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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

Diffusion Models (Score-Based)

Score-based diffusion models corrupt data by gradually adding Gaussian noise and then learn to reverse this process by estimating the score, the gradient of the log-density.

#diffusion models#score-based modeling#ddpm+7
📚TheoryAdvanced

Normalizing Flows

Normalizing flows transform a simple base distribution (like a standard Gaussian) into a complex target distribution using a chain of invertible functions.

#normalizing flows
12345
Advanced
#change of variables
#jacobian determinant
+12
📚TheoryAdvanced

GAN Theory & Training Dynamics

GANs frame learning as a two-player game where a generator tries to fool a discriminator, and the discriminator tries to detect fakes.

#gan#generator#discriminator+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

In-Context Learning Theory

In-context learning (ICL) means a model learns from examples provided in the input itself, without updating its parameters.

#in-context learning#transformer#attention+12
📚TheoryAdvanced

Transformer Expressiveness

Transformer expressiveness studies what kinds of sequence-to-sequence mappings a Transformer can represent or approximate.

#transformer expressiveness#universal approximation#self-attention+12
📚TheoryAdvanced

Feature Learning vs Kernel Regime

The kernel (lazy) regime keeps neural network parameters close to their initialization, making training equivalent to kernel regression with a fixed kernel such as the Neural Tangent Kernel (NTK).

#neural tangent kernel#kernel ridge regression#lazy training+12
📚TheoryAdvanced

Mean Field Theory of Neural Networks

Mean field theory treats very wide randomly initialized neural networks as averaging machines where each neuron behaves like a sample from a common distribution.

#mean field theory#neural tangent kernel#neural network gaussian process+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

Neural Tangent Kernel (NTK)

Neural Tangent Kernel (NTK) describes how wide neural networks train like kernel machines, turning gradient descent into kernel regression in the infinite-width limit.

#neural tangent kernel#ntk#nngp+12
📚TheoryAdvanced

Spectral Convolution on Graphs

Spectral convolution on graphs generalizes the classical notion of convolution using the graph’s Laplacian eigenvectors as “Fourier” basis functions.

#spectral graph theory#graph fourier transform#laplacian eigenvectors+12