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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

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AllBeginnerIntermediate
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
23456
Advanced
#random matrix
#empirical spectral distribution
+12
๐Ÿ“šTheoryAdvanced

Reproducing Kernel Hilbert Spaces (RKHS)

An RKHS is a space of functions where evaluating a function at a point equals taking an inner product with a kernel section, which enables the โ€œkernel trick.โ€

#rkhs#kernel trick#gram matrix+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
โš™๏ธAlgorithmAdvanced

Natural Gradient Method

Natural gradient scales the ordinary gradient by the inverse Fisher information matrix to account for the geometry of probability distributions.

#natural gradient#fisher information#empirical fisher+12
โˆ‘MathAdvanced

Lie Groups & Lie Algebras

Lie groups model continuous symmetries like rotations and rigid-body motions, combining algebra (group law) and calculus (smooth manifolds).

#lie group#lie algebra#so(3)+12
โˆ‘MathAdvanced

Curvature

Curvature measures how a geometric object bends, and it comes in several flavors: Gaussian, sectional, and Ricci curvature.

#gaussian curvature#sectional curvature#ricci curvature+11
โˆ‘MathAdvanced

Geodesics & Exponential Map

Geodesics are the โ€œstraightest possibleโ€ paths on curved spaces (manifolds) and locally minimize distance.

#geodesic#exponential map#riemannian metric+12
โˆ‘MathAdvanced

Smooth Manifolds & Tangent Spaces

A smooth manifold is a space that looks like ordinary Euclidean space when you zoom in, glued together using charts that transition smoothly.

#smooth manifolds#tangent space#chart+11