# WaLRUS: Wavelets for Long-range Representation Using SSMs

arXiv: https://arxiv.org/abs/2505.12161 · HTML: https://mlsanity.com/paper/2505.12161/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 43 references that are in the map.
- First posted on arXiv 17 May 2025.

## Builds on (most cited first, 15 of 15)

- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [Speech Commands: A Dataset for Limited-Vocabulary Speech Recognition](https://mlsanity.com/paper/1804.03209/) (2018)
- [HiPPO: Recurrent Memory with Optimal Polynomial Projections](https://mlsanity.com/paper/2008.07669/) (2020)
- [On the Parameterization and Initialization of Diagonal State Space Models](https://mlsanity.com/paper/2206.11893/) (2022)
- [Diagonal State Spaces are as Effective as Structured State Spaces](https://mlsanity.com/paper/2203.14343/) (2022)
- [Liquid Structural State-Space Models](https://mlsanity.com/paper/2209.12951/) (2022)
- [How to Train Your HiPPO: State Space Models with Generalized Orthogonal Basis Projections](https://mlsanity.com/paper/2206.12037/) (2022)
- [State Space Models for Event Cameras](https://mlsanity.com/paper/2402.15584/) (2024)
- [Wave-Mamba: Wavelet State Space Model for Ultra-High-Definition Low-Light Image Enhancement](https://mlsanity.com/paper/2408.01276/) (2024)
- [Wearing a MASK: Compressed Representations of Variable-Length Sequences Using Recurrent Neural Tangent Kernels](https://mlsanity.com/paper/2010.13975/) (2020)
- [SaFARi: State-Space Models for Frame-Agnostic Representation](https://mlsanity.com/paper/2505.08977/) (2025)
- [Exploring State Space Model in Wavelet Domain: An Infrared and Visible Image Fusion Network via Wavelet Transform and State Space Model](https://mlsanity.com/paper/2503.18378/) (2025)

## Abstract (arXiv)

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.