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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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📚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#variational inference#dropout+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
Advanced
Filtering by:
#kl divergence
#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
📚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
📚TheoryAdvanced

Variational Inference Theory

Variational Inference (VI) replaces an intractable posterior with a simpler distribution and optimizes it by minimizing KL divergence, which is equivalent to maximizing the ELBO.

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

Information Bottleneck Theory

Information Bottleneck (IB) studies how to compress an input X into a representation Z that still preserves what is needed to predict Y.

#information bottleneck#mutual information#variational information bottleneck+12