![[2602.12499] A Theoretical Analysis of Mamba's Training Dynamics: Filtering Relevant Features for Generalization in State Space Models](https://arxiv.org/static/browse/0.3.4/images/arxiv-logo-fb.png){kind=logo}
[2602.12499] A Theoretical Analysis of Mamba's Training Dynamics: Filtering Relevant Features for Generalization in State Space Models
Summary
This article presents a theoretical analysis of Mamba's training dynamics, focusing on feature selection in state space models and their generalization capabilities.
Why It Matters
Understanding the theoretical foundations of Mamba and similar selective state space models is crucial as they offer alternatives to attention-based architectures, which dominate current sequence modeling. This analysis provides insights into their efficiency and potential applications in machine learning.
Key Takeaways
- Mamba's selective state space models show guaranteed generalization under specific conditions.
- The model's gating mechanism effectively filters out irrelevant features, similar to attention mechanisms.
- Numerical experiments support the theoretical findings, emphasizing the model's practical relevance.
Computer Science > Machine Learning arXiv:2602.12499 (cs) [Submitted on 13 Feb 2026] 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 View a PDF of the paper titled A Theoretical Analysis of Mamba's Training Dynamics: Filtering Relevant Features for Generalization in State Space Models, by Mugunthan Shandirasegaran and 4 other authors View PDF HTML (experimental) 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...