A guided route through prerequisites, notation, code, and demos.
Start from a path, predict the demo, then ask the companion to repair the exact gap.
Start foundationsDomain Atlas
Choose the territory by the question you are trying to answer
Every domain is a route into the same learning loop: intuition, math, code, interactive evidence, and AI-assisted repair when the idea gets slippery.
01Foundationsgeometry, probability, calculus
02Mechanicsnetworks, attention, generation
03Systemsscaling, efficiency, decoding
04Frontiersalignment, interpretation, causality
AI companionask, test, repair
Reader Lenses
One atlas, different depths of use.
A quick way to inspect the mechanism, assumptions, and executable witness.
Use concept pages as small, testable models before jumping back to papers or experiments.
Inspect a bridgeA teachable sequence with visual hooks, derivation checkpoints, and failure regimes.
Use the same page as a lecture spine: intuition first, then math, code, and manipulation.
Open a lessonChoose By Need
The same atlas should support first contact, research recall, and teaching prep.
LearnerBuild the missing prerequisite.
Start with the mathematical object, then watch it become a model behavior.
ResearcherInspect the mechanism fast.Jump to assumptions, failure regimes, and executable witnesses before returning to papers.
ProfessorFind a lecture spine.Use domains as teachable arcs with demos, derivation checkpoints, and next questions.
01 / Foundations
I need the math underneath the model.
Start here when notation, geometry, probability, or optimization is the blocker.
9 concepts
Linear Algebra
Vectors, matrices, and linear maps: the language of representations, optimization, and modern deep learning.
Best when you want to read, run, and manipulate the idea in one sitting.
5 ready5 demos
6 concepts
Calculus
Rates of change and accumulation. Calculus is the language behind gradients, optimization, continuous-time dynamics, and why backprop works as efficiently as it does.
Best when you want to read, run, and manipulate the idea in one sitting.
4 ready4 demos
10 concepts
Optimization
How we train models: gradients, learning rates, curvature, and the practical tricks that make deep nets converge.
Best when you want to read, run, and manipulate the idea in one sitting.
4 ready4 demos
6 concepts
Probability
Uncertainty made precise: events, random variables, expectations, and the distributions that models learn.
Best when you want to read, run, and manipulate the idea in one sitting.
6 ready6 demos
1 concepts
Information Theory
How we measure information and mismatch between distributions: entropy, cross-entropy, KL divergence, mutual information, and why they appear everywhere in ML.
Best when you want to read, run, and manipulate the idea in one sitting.
1 ready1 demos
02 / Model Mechanics
I want to see how the architecture actually behaves.
Move here once the primitives are clear enough to explain a network component.
12 concepts
Attention & Transformers
The sequence model backbone: tokenization, self-attention, positional encodings, and the transformer block that powers modern LLMs.
Best when you want to read, run, and manipulate the idea in one sitting.
9 ready11 demos
3 concepts
Representation Learning
Embeddings and the geometry of meaning: similarity, normalization, contrastive objectives, and why vector spaces become usable interfaces for models.
Best when you want to read, run, and manipulate the idea in one sitting.
2 ready3 demos
5 concepts
Generative Models
How models generate: likelihood, latent variables, diffusion/score models, flows, and the training tricks that make sampling work.
Best when you want to read, run, and manipulate the idea in one sitting.
5 ready5 demos
03 / Systems & Practice
I care about how these ideas run at scale.
Use this band when correctness, latency, memory, and serving constraints matter.
6 concepts
Scaling
How loss and capability change with parameters, data, and compute; how to allocate a training budget; and why some abilities appear suddenly at scale.
Best when you want to read, run, and manipulate the idea in one sitting.
2 ready6 demos
5 concepts
Efficiency
How we make models cheaper to train and serve: quantization, distillation, low-rank adapters, sparsity, and the memory/latency tradeoffs that dominate real deployments.
Best when you want to read, run, and manipulate the idea in one sitting.
5 ready5 demos
6 concepts
LLM Systems
How models run in production: prefill vs decode, KV cache memory, batching and scheduling, and the techniques that make latency and throughput practical.
Best when you want to read, run, and manipulate the idea in one sitting.
5 ready6 demos
04 / Frontier Bridges
I am connecting the atlas to open research questions.
Use these bridges when the same mathematics reappears as alignment, interpretability, or causal structure.
9 concepts
Machine Learning
The classical supervised-learning spine: models, losses, generalization, evaluation, and the experiment habits that make modern AI results trustworthy.
Best when you want to read, run, and manipulate the idea in one sitting.
9 ready9 demos
5 concepts
Alignment
How we shape model behavior: preference learning, reward modeling, KL-regularized fine-tuning, and the failure modes that appear when you optimize the wrong thing.
Best when you want to read, run, and manipulate the idea in one sitting.
5 ready5 demos
1 concepts
Production ML
The engineering discipline around trustworthy model use: evaluation pipelines, dataset and model versioning, monitoring, drift, reproducibility, and operational tradeoffs.
Best when you want to read, run, and manipulate the idea in one sitting.
1 ready1 demos