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Concepts14

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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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⚙️AlgorithmAdvanced

Wake-Sleep Algorithm

The Wake–Sleep algorithm trains a pair of models: a generative model that explains how data are produced and a recognition model that guesses hidden causes from observed data.

#wake-sleep#helmholtz machine#generative model+12
📚TheoryAdvanced

Variational Dropout & Bayesian Deep Learning

Dropout can be interpreted as variational inference in a Bayesian neural network, where applying random masks approximates sampling from a posterior over weights.

#bayesian neural networks
12
Advanced
Filtering by:
#kl divergence
#variational inference
#dropout
+12
∑MathAdvanced

Evidence Lower Bound (ELBO)

The Evidence Lower Bound (ELBO) is a tractable lower bound on the log evidence log p(x) used to perform approximate Bayesian inference.

#elbo#variational inference#vae+12
📚TheoryAdvanced

Disentangled Representations

Disentangled representations aim to encode independent factors of variation (like shape, size, or color) into separate coordinates of a latent vector.

#disentangled representations#independent factors#total correlation+12
📚TheoryAdvanced

Variational Autoencoders (VAE) Theory

A Variational Autoencoder (VAE) is a probabilistic autoencoder that learns to generate data by inferring hidden causes (latent variables) and decoding them back to observations.

#variational autoencoder#elbo#kl divergence+12
📚TheoryAdvanced

Information Bottleneck in Deep Learning

The Information Bottleneck (IB) principle formalizes learning compact representations T that keep only the information about X that is useful for predicting Y.

#information bottleneck#variational information bottleneck#mutual information+11
📚TheoryAdvanced

Generalization Bounds for Deep Learning

Generalization bounds explain why deep neural networks can perform well on unseen data despite having many parameters.

#generalization bounds#pac-bayes#compression bounds+12
⚙️AlgorithmAdvanced

Natural Gradient Method

Natural gradient scales the ordinary gradient by the inverse Fisher information matrix to account for the geometry of probability distributions.

#natural gradient#fisher information#empirical fisher+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

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

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