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Concepts95

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📐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

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🔷All∑Math⚙️Algo🗂️DS📚Theory

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📚TheoryIntermediate

Topological Data Analysis (TDA)

Topological Data Analysis (TDA) studies the shape of data using tools from algebraic topology, producing summaries like Betti numbers, barcodes, and persistence diagrams.

#topological data analysis#persistent homology#vietoris–rips complex+12
📚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.

34567
Advanced
#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
📚TheoryIntermediate

Cross-Entropy

Cross-entropy measures how well a proposed distribution Q predicts outcomes actually generated by a true distribution P.

#cross-entropy#entropy#kl divergence+12
📚TheoryIntermediate

KL Divergence

KL divergence measures how much information is lost when using model Q to approximate the true distribution P.

#kl divergence#relative entropy#cross-entropy+12
📚TheoryIntermediate

Empirical Risk Minimization

Empirical Risk Minimization (ERM) chooses a model that minimizes the average loss on the training data.

#empirical risk minimization#expected risk#loss function+12
📚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#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
📚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
📚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