Dataset card: license, code link, cost types

README.md

@@ -1,4 +1,6 @@
 ---
+license: mit
+pretty_name: ToR-OT synthetic discrete OT instances
 dataset_info:
   features:
   - name: n
@@ -74,10 +76,10 @@ configs:
     path: data/test_ood-*
 ---
 
-# ToR-OT v2 synthetic optimal-transport corpus
+# 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
+`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:
@@ -96,6 +98,20 @@ Each record is one instance:
 
 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 |