This paper provides a theoretical analysis of the training dynamics of Transformers with nonlinear self-attention and nonlinear MLP, focusing on their in-context learning (ICL) generalization capability. The authors investigate how various factors, such as the magnitude of relevant features and the fraction of context examples with the same relevant pattern as the query, impact ICL performance. They prove that the learned Transformer can generalize to new tasks based on relevant patterns and linear combinations of these patterns, even with data distribution shifts. Additionally, the paper analyzes the effect of magnitude-based pruning on ICL performance, showing that pruning neurons with small magnitudes has minimal impact on generalization while pruning neurons with large magnitudes significantly reduces it. The theoretical findings are validated through numerical experiments, demonstrating the effectiveness of the proposed methods in enhancing ICL capabilities and reducing inference costs.This paper provides a theoretical analysis of the training dynamics of Transformers with nonlinear self-attention and nonlinear MLP, focusing on their in-context learning (ICL) generalization capability. The authors investigate how various factors, such as the magnitude of relevant features and the fraction of context examples with the same relevant pattern as the query, impact ICL performance. They prove that the learned Transformer can generalize to new tasks based on relevant patterns and linear combinations of these patterns, even with data distribution shifts. Additionally, the paper analyzes the effect of magnitude-based pruning on ICL performance, showing that pruning neurons with small magnitudes has minimal impact on generalization while pruning neurons with large magnitudes significantly reduces it. The theoretical findings are validated through numerical experiments, demonstrating the effectiveness of the proposed methods in enhancing ICL capabilities and reducing inference costs.