Learn the mathematics of machine learning by moving it.
Free, open tutorials on the mathematics of machine learning and on machine learning. Each lesson has interactive figures, worked examples with answers, quizzes, curated videos and a Colab notebook to code along.
Mathematics for machine learning
The language every model is written in.Start here: notation and Python
Math notation, functions, sums and logs, NumPy, plotting, and how to read a proof.
LiveLinear Algebra
From matrices as maps to the SVD, PCA, numerical methods and the linear algebra inside LoRA, attention and neural operators.
LiveCalculus for ML
Multivariable and matrix calculus, the chain rule behind backpropagation, Jacobians, Hessians and automatic differentiation.
LiveProbability and Statistics
Random variables, the multivariate Gaussian, concentration, maximum likelihood, Bayesian inference, Monte Carlo and testing.
LiveOptimization
Convexity, gradient descent and its rates, momentum, SGD and Adam, Newton and quasi-Newton methods, duality.
LiveInformation Theory
Entropy, cross-entropy and KL divergence, mutual information, the ELBO and compression.
Machine learning
From linear models to transformersML Fundamentals
Linear and logistic regression, regularization, bias and variance, kernels and SVMs, trees and boosting, clustering and evaluation.
Deep Learning
MLPs and backpropagation, initialization and normalization, CNNs and RNNs, attention and the transformer, state-space models.
LiveGenerative Models
VAEs, autoregressive models, normalizing flows, GANs, diffusion and flow matching.
LiveReinforcement Learning
MDPs and Bellman equations, bandits, Q-learning, policy gradients, PPO and RL for language models.
Large Language Models
Tokenization, pretraining, scaling laws, efficient inference, fine-tuning, RAG and alignment.
Computer Vision
Images as tensors, convolutions and CNN architectures, detection, segmentation, vision transformers and self-supervised vision.
Graph Machine Learning
Graphs and their matrices, spectral methods, message passing, GCN, GAT and graph transformers, with applications in science.
Applied and engineering
Machine learning for scienceML for Science
Differentiable simulation, neural ODEs and SDEs, data assimilation, neural operators, Gaussian processes and physics-informed learning.
LiveML Systems
GPUs and the roofline model, mixed precision, memory, parallelism (data, tensor, pipeline), FlashAttention and serving.
LiveMLOps
Reproducibility, testing ML code, containers, serving APIs, CI/CD, monitoring and drift.
LiveTime Series and Forecasting
Trends and seasonality, autocorrelation, ARIMA and state-space models, forecasting with ML and deep learning, and probabilistic forecasts.
LiveCausal Inference
Correlation versus causation, causal graphs, interventions and do-calculus, randomized experiments, matching, instrumental variables and causal ML.
LiveML Interview Prep
Coding rounds, ML breadth questions, ML system design and research talks, with worked practice problems.