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Concepts532

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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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⚙️AlgorithmIntermediate

Short-Time Fourier Transform (STFT)

The Short-Time Fourier Transform (STFT) breaks a signal into small overlapping windows and computes a Fourier transform on each window to reveal how frequencies evolve over time.

#stft#short-time fourier transform#spectrogram+12
∑MathIntermediate

Convolution Theorem

The Convolution Theorem says that convolving two signals in time (or space) equals multiplying their spectra in the frequency domain.

#convolution theorem
910111213
#fft
#dft
+12
⚙️AlgorithmIntermediate

Discrete Fourier Transform (DFT) & FFT

The Discrete Fourier Transform (DFT) converts a length-N sequence from the time (or spatial) domain into N complex frequency coefficients that describe how much of each sinusoid is present.

#dft#fft#cooley-tukey+12
∑MathIntermediate

Fourier Transform

The Fourier Transform converts a signal from the time domain into the frequency domain, revealing which sine and cosine waves (frequencies) make up the signal.

#fourier transform#fft#dft+12
∑MathIntermediate

Fourier Series

A Fourier series rewrites any reasonable periodic function as a weighted sum of sines and cosines (or complex exponentials).

#fourier series#harmonics#fourier coefficients+12
📚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#eigenvalues#singular values+12
∑MathAdvanced

Free Probability Theory

Free probability studies "random variables" that do not commute, where independence is replaced by freeness and noncrossing combinatorics replaces classical partitions.

#free probability#freeness#r-transform+11
∑MathAdvanced

Marchenko-Pastur Distribution

The Marchenko–Pastur (MP) distribution describes the limiting eigenvalue distribution of sample covariance matrices S = (1/n) XX^{\top} when both the dimension p and the sample size n grow with p/n \to \gamma.

#marchenko-pastur#random matrix theory#sample covariance+10
∑MathAdvanced

Wigner Semicircle Law

The Wigner Semicircle Law says that the histogram of eigenvalues of large random symmetric matrices converges to a semicircle-shaped curve.

#wigner semicircle law#random matrix#empirical spectral distribution+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#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