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.
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
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).