Lab
Diffusion Lab
Step the forward and reverse processes of a 2D toy diffusion. Watch noise schedules, score estimates, and DDIM vs DDPM samplers side by side.
Blog
Writing and Updates
Posts plus selected topic and lab updates that changed how a learner moves through the site.
Updates
Recent changes
Lab
Induction Heads Lab
Train a 2-layer attention-only transformer in your browser. Watch the induction circuit form during the loss-cliff phase transition; ablate any head to see in-context learning collapse.
Topic
Model Comparison Table
Current frontier snapshot (Apr 2026): Claude Opus 4.7, GPT-5.4, Gemini 3.1 Pro, Llama 4, DeepSeek-R1, Kimi K2.6, GLM-5. Provider-backed numbers, benchmark variance bounds, MoE vs dense, context-length and open-weights notes.
Lab
High-Dimensional Probability Lab
Thin shells, random projections, Marchenko-Pastur spectra, and spiked PCA on one interactive board.
Lab
Random Matrix / Spectral Geometry Lab
A visual lab for Marchenko-Pastur bulk behavior, conditioning, ridge stabilization, and spiked covariance.
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
Kernels and RKHS
A stronger bridge from similarity functions to RKHS geometry, the representer theorem, and why kernel methods still matter for modern ML.
Lab
Spectral PDE Lab
A Fourier-solver lab for inspecting heat, transport, Schrodinger, and Poisson dynamics under stated assumptions.
Writing
Posts
What OpenAI's goblin episode reveals about reward models
A small creature-metaphor habit in GPT-5.5 becomes a clean case study in reward models, proxy objectives, behavior transfer, and synthetic-data feedback loops.
ReadFree Energy Is a Serious Language for Generative AI
A book note on Welling, Lu, and Holdijk's Generative AI and Stochastic Thermodynamics: variational free energy as a unifying language for VAEs, normalizing flows, diffusion, flow matching, and Schrödinger bridges.
ReadScaling Made AI Legible
A book note on The Scaling Era: An Oral History of AI, 2019-2025. Scaling made AI progress legible. The next edge will come from research, judgment, and tool fluency.
ReadFast Tools, Slow Understanding
A short note on fast tools, fluent output, and the slower work of understanding machine learning.
Read