The Expressive Limits of Diagonal SSMs for State-Tracking
State-Space Models (SSMs) have recently been shown to achieve strong empirical performance on a variety of long-range sequence modeling tasks while remaining efficient and highly-parallelizable. However, the theoretical understanding of their expressive power remains limited. In this work, we study the expressivity of input-Dependent Complex-valued Diagonal (DCD) SSMs on sequential state-tracking tasks. We show that single-layer DCD SSMs cannot express state-tracking of any non-Abelian group at finite precision. More generally, we show that $k$-layer DCD SSMs can express state-tracking of a group if and only if that group has a subnormal series of length $k$, with Abelian factors. That is...
| Authors | Mehran Shakerinava, Behnoush Khavari, Siamak Ravanbakhsh et al. |
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| Primary category | cs.LG |
| Published | 2 March 2026 |
| Last updated at source | 14 August 2026 |
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