Thanks for your recognition and the valuable suggestions. Please find our response below.

1. Evaluation on the not-demonstration-selection-based baselines [W1, L1]

Thank you for the great suggestion. Here, we add Zero-Shot baseline, as well as some CoT-related baselines, including Zero-Shot-CoT [1] and Manual-CoT [4], Auto-CoT [5]. Specifically, Manual-CoT [4] and Auto-CoT [5] require to select demonstrations from an annotated examples set. The table below presents the BLEU score [2, 3] of the baselines and our method on the two code generation tasks: Geoquery and NL2Bash. We use Llama2-7B as the LLM throughout our experiments. The results show that our method can outperform Zero-Shot and Zero-Shot-CoT, and improve the noise robustness of Manual-CoT and Auto-CoT. We will add the results in the final version.

2. Justification of perplexity disentanglement [Q1]

Thank you for pointing out the potential confusion due to ambiguous descriptions. We would like to clarify that the disentanglement is conceptual rather than mathematical, which is provided to help the reader understand the justification of LPR. We provide a detailed explanation of the concept below.

• Given a matched input-output pair $**z**=(**x**, **y**)$, the $\operatorname{Perplexity}(**z**)$ measures how the model is familiar with the task. In this case, we define inherent perplexity = $\operatorname{Perplexity}(**z**)$ and matching perplexity=0.
• By replacing the output with a wrong one, we obtain a mismatched input-output pair $\tilde{**z**}=(**x**, \tilde{**y**})$. During the replacement, inherent perplexity is not changed as it only depends on the input and its ground-truth output. We define the matching perplexity as the increased perplexity caused by the wrong output ($\operatorname{Perplexity}(\tilde{**z**})-\operatorname{Perplexity}(**z**)$).

Therefore, the disentanglement naturally holds due to their definitions. The concept of matching perplexity enables us to compare the correctness of different examples regardless of their inherent perplexity (i.e., task difficulty): a higher matching perplexity indicates that the output is more likely to be incorrect for the input. As the ground-truth is unknown in the dataset, it is non-trivial to explicitly compute the inherent and matching perplexity, which motivates our method. In the final version, we will improve the writing of the perplexity disentanglement to avoid any potential confusion.

3. Results of other LLMs [Q2]

Great suggestion. To demonstrate that our perplexity analysis is model-agnostic, we add an experiment that presents the perplexity distribution shift of Llama2-13B and OPT-6.7B on clean and noisy annotations. The results are presented in Figures 2 and 3 in the submitted PDF. The results show that examples with noisy annotations exhibit higher perplexity than those with clean annotations for both Llama2-13B and OPT-6.7B, which aligns with our previous findings using the Llama2-7B model.

4. Analysis of threshold $\gamma$ [Q3]

Sorry for the confusion. The experimental results of various thresholds $\gamma$ are presented on Figure 3 (a) and (b), which report the average test performance across various noise types. Three colors indicate different values of thresholds $\gamma$ (e.g., 25%, 50%, 75%), as presented in the legend. The results show that the performance of LPR is insensitive to the hyperparameter $\gamma$. For example, LPR yields significant improvements of EM score even when $\gamma$=75%. Therefore, we simply set the threshold $\gamma$= 50% by default, in our experiments. To avoid any potential confusion, we will improve the legend and caption of Figure 3 in the final version.

5. Concerns of presentation [Q4]

Thank you for pointing out the issues of presentations. We reply to each question below.

• We use Llama2-7B as the LLM throughout our experiments, which is described in Subsection 5.1.
• In Table 3, we report the average Exact Match (EM) score of baselines and LPR using various LLMs.
• In Figure 3 (a) and (b), we analyze how the hyperparameter $\gamma$ affects the performance of LPR. We present the value of $\gamma$ by the percentages in the legend of Figure 3 (a) and (b) (i.e., 25%, 50%, and 75%), represented by different colors.

As the reviewer suggested, we will improve the presentation in the final version.

[1] Kojima T, et al. Large language models are zero-shot reasoners. NeurIPS 2022.

[2] Li X, et al. Unified demonstration retriever for in-context learning. ACL 2023.

[3] Lin X, et al. Nl2bash: A corpus and semantic parser for natural language interface to the Linux operating system. LREC 2018.

[4] Wei J, et al. Chain-of-thought prompting elicits reasoning in large language models. NeurIPS 2022.

[5] Zhang Z, et al. Automatic chain of thought prompting in large language models. ICLR 2023.

Thanks for your recognition and the valuable suggestions. Please find our response below.

1. The implementation code is missing [W1]

The code and data have been provided in the Supplementary Material of the original submission. Once published, we will upload the code and data to GitHub for reproduction.

2. Analysis of error types [W2]

We guess your concern is about type I and type II errors that LPR makes versus the baseline methods. However, we primarily focus on text-generation tasks, such as question-answering and code-generation tasks, where type I and type II errors are not applicable. We would be grateful if you could give clear information about the error types here.

3. Comparison with other methods for noisy ICL [W3]

Thanks for the suggestion. To the best of our knowledge, this work is the first to explore the noise robustness of in-context learning for text-generation tasks. Indeed, some works focus on the noisy ICL for classification, but they do not propose methods as noisy annotations are not harmful in their analysis. Therefore, our evaluations are conducted to show the improvements of LPR based on existing selection methods. We would be grateful if you could share some related methods we can include in the comparison.

4. Potential failure modes of LPR [Q1, L1]

Thank you for the suggestion on potential failure cases for our method. Please find the detailed analysis in the General Response.

5. Details of noise generation [Q2]

Thank you for the questions. We respond to these questions point by point below.

• Version & expenses. The model version of GPT-4 we used is GPT-4-0125-preview. The approximate expense is $20 (2M tokens) per task for open-domain question-answering and code-generation tasks. For the reading comprehension task, the approximate expense is 50 (5M tokens) per task.
• Method & Prompt. For irrelevant noise, we collect multiple irrelevant text-generation datasets and randomly match the answers from the irrelevant datasets as irrelevant noise. Based on the previous works on modeling relevant noise [1, 2, 3], we simulate the relevant noise by generating related yet incorrect outputs using GPT-4-0125-preview. Taking the Natural Questions (NQ) dataset as an example, we generated relevant noises using GPT-4-0125-preview with the following prompt:

Hello, you are now a data annotation engineer. You will be provided with a question and its correct answer. You need to generate answers that are related but contain obvious errors. Below are two examples.

Example 1

Question: Where is the liver in the human body located?

Correct Answer: The right upper quadrant.

Incorrect Answer: The left lower quadrant.

Example 2

Question: What major cellular event happens during the S phase of interphase?

Correct Answer: DNA replication.

Incorrect Answer: RNA replication.

Question: What is the term given to the energy released into space?

Correct Answer: Radiant light energy.

Incorrect Answer:

Given the above prompt, the output of GPT-4-0125-preview is "Gravitational potential energy". We will add details of noise generation in the appendix of the final version.

[1] Alexandrov D, et al. Does noise really matter? investigation into the influence of noisy labels on Bert-based question-answering system. International Journal of Semantic Computing, 2024.

[2] Welbl, et al. Crowdsourcing Multiple Choice Science Questions. WNUT 2017.

[3] Wretblad N, et al. Understanding the Effects of Noise in Text-to-SQL: An Examination of the BIRD-Bench Benchmark. ACL 2024.

Thank you for the constructive and elaborate feedback. Please find our response below.

1. Clarification of motivation and evaluation [W1, Q1]

There might be some misunderstandings, which are clarified in the following.

• "The evaluated tasks are simple". In this work, we evaluate the effectiveness of our method(LPR) on six datasets of text generation (See Sections 3 and 5), including Open-Domain Question Answering: NQ, WebQ; Reading Comprehension: SQuAD and SCIQ; Code Generation: GeoQuery and NL2Bash. With these tasks ranging from easy to hard, we provide an extensive evaluation for the efficacy of LPR. As suggested by the reviewer, we also add two long-form and open-domain QA tasks, MT-Bench [6] and Arena-Hard [3].
• "Ensuring the correctness of a few (fewer than 10) in-context samples shouldn't be challenging". We would like to justify that noisy annotations we considered exist in the large-scale dataset with annotations, instead of simply the selected in-context samples. The in-context samples for each test instance are unique, which depend on the selection methods (e.g., Random, TopK, DPP). Thus, it is impractical to ensure the correctness of in-context samples for all test instances by human intervention.

The results on MT-Bench [6] and Arena-Hard [3] are shown in the table below, which presents the average answer grading (0-10) [6] of baselines and our method. The results show that our approach significantly improves the efficacy of existing selection methods on long-form question-answering tasks. We will add the detailed results in the final version.

2. Analysis of small noise ratios [Q2]

Thank you for the suggestion. Following the reviewer's advice, we conduct experiments on datasets with smaller noise ratios (e.g. 2%, 5%, 10%, 15%). The table below presents the average EM score on four generation tasks, including NQ, WebQ, SCIQ, and SQuAD. The Table shows that our method can benefit the ICL performance from a small noise rate (e.g. 2%). We will add the results in the final version.

3. Noise ratios exceeding 20% are unrealistic [W2]

Thank you for the good question about the noisy settings of ICL. We have provided more results with noise ratios under 20% in the above. Here, we provide justifications of high noise ratios below:

• The evaluated tasks are not simple. As clarified above, we conducted evaluations on various tasks ranging from easy to hard. In hard tasks, e.g., code generation, it is reasonable to utilize a large-scale dataset collected from forums, where the noise rate exceeds 20%.
• It is common practice to explore the issue of noisy annotations with high ratios in the literature. Recent work shows that numerous QA datasets annotated by humans or LLMs exhibit a high proportion of corrupted outputs ranging from 8% to 38.5% [4]. Jindal et al. (2019) [2] and Xu et al. (2024) [5] introduced noisy labels, ranging from 20% to 60%, into text classification datasets. Alexandrov et al. (2024) [1] define four levels of injected noises from 20% to 80% for the finetuning of Bert. Thus, it is necessary to justify the benefits of LPR with noise ratios exceeding 20%.
• There is a lack of real-world benchmarks for noisy ICL research. While the conventional wisdom in the ICL community is that noisy annotations do not affect the efficacy of ICL in classification tasks [2, 5], this work is the first to show the harmfulness of noisy annotations in ICL. Thus, there is no existing real-world benchmark for noisy ICL, which will be urgently needed after the publication of this work.

In summary, conducting evaluation on synthetic datasets with high noise ratios is reasonable due to the task difficulty, common practices, and the lack of real-world benchmarks. We hope this work can attract the attention of researchers on the label quality of ICL datasets, such as collecting real-world benchmarks.

4. Clear illustration of LPR [W3]

Thank you for the great suggestion. We provide a clear illustration to express the framework of LPR, as shown in Figure 1 in the submitted PDF. We will add the illustration in the revised version.

5. Potential failure of LPR [L1]

Thank you for the suggestion on potential failure cases for our method. Please find the detailed analysis in the General Response.

[1]Alexandrov D, et al. Does noise really matter? investigation into the influence of noisy labels on Bert-based question-answering system. IJSC 2024.

[2]Jindal I, et al. An effective label noise model for DNN text classification. NAACL 2019.

[3]Li T, et al. From Crowdsourced Data to High-Quality Benchmarks: Arena-Hard and BenchBuilder Pipeline. arXiv 2024.

[4]Song H, et al. Learning from noisy labels with deep neural networks: A survey. TNNLS 2022.

[5]Xu P, et al. Noisy Multi-Label Text Classification via Instance-Label Pair Correction. NAACL 2024.

[6]Zhang L, et al. Judging llm-as-a-judge with mt-bench and chatbot arena. NeurIPS 2023.