Dataset Viewer
The dataset viewer is not available for this split.
Cannot load the dataset split (in streaming mode) to extract the first rows.
Error code: StreamingRowsError
Exception: CastError
Message: Couldn't cast
meta: struct<N: int64, M: int64, R: int64, d_grid: list<item: int64>, eps_multipliers: list<item: double>, (... 83 chars omitted)
child 0, N: int64
child 1, M: int64
child 2, R: int64
child 3, d_grid: list<item: int64>
child 0, item: int64
child 4, eps_multipliers: list<item: double>
child 0, item: double
child 5, initTol: double
child 6, tau: double
child 7, base: double
child 8, a: int64
child 9, solvers: list<item: string>
child 0, item: string
records: list<item: struct<d: int64, seed: int64, solver: string, c_med: double, eps_actual: list<item: doubl (... 210 chars omitted)
child 0, item: struct<d: int64, seed: int64, solver: string, c_med: double, eps_actual: list<item: double>, dbias: (... 198 chars omitted)
child 0, d: int64
child 1, seed: int64
child 2, solver: string
child 3, c_med: double
child 4, eps_actual: list<item: double>
child 0, item: double
child 5, dbias: list<item: double>
child 0, item: double
child 6, converged: list<item: bool>
child 0, item: bool
child 7, n_active: list<item: int64>
child 0, item: int64
child 8, iters: list<item: int64>
child 0, item: int64
child 9, warm_start: string
child 10, n_points_fit: int64
child 11, alpha_hat: double
child 12, beta_hat: double
child 13, rel_err: double
summary: list<item: struct<d: int64, solver: string, theory: double, beta_mean: double, beta_std: double, rel (... 56 chars omitted)
child 0, item: struct<d: int64, solver: string, theory: double, beta_mean: double, beta_std: double, rel_err_mean: (... 44 chars omitted)
child 0, d: int64
child 1, solver: string
child 2, theory: double
child 3, beta_mean: double
child 4, beta_std: double
child 5, rel_err_mean: double
child 6, rel_err_std: double
child 7, n_seeds: int64
exp01: string
to
{'exp01': Value('string')}
because column names don't match
Traceback: Traceback (most recent call last):
File "/src/services/worker/src/worker/utils.py", line 149, in get_rows_or_raise
return get_rows(
dataset=dataset,
...<4 lines>...
column_names=column_names,
)
File "/src/libs/libcommon/src/libcommon/utils.py", line 272, in decorator
return func(*args, **kwargs)
File "/src/services/worker/src/worker/utils.py", line 129, in get_rows
rows_plus_one = list(itertools.islice(safe_iter(ds, dataset=dataset), rows_max_number + 1))
File "/src/services/worker/src/worker/utils.py", line 489, in safe_iter
yield from ds.decode(False) if ds.features else ds
File "/usr/local/lib/python3.14/site-packages/datasets/iterable_dataset.py", line 2818, in __iter__
for key, example in ex_iterable:
^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/iterable_dataset.py", line 2355, in __iter__
for key, pa_table in self._iter_arrow():
~~~~~~~~~~~~~~~~^^
File "/usr/local/lib/python3.14/site-packages/datasets/iterable_dataset.py", line 2380, in _iter_arrow
for key, pa_table in self.ex_iterable._iter_arrow():
~~~~~~~~~~~~~~~~~~~~~~~~~~~~^^
File "/usr/local/lib/python3.14/site-packages/datasets/iterable_dataset.py", line 536, in _iter_arrow
for key, pa_table in iterator:
^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/iterable_dataset.py", line 419, in _iter_arrow
for key, pa_table in self.generate_tables_fn(**gen_kwags):
~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/packaged_modules/json/json.py", line 343, in _generate_tables
self._cast_table(pa_table, json_field_paths=json_field_paths),
~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/packaged_modules/json/json.py", line 132, in _cast_table
pa_table = table_cast(pa_table, self.info.features.arrow_schema)
File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 2369, in table_cast
return cast_table_to_schema(table, schema)
File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 2297, in cast_table_to_schema
raise CastError(
...<3 lines>...
)
datasets.table.CastError: Couldn't cast
meta: struct<N: int64, M: int64, R: int64, d_grid: list<item: int64>, eps_multipliers: list<item: double>, (... 83 chars omitted)
child 0, N: int64
child 1, M: int64
child 2, R: int64
child 3, d_grid: list<item: int64>
child 0, item: int64
child 4, eps_multipliers: list<item: double>
child 0, item: double
child 5, initTol: double
child 6, tau: double
child 7, base: double
child 8, a: int64
child 9, solvers: list<item: string>
child 0, item: string
records: list<item: struct<d: int64, seed: int64, solver: string, c_med: double, eps_actual: list<item: doubl (... 210 chars omitted)
child 0, item: struct<d: int64, seed: int64, solver: string, c_med: double, eps_actual: list<item: double>, dbias: (... 198 chars omitted)
child 0, d: int64
child 1, seed: int64
child 2, solver: string
child 3, c_med: double
child 4, eps_actual: list<item: double>
child 0, item: double
child 5, dbias: list<item: double>
child 0, item: double
child 6, converged: list<item: bool>
child 0, item: bool
child 7, n_active: list<item: int64>
child 0, item: int64
child 8, iters: list<item: int64>
child 0, item: int64
child 9, warm_start: string
child 10, n_points_fit: int64
child 11, alpha_hat: double
child 12, beta_hat: double
child 13, rel_err: double
summary: list<item: struct<d: int64, solver: string, theory: double, beta_mean: double, beta_std: double, rel (... 56 chars omitted)
child 0, item: struct<d: int64, solver: string, theory: double, beta_mean: double, beta_std: double, rel_err_mean: (... 44 chars omitted)
child 0, d: int64
child 1, solver: string
child 2, theory: double
child 3, beta_mean: double
child 4, beta_std: double
child 5, rel_err_mean: double
child 6, rel_err_std: double
child 7, n_seeds: int64
exp01: string
to
{'exp01': Value('string')}
because column names don't matchNeed help to make the dataset viewer work? Make sure to review how to configure the dataset viewer, and open a discussion for direct support.
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).
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