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Concepts46

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

AllBeginnerIntermediate
⚙️AlgorithmAdvanced

Wake-Sleep Algorithm

The Wake–Sleep algorithm trains a pair of models: a generative model that explains how data are produced and a recognition model that guesses hidden causes from observed data.

#wake-sleep#helmholtz machine#generative model+12
⚙️AlgorithmAdvanced

Stochastic Variational Inference

Stochastic Variational Inference (SVI) scales variational inference to large datasets by taking noisy but unbiased gradient steps using minibatches.

#stochastic variational inference
1234
Advanced
#elbo
#variational inference
+12
⚙️AlgorithmAdvanced

Langevin Dynamics & Score-Based Sampling

Langevin dynamics is a noisy gradient-ascent method that moves particles toward high probability regions while adding Gaussian noise to ensure proper exploration.

#langevin dynamics#mala#ula+12
⚙️AlgorithmAdvanced

Hamiltonian Monte Carlo (HMC)

Hamiltonian Monte Carlo (HMC) uses gradients of the log-density to propose long-distance moves that still land in high-probability regions.

#hamiltonian monte carlo#hmc#mcmc+11
⚙️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
⚙️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
⚙️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
⚙️AlgorithmAdvanced

3D Geometry Basics

3D geometry relies on a small toolkit: vectors, dot products, cross products, and planes; mastering these unlocks most 3D problem-solving.

#3d geometry#dot product#cross product+12
⚙️AlgorithmAdvanced

Directed MST (Edmonds/Chu-Liu Algorithm)

A directed minimum spanning arborescence (MSA) is a minimum-cost set of edges that makes every vertex reachable from a chosen root with exactly one incoming edge per non-root vertex.

#directed mst#edmonds algorithm#chu-liu+11
⚙️AlgorithmAdvanced

DP on Broken Profile - Plug DP

Plug DP (DP on broken profile with plugs) sweeps a grid cell by cell while remembering how partial path segments cross the frontier as labeled “plugs.”

#plug dp#broken profile#hamiltonian path+12
⚙️AlgorithmAdvanced

Matrix Exponentiation - Advanced

Matrix exponentiation turns repeated linear transitions into fast O(n^{3} log k) computation using exponentiation by squaring.

#matrix exponentiation#adjacency matrix#walk counting+12