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

• URL: http://arxiv.org/abs/2602.12499v1
• Date: Fri, 13 Feb 2026 00:44:26 GMT
• Title: A Theoretical Analysis of Mamba's Training Dynamics: Filtering Relevant Features for Generalization in State Space Models
• Authors: Mugunthan Shandirasegaran, Hongkang Li, Songyang Zhang, Meng Wang, Shuai Zhang,
• Abstract summary: We present a first-step analysis of generalization and learning dynamics for a simplified but representative Mamba block.<n>Our study adopts a structured data model with tokens that include both class-relevant and class-irrelevant patterns under token-level noise.<n>We prove that the model achieves guaranteed generalization by establishing non-asymptotic sample complexity and convergence rate bounds.
• Score: 36.99162631444728
• License: http://creativecommons.org/licenses/by/4.0/
• 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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