A Theoretical Analysis of Mamba's Training Dynamics: Filtering Relevant Features for Generalization in State Space Models

Mugunthan Shandirasegaran; Hongkang Li; Songyang Zhang; Meng Wang; Shuai Zhang

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arXiv · 2602.12499

A Theoretical Analysis of Mamba's Training Dynamics: Filtering Relevant Features for Generalization in State Space Models

Mugunthan Shandirasegaran·Hongkang Li·Songyang Zhang·Meng Wang·Shuai Zhang

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Abstract

The recent empirical success of Mamba and other selective state space models (SSMs) has renewed interest in non-attention architectures for sequence modeling, yet their theoretical foundations remain underexplored. We present a first-step analysis of generalization and learning dynamics for a simplified but representative Mamba block: a single-layer, single-head selective SSM with input-dependent gating, followed by a two-layer MLP trained via gradient descent (GD). Our study adopts a structured data model with tokens that include both class-relevant and class-irrelevant patterns under token-level noise and examines two canonical regimes: majority-voting and locality-structured data sequences. We prove that the model achieves guaranteed generalization by establishing non-asymptotic sample complexity and convergence rate bounds, which improve as the effective signal increases and the noise decreases. Furthermore, we show that the gating vector aligns with class-relevant features while ignoring irrelevant ones, thereby formalizing a feature-selection role similar to attention but realized through selective recurrence. Numerical experiments on synthetic data justify our theoretical results. Overall, our results provide principled insight into when and why Mamba-style selective SSMs learn efficiently, offering a theoretical counterpoint to Transformer-centric explanations.

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Mugunthan Shandirasegaran, Hongkang Li, Songyang Zhang, Meng Wang, Shuai Zhang. 2026-02-13. A Theoretical Analysis of Mamba's Training Dynamics: Filtering Relevant Features for Generalization in State Space Models. https://arxiv.org/abs/2602.12499

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