ivanjaenm/torot_data_4M_2d

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 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

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	4000000
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
  ],
  "empty_bins_prob": 0.5,
  "empty_frac_min": 0.1,
  "empty_frac_max": 0.7
}

Command:

python -m torot.data.generate --dim 2 --out_dir ./torot_data_4M_2d --repo_id ivanjaenm/torot_data_4M_2d --push --train 4000000 --val 2500 --test_id 5000 --test_extrap 5000 --seed 3 --workers 8 --empty_bins 0.5

Empty bins

In the random splits (train, val, test_id, test_extrap) each marginal independently, with probability 0.5, has a fraction f ~ U(0.1, 0.7) of its bins set to exactly 0 and is renormalised (at least one bin keeps mass). The emptied bins are, with equal probability, a uniformly random subset (family_* = <sampler>+empty_random), the bins farthest from 1-4 random Gaussian bumps (+empty_blobs), or the bins nearest to them (+empty_holes); see torot.data.generate.empty_bins. Every other draw of an instance (support, marginals before emptying, cost type) is the same as without empty bins.