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It is shown that when only a few dimensions can be kept, charts trained under the functional's metric preserve the model's predictions better than variance-based or optimal linear compression.
Across three datasets with non-trivial linguistic structure (CoLA, CREAK, RTE), RMP outperforms Euclidean mean pooling, while on FEVER-Symmetric, a benchmark constructed to remove annotation-driven lexical artifacts, the method correctly stays at chance.
This work asks 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, along the map that pairs each token with its optimal destination.
This work fits this flow's equation of motion as a discrete Langevin model over corpus-mean trajectories of Pythia-160M and Pythia-410M, and scores the predicted steps on held-out tokens.
A token-embedding table holds a hub of short rows near its origin, and it is shown that this cluster biases what nearest-neighbor intrinsic-dimension (ID) estimators report, and it is shown that normalizing the rows instead of removing them gives the same lower reading.
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