arXiv:2505.11602v3 Announce Type: replace Abstract: Selective State-Space Models (SSMs) such as Mamba have become central to long-sequence modeling. Still, their stability is poorly understood: their state-space coefficients are modulated online by a token-dependent gating signal, making the recurrence neither linear time-invariant nor classically nonlinear. We study continuous-time selective SSMs through passivity, dissipativity, and Input-to-State Stability (ISS), explicitly separating the selection signal $x(\cdot)$ from the driving input $u(\cdot)$. We obtain four results: exponential forg
The paper addresses fundamental stability questions for Selective State-Space Models (SSMs) like Mamba, which have recently gained significant traction in long-sequence modeling, making their theoretical understanding critical for further development.
Understanding the stability properties of selective SSMs is crucial for their reliable deployment in real-world AI applications, especially in safety-critical systems, and for guiding architectural improvements.
This research provides a more robust theoretical foundation for selective SSMs, potentially leading to more stable, predictable, and scalable AI models that can process longer sequences with greater confidence.
- · AI researchers
- · ML framework developers
- · Industries using long-sequence AI models
- · Developers relying on ad-hoc stability solutions
- · AI models without strong theoretical guarantees
Improved understanding of Mamba-like architectures allows for more principled design and deployment.
Increased adoption of selective SSMs in applications requiring high reliability and long context windows due to better theoretical guarantees.
New AI safety standards and regulations might incorporate such stability analysis as a foundational requirement for advanced models.
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Read at arXiv cs.LG