
โˆ‘MathAdvanced

Wigner Semicircle Law

The Wigner Semicircle Law says that the histogram of eigenvalues of large random symmetric matrices converges to a semicircle-shaped curve.

#wigner semicircle law#random matrix#empirical spectral distribution+12
โˆ‘MathAdvanced

Banach Spaces

A Banach space is a vector space with a norm where every Cauchy sequence actually converges within the space.

#banach space#normed vector space#completeness+11
โˆ‘MathAdvanced

Hilbert Spaces

A Hilbert space is an inner product space that is complete, meaning Cauchy sequences converge to points inside the space.

#hilbert space#inner product#l2 space+12
โˆ‘MathAdvanced

Lebesgue Integration

Lebesgue integration measures how much time a function spends near each value and adds up value ร— size of the set where it occurs.

#lebesgue integral#riemann integral#measure theory+12
โˆ‘MathAdvanced

Sigma-Algebras & Measure Spaces

A ฯƒ-algebra is a collection of subsets that is closed under complements and countable unions, giving us a stable universe of sets where measure makes sense.

#sigma-algebra#measure space#measurable sets+12