Study Explains Why Deeper Sequence Models Perform Better Using Lie Algebraic Theory
Researchers have published a theoretical framework showing that the depth of parallelizable sequence models — such as Transformers and structured state-space models — governs their expressivity, with approximation error decreasing exponentially as depth increases. The work draws on Lie-algebraic control theory to establish a correspondence between model depth and a tower of Lie algebra extensions, characterizing the fundamental limits of constant-depth models. The findings help explain strong empirical performance of deep sequence models and offer a principled basis for architectural design choices in machine learning.
A preprint posted to arXiv by Gyuryang Heo and colleagues presents a Lie-algebraic framework for understanding the expressive power of scalable sequence models, including Transformer variants and structured state-space models. These model classes are widely used because they allow parallel processing of sequences during training, but this efficiency often comes at a cost to expressivity. The authors formalize this trade-off by mapping model depth to a tower of Lie algebra extensions, a structure borrowed from control theory. A central result is an analytically derived approximation error bound showing that error shrinks exponentially with increasing depth, providing a theoretical grounding for the well-known empirical advantage of deeper architectures. The paper also characterizes the Lie-algebraic class of constant-depth models and their inherent expressivity ceilings. Theoretical predictions were validated through experiments on both symbolic word problems and continuous-valued state-tracking tasks. The paper is currently in its second version, which corrects an indexing error and clarifies the presentation of several theorems.
What's missing
The study is a preprint and has not yet undergone formal peer review. It remains an open question how tightly the derived bounds hold in large-scale, real-world training regimes beyond the symbolic and state-tracking benchmarks tested.
What different sources said
- arXiv cs.LGCenter
Why Depth Matters in Parallelizable Sequence Models: A Lie Algebraic View
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