Why Depth Matters in Parallelizable Sequence Models: A Lie Algebraic View
Scalable sequence models, such as Transformer variants and structured state-space models, often trade expressivity power for sequence-level parallelism, which enables efficient training. Here we examine the bounds on error and how error scales when models operate outside of their expressivity regimes using a Lie-algebraic control perspective. Our theory formulates a correspondence between the depth of a sequence model and the tower of Lie algebra extensions. Echoing recent theoretical studies, we characterize the Lie-algebraic class of constant-depth sequence models and their corresponding expressivity bounds. Furthermore, we analytically derive an approximation error bound and show that ...
| Authors | Gyuryang Heo, Timothy Ngotiaoco, Kazuki Irie et al. |
|---|---|
| Primary category | cs.LG |
| Published | 5 March 2026 |
| Last updated at source | 9 June 2026 |
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