They keep the big mathematical story visible before a learner drops into a single concept page.
Read the visionSynthesis Layer
Five Pillars
Use pillars when you want the map before the territory: the same notebooks can serve a learner, a researcher, or a professor, but each needs a different scale of orientation.
atlas
Ssequence
Ooptimize
Ggenerate
Egeometry
Mmechanism
Route Logic
A pillar should feel like a conceptual zoom level.
It starts with a research question, names the mathematical pattern, and hands the learner to a notebook where the idea becomes testable.Each pillar points toward notebooks with prerequisites, code witnesses, demos, and AI companion context.
Browse domainsWhen a pillar crosses into another field, the graph should reveal the edge instead of hiding the jump.
Open graphS
The architecture of memory and attention
Sequence Modeling
y = softmax(QK^T / sqrt(d))VMove from recurrence to attention to state-space models, watching how different architectures remember, retrieve, and compress context.AttentionSSMsMambaMemory
O
Navigating the loss landscape
Optimization
theta <- theta - eta grad L(theta)Treat training as dynamics: gradients, curvature, stability, averaging, and the practical geometry that makes models learn.SGDAdamMuonSharpness
G
Diffusion, flow, and the geometry of data
Generative Physics
dx = f(x,t)dt + g(t)dWSee generation as transport: noisy particles, score fields, flow matching, and probability paths becoming manipulable systems.DiffusionFlow MatchingScoreSDEs
E
Symmetry as inductive bias
Geometric Deep Learning
f(rho(g)x) = rho'(g)f(x)Use symmetry to explain why architecture should respect the structure of the data, from grids to graphs to manifolds.EquivarianceGNNsSymmetryLie Groups
M
Reverse-engineering neural computation
Mechanistic Interpretability
x ~= sum_i a_i f_iConnect representations to mechanisms: features, superposition, circuits, probes, and interventions that make models inspectable.SAEsCircuitsFeaturesProbing