| --- |
| 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 |
|
|
| ```json |
| { |
| "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 |
| ``` |
|
|
