StableSSM: Alleviating the Curse of Memory in State-space Models through Stable Reparameterization

• URL: http://arxiv.org/abs/2311.14495v4
• Date: Wed, 5 Jun 2024 05:15:16 GMT
• Title: StableSSM: Alleviating the Curse of Memory in State-space Models through Stable Reparameterization
• Authors: Shida Wang, Qianxiao Li,
• Abstract summary: We prove that state-space models without any re parameterization exhibit a memory limitation similar to that of traditional RNNs. Our analysis identifies this "curse of memory" as a result of the recurrent weights converging to a stability boundary.
• Score: 12.707050104493218
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we investigate the long-term memory learning capabilities of state-space models (SSMs) from the perspective of parameterization. We prove that state-space models without any reparameterization exhibit a memory limitation similar to that of traditional RNNs: the target relationships that can be stably approximated by state-space models must have an exponential decaying memory. Our analysis identifies this "curse of memory" as a result of the recurrent weights converging to a stability boundary, suggesting that a reparameterization technique can be effective. To this end, we introduce a class of reparameterization techniques for SSMs that effectively lift its memory limitations. Besides improving approximation capabilities, we further illustrate that a principled choice of reparameterization scheme can also enhance optimization stability. We validate our findings using synthetic datasets, language models and image classifications.

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