Interpret the block substructure in adjacent-transposition position embeddings

Determine what meaning, if any, should be attributed to the block substructure observed in the position-embedding self-similarity matrix for adjacent-transposition words, particularly within the first 120 rows and columns corresponding to transposition-token positions.

Background

The paper analyzes self-similarity heatmaps of the learned token and position embeddings. For the adjacent-transposition experiment, the position-embedding heatmap contains a block substructure in the portion corresponding to positions of transposition tokens.

The authors note that this pattern was not consistently observed for other group sizes, which makes its significance uncertain. They therefore identify the interpretation of this learned structure as unresolved rather than presenting it as an established feature of the model.

References

The somewhat surprising block substructure within the first $120$ rows and columns in Figure~\ref{fig:adjacent_heatmaps_pos}, corresponding to the positions of transposition tokens in a word, was not always observed in experiments with other group sizes, and it is unclear what meaning, if any, should be attributed to it.

— Learning the symmetric group: large from small  (2502.12717 - Petschack et al., 18 Feb 2025) in Section 5, subsection “Interpretation,” subsubsection “Adjacent transpositions”