Measuring Optimal Transport in Transformer Depth
A transformer carries each token's state from layer to layer, and the whole vocabulary carried together forms a cloud that moves with depth. We ask whether a trained network moves this cloud the way optimal transport would: at the cheapest cost, and along the map that pairs each token with its optimal destination. We measure both on Pythia-160m and Pythia-410m, with an exact assignment between consecutive layer clouds, a measured sampling floor, calibration on couplings known to be optimal, and a split of the cost into the common shift of the cloud and the token-specific moves. At the last layer, both models move their tokens where the optimal-transport map sends them, at the optimal cost...
| Authors | Alexandre Quemy |
|---|---|
| Primary category | cs.CL |
| Published | 1 September 2026 |
| Last updated at source | 1 September 2026 |
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