arXiv:2603.05573v2 Announce Type: replace Abstract: 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 consta
The continuous push for more efficient and scalable AI models, particularly for sequential data, drives theoretical exploration into architectural limitations and optimizations.
Understanding the fundamental mathematical reasons behind the performance and expressivity of sequence models is crucial for future AI development, enabling more informed architectural choices.
This research provides a deeper theoretical framework for why depth is critical in parallelizable sequence models, moving beyond empirical observations to foundational principles.
- · AI researchers
- · Transformer architecture developers
- · High-performance computing sector
- · Inefficient AI model designs
- · Organizations relying on shallow models for complex sequence tasks
Improved design principles for next-generation sequence models.
Faster and more powerful AI applications due to theoretically optimized architectures.
Reduced computational costs for training complex sequence models, making advanced AI more accessible.
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Read at arXiv cs.LG