FormalizeSampling: Sampling and diffusion convergence theorems machine-checked in Lean 4
TianbaoX · x · 2026-10-24
Hendry Dong open-sourced FormalizeSampling, a Lean 4/Mathlib library that machine-checks published convergence theorems for sampling algorithms and diffusion models, with a literature map.
- Connects Langevin dynamics, proximal sampling, and diffusion models, with end-to-end convergence proofs, analytic counterexamples, and separations between path and output convergence
- The goal is a reusable mathematical foundation: explicit assumptions, checked proofs, and cross-literature connections
- The author says recent frontier-model progress brought him back to sampling theory: conversing with agents makes math easier to explore, while formalization keeps results checkable and reusable; the workflow could extend to other fields
- The accompanying figure shows a compiled LSI decay theorem verified under Lean 4.35.0 via #print axioms
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