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arxiv: 2604.23818 · v1 · submitted 2026-04-26 · 📡 eess.SY · cs.SY

On the Generalization Properties of Selective State-Space Models for Filtering Tasks for Unknown Systems

Alex Tang , M. Emrullah Ildiz , Batin Kurt , Samet Oymak , Necmiye Ozay This is my paper

Pith reviewed 2026-05-08 05:19 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords selective state-space modelsgeneralization boundsfiltering tasksunknown systemsin-context learningonline predictiondynamical systemsMamba
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The pith

Selective state-space models generalize to filter and predict outputs from unknown systems drawn from a trained class, supported by derived bounds.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper studies whether selective state-space models can perform online filtering and next-output prediction for dynamical systems whose parameters are unknown at run time. It trains the model on trajectories sampled from a family of systems, then feeds only the output sequence of a new system from the same family and requires the model to forecast future outputs without further adaptation. Under appropriate assumptions the authors derive generalization bounds that account for this success, and they illustrate the result with numerical examples while comparing SSMs to transformer baselines for the same task.

Core claim

Under appropriate assumptions, selective state-space models trained on trajectory samples from a set of systems generalize to perform online output prediction for an unknown system from the same set, as established by the derived generalization bounds.

What carries the argument

Generalization bounds for selective state-space models in the in-context filtering setting for unknown dynamical systems.

If this is right

  • SSMs can be trained once on a family of systems and then deployed for online filtering of new members without explicit parameter identification.
  • The bounds imply that prediction accuracy improves when training trajectories cover more of the system class.
  • Structured SSMs may replace attention-based models for filtering tasks where linear scaling with sequence length is required.
  • Empirical demonstrations confirm that the theoretical guarantees align with observed performance on concrete examples.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar bounds could be derived when the test system lies slightly outside the convex hull of the training distribution, testing robustness of the in-context mechanism.
  • The comparison between SSMs and transformers could be sharpened by measuring sample complexity needed to reach a target filtering error on the same system class.
  • The framework might be extended to derive bounds for tasks that combine filtering with control inputs generated by the model itself.

Load-bearing premise

The appropriate assumptions on the system family, model structure, and data distribution that make the generalization bounds hold.

What would settle it

An experiment in which the online prediction error for a new system stays above the rate guaranteed by the bound even after the number of training trajectories from the system class is increased.

Figures

Figures reproduced from arXiv: 2604.23818 by Alex Tang, Batin Kurt, M. Emrullah Ildiz, Necmiye Ozay, Samet Oymak.

Figure 1
Figure 1. Figure 1: Comparison of RMS prediction errors for the selective SSM, GPT-2, and the Kalman filter in online prediction tasks. view at source ↗
read the original abstract

Selective State-Space Models (SSMs) such as Mamba have emerged as an alternative architecture to self-attention based transformers in sequence modeling tasks. Recent works have demonstrated the use of transformers in some filtering and output prediction tasks via in-context learning. In this paper, we analyze whether structured SSMs can work equally well for filtering of unknown systems. In particular, we train the SSM on trajectory samples from a set of systems. At run-time, the SSM is given the outputs of an unknown system from the same set and is expected to predict the next output online. Theoretically, under appropriate assumptions, we derive generalization bounds as to why SSMs succeed in such tasks. Empirically, we demonstrate the performance via several numerical examples. We also discuss the advantages and disadvantages of SSMs versus transformers for this task.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The paper claims that selective state-space models (SSMs) can perform online output prediction and filtering for unknown systems drawn from a fixed class by training on trajectory samples. Under assumptions of stable LTI systems with bounded parameters and Lipschitz dynamics, with the SSM trained near-optimally and the selective mechanism preserving contraction, generalization bounds are derived via a covering-number argument on the induced function class. Numerical examples demonstrate performance, and advantages/disadvantages versus transformers are discussed.

Significance. If the bounds hold, the work supplies a rigorous, non-circular explanation for SSM success in filtering tasks on unknown dynamical systems, using standard covering-number techniques and explicit assumptions. This strengthens the case for SSMs as efficient alternatives to transformers in systems applications, with the numerical examples providing concrete empirical support.

minor comments (3)
  1. [Abstract] The abstract refers to 'appropriate assumptions' without enumeration; while the theory section states them explicitly (stable LTI, bounded parameters, Lipschitz, near-optimal training, contraction preservation), a one-sentence summary in the abstract would aid readers.
  2. [Numerical examples] In the numerical examples section, the performance plots lack error bars or multiple random seeds; reporting variability would strengthen the empirical claims of generalization.
  3. [Discussion] The discussion of SSM vs. transformer advantages would benefit from a brief complexity table (e.g., inference cost per step) to make the comparison more quantitative.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our work on the generalization properties of selective state-space models for filtering unknown systems. The summary accurately captures the main contributions, including the derivation of bounds under stability and Lipschitz assumptions, the covering-number argument, and the empirical demonstrations. We appreciate the recognition of the potential implications for SSMs versus transformers in systems applications. As no specific major comments were provided in the report, we have no points to rebut or revise at this stage, though we will carefully incorporate any minor suggestions during the revision process.

Circularity Check

0 steps flagged

No significant circularity in generalization bound derivation

full rationale

The paper derives generalization bounds for selective SSMs on filtering tasks for unknown LTI systems via a standard covering-number argument applied to the function class induced by the SSM recurrence. This proceeds from explicitly stated assumptions (stable systems with bounded parameters, Lipschitz dynamics, near-optimal training on sufficient trajectories, and preservation of contraction properties by the selective mechanism) without any reduction of the bounds to fitted quantities, self-definitions, or load-bearing self-citations by construction. The central theoretical claim retains independent content from the proof technique and external statistical learning tools.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated.

pith-pipeline@v0.9.0 · 5458 in / 932 out tokens · 63912 ms · 2026-05-08T05:19:13.912830+00:00 · methodology

discussion (0)

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Reference graph

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