arXiv Computation and Language By Alexandre Quemy

Measuring Optimal Transport in Transformer Depth

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The study investigates whether transformer models transport token representations across layers in a manner consistent with optimal transport theory. Using Pythia-160m and Pythia-410m, the authors measure exact assignments between consecutive layer clouds, calibrate couplings, and decompose the transport cost into common shifts and token‑specific moves. Results show that at the final layer both models align closely with the optimal‑transport map—Pythia‑410m at optimal cost and Pythia‑160m slightly above—while earlier layers deviate, and the agreement improves with training.

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