In-Context Learning of a Linear Transformer Block: Benefits of the MLP Component and One-Step GD Initialization

摘要: We study the \emph{in-context learning} (ICL) ability of a \emph{Linear Transformer Block} (LTB) that combines a linear attention component and a linear multi-layer perceptron (MLP) component. For ICL of linear regression with a Gaussian prior and a \emph{non-zero mean}, we show that LTB can achieve nearly Bayes optimal ICL risk. In contrast, using only linear attention must incur an irreducible additive approximation error. Furthermore, we establish a correspondence between LTB and one-step gradient descent estimators with learnable initialization (), in the sense that every estimator can be implemented by an LTB estimator and every optimal LTB estimator that minimizes the in-class ICL risk is effectively a estimator. Finally, we show that estimators can be efficiently optimized with gradient flow, despite a non-convex training objective. Our results reveal that LTB achieves ICL by implementing , and they highlight the role of MLP layers in reducing approximation error.