SaFARi: State-Space Models for Frame-Agnostic Representation

2025-05-13

AI Summary

Existing state space models (SSMs) heavily rely on restrictive polynomial bases—such as HiPPO—limiting their adaptability to arbitrary signal representation frameworks and thereby impairing flexibility and robustness in long-range dependency modeling. To address this, we propose a frame-agnostic, universal SSM construction paradigm that rigorously generalizes SSMs to arbitrary orthonormal bases—including Fourier and wavelet bases—as well as general Parseval frames. Methodologically, our approach unifies functional space analysis with structured state-space modeling by integrating generalized orthogonal projection theory with continuous-time system discretization techniques. This framework subsumes HiPPO as a special case while enabling infinitely many novel SSM instantiations. Crucially, it preserves theoretical soundness while substantially enhancing robustness to sequence length variation and expanding modeling diversity across signal domains.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

State-Space Models (SSMs) have re-emerged as a powerful tool for online function approximation, and as the backbone of machine learning models for long-range dependent data. However, to date, only a few polynomial bases have been explored for this purpose, and the state-of-the-art implementations were built upon the best of a few limited options. In this paper, we present a generalized method for building an SSM with any frame or basis, rather than being restricted to polynomials. This framework encompasses the approach known as HiPPO, but also permits an infinite diversity of other possible"species"within the SSM architecture. We dub this approach SaFARi: SSMs for Frame-Agnostic Representation.

Problem

• Generalizing SSM construction beyond polynomial bases
• Enabling diverse frame-agnostic representations in SSMs
• Extending HiPPO framework to infinite basis options

Innovation

• Generalized SSM method with any frame or basis
• Extends beyond polynomial bases like HiPPO
• Enables diverse SSM architecture species