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

Concepts98

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‘MathIntermediate

Rรฉnyi Entropy & Divergence

Rรฉnyi entropy generalizes Shannon entropy by measuring uncertainty with a tunable emphasis on common versus rare outcomes.

#renyi entropy#renyi divergence#shannon entropy+12
โˆ‘MathIntermediate

Law of Large Numbers

The Weak Law of Large Numbers (WLLN) says that the sample average of independent, identically distributed (i.i.d.) random variables with finite mean gets close to the true mean with high probability as the sample size grows.

#law of large numbers
12345
Advanced
#weak law
#sample mean
+12
โˆ‘MathIntermediate

Pseudoinverse (Moore-Penrose)

The Mooreโ€“Penrose pseudoinverse generalizes matrix inversion to rectangular or singular matrices and is denoted Aโบ.

#pseudoinverse#moore-penrose#least squares+12
โˆ‘MathIntermediate

Kronecker Product & Vec Operator

The Kronecker product A โŠ— B expands a small matrix into a larger block matrix by multiplying every entry of A with the whole matrix B.

#kronecker product#vec operator#block matrix+12
โˆ‘MathIntermediate

Orthogonal & Unitary Matrices

Orthogonal (real) and unitary (complex) matrices are length- and angle-preserving transformations, like perfect rotations and reflections.

#orthogonal matrix#unitary matrix#conjugate transpose+12
โˆ‘MathIntermediate

Group Theory for Neural Networks

Group theory gives a precise language for symmetries, and neural networks can exploit these symmetries to learn faster and generalize better.

#group theory#neural networks#equivariance+12
โˆ‘MathIntermediate

Hidden Markov Models

A Hidden Markov Model (HMM) describes sequences where you cannot see the true state directly, but you can observe outputs generated by those hidden states.

#hidden markov model#forward algorithm#viterbi+12
โˆ‘MathIntermediate

State Space Models (SSM)

A State Space Model (SSM) describes a dynamical system using a state vector x(t) that evolves via a first-order matrix differential equation and produces outputs y(t).

#state space#matrix exponential#controllability+12
โˆ‘MathIntermediate

Surrogate Loss Theory

0-1 loss directly measures classification error but is discontinuous and non-convex, making optimization computationally hard.

#surrogate loss#0-1 loss#hinge loss+12
โˆ‘MathIntermediate

Huber Loss & Smooth L1

Huber loss behaves like mean squared error (quadratic) for small residuals and like mean absolute error (linear) for large residuals, making it both stable and robust.

#huber loss#smooth l1#robust regression+12
โˆ‘MathIntermediate

Cross-Entropy Loss

Cross-entropy loss measures how well predicted probabilities match the true labels by penalizing confident wrong predictions heavily.

#cross-entropy#binary cross-entropy#softmax+11
โˆ‘MathIntermediate

Discount Factor & Return

The discounted return G_t sums all future rewards but down-weights distant rewards by powers of a discount factor ฮณ.

#discount factor#discounted return#reinforcement learning+12