Reproduction package for "Selection Under an Imperfect Verifier" and "The Spectrum, Not the Norm"
Code, derived results and figures for two papers on selection and geometry in machine learning. Paper 1, Selection Under an Imperfect Verifier, develops an extreme-value theory of test-time compute: best-of-n delivers a concomitant of an extreme order statistic, which yields the log-linear gain curve, a proof that long-tailed verifier error forces a finite optimal sample count, an unbiased U-statistic estimator of the whole gain curve from one pool, and exact greedy budget allocation. It is tested on 128,000 real completions (MATH-500, Llama-3.2-1B-Instruct, 8B process reward model). Paper 2, The Spectrum, Not the Norm, analyses orthogonalise
Resource information
- Format
- zip
- Original repository
- 21976483
- DOI
- 10.5281/zenodo.21976483
- Credit basis
- Creators in Zenodo record metadata
- Access
- Open files available from the original Zenodo deposit
- Last checked
- Nov 5, 2026
- License
- mit-license
- Last record update
- Nov 5, 2026
About this resource
Code, derived results and figures for two papers on selection and geometry in machine learning. Paper 1, Selection Under an Imperfect Verifier, develops an extreme-value theory of test-time compute: best-of-n delivers a concomitant of an extreme order statistic, which yields the log-linear gain curve, a proof that long-tailed verifier error forces a finite optimal sample count, an unbiased U-statistic estimator of the whole gain curve from one pool, and exact greedy budget allocation. It is tested on 128,000 real completions (MATH-500, Llama-3.2-1B-Instruct, 8B process reward model). Paper 2, The Spectrum, Not the Norm, analyses orthogonalised steepest descent under the two approximations every implementation makes - inexact Newton-Schulz orthogonalisation and full-rank gradient noise - and measures its quantities on the gradients of a pretrained 0.5B transformer. Contents: LaTeX sources, all experiment code, every derived result as JSON, every figure, and reproduce.py which re-runs each stage end to end. Third-party corpora are NOT redistributed here; DATA.md records the provenance of each and the code fetches them on demand. Code is MIT licensed; sources, figures and derived results are additionally CC BY 4.0.