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Concepts57

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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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📚TheoryAdvanced

Random Matrix Theory in High-Dimensional Statistics

Random Matrix Theory (RMT) explains how eigenvalues of large random matrices behave when the dimension p is comparable to the sample size n.

#random matrix theory#marchenko-pastur#wigner semicircle+12
📚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
12345
Advanced
#eigenvalues
#singular values
+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
📚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
📚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
📚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
📚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
📚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
📚TheoryAdvanced

Quantum Computing Theory

Quantum computing uses qubits that can be in superpositions, enabling interference-based computation beyond classical bits.

#quantum computing#qubit#superposition+12