n int32 9 100 | m int32 9 100 | dim int32 2 2 | cost_type class label 6
classes | family_src stringclasses 1
value | family_tgt stringclasses 1
value | coords_src listlengths 9 100 | coords_tgt listlengths 9 100 | a listlengths 9 100 | b listlengths 9 100 | plan_rows listlengths 17 199 | plan_cols listlengths 17 199 | plan_vals listlengths 17 199 | ot_cost float64 0 0.82 | seed int64 20B 20B |
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End of preview. Expand in Data Studio
ToR-OT v2 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
("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 or 2) |
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]^dim, canonical order (2D: k x k grid, x-major) |
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 |
2000000 |
val |
2500 |
test_id |
5000 |
test_extrap |
5000 |
test_ood |
588 |
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
],
"dim": 2,
"side_min": 3,
"side_max": 10,
"extrap_side_min": 11,
"extrap_side_max": 14,
"ood_sides": [
6,
10
]
}
Command:
python -m torot.data.generate --dim 2 --out_dir ./torot_data_2M_2d --repo_id ivanjaenm/torot_data_2M_2d --push --train 2000000 --val 2500 --test_id 5000 --test_extrap 5000 --seed 2 --workers 8
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