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Concepts532

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
∑MathAdvanced

Persistent Homology

Persistent homology tracks how topological features (components, loops, voids) appear and disappear as you grow a scale parameter over a filtered simplicial complex.

#persistent homology#filtration#vietoris-rips+12
∑MathAdvanced

Manifolds & Manifold Hypothesis

A manifold is a space that locally looks like Euclidean space, stitched together by coordinate charts and smooth transition maps.

#manifold
1112131415
#topological manifold
#smooth manifold
+12
∑MathAdvanced

Topological Spaces & Continuity

A topological space abstracts the idea of “closeness” using open sets instead of distances, allowing geometry without measuring lengths.

#topological space#open set#continuity+12
∑MathIntermediate

Random Walks on Graphs

A random walk on a graph moves from a node to one of its neighbors chosen uniformly at random at each step.

#random walk#transition matrix#stationary distribution+11
📚TheoryIntermediate

Graph Isomorphism & WL Test

Graph isomorphism asks whether two graphs are the same up to renaming vertices; the Weisfeiler–Leman (WL) test is a powerful heuristic that often distinguishes non-isomorphic graphs quickly.

#weisfeiler-leman#color refinement#graph isomorphism+10
📚TheoryIntermediate

Message Passing Framework

Message Passing Neural Networks (MPNNs) learn on graphs by letting nodes repeatedly exchange and aggregate messages from their neighbors.

#message passing neural network#mpnn#graph neural network+12
∑MathIntermediate

Graph Laplacian

The graph Laplacian translates a graph’s connectivity into a matrix that measures how much a function varies across edges.

#graph laplacian#laplacian matrix#normalized laplacian+11
∑MathBeginner

Graph Fundamentals

A graph models relationships between items using vertices (nodes) and edges (links).

#graph#vertex#edge+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