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How I Study AI - Learn AI Papers & Lectures the Easy Way

Concepts140

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๐Ÿ“Linear Algebra15๐Ÿ“ˆCalculus & Differentiation10๐ŸŽฏOptimization14๐ŸŽฒProbability Theory12๐Ÿ“ŠStatistics for ML9๐Ÿ“กInformation Theory10๐Ÿ”บConvex Optimization7๐Ÿ”ขNumerical Methods6๐Ÿ•ธGraph Theory for Deep Learning6๐Ÿ”ตTopology for ML5๐ŸŒDifferential Geometry6โˆžMeasure Theory & Functional Analysis6๐ŸŽฐRandom Matrix Theory5๐ŸŒŠFourier Analysis & Signal Processing9๐ŸŽฐSampling & Monte Carlo Methods10๐Ÿง Deep Learning Theory12๐Ÿ›ก๏ธRegularization Theory11๐Ÿ‘๏ธAttention & Transformer Theory10๐ŸŽจGenerative Model Theory11๐Ÿ”ฎRepresentation Learning10๐ŸŽฎReinforcement Learning Mathematics9๐Ÿ”„Variational Methods8๐Ÿ“‰Loss Functions & Objectives10โฑ๏ธSequence & Temporal Models8๐Ÿ’ŽGeometric Deep Learning8

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๐Ÿ”ทAllโˆ‘Mathโš™๏ธAlgo๐Ÿ—‚๏ธDS๐Ÿ“šTheory

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โˆ‘MathIntermediate

L1 Regularization (Lasso)

L1 regularization (Lasso) adds a penalty \(\lambda \sum_{i=1}^{p} |w_i|\) to the loss, which pushes many coefficients exactly to zero and performs feature selection.

#lasso#l1 regularization#soft-thresholding+12
โˆ‘MathIntermediate

Wavelet Transform

The wavelet transform splits a signal into โ€œcoarseโ€ trends and โ€œfineโ€ details at multiple scales, like zooming in and out with a smart magnifying glass.

#wavelet transform
12345
#haar wavelet
#multiresolution analysis
+12
โˆ‘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#fft#dft+12
โˆ‘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
โˆ‘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
โˆ‘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
โˆ‘MathAdvanced

Marchenko-Pastur Distribution

The Marchenkoโ€“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
โˆ‘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
โˆ‘MathAdvanced

Banach Spaces

A Banach space is a vector space with a norm where every Cauchy sequence actually converges within the space.

#banach space#normed vector space#completeness+11
โˆ‘MathAdvanced

Hilbert Spaces

A Hilbert space is an inner product space that is complete, meaning Cauchy sequences converge to points inside the space.

#hilbert space#inner product#l2 space+12
โˆ‘MathAdvanced

Lebesgue Integration

Lebesgue integration measures how much time a function spends near each value and adds up value ร— size of the set where it occurs.

#lebesgue integral#riemann integral#measure theory+12
โˆ‘MathAdvanced

Sigma-Algebras & Measure Spaces

A ฯƒ-algebra is a collection of subsets that is closed under complements and countable unions, giving us a stable universe of sets where measure makes sense.

#sigma-algebra#measure space#measurable sets+12