Topic
Jacobian Lens and Global Workspace Interpretability
A 2026 Transformer Circuits study maps intermediate activations into final-layer coordinates, then uses interventions to test a small token-aligned broadcast component.
TheoremPath Know what to learn next.
A study map for machine learning foundations. Pick a goal, find gaps, save useful notes, and come back to a clear review path.
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TheoremPath gives you a path, a gap check, and a place to come back to. Start broad, then go deeper when the next topic needs it.
Featured lesson
Exact attention across a cluster.
Step through ring and tree schedules, compare what each transmits, and see why their online-softmax normalizers agree in exact arithmetic.
Advanced40 minInteractive
Compare ring and tree reductionNormalizer merge order
4 devices
Ring order
3 roundsRotates full K/V shards
- round 10 + 1
- round 2(0,1) + 2
- round 3(0,1,2) + 3
Tree order
2 roundsMerges compact partial states
- round 10 + 1 and 2 + 3
- round 2(0,1) + (2,3)
Normalizer state only. Both schedules reach the same (m, l) in exact arithmetic. Exact attention also carries an output accumulator; floating-point order can change the last few bits.
Atlas
See what blocks the next topic.
The Atlas is the map behind the study loop: where you are, what comes first, and what opens after this step.
600
topics
4395
edges
0A to 5
layers
GraphAtlasSee where a topic sits, what blocks it, and what it opens next.ClaimsEvidenceInspect claim labels, source support, and verification boundaries when you want the proof layer.MethodMethodologySee how pages, claims, diagnostics, learner state, and proof records fit together.ProjectProjectsSee the topic library, evidence ledger, learner loop, and iOS companion as one system.ProofsLeanReview checked declarations, proof scopes, axiom profile, and manifest status.
Concentration inequalitiesMarkov, Chebyshev, Hoeffding, BernsteinUniform convergenceFinite-class bounds, ERM, and generalization gapsVC dimensionShattering, growth functions, and sample complexityRademacher complexitySymmetrization and data-dependent capacityTransformer architectureSelf-attention, FFN blocks, and residual streamsScaling lawsCompute allocation, data scaling, and fit limits
Recent work
Recent topics and labs.
Topic
AlphaProof and AI-Assisted Theorem Proving
An updated guide to AlphaProof's three Lean-checked IMO 2024 solutions, AlphaGeometry 2, reinforcement-learning proof search, and the kernel trust boundary.
Topic
Model Comparison Table
A July 11 snapshot of GPT-5.6 Sol, Terra, and Luna; GPT-Live; Claude Fable 5 and Sonnet 5; restricted Mythos 5; and other major families, using official release material and leaving undisclosed architecture fields unknown.
Method
Go deeper when you need the proof layer.
The main product helps you study. The evidence pages, source roles, and Lean wrappers are there when you want to inspect why a topic or claim is trustworthy.
01
Claims are scoped
The site separates a theorem statement, its assumptions, and the page-level explanation so evidence attaches to the claim it actually supports.
02
Diagnostics route gaps
Missed items map to prerequisite concepts, not broad topic pages. The next step is a graph repair, not another generic lesson.
03
Lean evidence stays narrow
Formal wrappers appear only when the Lean theorem matches the governed claim scope and the manifest records the exact proof object.
Labs
Learn with diagrams, not only pages.
Labs make the mechanics visible: gradients moving, random vectors concentrating, and matrix maps changing geometry.
Browse all demosOptimizationOptimizer pinballCompare GD, Momentum, Nesterov, and Adam across convex and non-convex surfaces.
Probability geometryHigh-dimensional probabilityWatch concentration, spectra, and spike separation as dimension changes.
Linear algebraMatrix mechanicsManipulate maps, rank, eigenvectors, determinants, trace, and SVD directly.
Private beta
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The public library, Atlas, diagnostics, saved topics, notes, and review tools are free during private beta. There is no paid checkout yet. Future paid tools will be tested only after activation and return use are measured.
Start with one next step.
The fastest route is not more tabs or another syllabus. It is a visible path, saved context, and one useful move when you return.