Lab
Random Matrix / Spectral Geometry Lab
A visual lab for Marchenko-Pastur bulk behavior, conditioning, ridge stabilization, and spiked covariance.
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.
Start
Choose your first useful move.
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.
Browse starter pathsAtlas
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
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.
Recent work
Essays, labs, and topic updates.
Topic
Sub-Gaussian and Sub-Exponential Tails
Interactive tail boards now compare Gaussian-like, Bernstein-style, and heavy-tail decay without raw formula clutter.
Topic
Neural Tangent Kernel
A compact route through the lazy-training limit, kernel regression equivalence, and why NTK theory does not by itself explain feature learning.
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.