WaLRUS: Wavelets for Long-range Representation Using SSMs
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909614902083584 |
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| author | Babaei, Hossein White, Mel Alemohammad, Sina Baraniuk, Richard G. |
| author_facet | Babaei, Hossein White, Mel Alemohammad, Sina Baraniuk, Richard G. |
| contents | State-Space Models (SSMs) have proven to be powerful tools for modeling long-range dependencies in sequential data. While the recent method known as HiPPO has demonstrated strong performance, and formed the basis for machine learning models S4 and Mamba, it remains limited by its reliance on closed-form solutions for a few specific, well-behaved bases. The SaFARi framework generalized this approach, enabling the construction of SSMs from arbitrary frames, including non-orthogonal and redundant ones, thus allowing an infinite diversity of possible "species" within the SSM family. In this paper, we introduce WaLRUS (Wavelets for Long-range Representation Using SSMs), a new implementation of SaFARi built from Daubechies wavelets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_12161 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | WaLRUS: Wavelets for Long-range Representation Using SSMs Babaei, Hossein White, Mel Alemohammad, Sina Baraniuk, Richard G. Image and Video Processing Machine Learning Systems and Control Audio and Speech Processing Signal Processing State-Space Models (SSMs) have proven to be powerful tools for modeling long-range dependencies in sequential data. While the recent method known as HiPPO has demonstrated strong performance, and formed the basis for machine learning models S4 and Mamba, it remains limited by its reliance on closed-form solutions for a few specific, well-behaved bases. The SaFARi framework generalized this approach, enabling the construction of SSMs from arbitrary frames, including non-orthogonal and redundant ones, thus allowing an infinite diversity of possible "species" within the SSM family. In this paper, we introduce WaLRUS (Wavelets for Long-range Representation Using SSMs), a new implementation of SaFARi built from Daubechies wavelets. |
| title | WaLRUS: Wavelets for Long-range Representation Using SSMs |
| topic | Image and Video Processing Machine Learning Systems and Control Audio and Speech Processing Signal Processing |
| url | https://arxiv.org/abs/2505.12161 |