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Concepts11

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

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🔷All∑Math⚙️Algo🗂️DS📚Theory

Level

AllBeginnerIntermediate
∑MathIntermediate

Softmax & Temperature Scaling

Softmax turns arbitrary real-valued scores (logits) into probabilities that sum to one.

#softmax#temperature scaling#logits+12
📚TheoryAdvanced

Feature Learning vs Kernel Regime

The kernel (lazy) regime keeps neural network parameters close to their initialization, making training equivalent to kernel regression with a fixed kernel such as the Neural Tangent Kernel (NTK).

#neural tangent kernel
Advanced
Filtering by:
#jacobian
#kernel ridge regression
#lazy training
+12
📚TheoryAdvanced

Neural Tangent Kernel (NTK)

Neural Tangent Kernel (NTK) describes how wide neural networks train like kernel machines, turning gradient descent into kernel regression in the infinite-width limit.

#neural tangent kernel#ntk#nngp+12
∑MathAdvanced

Smooth Manifolds & Tangent Spaces

A smooth manifold is a space that looks like ordinary Euclidean space when you zoom in, glued together using charts that transition smoothly.

#smooth manifolds#tangent space#chart+11
∑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

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

Partial Derivatives

Partial derivatives measure how a multivariable function changes when you wiggle just one input while keeping the others fixed.

#partial derivatives#gradient#jacobian+12
∑MathIntermediate

Matrix Calculus Fundamentals

Matrix calculus extends single-variable derivatives to matrices so we can differentiate functions built from matrix multiplications, traces, and norms.

#matrix calculus#frobenius norm#trace trick+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
∑MathIntermediate

Determinant

The determinant of a square matrix measures how a linear transformation scales volume and whether it flips orientation.

#determinant#gaussian elimination#lu decomposition+12