mlsanityData to 14 Oct 2026

WaLRUS: Wavelets for Long-range Representation Using SSMs

arXiv 2505.12161 ↗First posted 17 May 2025eess.IV cs.LG cs.SYcited by 0

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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.

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.

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15 of 43 references.

References · 15

  1. 2023Mamba: Linear-Time Sequence Modeling with Selective State Spacescited by 4,718
  2. 2014Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translationcited by 4,057
  3. 2021Efficiently Modeling Long Sequences with Structured State Spacescited by 2,465
  4. 2022Simplified State Space Layers for Sequence Modelingcited by 788
  5. 2018Speech Commands: A Dataset for Limited-Vocabulary Speech Recognitioncited by 752
  6. 2020HiPPO: Recurrent Memory with Optimal Polynomial Projectionscited by 605
  7. 2022On the Parameterization and Initialization of Diagonal State Space Modelscited by 424
  8. 2022Diagonal State Spaces are as Effective as Structured State Spacescited by 350
  9. 2022Liquid Structural State-Space Modelscited by 136
  10. 2022How to Train Your HiPPO: State Space Models with Generalized Orthogonal Basis Projectionscited by 122
  11. 2024State Space Models for Event Camerascited by 75
  12. 2024Wave-Mamba: Wavelet State Space Model for Ultra-High-Definition Low-Light Image Enhancementcited by 48
3 more
  1. 2020Wearing a MASK: Compressed Representations of Variable-Length Sequences Using Recurrent Neural Tangent Kernelscited by 3
  2. 2025SaFARi: State-Space Models for Frame-Agnostic Representationcited by 3
  3. 2025Exploring State Space Model in Wavelet Domain: An Infrared and Visible Image Fusion Network via Wavelet Transform and State Space Modelcited by 2

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  1. 2025W4S4: WaLRUS Meets S4 for Long-Range Sequence Modeling
  2. 2026WaveSSM: Multiscale State-Space Models for Non-stationary Signal Attention
  3. 2026HiPPO Zoo: Explicit Memory Mechanisms for Interpretable State Space Models
  4. 2023Robustifying State-space Models for Long Sequences via Approximate Diagonalization
  5. 2026On the Relation of State Space Models and Hidden Markov Models
  6. 2024MatMamba: A Matryoshka State Space Model
  7. 2023Structured state-space models are deep Wiener models
  8. 2022Simplifying and Understanding State Space Models with Diagonal Linear RNNs