Title: Can Mamba Learn In Context with Outliers? A Theoretical Generalization Analysis
Primary area: learning theory
Keywords: Mamba, in-context learning, Transformer, generalization, training dynamics, deep learning theory

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.

TL;DR: This paper provide the first theoretical analysis of the training dynamics of a one-layer Mamba model and characterizes its in-context learning generaization ability with additive outliers in the prompt