Expressivity-Efficiency Tradeoffs for Hybrid Sequence Models

TL;DR

This paper investigates the tradeoffs in hybrid sequence models combining Transformers and state-space layers, demonstrating their advantages in efficiency and generalization through theoretical proofs and empirical validation on synthetic tasks.

Contribution

It provides the first theoretical analysis of hybrid models' benefits and limitations, and empirically shows learned hybrids outperform non-hybrids in various metrics.

Findings

Hybrid models solve synthetic tasks with fewer parameters and less memory.

Learned hybrid models outperform non-hybrids with up to 6x parameters.

Hybrid models show improved length generalization and robustness.

Abstract

Hybrid sequence models--combining Transformer and state-space model layers--seek to gain the expressive versatility of attention as well as the computational efficiency of state-space model layers. Despite burgeoning interest in hybrid models, we lack a basic understanding of the settings where--and underlying mechanisms through which--they offer benefits over their constituent models. In this paper, we study this question, focusing on a broad family of core synthetic tasks. For this family of tasks, we prove the existence of fundamental limitations for non-hybrid models. Specifically, any Transformer or state-space model that solves the underlying task requires either a large number of parameters or a large working memory. On the other hand, for two prototypical tasks within this family--namely selective copying and associative recall--we construct hybrid models of small size and working memory that provably solve these tasks, thus achieving the best of both worlds. Our experimental evaluation empirically validates our theoretical findings. Importantly, going beyond the settings in our theoretical analysis, we empirically show that learned--rather than constructed--hybrids outperform non-hybrid models with up to 6x as many parameters. We additionally demonstrate that hybrid models exhibit stronger length generalization and out-of-distribution robustness than non-hybrids.