Summary of The Expressive Capacity Of State Space Models: a Formal Language Perspective, by Yash Sarrof et al.
The Expressive Capacity of State Space Models: A Formal Language Perspective
by Yash Sarrof, Yana Veitsman, Michael Hahn
First submitted to arxiv on: 27 May 2024
Categories
- Main: Computation and Language (cs.CL)
- Secondary: Formal Languages and Automata Theory (cs.FL); Machine Learning (cs.LG)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary Recurrent models based on linear state space models (SSMs) have recently shown promising performance in language modeling (LM), competitive with transformers. This paper presents a comprehensive theoretical study to understand the capacity of such SSMs compared to transformers and traditional RNNs. The results show that SSMs and transformers have overlapping but distinct strengths. While SSMs are better at implementing exact solutions to certain problems, transformers struggle to represent these exactly. SSMs can also model hierarchical structure with optimal memory without simulating a stack. However, the authors identify a design choice in current SSMs that limits their expressive power. The implications of these findings for SSM and LM research are discussed, and empirical verification is provided on a recent SSM, Mamba. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Recently, researchers have found that recurrent models based on linear state space models (SSMs) can do well at language modeling (LM), just like transformers. But we don’t really know why this works or how to make it even better. This paper tries to figure out what SSMs are good at and where they fall short compared to transformers and other kinds of RNNs. The results show that SSMs and transformers both have their strengths, but in different areas. For example, SSMs can solve certain problems exactly, while transformers struggle with those same problems. This helps us understand how we can use SSMs for language modeling better. |
