| --- |
| license: mit |
| tags: |
| - icml2026-repro |
| - optimal-transport |
| - reproduction-bundle |
| --- |
| |
| # Reproduction bundle — Quadratically Regularized Optimal Transport: Localization Bounds and Affine Case Analysis |
|
|
| Paper: *Quadratically Regularized Optimal Transport: Localization Bounds and Affine Case Analysis* |
| (ICML 2026, OpenReview `kcnuX4xEpL`, arXiv `2605.24644`). |
|
|
| This bundle contains everything needed to re-run the reproduction described in the Trackio logbook |
| [JG1310/repro-quadratically-regularized-optimal-transport-localization-bounds-and-affine](https://huggingface.co/spaces/JG1310/repro-quadratically-regularized-optimal-transport-localization-bounds-and-affine). |
|
|
| Both extracted claims are **proven theorems**. The reproduction is therefore an **independent |
| numerical audit** (per the challenge guide's theory-paper clause), not a GPU benchmark: |
|
|
| - **Claim 1 (Theorem 3.3):** directed-Hausdorff support cannot concentrate around the Monge graph |
| faster than `ε^(1/(d+2))` — a *lower* bound. |
| - **Claim 2 (Theorem 3.7):** in the affine Brenier regime (incl. Gaussian→Gaussian) a sharp |
| pointwise tube bound of order `ε^(1/(d+2))` holds — a matching *upper* bound. |
|
|
| ## Contents |
|
|
| | Path | What it is | |
| |---|---| |
| | `DERIVATIONS.md` | Step-by-step re-derivation of both theorems (D1–D6c), each paired with an executable check | |
| | `scripts/derivation_checks.py` | 13 numerical audits of the algebra/lemmas (CHK-D1..D6c), CPU-only, <0.5 s | |
| | `scripts/exp01_affine_scaling.py` | Full-scale affine-scaling diagnostic (paper §5 / Appendix B.2–B.6) | |
| | `specs/exp01_affine_scaling.md` | Exact experiment spec (parameters, solvers, acceptance gate) | |
| | `gates.py` | Structural acceptance gate for `results/exp01.json` | |
| | `results/exp01.json` | Full-scale run output: 80 records, 8 summary rows (N=M=2000, R=10, d∈{100,200,500,1000}) | |
| | `results/GATE_REPORT.txt` | `gates.py --full` report (21/21 PASS) | |
| | `results/derivation_checks.log` | `derivation_checks.py` output (13/13 PASS) | |
| | `results/DRIVER_REPORT.json` | Driver status (`{"exp01":"PASS"}`) | |
| | `logs/exp01.log` | Verbatim stderr trace of the 800-solve full run | |
| | `BRIEF_WRITER.md`, `STATE.md` | Planner's claim→evidence map and in-regime honesty notes | |
|
|
| ## How to re-run |
|
|
| ```bash |
| python3 -m venv .venv && . .venv/bin/activate |
| pip install numpy scipy joblib # derivation_checks also uses scipy |
| |
| # 1) Derivation audit (seconds, CPU): re-verifies every algebraic step of both theorems. |
| python3 scripts/derivation_checks.py # expect "13/13 PASS", exit 0 |
| |
| # 2) Full-scale empirical diagnostic (~8.5 h on 8 cores; d-independent 2000x2000 solves). |
| JOB_CORES=8 python3 scripts/exp01_affine_scaling.py # writes results/exp01.json (+ work/ checkpoints) |
| |
| # 3) Structural gate on the produced results file. |
| python3 gates.py --full # expect "ALL PASS (21/21)" |
| |
| # Smoke test only (minutes): a d=10, N=M=200, R=2 toy of the same code path. |
| python3 scripts/exp01_affine_scaling.py --toy |
| ``` |
|
|
| `exp01` is checkpointed per `(d, seed)` unit under `work/`; a restart skips completed units, so |
| a kill loses at most one in-flight unit. |
|
|
| ## Outcome |
|
|
| Both claims **VERIFIED** via the derivation audit (13/13 machine-precision checks, incl. an |
| in-regime confirmation of the shared `ε^(2/(d+2))` value-gap rate at d=1). The full-scale `exp01` |
| diagnostic reproduces the paper's qualitative Figure-1 pattern (β̂ decreasing with d, tight |
| two-solver agreement, correct order of magnitude, monotonically increasing RelErr) with **one |
| honestly documented quantitative discrepancy**: the RelErr zero-crossing occurs between d=100 and |
| d=200 here, versus the paper's reported crossing between d=500 and d=1000. Because the theorem's |
| strict asymptotic regime (`ε ≤ ε₀ ≈ 10^(−152)` at d=100) is unreachable in double precision for any |
| tested d, the entire β̂(d) curve is pre-asymptotic — the discrepancy reflects how far pre-asymptotic |
| effects push each implementation, not a violation of the theorems (whose correctness is established |
| by the derivation audit). |
|
|
