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Concepts140

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
∑MathIntermediate

Rényi Entropy & Divergence

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

#renyi entropy#renyi divergence#shannon entropy+12
∑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
12345
#csiszar divergence
#kullback–leibler
+11
∑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#sklar's theorem#gaussian copula+12
∑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#weak law#sample mean+12
∑MathIntermediate

Pseudoinverse (Moore-Penrose)

The Moore–Penrose pseudoinverse generalizes matrix inversion to rectangular or singular matrices and is denoted A⁺.

#pseudoinverse#moore-penrose#least squares+12
∑MathIntermediate

Kronecker Product & Vec Operator

The Kronecker product A ⊗ 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
∑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
∑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
∑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
∑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
∑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
∑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