gpu/GPU_JOB_REPORT.md

# GPU Monte Carlo audit — ICML 2026 paper #8097

This independent PyTorch audit exercises the stochastic finite-temperature process in Eq. (5.3) at substantially larger Monte Carlo scale than the compact public logbook run. It is supplemental evidence and no GPU output was added to the Trackio Space. After an unrelated duplicate-page sync, the Space was restored in a normal commit to an exact file/OID match with its known-good 6/6 content revision.

## Provenance and cost

- Paper: *Attention's forward pass and Frank-Wolfe* (OpenReview `zrn7rRuvhW`, arXiv `2508.09628`)
- Completed job: <https://huggingface.co/jobs/SabaPivot/6a58f642b1669a49bf077d0d>
- Hardware: one Tesla T4 (`t4-medium`, 15.8 GB reported)
- Container: `pytorch/pytorch:2.7.1-cuda12.8-cudnn9-runtime`
- Runtime: 59 s allocated; simulation wall time 53.05 s
- Approximate compute cost: USD 0.0098 (59 s at USD 0.60/hour; queue time excluded)
- Script SHA-256: `b4b7dd9a13205352941d413d22dd703c39c6e3ea0faf7a8238b177426cdfe1fd`
- Reproducibility seed: `809704`; PyTorch `2.7.1+cu128`; CUDA runtime `12.8`; float32
- A queued L4 duplicate was cancelled before start, so it incurred no compute run.
- Restored Trackio SHA: `7f98d3e41e66736b5b253efa30e48e51d7257fc6`, exactly matching the 20-file contents/OIDs of known-good revision `22953a5f22643808da02d0195ff1b8bc1d18289f`

## Results

The first-phase test used 262,144 replicas at `beta=1e6`, `gamma=0.1`, and `T1=5`. All 262,144 replicas reached the prescribed cell: empirical probability `1.000000`, above the paper-derived lower bound `0.822172`.

For metastability, 16,384 replicas were run at each `beta` in `{4, 8, 12, 16, 20, 24}`. Median exit times were `{6, 16, 58, 233, 963, 4088}` steps. Regressing `log(median exit time)` on `beta` gave a positive slope of `0.330737` and `R^2=0.996331`, supporting exponential-in-beta residence time in this scaled synthetic geometry. No run was censored at the 25,000-step cutoff.

The moderate-beta first-phase sweep also moved monotonically toward certainty: correct-cell fraction rose from `0.888891` at `beta=2` to `1.000000` by `beta=32`.

## Scope

This is a direct numerical check of the paper's stochastic particle dynamics, not a large language-model benchmark and not a proof of the theorem. The exact machine-readable output is in `gpu_job_result.json`; the source is in `gpu_monte_carlo.py`.