Lab
Random Matrix / Spectral Geometry Lab
A visual lab for Marchenko-Pastur bulk behavior, conditioning, ridge stabilization, and spiked covariance.
TheoremPath Learn the theory in proof order.
Source-backed machine learning theory, statistics, optimization, and deep learning, organized by the prerequisites that actually connect.
Start
Start from the right layer.
TheoremPath is not a flat syllabus. Pick the layer that matches the missing prerequisite, then move through the graph in order.
Take the diagnosticFoundationsCalculus, linear algebra, and probabilityUse this route when the notation is the blocker: gradients, matrix maps, distributions, and proof moves before ML theory.
Core pathMath to MLMove from probability and optimization into empirical risk, concentration bounds, and the first generalization proofs.
Practice bridgeEngineer to ML theoryStart from working ML intuition and attach the assumptions, failure modes, and theorem statements underneath it.
Statistics bridgeStats to deep learningConnect likelihood, inference, bias-variance, and asymptotics to modern deep-learning theory and transformer papers.
Research pathML research readinessFollow concentration, VC/PAC, Rademacher complexity, optimization, attention, and scaling laws in dependency order.
Graph
Follow the prerequisite graph.
The important objects are dependencies: probability before concentration, concentration before uniform convergence, optimization before training dynamics.
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
Browse the curriculumMethod
Read claims with evidence attached.
Topic pages stay public. Sign-in is for saved notes, diagnostics, and review state; the theory itself remains readable without an account.
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
Use the diagrams.
Interactive work is for mechanics: gradients moving, random vectors concentrating, 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.
Choose one theorem and trace what it depends on.
The fastest route through hard theory is not more pages. It is a visible dependency path and one honest next step.