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18,
19,
20,
20,
21,
22,
23,
24,
24,
25,
25,
26,
26,
26,
27,
27,
27,
28,
29,
... | [
0,
1,
2,
1,
2,
3,
4,
5,
5,
6,
6,
7,
8,
9,
8,
9,
10,
8,
11,
1,
5,
6,
8,
12,
14,
13,
14,
14,
14,
15,
16,
16,
17,
16,
18,
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21,
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22,
23,
23,
24,
23,
25,
22,
23,
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21,
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28,
29,
28,
2... | [
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0.0066959662298995155,
0.0022863120965062635,
0.010434034327830617,
0.011030066748173323,
0.001491469096218103,
0.007355277815526331,
0.00016651013941457182,
0.006616678059126465,
0.0012554188458090414,
0.0002563464137373831,
0.006261302038521817,
0.0008010844076161932,
... | 0.071758 | 18 |
61 | 61 | 1 | 2canberra | simplex | simplex | [
[
0.00819672131147541
],
[
0.02459016393442623
],
[
0.040983606557377046
],
[
0.05737704918032787
],
[
0.07377049180327869
],
[
0.09016393442622951
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[
0.10655737704918032
],
[
0.12295081967213115
],
[
0.13934426229508196
],
[
0.1557377049... | [
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0.02459016393442623
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0.040983606557377046
],
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0.05737704918032787
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0.07377049180327869
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[
0.09016393442622951
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[
0.10655737704918032
],
[
0.12295081967213115
],
[
0.13934426229508196
],
[
0.1557377049... | [
0.019414294489273405,
0.00920977518711806,
0.0014282271822541283,
0.015596761633056518,
0.029926128977354537,
0.045229029284558145,
0.02210755540683442,
0.001607583514632606,
0.0049829294836035935,
0.02370412010472745,
0.007494911876599674,
0.020048831179943296,
0.013541017934874075,
0.042... | [
0.020614591094726974,
0.02022698852648422,
0.0005136672869670826,
0.03662001906807219,
0.006178099546441168,
0.01543852587954454,
0.0022795094282665727,
0.02076090355213691,
0.03938462592381949,
0.008229706127196161,
0.00802992003719651,
0.026619008374832574,
0.020538489232867847,
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10,
11,
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11,
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11,
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14,
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60,
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17,
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17,
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19,
20,
20,
21,
60,
22,
60,
23,
26,
59,
60,
24,
26,
25,
26,
26,
27,
... | [
0.01941429448927341,
0.00920977518711806,
0.0009145598952870459,
0.0005136672869670824,
0.015596761633056518,
0.0027247719958977097,
0.021023257435015662,
0.006178099546441165,
0.0012002966054535588,
0.007377881448181398,
0.015438525879544534,
0.02121232535137864,
0.002279509428266572,
0.0... | 0.076635 | 19 |
End of preview. Expand in Data Studio
ToR-OT synthetic optimal-transport corpus
Discrete Kantorovich instances with exact sparse optimal plans, generated by
python -m torot.data.generate from the ToR-OT code release (https://github.com/vsingh-group/TOR-OT)
("Learning Optimal Transport Plans Via Autoregressive Token Regression", NeurIPS 2026).
Each record is one instance:
| field | description |
|---|---|
n, m |
number of source / target bins |
dim |
support dimension (1) |
cost_type |
one of sqeuclidean, euclidean, canberra, sqrt_euclidean, cubic_euclidean, gaussian |
coords_src, coords_tgt |
bin centres of a regular grid on [0,1], canonical order |
a, b |
marginals (float64, sum to 1); for the random splits drawn by the marginals sampler of the generation config (simplex: uniform on the probability simplex, Dirichlet(1,…,1); normalized_uniform: normalised i.i.d. U(0,1) weights) |
plan_rows, plan_cols, plan_vals |
COO of the optimal plan returned by POT's network simplex (ot.emd) |
ot_cost |
optimal cost with the max-normalised cost matrix |
family_src, family_tgt |
the marginal sampler (simplex or normalized_uniform), or the named density for the OOD evaluation split |
seed |
per-instance seed (instances are fully reproducible) |
The cost matrix is not stored; it is torot.data.cost.cost_matrix(coords_src, coords_tgt, cost_type).
Cost types
cost_type holds the code name; the paper writes the costs as below. L2^p is the Euclidean distance to the power p
(in 1D, L2 = |x - y|, which on a line also equals L1 and L∞). Each cost matrix is divided by its largest entry.
cost_type |
paper | c(x, y) |
|---|---|---|
euclidean |
L2 | ‖x − y‖₂ |
sqrt_euclidean |
L2^(1/2) | ‖x − y‖₂^(1/2) |
sqeuclidean |
L2^2 | ‖x − y‖₂² |
cubic_euclidean |
L2^3 | ‖x − y‖₂³ |
canberra |
Canberra | Σ_d |x_d − y_d| / (|x_d| + |y_d|) |
gaussian |
Gaussian | 1 − exp(−‖x − y‖₂² / 2σ²), σ = 0.2 |
Splits
| split | instances |
|---|---|
train |
1000000 |
val |
2500 |
test_id |
5000 |
test_extrap |
5000 |
test_ood |
1728 |
Generation configuration
{
"n_min": 5,
"n_max": 100,
"extrap_n_min": 120,
"extrap_n_max": 200,
"equal_sizes": true,
"marginals": "simplex",
"cost_types": [
"sqeuclidean",
"euclidean",
"canberra",
"sqrt_euclidean",
"cubic_euclidean",
"gaussian"
],
"ood_sizes": [
30,
100
]
}
Command:
python -m torot.data.generate --out_dir ./torot_data_1M --repo_id ivanjaenm/torot_data_1M --push --train 1000000 --val 2500 --test_id 5000 --test_extrap 5000 --seed 0 --workers 16
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