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How I Study AI - Learn AI Papers & Lectures the Easy Way

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
📚TheoryAdvanced

Spectral Analysis of Neural Networks

Spectral analysis studies the distribution of eigenvalues and singular values of neural network weight matrices during training.

#spectral analysis#eigenvalues#singular values+12
📚TheoryIntermediate

Universal Approximation Theorems

The Universal Approximation Theorems say that a neural network with at least one hidden layer and a suitable activation can approximate any continuous function on a compact domain as closely as you like.

#universal approximation theorem
56789
#cybenko
#hornik
+12
📚TheoryAdvanced

Reproducing Kernel Hilbert Spaces (RKHS)

An RKHS is a space of functions where evaluating a function at a point equals taking an inner product with a kernel section, which enables the “kernel trick.”

#rkhs#kernel trick#gram matrix+12
📚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.

#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
📚TheoryAdvanced

Maximum Entropy Principle

The Maximum Entropy Principle picks the probability distribution with the greatest uncertainty (entropy) that still satisfies the facts you know (constraints).

#maximum entropy principle#jaynes#exponential family+12
📚TheoryAdvanced

Rate-Distortion Theory

Rate–distortion theory tells you the minimum number of bits per symbol needed to represent data while keeping average distortion below a target D.

#rate-distortion#mutual information#blahut-arimoto+12
📚TheoryAdvanced

Information Bottleneck

The Information Bottleneck (IB) principle formalizes the tradeoff between compressing an input X and preserving information about a target Y using the objective min_{p(t|x)} I(X;T) - \beta I(T;Y).

#information bottleneck#mutual information#kl divergence+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