On the Expressivity of Selective State-Space Layers: A Multivariate Polynomial Approach

• URL: http://arxiv.org/abs/2502.02209v1
• Date: Tue, 04 Feb 2025 10:46:39 GMT
• Title: On the Expressivity of Selective State-Space Layers: A Multivariate Polynomial Approach
• Authors: Edo Cohen-Karlik, Itamar Zimerman, Liane Galanti, Ido Atad, Amir Globerson, Lior Wolf,
• Abstract summary: selective state-space layers are a key component of the Mamba architecture. Mamba offers superior representational power over linear attention-based models for long sequences. Our findings are validated by a comprehensive set of empirical experiments on various datasets.
• Score: 64.03138838775456
• License:
• Abstract: Recent advances in efficient sequence modeling have introduced selective state-space layers, a key component of the Mamba architecture, which have demonstrated remarkable success in a wide range of NLP and vision tasks. While Mamba's empirical performance has matched or surpassed SoTA transformers on such diverse benchmarks, the theoretical foundations underlying its powerful representational capabilities remain less explored. In this work, we investigate the expressivity of selective state-space layers using multivariate polynomials, and prove that they surpass linear transformers in expressiveness. Consequently, our findings reveal that Mamba offers superior representational power over linear attention-based models for long sequences, while not sacrificing their generalization. Our theoretical insights are validated by a comprehensive set of empirical experiments on various datasets.

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