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Concepts98

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

AllBeginnerIntermediate
∑MathIntermediate

Markov Chains

A Markov chain models a system that moves between states where the next step depends only on the current state, not the past.

#markov chain#transition matrix#stationary distribution+11
∑MathIntermediate

Multivariate Gaussian Distribution

A multivariate Gaussian (normal) distribution models a vector of real-valued variables with a bell-shaped probability hill in many dimensions.

#multivariate normal
23456
Advanced
#gaussian distribution
#covariance matrix
+11
∑MathIntermediate

Expectation, Variance & Moments

Expectation is the long-run average value of a random variable and acts like the balance point of its distribution.

#expectation#variance#moments+12
∑MathIntermediate

Random Variables & Distributions

A random variable maps uncertain outcomes to numbers and is described by a distribution that assigns likelihoods to values or ranges.

#random variable#pmf#pdf+12
∑MathIntermediate

Probability Axioms & Rules

Kolmogorov’s axioms define probability as a measure on events: non-negativity, normalization, and countable additivity.

#kolmogorov axioms#probability measure#sample space+12
∑MathIntermediate

Lagrange Multipliers & Constrained Optimization

Lagrange multipliers let you optimize a function while strictly satisfying equality constraints by introducing auxiliary variables (the multipliers).

#lagrange multipliers#constrained optimization#kkt conditions+11
∑MathIntermediate

Implicit Differentiation & Implicit Function Theorem

Implicit differentiation lets you find slopes and higher derivatives even when y is given indirectly by an equation F(x,y)=0.

#implicit differentiation#implicit function theorem#jacobian+12
∑MathIntermediate

Taylor Series & Approximation

Taylor series approximate a complicated function near a point by a simple polynomial built from its derivatives.

#taylor series#taylor polynomial#maclaurin series+12
∑MathIntermediate

Hessian Matrix

The Hessian matrix collects all second-order partial derivatives of a scalar function and measures local curvature.

#hessian matrix#second derivatives#curvature+11
∑MathIntermediate

Jacobian Matrix

The Jacobian matrix collects all first-order partial derivatives of a vector-valued function, describing how small input changes linearly affect each output component.

#jacobian matrix#partial derivatives#multivariable calculus+11
∑MathIntermediate

Multivariable Chain Rule

The multivariable chain rule explains how rates of change pass through a pipeline of functions by multiplying the right derivatives (Jacobians) in the right order.

#multivariable chain rule#jacobian#gradient+12
∑MathIntermediate

Gradient & Directional Derivatives

The gradient \(\nabla f\) points in the direction of steepest increase of a scalar field and its length equals the maximum rate of increase.

#gradient#directional derivative#partial derivative+12