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Concepts187

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
⚙️AlgorithmIntermediate

Discrete Fourier Transform (DFT) & FFT

The Discrete Fourier Transform (DFT) converts a length-N sequence from the time (or spatial) domain into N complex frequency coefficients that describe how much of each sinusoid is present.

#dft#fft#cooley-tukey+12
⚙️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
12345
#fisher information
#empirical fisher
+12
⚙️AlgorithmIntermediate

Numerical Differentiation & Finite Differences

Numerical differentiation uses finite differences to estimate derivatives when an analytical derivative is hard or impossible to obtain.

#numerical differentiation#finite differences#forward difference+12
⚙️AlgorithmIntermediate

Numerical Integration & Monte Carlo

Numerical integration approximates the area under a curve when an exact antiderivative is unknown, using deterministic quadrature rules or random sampling (Monte Carlo).

#numerical integration#quadrature#trapezoidal rule+11
⚙️AlgorithmIntermediate

Matrix Factorizations (Numerical)

Matrix factorizations rewrite a matrix into simpler building blocks (triangular or orthogonal) that make solving and analyzing linear systems much easier.

#lu decomposition#qr factorization#householder reflections+12
⚙️AlgorithmIntermediate

Iterative Methods for Linear Systems

The Conjugate Gradient (CG) method solves large, sparse, symmetric positive definite (SPD) linear systems Ax = b using only matrix–vector products and dot products.

#conjugate gradient#iterative solver#krylov subspace+12
⚙️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
⚙️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
⚙️AlgorithmIntermediate

Proximal Operators & Methods

A proximal operator pulls a point x toward minimizing a function f while penalizing how far it moves, acting like a denoiser or projector depending on f.

#proximal operator#ista#fista+12
⚙️AlgorithmIntermediate

Bootstrap & Resampling Methods

Bootstrap is a resampling method that estimates uncertainty by repeatedly sampling with replacement from the observed data.

#bootstrap#resampling#confidence intervals+12
⚙️AlgorithmIntermediate

Gradient Clipping & Normalization

Gradient clipping limits how large gradient values or their overall magnitude can become during optimization to prevent exploding updates.

#gradient clipping#clipping by norm#clipping by value+12
⚙️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