README.md

metadata

license: mit
pretty_name: ToR-OT synthetic discrete OT instances
dataset_info:
  features:
    - name: 'n'
      dtype: int32
    - name: m
      dtype: int32
    - name: dim
      dtype: int32
    - name: cost_type
      dtype:
        class_label:
          names:
            '0': sqeuclidean
            '1': euclidean
            '2': canberra
            '3': sqrt_euclidean
            '4': cubic_euclidean
            '5': gaussian
    - name: family_src
      dtype: string
    - name: family_tgt
      dtype: string
    - name: coords_src
      list:
        list: float64
    - name: coords_tgt
      list:
        list: float64
    - name: a
      list: float64
    - name: b
      list: float64
    - name: plan_rows
      list: int32
    - name: plan_cols
      list: int32
    - name: plan_vals
      list: float64
    - name: ot_cost
      dtype: float64
    - name: seed
      dtype: int64
  splits:
    - name: train
      num_bytes: 19249854200
      num_examples: 5000000
    - name: val
      num_bytes: 9494824
      num_examples: 2500
    - name: test_id
      num_bytes: 19330928
      num_examples: 5000
    - name: test_extrap
      num_bytes: 57781232
      num_examples: 5000
    - name: test_ood
      num_bytes: 7858384
      num_examples: 1728
  download_size: 17054524157
  dataset_size: 19344319568
configs:
  - config_name: default
    data_files:
      - split: train
        path: data/train-*
      - split: val
        path: data/val-*
      - split: test_id
        path: data/test_id-*
      - split: test_extrap
        path: data/test_extrap-*
      - split: test_ood
        path: data/test_ood-*

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	5000000
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_5M --repo_id ivanjaenm/torot_data_5M --push --train 5000000 --val 2500 --test_id 5000 --test_extrap 5000 --seed 0 --workers 32