LATENT SPACE LAB · TRAINING · EPOCH ∞

Machine Learning & Artificial Intelligence
From First Principles to Agentic AI

Mathematical derivations × from-scratch implementations × curated video lectures × interactive experiments · continuously updated

This course walks you down one complete path: starting from the first-principles question of "what is machine learning," through classical algorithms, deep learning, and the Transformer architecture, all the way to the most cutting-edge large language model training techniques and Agentic AI system design. Every chapter includes detailed mathematical derivations, from-scratch code implementations, curated videos with viewing guides, and hands-on interactive experiments and chapter quizzes.

AUDIO // Course Audio Introduction · 0:25

How to Use This Course

Written lessons: each chapter is a complete, in-depth tutorial; every formula is derived step by step. Just read them in order.
Video cards: embedded at the relevant points in the text, right where the topic comes up. Each video comes with a "viewing guide" — which minutes to focus on, and what questions to keep in mind. Click the thumbnail to play (captions recommended).
Interactive experiments: visual playgrounds with adjustable parameters — crank up the learning rate yourself and watch gradient descent diverge on the spot.
Chapter quizzes: every question comes with a detailed explanation, and your progress is saved automatically in your browser.
Thought questions: collapsible deep-dive questions — think it through yourself first, then expand to see a reference answer.

Course Outline

Prologue · Seventy Years of AI: An Interactive History Timeline

An infinitely pannable, zoomable history canvas: 7 main storyline lanes · 55+ milestones (click for technical deep dives) · two AI winters · from the 1943 McCulloch-Pitts neuron to 2026 Agentic AI · the AlphaGo documentary

Introduction to Machine Learning & Core Concepts

The essence of machine learning · supervised/unsupervised/reinforcement learning · loss functions and generalization · the full derivation of linear regression (normal equations + gradient descent) · the bias-variance decomposition · from-scratch implementation in NumPy · an interactive gradient descent lab

Classical Machine Learning Algorithms

The full derivation of logistic regression and cross-entropy · softmax and the temperature parameter · decision trees (information gain / Gini) · random forests and gradient boosting / XGBoost · the SVM dual and the kernel trick · a decision-boundary showdown lab (three algorithms visualized in real time)

Foundations of Deep Learning

Paying off the XOR setup · the universal approximation theorem and how it's misread · the full four-step derivation of backpropagation (the δ recurrence) · the evolution of activation functions (sigmoid → ReLU → SwiGLU) · SGD → Momentum → Adam → AdamW derived term by term · He/Xavier initialization · Dropout/BatchNorm/LayerNorm/RMSNorm · a lab that trains a real neural network in the browser · hand-written backprop in NumPy vs. PyTorch

CNNs & Computer Vision

Inductive biases: local connectivity + weight sharing · output size / channels / receptive field · the five epiphanies from LeNet to ResNet · residual connections = a gradient highway (∂y/∂x = ∂F/∂x + I) · ViT and the bitter lesson · a convolution-kernel lab (edit a 3×3 kernel by hand and watch the feature map)

Sequence Models: RNNs/LSTMs and the Birth of Attention

Weight sharing across the time dimension · BPTT and the exponential fate of repeatedly multiplying W_h · gradient clipping · the derivation of the LSTM's three gates (the cell state = a residual across time) · the fixed-vector bottleneck of Seq2Seq · the three-step Bahdanau attention (the prototype of Q/K/V) · teacher forcing and exposure bias · an attention-alignment heatmap lab

The Transformer Architecture in Depth ★ Core Chapter

The three-step transformation from Bahdanau attention to self-attention · the √d_k variance derivation · causal masking and training parallelism · the division of labor across multi-head subspaces · positional encoding (sinusoidal → RoPE rotation) · assembling a GPT block from FFN/Pre-LN/residuals · the 12Ld² parameter shortcut verified against GPT-2 · a step-by-step self-attention calculator · Karpathy's nanoGPT, a must-do follow-along

Large Language Models I: Pretraining

Next-token prediction = compression · BPE and the blame the tokenizer takes · Kaplan → Chinchilla → overtraining (inference-optimal) · the FineWeb data pipeline · 3D parallelism and ZeRO · Dense vs. MoE, the detailed accounting · linear/hybrid attention and framework maturity (a 15× throughput case study) · practical training hyperparameters · a scaling-law calculator lab

Large Language Models II: Alignment & Fine-Tuning

Base model = document simulator · SFT engineering (chat template / loss mask / LIMA) · a methodology for the small-model + SFT vertical loop (evaluation first / a 0 → 9 baseline) · the math of LoRA and QLoRA · RLHF and reward hacking · the full three-step derivation of DPO · GRPO/RLVR, the engine behind reasoning models · a LoRA memory calculator · hands-on MLX commands

LLM Inference & Deployment

Prefill/decode and roofline mental math · the KV cache formula and the memory budget · MQA → GQA → MLA · PagedAttention/vLLM · the quantization family tree · why speculative decoding is lossless · the full sampling toolkit · cost engineering (cache hit rates / usage funnels / model tiering) · two labs: a KV calculator + a product cost estimator

RAG & Vector Retrieval

The three cardinal sins of parametric knowledge · contrastive learning and the bi-encoder / cross-encoder trade-off · HNSW, "fly first, then bike" · parent-child chunking strategies · hybrid retrieval + RRF + reranking as a two-stage funnel · a failure-mode checklist (lost in the middle…) · long context vs. RAG · Agentic RAG · a semantic vs. keyword retrieval lab · a 60-line minimal RAG

Agentic AI System Design ★ Key Chapter

Agent = the demystified definition as a while loop · breaking down the tool-calling mechanism · the spectrum of workflows and the "three questions" · five techniques of context engineering · memory and the accretion of Skills · a deep dive into Memory as a standalone system design (precise writes / precise reads) · the MCP protocol · multi-agent orchestration · the design discipline of small-model tasks · an anatomy of a real coding-agent architecture · pass^k and guardrails · six frontier research directions for 2026 · a three-trajectory simulator · an 80-line bare-bones agent

Multimodality & the Frontier

The math of diffusion models (closed-form forward process / ε-prediction = regression / CFG) · latent space = paying off the course's name · DiT · multimodal LLMs (everything ends up as tokens) · the world-model debate · four filters for evaluation · SAE interpretability · three unfinished curves · a 50-step denoising lab (a 16×16-pixel cat)

Putting It All Together · Post-Training a Small Model for a Vertical Use Case ★ Capstone Project

Eight end-to-end steps: schema design (verifiability is something you design in) · eval.py and a 0/12 baseline · a reverse-engineered data pipeline · an architecture comparison experiment (the 15× throughput trap) · two-stage MLX training (600-step validation → an overnight full run) · failure attribution and data iteration · quantized deployment and cost accounting · agentic integration and the road to RLVR · a verifier lab

Appendix · Information Sources Worth Following

Curated blogs (Karpathy, Lilian Weng, Jianlin Su…) · courses and books (CS231n, d2l.ai…) · video channels · papers and leaderboards · newsletters and podcasts · official lab blogs · plus suggested strategies for keeping up

The main course is complete (the Prologue + 13 chapters + the Appendix are all live): 26 curated videos all backed up offline, 14 interactive labs, 13 audio introductions, and 120+ quiz questions with explanations. The recommended study order is simply the chapter order; the appendix's list of sources will help you stay on the frontier after the course. New material will still be added from time to time (new nodes on the timeline, new sources in the appendix).

Prerequisites

Math: high-school math is enough to get started. When we use calculus (derivatives, the chain rule) and linear algebra (matrix multiplication), the course supplies the intuition on the spot.
Programming: you can read basic Python. All code is commented line by line.
Tools: we recommend installing Python 3.10+ and running pip install numpy scikit-learn matplotlib torch.