Instance-adaptive Zero-shot Chain-of-Thought Prompting
Authors: Xiaosong Yuan
Chen Shen
Shaotian Yan
Xiaofeng Zhang
Liang Xie
Wenxiao Wang
Renchu Guan
Ying Wang
Jieping Ye
Venue: NeurIPS 2024 poster (2024)
Keywords: Large Language Models
Chain-of-Thought Reasoning
Instance-adaptive
Zero-shot
Primary area: natural_language_processing
TL;DR: This paper conducts analysis on LLM's zero-shot CoT, discovering an information flow pattern, furthermore, this paper proposes an instance-adaptive zero-shot prompting strategy to improve LLM's performance on several reasoning tasks.

Abstract: Zero-shot Chain-of-Thought (CoT) prompting emerges as a simple and effective strategy for enhancing the performance of large language models (LLMs) in real-world reasoning tasks. Nonetheless, the efficacy of a singular, task-level prompt uniformly applied across the whole of instances is inherently limited since one prompt cannot be a good partner for all, a more appropriate approach should consider the interaction between the prompt and each instance meticulously. This work introduces an instance-adaptive prompting algorithm as an alternative zero-shot CoT reasoning scheme by adaptively differentiating good and bad prompts. Concretely, we first employ analysis on LLMs through the lens of information flow to detect the mechanism under zero-shot CoT reasoning, in which we discover that information flows from question to prompt and question to rationale jointly influence the reasoning results most. We notice that a better zero-shot CoT reasoning needs the prompt to obtain semantic information from the question then the rationale aggregates sufficient information from the question directly and via the prompt indirectly. On the contrary, lacking any of those would probably lead to a bad one. Stem from that, we further propose an instance-adaptive prompting strategy (IAP) for zero-shot CoT reasoning. Experiments conducted with LLaMA-2, LLaMA-3, and Qwen on math, logic, and commonsense reasoning tasks (e.g., GSM8K, MMLU, Causal Judgement) obtain consistent improvement, demonstrating that the instance-adaptive zero-shot CoT prompting performs better than other task-level methods with some curated prompts or sophisticated procedures, showing the significance of our findings in the zero-shot CoT reasoning mechanism.

Instance-adaptive Zero-shot Chain-of-Thought Prompting
Xiaosong Yuan 1,2f, Chen Shen Shaotian Yan Xiaofeng Zhang"
Liang Xie Wenxiao Wang Renchu Guan 1.2 Ying Wang'. Jieping Ye
College of Computer Science and Technology, Jilin University
Key Laboratory of Symbolic Computation and Knowledge Engineering, MoE, Jilin University
Alibaba Cloud Computing
Shanghai Jiao Tong University
5 College of Computer Science and Technology, Zhejiang University of Technology
CCollege of Software, Zhejiang University
yuanxs19@ mails.jlu.edu..c jlu.edu.cn, zjushenchen @ gmail.com
Abstract
Zero-shot ofain-of-Thhught (CoT) prompting emerges as a simple and effective strategy for enhancing the performance of large language models (LLMs) in real- world reasoning tasks. Nonetheless, the efficacy of a singular, task-level prompt uniformly applied across the whole of instances is inherently limited since one prompt cannot be a good partner for all, a more appropriate approach should con- sider the interaction between the prompt and each instance meticulously. This work introduces an instance-adaptivy prompting algorithm as an alternative zero-shot CoT reasoning scheme by adaptively differentiating good and bad prompts. Con- cretely, we first employ analysis LLMs through the lens of information flow to detect the mechanism under zero-shot CoT reasoning, in which we discover that in- formation flows from question to prompt and question to rationale jointly influence the reasoning results most. We notice that a better zero-shot CoT reasoning needs the prompt to obtain semantic information from the question, and then the rationale aggregates sufficient information from the question directly and via the prompt indirectly. On the contrary, lacking any of those would probably lead to bad one. Stem from that, we further propose an instance-adaptive prompting strategy (IAP) for zero-shot CoT reasoning. Experiments conducted with LLaMA-2, LLaMA- 3, and Qwen on math, logic, and commonsense reasoning tasks (e.g., GSM8k, MMLU, Causal Judgement) obtain consistent improvement, demonstrating that the instance-adaptive zero-shot CoT prompting performs better than other task-level methods with some curated prompts sophisticated procedures, showing the significance of our findings in the zero-shot CoT reasoning mechanism.
Introduction
Large language models (LLMs) have demonstrated capabilities at tackling copious reasoning tasks through Chain-of-Thought (CoT) I.IO.. Compared to the few-shot setting for CoT generally, zero-shot CoT prompting can achieve approximate performance with merely one natural language prompt rather than complicated demonstrations, which has been proven as a simple and efficient paradigm (2]. Numerous efforts have been thrown into searching for better prompts that can benefit zero-shot CoT reasoning. Plan-and-Solle
[6] employs a human-crafted prompt to break down the
Work done during an internship Alibaba Cloud Computing Corresponding author
t Project lead
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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Question: There are five phones on a phone plan. The main phone costs twice much as each additional phone. If main phone plan costs $20, how much does the whole phone plan cost?
Question; There are five phones on a phone plan. The main phone costs twice as much each additional phone. If main phone plan costs $20, how much does the whole phone plan cost?
Let's think step by step.
Don't think. Just feel.
LLM
LLM
The udditional phone costs 200/2=110 The total cost of udditional phones is 5 $10 $50. The whole phone plan costs S50 $20 $70. The answer 70. The answer is 70. X
The answer is 60. v
Figure 1: Input the same question with two different prompts to guide the LLM to answer it. Blue words are format tokens and prompts, red words mark wrong reasoning steps.
question and automatically generates reasoning steps. OPRO 7 takes the LLM optimizer to update zero-shot CoT prompt iteratively and produce corresponding optimized prompts for a given task. Self-discover [9] selects relevant atomic reasoning modules (e.g. breaking down problems, critical thinking) for a given task, then adapts and customizes those modules to fit the task.
All prior methods focused on constructing prompts from the task perspective, aiming to find the optimal task-level prompt. Seeking the optimal prompt for a given task may achieve compelling performance, beating other prompts on the dataset scale. However, from the perspective of instance, the task-level optimal prompt within a dataset may have adverse effects on certain instances, whereby the model, capable of correctly answering them under other sub-optimal task-level prompts [1H Figure T illustrates an instance from GSM8K dataset [17, this simple question that can be straightTorwardly answered correctly under "Don't 't think. Just feel.", which is generally regarded as less favorable prompt, but "Let's 's think step by step" guides the LLM to bad reasoning in some steps. Therefore, instance-wist zero-shot CoT prompt more plausible for better reasoning and may achieve a cap- breaking performance compared to the task-level optimal prompt.
Nevertheless, the severe challenge of choosing one of the suitable prompts for each instance remains: the difficulty of understanding why some reasoning processes succeed while others fail. To meet such challenge, we intend to detect the mechanism of zero-shot CoT which is an unclear mystery 218 Neuron saliency score analysis is an important approach for observing the information flow during the model inference 25) by which we can observe a click of the dynamic reasoning process in certain steps. After comprehensive investigation across several LLMs and tasks, we find that a successful reasoning procedure tends satisfy the following conditions: the semantic information of the question should be aggregated to the prompt first, and the reasoning steps gather information from both the original question and the synthesized dnestion-prompp semantic information. Otherwise, it is more likely to be a failure reasoning. Such a saliency score phenomenon in line with human intuition, the question is the beginning of reasoning, one needs understand it first, then solve it following the rules within the prompt while always concerning the question itself.
Inspired by the above findings, we further propose instance-adaptive prompting strategy (IAP) for zero-shot CoT reasoning. Given a list of prompts in distinct styles, we try to recognize good ones that elicit LLMs to reason toward the correct answer while avoiding bad CoT reasoning, referring to the analytical results. We conduct comprehensive experiments with IAP and existing methods with multiple LLMs various tasks. Experimental results show that the IAP consistently improve the overall performance of LLMs such as LLaMA-2-13B 2---------B-Chat kinds of reasoning tasks including math, logic, and commonsense reasoning.
and
Qwen-14B 14hthhtt Specifically, the IAP strategy achieves a 2%%-4% accuracy enhancement across tasks and models compared to the optimal task-level prompt. Our contributions can be summarized follows:
We look into the inside interactions among three components (i.e., question, prompt, ratio- nale) zero-shot CoT reasoning through the saliency score analysis and discover that good reasoning rationale tends aggregate information from both the question and the prompt,

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in which the prompt first gathers information from the question. In contrast, bad reasoning probably ignores one them.
We propose the IAP an instance-level adaptive prompting strategy based on our findings achieve better CoT reasoning by selecting a proper prompt that can elicit LLMs to reason from some given prompts for each question correctly.
Extensive experiments illustrate the superior performance of our instance-level adaptive prompting zero-shot CoT strategy, demonstrating the effectiveness of our findings for differentiating the reasoning processes with saliency scores.
2 Information Flow Analysis on Zero-shot CoT
It is critical to determine the key factors for good zero-shot CoT reasoning, therefore we dive into the LLMs inference process in disparate parts. There are three main components zero-shot CoT: question prompt p. and rationale r, and we need to choose a proper tool to analyze the semantic information interactions among these components. The saliency score is a common practice for analyzing the information flow in In-Context Learning [22 24], and we intend to adapt it to CoT zero-shot setting. The saliency matrix is computed
reasoning to observe the information flow by multiplying attention matrix and its gradient for the target output element-wise as follows:
OC(x) dAlCA
I(C,)) A(CA))
(1)
where æ the input the model, (e,,) represents the value of the attention matrix of the h-th head in the f-th layer, C represents the operation of element-wise multiplication, and 2(-) is the loss function, which is the cross-entropy in our implementation. Since the attention module involves interactions among the whole sequence, view of information flow, compute the saliency scores between dispersed parts during zero-shot CoTT reasoning.
2.1 Preliminary analysis
We define the reasoning that produces the right answer to a given question as good reasoning, otherwise as bad reasoning. Given various information interactions happen among reasoning steps during the model inference, choosing which step (i.e., output token) to explore is critical. Despite the most popular practice being the last step for the In-Context Learning 122 24, there are distinct circumstances in the CoT reasoning (25), our investigation shows that not all the final answers appear at the reasoning last step. To eliminate the effect of distinct LLM generation styles as much as possible, we adopt uniformly the answer generation step for all tasks as our observation time, concretely, we implement that with several regular expressions to recognize the answer step during model inference. More details are in Appendix A.2
Bulle ri. bonn all ta
14
19999 10
(d) Figure 2: The visualization comparison of the saliency matrices between good and bad reasoning instances with two prompts, the darker the color of the pixel point in the image represents a larger saliency score. (a) and (b) are good and bad reasoning instances under "Let's think step by step.", and so as (c) and (d) under "Don't 't think. Just feel.", ", respectively. The red, blue, and green boxes in each subfigure depict the question-to-prompt, question-to-rationall and prompt-to-rationale information flow, respectively.
(a)
(b)
(c)

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Since "Let's think step by step." and "Don't think. Just feel." are two representative good and bad zero-shot prompts on task-level in (2]. we select them as our test prompts. We explore the saliency score with Qwen-14p 14B (26) on GSM8k [17] and maintain consistency in the following analysis, and we also put similar visual analysis on other models and datasets in the Appendix. To inspect saliency scores of good reasonings and bad ones, we randomly pick two pairs of good-bad reasoning instances under two prompts and visualize the saliency scores inside them in Figure 2 each subfigure depicts the mean of saliency matrices of all layers and all heads, i.e., 1 = LH Σn - T(t.)) where L and H the numbers of layer and head. As mentioned earlier, we emphasize the question, prompt, and rationale during reasoning. In Figure 22 tokens from the first to the last of the prompt collect information from the question tokens evidently, and some tokens especially those near the answer in the rationale aggregate information from the question and prompt tokens evidently, either. In Figure 2b things start to change, seems that the prompt tokens fail to gather information from question tokens, not sufficiently at least, and tokens in the rationale are unable to gain much information from the question or the prompt.
The good and bad reasoning patterns under "Don't think. Just feel." " are in line with the ones under "Let's think step by step.", which is shown in Figure 2c and 2d Figure [c illustrates that even such a prompt may guide I.LSs to output the answer in very few steps after the question, the prompt tokens still capture information from the question plainly, and the limited rationale tokens proactively take advan- tage of information from both the question and prompt. The phenomenon in few cases cannot illustrate any universal pattern, hence, we randomly sample 100 instances including an even num- ber of good and bad ones to test the suitability in larger scope. Figure eelaboraess that good reasonings have higher mean values on the question-ter cistiiontt--poe prompt, rationale than those bad, justifying the above phenomenon broader context. We can conclude that: For prompts that enable LLMs to reason correctly, there are significant saliency scores in the question-to- toopppp and pronounced saliency scores from the question and prompt to the rationale; contrast, for the prompts that do not lead LLMs to reason correctly, the saliency scores from the question to the prompt are usually not significant, or the flow from the question and the prompt to the rationale is not substantial. These findings align with the human cognitive process: given a question, applying the guidelines provided in the prompt while always concerning the question itself.
Meen salienty
Radrrasoring Good reasening
cesstionnto-rational
and prompt-to-
P_
Figure 3: Comparison between mean values of randomly sam- pled 50 good and bad instances from GSM8K in question-to- prompt, question-to--ationaal and prompt-to-rations
needs to comprehend it first, and then address by
With the saliency scores phenomenon during zero-shot CoT reasoning, we believe the strength of saliency scores among them may affect LLMs' reasoning quality. Hence, we obtain the saliency scores among the question, prompt, and CoT rationale:
EGsJEC. (i,5)
((E)) 9p
1Cppl
Cop = ((i,)) sis go, P. S Sp}
where (i. represents the intensity of information flow from the i-th token the j-th token in the h-th head of f-th attention layer, |Copl denotes the number of interactions among question tokens and prompt tokens, ys and ps the start tokens the question and the prompt, respectively, and ge and pe are the end tokens. The saliency score of the question-to-rationn
r((_.)) and the prompt to the
rationale 1
(f.M) share the same computing process, only with alteration of start and end tokens.
2.2 Layer analysis
Popular LLMs are Transformer decoder-only models numbers of stacked layers, and these decoder blocks play distinct roles in processing information during model reasoning. To determine the discrepancy between good reasoning and bad, we intend to check layer-wise saliency scores. In Figure 4 we visualize the saliency scores within the LLM it processes input through its multiple

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layers, and each sub-figun depicts the mean of the saliency scores of all heads in a certain layer, i.e., 10 = मे Σn (p depict saliency scores that indicate the semantic information transfer between different components of the input: the question
f I. L. 1 and 1/0 follows the same principle. The sub-figures
the prompt, the question The saliency scores here serve as a quantified metric to display how the semantics of the given question and the provided prompt contribute to a well articultee rationale. Good and bad prompts' representation across the layers enables deeper understanding of the internal dynamics and the efficacy with which the model synthesizes input information.
rationale, and the prompt to rationale.
Question prompe
Quisstio to rationate
Frompt rationale
c.05
0.014
aree
6002
6.00
6003
39
95
25
35
25
25
(b)
(c)
Figure 4: Saliency scores of question-to-promee proottt,ppppp..ommmmmm inrestion-to-rationnal and prompt-to-rationale across layers. The yellow lines represent prompts that effectively guide the LLMs generate the correct answer, indicating good prompts. Conversely, the blue lines denote ineffective prompts.
As observed in Figure 4a there is pronounced peak in shallow layers of the LLM, demonstrating a substantial transfer of semantic content from the question to prompt in the good reasoning. This trend suggests that when the model formulates a robust prompt, it effectively aggregates the critical aspects of the original question at the outset, setting a strong foundation for later steps. Figure (4b maintains lower, yet consistent, saliency scores through the majority layers for both good and bad prompts when transferring information from the question to the rationale. This implies that while the question's semantics initial aggregation seen in question to prompt saliency scores. Figure depicts the information flow from the prompt to the rationale, we observe minor but stable ascending trend for good prompts. This gradual integration underscores the importance of the prompt in orchestrating the connection between the given question and rationale, particularly in the later stages process within the LLM.
integral to crafting the rationale, the direct influence is far less than the
Through a layer-wise analysis, we notice that the question's 's information first aggregates to the prompt in shallow layers, which suggests that appropriate prompt acts as catalyst, en- hancing the model's ability to integrate and leverage the question's meaning. Subsequently, the reasoning gathers and refines information from both the original question and the synthesized question-prompl semantics, culminating in a coherent and contextually informed rationale. These information aggregation phenomena signify that shallow layers of the model are capable of encoding the semantic information of the question and prompt. The insights drawn from these findings evoke the potential for interpretability and reasoning capabilities of LLMs, indicating that the judicious formation of prompts can orchestrate the saliency scores in ways that affect rationales' quality.
2.3 Head analysis
Multi-head attention is the fundamental component in the Transformer decoder to learn the same sequence from multi-view, like different positions of Transformer blocks, scattered heads are sen- sitive to their locations. Figure 5 provides an in-depth examination of the instance-level saliency scores within the attention mechanism of the LLM. Representation of saliency scores as heatmap visualizations offers detailed perspective on how semantics flow the question, prompt, and rationale propagates through individual attention heads across various layers.
Figure 5a highlights the saliency scores from the question to the prompt, attention heads at the front of the middle and end positions effectively concentrate question semantics and aid their embedding into the prompt context. Notably, this pattern corroborates our understanding that certain heads are specialized in aggregating the shallow layers, which essential for formulating coherent prompts. Figure 5b) shows the transition from the question to the rationale, reflecting the model's nuanced strategy of parsing the question to spawn rationale and this aligns with the layer-level analysis, asserting the importance of inheriting question semantics, albeit less evidently than the question-to-
5

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question to prompt
question to rationale
prompt to rationale
24 Heads
(b)
Figure 5: Saliency scores from question to prompt, question to rationale, and prompt rationale. The color intensity across the heatmap denotes varying degrees of engagement among heads, the darker color denotes the higher score.
prompt transition. Sigure[5c]delingg scores across heads denote that while all heads partake in the progression towards rationale, middle and behind heads are pivotal in harmonizing the prompt with the rationale context. This staged intertwining of prompt and rationale semantics accentuates the sophisticated nature of information assimilation in the latter reasoning.
the flow from the prompt to the rationale, scattered saliency
Combining the above 3 types of head- wise analysis, we note that the distribution and intensity of attention across heads are not homogeneous but are rather intricately patterned to orchestrate a hierarchical and systematic progression of semanties. The saliency scores from the question to the prompt and rationale are proven to be the core in the early phase, setting a solid foundation for rational derivation. The subsequent interactions that spawn the rationale further underscore the nuanced employment of attention heads in synthesizing compounds of the initial question with emergent prompt semantics. The intelligence encapsulated in this tin-ggraine attention tracing elucidates the role of discrete heads in sculpting the LLM's reasoning.
3 Adaptive Instance-level Zero-shot CoT
To discover the zero-shot CoT reasoning capabilities of LLMs, we meticulously decompose the saliency score inherent in layers and heads to discern patterns of good and bad CoT reasonings in fine-gran -me-grained manner. In Section 2.2 and 2.3 we find that good reasonings always have higher saliency scores than bad ones in the question-to-prompt, question-to-rationale and prompt-to-ran to-tiinall, we further discover the front heads of the middle and end positions shallow layers contribute to the saliency scores in both the question-to- to-poopp and question-to-ratiooall.
We first compute the saliency scores of question-to to-promp,, cesstion-to-rationll as well as prompt- to-rationale. Then, for each question and a certain prompt, we compute the synthesized saliency score as follows:
S
Σ
(E.h) X1 )(L,( + A2 I(..)) + A3 (l.A)
5
F.
where I((AA) 7(E.N) and r(caA) are the question-to-prompp rationale saliency scores computed as Eq. [ Σ, 5) are the indices set of the selected layers and heads, & x f) the cartesian product of two sets, |S] and [S]] are the number of the elements in the set, and the \1, X2, and X3 are hyperparameters to adjust the ratio of different saliency scores and obey \ + > A3- = After engaging in a comparative analysis of numerous instances from various datasets with distinct LLMs and prompts, we summarize different saliency score thresholds of question-to- tuestion-to-promptt question-to. muestion-to-rationalll to-rationale, and prompt-to-rational reasonings when the inference reaches the answer step. Inspired by these analytical findings, we present a novel Instance- Instance-Adaptive Prompting strategy, dubbed IAP, which leverages the qualitative and quantitive saliency scores to tailor the zero-shot CoT prompting process instance-wise, thereby enhancing I.I.s' reasoning ability. Our IAP framework can instantiated through two distinct methodologies: Sequential Substitution (IAP-ss) and Majority Vote (IAP-mv).
question-to-rationnn and prompt-to-
delimit the good and bad

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Sequential Substitution (IAP-ss) Based on the above findings, we believe that prompt with saliency scores surpassing the corresponding threshold is considered a good prompt for given question, consequently mitigating the need to explore further prompts. Given the training data, we can search for an appropriate threshold. This process terminates upon either identifying an optimal prompt or traversing all candidates.
Majority Vote (IAP-mv) Alternatively, the IAP-mv necessitates the computation in Eq. across all candidate prompts, then preserves the top maximum scores, predominant answer among these top scores is selected as the final answer. This synergistic combination ensures that the chosen prompt not only aligns with the LLM's inherent reasoning pattern but also complies with the collective intelligence inferred from an assorted selection of potential prompts.
Both methods have pros and cons: IAP-ss possesses the efficiency of heuristic-based sequential evaluation, which needs less computational resource; while IAP-mv owns the robustness supported by the consensus-based vote. Correspondingly, IAP-ss can be constrained in its performance potency since a few irregular instances may depart from our findings; though IAP-mv may achieve better performance, it demands the comprehensive evaluation of all candidate prompts. In summary, the IAP contributes a novel perspective on the paradigm of instance-level prompting strategies that drive the frontier of zero-shot CoT reasoning with LLMs.
4 Experiments
4.1 Implementation
Models. We test IAP and comparison methods on LLaMA-3-8B-Insttree [27], LLaMA-3-70E Instruct [J. LLaMA-2-13B-CCT
(28), and Dwhh--44B-hat (66 since they are popular Transformer decoder-only LLMs, which is convenient for exploiting and analyzing inside architectures. For the IAP-ss, we obtain threshold values w.r.t distinct LLMs on different datasets, we compute the overall synthesized scores as defined in E We set the generation mode to greedy-decoding to minimize irrelevant confounders during the model inference ensure the answers fixed questions under the same model and prompt, and all the experiments are run on an 8x NVIDIA A100 GPU server.
Answer majority vote (AMV) is a simple method implemented by choosing the most popular result of all prompt candidates for given question as its final answer. OPRO 7 takes the LLM as an optimizer to update zeros-hot CoT prompt iteratively and produce corresponding optimized prompts for copious tasks. Self-Discover g selects relevant atomic reasoning modules (e.g., decomposing problems, critical thinking) for given task, then adapts and customizes those modules to fit the task. These two frameworks aim to search for an appropriate prompt, similar to purpose. We choose them comparisons with the IAP to observe the performance difference between instance-level and task-level zero-shot CoT prompting.
Baselines.
Tasks & Metrics. GSM8k [17] is a challenging dataset for assessing the capability of language models in multi-step math reasoning. SVAMP 29 is presented for one-step math reasoning, which is easier than GSM8k. CommonsenseQA B0 is designed to evaluate a model's 's capacity for commonsense reasoning with questions that demand commonsense knowledge. The MMLU BT can assess a model's multi-task learning abilities across natural language inference, commonsense reasoning, question answering, etc. Causal Judgement and Tracking Shufiled Objects are two sub-tasks in BBH 32), the former specifically tests model's 's ability reason about the dynamics and interactions of objects in a given scenario and the latter presents scenarios that require identifying the underlying causes and effects of specific events phenomena. We select the GSM8k and SVAMP for math reasoning, Causal Judgement, and Tracking Shuffled Objects-5-Objeet for logic reasoning, CSQA, and MMLU for Commonsense reasoning. For all tasks, we adopt Accuracy as the only evaluation metric.
Zero-shot CoT Prompts. In the following part, we use #1 to represent "Let's 's think step by step.", #2 denotes "First,", " #3 is "The answer is after the proof.", ", #4 is "Before we dive into the answer," #5 is "Let's solve this problem by splitting it into steps.". ", #6 is "Let's think about this logically.", #7 is "It's a beautiful day.". ", #8 "Don't think. Just feel.". ", and #9 "By the fact that the earth is round," and we implement the IAP by enabling these 9 prompts as the candidates.
7

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Table 1: Zero-shot CoT results with LLaMA-3-8B-Instruu and Qwen-14B-Chai under various prompts, the results of LLaMA-3-70B-Instrucc and LLaMA-2-13B-hhrt is in Appendix [A.] Each column stands for a group of task categories, T-Obj. for Tracking Shuffled Objects which are from
the BBH. The "Optiizzr-generateed prompt" refers to the prompts for each task generated with the algorithm in
Mach
Logic
Prompt
GSM8K
SVAMP
Judge.
T-Obj.
CSQA
MMLU
LLaMA3
Qwen
LLaMA3
Qwen
LLaMA3
Qwen
LLaMA3
Qwen
LLaMA3
Qwen
LLaMA3
Qwen
#1
64.52
56.00
73.67
66.00
4.28
9.00
40.00
13.20
39.87
54.63
55.79
42.48
42
57.54
52.01
67.00
51.67
14.97
17.11
29.60
16.80
64.95
49.06
50.35
61.93
43
41.62
60.50
62.00
67.33
12.30
9.63
12.40
23.20
39.62
18.73
43.51
48.25
#4
58.98
37.17
60.33
72,00
13.90
6.95
21.10
13.60
61.95
36.61
18.95
71.21
45
56,25
35.50
57.33
60.67
5.35
28.34
20.00
16.00
55,28
41.20
46.67
76.84
46
62.71
58.07
76.00
71.33
3.74
3.21
21.40
17.60
39.87
63.23
56.62
35.25
47
61.79
27.82
66.67
42.67
2.14
1,07
24.00
16.80
33.25
23.42
42.25
57.19
#8
31.69
26.25
57.00
57 57.67
16.04
1.07
16,80
2.00
35.71
31.56
26.32
9.30
20.39
AMV (all)
52.54
28.
74.33
51.33
17.06
26.10
12.60
1.44
62.41
46.52
52.53
52.46
(81-7)
77.00
27.50
57.70
41.23
OPRO
65.96
36.01
18.18
19.79
28.
3.000
Self-dis
8.50
56.33
15.33
10.70
11:23
24.00
57.33
37.37
TAP-ss
65.36
61.57
75.33
71.67
16.57
26.74
38.80
24.00
65.68
64.37
56.49
77.07
IAP-mv
66.34
62.81
77.33
73.33
19.25
29.95
42.40
25.60
68.39
65.68
59.65
78.95
4.2 Results
Prompts steer these LLMs to achieve different results in multiple tasks, and no single prompt can get an overwhelming performance on all datasets, which makes our research on the mechanism of zero- shot CoT valuable. Table[T]showe the zero-shot CoT reasoning results with LLaMA-3-8B 1--MA-3--B-Insse Instrucct and Owen-14B-Che and various prompts on 3 reasoning tasks, we put the results of LLaMA-2- 2-1BBB--BBB----- 33B-Chat and larger LLaMA-3 70B in the Appendix since LLaMA models share a quite similar architecture.
Math reasoning. Compared with these prompts, IAP-mv improves the LLaMA-3 and Qwen's accuracy on GSM8k from 64.52%, 60.50% to 66.34%, 62.81 1 respectively. On SVAMP, IAP-mv obtains a 1.33% improvement on both models compared to the lask-levelooptmmll prompt. It is worth noting that OPRO and Self-discove are unstable with different LLMs and datasets, indicating the unstable characteristics of task-level prompting. Results on these two math reasoning datasets demonstrate the IAP can benefit the math reasoning task.
Logic reasoning. For Causal Judgement, IAP-ss and IAP-mv enhance the accuracy of the task-level optimal prompt and IAP-mV outperforms OPRO, which is optimized by numerous iterations. For Tracking shuffle Objects, IAP-my performs well with Qwen while achieving sub-optimal accuracy with LLaMA-3, IAP-mv still obtains strong results, improving 2.4% and 2.3% with LLaMA-3 and Qwen, separately.
Commonsense reasoning, On CSQA, the IAP improves the accuracy of the former best for 3.44% with LLaMA-3, and 2.45% with Qwen. On MMLU, LLaMA-3 and Qwen obtain improvement to large margin, either. We note that improving IAP-mv and IAP-ss on commonsense reasoning is more salient than the other two reasoning tasks, demonstrating the effectiveness of the saliency score-based prompting strategies.
Table 2: Accuracy (%) of Consistency and Complementary prompts with IAP-mv on 3 tasks with Appendix A.I.
and Qwen-14B-Chn The results LLaMA-2-13B-Chm are at
Math
Logic
Commonsense
GSMBL
SVAMP
C. Cudge
T.Obj.
CSQA
MMLU
LLaMA3
Qwen
LLaMA3
Qwen
LLaMA3
Qwen
LLaMA3
Qwen
LLaMA3
Qwen
LLaMA3
Qwen
Insir:
65.05
61.18
76.33
72.67
17.11
29.41
41.60
24.80
67.57
64.54
57.89
78.25
27.37
57.67
2.14
17.20
51.27
26.84
31.05
Instr+IIrr
65.35
61.49
76.67
73.00
18.18
28.34
42.00
24.00
67.24
64.21
58.77
78.42
Misl.+Im:
67.33
2.14
$2.83
44.56
58.95
Mist.
64.90
61.41
77.00
72.67
18.72
2.14
41.60
23.60
$2.17
62.49
57.54
78.24
8

---

Apart from the above comparison, we can also observe that the answer majority vote among all prompts performs poorly in some tasks, in contrast, AMV (#1-7) can enhance it by eliminating misleading prompts. Such results indicate the instability of the AMV, whose performance can be affected by prompt candidates. Our IAP-mv outperforms by a large margin, demonstrating that most prompts can lead the LLM to generate wrong answers for a given question, reaching only few correct answers, i.e., such methods cannot recognize good or bad reasoning. Our IAP-mv can handle that with the analysis for information flow in reasoning, i.e., IAP-mv can differentiate good and bad reasoning, validating the effectiveness of our proposed strategy.
4.3 Ablation Studies
Consistency & Complementary The success of zero-shot prompting for CoT reasoning lies in the semantic information within those prompts, when the LLM receives a prompt, would generate rationales by obeying the meaning of the prompt as much as possible. According to semantics, (2) categorizes these zero- shot CoT prompts into 3 types: instructive, misleading, and irrel- evant, and we further define that prompts in the same category are consistent, or otherwise they are complementary. To detect which type of prompt combination contributed to the performance, we divide the 9 prompts into consistency groups, but the irrelevant group contains only one prompt, thus we evaluate the comple- mentary on the other two. For the complementary groups, we build them two-by-two. Sable[depicts the performance of each group. We employ IAP-mv since it manifests a stronger capability in harnessing multiple prompts. we can observe that each pair of combinations can improve the performance, and instructive and irrelevant combinations achieve better outcomes than others, which comes from the base performance of instructive prompts.
SANGRGIe 10-6
Figure 6: Efficiency comparison with LLaMA-3-888 -nnss-rett on the Tracking Shuffle Objects, 0- shot denotes the best task-level prompt.
Efficacy The order and number of prompt candidates are critical for the accuracy and effi- cacy of IAP-ss, in this paper, we adopt the #1-9 order to conduct IAP, and we also tried other settings. In Table 3 #9 is the worst task-level prompt, and #6 is the best task-level prompt, achieving the highest accuracy among all the prompt candidates while consuming the least time. The prompt order of the 3rd row is accuracy-decrease SVAMP, the 4th row is accuracy- -inrraccdinceeaedd, and the last row is our default setting, which obtains the best perfor- mance. This table shows that IAP-ss can cost less time with fewer prompt candidates but may obtain limited re- sults, however, even fewer improper candidates could take a lot of computing time. Therefore, the time cost of IAP-ss a major issue prompt candidates are in an appro- priate order. As we mentioned in Section 3 the IAP-mv trades efffciency for performance, and IAP-sS emphasizes efficiency. We introduce the reasoning time (seconds) for each iteration complete as the metric to measure the efficiency and conduct time-consuming ex- periments under the same setting to show the cost of IAP-mv, IAP-ss, and Belf-Discover on the Tracking Shuffle Objects dataset, results are shown in Figure 6 All these strategies increase the computation cost to certain degree, while IAP-ss may bring accuracy decreases than the task-level optimal prompt, it beats Self-discover. Though IAP-mv the most time-consuming. it can improve performance, therefore, the two IAP strategies can be employed as trade-off's in different demand prioritization applications.
on
Table 3:
Accuracy and inference time (s) with different prompt orders and numbers of LLaMA-3-8B-Inan Instruutt SVAMP.
Order
Acc
Time
#9
39.67
2860
#6
76.00
2657
#9, 8, 5,
63.66
3870
#6, 2,
76.66
5216
2,, 7,
77.33 4751
5 Related Work
CoT reasoning [1 advances the reasoning abilities of LLMS by demonstrating a series of logical steps preceding the input demonstration. Building on the groundwork laid by CoT, Self-consistency [3] innovates through a margin decoding strategy that emphasizes the majority paths to derive the final

---

answer, presenting a significant leap in CoT reasoning. Similarly, the -oost-to-most 33 strategy decomposes a complex question into manageable subquestions, addressing them progressively to achieve comprehensive solution. Furthermore, the Plan-and-Solve [G] automates the generation of reasoning steps through a meticulously crafted prompt, streamlining the breakdown of questions into digestible parts that can be tackled sequentially.
Promisingly, the AutoHint framework [3 augments the original prompt with enriched instructions extracted from contextual demonstrations. Similarly, the COSP [35] capitalizes on answer pools derived from training sets to compute outcome entropy, inspired by the notion of ceff-consistency. thereby refining the selection process for QA pairs used during test set demonstrations. In specialized prompting, MathPrompter [36] specifically caters to mathematics problems, employing handcrafted prompts to generate diverse algebraic expressions or Python functions, In contrast, Progressive- Hint Prompting (37 facilitates dynamic interactions between users and L.MMs, guiding the reasoning with hints to generate from previous answers. Moreover, InstructZero 3X leverages an open-source LLM to enhance soft prompts relevant to Bayesian tasks, iteratively optimizing prompts to navigate through complex reasoning landscapes.
Advanced prompting approaches such SelfzCoT 39 and Meta-prompting 40 showcase the evolutionary trajectory of prompting, which generates semantic and code prompts through root prompt to obtain precise answers, while heommpnro deconstructs complex tasks into simpler sub-tasks, each addressed by specialized models to foster inter-model communication and apply intricate reasoning. Lastly, methodologies like OPRO 7 and the innovative concept of evolutionary prompting [16] aim to recursively optimize CoT prompts and generate varied prompts through mutations and crossovers. Self-discover selects relevant atomic reasoning modules (e.g., breaking down problems, critical thinking) for given task, then adapts and customizes those modules to fit the task. Implement the customized reasoning structure when solving task instances. These workarounds significantly contribute to developing zero-shot CoT prompts that guide LLMs toward more accurate problem framing, intermediate reasoning, and final answers.
6 Conclusion
In this paper, we aim to delve into the mechanism of LLMs zero-shot CoT reasoning from the perspective of information flow to understand what happened during this process, and we find stronger saliency scores within To investigate these phenomena nuancedly, heads in the L.M and find the front of the middle and final heads in shallow layers carry more information during information flows. Inspired by that, present an instance-adaptive zero-shot prompting strategy for better CoT reasoning. To demonstrate our findings, we conduct comprehensive experiments on several LLMs and tasks, and the results show our proposed strategies can improve the performance of LLMs on all candidate prompts, highlighting our interpretation of zero-shot CoT in the view of information flow.
cepustionntt-rrmppe and coestion-to-rationne go deep into the Transformer layers and attention
can lead to better LLM reasoning.
Limitations
In this work, we select the answer step the key step investigate and visualize the saliency scores, even in most instances it can be located well, and some irregular answers can not be identified precisely, such a factor may affect the generality and accuracy of our analysis. Different LLMs may have distinct patterns under the zero-shot CoT reasoning, for example, our analysis and conclusion can not meet all models. Despite our research providing insight into understanding the underlying workflow of zero-shot CoT reasoning, it cannot be the only interpretation, and we believe there must be better means to explain that.
Acknowledgement
This work is supported in part by Alibaba Research Intern Program, the National Natural Science Foundation of China (No.62272191, No,62402440), the International Science and Technology Cooperation Program of Jilin Province (No. 20240402067GH), and the Science and Technology Development Program of Jilin Province (No. 20220201
10

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12

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A Appendix
A.1 IAP & Baseline Experiments on LLaMA-2-13B- and -LaMA-3 70B
Table and Table 6 are supplementary for Table | and Table 2 the results here basically are coincidence with the Experiment section in the main body. Table 5 shows the results of single prompts and IAP-mv to demonstrate the generality for large LLM. However, the IAP did not obtain salient enhancement, which may caused by the irregular output formats LLaMA-2.
Table 4: Zero-shot CoT results with LLaMA-2-13B-Cha. under various prompts and other baselines.
Math
Logic
Commonsense
sero CoT Prompt
GSM8k
SVAMP
C-Judge
T-Obj.
CSQA
MMLU
#1
30.86
37.33
11.76
5.60
31.29
37.54
#2
32.90
43.67
13.90
8.00
32.02
42.81
#3
23.20
40.33
24.06
4.80
38.08
41.23
#4
29.34
36.33
16.58
1.60
27.44
47.89
#5
29.19
41.67
14.97
0.80
43.41
39.30
#6
30.93
41.33
32.68
9.20
44.06
26.14
#7
19.94
36.67
14.97
2.80
4.50
55.61
#8
14.03
42.33
7.49
3.20
1.72
57.37
#9
18.50
45.67
9.62
1.60
37.67
28.77
OPRO
33.66
13.37
0.08
Self-disc
7.43
17.33
10.16
2.40
33.01
58.07
IAP-ss
31.35
45.36
32.56
8.80
44.55
57.72
IAP-mv
32.78
47.15
33.47
9.60
45.76
58.25
Table 5: Zero-shot CoT results with LLaMA-3 70B under various prompts.
Math
Logic
Commonsense
Zero-shot COT Prompt
GSM8k
SVAMP
C-Judge
T-Obj.
CSQA
MMLU
#1
87.79
82.33
38.50
12.40
67.73
37.02
#2
89.16
86.33
54.55
30.00
56.10
50.18
#3
81.73
83.33
49.73
23.20
55.69
44.56
#4
82.64
84.33
42.25
60.40
41.36
52.11
#5
82.71
84.00
36.36
6.80
61.75
52.63
#6
87.79
82.33
44.39
16.00
67.73
35.79
#7
81.43
85.67
47.59
24.00
29.98
14.56
#8
53.53
75.67
55.61
18.40
29.24
22.56
#9
51.71
58.33
44.92
20.40
36.94
43.33
IAP-mv
89.84
87.33
56.20
62.00
69.04
54.39
Table 6: Accuracy (%) of Consistency and Complementary prompts with IAP-mv tasks with LLaMA-2-13B-Chat
Math
Logic
Commonscnse
GSM8K
SVAMP
C-Judge.
T-Obj.
CSQA
MMLU
Instr.
32.22
44.58
33.15
9.60
45.21
48.42
Misl.
19.48
46.70
10.16
3.20
37.67
57.54
Instr
31.39
44.66
32.62
9.60
44.39
56.49
Misl.
20.47
46.10
15.51
3.20
38.17
58.07
Instr. Misl.
32.52
46.32
33.16
9.60
44.39
57.89
13

---

A.2 Answer Step Recognition
We prepare 3 types of answer formats to recognize the answer step while LLMs reasoning. concretely, employs the regular expression to judge whether the model has just output the answer to the given question. Once we detect some pre-defined patterns, we break the LLM's generation for loop and compute the saliency scores at this time step. We put the recognition formats in Table 7
Table 7: Regular expressions for answer step recognition.
Style.
RegExp
Numbers.
(Therefore, the) answer is(:) (Arabie numerals)(.))
Choices. (Therefore, the) (answerlchoice) is(:) (A-Za-z)(l)) (Therefore, the) answer is (YesINo)(J.)
Y/N.
A.3 Information Flow Analysis on Other LLMs
In our investigation, we analyzed the information flow with the same method in different LLMs on various datasets and found that the phenomena of saliency scores for all LLMs on most datasets are quite similar, so we put the analysis process of Qwen- 14m--11BBChaat on GSM8k to maintain consistency the narrative subject and present our analysis conclusion. Similarly, the head analysis results for good and bad reasoning are consistent with other LLMs datasets.
Duostion to promst
Quustin rattorate
rational
0.00
0.004
60033
coess
60065
6000
Lxyer
laper
Dhyer
(b)
(c)
Figure 7: Saliency scores across layers of LLaMA 1-1-BBhha on CSQA, in contrast to Qwen- 14B- Chat on GSM8k in the main text.
question to
question to rationale
rationale
2 6 woniiiott
0 2 6 uosa 24 www.eeaaaiiiiiaaaaaoooooo.
3. 5 co0a 24 ai
Heads
Head:
(b)
(c)
Figure 8: Saliency scores heads distribution of bad reasoning instance, in contrast the good reasoning in the main text.
A.4 Thresholds and Majority Number
For IAP-ss, we obtain threshold values with regard to distinct LLMs on different training sets, we compute the overall synthesized scores (defined in eq (4) in Section 3) to divide up the good and bad reasoning paths and adopt the thresholds that classify reasoning well. Such as, the threshold of LLaMA-3 8B on GSM8k is 5.5e-6, and the identification of the thresholds of different LLMs on different datasets is the same and it is simple and doesn't not need much time. In practice, we consider reasoning with a value higher than the threshold as good, otherwise bad. We have tried different thresholds, and the best performance is shown in Table g As for the IAP-my, we select
14

---

top-k Soyper-pramettr, k=3) values and use the majority result as the final result, we also tried other values and k=3 the best among all other values with CAAMMA----B-nsteeee and pick some results on 3 datasets in Table g
Table 8: Accuracy of different thresholds with LLaMA-3-8B-Inse on GSM8k.
Threshold
Acc
7.0c-6
59.82
6.0e-6
62.77
5,0e-6
64.67
4.0c-6
62.40
5.5e-6
65.36
Table 9: Accuracy of different thresholds with LLaMA-3-8D-Instuuu GSM8K.
K MMLU
C-Judge
T-Obj
52.98
15.51
36.80
55.96
18.72
40.00
59.65
19.25
42.40
15

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18


Reviews:
[{"review_id": "ybuYcyY3tE", "reviewer": "Reviewer_dc7a", "summary": "The authors argue that a single, task-level prompt is insufficient for addressing the diverse needs of different instances within a dataset. To overcome this limitation, they propose an instance-adaptive prompting (IAP) algorithm that differentiates between effective and ineffective prompts for individual instances. The authors also provide a detailed examination of the information flow at different layers and heads of the LLMs, offering insights into the internal mechanisms that contribute to reasoning quality. The proposed IAP strategy is shown to be effective across multiple models and tasks, highlighting its potential for advancing zero-shot reasoning in LLMs.", "questions": "1. How were the saliency score thresholds determined, how do these thresholds affect the results?\n\n2. In some paragraphs, full stops are missing, for example, at the end of the \"Experiments\" section and at the end of the first paragraph in the \"Preliminary analysis\" section.", "limitations": "it appears that the authors have made an effort to address the limitations of their work.", "rating": 7, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "1. The IAP algorithm is a creative solution that addresses the limitations of previous prompt strategy. The originality lies in the adaptive differentiation of prompts for individual instances and the use of information flow analysis to understand and enhance reasoning mechanisms within LLMs.\n\n2. The quality of the experimental design is high, with comprehensive testing across different models and reasoning tasks.", "weaknesses": "1. As the number of available prompts grows, the strategy for selecting the best prompt could become increasingly complex.\n\n2. The titles of some figures are verbose (e.g. Figure 2). Keeping the title concise and giving a detailed explanation of the figures in the main text will make the paper better.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We deeply appreciate the time and effort you invested in reviewing our paper, and we are glad to answer your questions.\n\n### **Responses to Weaknesses**\n\n**Weakness 1:** \nAs the number of available prompts grows, the strategy for selecting the best prompt could become increasingly complex.\n\n**Response to Weakness 1:**\nFor IAP-ss, we obtained threshold values with regard to distinct LLMs on different training sets, we computed the overall synthesized scores (defined in eq (4) in Section 3) to divide up the good and bad reasoning paths and adopted the thresholds whose classify reasoning well. Such as, the threshold of LLaMA-3 8B on GSM8K is 5.5e-6, and the identification of the thresholds of different LLMs on different datasets is the same and it is simple and doesn't not need much time. In practice, we considered reasoning with a value higher than the threshold as good, otherwise bad. We have tried different thresholds, and the best performance is shown in the following table.\n\n| threshold | accuracy |\n| --- | --- |\n| 7.0e-6 | 59.82 |\n| 6.0e-6 | 62.77 |\n| 5.0e-6 | 64.67 |\n| 4.0e-6 | 62.40 |\n| 5.5e-6 | **65.36** |\n\nWe can see that an improper threshold can affect the performance of the IAP-ss, no matter higher or lower. It comes from that higher thresholds tend to recognize some good reasoning instances as bad ones, and lower thresholds may overlook some bad reasoning.\n\nAs we discussed in the last paragraph in Section 3 and Section 4, IAP-mv can achieve better performance with more computing, while IAP-ss can be a choice under the resource-limited scenario, and it would be faster if the order of prompt candidates were arranged properly. We conducted the time experiments with LLaMA-3 8B on SVAMP under different orders of prompt candidates, and the results are shown in the table below (The numbers in the order column represent the prompt candidates as we introduced in Section 4.1 Zero-shot CoT prompts paragraph.):\n\n| order | accuracy | time |\n| --- | --- | --- |\n| #9  | 39.67 | 2860s |\n| #6  | 76.00 | **2657s** |\n| #9, 8, 5, 4, 3  | 63.66 | 3870s |\n| #6, 1, 2, 7, 3 | 76.66 | 5216s |\n| #1, 2, 3, 4, 5, 6, 7, 8, 9 | **77.33** | 4751s |\n\nWhere #9 is the worst task-level prompt, and #6 is the best task-level prompt, achieving the highest accuracy among all the prompt candidates while consuming the least time. The prompt order of the 3rd row is accuracy-decreased on SVAMP, the 4th row is accuracy-increased, and the last row is our default setting, which obtains the best performance. This table shows that IAP-ss can cost less time with fewer prompt candidates but may obtain limited results, however, even fewer improper candidates could take a lot of computing time. Therefore, we think that the time cost of IAP-ss is not a major issue if prompt candidates are in an appropriate order.\n\n\n**Weakness 2:** \nThe titles of some figures are verbose (e.g. Figure 2).\n\n**Response to Weakness 2:**\nThanks for your meticulous reviews and suggestions, we have moved that verbose explanation from the figures to the main body in the new version. Now, the explanation of Figure 2 and Figure 4 are as follows: \n   \n   > (Figure 2) The visualization comparison of the saliency matrices between good and bad reasoning instances with two prompts, the darker the color of the pixel point in the image represents a larger saliency score. (a) and (b) are good and bad reasoning instances under \"Let's think step by step.\", and so as (c) and (d) under \"Don't think. Just feel.\", respectively. The red, blue, and green boxes in each subfigure depict the question-to-prompt, question-to-rationale, and prompt-to-rationale information flow, respectively.\n\n   > (Figure 4) Saliency scores of question-to-prompt, question-to-rationale, and prompt-to-rationale across layers. The yellow lines represent prompts that effectively guide the LLMs to generate the correct answer, indicating good prompts. Conversely, the blue lines denote ineffective prompts.\n\nAnd we have moved the previous definitions of the saliency matrices to the main body in the new version to make the presentation more clear.\n\n### **Response to Questions**\n\n**Question 1:**\nHow were the saliency score thresholds determined, and how do these thresholds affect the results?\n\n**Response to Question 1:**\nFor the IAP-ss, we obtained threshold values with regard to distinct LLMs on different training sets, we computed the overall synthesized scores (defined in eq (4) in Section 3) to divide up the good and bad reasoning paths and adopted the thresholds whose classify reasoning well. In practice, we considered reasoning with a value higher than the threshold is good, otherwise bad. From this, it is evident that an improper threshold may lead to inaccurate judgment for good and bad reasoning, thereby hurting the overall performance. The current threshold of LLaMA-3 8B on GSM8K we adopted is 5.5e-6, we also tried other thresholds while keeping other settings, and the results are shown in the table below.\n\nTable caption LLaMA 3 on GSM8k, different thresholds from repeating the experiment on other LLMs and datasets. (validation selection, fast)\n\n| threshold | accuracy |\n| --- | --- |\n| 7.0e-6 | 59.82 |\n| 6.0e-6 | 62.77 |\n| 5.0e-6 | 64.67 |\n| 4.0e-6 | 62.40 |\n| 5.5e-6 | **65.36** |\n\nWe can see that an improper threshold can affect the performance of the IAP-ss, whether it is higher or lower. It comes from that higher thresholds tend to recognize some good reasoning instances as bad ones, and lower thresholds may overlook some bad reasoning. Therefore, a proper threshold benefits the IAP-ss a lot, and vice versa.\n\n\n**Question 2:**\nIn some paragraphs, full stops are missing.\n\n**Response to Question 2:**\nWe appreciate your careful review of our paper, and we have revised all full stops missing issues in the new version and checked the entire manuscript to avoid any similar issues.\n\nFor some common questions, we made a unified reply in the Author Rebuttal part (see at top) which you can look up.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "4mbWhOOM8L", "reviewer": "Reviewer_UGUn", "summary": "This paper analyzed the mechanism of the large language models (LLMs) zero-shot Chain-of-Thought (CoT) reasoning, in which the authors found a pattern to discriminate a good reasoning path and a bad one with the saliency scores. Based on the findings, this paper proposed a set of instance-adaptive prompting approaches for zero-shot CoT reasoning. Experimental results on various tasks with distinct LLMs demonstrated the effectiveness of the proposed methods, validating the correctness of the findings.", "questions": "1. Why did the authors choose the saliency score instead of the widely used attribution score as the information flow analysis method?\n2. What did some results with underlines in Table 1 mean?\n3. Should the colon after the “remains” in the line 44 be removed?\n4. Should the “and” in the “, and Tracking Shuffled Objects …” in line 258 be removed?\n5. In Table 3 in the Appendix, why didn’t the authors highlight the best results and explain the results more?\n\nAll my concerns have been addressed by the authors' rebuttal.", "limitations": "The authors have adequately clarified the limitations of this work.", "rating": 8, "confidence": 4, "soundness": 4, "presentation": 4, "contribution": 3, "strengths": "1. This paper is well-written and easy to follow.\n2. This paper emphasized the instance-level CoT prompting rather than the task-level, providing a novel and fine-grained research object for LLM reasoning, which had not been explored in earlier works.\n3. This work employed an interesting information flow analysis to delve into the mechanism of zero-shot CoT during the LLM inference, encouraging relevant CoT research.\n4. The authors presented two simple yet effective instance-adaptive zero-shot CoT prompting approaches based on elaborative analysis, and empirical results verified their observations.", "weaknesses": "1. Experiments only covered 7B and 13/14B models, involving larger model in the experiments would be more marvelous.\n2. In Section 4.3, the authors didn’t interpret the results of consistency and complementary results in detail.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks a lot for the time and effort you invested in providing the detailed reviews. Regarding the current weaknesses and questions you pointed out, we are glad to give our responses.\n\n### **Response to Weaknesses**\n**Weakness 1:** \nExperiments only covered 7B and 13/14B models, involving larger models in the experiments would be more marvelous.\n\n**Response to Weakness 1:**\nIn this work, we conducted experiments on 8B, 13B, and 14B LLMs with different architectures (LLaMA-2, LLaMA-3, and Qwen), and empirical results validated our initiative observation and assumption. The current evaluation across model sizes has provided a broad view of how different scales of models may perform under various prompt candidates.\n\nWe conducted the experiments with LLaMA-3 70B using the same 9 prompts as the main experiments and IAP-mv, the table below shows the results:\n\n| Prompt | GSM8K | SVAMP | C-Judge. | T-Obj. | CSQA | MMLU |\n| ------ | ----- | ----- | -------  | ------ | ---- | ---- |\n| #1 | 87.79 | 82.33 | 38.50 | 12.40 | 67.73 | 37.02 |\n| #2 | 89.16 | 86.33 | 54.55 | 30.00 | 56.10 | 50.18 |\n| #3 | 81.73 | 83.33 | 49.73 | 23.20 | 55.69 | 44.56 |\n| #4 | 82.64 | 84.33 | 42.25 | 60.40 | 41.36 | 52.11 |\n| #5 | 82.71 | 84.00 | 36.36 | 6.80 | 61.75 | 52.63 |\n| #6 | 87.79 | 82.33 | 44.39 | 16.00 | 67.73 | 35.79 |\n| #7 | 81.43 | 85.67 | 47.59 | 24.00 | 29.98 | 14.56 |\n| #8 | 53.53 | 75.67 | 55.61 | 18.40 | 29.24 | 22.56 |\n| #9 | 51.71 | 58.33 | 44.92 | 20.40 | 36.94 | 43.33 |\n| IAP-mv | **89.84** | **87.33** | **56.20** | **62.00** | **69.04** | **54.39** |\n\nThe empirical results of the LLaMA-3 70B with IAP-mv are better than any task-level hard prompt, which demonstrates the effectiveness of the IAP-mv under broader model scales.\n\n\n**Weakness 2:** \nIn Section 4.3, the authors didn’t interpret the results of consistency and complementary results in detail.\n\n**Response to Weakness 2:**\nIn the ablation studies, we conducted the consistency and complementary experiment to detect which type of prompt combination contributed to the performance. Table 2 shows the results, and referring to the main results in Table 1, we can observe that each pair of combinations can improve the performance, and instructive and irrelevant combinations achieve better outcomes than others, which comes from the base performance of instructive prompts.\n\n\n### **Response to Questions**\n**Question 1:**\nWhy did the authors choose the saliency score instead of the widely used attribution score as the information flow analysis method?\n\n**Response to Question 1:**\nThere are two reasons that we didn't employ the attribution score: (1) the attribution score is designed for knowledge-oriented tasks, which have been discussed in the related work section; (2) the saliency score is more suitable for the in-context learning scenario, and may not perform well on the reasoning tasks. These two reasons had been demonstrated by [1][2][3][4].\n[1] Dai, D., L. Dong, Y. Hao, et al. Knowledge neurons in pretrained transformers.\n[2] Hao, Y., L. Dong, F. Wei, et al. Self-attention attribution: Interpreting information interactions inside transformer.\n[3] Wang, L., L. Li, D. Dai, et al. Label words are anchors: An information flow perspective for understanding in-context learning.\n[4] Li, J., P. Cao, C. Wang, et al. Focus on your question! interpreting and mitigating toxic cot problems in commonsense reasoning.\n\n**Question 2:**\nWhat did some results with underlines in Table 1 mean?\n\n**Response to Question 2:**\nIn Table 1, we underlined some numbers which means these results are task-level optimal prompts among all candidates, we are sorry for not elaborating on this, and we have explained in the new version.\n\n**Question 3:**\nShould the colon after the “remains” in line 44 be removed?\n\n**Response to Question 3:**\nThank you for your detailed review, we have removed the colon after the “remains” in line 44 in the updated manuscript.\n\n**Question 4:**\nShould the “and” in the “, and Tracking Shuffled Objects …” in line 258 be removed?\n\n**Response to Question 4:**\nWe have removed the “and” in the “, and Tracking Shuffled Objects …”, and we have checked all the grammar issues in the new manuscript.\n\n**Question 5:**\nIn Table 3 in the Appendix, why didn’t the authors highlight the best results and explain the results more?\n\n**Response to Question 5:**\nSince Table 3 in the Appendix is the supplement of Table 1, and the IAP shows similar performance on LLaMA-2 13B with LLaMA-3 8B and Qwen 14B, thus we didn’t repeat similar explanations. Also, we have highlighted the best results as we did in Table 1 in the updated manuscript.\n\nFor some common questions, we made a unified reply in the Author Rebuttal part (see at top) which you can look up.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "VawwGmadkf", "reviewer": "Reviewer_WuYd", "summary": "The paper introduces an instance-adaptive prompting algorithm for zero-shot Chain-of-Thought (CoT) reasoning in large language models (LLMs). Traditional task-level prompts are insufficient for all instances, so the authors propose a strategy that differentiates good and bad prompts based on information flow from the question to the prompt and rationale. Using neuron saliency score analysis, the study reveals that successful reasoning requires prompts to aggregate semantic information from the question. The proposed instance-adaptive prompting strategy (IAP) demonstrates consistent improvements across multiple reasoning tasks with LLaMA-2, LLaMA-3, and Qwen models.", "questions": "N/A", "limitations": "N/A", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "- **Comprehensive Analysis**: Uses neuron saliency scores to understand information flow during reasoning.\n- **Innovative Approach**: Tailors prompts to individual instances, improving upon uniform task-level prompts.", "weaknesses": "- **Limited Scope of Neuron Saliency Score Analysis**: The neuron saliency score analysis in Section 2 is conducted on only one LLM (not state in paper, personal guess) and one dataset, GSM8K. More evidence and diverse datasets are needed to support this analysis comprehensively. Additionally, Section 2.3, \"Head Analysis,\" lacks a comparative study between good and bad reasoning instances.\n- **Insufficient Experimental Details**: The experimental details provided are not sufficiently clear. Based on lines 263-264, my understanding is that IAP uses 9 different zero-shot CoT prompts to compute the S score. For IAP-ss, the process stops and uses the current result upon encountering the first prompt that meets the threshold. For IAP-mv, results from all 9 prompts are saved, and the top K are used for voting. This raises several questions: 1. How does the performance of IAP-mv compare to directly using a majority vote across the 9 prompt results? 2. What is the distribution of results for each method? For instance, which prompts tend to have higher S scores? This analysis could reveal conclusions such as \"Let’s think step by step\" being more suitable for math questions, while \"Don’t think. Just feel.\" may be better for MMLU, aligning more closely with the instance-wise topic.\n- **Figure 1 Inconsistency**: Figure 1 does not align with the rest of the paper. The figure and its description suggest addressing an overly complex problem, which is not the case in practice.\n- **More Model Variants**: There is a need for experiments on larger model sizes to validate the findings.\n- **Terminology Inconsistency**: The terminology used is inconsistent. In Figure 3, the terms \"Good reasoning\" and \"Bad reasoning\" are used, while in Figure 4, the terms change to \"Good prompt\" and \"Bad prompt.\"", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks a lot for your valuable reviews, and we appreciate the time and effort you have taken. Regarding the weaknesses and questions, we would like to elaborate and address your concerns on this work.\n\n### **Response to Weaknesses**\n\n**Weakness 1:**\nLimited Scope of Neuron Saliency Score Analysis: The neuron saliency score analysis in Section 2 is conducted on only one LLM (not stated in the paper, personal guess) and one dataset, GSM8K. More evidence and diverse datasets are needed to support this analysis comprehensively. Additionally, Section 2.3, \"Head Analysis,\" lacks a comparative study between good and bad reasoning instances.\n\n**Response to Weakness 1:**\nIn our investigation, we analyzed the information flow with the same method in different LLMs on various datasets and found that the phenomena of saliency scores for all LLMs on most datasets are quite similar, so we put the analysis process of Qwen-14B on GSM8K to maintain consistency in the narrative subject and present our analysis conclusion. Similarly, the head analysis results for good and bad reasoning are consistent, we are sorry for not elaborating on that in this subsection. We apologize for not putting more figures in the Appendix to make our analysis more complete and well-supported, and we have updated our manuscript. We also put a few samples of the analysis process in the pdf file attached in the Author Rebuttal (see at top).\n\n\n**Weakness 2:**\nInsufficient Experimental Details\n\n**Response to Weakness 2:**\nYour understanding of IAP is correct, and your suggestion of supplementing answers to the majority vote experiment would make our work more complete. The results comparison between our IAP-mv and the direct answers majority vote is as follows:\n\n| Method | GSM8K | SVAMP | C-Judge. | T-Obj. | CSQA | MMLU |\n| ------ | ----- | ----- | -------  | ------ | ---- | ---- |\n| Majority Vote. (Qwen 14B) | 28.22 | 51.33 | 26.10 | 1.44 | 46.52 | 52.46 |\n| IAP-mv (Qwen 14B) | **62.81 (+34.59)** | **73.33 (+22.00)** | **29.95 (+3.85)** | **25.60 (+24.16)** | **65.68 (+19.16)** | **78.95 (+26.49)** |\n| Majority Vote. (LLaMA-3 8B) | 52.54 | 74.33 | 17.06 | 12.60 | 62.41 | 52.53 |\n| IAP-mv (LLaMA-3 8B) | **66.34 (+13.80)** | **77.33 (+3.00)** | **19.25 (+2.19)** | **42.40 (+29.80)** | **68.39 (+5.98)** | **59.65 (+7.12)** |\n\nThe results show that the majority vote approach performs poorly, and our IAP-mv outperforms it by a large margin, demonstrating that most prompts can lead the LLM to generate wrong answers for a given question, reaching only a few correct answers, i.e., such methods cannot recognize good/bad reasoning. Our IAP-mv can handle that with the analysis for information flow in reasoning, i.e., IAP-mv can differentiate good and bad reasoning, validating the effectiveness of our proposed strategy.\n\nThe most adopted prompts in IAP-mv of distinct LLMs on different datasets are the former task-level optimal (among all prompt candidates) since they are suitable for most instances in corresponding datasets, respectively. We display the top-3 prompts for different LLMs on different datasets in the table below:\n\n| Model | GSM8K | SVAMP | C-Judge. | T-Obj. | CSQA | MMLU |\n| ------ | ----- | ----- | -------  | ------ | ---- | ---- |\n| LLaMA-3 8B | #1, 6, 7 | #1, 2, 6 | #2, 4, 8 | #1, 2, 4 | #2, 4, 6 | #1, 2, 6 |\n| Qwen 14B | #1, 3, 6 | #3, 4, 6 | #2, 3, 5 | #2, 3, 5 | #1, 6, 9 | #2, 4, 5 |\n\nWe can observe that the most adopted prompt candidates are the former task-level optimal ones, which is consistent with our analysis in the paper.\n\n\n**Weakness 3:**\nFigure 1 Inconsistency: Figure 1 does not align with the rest of the paper.\n\n**Response to Weakness 3:**\nFigure 1 offered a representative case to illustrate that: the worst task-level prompt can beat the optimal prompt for some instances, which is counterintuitive as we discussed in the 2nd paragraph in the Introduction section, such a case encouraged us to detect the inner mechanism for zero-shot CoT, further trigged us to propose instance-level prompting strategy. \n\n\n**Weakness 4:**\nMore Model Variants.\n\n**Response to Weakness 4:**\nIn this paper, we conducted experiments on 8B, 13B, and 14B LLMs with different architectures (LLaMA-2, LLaMA-3, and Qwen), and the results validated our initiative observation and analysis. The current evaluation across model sizes has provided a broad view of how different scales of models may perform under various prompt candidates. However, your suggestion is also valuable, and we conducted the experiments with LLaMA-3 70B using the same 9 prompts as the main experiments and IAP-mv, the table below shows the results:\n\n| Prompt | GSM8K | SVAMP | C-Judge. | T-Obj. | CSQA | MMLU |\n| ------ | ----- | ----- | -------  | ------ | ---- | ---- |\n| #1 | 87.79 | 82.33 | 38.50 | 12.40 | 67.73 | 37.02 |\n| #2 | 89.16 | 86.33 | 54.55 | 30.00 | 56.10 | 50.18 |\n| #3 | 81.73 | 83.33 | 49.73 | 23.20 | 55.69 | 44.56 |\n| #4 | 82.64 | 84.33 | 42.25 | 60.40 | 41.36 | 52.11 |\n| #5 | 82.71 | 84.00 | 36.36 | 6.80 | 61.75 | 52.63 |\n| #6 | 87.79 | 82.33 | 44.39 | 16.00 | 67.73 | 35.79 |\n| #7 | 81.43 | 85.67 | 47.59 | 24.00 | 29.98 | 14.56 |\n| #8 | 53.53 | 75.67 | 55.61 | 18.40 | 29.24 | 22.56 |\n| #9 | 51.71 | 58.33 | 44.92 | 20.40 | 36.94 | 43.33 |\n| IAP-mv | **89.84** | **87.33** | **56.20** | **62.00** | **69.04** | **54.39** |\n\nIn this table, IAP-mv demonstrates its effectiveness on LLaMA-3 70B, consistent with the results on LLaMA-3 8B and Qwen 14B, broadening the model scale impact of the IAP-mv.\n\n\n**Weakness 5:**\nIn Figure 3, the terms \"Good reasoning\" and \"Bad reasoning\" are used, while in Figure 4, the terms change to \"Good prompt\" and \"Bad prompt.\"\n\n**Response to Weakness 5:**\nWe are sorry for not using the same statement in different figures, and we have rectified such issues to keep the claims consistent in the updated manuscript.\n\nFor some common questions, we made a unified reply in the Author Rebuttal part (see at top) which you can look up.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "PfGsOiJep2", "reviewer": "Reviewer_43EH", "summary": "This paper explores the inside interactions among three components(i.e., question, prompt, rationale) in zero-shot CoT reasoning through the saliency score analysis, and discover the distinct characteristics of good and bad reasoning in terms of information flow. Based on above findings, the authors propose the IAP - an instance-level adaptive prompting strategy designed to enhance CoT reasoning by selecting an appropriate prompt that can guide LLMs to reason correctly from a given set of prompts for each question. To demonstrate the effectiveness of the proposed method, the authors conducted extensive experiments on the LLaMA-3 8B, LLaMA-2 13B, and Qwen14B models across Math, Logic, and Commonsense tasks.", "questions": "See weeknesses. \n\nAlthough this paper performs quite well in the section of Information Flow Analysis on Zero-shot CoT, there are numerous flaws in its experiments that fail to convince me.  If the authors can address my concerns, I would consider raising my score.", "limitations": "I think the authors have addressed their limitations.", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "* **The motivation  of this paper is quite intuitive.** Through the example in Figure 1, the authors illustrate that an instance-wise zero-shot CoT prompt is more plausible for better reasoning and may achieve a cap-breaking performance compared to the task-level optimal prompt, which is easy to understand.\n\n* **Using Neuron saliency score to analyze the information flow of the question, prompt, and rationale is innovative and promising.** The authors conduct both qualitative and quantitative analyses on good-bad reasoning instances, discovering different patterns of information flow in good-bad reasoning. They further delve into a deeper analysis from the perspectives of Layer and Head, yielding valuable conclusions.\n\n* **Extensive experiments are conducted to validate the effectiveness of proposed method.** The authors test the proposed IAP and comparison methods on LLaMA-3 8B, LLaMA-2 13B, and Qwen14B across Math, Logic, and Commonsense reasoning tasks.", "weaknesses": "* **The  proposed method is not clearly explained, some details are missing.** For instance, in Sequential Substitution (IAP-ss), it is not specified what the corresponding threshold is or how it was obtained. Similarly, in Majority Vote (IAP-mv), there is no explanation provided for how many top maximum scores are preserved. The lack of details in the proposed methods can be quite confusing.\n\n* **The experimental setup is unfair.** For the main \"effective\" method proposed, IAP-mv, which obtains the final results through Majority Vote (similar to self consistency), it is unreasonable to compare it with baselines that only perform inference once. The improvement brought about by this method could very well be the result of ensemble inference from multiple reasoning paths [1][2][3], rather than the strategy implemented by the author's previous good-bad reasoning findings.\n\n* **Some experimental conclusions are missing or somewhat unreasonable.** For instance, in the experiment of Consistency & Complementary, the authors only provide the experimental setup and show the corresponding results in Table 2 without giving any conclusions or analysis. Furthermore, in the analysis experiment for Efficacy, the author demonstrated through Figure 6 that while IAP-ss also incurs additional overhead, its accuracy compared to 0-shot also declines to some extent. Therefore, the conclusion stated by the authors that \"the two IAP strategies can be employed as trade-offs in different demand prioritization applications\" is not in line with the facts, as IAP-ss does not provide any gain compared to the baseline 0-shot.\n\n\n[1] Making Large Language Models Better Reasoners with Step-Aware Verifier\n\n[2] Diversity of Thought Improves Reasoning Abilities of LLMs\n\n[3] Answering Questions by Meta-Reasoning over Multiple Chains of Thought", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for the constructive advice and comments, which have greatly improved our manuscript, and we are glad to reply to your invaluable suggestions and questions.\n\n### **Response to Weaknesses**\n\n**Weakness 1:**\nThe proposed method is not clearly explained, some details are missing.\n\n**Response to Weakness 1:**\nFor IAP-ss, we obtained threshold values with regard to distinct LLMs on different training sets, we computed the overall synthesized scores (defined in eq (4) in Section 3) to divide up the good and bad reasoning paths and adopted the thresholds whose classify reasoning well. Such as, the threshold of LLaMA-3 8B on GSM8K is 5.5e-6, and the identification of the thresholds of different LLMs on different datasets is the same and it is simple and doesn't not need much time. In practice, we considered reasoning with a value higher than the threshold as good, otherwise bad. We have tried different thresholds, and the best performance is shown in the following table.\n\n| threshold | accuracy |\n| --- | --- |\n| 7.0e-6 | 59.82 |\n| 6.0e-6 | 62.77 |\n| 5.0e-6 | 64.67 |\n| 4.0e-6 | 62.40 |\n| 5.5e-6 | **65.36** |\n\nWe can see that an improper threshold can affect the performance of the IAP-ss, whether higher or lower. It comes from that higher thresholds tend to recognize some good reasoning instances as bad ones, and lower thresholds may overlook some bad reasoning. \n\nAs for the IAP-mv, we selected top-k (hyper-parameter, k=3) values and adopted the majority result as the final result, we also tried other k values and k=3 is the best among all other values with LLaMA-3 8B and picked some results on 3 datasets in the following table.\n\n| k | MMLU | C-Judge. | T-Obj |\n| --- | --- | --- | --- |\n| 1 | 52.98 | 15.51 | 36.80 |\n| 5 | 55.96 | 18.72 | 40.00 |\n| 3 | **59.65** | **19.25** | **42.40** |\n\nThe k=3 achieves the best performance on most datasets, therefore, we selected the hyper-parameter k=3 as the default value in the paper. We are sorry for confusing you in this part and we have elaborated these details in the new version. \n\n\n**Weakness 2:**\nThe experimental setup is unfair.\n\n**Response to Weakness 2:**\nWe are sorry for not introducing the comparable approaches thoroughly in the baseline paragraph of Section 4.1, and we would like to replace the current version with the new one: \n   \n   > In practice, the OPPR optimizes a meta prompt on different datasets with distinct LLMs for multiple rounds to guide LLMs to produce better prompts, requiring numerous optimization steps (i.e., inferences). As for Self-Discover, it consists of selecting, adapting, implementing, and reasoning, which also needs multi-round inference in every step. \n\nGiven the above description, we think that comparing the IAP with the above methods is not unfair. \n\nThe profits of IAP-mv didn't simply come from the multiple reasoning path, we computed the synthesized saliency scores (defined in eq (4)., as an application of former analysis) of all prompt candidates, and conducted a majority vote based on these synthesized scores. For a considerable proportion of questions, the LLM could be guided to generate wrong results with most prompts but only a few right results and our IAP-mv can handle it, thereby outperforming the majority final results vote. We compared the IAP-mv and direct majority results vote results in the following table:\n\n| Method | GSM8K | SVAMP | C-Judge. | T-Obj. | CSQA | MMLU |\n| ------ | ----- | ----- | -------  | ------ | ---- | ---- |\n| Majority Vote. (Qwen 14B) | 28.22 | 51.33 | 26.10 | 1.44 | 46.52 | 52.46 |\n| IAP-mv (Qwen 14B) | **62.81 (+34.59)** | **73.33 (+22.00)** | **29.95 (+3.85)** | **25.60 (+24.16)** | **65.68 (+19.16)** | **78.95 (+26.49)** |\n| Majority Vote. (LLaMA-3 8B) | 52.54 | 74.33 | 17.06 | 12.60 | 62.41 | 52.53 |\n| IAP-mv (LLaMA-3 8B) | **66.34 (+13.80)** | **77.33 (+3.00)** | **19.25 (+2.19)** | **42.40 (+29.80)** | **68.39 (+5.98)** | **59.65 (+7.12)** |\n\nThe results show that the majority vote approach performs poorly, and our IAP-mv outperforms it by a large margin, demonstrating that most prompts can lead the LLM to generate wrong answers for a given question, reaching only a few correct answers, i.e., such methods cannot recognize good/bad reasoning. Our IAP-mv can handle that with the analysis for information flow in reasoning, i.e., IAP-mv can differentiate good and bad reasoning, validating the effectiveness of our proposed strategy, rather than benefiting from multiple reasoning paths.\n\n\n**Weakness 3:**\nSome experimental conclusions are missing or somewhat unreasonable.\n\n**Response to Weakness 3:**\nWe apologize for not providing an extensive explanation of the consistency and complementary experiments, we have discussed adding the following part to the 1st paragraph of Section 4.3 in our new manuscript: \n   \n   > We can observe that the great performance of the instructive group outperforms our groups, which comes from the base of all instructive prompts. Furthermore, the combination of the instructive group and the other two can continue to improve the performance of both, demonstrating that complementary is critical for IAP-mv, and IAP-mv can take advantage of these complementary prompts. \n\nIn the Efficacy part, we intended to express that IAP-ss and IAP-mv can be chosen with different time budgets, and we are sorry for selecting an improper figure to confuse you. In fact, the IAP-ss outperforms all the task-level optimal prompts of most LLMs and datasets, as shown in Table 1, showing that people can still employ different strategies to achieve better zero-shot prompting. We have also conducted other time experiments, and plan to replace the current figure with the new one in the updated manuscript.\n\nFor some common questions, we made a unified reply in the Author Rebuttal part (see at top) which you can look up.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:
We want to thank each reviewer for your thoughtful reviews and constructive feedback on our manuscript. We appreciate the time you invested in evaluating our submission, and we are grateful for your detailed suggestions and recommendations. We have carefully considered each of your comments and have made corresponding revisions to our manuscript in response. We noticed that some reviewers raised similar questions, so we consolidated the responses first.

### **Experiment Details**
For IAP-ss, we obtained threshold values with regard to distinct LLMs on different training sets, we computed the overall synthesized scores (defined in eq (4) in Section 3) to divide up the good and bad reasoning paths and adopted the thresholds whose classify reasoning well. Such as, the threshold of LLaMA-3 8B on GSM8K is 5.5e-6, and the identification of the thresholds of different LLMs on different datasets is the same and it is simple and doesn't not need much time. In practice, we considered reasoning with a value higher than the threshold as good, otherwise bad. We have tried different thresholds, and the best performance is shown in the following table.

| threshold | accuracy |
| --- | --- |
| 7.0e-6 | 59.82 |
| 6.0e-6 | 62.77 |
| 5.0e-6 | 64.67 |
| 4.0e-6 | 62.40 |
| 5.5e-6 | **65.36** |

We can see that an improper threshold can affect the performance of the IAP-ss, no matter higher or lower. It comes from that higher thresholds tend to recognize some good reasoning instances as bad ones, and lower thresholds may overlook some bad reasoning. 

As for IAP-mv, there is no need to compute thresholds for each LLM and dataset, we need to compute the overall synthesized saliency scores for all prompt candidates and recognize the good and bad reasoning with top-3 highest scores. **The IAP-mv is different from the direct answers majority vote strategy.** Specifically, the IAP-mv is to find the top-k (k=3) highest scores among all prompt candidates based on the analysis of information flow, in which the IAP-mv can recognize the correct answer from good and bad reasoning. We appreciate the reviewers' suggestion of supplementing the answers majority vote experiment, we did a comparison between our IAP-mv and the direct answers majority vote as follows:

| Method | GSM8K | SVAMP | C-Judge. | T-Obj. | CSQA | MMLU |
| ------ | ----- | ----- | -------  | ------ | ---- | ---- |
| Majority Vote. (Qwen 14B) | 28.22 | 51.33 | 26.10 | 1.44 | 46.52 | 52.46 |
| IAP-mv (Qwen 14B) | **62.81 (+34.59)** | **73.33 (+22.00)** | **29.95 (+3.85)** | **25.60 (+24.16)** | **65.68 (+19.16)** | **78.95 (+26.49)** |
| Majority Vote. (LLaMA-3 8B) | 52.54 | 74.33 | 17.06 | 12.60 | 62.41 | 52.53 |
| IAP-mv (LLaMA-3 8B) | **66.34 (+13.80)** | **77.33 (+3.00)** | **19.25 (+2.19)** | **42.40 (+29.80)** | **68.39 (+5.98)** | **59.65 (+7.12)** |

The results show that the majority vote approach performs poorly, and our IAP-mv outperforms it by a large margin, demonstrating that most prompts can lead the LLM to generate wrong answers for a given question, reaching only a few correct answers, i.e., such methods cannot recognize good/bad reasoning. Our IAP-mv can handle that with the analysis for information flow in reasoning, i.e., IAP-mv can differentiate good and bad reasoning, validating the effectiveness of our proposed strategy.


### **Explanation for Ablation Study**
We apologize for not providing an elaborative explanation of the consistency and complementary experiments, we have discussed adding the following part to the 1st paragraph of Section 4.3 in our new manuscript: 
   
   > We can observe that the great performance of the instructive group outperforms our groups, which comes from the base of all instructive prompts. Furthermore, the combination of the instructive group and the other two can continue to improve the performance of both, demonstrating that complementary is critical for IAP-mv, and IAP-mv can take advantage of these complementary prompts. 


### **Larger LLMs**
We have conducted experiments with several LLMs of 8B, 13B, and 14B in different architectures, shown and discussed in the original manuscript. To broaden the generalizability of our method, we further implemented experiments with LLaMA-3 70B on different datasets, results are shown in the table below:

| Prompt | GSM8K | SVAMP | C-Judge. | T-Obj. | CSQA | MMLU |
| ------ | ----- | ----- | -------  | ------ | ---- | ---- |
| #1 | 87.79 | 82.33 | 38.50 | 12.40 | 67.73 | 37.02 |
| #2 | 89.16 | 86.33 | 54.55 | 30.00 | 56.10 | 50.18 |
| #3 | 81.73 | 83.33 | 49.73 | 23.20 | 55.69 | 44.56 |
| #4 | 82.64 | 84.33 | 42.25 | 60.40 | 41.36 | 52.11 |
| #5 | 82.71 | 84.00 | 36.36 | 6.80 | 61.75 | 52.63 |
| #6 | 87.79 | 82.33 | 44.39 | 16.00 | 67.73 | 35.79 |
| #7 | 81.43 | 85.67 | 47.59 | 24.00 | 29.98 | 14.56 |
| #8 | 53.53 | 75.67 | 55.61 | 18.40 | 29.24 | 22.56 |
| #9 | 51.71 | 58.33 | 44.92 | 20.40 | 36.94 | 43.33 |
| IAP-mv | **89.84** | **87.33** | **56.20** | **62.00** | **69.04** | **54.39** |

The empirical results of the LLaMA-3 70B with IAP-mv are better than any task-level hard prompt, demonstrating the IAP-mv's effectiveness under broader model scales.


### **Grammar Error**
We have checked and modified the grammar errors in the original paper, and updated a new manuscript to avoid such issues, making the presentation more clear.

Meta-review: The paper introduces an instance-adaptive prompting algorithm for zero-shot Chain-of-Thought (CoT) reasoning in large language models (LLMs). This includes an analysis of LLMs CoT reasoning, which identifies a way to discriminate good from bad reasoning paths using saliency scores, and proposes a method to enhance CoT reasoning by selecting an appropriate prompt from a given set in response to the specific query. In experiments, the proposed IAP strategy is shown to be effective across multiple models and tasks.

The reviewers identified a number of strengths for the paper. It is well written with an intuitive motivation. The emphasis on instance-level CoT prompting and the use of saliency scores to analyse information flow appears to be innovative and promising. The experimental design is sound, the evaluations extensive, and results are promising.

There were some concerns about the generality of the analysis and experimentation, and whether the advantages seen were at least partly a result of the fairness of the comparison. Many of the reviewer concerns were addressed by author rebuttal and further results and explanations. It is unclear how much room there will be in the final manuscript for all these additional points though. Nonetheless, the submission is of sufficiently high quality to warrant acceptance, and to garner interest.
Decision: Accept (poster)