We thank the reviewer for their thoughtful comments. We address the main points below:
**Simplified Architecture**: While we analyze a 1-layer linear transformer, this simplification allows us to rigorously characterize fundamental properties of in-context learning that may extend to more complex architectures. Similar to how early theoretical works on neural networks focused on simplified architectures to establish foundational results (citation), our work provides a theoretical framework that can guide future analyses of more complex transformers. Moreover, prior works have utilized the same architecture to derive theoretical insights ([Wu et al. 2024](https://arxiv.org/abs/2310.08391), [Kim et al. 2024](https://arxiv.org/abs/2408.12186)).
Regarding more complex architecture, as we mention in the conclusion we believe our techniques can be extended to more complex linear transformer architectures as the last-token prediction would still be homogeneous in the network parameters, enabling the usage of the implicit regularization of GD on the logistic loss for such architectures [(Lyu & Li, 2020\)](https://arxiv.org/abs/1906.05890). We think an interesting but more challenging question is to extend our results to softmax attention architectures.
**Numerical Validation**: We agree that empirical validation with GD would be valuable, and we have added these in the revised PDF; see Figures 2 and 3 with details on the experiments in lines 377-400 and Appendix E. The experiments broadly support our theoretical findings, demonstrating that benign overfitting in-context occurs for particular settings of $\\tilde R$, $d$, $M$, and $B$.
However, like other foundational theoretical works in this area [(Von Oswald et al 2022](https://arxiv.org/abs/2212.07677), [Akyurek et al 2022](https://arxiv.org/abs/2211.15661), [Zhang et al 2023](https://arxiv.org/abs/2306.09927)), our focus is on establishing theoretical guarantees and understanding the principles of in-context learning. We believe our theoretical results are valuable on their own, as they:
1\. Provide precise analysis of the test-time performance of a pre-trained model and how this depends on the number of pre-training tasks, the signal-to-noise ratio, the number of in-context examples, and the noise rate. To the best of our knowledge, prior works fail to capture all of these properties simultaneously, and none covered the linear classification setting.
2\. Demonstrate the possibility of benign overfitting in the forward pass of transformers: we believe this is a novel setting and finding which is of interest to theorists working on understanding LLM generalization.
**Pre-training with noisy labels**: We think this is an interesting question. We think the theoretical analysis of pre-training with noisy labels would be significantly different. If we aimed to use the implicit regularization approach based on analyzing solutions to our equation (3), because in this setting there may not be a $U$ which satisfies the constraints of (3), and even if such a $U$ does exist then we would be investigating the behavior of a pre-trained transformer which has memorized noisy labels. In this setting it is not clear that generalization is possible, and we believe a resolution to this question would be very challenging. On the other hand, if we looked directly at the dynamics of GD, we conjecture that if GD is early-stopped before overfitting, we might expect similar behavior as to what we see for the max-margin in our paper. We have added comments on this to our discussion in lines 506-513.