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Concepts356

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

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
910111213
Advanced
#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
📚TheoryIntermediate

Loss Landscape Analysis

A loss landscape is the “terrain” of a model’s loss as you move through parameter space; valleys are good solutions and peaks are bad ones.

#loss landscape#sharpness#hessian eigenvalues+12
📚TheoryIntermediate

Weight Initialization Strategies

Weight initialization sets the starting values of neural network parameters so signals and gradients neither explode nor vanish as they pass through layers.

#xavier#glorot#he+12
⚙️AlgorithmIntermediate

Gradient Clipping & Normalization

Gradient clipping limits how large gradient values or their overall magnitude can become during optimization to prevent exploding updates.

#gradient clipping#clipping by norm#clipping by value+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
⚙️AlgorithmIntermediate

Learning Rate Schedules

Learning rate schedules control how fast a model learns over time by changing the learning rate across iterations or epochs.

#learning rate schedules#step decay#cosine annealing+12
⚙️AlgorithmIntermediate

Adam & Adaptive Methods

Adam is an optimization algorithm that combines momentum (first moment) with RMSProp-style adaptive learning rates (second moment).

#adam#adaptive methods#rmsprop+12
⚙️AlgorithmIntermediate

Momentum Methods

Momentum methods add an exponentially weighted memory of past gradients to make descent steps smoother and faster, especially in ravines and ill-conditioned problems.

#momentum#heavy-ball#polyak momentum+12
⚙️AlgorithmIntermediate

Stochastic Gradient Descent (SGD)

Stochastic Gradient Descent (SGD) updates model parameters using small random subsets (mini-batches) of data, making learning faster and more memory-efficient.

#stochastic gradient descent#mini-batch#random shuffling+12
⚙️AlgorithmIntermediate

Gradient Descent

Gradient descent is a simple, repeatable way to move downhill on a loss surface by stepping in the opposite direction of the gradient.

#gradient descent#batch gradient descent#learning rate+12