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Concepts152

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
📚TheoryIntermediate

Bayesian Inference

Bayesian inference updates prior beliefs with observed data to produce a posterior distribution P(\theta\mid D).

#bayesian inference#posterior#prior+12
📚TheoryIntermediate

Loss Landscape Analysis

A loss landscape is the “terrain” of a model’s loss as you move through parameter space; valleys are good solutions and peaks are bad ones.

#loss landscape
678910
#sharpness
#hessian eigenvalues
+12
📚TheoryIntermediate

Weight Initialization Strategies

Weight initialization sets the starting values of neural network parameters so signals and gradients neither explode nor vanish as they pass through layers.

#xavier#glorot#he+12
📚TheoryIntermediate

Automatic Differentiation

Automatic differentiation (AD) computes exact derivatives by systematically applying the chain rule to your program, not by symbolic algebra or numerical differences.

#automatic differentiation#dual numbers#forward mode+12
📚TheoryAdvanced

PAC-Bayes Theory

PAC-Bayes provides high-probability generalization bounds for randomized predictors by comparing a data-dependent posterior Q to a fixed, data-independent prior P through KL(Q||P).

#pac-bayes#generalization bound#kl divergence+12
📚TheoryIntermediate

Concentration Inequalities

Concentration inequalities give high-probability bounds that random outcomes stay close to their expectations, even without knowing the full distribution.

#concentration inequalities#hoeffding inequality#chernoff bound+12
📚TheoryAdvanced

MCMC Theory

MCMC simulates a Markov chain whose long-run behavior matches a target distribution, letting us sample from complex posteriors without knowing the normalization constant.

#mcmc#metropolis-hastings#gibbs sampling+11
📚TheoryIntermediate

Markov Chain Theory

A Markov chain is a random process where the next state depends only on the current state, not the full history.

#markov chain#transition matrix#stationary distribution+12
📚TheoryAdvanced

Graph Neural Network Theory

Graph Neural Networks (GNNs) learn on graphs by repeatedly letting each node aggregate messages from its neighbors and update its representation.

#graph neural networks#message passing#weisfeiler-leman+12
📚TheoryAdvanced

Differential Privacy Theory

Differential privacy (DP) guarantees that the output of a randomized algorithm does not change much when one person’s data is added or removed.

#differential privacy#epsilon delta dp#laplace mechanism+12
📚TheoryIntermediate

Spectral Graph Theory

Spectral graph theory studies graphs by looking at eigenvalues and eigenvectors of matrices like the adjacency matrix A and Laplacians L and L_norm.

#spectral graph theory#laplacian#normalized laplacian+12
📚TheoryAdvanced

Information-Theoretic Lower Bounds

Information-theoretic lower bounds tell you the best possible performance any learning algorithm can achieve, regardless of cleverness or compute.

#information-theoretic lower bounds#fano inequality#le cam method+12