Can Mamba Learn In Context with Outliers? A Theoretical Generalization Analysis

2025-09-30

AI Summary

This work addresses the lack of theoretical understanding of Mamba’s in-context learning (ICL) generalization under outlier-contaminated prompts. We present the first theoretical analysis of training dynamics for a single-layer Mamba model. By decoupling its linear state-space attention from the nonlinear gating mechanism, we show that the gating unit actively suppresses outlier-induced interference, thereby substantially enhancing noise robustness. Both theoretical analysis and empirical experiments demonstrate that, although Mamba converges more slowly than linear Transformers, it maintains high prediction accuracy even when the outlier ratio exceeds the tolerance threshold of linear Transformers—exhibiting superior fault tolerance. This study establishes the first analytically tractable theoretical framework for understanding Mamba’s ICL behavior and clarifies the critical role of gated design in enabling robust generalization.

Technology Category

• Machine Learning: Mixture of Experts (MoE)
• Natural Language Processing: Safety and Robustness
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

The Mamba model has gained significant attention for its computational advantages over Transformer-based models, while achieving comparable performance across a wide range of language tasks. Like Transformers, Mamba exhibits in-context learning (ICL) capabilities, i.e., making predictions for new tasks based on a prompt containing input-label pairs and a query, without requiring fine-tuning. Despite its empirical success, the theoretical understanding of Mamba remains limited, largely due to the nonlinearity introduced by its gating mechanism. To the best of our knowledge, this paper presents the first theoretical analysis of the training dynamics of a one-layer Mamba model, which consists of a linear attention component followed by a nonlinear gating layer, and its ICL generalization on unseen binary classification tasks, even when the prompt includes additive outliers. Our analysis shows that Mamba leverages the linear attention layer to select informative context examples and uses the nonlinear gating layer to suppress the influence of outliers. By establishing and comparing to the analysis of linear Transformers under the same setting, we show that although Mamba may require more training iterations to converge, it maintains accurate predictions even when the proportion of outliers exceeds the threshold that a linear Transformer can tolerate. These theoretical findings are supported by empirical experiments.

Problem

• Theoretical analysis of Mamba's in-context learning with outlier presence
• Understanding Mamba's training dynamics and generalization on classification tasks
• Comparing Mamba's outlier robustness against linear Transformer models

Innovation

• Mamba uses linear attention to select informative examples
• Nonlinear gating layer suppresses influence of outliers
• Maintains accuracy with more outliers than Transformers