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

Fuente: arXiv
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Main Authors: Wang, Shida, Li, Qianxiao
Format: Preprint
Published: 2023
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author Wang, Shida
Li, Qianxiao
author_facet Wang, Shida
Li, Qianxiao
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2311_14495
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle StableSSM: Alleviating the Curse of Memory in State-space Models through Stable Reparameterization
Wang, Shida
Li, Qianxiao
Machine Learning
Artificial Intelligence
Computation and Language
Dynamical Systems
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.
title StableSSM: Alleviating the Curse of Memory in State-space Models through Stable Reparameterization
topic Machine Learning
Artificial Intelligence
Computation and Language
Dynamical Systems
url https://arxiv.org/abs/2311.14495