WaLRUS: Wavelets for Long Range Representation Using State Space Methods
Abstract
State-Space Models (SSMs) have proven to be powerful tools for online function approximation and for modeling long-range dependencies in sequential data. While recent methods such as HiPPO have demonstrated strong performance using a few polynomial bases, they remain limited by their reliance on closed-form solutions for specific, well-behaved bases. The SaFARi framework generalizes 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 species of SaFARi built from Daubechies wavelet frames. We instantiate two variants, scaled-Walrus and translated-Walrus, and show that their multiresolution and localized nature offers significant advantages in representing non-smooth and transient signals. We compare Walrus to HiPPO-based models and demonstrate improved accuracy, better numerical properties, and more efficient implementations for online function approximation tasks.
Cite
Text
Babaei et al. "WaLRUS: Wavelets for Long Range Representation Using State Space Methods." Advances in Neural Information Processing Systems, 2025.Markdown
[Babaei et al. "WaLRUS: Wavelets for Long Range Representation Using State Space Methods." Advances in Neural Information Processing Systems, 2025.](https://mlanthology.org/neurips/2025/babaei2025neurips-walrus/)BibTeX
@inproceedings{babaei2025neurips-walrus,
title = {{WaLRUS: Wavelets for Long Range Representation Using State Space Methods}},
author = {Babaei, Hossein and White, Mel and Alemohammad, Sina and Baraniuk, Richard},
booktitle = {Advances in Neural Information Processing Systems},
year = {2025},
url = {https://mlanthology.org/neurips/2025/babaei2025neurips-walrus/}
}