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Advanced Labs

114 deep, interactive labs — from the math foundations through classical ML and deep learning to modern LLMs. Each one runs in your browser, every number real.

Advanced Labs

Summation Product Notation

Functions Limits Continuity

Sequences Series Convergence

Exp, Log & Softmax

Complex Numbers Euler

Derivatives Rules

Chain Rule

Partial Derivatives Gradient

Partial Derivatives Optimization

Jacobian Hessian

Integrals Expectation

Taylor Series

Convexity Optimization

Lagrange Multipliers

Vectors & Vector Spaces

Dot Product Cosine Similarity

Norms & Distances

Matrices & Arithmetic

Matrix Multiplication

Linear Transformations

Span Basis Independence

Rank Subspaces

Linear Systems Inverse

Determinants

Eigenvalues Eigenvectors

Orthogonality Projections

Quadratic Forms

Singular Value Decomposition

Probability Foundations

Joint Conditional Marginal

Bayes Probability

Random Variables Distributions

Common Distributions

Gaussian Distribution

Expectation Variance Moments

Covariance Correlation

Law of Large Numbers & CLT

Sampling Monte Carlo

Estimators & MLE

Maximum Likelihood Estimation

Bayesian Inference MCMC

Entropy Information

Train Test Cross Validation

Bias Variance Overfitting

Regularization Overfitting

Evaluation Metrics

Gradient Descent Intuition

Linear Regression

Logistic Regression

k-Nearest Neighbors

Naive Bayes

Support Vector Machines

Decision Tree

Random Forest

Gradient Boosting

k-Means Clustering

Gaussian Mixture

Principal Component Analysis

t-SNE

Gaussian Processes

Hidden Markov Models

Recommender Matrix Factorization

Calibration Confidence

Class Imbalance Threshold

Curse of Dimensionality

Hyperparameter Optimization

Model Interpretability

Reinforcement Learning

Time Series Forecasting

Neural Network Basics

Neural Network — Deep Dive

Activation Functions Basics

Activation Functions

Loss Functions

Backpropagation Autograd

Gradient Descent Optimizers

Learning Rate Schedules

Optimization Landscape Normalization

Batch Layer Normalization