Relevant or Random: Can LLMs Truly Perform Analogical Reasoning?
Authors: Chengwei Qin, Wenhan Xia, Tan Wang, Fangkai Jiao, Yuchen Hu, Bosheng Ding, Ruirui Chen, Shafiq Joty
Accepted at: acl25

Relevant or Random: Can LLMs Truly Perform Analogical Reasoning?

Chengwei Qin*†*, Wenhan Xia*†*, Tan Wang†*, Fangkai Jiao†, Yuchen Hu†, Bosheng Ding†, Ruirui Chen♦, Shafiq Joty†♦
*The Hong Kong University of Science and Technology (Guangzhou) †Princeton University
†Nanyang Technological University ♦Salesforce Research
♦Institute of High Performance Computing (IHPC),
Agency for Science, Technology and Research (A*STAR), Singapore

Abstract

Analogical reasoning is a unique ability of humans to address unfamiliar challenges by transferring strategies from relevant past experiences. One key finding in psychology is that compared with irrelevant past experiences, recalling relevant ones can help humans better handle new tasks. Coincidentally, the NLP community has also recently found that self-generating relevant examples in the context can help large language models (LLMs) better solve a given problem than hand-crafted prompts. However, it is yet not clear whether relevance is the key factor eliciting such capability, i.e., can LLMs benefit more from self-generated relevant examples than irrelevant ones? In this work, we systematically explore whether LLMs can truly perform analogical reasoning on a diverse set of reasoning tasks. With extensive experiments and analysis, we show that self-generated random examples can surprisingly achieve comparable or even better performance on certain tasks, e.g., 4% performance boost on GSM8K with random biological examples. We find that the accuracy of self-generated examples is the key factor and subsequently design two novel methods with improved performance and significantly reduced inference costs. Overall, we aim to advance a deeper understanding of LLM analogical reasoning and hope this work stimulates further research in the design of self-generated contexts.

1 Introduction

A hallmark of human intelligence is that they can solve novel problems by drawing analogy from relevant past experiences, a concept known as analogical reasoning in cognitive science (Vosniadou and Ortony, 1989). As indicated by the name, recalling previously acquired relevant experiences can facilitate humans to better tackle new tasks, whereas irrelevant ones are rarely beneficial and can even be distracting (Gentner and Smith, 2012). For instance, when faced with a novel math problem about determinants (e.g., calculating the value of a given fourth-order determinant), humans can resolve this by reflecting upon the methodology employed to ascertain the value of a third-order determinant, whereas biological knowledge (e.g., how the human body regulates its temperature) can generally be considered irrelevant.

With the recent advancements in scaling up model size and data, LLMs have demonstrated impressive zero-shot and few-shot performance across various reasoning tasks, especially, through advanced prompting methods like chain-of-thought (CoT) (Wei et al., 2022). Compared to common approaches such as zero or few-shot CoT (Zhou et al., 2022; Kojima et al., 2022; Zhang et al., 2023a), Yasunaga et al. (2024) introduce LLM analogical reasoning, i.e., LLMs self-generate examples rel-

![Illustration of LLM analogical reasoning in Yasunaga et al. (2024). LLMs are prompted to self-generate relevant examples as context before solving the new problem.](page_1012_370_367_246.png)

Figure 1: Illustration of LLM analogical reasoning in Yasunaga et al. (2024). LLMs are prompted to self-generate relevant examples as context before solving the new problem.
evant to the query as context to better solve new problems; see Fig. 1 for an example. However, it remains unclear whether relevance is the key to eliciting such capability in LLMs. While several studies explore the influence of the relevance of demonstrations in in-context learning (ICL) and CoT (Liu et al., 2022; Kim et al., 2022; Lyu et al., 2023; Chen et al., 2023; Yang et al., 2023; Wang et al., 2023a; Alkhamissi et al., 2023; Yasunaga et al., 2024; Luo et al., 2024), none of them investigate whether self-generated relevant examples consistently outperform irrelevant ones in LLM analogical reasoning.

In this paper, to systematically assess the capability of LLMs to perform analogical reasoning, we conduct a series of ablation experiments on a variety of reasoning tasks including problems from GSM8K (Cobbe et al., 2021), MATH (Hendrycks et al., 2021), and BIG-Bench Hard (BBH) (Suzgun et al., 2022). Furthermore, we evaluate the generalizability of our findings to other reasoning tasks, e.g., GPQA (Rein et al., 2024), in Section 4.3. With extensive experiments, we aim to address the following two research questions:

• Q1. Are self-generated relevant examples more beneficial to LLMs than random ones?
• Q2. If not, what is the pivotal factor for LLMs’ performance in analogical reasoning?

To answer these questions, we empirically analyze the analogical reasoning abilities of GPT-3.5 (turbo), GPT-4o-mini, the Llama series (Touvron et al., 2023), and Qwen 2.5 (Yang et al., 2024) models. Surprisingly, experimental results show that prompting LLMs to self-generate random examples can achieve comparable or even better performance on certain tasks which is not in line with the key claim of analogical reasoning in Gentner and Smith (2012), indicating that LLMs cannot always perform analogical reasoning. As for Q2, we point out through controlled experiments that the key factor is the accuracy of self-generated examples. Informed by these findings, we design two approaches that can outperform existing methods with significantly reduced inference costs. Specifically, we ask LLMs to randomly generate a few problems and manually verify their correctness, then use this fixed set of problems as in-context learning demonstrations for all test samples. Consistent observations across different model types and scales consolidate the conclusions. We summarize the major contributions of our work below:

• To the best of our knowledge, we, for the first time, extensively assess the ability of LLMs to perform analogical reasoning and explore their counterintuitive behavior on certain tasks.
• With extensive experiments and analysis, we demonstrate the effectiveness and limitations of different types of self-generated contexts.
• Building on the findings, we propose two novel ICL-based approaches that improve performance while significantly reducing inference costs.

2 Related Work

This work mainly explores whether LLMs can truly perform analogical reasoning. In light of this, we review two lines of research that form the basis of this work: chain-of-thought prompting and LLM analogical reasoning.

2.1 Chain-of-Thought Prompting

Chain-of-thought (CoT) prompting induces LLMs to generate intermediate reasoning steps before generating the final answer (Wei et al., 2022), greatly improving the reasoning capabilities of LLMs. Typical CoT prompting approaches include few-shot CoT (Wei et al., 2022; Zhou et al., 2022; Wang et al., 2022b; Li et al., 2022; Wang et al., 2022a), taking several labeled demonstrations of the reasoning process, and zero-shot CoT, comprising only instructions like “Let’s think step by step” (Kojima et al., 2022; Zelikman et al., 2022; Zhang et al., 2023a). Other ongoing research on CoT has also explored (i) optimizing the demonstration selection (Fu et al., 2022; Li and Qiu, 2023; Qin et al., 2024), (ii) optimizing the quality of reasoning chains (Khot et al., 2022; Chen et al., 2022; Shinn et al., 2023; Besta et al., 2024), and (iii) CoT in smaller models (Magister et al., 2022; Ho et al., 2022; Fu et al., 2023; Ranaldi and Freitas, 2024).

2.2 LLM Analogical Reasoning

While few-shot CoT can provide more detailed reasoning guidance, it requires labeled examples which can be unavailable for a new task. To tackle this problem, Yasunaga et al. (2024) propose analogical prompting to guide LLMs to self-generate relevant exemplars as few-shot demonstrations, which is similar to analogical reasoning, i.e., humans can address new problems by drawing analogy from relevant past experience (Vosniadou and Ortony, 1989; Holyoak, 2012). LBS3 (Luo et al.,
Prompt: self-generate relevant examples
Your task is to tackle mathematical problems. When presented with a math problem, recall relevant problems as examples. Afterward, proceed to solve the initial problem.

# Initial Problem: [The target problem]

# Instructions:
Make sure that your response follows the instructions below.

## Analogous Problems:
Offer five diverse examples of math problems that are relevant or analogous to the initial problem. For each problem, elaborate on the solution and conclude with the ultimate answer (enclosed in 'boxed{}'). For each problem:
- After "Q:", describe the problem
- After "A:", explain the solution and enclose the ultimate answer in 'boxed{}'.

## Solve the Initial Problem:
Q: Copy and paste the initial problem here.
A: Explain the solution and enclose the ultimate answer in 'boxed{}' here.

Prompt: self-generate random examples
Your task is to tackle mathematical problems. When presented with a math problem, recall random problems as examples. Afterward, proceed to solve the initial problem.

# Initial Problem: [The target problem]

# Instructions:
Make sure that your response follows the instructions below.

## Random Problems:
Randomly offer five diverse examples of math problems. For each problem, elaborate on the solution and conclude with the ultimate answer (enclosed in 'boxed{}'). For each problem:
- After "Q:", describe the problem
- After "A:", explain the solution and enclose the ultimate answer in 'boxed{}'.

## Solve the Initial Problem:
Q: Copy and paste the initial problem here.
A: Explain the solution and enclose the ultimate answer in 'boxed{}' here.

Figure 2: Example prompts for GSM8K (mathematical reasoning). Top: The original prompt used in Yasunaga et al. (2024) for self-generating relevant math problems. Bottom: The prompt designed for self-generating random math problems. We mark the differences between these two prompts in blue and green respectively.

2024) explores curriculum learning which can better reflect human learning habits. In this work, we step forward to explore the intrinsic principle of LLM analogical reasoning. Specifically, we aim to investigate whether LLMs can authentically exhibit such reasoning capabilities and determine the extent to which the relevance of self-generated examples contributes to enhancing this process.

3 Methodology

Our analysis is based on the analogical prompting approach outlined in Yasunaga et al. (2024). Specifically, for a given target problem \( x \), analogical prompting introduces instructions like:

# Problem: [x]
# Relevant problems: Recall five relevant and diverse problems. For each problem, describe it and explain the solution.
# Solve the initial problem:

The goal is to induce LLMs to self-generate relevant examples, aiding them to solve the target problem via in-context learning. To ensure better performance and efficiency, several key technical decisions are made in Yasunaga et al. (2024):
• The self-generated examples should be relevant and diverse, achieved through a specially designed instruction.
• Generate relevant problems and the solution to the initial problem in one pass.
• 3 to 5 self-generated examples perform the best.

In this work, we leverage similar prompts\(^1\) to guide LLMs to generate different types of irrelevant examples as context; see Fig. 2 for example prompts:

• N/A: generate problems that are N/A (not applicable) to the initial problem.
• Random\(_{same}\): randomly generate examples of the same problem type (\(e.g.\), math).
• Random\(_{diff}\): randomly generate examples of different problem types (\(e.g.\), any type except math).
• Random\(_{bio}\): randomly generate biological problems.

Yasunaga et al. (2024) demonstrate that self-

\(^1\)Since our work aims to comprehensively explore and analyze the intrinsic principle of LLM analogical reasoning proposed in Yasunaga et al. (2024), we should follow the original design of the instructions to have a fair comparison and reliable analysis.
generating relevant examples can consistently outperform zero-shot CoT and few-shot CoT (hand-crafted examples or retrieved top- \( k \) most similar training samples) on different tasks. Therefore, we do not include these two methods in our work. Interested readers can refer to the corresponding results and analysis in Yasunaga et al. (2024). In addition, we show prompts for different methods on all datasets in Appendix A.1.

4 Experiment

4.1 Experimental Setup

We construct the evaluation suite based on diverse reasoning-intensive tasks, including mathematical reasoning and other reasoning (\( e.g. \), logical and temporal reasoning) tasks:

• Mathematical reasoning. We work with two commonly used datasets, GSM8K (Cobbe et al., 2021) and MATH (Hendrycks et al., 2021). For each dataset, we randomly sample 500 examples from the original test set and run experiments three times with different random seeds (resulting in different test samples).

• Other reasoning. Following Yasunaga et al. (2024), we evaluate five reasoning tasks in BIG-Bench Hard (BBH) (Suzgun et al., 2022): temporal sequences (temporal reasoning), logical deduction five objects and reasoning about colored objects (logical reasoning), formal fallacies (deductive reasoning) and word sorting (symbolic reasoning). For each task, we use all test samples for evaluation and run experiments three times with different random seeds.

We mainly use GPT-3.5 (gpt-3.5-turbo) as the LLM (see Appendix A.3 for more results with GPT-4o-mini) and obtain all outputs from it with the temperature set to 0. We ask the LLM to self-generate 5 examples for GSM8K, 3 examples for MATH and BBH following Yasunaga et al. (2024).

4.2 Main Results

We now address the research questions asked in §1 with empirical results.

Q1. Are self-generated relevant examples more beneficial to LLMs than random ones?

The results averaged over all random seeds are reported in Table 1 and Table 2; more detailed results for every seed are shown in Appendix A.2.

Figure 3: Comparison of all methods at different difficulty levels on MATH. Level 1 represents the easiest and level 5 is the hardest. ‘relevant’ clearly performs worse than other approaches at all difficulty levels.

• Self-generated relevant examples achieve the best average performance on BBH. From the results in Table 1, we can observe that the superiority of self-generated relevant examples is empirically substantiated on BBH. Specifically, using relevant examples, denoted by ‘relevant’, outperforms other approaches on temporal and logical reasoning tasks. While it performs worse than ‘N/A’ on deductive and symbolical reasoning, it can still improve the accuracy by **1.3%** on average compared to ‘N/A’.

However, the results on mathematical reasoning tasks are quite counterintuitive as described below:

• Relevant examples do not guarantee better performance. Different from BBH, all types of self-generated irrelevant examples consistently outperform relevant ones on both mathematical reasoning datasets, showing that LLMs cannot yet perform analogical reasoning on these tasks. Interestingly, when we use randomly generated biological examples (\( e.g. \), how the process of photosynthesis occurs in plants), they can yield about **2.5%** better results on average compared to generating relevant math problems. Besides, ‘N/A’ achieves the best average result as it is the second-best on both datasets.

Problems in MATH span various subjects and difficulty levels. To investigate whether the inferior performance of relevant examples on MATH is accidentally caused by certain categories, we further report the accuracy across different subjects and difficulty levels in Table 3 and Fig. 3. The consistent performance gap between ‘relevant’ and other methods across different problem categories
<table>
  <tr>
    <th>Method</th>
    <th>Temporal sequences</th>
    <th>Logical deduction five objects</th>
    <th>Reasoning about colored objects</th>
    <th>Formal fallacies</th>
    <th>Word sorting</th>
    <th>Average</th>
  </tr>
  <tr>
    <td>Relevant</td>
    <td><b>60.0</b></td>
    <td><b>51.2</b></td>
    <td><b>76.7</b></td>
    <td>51.2</td>
    <td>76.9</td>
    <td><b>63.2</b></td>
  </tr>
  <tr>
    <td>N/A</td>
    <td>57.5</td>
    <td>45.3</td>
    <td>75.5</td>
    <td><b>53.3</b></td>
    <td><b>77.7</b></td>
    <td>61.9</td>
  </tr>
  <tr>
    <td>Random<sub>same</sub></td>
    <td>53.1</td>
    <td>48.8</td>
    <td>73.5</td>
    <td>52.4</td>
    <td>74.1</td>
    <td>60.4</td>
  </tr>
  <tr>
    <td>Random<sub>diff</sub></td>
    <td>44.3</td>
    <td>44.8</td>
    <td>72.4</td>
    <td>51.2</td>
    <td>69.2</td>
    <td>56.4</td>
  </tr>
  <tr>
    <td>Random<sub>bio</sub></td>
    <td>57.1</td>
    <td>49.5</td>
    <td>76.1</td>
    <td>50.8</td>
    <td>74.9</td>
    <td>61.7</td>
  </tr>
</table>

Table 1: Accuracy (%) of different methods on five reasoning tasks in BBH. Bold indicates the best results. Self-generated relevant examples achieve the best average performance. Detailed results for different seeds are reported in Appendix A.2.

<table>
  <tr>
    <th rowspan="2">Method</th>
    <th colspan="2">Task</th>
    <th rowspan="2">Average</th>
  </tr>
  <tr>
    <th>GSM8K</th>
    <th>MATH</th>
  </tr>
  <tr>
    <td>Relevant</td>
    <td>71.5</td>
    <td>33.3</td>
    <td>52.4</td>
  </tr>
  <tr>
    <td>N/A</td>
    <td>75.5</td>
    <td>36.1</td>
    <td><b>55.8</b></td>
  </tr>
  <tr>
    <td>Random<sub>same</sub></td>
    <td>75.1</td>
    <td><b>36.3</b></td>
    <td>55.7</td>
  </tr>
  <tr>
    <td>Random<sub>diff</sub></td>
    <td><b>76.3</b></td>
    <td>34.1</td>
    <td>55.2</td>
  </tr>
  <tr>
    <td>Random<sub>bio</sub></td>
    <td>75.3</td>
    <td>34.6</td>
    <td>54.9</td>
  </tr>
</table>

Table 2: Accuracy (%) of different methods on two mathematical reasoning tasks. Self-generated irrelevant examples are consistently better than relevant ones. Table 13 in Appendix A.2 reports detailed results for different seeds.

demonstrates the inherent flaws of relevant examples, indicating that mathematical reasoning tasks exhibit different analogical reasoning paradigms from BBH.

It might present challenges to prompt LLMs to accurately generate specific types of demonstrations. Therefore, given the unexpected results on mathematical reasoning tasks, one may wonder:

Q1-1. Are self-generated examples really relevant or irrelevant to the query?

To quantitatively measure the relevance between the generated examples and the query, we compute the average cosine similarity between them. Following Zhang et al. (2023a), we use the sentence transformer (Reimers and Gurevych, 2019) to encode all samples. For each method, the reported result is averaged across three seeds (see Appendix A.4 for the decomposition of relevance).

As observed from Table 4, relevant examples are much more semantically similar to the query than irrelevant ones and the relevance score of ‘relevant’ is more biased towards ‘oracle’ rather than ‘random’ or ‘N/A’, demonstrating that LLMs indeed follow instructions to generate specific types of demonstrations. Furthermore, we calculate the average similarity score between self-generated relevant examples and queries for BBH (0.46), which is slightly lower than the score of mathematical reasoning tasks (0.48). This result demonstrates that the difference in analogical reasoning performance between BBH (Table 1) and mathematical reasoning (Table 2) is not because LLMs can generate more relevant examples for BBH.

We provide a case study in Table 6 to delve deeper into the demonstrations of different methods. As we can notice, the example generated by ‘relevant’ is more related to the query as they both involve the mathematical concept ‘number bases’. In contrast, examples such as ‘What is the value of x in the equation 2x + 5 = 10?’ (N/A) or ‘How do you bake chocolate chip cookies?’ (Random<sub>diff</sub>) are less relevant to the query. This comparison highlights once again that relevance may not be the key factor for analogical reasoning performance on mathematical reasoning tasks. To understand better the underlying reasons for the counterintuitive results, we then ask the following question:

Q2. If relevance is not the key factor, what is more important for the accuracy of analogical reasoning?

Looking back at Table 6, an interesting observation is that the self-generated relevant example appears to be more difficult to solve than the irrelevant ones, regardless of whether they are math problems or not. Consequently, the accuracy of relevant examples may be lower. To verify this, we conduct a pilot experiment on MATH. Specifically, we randomly select 50 samples for different types of generated math problems, i.e., Relevant, N/A and Random<sub>same</sub>, and manually evaluate their ac-
<table>
  <tr>
    <th>Method</th>
    <th>Precalculus</th>
    <th>Intermediate Algebra</th>
    <th>Algebra</th>
    <th>Prealgebra</th>
    <th>Counting & Probability</th>
    <th>Geometry</th>
    <th>Number Theory</th>
  </tr>
  <tr>
    <td>Relevant</td>
    <td>10.4</td>
    <td>9.8</td>
    <td>51.8</td>
    <td>56.8</td>
    <td>22.1</td>
    <td>24.2</td>
    <td><b>37.0</b></td>
  </tr>
  <tr>
    <td>N/A</td>
    <td>9.1</td>
    <td>15.7</td>
    <td><b>55.5</b></td>
    <td><b>61.0</b></td>
    <td><b>28.7</b></td>
    <td><b>25.8</b></td>
    <td>34.2</td>
  </tr>
  <tr>
    <td>Random<sub>same</sub></td>
    <td>12.3</td>
    <td><b>17.6</b></td>
    <td>54.4</td>
    <td>60.6</td>
    <td>25.4</td>
    <td><b>25.8</b></td>
    <td>34.9</td>
  </tr>
  <tr>
    <td>Random<sub>diff</sub></td>
    <td><b>13.0</b></td>
    <td>14.1</td>
    <td>52.7</td>
    <td>56.8</td>
    <td>26.2</td>
    <td>24.2</td>
    <td>33.6</td>
  </tr>
  <tr>
    <td>Random<sub>bio</sub></td>
    <td><b>13.0</b></td>
    <td>12.2</td>
    <td>53.0</td>
    <td>59.2</td>
    <td><b>28.7</b></td>
    <td><b>25.8</b></td>
    <td>32.2</td>
  </tr>
</table>

Table 3: Accuracy (%) across different subjects in the MATH dataset. Self-generated irrelevant examples outperform relevant ones on 6 out of 7 subjects.

<table>
  <tr>
    <th>Method</th>
    <th>GSM8K</th>
    <th>MATH</th>
    <th>Average</th>
  </tr>
  <tr>
    <td>Relevant</td>
    <td><b>0.54</b></td>
    <td><b>0.41</b></td>
    <td><b>0.48</b></td>
  </tr>
  <tr>
    <td>N/A</td>
    <td>0.19</td>
    <td>0.28</td>
    <td>0.24</td>
  </tr>
  <tr>
    <td>Random<sub>same</sub></td>
    <td>0.30</td>
    <td>0.20</td>
    <td>0.25</td>
  </tr>
  <tr>
    <td>Random<sub>diff</sub></td>
    <td>0.15</td>
    <td>0.10</td>
    <td>0.13</td>
  </tr>
  <tr>
    <td>Random<sub>bio</sub></td>
    <td>0.06</td>
    <td>0.11</td>
    <td>0.09</td>
  </tr>
  <tr>
    <td>Oracle</td>
    <td>0.65</td>
    <td>0.63</td>
    <td>0.64</td>
  </tr>
</table>

Table 4: Average relevance score (semantic similarity) between self-generated examples and the query. 'Oracle' stands for the average similarity score between the query and \( k \) most similar training samples (\( k \) is the number of self-generated examples).

<table>
  <tr>
    <th></th>
    <th>Relevant</th>
    <th>N/A</th>
    <th>Random<sub>same</sub></th>
  </tr>
  <tr>
    <td>Accuracy</td>
    <td>62.0</td>
    <td>72.0</td>
    <td>86.0</td>
  </tr>
</table>

Table 5: Accuracy (%) of self-generated examples on the MATH dataset. The examples generated by ‘relevant’ are less accurate.

curacy. We exclude other methods as it is difficult to define the ‘accuracy’ of the examples they generate. From the results in Table 5, we can observe that while the examples generated by ‘relevant’ are more related to the test query, <i>they are less accurate</i>, raising the question whether the performance of different approaches on mathematical reasoning tasks is strongly correlated with the accuracy of self-generated examples.

Proxy Approaches However, as the accuracy of the examples located at the output cannot be directly controlled, we meticulously design a variant called <i>ICL</i>, which extracts the generated examples from the model output as in-context learning (ICL) demonstrations and combines them with the query as input to LLMs, as a proxy for the original method. We also consider the following two variants: (<i>a</i>) <i>GPT4-Calibration</i> which replaces the answers of demonstrations in <i>ICL</i> with GPT4-generated answers, and (<i>b</i>) <i>Random</i> changes the answers of demonstrations in <i>ICL</i> to random numbers. Our manual verification confirmed that GPT4-generated answers were mostly accurate. We conduct this experiment on GSM8K and MATH with GPT-3.5 as the LLM reasoner.

From the results of different variants reported in Table 7, we can see that increasing the accuracy of generated examples can indeed improve the performance: <i>GPT4-Calibration</i> consistently outperforms <i>ICL</i> by incorporating more accurate answers. In contrast, <i>random</i> always performs the worst among all variants. Therefore, the key factor influencing the performance on mathematical reasoning is <i>the accuracy of self-generated examples</i> rather than their relevance.

It is worthwhile to note that while several papers explore how the correctness of demonstration answers influences in-context learning (Min et al., 2022; Yoo et al., 2022; Wei et al., 2023; Pan et al., 2023; Kossen et al., 2024), our work differs from them in the following aspects: (<i>i</i>) The examples in our work are generated by LLMs rather than real data from NLP benchmarks, <i>i.e.</i>, randomly sampled from the training set. In addition, there are rationales (CoT) in self-generated examples, which are different from the input-label format of in-context learning investigated in these papers; and (<i>ii</i>) These studies mainly evaluate in-context learning on different classification or multi-choice datasets, <i>i.e.</i>, the output space is a finite set. In contrast, we are evaluating mathematical reasoning tasks, where the output space is infinite.

Given the above findings, a natural question is:

Q2-1. Can we ask the LLM to randomly generate a few math or biological problems and manually verify their correctness, then use this fixed set of problems as ICL demonstrations for all test queries?
Query: For how many ordered pairs \((A, B)\) where \(A\) and \(B\) are positive integers is \(AAA_7 + BBB_7 = 666_7\)?

<table>
  <tr>
    <th>Relevant</th>
    <td>In a certain base, the sum of two three-digit numbers is 777. If the digits of one of the numbers are reversed, the sum becomes 888. What is the base of this number system?</td>
  </tr>
  <tr>
    <th>N/A</th>
    <td>What is the value of \(x\) in the equation \(2x + 5 = 10\)?</td>
  </tr>
  <tr>
    <th>Random<sub>same</sub></th>
    <td>In a bag, there are 5 red marbles, 3 blue marbles, and 2 green marbles. If you randomly pick 2 marbles from the bag without replacement, what is the probability that both marbles are red?</td>
  </tr>
  <tr>
    <th>Random<sub>diff</sub></th>
    <td>How do you bake chocolate chip cookies?</td>
  </tr>
  <tr>
    <th>Random<sub>bio</sub></th>
    <td>How does the process of photosynthesis occur in plants?</td>
  </tr>
  <tr>
    <th>Oracle</th>
    <td>Find the number of ordered pairs \((a, b)\) of complex numbers such that \(a^3 b^5 = a^7 b^2 = 1\).</td>
  </tr>
</table>

Table 6: Demonstration examples of different methods on the MATH dataset. The example generated by ‘relevant’ is more related to the query than other examples generated by ‘N/A’ or ‘random’.

<table>
  <tr>
    <th rowspan="2">Variant</th>
    <th colspan="3">GSM8K</th>
    <th colspan="3">MATH</th>
  </tr>
  <tr>
    <th>Relevant</th>
    <th>N/A</th>
    <th>Random<sub>same</sub></th>
    <th>Relevant</th>
    <th>N/A</th>
    <th>Random<sub>same</sub></th>
  </tr>
  <tr>
    <td>ICL</td>
    <td>71.2</td>
    <td>73.8</td>
    <td>72.0</td>
    <td>37.0</td>
    <td>39.8</td>
    <td>39.2</td>
  </tr>
  <tr>
    <td>GPT4-Calibration</td>
    <td><b>75.2</b></td>
    <td><b>75.6</b></td>
    <td><b>75.6</b></td>
    <td><b>44.4</b></td>
    <td><b>41.2</b></td>
    <td><b>40.0</b></td>
  </tr>
  <tr>
    <td>Random</td>
    <td>70.0</td>
    <td>72.0</td>
    <td>68.4</td>
    <td>36.0</td>
    <td>38.0</td>
    <td>37.8</td>
  </tr>
</table>

Table 7: Accuracy (%) of different variants on GSM8K and MATH. When using GPT4-generated answers (mostly accurate), ‘GPT4-Calibration’ consistently outperforms ‘ICL’ for all methods. In contrast, ‘random’ always performs worse than ‘ICL’.

<table>
  <tr>
    <th rowspan="2">Method</th>
    <th colspan="2">Task</th>
    <th rowspan="2">Average</th>
  </tr>
  <tr>
    <th>GSM8K</th>
    <th>MATH</th>
  </tr>
  <tr>
    <td>Relevant</td>
    <td>71.5</td>
    <td>33.3</td>
    <td>52.4</td>
  </tr>
  <tr>
    <td>N/A</td>
    <td>75.5</td>
    <td>36.1</td>
    <td>55.8</td>
  </tr>
  <tr>
    <td>Random<sub>same</sub></td>
    <td>75.1</td>
    <td>36.3</td>
    <td>55.7</td>
  </tr>
  <tr>
    <td>Random<sub>diff</sub></td>
    <td>76.3</td>
    <td>34.1</td>
    <td>55.2</td>
  </tr>
  <tr>
    <td>Random<sub>bio</sub></td>
    <td>75.3</td>
    <td>34.6</td>
    <td>54.9</td>
  </tr>
  <tr>
    <td>ICL<sub>math</sub></td>
    <td>75.7</td>
    <td><b>36.8</b></td>
    <td>56.3</td>
  </tr>
  <tr>
    <td>ICL<sub>bio</sub></td>
    <td><b>77.9</b></td>
    <td>34.9</td>
    <td><b>56.4</b></td>
  </tr>
</table>

Table 8: Comparison of different methods on two mathematical reasoning tasks.

We refer to these two methods as ICL<sub>math</sub> and ICL<sub>bio</sub>, and conduct experiments with them on GSM8K and MATH (see Fig. 4 for example prompts and outputs for generating math problems). Detailed prompts and outputs for different methods are provided in Appendix A.5. Following the original setting, we ask the LLM to randomly generate 5 examples for GSM8K and 3 examples for MATH. As observed from Table 8, ensuring the accuracy of self-generated examples does lead to better performance regardless of the problem type. ICL<sub>math</sub> and ICL<sub>bio</sub> achieve similar average performance, once again demonstrating that relevance does not matter (see Appendix A.6 for more analysis on relevance). Moreover, both ICL variants only need to generate examples once, which significantly reduces the inference cost and further demonstrates their superiority.

4.3 Further Analysis

Difference from Previous Work Apart from the comprehensive analysis, we have designed two novel ICL-based approaches that are completely different from the one in Yasunaga et al. (2024) (Q2-1). The difference lies mainly in the following two aspects: (i) The key claim in Yasunaga et al. (2024) is that we should guide the model to self-generate relevant examples as context. Motivated by the analysis and findings in our work (Q1 and Q2), our methods focus on ensuring the accuracy of self-generated examples rather than their relevance, which leads to better performance regardless of the problem type. (ii) As we have demonstrated that the relevance of self-generated examples does not matter, there is no need to generate relevant examples for each test query (the original method in Yasunaga et al. (2024)). In contrast, our methods use a fixed set of examples for all test queries, which significantly reduces the inference cost.

Generalization to Open-Source LLMs Our experiments and analysis so far used GPT-3.5 as the LLM, which is closed-source and gets updated over time. To verify whether the observations and conclusions are consistent across different models and
Input
Randomly recall five examples of math problems. Note that your problems should be distinct from each other (e.g., involving different numbers and names). For each problem:
- After “Q: ”, describe the problem
- After “A: ”, explain the solution and enclose the ultimate answer in \boxed{}.

Output
Q: If John has 5 apples and he buys 8 more, how many apples does he have in total?
A: To find the total number of apples John has, we add the number of apples he initially has to the number of apples he buys. So, we calculate 5 + 8 = 13. Therefore, John has \boxed{13} apples in total.
...
Q: Find the derivative of the function f(x) = 3x^2 + 2x - 5.
A: To find the derivative of f(x), we apply the power rule to each term. The derivative of 3x^2 is 6x, the derivative of 2x is 2, and the derivative of a constant -5 is 0. Therefore, the derivative of f(x) is f'(x) = 6x + 2. So, the derivative is \boxed{6x + 2}.

Figure 4: Example prompts and outputs for randomly generating math problems. We manually verify the answers to ensure the correctness of the generated examples.

<table>
  <tr>
    <th>Method</th>
    <th>Relevant</th>
    <th>N/A</th>
    <th>Random_same</th>
    <th>Random_diff</th>
    <th>Random_bio</th>
    <th>ICL_math</th>
    <th>ICL_bio</th>
  </tr>
  <tr>
    <td>Llama-2-70b-Chat</td>
    <td>45.1</td>
    <td>51.4</td>
    <td>50.9</td>
    <td>54.3</td>
    <td>47.1</td>
    <td>55.5</td>
    <td><b>56.1</b></td>
  </tr>
  <tr>
    <td>Llama-3-8B-Instruct</td>
    <td>69.5</td>
    <td>72.3</td>
    <td>72.6</td>
    <td>74.1</td>
    <td>73.5</td>
    <td>75.8</td>
    <td><b>76.8</b></td>
  </tr>
  <tr>
    <td>Llama-3.1-8B-Instruct</td>
    <td>74.8</td>
    <td>77.3</td>
    <td>78.4</td>
    <td>78.8</td>
    <td>77.6</td>
    <td>80.2</td>
    <td><b>81.0</b></td>
  </tr>
  <tr>
    <td>Qwen2.5-14B-Instruct</td>
    <td>86.5</td>
    <td>89.1</td>
    <td>88.2</td>
    <td>89.7</td>
    <td>88.4</td>
    <td><b>91.1</b></td>
    <td>90.6</td>
  </tr>
</table>

Table 9: Accuracy (%) of different methods on GSM8K using Llama-2-70b-Chat, Llama-3-8B-Instruct, Llama-3.1-8B-Instruct and Qwen2.5-14B-Instruct models. Self-generated relevant examples always perform worse than irrelevant ones and both ICL variants outperform other approaches.

<table>
  <tr>
    <th rowspan="2">Variant</th>
    <th colspan="3">Method</th>
  </tr>
  <tr>
    <th>Relevant</th>
    <th>N/A</th>
    <th>Random_same</th>
  </tr>
  <tr>
    <td>ICL</td>
    <td>56.2</td>
    <td>58.2</td>
    <td>58.6</td>
  </tr>
  <tr>
    <td>GPT4-Calibration</td>
    <td><b>60.8</b></td>
    <td><b>61.0</b></td>
    <td><b>60.8</b></td>
  </tr>
  <tr>
    <td>Random</td>
    <td>53.2</td>
    <td>54.0</td>
    <td>59.6</td>
  </tr>
</table>

Table 10: Accuracy (%) of different variants on GSM8K using Llama-2-70b-Chat. ‘GPT4-Calibration’ consistently performs better than ‘ICL’ and ‘random’.

additionally for reproducibility, we extend the experiments to Llama-2-Chat (Touvron et al., 2023). Specifically, we use vLLM to serve a Llama-2-70b-Chat model for experiments and report the results of different methods/variants on GSM8K in Table 9 and Table 10. We can draw similar observations: (i) self-generated relevant examples underperform all types of irrelevant ones, (ii) ‘GPT4-Calibration’ consistently outperforms the other two variants, and (iii) ICL_math and ICL_bio perform better than other approaches, demonstrating that the conclusions can be generalized to different models.

We further conduct experiments with Llama-3-8B-Instruct, Llama-3.1-8B-Instruct (Dubey et al., 2024) and Qwen2.5-14B-Instruct (Yang et al., 2024). The results reported in Table 9 demonstrate the generalizability of the conclusions across different model types and scales. In addition, since investigating analogical reasoning requires LLMs to self-generate different types of problems, we only experiment with instruction-tuned LLMs to ensure that they can follow the given instructions.

Generalization to Different Tasks To test the generalizability of our findings beyond the math domain, we further conduct experiments on CommonsenseQA (commonsense reasoning) (Talmor et al., 2019), MBPP (code generation) (Austin et al., 2021) and GPQA (question answering of very hard questions) (Rein et al., 2024). The comparison between different methods is shown in Table 11, which demonstrates that our findings can be generalized to different types of tasks.

Comparison Beyond Analogical Reasoning We consider two widely used methods Self-consistency (Wang et al., 2023b) and Auto-CoT (Zhang et al., 2023b), and compare our designed approaches with them on GSM8K using Llama-3.1-8B-Instruct. For Self-consistency, we employ 5 decoding paths for majority voting. The results reported in Table 12 demonstrate that our methods can also outperform other baselines beyond analogical reasoning.

In addition, we show the robustness to prompt format, the effect of the number of demonstrations,
<table>
  <tr>
    <th>Dataset</th>
    <th>Relevant</th>
    <th>N/A</th>
    <th>Random<sub>same</sub></th>
    <th>Random<sub>diff</sub></th>
    <th>Random<sub>bio</sub></th>
    <th>ICL<sub>same</sub></th>
    <th>ICL<sub>bio</sub></th>
  </tr>
  <tr>
    <td>CSQA</td>
    <td>70.8</td>
    <td>73.4</td>
    <td>71.2</td>
    <td>72.9</td>
    <td>72.6</td>
    <td><b>74.6</b></td>
    <td>74.1</td>
  </tr>
  <tr>
    <td>MBPP</td>
    <td>58.2</td>
    <td>59.8</td>
    <td>60.6</td>
    <td>59.6</td>
    <td>60.2</td>
    <td><b>62.0</b></td>
    <td>61.4</td>
  </tr>
  <tr>
    <td>GPQA</td>
    <td>31.6</td>
    <td>34.4</td>
    <td>33.7</td>
    <td>33.1</td>
    <td>32.6</td>
    <td>35.8</td>
    <td><b>36.2</b></td>
  </tr>
</table>

Table 11: Accuracy (%) of different methods on CommonsenseQA, MBPP, and GPQA. ‘same’ in ICL<sub>same</sub> stands for ‘generating correct problems of the same type as the dataset’.

<table>
  <tr>
    <th>Relevant</th>
    <th>Self-consistency</th>
    <th>Auto-CoT</th>
    <th>ICL<sub>math</sub></th>
    <th>ICL<sub>bio</sub></th>
  </tr>
  <tr>
    <td>74.8</td>
    <td>77.6</td>
    <td>75.9</td>
    <td>80.2</td>
    <td><b>81.0</b></td>
  </tr>
</table>

Table 12: Comparison between our designed methods and baselines beyond analogical reasoning.

more analysis on ICL<sub>math</sub> and ICL<sub>bio</sub>, the results of repeating problems and explicitly controlling the semantics of generated examples in Appendix A.7 ~ A.11, respectively.

5 Conclusion

In this work, we have systematically assessed the capability of LLMs to perform analogical reasoning. We have identified key research questions and empirically analyzed a representative set of LLMs on a diverse collection of reasoning tasks. Extensive experimental results and analysis show that LLMs cannot always perform analogical reasoning and the key influencing factor is the accuracy of self-generated examples rather than their relevance. Given these findings, we have designed two ICL-based approaches with better performance and significantly reduced inference costs. In the future, we would like to investigate additional analogical prompting methods to generate more accurate examples.

Limitations

This work has several limitations. First, due to the inference cost of ChatGPT, we conduct experiments on subsets of the test data for mathematical reasoning tasks. Besides, we include 6 datasets requiring different reasoning capabilities in this work. A further improvement could be to explore more diverse types of tasks.

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A Appendix

A.1 Prompts for Different Methods
The prompts for different methods on all datasets are shown in Fig. 5 ~ Fig. 7.

A.2 Detailed Results for Different Random Seeds
We report detailed results for different random seeds in Table 13 ~ Table 14.

A.3 Results with GPT-4o-mini
We conduct experiments with GPT-4o-mini on GSM8K and present the results in Table 15, verifying the generalizability of our findings to GPT-4o-mini.
<table>
  <tr>
    <th rowspan="2">Seed</th>
    <th colspan="5">GSM8K</th>
    <th colspan="5">MATH</th>
  </tr>
  <tr>
    <th>Relevant</th>
    <th>N/A</th>
    <th>Random<sub>same</sub></th>
    <th>Random<sub>diff</sub></th>
    <th>Random<sub>bio</sub></th>
    <th>Relevant</th>
    <th>N/A</th>
    <th>Random<sub>same</sub></th>
    <th>Random<sub>diff</sub></th>
    <th>Random<sub>bio</sub></th>
  </tr>
  <tr>
    <td>42</td>
    <td>71.8</td>
    <td><b>76.6</b></td>
    <td>73.2</td>
    <td>74.0</td>
    <td>74.0</td>
    <td>37.4</td>
    <td><b>42.2</b></td>
    <td>41.6</td>
    <td>39.0</td>
    <td>39.2</td>
  </tr>
  <tr>
    <td>100</td>
    <td>71.2</td>
    <td>75.2</td>
    <td>75.2</td>
    <td><b>75.8</b></td>
    <td>74.8</td>
    <td>29.0</td>
    <td>30.6</td>
    <td><b>32.6</b></td>
    <td>29.4</td>
    <td>31.2</td>
  </tr>
  <tr>
    <td>1000</td>
    <td>71.4</td>
    <td>74.8</td>
    <td>77.0</td>
    <td><b>79.2</b></td>
    <td>77.0</td>
    <td>33.6</td>
    <td><b>35.6</b></td>
    <td>34.6</td>
    <td>34.0</td>
    <td>33.4</td>
  </tr>
  <tr>
    <td>Average</td>
    <td>71.5<sub>±0.3</sub></td>
    <td>75.5<sub>±0.8</sub></td>
    <td>75.1<sub>±1.5</sub></td>
    <td><b>76.3<sub>±2.1</sub></b></td>
    <td>75.3<sub>±1.2</sub></td>
    <td>33.3<sub>±3.4</sub></td>
    <td><b>36.1<sub>±4.7</sub></b></td>
    <td><b>36.3<sub>±3.8</sub></b></td>
    <td>34.1<sub>±3.9</sub></td>
    <td>34.6<sub>±3.3</sub></td>
  </tr>
</table>

Table 13: Accuracy (%) of all methods with different random seeds on two mathematical reasoning tasks.

<table>
  <tr>
    <th rowspan="2">Seed</th>
    <th colspan="2">Temporal sequences</th>
    <th colspan="2">Logical deduction five objects</th>
    <th colspan="2">Reasoning about colored objects</th>
    <th colspan="2">Formal fallacies</th>
    <th colspan="2">Word sorting</th>
    <th colspan="1">Average</th>
  </tr>
  <tr>
    <th>Relevant</th>
    <th>N/A</th>
    <th>Relevant</th>
    <th>N/A</th>
    <th>Relevant</th>
    <th>N/A</th>
    <th>Relevant</th>
    <th>N/A</th>
    <th>Relevant</th>
    <th>N/A</th>
    <th>Average</th>
  </tr>
  <tr>
    <td rowspan="4">42</td>
    <td>58.0</td>
    <td>52.8</td>
    <td>76.0</td>
    <td>50.4</td>
    <td>77.2</td>
    <td>62.9</td>
    <td></td>
    <td></td>
    <td></td>
    <td></td>
    <td></td>
  </tr>
  <tr>
    <td>56.4</td>
    <td>44.8</td>
    <td><b>77.6</b></td>
    <td><b>54.0</b></td>
    <td>76.8</td>
    <td>61.9</td>
    <td></td>
    <td></td>
    <td></td>
    <td></td>
    <td></td>
  </tr>
  <tr>
    <td>52.4</td>
    <td>48.8</td>
    <td>74.8</td>
    <td>51.6</td>
    <td>72.8</td>
    <td>60.1</td>
    <td></td>
    <td></td>
    <td></td>
    <td></td>
    <td></td>
  </tr>
  <tr>
    <td>43.2</td>
    <td>46.8</td>
    <td>74.0</td>
    <td>52.4</td>
    <td>67.6</td>
    <td>56.8</td>
    <td></td>
    <td></td>
    <td></td>
    <td></td>
    <td></td>
  </tr>
  <tr>
    <td rowspan="4">100</td>
    <td>58.4</td>
    <td>50.8</td>
    <td>78.4</td>
    <td>51.2</td>
    <td>76.8</td>
    <td>63.1</td>
    <td></td>
    <td></td>
    <td></td>
    <td></td>
    <td></td>
  </tr>
  <tr>
    <td>55.2</td>
    <td>46.0</td>
    <td>74.8</td>
    <td>52.8</td>
    <td><b>79.2</b></td>
    <td>61.6</td>
    <td></td>
    <td></td>
    <td></td>
    <td></td>
    <td></td>
  </tr>
  <tr>
    <td>50.8</td>
    <td>48.4</td>
    <td>73.6</td>
    <td><b>53.2</b></td>
    <td>75.2</td>
    <td>60.2</td>
    <td></td>
    <td></td>
    <td></td>
    <td></td>
    <td></td>
  </tr>
  <tr>
    <td>46.4</td>
    <td>46.8</td>
    <td>72.8</td>
    <td>50.0</td>
    <td>70.4</td>
    <td>57.3</td>
    <td></td>
    <td></td>
    <td></td>
    <td></td>
    <td></td>
  </tr>
  <tr>
    <td rowspan="4">1000</td>
    <td>58.0</td>
    <td>48.4</td>
    <td><b>78.4</b></td>
    <td>51.2</td>
    <td>73.6</td>
    <td>61.9</td>
    <td></td>
    <td></td>
    <td></td>
    <td></td>
    <td></td>
  </tr>
  <tr>
    <td>63.6</td>
    <td>50.0</td>
    <td>75.6</td>
    <td>52.0</td>
    <td>76.8</td>
    <td><b>63.6</b></td>
    <td></td>
    <td></td>
    <td></td>
    <td></td>
    <td></td>
  </tr>
  <tr>
    <td>60.8</td>
    <td>45.2</td>
    <td>74.0</td>
    <td><b>53.2</b></td>
    <td><b>77.2</b></td>
    <td>62.1</td>
    <td></td>
    <td></td>
    <td></td>
    <td></td>
    <td></td>
  </tr>
  <tr>
    <td>56.0</td>
    <td>49.2</td>
    <td>72.0</td>
    <td>52.4</td>
    <td>74.4</td>
    <td>60.8</td>
    <td></td>
    <td></td>
    <td></td>
    <td></td>
    <td></td>
  </tr>
  <tr>
    <td rowspan="4">Average</td>
    <td>60.0<sub>±2.6</sub></td>
    <td><b>51.2</b><sub>±1.2</sub></td>
    <td><b>76.7</b><sub>±1.2</sub></td>
    <td>51.2<sub>±0.7</sub></td>
    <td>76.9<sub>±0.2</sub></td>
    <td><b>63.2</b><sub>±0.3</sub></td>
    <td></td>
    <td></td>
    <td></td>
    <td></td>
    <td></td>
  </tr>
  <tr>
    <td>57.5<sub>±2.4</sub></td>
    <td>45.3<sub>±0.5</sub></td>
    <td>75.5<sub>±1.5</sub></td>
    <td><b>53.3</b><sub>±0.5</sub></td>
    <td><b>77.7</b><sub>±1.0</sub></td>
    <td>61.9<sub>±0.2</sub></td>
    <td></td>
    <td></td>
    <td></td>
    <td></td>
    <td></td>
  </tr>
  <tr>
    <td>53.1<sub>±2.1</sub></td>
    <td>48.8<sub>±0.3</sub></td>
    <td>73.5<sub>±1.1</sub></td>
    <td>52.4<sub>±0.6</sub></td>
    <td>74.1<sub>±1.0</sub></td>
    <td>60.4<sub>±0.3</sub></td>
    <td></td>
    <td></td>
    <td></td>
    <td></td>
    <td></td>
  </tr>
  <tr>
    <td>44.3<sub>±1.5</sub></td>
    <td>44.8<sub>±2.8</sub></td>
    <td>72.4<sub>±1.5</sub></td>
    <td>51.2<sub>±1.0</sub></td>
    <td>69.2<sub>±1.2</sub></td>
    <td>56.4<sub>±1.0</sub></td>
    <td></td>
    <td></td>
    <td></td>
    <td></td>
    <td></td>
  </tr>
  <tr>
    <td rowspan="4">Random<sub>bio</sub></td>
    <td>57.1<sub>±0.7</sub></td>
    <td>49.5<sub>±1.8</sub></td>
    <td>76.1<sub>±1.8</sub></td>
    <td>50.8<sub>±1.2</sub></td>
    <td>74.9<sub>±1.1</sub></td>
    <td>61.7<sub>±0.6</sub></td>
    <td></td>
    <td></td>
    <td></td>
    <td></td>
    <td></td>
  </tr>
</table>

Table 14: Accuracy (%) of all methods with different random seeds on BBH.

A.4 Decomposition of Relevance

The relevance can be further separated into semantic relevance and procedure (reasoning steps) relevance. Our analysis in Q1-1 has demonstrated that semantic relevance does not matter. To investigate the importance of procedure relevance, we perform a similar analysis. Specifically, we compute the average cosine similarity between the rationales of the generated examples and the rationale of the query to quantitatively measure their relevance. The results on GSM8K are reported in Table 16, which highlight that procedure relevance is not the key factor for analogical reasoning performance on mathematical reasoning tasks.

A.5 Prompts and Outputs for Example Generation

We show detailed prompts and outputs for randomly generating math and biological problems in Fig. 8 and Fig. 9, respectively.

A.6 Guided Problem Generation

In addition to random problem generation in §4.2-Q2-1, we further investigate guided problem generation. Specifically, we randomly select 5 training samples to guide LLMs to self-generate relevant math problems. We then manually verify their correctness and use this fixed set of problems as ICL demonstrations for experiments. The performance of this approach (56.1) is slightly lower than that of ICL<sub>math</sub> (56.3), verifying that relevance is not the key influencing factor.

A.7 Robustness to Prompt Format

To verify the robustness of different methods to prompt format, we experiment with two new prompts paraphrased from the original one by GPT-4 and present the results on GSM8K in Table 17.
<table>
  <tr>
    <th>Method</th>
    <th>Relevant</th>
    <th>N/A</th>
    <th>Random_same</th>
    <th>Random_diff</th>
    <th>Random_bio</th>
    <th>ICL_math</th>
    <th>ICL_bio</th>
  </tr>
  <tr>
    <td>GPT-4o-mini</td>
    <td>90.7</td>
    <td>91.9</td>
    <td>92.6</td>
    <td>92.3</td>
    <td>93.2</td>
    <td>94.2</td>
    <td><b>94.5</b></td>
  </tr>
</table>

Table 15: Accuracy (%) of different methods on GSM8K using GPT-4o-mini. Self-generated relevant examples always underperform irrelevant ones and both ICL variants perform better than other approaches.

<table>
  <tr>
    <th></th>
    <th>Relevant</th>
    <th>N/A</th>
    <th>Random_same</th>
    <th>Random_diff</th>
    <th>Random_bio</th>
    <th>Oracle</th>
  </tr>
  <tr>
    <td>GSM8K</td>
    <td>0.50</td>
    <td>0.16</td>
    <td>0.28</td>
    <td>0.19</td>
    <td>0.08</td>
    <td>0.62</td>
  </tr>
</table>

Table 16: Procedure (reasoning steps) relevance between self-generated examples and the query.

<table>
  <tr>
    <th></th>
    <th>Relevant</th>
    <th>N/A</th>
    <th>Random_same</th>
    <th>Random_diff</th>
    <th>Random_bio</th>
  </tr>
  <tr>
    <td>Prompt_1</td>
    <td>71.2</td>
    <td>74.9</td>
    <td>75.3</td>
    <td><b>75.9</b></td>
    <td>74.3</td>
  </tr>
  <tr>
    <td>Prompt_2</td>
    <td>72.0</td>
    <td>75.2</td>
    <td>74.7</td>
    <td><b>76.2</b></td>
    <td>75.5</td>
  </tr>
</table>

Table 17: Accuracy (%) of different methods with two new prompts.

<table>
  <tr>
    <th>Number</th>
    <th>Relevant</th>
    <th>N/A</th>
    <th>Random_same</th>
    <th>Random_diff</th>
    <th>Random_bio</th>
  </tr>
  <tr>
    <td>3</td>
    <td>73.1</td>
    <td><b>77.3</b></td>
    <td>75.0</td>
    <td>75.3</td>
    <td>75.5</td>
  </tr>
  <tr>
    <td>5</td>
    <td>71.5</td>
    <td>75.5</td>
    <td>75.1</td>
    <td><b>76.3</b></td>
    <td>75.3</td>
  </tr>
</table>

Table 18: Accuracy (%) of all methods with different numbers of demonstrations.

<table>
  <tr>
    <th>ICL_math</th>
    <th>ICL_math<sup>wrong</sup></th>
    <th>ICL_bio</th>
    <th>ICL_bio<sup>wrong</sup></th>
  </tr>
  <tr>
    <td>56.3</td>
    <td>50.9</td>
    <td>56.4</td>
    <td>51.3</td>
  </tr>
</table>

Table 19: Comparison between different ICL variants.

We also observe better performance with irrelevant examples than relevant ones, showing the robustness.

A.8 Different Numbers of Demonstrations

While we mainly follow the setting in Yasunaga et al. (2024) to ask the LLM to generate \( k = 5 \) examples for GSM8K, we further investigate the effect of the number of demonstrations. Specifically, we conduct controlled experiments with \( k = 3 \) and report the results in Table 18. We can observe that irrelevant examples consistently outperform relevant ones across different numbers of demonstrations, emphasizing their effectiveness.

A.9 More Analysis on ICL_math and ICL_bio

Our designed method ICL_math generates correct and relevant examples, and ICL_bio generates correct and irrelevant examples. From the results in Table 8, we can see that ICL_math and ICL_bio achieve similar average performance, demonstrating that relevance does not matter.

We further change the correct answers of the demonstrations in ICL_math and ICL_bio to random answers, obtaining ICL_math<sup>wrong</sup> and ICL_bio<sup>wrong</sup>. Obviously, ICL_math<sup>wrong</sup> generates incorrect and relevant examples, and ICL_bio<sup>wrong</sup> generates incorrect and irrelevant examples. The comparison between these four methods in Table 19 further supports our claim that the key factor influencing the performance on mathematical reasoning is the accuracy of self-generated examples rather than their relevance.

A.10 Repeating Problems

While generating a few accurate problems as ICL demonstrations can achieve better performance, a bolder idea might be to generate one problem and repeat it multiple times as few-shot demonstrations for ICL. To investigate this, we randomly select a generated math problem and repeat it to perform ICL, denoted by ICL_math_repeat. From the results shown in Table 20, we can see that ICL_math_repeat consistently performs worse than ICL_math on both datasets, indicating that the diversity of generated problems also matters.

A.11 Explicit Semantic Control

We explore explicitly controlling the semantics of generated examples (including both problems and reasoning paths) on GSM8K using Llama-3.1-8B-Instruct. Specifically, we investigate the following two approaches: (i) prompting the model to generate semantically similar and correct examples, and (ii) prompting the model to generate semantically different and correct examples. The results reported in Table 21 further verify the correctness of our conclusions.
<table>
  <tr>
    <th rowspan="2">Method</th>
    <th colspan="3">Task</th>
  </tr>
  <tr>
    <th>GSM8K</th>
    <th>MATH</th>
    <th>Average</th>
  </tr>
  <tr>
    <td>ICL-math</td>
    <td><b>75.7</b></td>
    <td><b>36.8</b></td>
    <td><b>56.3</b></td>
  </tr>
  <tr>
    <td>ICL-math_repeat</td>
    <td>73.8</td>
    <td>36.2</td>
    <td>55.0</td>
  </tr>
</table>

Table 20: Comparison of two ICL variants on the GSM8K and MATH datasets.

<table>
  <tr>
    <th>Relevant</th>
    <th>N/A</th>
    <th>Random_same</th>
    <th>Similar and Correct</th>
    <th>Different and Correct</th>
  </tr>
  <tr>
    <td>74.8</td>
    <td>77.3</td>
    <td>78.4</td>
    <td>80.3</td>
    <td><b>80.6</b></td>
  </tr>
</table>

Table 21: Accuracy (%) of different methods on GSM8K using Llama-3.1-8B-Instruct.
Prompt: self-generate relevant examples
Your task is to tackle mathematical problems. When presented with a math problem, recall relevant problems as examples. Afterward, proceed to solve the initial problem.

# Initial Problem:
[The target problem]

# Instructions:
Make sure that your response follows the instructions below.

## Analogous Problems:
Offer five diverse examples of math problems that are relevant or analogous to the initial problem. For each problem, elaborate on the solution and conclude with the ultimate answer (enclosed in 'boxed[]'). For each problem:
- After "O": describe the problem
- After "A": explain the solution and enclose the ultimate answer in 'boxed[]'.

## Solve the Initial Problem:
Q: Copy and paste the initial problem here.
A: Explain the solution and enclose the ultimate answer in 'boxed[]' here.

Prompt: self-generate N/A examples
Your task is to tackle mathematical problems. When presented with a math problem, recall n/a problems as examples. Afterward, proceed to solve the initial problem.

# Initial Problem:
[The target problem]

# Instructions:
Make sure that your response follows the instructions below.

## N/A Problems:
Offer five diverse examples of math problems that are n/a to the initial problem. For each problem, elaborate on the solution and conclude with the ultimate answer (enclosed in 'boxed[]'). For each problem:
- After "O": describe the problem
- After "A": explain the solution and enclose the ultimate answer in 'boxed[]'.

## Solve the Initial Problem:
Q: Copy and paste the initial problem here.
A: Explain the solution and enclose the ultimate answer in 'boxed[]' here.

Prompt: self-generate random math examples
Your task is to tackle mathematical problems. When presented with a math problem, recall random problems as examples. Afterward, proceed to solve the initial problem.

# Initial Problem:
[The target problem]

# Instructions:
Make sure that your response follows the instructions below.

## Random Problems:
Randomly offer five diverse examples of math problems. For each problem, elaborate on the solution and conclude with the ultimate answer (enclosed in 'boxed[]'). For each problem:
- After "O": describe the problem
- After "A": explain the solution and enclose the ultimate answer in 'boxed[]'.

## Solve the Initial Problem:
Q: Copy and paste the initial problem here.
A: Explain the solution and enclose the ultimate answer in 'boxed[]' here.

Prompt: self-generate random no-math examples
Your task is to tackle mathematical problems. When presented with a math problem, recall random problems (remember not to output math problems) as examples. Afterward, proceed to solve the initial problem.

# Initial Problem:
[The target problem]

# Instructions:
Make sure that your response follows the instructions below.

## Random Problems:
Randomly offer five diverse examples of any type, except math problems. For each problem, elaborate on the solution and conclude with the ultimate answer (enclosed in 'boxed[]'). For each problem:
- After "O": describe the problem
- After "A": explain the solution and enclose the ultimate answer in 'boxed[]'.

## Solve the Initial Problem:
Q: Copy and paste the initial problem here.
A: Explain the solution and enclose the ultimate answer in 'boxed[]' here.

Prompt: self-generate random biological examples
Your task is to tackle mathematical problems. When presented with a math problem, recall random biological problems (remember not to output math problems) as examples. Afterward, proceed to solve the initial problem.

# Initial Problem:
[The target problem]

# Instructions:
Make sure that your response follows the instructions below.

## Random Problems:
Randomly offer five diverse examples of biological problems (remember not to output math problems). For each problem, elaborate on the solution and conclude with the ultimate answer (enclosed in 'boxed[]'). For each problem:
- After "O": describe the problem
- After "A": explain the solution and enclose the ultimate answer in 'boxed[]'.

## Solve the Initial Problem:
Q: Copy and paste the initial problem here.
A: Explain the solution and enclose the ultimate answer in 'boxed[]' here.

Figure 5: Prompts for different methods on GSM8K.
Prompt: self-generate relevant examples
Your task is to tackle mathematical problems. When presented with a math problem, recall relevant problems as examples. Afterward, proceed to solve the initial problem.

# Initial Problem:
[The target problem]

# Instructions:
Make sure to include all of the following points:

## Relevant Problems:
Recall three examples of math problems that are relevant to the initial problem. Note that your problems should be distinct from each other and from the initial problem (e.g., involving different numbers and names). For each problem:
- "After 'Q':", describe the problem
- "After 'A':", explain the solution and enclose the ultimate answer in [boxed()].

## Solve the Initial Problem:
Say "Let's solve the following math problem." Then formulate your response in the following format:
Q: Copy and paste the initial problem here.
A: Explain the solution and enclose the ultimate answer in [boxed()] here.

Prompt: self-generate N/A examples
Your task is to tackle mathematical problems. When presented with a math problem, recall n/a problems as examples. Afterward, proceed to solve the initial problem.

# Initial Problem:
[The target problem]

# Instructions:
Make sure to include all of the following points:

## N/A Problems:
Recall three examples of math problems that are n/a to the initial problem. Note that your problems should be distinct from each other and from the initial problem (e.g., involving different numbers and names). For each problem:
- "After 'Q':", describe the problem
- "After 'A':", explain the solution and enclose the ultimate answer in [boxed()].

## Solve the Initial Problem:
Say "Let's solve the following math problem." Then formulate your response in the following format:
Q: Copy and paste the initial problem here.
A: Explain the solution and enclose the ultimate answer in [boxed()] here.

Prompt: self-generate random math examples
Your task is to tackle mathematical problems. When presented with a math problem, recall random problems as examples. Afterward, proceed to solve the initial problem.

# Initial Problem:
[The target problem]

# Instructions:
Make sure to include all of the following points:

## Random Problems:
Randomly recall three examples of math problems. Note that your problems should be distinct from each other and from the initial problem (e.g., involving different numbers and names). For each problem:
- "After 'Q':", describe the problem
- "After 'A':", explain the solution and enclose the ultimate answer in [boxed()].

## Solve the Initial Problem:
Say "Let's solve the following math problem." Then formulate your response in the following format:
Q: Copy and paste the initial problem here.
A: Explain the solution and enclose the ultimate answer in [boxed()] here.

Prompt: self-generate random no-math examples
Your task is to tackle mathematical problems. When presented with a math problem, recall random problems (remember not to output math problems) as examples. Afterward, proceed to solve the initial problem.

# Initial Problem:
[The target problem]

# Instructions:
Make sure to include all of the following points:

## Random Problems:
Randomly recall three examples of any type, except math problems. Note that your problems should be distinct from each other and from the initial problem. For each problem:
- "After 'Q':", describe the problem
- "After 'A':", explain the solution and enclose the ultimate answer in [boxed()].

## Solve the Initial Problem:
Say "Let's solve the following math problem." Then formulate your response in the following format:
Q: Copy and paste the initial problem here.
A: Explain the solution and enclose the ultimate answer in [boxed()] here.

Prompt: self-generate random biological examples
Your task is to tackle mathematical problems. When presented with a math problem, recall random biological problems (remember not to output math problems) as examples. Afterward, proceed to solve the initial problem.

# Initial Problem:
[The target problem]

# Instructions:
Make sure to include all of the following points:

## Random Problems:
Randomly recall three examples of biological problems (remember not to output math problems). Note that your problems should be distinct from each other and from the initial problem. For each problem:
- "After 'Q':", describe the problem
- "After 'A':", explain the solution and enclose the ultimate answer in [boxed()].

## Solve the Initial Problem:
Say "Let's solve the following math problem." Then formulate your response in the following format:
Q: Copy and paste the initial problem here.
A: Explain the solution and enclose the ultimate answer in [boxed()] here.

Figure 6: Prompts for different methods on MATH.
Prompt: self-generate relevant examples

Your task is to tackle reasoning problems. When presented with a problem, recall relevant problems as examples. Afterward, proceed to solve the initial problem.

# Initial Problem:
[The target problem]

# Instructions:
Make sure to include all of the following points:

## Relevant Problems:
Recall three examples of problems that are relevant to the initial problem. Note that your problems must be distinct from each other and from the initial problem. For each problem:
- After "Q.": describe the problem
- After "A.": explain the solution and enclose the ultimate answer in [boxed[]].

## Solve the Initial Problem:
Say "Let's solve the following reasoning problem." Then formulate your response in the following format:
Q: Copy and paste the initial problem here.
A: Explain the solution and enclose the ultimate answer in [boxed[]] here.

Prompt: self-generate N/A examples

Your task is to tackle reasoning problems. When presented with a problem, recall n/a problems as examples. Afterward, proceed to solve the initial problem.

# Initial Problem:
[The target problem]

# Instructions:
Make sure to include all of the following points:

## N/A Problems:
Recall three examples of problems that are n/a to the initial problem. Note that your problems must be distinct from each other and from the initial problem. For each problem:
- After "Q.": describe the problem
- After "A.": explain the solution and enclose the ultimate answer in [boxed[]].

## Solve the Initial Problem:
Say "Let's solve the following reasoning problem." Then formulate your response in the following format:
Q: Copy and paste the initial problem here.
A: Explain the solution and enclose the ultimate answer in [boxed[]] here.

Prompt: self-generate random reasoning examples

Your task is to tackle reasoning problems. When presented with a problem, recall random problems as examples. Afterward, proceed to solve the initial problem.

# Initial Problem:
[The target problem]

# Instructions:
Make sure to include all of the following points:

## Random Problems:
Randomly recall three examples of reasoning problems. Note that your problems must be distinct from each other and from the initial problem. For each problem:
- After "Q.": describe the problem
- After "A.": explain the solution and enclose the ultimate answer in [boxed[]].

## Solve the Initial Problem:
Say "Let's solve the following reasoning problem." Then formulate your response in the following format:
Q: Copy and paste the initial problem here.
A: Explain the solution and enclose the ultimate answer in [boxed[]] here.

Prompt: self-generate random no-reasoning examples

Your task is to tackle reasoning problems. When presented with a problem, recall random problems (remember not to output reasoning problems) as examples. Afterward, proceed to solve the initial problem.

# Initial Problem:
[The target problem]

# Instructions:
Make sure to include all of the following points:

## Random Problems:
Randomly recall three examples of any type, except reasoning problems. Note that your problems must be distinct from each other and from the initial problem. For each problem:
- After "Q.": describe the problem
- After "A.": explain the solution and enclose the ultimate answer in [boxed[]].

## Solve the Initial Problem:
Say "Let's solve the following reasoning problem." Then formulate your response in the following format:
Q: Copy and paste the initial problem here.
A: Explain the solution and enclose the ultimate answer in [boxed[]] here.

Prompt: self-generate random biological examples

Your task is to tackle reasoning problems. When presented with a problem, recall random biological problems (remember not to output reasoning problems) as examples. Afterward, proceed to solve the initial problem.

# Initial Problem:
[The target problem]

# Instructions:
Make sure to include all of the following points:

## Random Problems:
Randomly recall three examples of biological problems (remember not to output reasoning problems). Note that your problems must be distinct from each other and from the initial problem. For each problem:
- After "Q.": describe the problem
- After "A.": explain the solution and enclose the ultimate answer in [boxed[]].

## Solve the Initial Problem:
Say "Let's solve the following reasoning problem." Then formulate your response in the following format:
Q: Copy and paste the initial problem here.
A: Explain the solution and enclose the ultimate answer in [boxed[]] here.

Figure 7: Prompts for different methods on BBH.
Input
Randomly recall five examples of math problems. Note that your problems should be distinct from each other (e.g., involving different numbers and names). For each problem:
- After "Q:", describe the problem
- After "A:", explain the solution and enclose the ultimate answer in 'boxed()'.

Output
Q: If John has 5 apples and he buys 8 more, how many apples does he have in total?
A: To find the total number of apples John has, we add the number of apples he initially has to the number of apples he buys. So, we calculate 5 + 8 = 13. Therefore, John has 'boxed(13)' apples in total.

Q: Solve for x in the equation 2x - 4 = 10.
A: To solve for x, we first add 4 to both sides of the equation to get 2x = 14. Then, we divide both sides by 2 to isolate x, resulting in x = 7. Thus, the solution is 'boxed(x = 7)'.

Q: A rectangle has a length of 10 cm and a width of 4 cm. What is its area?
A: The area of a rectangle is found by multiplying its length by its width. Therefore, the area of this rectangle is 10 * 4 = 40 square centimeters. So, the area is 'boxed(40)'.

Q: A fair six-sided die is rolled. What is the probability of rolling a number greater than 4?
A: A six-sided die has numbers 1 through 6. The numbers greater than 4 are 5 and 6, which are 2 out of the 6 possible outcomes. Therefore, the probability of rolling a number greater than 4 is \( \frac{2}{6} = \frac{1}{3} \). Thus, the probability is 'boxed(\frac{1}{3})'.

Q: Find the derivative of the function f(x) = 3x^2 + 2x - 5.
A: To find the derivative of f(x), we apply the power rule to each term. The derivative of 3x^2 is 6x, the derivative of 2x is 2, and the derivative of a constant -5 is 0. Therefore, the derivative of f(x) is f'(x) = 6x + 2. So, the derivative is 'boxed(6x + 2)'.

Figure 8: Prompts and outputs for generating math problems.

Input
Randomly recall five diverse examples of biological problems (remember not to output math problems). For each problem:
- After "Q:", describe the problem
- After "A:", explain the solution and enclose the ultimate answer in 'boxed()'.

Output
Q: In a certain species of plant, the allele for red flowers (R) is dominant over the allele for white flowers (r). If two heterozygous plants are crossed, what is the probability that all offspring will have red flowers?
A: To solve this problem, we use a Punnett square to determine the genotypes of the offspring. The cross of two heterozygous plants Rr x Rr produces the following genotypes: RR, Rr, Rr, and rr. The probability of an offspring having white flowers rr is 1 out of 4, since only one genotype out of the four possible genotypes results in white flowers. Therefore, the probability is 'boxed(\frac{1}{4})'.

Q: A small pond is introduced with 10 fish, and the fish population doubles every month. How many fish will there be in the pond after 6 months?
A: To find the fish population after 6 months, we use the formula for exponential growth: P = P_0 * 2^n, where P is the final population, P_0 is the initial population, and n is the number of time periods (months, in this case). Plugging in the values, we get P = 10 * 2^6. Calculating this gives P = 10 * 64 = 640. Therefore, there will be 'boxed(640)' fish in the pond after 6 months.

Q: What is the primary mechanism by which the human kidney concentrates urine?
A: The human kidney uses a countercurrent multiplier system through the loop of Henle. This system allows for the reabsorption of water and solutes from the filtrate back into the bloodstream, which concentrates the urine. The key to this process is the creation of a high osmolarity in the medullary interstitial fluid, which draws water out of the filtrate in the collecting ducts, concentrating the urine. The ultimate answer is the 'boxed(counter-current multiplier system)'.

Q: What is the principle behind the theory of natural selection as proposed by Charles Darwin?
A: The principle behind the theory of natural selection is that individuals within a species show variation in physical characteristics and behaviors. These variations allow the individuals to compete for resources in their environment. Individuals with traits that are better suited to their environment are more likely to survive and reproduce, passing on those advantageous traits to their offspring. Over time, this can lead to changes in the species as a whole. The ultimate answer is the 'boxed(survival and reproduction of the fittest)'.

Q: How do antibiotics kill bacteria?
A: Antibiotics can kill bacteria through several mechanisms, including inhibiting cell wall synthesis, disrupting protein synthesis, impairing nucleic acid synthesis, and interfering with metabolic pathways. The specific mechanism depends on the class of antibiotic. For example, penicillin disrupts the synthesis of the bacterial cell wall, leading to cell lysis and death. Therefore, the ultimate answer is by 'boxed(inhibiting vital processes)' specific to bacteria.

Figure 9: Prompts and outputs for generating biological problems.

Reviewer paper summaries: This paper is motivated by recent results using “analogical prompting,” which find that LLMs can self-generate *relevant* in-context demonstrations to improve performance on downstream mathematical and other reasoning tasks. Specifically, the paper asks whether relevant LLM-generated examples are more beneficial than “random” examples, finding that random examples enable similar performance to relevant examples (along with a follow-up analysis of the relevance of LLM-generated explanations). To follow this, they examine whether the accuracy of LLM-generated examples is really the driving factor behind performance gains. First, through human annotation, they find that irrelevant examples are more likely to be correct (possibly because relevant examples tended to be more difficult). They then apply two types of approaches to show the importance of accurate in-context examples: an approach that uses GPT-4 to correct LLM-generated examples, and an approach that conditions LLMs with human-corrected examples, finding that both approaches improve accuracy on the downstream tasks, while in some cases, the domain of the examples interestingly did not affect performance (e.g., using mathematics vs. biology examples to condition solving math problems).

The work is well motivated, the paper is well written, and the experiments presented in the paper are thorough in terms of the questions asked. However, the paper ignores a lot of relevant prior work, especially in evaluating analogical reasoning in LLMs, and thus over-claims the novelty of its contributions. Further, I have several issues with the methodology of presented experiments, and find most of them are not compelling in their current state. Due to a lack of defining terms like “relevant” and “random,” the line of inquiry often feels out of order, with initial experiments attempting to answer mal-formed questions and later experiments making up for their shortcomings. 

I give detailed comments in the Weaknesses section, which I tried to organize by each research question and/or table of results. I hope they help the authors in revising the paper.
Summary of strengths: **Strength A: Strong motivation.** This paper is well motivated. Specifically, the authors observe that prior work has investigated whether the relevance of manually provided in-context examples for reasoning tasks (including those with a “chain-of-thought” style rationale) impacts the performance of LLMs on downstream tasks, but it has not looked at the importance of relevance in LLM-generated in-context examples (i.e., like those self-generated by LLMs in the process of *analogical prompting*, which is cited in the paper). This begs a question of whether examples generated by LLMs are actually relevant to the task at hand, and whether relevance is the reason why an approach like analogical prompting improves the performance of LLMs on reasoning tasks.

**Strength B: Thorough experiments.** The authors thought of most of the reasonable questions to ask in this problem, and executed experiments for them. This included evaluating whether random examples (“random” being implemented in several more specific ways in the paper) are just as helpful as relevant examples in analogical prompting, confirming that examples thought to be relevant or irrelevant are actually so, exploring why random examples might be equally or more helpful in some cases (the authors attempt to show that accuracy of examples is crucial), and lastly curating accurate analogical prompting examples to further demonstrate the importance of accuracy. While I have gripes with how some of these experiments are carried out (described below), this inquiry is remarkably thorough and yields interesting insights about the utility of in-context examples and rationales.

**Strength C: Well-written paper.** The paper is mostly quite well organized and written, and intuitively explains the motivation, contributions, methods, and results.
Summary of weaknesses: **Weakness A: Ignores prior work in analogical reasoning and LLMs.** At L106, this paper claims to be the first to “extensively assess the ability of LLMs to perform analogical reasoning.” However, there are a number of papers that have already done this from various other perspectives besides analogical prompting (i.e., self-generating in-context examples when applying LLMs to reasoning tasks). These include (but are not limited to):

* A number of recent text-based analogy dataset papers that evaluate LLMs [1,2,3]. There are also earlier papers that might be relevant to cite, as recent works have evaluated LLMs on them, e.g., [4,5].

* Recent works that have thoroughly evaluated LLMs’ analogical reasoning capabilities in more abstract settings [6,7].

* An influential position paper about AI and analogy-making that might support some of the paper’s motivations [8].

* The ARC dataset for abstract analogical reasoning, which is still challenging to today’s LLMs [9], as well as recent follow ups that evaluate LLMs on it or variants of it [10,11].

Due to the broad body of work on this problem, I urge the authors to remove or refine this claim, and be careful to avoid making general conclusions about “analogical reasoning” as a whole (including in the title and abstract) when it has been viewed in these various ways in NLP research. In many cases where “analogical reasoning” is used in the paper, “analogical prompting” or similar should instead be used to be more specific and avoid over-claiming. Further, the authors should add these references to Section 2.2 in their Related Work to better contextualize their work. Meanwhile, the discussion on chain-of-thought can be reduced (as the contribution here is not to chain-of-thought style prompting approaches), as can the existing version of Section 2.2.


**Weakness B: Does not cite similar inquiries into in-context learning.** Related to the previous, while this paper demonstrates an understanding that prior work has performed similar studies on examples provided for in-context learning and chain-of-thought (L066), some additional relevant works seem to be missed [12,13,14,15]. These omissions are less problematic for me given that the paper already cites several similar studies in Section 1, but I would recommend later replacing the discussion on related work in chain-of-thought (Section 2.1) with a thorough discussion of all these works investigating properties of exemplars and rationales in in-context learning.

In case the authors have not seen, I would also like to point out a very relevant contemporaneous work that appeared in NeurIPS 2024 [16]. Assuming the authors submit this paper again in the future, it might become necessary to cite and rigorously compare it to this work. For now, though, the omission of this work does not factor into my score.

**Weakness C: Q1 experiments are lacking definition.** The experiments for Q1 (*Are self-generated relevant examples more beneficial to LLMs than random ones?*) presented in Tables 1-3 are lacking important definitions, which causes them to be (in my opinion) inconclusive by themselves and forces later experiments to have to account for their shortcomings. Here, LLMs are prompted to generate “relevant” problem examples in-context, and their performance is compared to cases where LLMs are prompted to generate other less relevant examples: not applicable examples (“N/A”), examples from the same domain (“Random_same”), examples from different domains (“Random_diff”), and examples specifically from biology (“Random_bio”). Considering this group of experiments in isolation, I do not think they are successful at answering Q1. This is for several reasons, mostly accountable to lacking definitions of the terms in Q1:

1. First, I am not convinced that LLMs are capable of reliably following the instructions given to them, i.e., to generate relevant vs. irrelevant “N/A”, same-domain, different-domain, and biological examples. As an aside, prompting LLMs to generate “n/a examples” feels like a vague instruction - at minimum, “n/a” should be capitalized or spelled out.

2. Moreover, we do not know whether the LLM-generated “relevant” examples are truly relevant, and if so, how. The only definition of “relevance” is given later through semantic similarity estimated by Sentence Transformer (this is discussed more below).

3. Lastly, the definition of “random” is important here. In fact, none of these generated examples are truly random - they are sampled from the LLMs’ learned distributions of what would be “N/A”, same domain, different domain, and biological examples. It is also worth noting that LLMs are not great estimators of randomness [17]. Making general conclusions about “random” examples is thus not really sound. I would recommend describing examples as “irrelevant” rather than “random.”

To answer research question Q1, the most direct and sound route would have been to curate data for relevant and random/irrelevant explanations, ideally judged by humans at least partly, then evaluating LLMs using these in-context. Instead, the authors attempt to address the above issues by adding experiments under a new Q1-1 (*Are self-generated examples really relevant or irrelevant to the query?*), where the relevance of each type of example (relevant and all 4 types of irrelevant explanations) is estimated by the Sentence Transformer embedding similarity to the task instance at hand (Table 4). Sentence Transformer is biased by overlap in noun participants of sentences and relies less on predicate information [18], which I imagine could cause the “relevant” examples to be scored overly similar to the task instance at hand. Even if we could rely on Sentence Transformer to give accurate judgements of semantic similarity here, all this tells us is the level of relevance of each type of example used. I notice the authors included additional qualitative examples in Table 6 to account for this limitation, but this is not compelling to me.

To close the loop and actually answer Q1, it may be best to perform a correlation analysis between the individual similarity of examples to the task instances at hand and the performance. The authors should also consider collecting human judgements of relevance similar to what they did to measure “accuracy” of examples later. Nonetheless, this route of experimentation is a bit backwards.

**Weakness D: Q2 experiment human annotation sample size is small.** After the Q1 and Q1-1 experiments, the authors proceed to Q2 (*If relevance is not the key factor, what is more important for the accuracy of analogical reasoning?*). To answer this question, the authors first annotate 50 LLM-generated examples for their accuracy on the MATH dataset (Table 5), finding that same-domain random examples were the most accurate. While interesting, this is only a small sample on one dataset; I would have liked to see this inquiry expanded to demonstrate a more general phenomenon. Furthermore, an analysis of how accuracy of examples and accuracy of individual test cases is correlated could have helped convey the importance of accurate examples.


**Weakness E: Missing details for Table 7 results.** Based on the above result, the authors explore an alternative method which uses LLM-generated examples as in-context demonstrates, then optionally corrects them using GPT-4. There are important experimental details missing here. First, it is unclear to me how using LLM-generated examples as in-context learning demonstrations is any different than the approaches presented in Tables 1 and 2. Is the LLM prompted to generate a “relevant” example in this experiment? Further, at L343, the authors claim to do “manual verification” to confirm that GPT-4’s answers are mostly accurate. They later conclude that “increasing the accuracy of generated examples can indeed improve the performance,” which improperly conflates “generated by GPT-4” with “accurate”. At minimum, the authors should manually verify some of GPT-4’s corrected examples to substantiate this claim.

**Weakness F: Table 8 results are not novel or compelling, and do not demonstrate the importance of accuracy.** After Q2, the authors again add a research question Q2-1 (*Can we ask the LLM to randomly generate a few math or biological problems and manually verify their correctness, then use this fixed set of problems as ICL demonstrations for all test queries?*). Like Q1-1, the experiments here are more sound and better defined than Q2, as we know that the math and biology examples used as in-context demonstrations are accurate. However, the results in Table 8 are not compelling. The best results in each column (which are all from the proposed approach using manually verified examples) exceed the earlier tested approaches (i.e., with LLM-generated relevant and various types of irrelevant examples) by a maximum of 1.6% accuracy. To me, rather than suggesting “ensuring the accuracy of self-generated examples does lead to better performance regardless of the problem type” (L383-384), this suggests that the impact of accuracy is minimal (not to mention, the statistical significance of performance differences is unclear).

Furthermore, while it is indeed true that “both ICL variants only need to generate examples once, which significantly reduces the inference cost,” this is essentially reinventing chain-of-thought as introduced in Wei et al. (2022), and not grounds to claim as a key contribution of this work (as seems to be done at L096-098 in the Introduction). These variants should only be used as a means to show how accuracy and domain of explanations impacts performance.

**Weakness G: Tables 9-12 distract from key messages in the paper.** The last several tables of results start to get messy and stray from the main point of the paper:

* Tables 9-10 list the corresponding accuracy of open-source models for earlier experiments. Where possible, I would recommend presenting a consistent set of models throughout the results rather than adding the open-source models at the end. I understand this may make some of your tables highly complex, so maybe another option is to just move these supplemental results to the appendix, and mention in the main paper that the trends of your results hold for other models (pointing to appendix).

* Table 11 applies compared methods to additional datasets not explored in Yasunaga et al. (2024; i.e., the original analogical prompting paper). This feels arbitrary - I would recommend to either include these datasets throughout the results, or just include this as a bonus result in the appendix.

* Table 12 compares the proposed “ICL” prompting methods to other methods like self-consistency. As mentioned above, these approaches are not novel contributions, so such a comparison is not necessary or insightful. I would recommend to delete or move to the appendix.

**Weakness H: On the randomness in results.** Lastly, there is a possible contradiction in the implementation details for the experiments. At L224, the authors claim that temperature is zero for generating texts with GPT 3.5. While this should make generated texts deterministic, the authors report different results for various random seeds in Appendix A.2 (which are then averaged in the tables in the main paper). How is this possible? How is there any randomness in generated texts when using zero temperature? Perhaps there are some additional missing details that need to be added to the paper. I appreciate the inclusion of multiple random seeds, but this discrepancy needs to be clarified.

References:

[1] Jiangjie Chen, Rui Xu, Ziquan Fu, Wei Shi, Zhongqiao Li, Xinbo Zhang, Changzhi Sun, Lei Li, Yanghua Xiao, and Hao Zhou. 2022. E-KAR: A Benchmark for Rationalizing Natural Language Analogical Reasoning. In Findings of the Association for Computational Linguistics: ACL 2022, pages 3941–3955, Dublin, Ireland. Association for Computational Linguistics. https://aclanthology.org/2022.findings-acl.311/ 

[2] Siyu Yuan, Jiangjie Chen, Xuyang Ge, Yanghua Xiao, and Deqing Yang. 2023. Beneath Surface Similarity: Large Language Models Make Reasonable Scientific Analogies after Structure Abduction. In Findings of the Association for Computational Linguistics: EMNLP 2023, pages 2446–2460. https://aclanthology.org/2023.findings-emnlp.160/ 

[3] Siyu Yuan, Jiangjie Chen, Changzhi Sun, Jiaqing Liang, Yanghua Xiao, and Deqing Yang. 2024. ANALOGYKB: Unlocking Analogical Reasoning of Language Models with A Million-scale Knowledge Base. In Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 1249–1265, Bangkok, Thailand. Association for Computational Linguistics. https://aclanthology.org/2024.acl-long.68/ 

[4] Boteanu, A., & Chernova, S. (2015). Solving and Explaining Analogy Questions Using Semantic Networks. Proceedings of the AAAI Conference on Artificial Intelligence, 29(1). https://doi.org/10.1609/aaai.v29i1.9400 

[5] Turney, Peter D., et al. "Combining independent modules to solve multiple-choice synonym and analogy problems." arXiv preprint cs/0309035 (2003). https://arxiv.org/abs/cs/0309035 

[6] Webb, T., Holyoak, K.J. & Lu, H. Emergent analogical reasoning in large language models. Nat Hum Behav 7, 1526–1541 (2023). https://doi.org/10.1038/s41562-023-01659-w 

[7] Xiaoyang Hu, Shane Storks, Richard Lewis, and Joyce Chai. 2023. In-Context Analogical Reasoning with Pre-Trained Language Models. In Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 1953–1969, Toronto, Canada. Association for Computational Linguistics. https://aclanthology.org/2023.acl-long.109/ 

[8] Mitchell M. Abstraction and analogy-making in artificial intelligence. Ann N Y Acad Sci. 2021 Dec;1505(1):79-101. doi: 10.1111/nyas.14619. Epub 2021 Jun 25. PMID: 34173249. https://pubmed.ncbi.nlm.nih.gov/34173249/ 

[9] Chollet, François. "On the measure of intelligence." arXiv preprint arXiv:1911.01547 (2019). https://arxiv.org/abs/1911.01547 

[10] Mitchell, Melanie, Alessandro B. Palmarini, and Arseny Moskvichev. "Comparing humans, gpt-4, and gpt-4v on abstraction and reasoning tasks." arXiv preprint arXiv:2311.09247 (2023). https://arxiv.org/abs/2311.09247 

[11] Moskvichev, Arseny, Victor Vikram Odouard, and Melanie Mitchell. "The ConceptARC benchmark: Evaluating understanding and generalization in the arc domain." arXiv preprint arXiv:2305.07141 (2023). https://arxiv.org/abs/2305.07141 

[12] Freda Shi, Xinyun Chen, Kanishka Misra, Nathan Scales, David Dohan, Ed Chi, Nathanael Schärli, and Denny Zhou. 2023. Large language models can be easily distracted by irrelevant context. In Proceedings of the 40th International Conference on Machine Learning (ICML'23), Vol. 202. JMLR.org, Article 1291, 31210–31227. https://dl.acm.org/doi/10.5555/3618408.3619699 

[13] Miles Turpin, Julian Michael, Ethan Perez, Samuel Bowman. 2023. Language Models Don't Always Say What They Think: Unfaithful Explanations in Chain-of-Thought Prompting. https://proceedings.neurips.cc/paper_files/paper/2023/hash/ed3fea9033a80fea1376299fa7863f4a-Abstract-Conference.html 

[14] Albert Webson, Alyssa Loo, Qinan Yu, and Ellie Pavlick. 2023. Are Language Models Worse than Humans at Following Prompts? It’s Complicated. In Findings of the Association for Computational Linguistics: EMNLP 2023, pages 7662–7686, Singapore. Association for Computational Linguistics. https://aclanthology.org/2023.findings-emnlp.514/ 

[15] Albert Webson and Ellie Pavlick. 2022. Do Prompt-Based Models Really Understand the Meaning of Their Prompts?. In Proceedings of the 2022 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, pages 2300–2344, Seattle, United States. Association for Computational Linguistics. https://aclanthology.org/2022.naacl-main.167/ 

[16] Zhanke Zhou, Rong Tao, Jianing Zhu, Yiwen Luo, Zengmao Wang, Bo Han. 2024. Can Language Models Perform Robust Reasoning in Chain-of-thought Prompting with Noisy Rationales? https://openreview.net/forum?id=FbuODM02ra 

[17] Hopkins, Aspen K., and Alex Renda. "Can LLMs generate random numbers? evaluating LLM sampling in controlled domains." Sampling and Optimization in Discrete Space (SODS) ICML 2023 Workshop, 2023. https://par.nsf.gov/biblio/10498692 

[18] Dmitry Nikolaev and Sebastian Padó. 2023. Representation biases in sentence transformers. In Proceedings of the 17th Conference of the European Chapter of the Association for Computational Linguistics, pages 3701–3716, Dubrovnik, Croatia. Association for Computational Linguistics. https://aclanthology.org/2023.eacl-main.268/
Comments, suggestions and typos: The below comments do not require any response, but I hope to see most of them addressed in a future version. This paper has much fewer typos and similar minor issues than most papers I have reviewed- I appreciate the authors submitting a polished manuscript.

**General suggestions:**

You **need** to cite GPT 3.5 and 4. Find the appropriate technical reports and cite them, and include the way you accessed the API and model/API versions if possible.

There are some weird places where the novelty of the work is over-explained, specifically in the paragraph beginning at L357 and the first paragraph of Section 4.3 (L394). Such discussions should primarily occur in Section 1 (Introduction) and 2 (Related Work), where you’re explaining the background and relevant prior work. Please try reducing the content here and moving to those sections where needed.

**Typos and other specific suggestions:**

Title: I already implied this above, but the title “Can LLMs Truly Perform Analogical Reasoning?” is way too general for a problem area that has already been studied a lot in LLMs. Please refine it - you may also consider making the title include something about the importance of accurate explanations, e.g., “Relevant or Accurate: …”.

L042-049: This is quite a specialized skill that surely not all humans possess. This needs citation to be justified.

Figure 1: I found this figure confusing, as it seems to omit a lot of the details from the prompt examples in the appendix. Is it possible to make this figure a bit more detailed? Later figures don’t have to be so detailed, but this would give a better initial impression to the reader.

L055 and other places: While not necessary, I try to avoid nested and back-to-back parentheses using \citealp in LaTeX.

L087-093: This sentence is very hard to parse, please rewrite.

Section 4.2: You use custom “Q1”/”Q2”/etc. boxes and bullet points to organize this section, which makes it a bit difficult to navigate. I would recommend replacing boxes with proper numbered subsubsections, and replacing bullet points with traditional paragraph headers where possible.

L278: You seem to have 2 copies of this same reference; consolidate.

L325, Table 11 caption, many other places: Please use quotation marks (“”) instead of apostrophes (‘’) for quotes; specifically, quotation marks should be written in LaTeX as ``’’.

Table 7 and relevant discussion: I don’t like the choice of the word “calibration” here, which has a specific meaning in machine learning research. Maybe use “correction”?

L464: “~” -> “and”? This seems to point to several appendices but to my understanding, should only point to 2.

Nitpick: In Tables 9-11, I found it jarring that suddenly “Relevant”, “N/A”, etc. were now column headings instead of row headings. I’m not sure how to fix it at first glance, but maybe you can think of something.
Overall assessment scores: 2