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Concepts532

Groups

📐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

Category

🔷All∑Math⚙️Algo🗂️DS📚Theory

Level

AllBeginnerIntermediateAdvanced
📚TheoryIntermediate

Lagrangian Duality

Lagrangian duality turns a constrained minimization problem into a related maximization problem that provides lower bounds on the original objective.

#lagrangian duality#kkt conditions#slater condition+11
📚TheoryAdvanced

Measure Theory

Measure theory generalizes length, area, and probability to very flexible spaces while keeping countable additivity intact.

#measure theory
2425262728
#sigma-algebra
#lebesgue integral
+12
📚TheoryIntermediate

Matrix Calculus

Matrix calculus extends ordinary calculus to functions whose inputs and outputs are vectors and matrices, letting you compute gradients, Jacobians, and Hessians systematically.

#matrix calculus#gradient#jacobian+12
📚TheoryIntermediate

Singular Value Decomposition (SVD)

Singular Value Decomposition (SVD) factors any m×n matrix A into A = UΣV^{T}, where U and V are orthogonal and Σ is diagonal with nonnegative entries.

#singular value decomposition#svd#truncated svd+12
📚TheoryIntermediate

Convex Optimization

Convex optimization studies minimizing convex functions over convex sets, where every local minimum is guaranteed to be a global minimum.

#convex optimization#convex function#convex set+12
📚TheoryIntermediate

Eigenvalue Decomposition

Eigenvalue decomposition rewrites a square matrix as a change of basis that reveals how it stretches and rotates space.

#eigenvalue decomposition#spectral theorem#power iteration+12
📚TheoryIntermediate

Optimization Theory

Optimization theory studies how to choose variables to minimize or maximize an objective while respecting constraints.

#optimization#convex optimization#gradient descent+12
📚TheoryIntermediate

Linear Algebra Theory

Linear algebra studies vectors, linear combinations, and transformations that preserve addition and scalar multiplication.

#linear algebra#vector space#basis+12
📚TheoryIntermediate

Gradient Descent Convergence Theory

Gradient descent updates parameters by stepping opposite the gradient: x_{t+1} = x_t - \eta \nabla f(x_t).

#gradient descent#convergence rate#l-smooth+12
📚TheoryIntermediate

Central Limit Theorem

The Central Limit Theorem (CLT) says that the sum or average of many independent, identically distributed variables with finite variance becomes approximately normal (Gaussian).

#central limit theorem#berry-esseen#lindeberg+12
📚TheoryIntermediate

Probability Distributions

Probability distributions describe how random outcomes are spread across possible values and let us compute probabilities, expectations, and uncertainties.

#probability distributions#pmf#pdf+12
📚TheoryIntermediate

Probability Theory

Probability theory formalizes uncertainty using a sample space, events, and a probability measure that obeys clear axioms.

#probability measure#random variable#expectation+12