Breaking Mental Set to Improve Reasoning through Diverse Multi-Agent Debate
Authors: Yexiang Liu
Jie Cao
Zekun Li
Ran He
Tieniu Tan
Venue: ICLR 2025 Poster (2025)
Keywords: Multi-Agent Debate
Large Language Models
Multimodal Large Language Models
Prompting
Self-Correction
Reasoning
Primary area: generative models

Abstract: Large Language Models (LLMs) have seen significant progress but continue to struggle with persistent reasoning mistakes.
Previous methods of *self-reflection* have been proven limited due to the models’ inherent fixed thinking patterns. 
While Multi-Agent Debate (MAD) attempts to mitigate this by incorporating multiple agents, it often employs the same reasoning methods, even though assigning different personas to models. This leads to a "fixed mental set", where models rely on homogeneous thought processes without exploring alternative perspectives.
In this paper, we introduce Diverse Multi-Agent Debate (DMAD), a method that encourages agents to think with distinct reasoning approaches. By leveraging diverse problem-solving strategies, each agent can gain insights from different perspectives, refining its responses through discussion and collectively arriving at the optimal solution. DMAD effectively breaks the limitations of fixed mental sets. We evaluate DMAD against various prompting techniques, including *self-reflection* and traditional MAD, across multiple benchmarks using both LLMs and Multimodal LLMs. Our experiments show that DMAD consistently outperforms other methods, delivering better results than MAD in fewer rounds. Code is available at https://github.com/MraDonkey/DMAD.

Published as a conference paper at ICLR 2025
BREAKING MENTAL SET TO IMPROVE REASONING THROUGH DIVERSE MULTI-AGENT DEBATE
Yexiang Liu L Jie Cao'; Zekun Li", Ran Hel Tieniu Tan
MAIS & NLPR. Institute of Automation, Chinese Academy of Sciences
2 Schooo of Artificial Intelligence, University of Chinese Academy of Sciences
3 University of California, Santa Barbara *Nanjing University
1iuyexiang202301:: cn, jie.caofcripac. ia..aaa..........
ABSTRACT
Large Language Models (LLMs) have seen significant progress but continue struggle with persistent reasoning mistakes. Previous methods of self-reflection have been proven limited due the models' inherent fixed thinking patterns. While Multi-Agent Debate (MAD) attempts to mitigate this by incorporating mul- tiple agents, often employs the same reasoning methods, even though assigning different personas to models. This leads to "fixed mental set",, where models rely on homogeneous thought processes without exploring alternative perspectives. In this paper, we introduce Diverse Multi-Agent Debate (DMAD), method that en- courages agents to think with distinct reasoning approaches. By leveraging diverse moblem--sllving strategies, each agent can gain insights from different perspec- tives, refining its responses through discussion and collectively arriving at the op- timal solution. DMAD effectively breaks the limitations of fixed mental sets. We evaluate DMAD against various prompting techniques, including self-reflection and traditional MAD, across multiple benchmarks using both LLMs and Multi- modal LLMs. Our experiments show that DMAD consistently outperforms other methods, delivering better results than MAD in fewer rounds. Code available :ettps:/qqil com Dttp////aaDDoe///AD
INTRODUCTION
In the past few years, Large Language Models (LLMs) have experienced unprecedented develop- ment (Brown et al. 2020 Touvron et al. [023a by Chowdhery et al. 2023 Amil et al. 2023 Achiam
al. 1023//pee 20240),,) demonstrating significant potential reasoning. Extensive research
has explored various methods to enhance their reasoning capabilities (Wei et al.) 2022] Wang et al.)
2023 Yao al. 2023 Besta et al. 2024, Gao et al. 2024a).. Despite these efforts, LLMs continue to make errors. Previous work has sought to address this through self-reflection (Madaan et al. 2023
Kim et al. 2023 Shinn et al., 2023), where the model generates an initial response, then evaluates feedback. However, recent studies have raised concerns about of this approach (Huang et al. 2024 Stechly et al. 2023] Valmeekam et al. 2023). They suggest that with- out external feedback or additional information, LLMs struggle to effectively correct their mistakes, often leading to worse performance due to their inherent fixed thinking patterns and perspectives.
and refines it based its
Another approach explored by many studies is the use of Multi-Agent Debate (MAD) address this dilemma (Liang et al., 2024 Du et al., 2024 Chan et al. 2024), where multiple agents debate with each other arrive the final answer. This paradigm helps mitigate the limitations of single inherent thinking process by introducing multiple models. However, existing methods often use the same LLM across different personas or roles as agents, or have the model answer the question multiple times for debate, while still relying on a homogeneous reasoning approach and thinking pattern. This is still constrained by the inherent thinking influenced by pre-training and sometimes constantly gets wrong answers even with multiple rounds.
The issue is analogous to the "mental set" phenomenon (Jersild 1927), a widely studied psycho- logical phenomenon. It refers to the cognitive tendency to approach problems in a particular way
"Jie Cao is the corresponding author.

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Published as a conference paper at ICLR 2025
OOT
SBP
CDaT
DOCOT
Setf-Refine
Rafine MAD (All ID)
CoT)
MAD
DMAD
MAD CDoT)
MAD DDCGT)
80
50
70
60
40
50
30
GPT-4o-mini
LLaMA-3-70B
LLaVA-1.6-138
Gemini-1.5
GPT-4o
(a) LLMs
(b) MLLMs
Figure 1: Overall performance of each method on all models and benchmarks. CoT: Chain-of-
Thought (Wei et al., 2022). SBP: Step-Back Prompting (Zheng et al. 2024). MRP: Meta-Reasoning
IO: Input Output Prompting. CCOT: Compositional Chain-of- Thought (Mitra et al. 2024). DDCoT: Duty-Distinct Chain-of-Thought (Zheng et al. 2023
Prompting (Gao et al. 2024a).
based on past experiences, learned behaviors. or established habits. While mental sets can enable quick solutions to familiar problems, they often hinder the ability to explore diverse approaches, particularly when faced with new or more complex tasks Öölinger et al. 2008
DeCaro 2016)).
To address this, we propose Diverse Multi-Agent Debate (DMAD), where multiple agents are guided employ diverse reasoning methods. During the debate, each agent adopts a different reasoning ap- proach and gathers insights from the reasoning methods of others. By comparing these approaches and extracting valuable insights, agents refine their solutions to reach the correct answer. Specifi- cally, given a question, each agent generates an individual solution using a unique given prompting strategy. Then, each agent reviews and critiques the diverse solutions from other agents, incorporat- ing this feedback to update its own response. This debate process is repeated over several rounds. Unlike traditional MAD, where models rely on fixed thinking, DMAD enhances interaction by pro- moting diverse reasoning, leading more robust solutions. It is worth noting that, unlike other works that rely on different models or experts collaborating, which assume access to multiple mod- els (Xiong al., 2023 Chen et al., 2023a Li et al., (024a),, agents, aiming to improve its reasoning accuracy, as in previous MAD approaches.
the same model as different
We compare our DMAD approach with various MAD settings, along with different prompting and self-reflection methods. Experiments are conducted on Large Language Models (LLMs) using text- only benchmarks, MATH (Hendrycks al. 2021b) and GPQA (Rein et al. 2024). well as Mul- timodal Large Language Models (MLLMs) using multimodal benchmarks, ScienceQA (Lu et al. 2022) and MM- Vet (Yu et al.) 20246). The evaluation includes two LLMs (GPT-4o-mini (Open Al, 2024a) and -LLMMA--77B--- al.; 2023a), Gemini-1.5 1.5-Flssh (Reid al. | 2024), and GPT-4o (Open AT 2024a)). As shown in Figure I experiments demonstrate that DMAD outperforms other MAD settings. including those using fixed reasoning methods (Du et al. 2024) and different personas (Liang et al. 2024). With the same number of agents and rounds, DMAD improves GPT-4o and Gemini performance on MM- Vet by 7.3% and 8.2%, respectively, compared to improvements of 5.5% and 5.3% with MAD. Notably, DMAD in just two rounds achieves much higher performance than MAD in five rounds, where MAD begins to converge. Additionally, DMAD surpasses all other prompting and self-reflection methods. These results demonstrate the generalization ability of DMAD, which effectively enhances reason- ing in both LLMs and MLLMs.
(Dubey et al. 20244) and three MLLMs (LLLVA--1661)
(Liu
The contributions of our work can be summarized as follows:
We introduce Diverse Multi-Agent Debate (DMAD), a novel and robust framework that guides agents to employ diverse reasoning methods, breaking mental set and improving reasoning performance.
We compare DMAD with various methods, including basic prompting techniques, self- reflection methods, and different MAD approaches. Our experiments, conducted on both LLMs and MLLMs, demonstrate that DMAD consistently enhances reasoning and achieves state-of-the-art performance across all benchmarks and models.
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We conduct systematic analysis various MAD settings. The results show that the per- formance of DMAD improves as the debate round and agent number increase, and DMAD in fewer rounds even outperforms MAD in more rounds.
Our experiments show that self-reflection also performs poorly on MILMS, even worse than LLMs, which is less explored on MLLMs.
RELATED WORKS
Prompting Reasoning Methods. Chain-of-Thought (CoT) (Wei et al. 2022 Kojima et al. 2022)
is a widely used prompting reasoning strategy to solve the problem step by step. After that, various
prompting reasoning methods are proposed (Yao et al. 2023 Chen et al. 2023b Besta et al.
2024
Zheng et al. [2024] Yasunaga et al. [2024) Yu et al., (2024a). Several works explore how employ
CoT on MLLMs (Lu et al.) 2022, /Zhan et al. 2024c Wang et al. 2024a). Based on COT, some
multimodal prompting reasoning methods are proposed, which can be categorized into types.
The first type emphasizes image understanding (Mitra et al., 2024] Zhang et al. 2024 Zhou et al.,
2024 Gao et al. 2024b), while the other one focuses on text understanding (Zheng et 2023
Correcting Reasoning. There many different ways to correct reasoning. Some researchers train or fine-tune the model with the collected high-quality data (Huang et al.] [202]] Liu et al.)
2023c An et al.) 2023). Others train corrector to help correct reasoning (Welleck al. (023)) or
collaborate with other models or tools (Zhang et al. 2023 Pan et al., 2023 Peng et al. (022)) ). Dif-
ferent from them, some works use the same LLM to self-correct completely relying on itself through
the three-step pipeline of self-reflection (Madaan et al. 2023 Kim et al. 2023; Shinn et al. 2023
Gero et al. 2023). However, several studies indicate that LLMs struggle to self-correct reasoning by self-reflection (Huang et al. 2024: Stechly al.) 2023 Valmeekam et al. 2023). We extend their methods to MLLMs, only to discover that such techniques also fail to facilitate self-correction in reasoning for MLLMs, especially on small open-source MLLMs.
Multi-Agent Debate and Diverse Solutions. Recently, significant attention has been dedicated to the development of Multi-Agent Debate. Many works have studied MAD from different perspec-
tives. Some assign different agents to play different roles (Liang et al. 2024 Wang et al. 2024b
Chan et al. 2024 Chen et al.) 2024). Some utilize several LLM instances to debate with each other and study the effect of the debate round, order, and agent number (Du et al. 2024 Li et al. 2024b).
Other researches leverage different models or expert modules to collaborate (Xiong et al. 2023
Chen al.) 2023a| HHng et al. 2024 Li et al., (024a). There are also other methods improving MAD through embeddings (Pham et al. 2024). However, most of them debate with single think- ing which may lead to mental set. Instead, we propose DMAD encourage different agents to think with distinct reasoning methods, which can break mental set. Similarly, ZZhng et al. (202bb) contrasts different reasoning solutions and revises them until they are consistent. Gao al. (2024a) dynamically selects the most suitable reasoning method to solve the problem.
METHOD
Our idea is inspired by the psychological theory of mental set, which may hinder diverse thinking and make it difficult to finish a task in the mental set way. However, if thinking in a different way, one may surprisingly find it is easy to address the problem. We observe that LLMs have an analogous phenomenon. MAD with a fixed prompting strategy may always get wrong answers to a problem, while changing to another one can correctly solve it. This applies to MAD with each single strategy. We elaborate on it and conduct experiments to verify this finding in Appendix E.I
Inspired by this, we argue the importance of utilizing different reasoning methods in debate to pro- mote diverse thinking. To fully hamnss the inherent capabilities of off-the-shelf models, we employ a variety of prompting reasoning techniques to represent distinct modes of thought, which do not need training or fine-tune mne-ttning. We endeavor select reasoning methods with significant divergence to avoid the issue of similar reasoning approaches potentially leading to mental set.
We select n different prompting reasoning methods R {Ri i 2, n. and set model instances (M, i = 2, J..,...n n as agents. Each agent M, is required to answer the question with the corresponding reasoning method R, At the first round of debate, each agent M, generates its
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mathematical What trinngle side lengths
Response
I'm debater affirmative side. think the currect arswer
Refine
O Am
Evaluate
a debater for the argatise side. don't agree with you.
I'm a moderator. After considering the opinions bfth give my finsl
Feedback
with SRP involves the principle of Pylhaggrrun thoorem
think with Let's solve this problem step by step!..
calcullaee the degree of angles triangle
sulve this problom step by step!
Agent
Agent
Agent
Agent
l
Agent 3
Agent
think with Co To solve this problem. should first..
think with Po?: Let's write Python program solve it...
Pipelines of different methods. (a) Self-reflection uses a three-step strategy: generate response evaluate it to get feedback refine the response according to feedback. (b) MAD- persona sets the same model as debaters for affirmative and negative sides, and assigns moderator summarize their opinions. (c) MAD uses model instances debate with each other in parallel. All agents think with the same reasoning method. (d) DMAD forces different agents to think with distinct reasoning methods. Each agent can extract useful information and gain insights from other agents to break mental set.
Figure 2:
solving processes 5;1 (the subscript "1" represents the first round) to the text question x (x can also contain images) guided by Rt.
st, M, (x h,; R.), i= 1,2,....,
where h, is the history messages for agent M,, its initial value is empty list []. According to the solving process 8;,1, each model M, generates final answer y corresponding to the reasoning method Ri,-
V:,1 = M, s;,1 R, i = 1,,,
(2)
Consequently, we collect the solving processes and answers to the question of all agents and sequen- tially extend the message from M, and other agents' messages the history h, of Mi
A (t.,) H (A,,1 2.2...,
h; <- [AA,), HA (A,)), 1,
(4)
where <- means extend, A, here denotes the message from M,, which is a collection of its solving process and answer, along with the question. H is the message pool of all agents. \ denotes set subtraction. h; represents the history of messages for Mr, extended with messages from other agents[] Next, another round of debate begins. Each agent receives other agents' solving processes and solutions as additional information, extracts useful messages from other diverse reasoning so- lutions, and updates its own answer. The subsequent debate follows the same process as described above, until reaching the maximum number N of rounds.
Optionally, judge & be get the final solution the debate in certain round. This can be achieved through Self-Consistency (Wang et al. (023) to extract the most repeated answer, or forcing the model M choose the best one from reasoning solutions {y,,1 1,2, ... n), or
'This is consistent with the original prompt of MAD Du et al. (2024) for fair comparison, which places agent's messages in front while others at the hack during each debate round.
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Published as a conference paper at ICLR 2025
other settings. Then, obtain the debate solution y; in the jth round. Algorithm | provides comprehensive summary of the procedures involved DMAD.
yj Φ ((yi, l ... n2)
(5)
Algorithm DMAD algorithm
Require: input query x, n model instances {M, i 1, 2,,,... reasoning methods (Di, 1, 2,.,, n. e)), debate rounds N, judge
debate histories (h; 1, 2, ...,
for Round j = 1, I,... do
2:
for Agent i 1, ..... do
3:
8i,j = M; (x h,; Ri),
Solving processes (Equation
4:
Yi,j = M₁ (x, S1, h,
Candidate answers (Fquation
5:
end for
6:
Aig (x, Stj S , H H= {Air | = 1.,,...,
Collecting messages (Equation
7:
for Agent i 1,
do
8: h; f |[ [A }: H {A ا, }
Updating histories (Equation
9:
end for
y;
(ty:,) 1,2 n2)
Obtaining debate solutions (Equation
11:
end for
EXPERIMENTS
We test multiple approaches different types both on LLMs and MLLMs. To avoid potential issues of mental sets caused by similar reasoning methods, we endeavor select methods with significant differences as much as possible. We will expound our experiments on LLMs Section 4. and
experiments MILMs in Section 4.2 respectively.
4.1 EXPERIMENTS ON LLMS
We test on two mainstream LLMs, a commercial closed-source model an open-source model LLaMA-3-70BB Instruct.. We use their default settings and hyper- pareeeearaemtess..
and
4.1.1 BASELINES
We select distinct reasoning methods IR (9,, Rg) We also compare method with these basic prompting reasoning methods and these with Self-Consistency (SC) (Wang et al. The model answers the question 3 times and extracts the most consistent answer.
2023
Chain-of-Thought Prompting (CoT) (Wii al. 2022) solves the problem step by step.
Step-Back Prompting (SBP) (Zheng et al.
2024 teaches the model to step back, derive
high-level abstractions such concepts and principles involved in solving the problem first, and then leverage these concepts and principles to solve the problem.
2023b) writes executable Python program to solve the problem, and stores the result as variable named "ans".
Program of Thoughts Prompting (PoTT (Chen et al.
We design and different MAD settings prove the effectiveness of our method. To make 3 agents and N 2 rounds for all MAD settings. We set as Self-Consistency to get a final solution each debate round. also compare with MAD-persona [Ling et al. 2024) with both discriminative and extractive modes.
fair comparison, we set
MAD-persona sets the model to play different roles: debaters in affirmative and negative sides, the moderator, and the judge. Debaters argue with the initial solution, the moderator summarizes their opinions to give final answer, and the judge chooses the side it supports.
MAD (All CoT) sets agents to think with CoT, i.e., Ri Ri = R, = COT.
MAD (All SBP) sets all agents to think with SBP, i.e., Ri Ri =Ra SBP.
MAD (All PoT) sets all agents to think with PoT, i.e., Ri Dig = Ri = -PT..
DMAD sets each agent with each distinct reasoning method, iee. R (CoT, SBP, PoT).

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Table 1: Detailed results of the accuracy on each subject on MATH. MAD-persona-D; MAD-
persona in discriminative mode. MAD-persona-E: MAD-persona in extractive mode. Alg.: Al-
gebra, C&P: Counting and Probability, Geom.: Geometry. Int. Alg.: Intermediate Algebra, Num. Th.: Number Theory, PreAlg.: PreAlgebra, PreCale: PreCalculus, Avg. Average.
Models
Methods
Alg..
C&P Geom.
Int. Alg.
Num. Th. PreAlg. PreCalc.
Avg.
CoT
92
55
54
77
82
37
67. 67.29
SBP
90
78
86
65.29
PoT
62
37
32
72
71
30
53.14
CoT
94
76
53
58
77
84
38
68.57
SC
89
78
54
43
82
84
35
66.43
PoT SC
64
68
40
34
79
74
34
56.14
Self-Refine
93
76
51
51
77
82
44
67.71
GPT-4o-mini
Self-Contrast
89
48
40
70
83
38
62.14
MRP
90
41
78
65.00
MAD-persona-D
92
69
44
39
78
81
34
62.43
MAD-persona
86
72
44
40
78
80
37
62.43
MAD (All CoTT
93
79
57
57
82
86
40
70.57
MAD (All SBP)
89
79
51
41
79
84
39
66.00
MAD (All PoT)
90
74
52
48
81
85
40
67.14
DMAD (Ours)
93
83
86
71.14
CoT
69
44
29
22
31
66
29
41 41.43
SBP
58
50
18
35
69
26
39.29
PoT
43
44
34.14
CoT SC
75
36
43.86
SBP-SC SC
65
50
20
21
36
69
27
41.14
PoT SC
45
40
27
13
48
51
22
35.14
Self-R Refine
64
35
20
16
36
59
20
35.71
LLaMA-3-70B
Self-Contrast
69
44
28
28
37
71
25
43.14
MRP
59
19
19
35
62
27
39.00
MAD-persona-D
21
23
24
18
33.00
MAD-persona-F
67
44
25
22
31
65
22
39.43
MAD (All CoT)
75
45
32
24
39
72
32
45.57
MAD (All SBP)
66
53
26
25
39
71
26
43.71
MAD (All PoT)
68
54
30
29
51
61
32
46.43
DMAD (Ours)
72
46
32
30
41
74
25
45.71
What's 's more, also test other self-correctin methods. Self-Contrast and MRP endowed with the same reasoning methods to make a fair comparison.
Self-Refine (Madaan et al. 2023 Kim et al. 2023) is typical and widely used self-
reflection method consisting of three steps: 1, generate an initial response, find problems and produce feedback. 3. refine the initial answer according to the feedback.
Self-Contrast /Zhang et al. 2024b) explores diverse reasoning solutions, contrasts their differences, and summarizes these discrepancies into checklist. The model reflects on the checklist and revises each reasoning solution for consensus.
Meta-Reasonie Prompting (MRP) (Gao et al. 2024a) guides the model to dynamically choose the most suitable prompting reasoning method solve the problem.
4.1.2 BENCHMARKS
MATH (Hendrycks 2021b) hard mathematics benchmark consisting of high school math competitions involving seven subjects. We randomly select 100 test samples" in each subject with random seed 0.
GPQA (Rein et al. 2024 a challenging graduate-level Q&A benchmark on multiple- choice questions written by domain experts in biology, chemistry and physics. We test all methods and models on the whole dataset.
2This is to API expenses and computation time, just like other works do Du al. 2024 Stechly et al. Valmeckam al. 2023 Yang
2023
2023 Yin al. 2024 Yu et al. 2024a)

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Published as a conference paper at ICLR 2025
Table 2: Detailed results of the accuracy on each subject on GPQA.
GPT-4o-mini
LLaMA-3-70B
Methods
Biology
Chemistry
Physics
Average
Biology
Chemistry Physics
Average
CoT
50.0
27.3
42.8
37.7
64.1
31.1
37.4
39.5
SBP
51.3
21.3
33.7
31.7
60.3
31.1
39.6
39.7
CoT-SC SC
55.1
30.6
42.8
40.0
65.4
31.7
36.9
39.7
SBP-SP
51.3
24.0
36.9
34.1
55.1
30.6
36.9
37.5
Self-Refine
41.0
29.5
43.9
37.5
41.0
18.0
30.5
27.2
Self-Contrast
53.8
25.7
36.4
35.1
64.1
33.3
38.5
40.8
MRP
51.3
21.9
34.8
32.4
59.0
35.5
39.0
41.1
MAD (All CoT)
55.1
32.2
42.2
40.4
61.5
31.7
35.8
38.6
MAD (All SBP)
56.4
27.9
45.5
40.2
61.5
31.1
38.5
39.5
DMAD (Ours)
59.0
33.3
43.3
41.9
66.7
32.3
39.0
41.1
4.1.3 RESULTS
Table I summarizes the experiment results MATH. On GPT-4o-mini, DMAD achieves the best average accuracy compared to any other method. While on LLaMA-3-70B, MAD (All PoT) per- forms the best and DMAD is the second. This is because PoT is skilled at calculation questions. For example, in the subject Number Theoryy we can see that LLaMAA3-70B with PoT, PoT SC, and MAD (All PoT)) all far exceed other methods. Due occasional errors in the DMAD agent with PoT and LLaMA's relatively weak capability to use diverse thinking for reasoning compared with GPT-4o-mini, DMAD does not achieve performance beyond MAD (All PoT). Nonetheless, the performance of DMAD is better than other methods apart from the PoT series. What's 's more, it can be observed that MAD-perse MAD-persona performs very poorly both in discriminative and extractive modes, even worse than COT. This indicates that MAD-persona may not be suitable for reasoning tasks, although has been proven effective in machine translation (Liang al. 2024).
We deprecate PoT when testing on GPQA, PoT is only suitable for calculation questions, while GPQA consists of biology, chemistry, and physics questions. Tablei]summarizes detailed results on GPQA. GPT-4o-mini achieves a 41.9% average accuracy with DMAD and LLaMA-3-70B achieves 41.1%. Both of them perform the best compared with other methods. In specific subjects, our method is also substantially superior to other MAD settings. These experiments demonstrate the effectiveness of our method, which can promote diversified thinking to improve reasoning.
4.2 EXPERIMENTS ON MLLMS
We test on three MLLMs: LLaVA-1.6-133 (Liu et al. 2023b Semini-1.5-FFie (Riid et al. 2024 and GPT-4o (gppt44-2024--00000
(Open Al 2024a).
4.2.1
BASELINES
Similar the experiments on LLMs, we also select n heterogenous prompting reasoning methods focusing on different aspects.
Input / Output Stanard Prompting (IO) is the standard mode of prompting. just inputs the images and text questions and other given information the model. The model directly outputs the solution based on the given question and available information.
Compositional Chain-of- Chain-of-Thought Thought (CCoT) (Mitra et al. 2024) first instructs MLLM to systematically generate scene graph of the input image in JSON format. Then MLLM is prompted with the original task prompt, image, and the corresponding scene graph to gen- erate answer. CCoT concentrates on image content and enhances the model's capability for visual understanding.
Duty mnty--istinet Chain-of-Thought (DDCoT) (Zheng et al. 2023) first prompts MILM to deconstruct the input question into a sequence of basic sub-questions and simultancously answer them. Then the MLLM gives solution according to these pieces of information related to the original question. DDCoT encourages the model to focus more on the text question and improves the model's I' ability of text understanding.

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Published as a conference paper at ICLR 2025
Table 3: Results on ScienceQA and MM-Vet. More detailed results can be found in Appendix C.I
LLaVA-1.6-13B
(emmii--.5-Flassh
GPT-40
Methods
ScienceQA
MM- Vet
ScienceQA
MM-Vet
ScieneoQA
MM- Vet
SC:
71.15
46.2
84.18
64.5
92
72.0
CCoT SC
69.66
47.6
84.18
65.7
89
74.
DDCoT SC
70.50
42
86.56
65.5
94
73.3
Self-Refine
45.71
26.8
47.99
38.1
69
73.1
Self-Contrast
71.24
37.1
83.94
65.8
75
72.1
MRP
70.35
46.5
85.13
65.6
93
73.3
MAD-persona-D
60.44
68.82
42.7
85
71.0
MAD-persona-E
69.66
82.70
54.6
88
71.5
MAD (All IO)
72.09
84.84
70.3
94
77.5
MAD (All CCoT)
70.00
84.63
67.8
90
78.3
MAD (All DDCoT)
68.77
86.66
66.7
95
77.8
DMAD (Ours)
72.78
85.57
71.4
95
79.3
Correspondingly, we use the same MILMM as agents to compare DMAD with MAD the fixed reasoning method and MAD-persona. We also test Self-Refine, Self-Contrase and Meta-Rest Pett-Reasoning Prompting on all benchmarks and MLLMs, where these methods are less explored in the vision- language domain. We further discuss about Self-Refine in Appendix E.4
4.2.2 BENCHMARKS
ScienceQA (Lu et al. 2022 benchmark on multimodal multiple-choice questions with diverse science topics and annotations of their answers with corresponding lectures and explanations. We use their "QCM" input format (Question, Context, Options) and test on all data containing images in the test split of ScienceQA, which comprises 2017 image- question pairs. GPT-4o is tested on 100 questions sampled using random seed 0.
MM-Vet (Yu et al.) 2024b) examines MLLMs on complicated multimodal reasoning tasks with open-ended Q&A. It focuses the integration of different core vision- lision-language pabilities, including general visual recognition, optical character recognition, knowledge, language generation, spatial awareness, and math. MM-Vet consistency the MILM responses and labeled answers, allowing MILMS to provide open-ended responses without being constrained by specific formats. We test all MLLMs and methods on the whole dataset.
GPT-4 evaluate the
4.2.3 RESULTS
Since MM-Vet is an open-ended Q&A benchmark, can not use Self-Consistency to choose the most repeated answer. So we don't test Consisonss and set 6 as judge to choose the best solution in each debate round MM-Vet. During experiments, nonsense sentences with MAD, especially on questions involving Chinese information, long context and response. Figure 16 shows example. This may be due the relatively weak capability and short context window of -LLVVA-16--1BB So we don't test LLaVA with MAD series on MM- Vet.
find LLaVA usually outputs
Table 3 the performance of each method on ScienceQA and MM-Vet. DMAD achieves the best performance on LLaVA and GPT-4o, while only not on Gemini on ScienceQA. We can observe the methods of the DDCoT series overall perform well, reflecting that Gemini may be skilled using DDCo'T to solve ScienceQA questions. However, we actually don't know how the reasoning method performs on a problem without post-test results. And thus, we cannot determine which one is the best. What's is more, DDCoT does not always perform well on other models and benchmarks, egg. MM-Vet. DMAD doesn't have this issue, which can leverage diverse reasoning solutions to refine each agent's answer. This is equivalent creating additional useful information by the model itself, which has been proven to be crucial for self-correction (Huang et al. 2024).
Figure 3 shows an illustration of DMAD on MM-Vet. We can see that in the 1st round, Agent and Agent give wrong answers, while Agent gives the right solving process and answer. In the 2nd round. Agent 1 and Agent 2 gain insights and extract useful messages from Agent 3. Agent corrects its original answer. Agent refines its solving process, adds the "30% discount" to the scene graph which is ignored in the 1st round, and gets the right answer. Agent retains its right solution.
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PORK BELLY
Question:
30%
9.80
What is the original price for pork belly before discount?
1st Round
2nd Round
Fihiok
mint with 10t
uriginal prive pork before discoumt
original price wis
Agent
ibiuk with
BEEORE DISCOUNTI 1. ("objes") "pork belly".
"object" "lex"" "atributee" [080I] "relation"
with CCoZ
"attribute"" [3304 "r"rlaatinn" IDSCOUUT PERCENTAGER
["object" "text"
DSSCUNITE Pinl I. "oojeet"
"relstion":
Agent
The originn price for pork belly before the discountt
"relation: "HAS PRICE")]
Agent
('object": poor belly.. "relction" :. "HAS, PRICE") The original for pork belly before the distount
Thiink with DDCoT.
Sub -ib-quustions ens:
think with DDCoZ.
What the
Sub questions:
price
tag original price
1. What a the discount percentage?
discounted
What the disouuned price of pork belly? What the original price the pork belly?
3. What is the ciscount percontage?
I. the price shown on the tag is the discounted price, how co wa calculate the original price?
BTD
discount percontage
Agont
Agent 3
The discounted price $3
tag
5. Len's say the critiral price is "x", Using the formula: Bisccunted Price Original Pilce
2. price shown
tag discounted price, as Inclicated by [308) discount sign.
[Dseomunt Percentage Original
We Simplif::
a. The dirmmnn perzentage is lios
vallses
4. To caliulate the or ignna price, we can use the formuls: Original Price
Combine lhe terms: 98
Price
sices 0.7: 50.00 Calouaate
Therwfarw, the original price of the park belly
be $8.90/12 0.30
Therefore, the original price for pork belly before the discount $58.00
Figure 3:
Illustration of DMAD. In the 1st round, Agent 1 and Agent give wrong answers while Agent 3 provides the right solution. In the 2nd round, Agent and Agent 2 gain insights to extract effective messages from Agent 3 and correctly update their solutions.
All agents get the right solution in 2nd Round. However, if all agents think with 1O or CCOT, they cannot get the right answer even rounds, as shown Figures [n] Similarly, there are also some questions that CCoT or IO is the most suitable method, while others cannot correctly answer. This explains the effectiveness of DMAD, whose agent can extract useful information from other agents. It uses diverse reasoning methods to teach agents to think in different ways. Without them, agents will persist in answering with a single thinking, trapped by the mental set.
4.3
DISCUSSIONS
4.3.1
NUMBER OF DEBATE ROUNDS N
Figure shows detailed performance vs the number of debate rounds of each model on each dataset. More results are displayed in Appendix C.2 MAD is conducted with default settings as Du et al. 2024). Both MAD and DMAD are assigned agents. In most cases, the overall trend of MAD and DMAD is the same, and their performance improves as the number of debate rounds increases. The overall performance of DMAD is superior to MAD. Even if DMAD performs worse than MAD the first round, it surpasses MAD in the second round. What's more, DMAD with rounds can even achieve hetter performance than MAD with 5 rounds, e.g. Gemini on ScienceQA and MM- Vet. On MM-Vet, MAD improves slowly as the number of rounds increases, while DMAD can achieve significant improvement.
4.3.2 NUMBER OF REASONING METHODS π
Figure reports the performance of DMAD with the different number of reasoning methods, i.e., 2,3. 3. As the number of reasoning methods increases, the overall performance shows an upward trend. Using as many distinct reasoning methods as possible to debate can promote more diverse thinking exchanges achieve better overall results.

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Published as a conference paper at ICLR 2025
GPT-4o-ming mo-iini on MATH
GPT-4o-mini on GPOA
Gemini on ScienceQA
Gemini on MM-VVt
Perforannc
Performars CC 52
Performa
DMAD
DMAD
DNAI
Figure 4: Performance with increased rounds. More results are shown in Figure
GPT-4o-mini on MATH
LLaVA ScienceQA
Gemini ScienceQA
62.3
sdear)
06.00
Accuracy (16)
12.3
30 t0.cca:: DA GALE 30 CO.CCTTDCM
Accuracy (56)
Accuracy
02.
05.00
00.0
94.15
55.0
3/5
Cool: o0F)
06.
8630
(MLCCaT)
DR bociry
Coal: 506.901 (m1)
664
(0 CCSTC000A
23.5
Number of Reasoning Methods
Number of Reasoning Methods
Number Reasoning Methods
Figure 5: Performance the number of reasoning methods DMAD,
Table 4: Accuracies of MAD and DAD without solving processes at the 2nd round (s;22 on Sci- enceQA. NAT: Nature Science. SOC: Social Science. LAN: Language Science. AVG: Average.
LLaVA-1.6-138
Gemini-1.5-Fiae
GPT-4o
Methods
NAT
SOC
LAN
AVG
NAT
SOC
LAN
AVG
AVG
DMAD
72.87 70.97
72.51
75
72.78
84.95
85.73
100
85.57
95
w/o S1,
71.07
75
71.10
85.28
84.95
100
85.47
94
4.3.3 WITHOUT SOLVING PROCESSES Si.j
We design experiments study whether the solving process is necessary. We remove the solv- ing processes {s in the 2nd round, i.e., just debating with the final answer without solving processes. Experiment results verify the necessity of solving processes, as shown in Table 4 The performance will decrease if the solving processes are removed.
4.3.4 BREAKING MENTAL SET
DMAD can correctly solve many problems that MAD fails due to its mental set. For For example, for the same problem, all agents in DMAD reach the optimal solutions in the 2nd round (Figure IT). while all agents in MAD (All CoT) and MAD (All SBP) get the wrong answers in all rounds (Figures 12 and (3). DMAD can even reach the right solutions when all agents give wrong answers the Ist round, as shown in Figure 22 Please refer to Appendix E and Appendix G for more analysis.
CONCLUSION
We have proposed Diverse Multi-Agent Debate (DMAD), an improved framework of Multi-Agent Debate (MAD) which leverages diverse reasoning methods to break mental set and improve rea- soning. DMAD forces each agent to think with each distinct method, enabling them to gain in- sights to extract useful information from other agents and correct their own solutions. Compre- hensive experiments on LLMs and MLLMs demonstrate the effectiveness and generalization of our method, which outperforms other methods including basic prompting techniques, Self-Refine, Self- Constrast, Meta-Res Rett-Rees Prompting, MAD- persona and MAD with each fixed reasoning method. DMAD can even reach higher performance in lower rounds than MAD. We hope that our study can bring new insights to MAD and self-correction, and promote broader research in the future.
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ACKNOWLEDGEMENT
We thank Junchi Yu for his insightful discussions, and extend our appreciation to Xintong Yao and Tao Wu for their assistance in manuscript preparation. This work is supported by National Natural Science Foundation of China (Grant No. 32341009, 62425606, U21B2045, and 62206277).
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A LIMITATIONS AND FUTURE WORK
The main limitation of DMAD is that the basic model needs to have a certain level of capability for reasoning and in-context learning. If the model's fundamental capability is weak, then it will be challenging to enhance its performance by DMAD and MAD. LLaVA-1.6-133 on MM-Vet is such an example, tends to generate nonsense sentences as the context length and debate round increase.
DMAD utilizes diverse reasoning methods to facilitate the interaction of different thinking to break mental set. Each agent can extract useful information from other agents that think with different per- spectives to correct its own solution. Although our method can improve the reasoning performance of both LLMs and MILMs,, it may not breakthrough the upper limit of the model's s capability. If the model fails to give the right solution no matter what method is used, and every reasoning method can not provide correct information, would be challenging for DMAD to get the correct answer. Please refer to Figure 23 for an example.
Despite these limitations, our method can demonstrate excellent performance on mainstream mod- els. Collecting data that conforms to DMAD to use reinforcement learning to train LLMs and MLLMs like ol (Open AI (024b) may lead to much stronger reasoning ability. In this work, each individual agent M; thinks with the same reasoning method during the debate. Going step further, we can dynamically allocate different methods to each agent in each round, i.e., assign Rj [R.,]
2.., n in the jth round, where Ri can be different each agent in each round. This can be achieved through hard allocation or random sampling. We can also dynamically guide agents to choose the method they deem appropriate independently. We leave this future work and believe this may further improve the models' reasoning performance.
B IMPLEMENTATION DETAILS
We specifically use different prompts for each benchmark to extract the final answer in the solution for evaluation. When testing each method on the multimodal benchmark ScienceQA consisting of multiple-choice questions, we prompt all MLLMs to provide the rationale behind their choices instead of just foreing the MILM to output the option only. Table lists the prompts used on each benchmark. We initially tested GPT-4o-mini and LLaMA-3-700 with IO and COT. We find that these two LLMs have been pretrained to solve the problem step by step. Even if we ask the LLMs to simplify their answers much as possible, and give 1-shot prompting
"Problem: The faces of an octahedral die are labeled with digits $1S through $8$. What is the probability, expressed as common fraction, of rolling sum of $15$ with a pair of such octahedral dice? Answer: Sy boxed Srac [ [3 to let LLMS directly output its final answer, it still always solves the problem step by step with long reasoning chain. What's more, find the performance of IO is better than COT. For example, 10 achieves 67. 67.29% accuracy on MATH while 1-shot CoT only achieves 65. 14%. So we replace I0 prompting with CoT prompting. Appendix H shows detailed prompts of each method.
C MORE DETAILED RESULTS
C.I DETAILED RESULTS ON SCIENCEQA AND MM- VET
We summarize the detailed results of each subentry on ScienceQA and MM-Vet. The test split of ScienceQA consists of 1209 natural science questions, 764 social science questions, and 44 language science questions. There are respectively 7, 117, 342, 361, 336, 271, 281, and 302 questions with levels ranging from 1-8. Figures 6 and 7 summarize the detailed results of LLaVA-L.6-13B and Gemini-1.5-Flas on each subject on ScienceQA. Figures [ and summarize the detailed results on each level. Figures 10 to 12 report the detailed results of LLa -166-6111BB Gemini- 1ominn--..--Faase 1-5sh and GPT-40 on MM-Vet, respectively.
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Table 5: Prompts each benchmark.
Benchmark
Prompt
Given mathematics problem, determine the answer. Your final answer should be in the form anxeed) at the end of your response.
MATH
Question:
<question>
Choices:
(A) <choice 1 >
GPQA
(B) <choice 2>
(C) <choice 3>
(D) <choice 4>
Please choose the correct choice. Your last sentence should be "The correct answer (insert answer here, which only the letter of the choice)".
Question:
<question>
Context: <hint>
Options:
(A) <option 1>
(B) <option 2>
ScienceQA
(C) <option 3>
(D) <option 4>
Only one option is correct. Please choose the right option and explain why you choose it. You must answer in the following format. For example, the right answer is A. you should answer: The answer is A.
Because
Question:
MM-Vet
<question>>
16

---

Published as a conference paper at ICLR 2025
Table 6: Detailed results LLaVA-1.6-133 with each method on each subject on ScienceQA.
LLaVA-1.6-13B
Methods
Nature
Social
Language
Average
I0
68.16
71.99
75.00
69.76
CCoT
69.56
69.63
77.27
69.76
DDCoT
68.91
66.75
81.82
68.91
SC
69.89
72.77
77.27
71.15
CCoT SC
69.48
69.76
72.73
69.66
DDCOT- SC
71.30
68.46
84.09
70.50
Relf-Refine Round)
46.73
43.59
54.55
45.71
Relf-Refine Rounds)
60.05
58.77
65.91
59.69
Self-Contrast
70.64
71.73
79.55
71.24
Meta Reasoning Prompting
69.23
72.38
65.91
70.35
MAD-persona-D
58.56
62.96
68.18
60.44
MAD-persona-E
68.16
71.20
84.09
69.66
MAD (All IO) (1 Round)
69.89
72.77
77.27
71.15
MAD (All IO) (2 Rounds)
71.13
72.77
86.36
72.09
MAD (All IO) (3 Rounds)
71.22
72.77
84.09
72.09
MAD (All IO) (4 Rounds)
69.64
72.12
84.09
70.90
MAD (All IO) (5 Rounds)
65.76
68.72
77.27
67.13
MAD (All CCoT) (1 Round)
69.15
69.90
72.73
69.51
MAD (All CCoT) (2 Rounds)
69.81
70.03
75.00
70.00
MAD (All DDCoT) Round)
71.30
68.46
84.09
70.50
MAD (All DDCoT) (2 Rounds)
69.56
66.75
81.82
68.77
DMAD (1 Round)
69.48
71.07
77.27
70.25
DMAD (2 Rounds)
72.87
72.51
75.00
72.78
DMAD (3 Rounds)
68.49
64.53
70.45
67.03
DMAD (4 Rounds)
65.92
59.95
70.45
63.76
DMAD (5 Rounds)
65.76
60.21
70.45
63.76
DMAD (IO, CCoT) (1 Round)
69.64
70.42
77.27
70.10
DMAD (IO, CCoT) (2 Rounds)
70.72
71.99
79.55
71.39
DMAD (IO, DDCoT) (1 Round)
70.31
69.11
77.27
70.00
DMAD (IO, DDCoT) (2 Rounds)
70.72
71.47
79.55
71.19
DMAD (CCoT, DDCoT) (1 Round)
69.98
67.67
81.82
69.36
DMAD (CCoT, DDCoT) (2 Rounds)
70.72
70.29
72.73
70.60
DMAD w/o s;2 (1 Round)
69.23
71.20
77.27
70.15
DMAD w/o 8:2 (2 Rounds)
70.97
71.07
75.00
71.10
17

---

Published as a conference paper at ICLR 2025
Table 7: Detailed results Gemini-1.5-Flash with each method on each subject on ScienceQA.
Semini-1.5--Faa
Methods
Nature
Social
Language
Average
10
82.88
85.08
100
84.09
CCoT
82.55
85.86
100
84.09
DDCoT
85.61
85,86
100
86.02
I0 SC
82.55
85.86
100
84.18
C
83.04
85.08
100
84.18
DDCoT
86.10
86.52
100
86.56
Self-Refine (1 Round)
43.67
55.76
31.82
47.99
Self-Refine (2 Rounds)
61.29
68.19
68.18
64.06
Self-Contrast
82.30
85.86
95.45
83.94
Meta Reasoning Prompting
85.44
84.82
81.82
85.13
MAD-persona-D
67.33
70.03
88.64
68.82
MAD-persona-E
82.55
82.33
93.18
82.70
MAD (All IO) (1 Round)
83.21
85.08
88.64
84.24
MAD (All IO) (2 Rounds)
83.71
85.86
88.64
84.84
MAD (All IO) (3 Rounds)
84.28
86.26
88.64
85.34
MAD (All IO) (4 Rounds)
84.53
85.99
86.36
85.34
MAD (All IO) (5 Rounds)
84.62
85.99
88.64
85.44
MAD (All CCoT) (1 Round)
83.04
85,08
100
84.18
MAD (All CCoT) (2 Rounds)
83.62
85.34
100
84.63
MAD (All DDCoT) (1 Round)
86.10
86.52
100
86.56
MAD (All DDCoT) (2 Rounds)
86.52
86.13
100
86.66
DMAD (1 Round)
83.46
85.47
100
84.58
DMAD (2 Rounds)
84.95
85.73
100
85.57
DMAD (3 Rounds)
85.03
85.73
100
85.62
DMAD (4 Rounds)
85.03
85.47
100
85.52
DMAD (5 Rounds)
85.11
85.34
100
85.52
DMAD (IO, CCoT) (1 Round)
83.21
84.82
100
84.18
DMAD (IO, CCoT) (2 Rounds)
83.79
85.08
100
84.63
DMAD (IO, DDCoT) (1 Round)
83.13
85,47
95.45
84.28
DMAD (IO, DDCoT) (2 Rounds)
84.45
84.82
100
84.93
DMAD (CCoT, DDCoT) Round)
84.04
84.95
100
84.73
DMAD (CCoT, (DCoT)(2 Rounds)
86.19
85.08
100
86.07
DMAD w/o S (1 Round)
83.46
85,47
100
84.58
DMAD w/o s.2 (2 Rounds)
85.28
84.95
100
85.47
18

---

Published as a conference paper at ICLR 2025
Table 8: Detailed results of LLaVA-1.6-138 with each method on each grade level on ScienceQA.
LLAVA-1.6-1
Method
Gradel
Grade2 Grade3 Grade4 Grade5 Grade6 Grade7
Grade8 Average
10
85.71
82.91
83.92
76.73
75.60
58.30
57.30
55.30
69.76
CCoT
85.71
87.18
84.50
77.01
75.89
59.04
56.23
52.65
69.76
DDCoT
85.71
80.34
82.16
76.45
75.30
60.89
57.65
50.66
68.91
-O-SC
85.71
88.03
86.84
78.95
75.89
58.67
58.01
55.30
71.15
CCoT SC
71.43
86.32
84.50
75.62
75.30
60.89
55.87
53.64
69.66
DDCoT SC
85.71
83.76
84.50
76.45
77.98
62.36
58.36
52.32
70.50
(1 Round)
57.14
64.96
58.19
52.08
51.79
35.79
33.10
30.13
45.71
Self-Refine (2 Rounds)
57.14
74.36
70.46
62.33
66.37
51.66
52.31
45.36
59.69
Self-Contrast
78.95
77.01
77.68
66.79
61.75
55.63
71.24
Meta Reasoning Prompting
71.43
68.38
73.39
70.08
69.35
75.28
66.19
68.54
70.35
MAD-persona
71.43
64.10
64.91
62.33
65.77
54,98
53.74
56.62
60.44
MAD-persona-E
85.71
78.63
83.63
74.52
76.79
61.25
58.36
54.30
69.66
MAD (All IO) Round)
85.71
88.03
86.84
78.95
75.89
$8.67
58.01
55.30
71.15
MAD (All IO) (2 Rounds)
85.71
89.74
87.72
79.22
77.68
62.73
55.32
56.29
72.09
MAD (All IO) (3 Rounds)
85.71
88.03
88.60
77.29
79.46
61.62
56,94
55.96
72.09
MAD (All 1O) (4 Rounds)
85.71
88.89
87.43
77.01
79.17
$7.93
55.87
$3.97
70.90
MAD (All IO) (5 Rounds)
85.71
88.89
85.38
74.79
77.68
53.14
50.18
45.03
67.13
MAD (All CCoT) (1 Round)
71.43
86.32
85.67
75.35
75.30
59.41
54.80
53.97
69.51
MAD (All CCoT) Rounds)
85.71
86.32
85,38
75.07
76.19
61.62
$7.65
51.99
MAD (All DDCoT) (1 Round)
85.71
83.76
84.50
76.45
77.98
62.36
58.36
52.32
70.50
MAD (All DDCoT) (2 Rounds)
85.71
78.63
81.87
76.45
75.3
60.89
58.01
50.33
68.77
DMAD (1 Round)
85.71
85.47
85,38
78.39
75.30
59.41
$7.30
53.31
70.25
DMAD (2 Rounds)
85.71
88.03
87.43
81.72
77.98
61.25
59.43
56.29
72.78
DMAD (3 Rounds)
71.43
88.89
79.82
72.58
71.13
56.83
54.45
53.64
67.03
DMAD (4 Rounds)
71.43
76.92
74.56
69.81
66.67
$7.20
54.09
50.66
63.76
DMAD (5 Rounds)
85.71
82.05
73.68
68.42
67.86
$7.93
$1.96
$0.99
63.76
DMAD (IO, CCoT) (1 Round)
85.71
85.47
85.09
76.45
76.49
59.04
56,94
54.30
70.10
DMAD (IO, CCoT) (2 Rounds)
85.71
84.62
85.38
78.12
77.98
60.15
58.72
56.62
71.39
DMAD (IO, DDCoT) (1 Round)
85.71
82.05
82.46
77.56
75.30
59.41
59.07
56.63
70.00
DMAD (IO, DDCoT) (2 Rounds)
85.71
81.20
86.55
78.39
76.19
61.25
58.72
55.96
71.19
DMAD (CCoT, DDCoT) Round)
85,71
85.47
81.58
78.39
75.89
59.04
57.30
51.32
69.36
DMAD (CCoT, DDCoT) Rounds)
71.43
86.32
84.21
79.22
77.08
59.04
58.01
53.64
70.60
DMAD w/o 5,2 Round)
85.71
84.62
84.80
78.12
75.60
59.04
56,94
54.30
70.15
DMAD w/o $;2 (2 Rounds)
85.71
83.76
86.26
77.56
78.57
61.25
55.87
55,30
71.10
19

---

Published as a conference paper at ICLR 2025
Table Detailed results of Gemini- 1.5-ii- with each method on each grade level on ScienceQA.
Gemini-1.55FFa
Method
Gradel Grade2 Grade3 Grade4 Grade5 Grade6 Grade7 Grade8 Average
I0
100
89.74
91.81
91.14
91.37
76.38
72.24
74.17
84.09
CCoT
92.69
90.3
91.96
77.49
70.82
73.51
84.09
DDCoT
100
85.47
93.86
87.53
93.15
82.29
79.36
76.82
86.02
SC
100
89.74
92.11
91.14
91.67
76.01
71.89
74.83
84.18
CCoT
91.45
92.11
90.86
91.67
76.75
71.17
74.5
84.18
DDCoT
100
87.18
92.69
88.37
93.75
81.55
79.36
80.13
86.56
Self-Refine (I Round)
14.29
35,9
55.85
$7.89
58.63
41.33
40.93
33.44
47.99
Self-Refine (2 Rounds)
42.86
65.81
72.22
71.75
73.21
56.83
52.31
52.65
64.06
Self-Contrast
85.71
92.31
93.27
90.3
90.18
75.28
74.73
71.85
83.94
Meta Reasoning Prompting
85.71
88.03
82.75
85.87
86.9
81.92
86.83
85.1
85.13
MAD-persona-D
57.14
68.38
67.25
73.13
73.51
64.58
66.55
66.56
68.82
MADD-prrsnn--i
71.43
86.32
88.3
89.75
88.1
77.86
71.89
75.17
82.7
MAD (All IO) (1 Round)
85.71
87.18
86.26
85.87
86.61
82.66
78.65
81.46
84.24
MAD (All 1O) (2 Rounds)
85.71
87.18
87.13
86.7
87.2
83.39
79
81.79
84.84
MAD (All IO) Rounds)
85.71
87.18
87.72
86.98
88.39
83.39
78.65
83.11
85.34
MAD (All IO) (4 Rounds)
71.43
88.03
87.43
86.98
88.69
83.03
79
83.11
85.34
MAD (All 1O) (5 Rounds)
85.71
88.03
87.43
86.98
88.69
83.03
79.36
83.11
85.44
MAD (All CCoT) Round)
91.45
92.11
90.86
91.67
76.75
71.17
74.5
84.18
MAD (All CCoT) (2 Rounds)
100
89.74
92.69
91.14
92.56
76.75
71.89
75.5
84.63
MAD (All DDCoT) (1 Round)
100
87.18
92.69
88.37
93.75
81.55
79.36
80.13
86.56
MAD (All DDCoT) (2 Rounds)
100
84.62
92.98
88.64
94.05
82,29
78.29
81.13
86.66
DMAD (1 Round)
100
90.6
93.27
90.86
91.67
76.75
72.24
75.17
84.58
DMAD (2 Rounds)
100
90.6
94.15
91.69
92.56
78.6
73.67
75.83
85.57
DMAD (3 Rounds)
100
88.89
94.15
91.14
93.15
77.86
74.73
76.49
85.62
DMAD (4 Rounds)
100
90.6
94.15
91.14
93.15
77.49
74.38
75.83
85.52
DMAD (5 Rounds)
100
89.74
94.44
91.14
93.15
77.49
74.38
75.83
85.52
DMAD (IO, CCoT) (1 Round)
100
90.6
92.4
91.14
91.37
76.75
71.89
73.84
84.18
DMAD (IO, CCoT) (2 Rounds)
89.74
92.69
91.41
92.56
76.38
72.95
74.5
84.63
DMAD (IO, DDCoT) (1 Round)
85.71
88.03
92.4
87.81
91.46
78.23
74.02
75.83
84.28
DMAD (IO, DDCoT) (2 Rounds)
100
87.18
92.11
90.86
92.86
77.86
73.67
76.49
84,93
DMAD (CCoT, DDCoT) Round)
92.69
88.09
92.86
78.60
74.02
75.5
84.73
DMAD (CCoT, DDCoT) Rounds)
100
88.89
92.69
89.75
94.05
79.7
76.87
78.15
86.07
DMAD w/o $,z (1 Round)
100
90.6
93.27
90.86
91.67
76.75
72.24
75.17
84.58
DMAD w/o $,2 Rounds)
88.89
93.57
91.14
92.56
78.23
74.73
76.49
85.47
Table 10: Detailed results of LLaVA-1.6-13B with each method MM-Vet. Rec: Recognition. OCR: Optical character recognition. Know: Knowledge. Gen: Language generation. Spat: Spatial awareness.
LLaVA-1.6-13BB
Method
Rec
OCR
Know
Gen
Spat
Math
Total
I0
48.8
42.8
37.7
41.2
43.6
26.5
46.2
CCoT
49.6
44.0
39.5
42.1
45.2
30.4
47.6
DDCoT
43.7
38.5
32.0
34.6
41.6
30.0
42.0
Self-Refine (1 Round)
27.9
27.8
23.6
27.9
20.7
19.2
26.8
Self-Refine Round)
30.1
27.8
23.6
27.3
23.5
19.2
28.7
Self-Contrast
41.5
30.9
28.8
30.9
36.8
18.8
37.2
Meta Reasoning Prompting
49.1
42.5
37.4
41.1
44.7
26.5
46.5
20

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Published as a conference paper at ICLR 2025
Table 11: Detailed results of Gemini-1.5-Flash with each method on MM- Vet. Rec: Recognition. OCR: Optical character recognition. Know: Knowledge. Gen: Language generation. Spat: Spatial awareness.
Method
Rec
OCR
Know
Gen
Spat
Math
Total
10 CCoT
60.1
72.5
51.2
49.8
67.1
65.4
64.5
61.1
74.4
49.6
48.0
72.5
63.1
65.7
DDCoT
59.5
76.5
45.8
45.1
72.8
88.5
65.5
Self-Refine Round)
34.9
49.5
32.7
37.9
41.3
60.8
38.1
Self-Refine (2 Rounds)
31.9
45.6
22.6
30.1
36.5
53.8
34.4
Self-Contrast
60.1
74.8
47.7
47.1
71.2
80.4
66.0
Meta-Reasone Prompting
60.9
73.6
50.4
48.1
71.2
66.5
65.6
MAD-persona-D
37.6
52.1
24.2
23.5
45.3
57.7
42.7
MAD-persona-E
48.1
67.0
33.2
35.6
60.4
69.2
54.6
MAD (All IO) (1 Round)
62.1
73.8
53.5
52.9
70.5
65.4
66.2
MAD (All IO) (2 Rounds)
66.5
79.3
59.4
60.9
72.8
65.8
70.3
MAD (All IO) (3 Rounds)
65.9
79.0
56.2
57.7
73.5
68.8
69.8
MAD (All IO) (4 Rounds)
67.5
78.1
58.9
60.0
75.9
65.4
70.5
MAD (All IO) (5 Rounds)
67.8
77.3
59.9
61.2
75.9
65.4
70.5
MAD (All CCoT) (1 Round)
62.6
74.8
51.2
49.5
71.3
69.2
66.7
MAD (All CCoT) (2 Rounds)
63.7
77.2
54.5
55.7
71.5
73.1
67.8
MAD (All DDCoT) (1 Round)
62.5
75.2
$2.5
50.3
71.5
84.6
67.1
MAD (All DDCoT) (2 Rounds)
62.3
75.7
50.8
49.4
73.3
88.5
66.7
DMAD (1 Round)
61.7
72.6
51.7
50.2
69.5
66.9
65.7
DMAD (2 Rounds)
65.5
81.0
55,6
55.7
77.9
88.5
71.4
DMAD (3 Rounds)
66.5
84.1
56.2
57.6
80.7
88.5
72.7
DMAD (4 Rounds)
66.7
85.1
55.2
56.6
82.0
84.6
72.9
DMAD (5 Rounds)
66.9
85.1
55.5
56.9
82.0
88.5
73.0
21

---

Published as a conference paper at ICLR 2025
Table 12: Detailed results of GPT-4o with each method on MM-Vet. Rec: Recognition. OCR: Opti-
cal character recognition. Know: Knowledge. Gen: Language generation. Spat: Spatial awareness.
GPT-4o
Method
Rec
OCR
Know
Gen
Spat
Math
Total
10
65.8
81.8
61.0
65.9
71.9
94.2
72.0
CCoT
67.8
83.1
64.5
65.7
73.7
95.8
74.1
DDCoT
66.9
85.2
59.0
59.4
78.1
91.9
73.3
Self-Refine Round)
67.5
86.3
66.0
68.6
80.0
91.9
73.2
Self-Contrast
65.3
83.5
59.2
60.6
74.4
91.9
72.1
Meta-Reasoning Prompting
67.1
82.7
64.3
63.5
73.9
90.4
73.3
MAD-persona-D
63.1
85.1
58.2
59.2
77.9
95.8
71.0
MAD-persona-E
65.8
80.1
60.5
60.7
76.9
88.1
71.5
MAD (All IO) (I Round)
69.5
82.9
65.6
68.2
74.1
96.2
74.8
MAD (All IO) (2 Rounds)
73.2
83.9
70.5
71.4
76.5
96.2
77.5
MAD (All IO) (3 Rounds)
73.4
84.5
71.0
72.1
76.9
96.2
77.8
MAD (All CCoT) (1 Round)
68.1
84.1
65.0
66.1
74.9
95.8
74.7
MAD (All CCoT) (2 Rounds)
74.9
84.3
72.3
73.4
78.1
92.3
78.3
MAD (All DDCoT) (1 Round)
70.1
86.3
63.1
64.0
81.3
99.6
76.0
MAD (All DDCoT) (2 Rounds)
72.3
86.8
67.9
68.4
80.8
95.8
77.8
DMAD (1 Round)
68.9
83.0
63.1
65.0
73.5
96.2
74.0
DMAD (2 Rounds)
75.2
85.3
74.8
76.7
77.2
96.2
79.3
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C.2 DETAILED RESULTS ABOUT THE PERFORMANCE WITH INCREASED ROUNDS
Figure 6 shows more results about the performance of MAD and DMAD with increased rounds. DMAD and MAD show the rounds than MAD, e.g., Gemini and GPT-4o on ScienceQA and MM-Vet. As the debate round increases, the performance of LLaVA on ScienceQA will first increase and then continuously de- crease. This is because the increasingly long context will cause LLaVA to output more meaningless sentences. DMAD degenerates after rounds faster than MAD as its context longer. Nevertheless, our method has a higher upper limit and can achieve higher performance than MAD. It can demon- strate sigmificant performance on powerful models like Gemini and GPT-4o. We also visualize the average performance of MAD, DMAD, and DMAD w/o Si,2 on each LLM and MLLM in different rounds in Figure and Figure respectively.
trend overall. DMAD can achieve better performance in lower
GPT-4o-mini MATH
LLaMA MATH
GPT-4o-mini GPQA
Performance
21
Performance
Performance
4:3
63-
46.
MAD
MAD
MAD
DMAD
DMAD
38.5
DMAD
Round
Round
Round
LLaMA on GPQA
LLavA on ScienceQA
Gemini on ScienceQA
15.6
Performance
Performance
Iiformance
$3.4
70-
25.3
MAD DMAD
33.0
MAD DMAD
MAD DMAD
Round
Round
Round
GPT-40 ScienceQA
Gemini MM-Vet
GPT-40 MM-Vet
$4.3
Performacee
rerformance
Performance
$3.0
72
DMAD
DMAD
Round
Round
Round
Figure 6: Performance with increased rounds. Note: MAD achieves the same accuracy as DMAD
when N 2 4 GPT-4o ScienceQA.
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MAD
DMAD
Peformance
50
Round
GPT-4o-mini
LLaMA-3-70B-Instrue
Figure 7: Average performance on MATH and GPQA of MAD and DMAD in different rounds.
MAD
DMAD
DMAD w/o
Neformance
Round
LLaVA-1.6-13BB
Gemini-1.5-Flash
GPT-4o ScienceQA
GPT-4o MM-Vet
Figure 8: Average performance on ScienceQA and MM-Vel Vet of MAD, DMAD, and DMAD w/o $;22 different rounds. LLaVA-1.6-13B only shows its performance on ScienceQA. Gemini-1.55Flash shows its average performance ScienceQA and MM- Vet.
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D EXPANDED EXPERIMENTS
D.1 EXPERIMENTS ON MORE CHALLENGING DATASET
To verify the effectiveness of MAD on more challenging reasoning tasks, we use GPT-4o-mini to conduct experiments on the subset "abstract algebra" of MMLU (Hendrycks et al. 2021a) and run 3 times to get the average accuracy and standard deviation for each method. this dataset consists of multi-choice questions and some options are not numbers, we replace PoT with Least-to-Most (L2M) prompting (Zhou al. 2023). Results are shown in Table 13 DMAD also outperforms other MAD settings on this challenging multi-hop reasoning task.
Table 13: Results the subset "abstract of MMLU.
MAD (All CoT)
MAD (All SBP)
MAD (All L2M)
DMAD
Accuracy
72.3
79.0a141
74.3
79.7.1.3
D.2 STATISTICAL SIGNIFICANCE
We run experiments with GPT-4o-mini and LLaMA-3-70B-Instruut on MATH 3 times to calculate the average accuracy and standard deviation. Table 14 and Table L5 report the results of GPT- 4o-mini and LLaMA-3-70BB --ntt------nnsttrett, respectively. Statistical experiments demonstrate that DMAD outperforms other MAD settings. DMAD on LLaMA-3- 3-OOB-Inst also gets better average accu- racy than MAD (All PoTT). This implies the gains come from method diversity rather than the debate process itself some extent.
Table 14: Results of GPT-4o-mini on MATH.
Methods
Alg.
C&P
Geom. Int. Alg. Num. Th. PreAlg, PreCalc.
Avg.
MAD (All CoT)
91.322.16
78.7
55.3,2.16
55.0
82.7.1.3
86.32082
39.72082
69.9.0.2
MAD (All SBP)
88.3
77.7
49.3a2.16
44.0.3.4
81.3:294
83.7.0.2
38.7 78.7.
2035
MAD (All PoT)
91.3+1.3
75.7x216 49.0s3.4 52. 22.725772
80.7=oa2
85.3+n82
39.7 7
27.8
DMAD
91.74163
81.0.t.1 57.3 53.740.82
82.7
86.320.2
40.0.1.1
70.4
Table 15: Results of LLaMA-3-70B-Instuue on MATH.
Methods
Alg.
C&P
Geom. Int. Alg. Num. Th. PreAlg, PreCalc.
Avg.
MAD (All CoT)
72.7
48.0
31.320.32 24.320.22
40.7=291
69.7.2.4
31.02141
45.6 45.6.023
MAD (All SBP)
69.3s4.32
51.0,283 29.3s4.32 25.0 25.0.0.00
42,0a374
70.0
27.0a141
44.8.1.52
MAD (All PoTT)
52.0 66.7+530
31.0+245 27. 37.7+2.16
49.0-490
67.0+7.3
32.7+163
46.6
DMAD (Ours)
22.7
49.0a424
32.7.1.3
29.3x2.9
44.3
72.3
27.3
46.8a1.3
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D.3 ON SMALLER MODELS
We test MAD (All COT), MAD (All SBP), MAD (PoT), DMAD on LLaMA-3-8B-Instrun on MATH. Results demonstrate DMAD is also effective on smaller models, as shown in T66
Table 16: Results of LLaMA-3-8B-Inttmunn on MATH.
Methods
Alg.
C&P
Geom. Int. Alg. Num. Th. PreAlg, PreCalc.
Avg.
MAD (All Co
49.7
19.3st.3
18.3s2.16
15.3s082
18.3.082
46.7
15.0s141
26.1
MAD (All SBP)
46.3,29
20.7x1.7
17.32160
15.32082
20.026.16
44.3u5.35
11.32082
25.3a191
MAD (All PoT)
41.3
20.0.2.3
16.0+14
13.7
21.0
39.7t4.7
19.0.424
24.4
DMAD
47.7
21.3
21.7
16.0ss.00
21.3=5.72
45.0st.11
15.0s141
26.9.0.40
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E MORE ANALYSIS
E MENTAL SET OF MAD
Here we provide specific definition mental set. Denote MAD (All CoT), MAD (All SBP), and MAD (All PoT) M1, M2 and M3 respectively. When using kind of MAD method M; to solve a problem, if all agents consistently get wrong answers in all debate rounds, we assume that M; is unable correctly solve the problem. Record all such problems for M; the set P.. and get P Pi P3 P3. For a problem p P. it satisfies & P. we define that the problem p causes mental set of M,, and define gets wrong solutions, the model can correctly solve the problem by changing to another strategy.
the mental set problem of M,. It means although M, constantly
We record the mental set problems of each method MATH with GPT-4o-mini, and the problems among them which at least one agent of other methods correctly solves. All methods have agents and debate for 2 rounds. The results prove the connection between LLM reasoning and the mental set phenomenon in psychology, and DMAD can more effectively solve other methods' mental set problems.
Table 17: Performance comparison of different methods on mental set problems.
MAD (All CoT) MAD (All SBP) MAD (All PoT)
Number of mental set problems
70
87
67
Problems that MAD (All CoT) correctly solves
0
45 (51.72%)
46 (68.7%)
Problems that MAD (All SBP) correctly solves
28 (40.0%)
31 (46.3%)
Problems that MAD (All PoT) correctly solves
49 (70.0%)
51 (58.62 (58.62%)
Problems that DMAD correctly solves
48 (68.6%)
60 (69.0%
49 (73.1 %)
E.2 STOP CRITERIA
To fairly compare with MAD, we adopt all the same settings in their paper (Du et al. 2024), which exccutes MAD in the fixed round. Without considering this, we can design different criteria to determine when the debate ends, such as:
1. Consistency-2: If there exist 2 agents getting the same answer, the debate ends. Otherwise, the debate continues unless reaching its maximum number of rounds.
2. Consistency-3: If all the 3 agents get the answer, the debate ends. Otherwise, the debate continues unless reaching its maximum number of rounds.
3. Deff-Determine: Set another model judge to determine whether the debate should be over. The judge can receive all agents' solutions in each round and save them in its history.
4. Hybrid: In each round, if all agents get the same answer, the debate ends. Otherwise, use Self- Determine to judge whether the debate should end or continue.
We the maximum number of the debate round to 5 with Gemini ScienceQA. With the stop criteria, MAD and DMAD can get relatively high accuracy with a low average round. Results show that the criteria of Consistency-3 is the best. However, DMAD with the stop criteria of Consistency- 3 needs more overhead with nearly 5 debate rounds.
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Table 18: Results of Gemini-I.5-Flash on ScienceQA with different stop criteria.
Methods
Stop Criteria
Average Round
Accuracy
Consistency-2
1.0977
85.09
Consistency-3
1.1076
85.14
Self-Determine
1.1091
84.89
Hybrid
1,0605
84.84
MAD (All 1O)
Fixed Round
84.24
Fixed Round
84.84
Fixed Round
85.34
Fixed Round
85.34
Fixed Round
85.44
Consistency-2
1.0788
84.93
Consistency-3
4.9861
85.32
Seff-Determine
1.6063
85.03
Hybrid
1.6063
85.03
DMAD
Fixed Round
84.58
Fixed Round
85.57
Fixed Round
85.62
Fixed Round
85.52
Fixed Round
85.52
E.3 DIVERSITY OF SELECTED BASIC PROMPTING STRATEGIES
In this section, explore the performance of other prompting strategy groups, such involv- ing ceast-to-Most prompting (Zhou et al. 2023). We design an objectively quantitative metric to measure the diversity of selected prompting strategies. Assuming we have K candidate reasoning strategies { and want to select k diverse ones, run each strategy N times, and record the problems which R. correctly solve at least once P. (Note that the definition of P, here different from P. when introducing mental set). Note all problems on the measured dataset as Patl. We can define the diversity of the selected strategies {
U (Psr Pard
diversily
[0,
where 8; (1, K),& # 8, for This represents the proportion of total questions that the selected & methods can answer correctly. The more diverse these methods are, the larger this proportion should be.
run N = 3 times for each reasoning strategy in { {CoT, L2M, SBP, PoT) and select 3 strategies to calculate diversity, and test DMAD with different strategy groups on MATH with GPT-4o-mini. We can see diversity of CoT, SBP, PoT is the highest. Experiment results show that using the strategy group with larger diversity can get better results.
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Table 19: Diversity of different strategy groups.
Models
R&1
R42
R43
diversity
CoT
L2M
SBP
0.8471
CoT
L2M
PoT
0,8643
GPT-44-mini
CoT
SBP
PoT
0.8657
L2M
SBP
PoT
0.8557
CoT
L2M
SBP
0.6743
CoT
L2M
PoT
0.6600
LLaMA-3-70B-Immn
CoT
SBP
PoT
0.7286
L2M
SBP
PoT
0.6386
Table 20: Performance of DMAD with different strategy groups on MATH with GPT-4o-mini.
Methods
Alg.
C&P
Geom.
Int. Alg. Num. Th. PreAlg. PreCalc.
Avg.
DMAD (CoT, L2M, SBP)
08.7
78.0s O 141 54.7.455 49.0
82.7.083
85.7+
37.7 68.0.
DMAD (CoT, L2M, PoT)
91.7=
81.3 294 54.0
54.7+082
82.3.
87.7+216
39.0+ 70. a6s
DMAD (CoT, SBP, PoT)
91.7
81.0s 141 57.
53.7
82.7.082
86.3+
40.0: 1.41 70.4.
DMAD (L2M, SBP, PoT)
87.02 1.41
81.3
54.7a327
51.32 1.65
80.7
85.0,
38.0
68.3
E.4 Self-Reflection ON MLLMS
Self-Refine (Madaan et al. 2023 Kim et al. 2023 is typical and widely used method of self- reflection, which uses the same model to provide feedback for output and uses to refine itself, iteratively. Several works show that LLMs struggle to self-correct reasoning in the way of Self- Refine (Huang et al. 2024 Stechly et al. 2023 Valmeekam et al. 2023). LLMS don't actually know the correctness of their solutions, sometimes they are overconfident or change their responses arbi- trarily. We revisit their method and use the same prompt as Kim et al. (2023;; Huang et al. (2024). We extend their experiments to MLLMs, just finding that it also performs poorly MLLMs, and even worse. We summarize the performance in different rounds again in Table 21 and Table 22 where "Round 0"" represents initial responses. We see that except for GPT-40 on MM-Vet, the performances of others consistently slump after Self-Refine.
We statistically analyze the distributions of the accuracy changes in the answers of Self-Refine on ScienceQA F as shown in Figure 9 It can be observed that MLLM will change a large number of originally correct answers into incorrect ones, while only small portion of wrong answers are correctly mended, which leads to much lower performance. This may be due to the underconfidence of MLLMs, while LLMs are mostly overconfident (Zhang et al., [2024b] [iang al., (0224). We find that MILLMs tend to believe that their initial answer is incorrect and modify it, even if most of their answers are right. Figure shows an example.
However, this may be affected by specific prompts. The evaluation prompt in Self-Refine "Review your previous answer and find problems with your answer.", and the refinement prompt, "Based on the problems you found, improve your answer.", may lead models to nitpick on correct answers and find problems of right solutions. Therefore, we change the evaluation prompt to "Review your previous answer and determine whether your previous answer is right wrong." to get feedback, and use "Based on your judgment, improve your answer. If your previous answer is judged as wrong, modify it be correct. Otherwise, keep your previous answer." to refine. We call this prompt setting Self- Self-Judge, and summarize the results in Table [24 contrasting with the distributions of the accuracy changes of Self-Refine Table 23 On LLaVA and Gemini, this prompt setting performs better than Self-Refine, while still getting worse results than before modification.
If the model does not answer in the given format, directly regard it wrong this section, while retaining the solution before revision in Section 4.2
Here we test accuracy in a different way from Section 4.2
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LLaVA-116-138
Geminl-1.5-flash
GPT-4o
Ching Payat
S677H
Eight Vingg
Figure 9: Distributions of the accuracy changes answers of Self-Refine on ScienceQA. Main- tain: The answer remains unchanged. Right Wrong: A right answer is changed wrong. Wrong to Right: wrong answer is changed to right. Wrong to Wrong: A wrong answer changed but remains incorrect.
Table 21: Self-Refine performance of MILMs on ScienceQA.
Model
Round
Nature
Social
Language
Average
0
68.16
71.99
75.00
69.76
LLaVA-1.6-13B
I
46.73
43.59
54.55
45.71
2
60.05
58.77
65.91
59.69
0
82.88
85.08
100
84.09
Le5ini-L.5-Flash
1
43.67
55.76
31.82
47.99
2
61.29
68.19
68.18
64.06
0
90
GPT-4o
1
69
2
Table 22: Self-Refine performance of MLLMs MM-Vet.
Model
Round
Rec
OCR
Know
Gen
Spat
Math
Total
0
48.8
42.8
37.7
41.2
43.6
26.5
46.2
LLaVA-1.6-13B
27.9
27.8
23.6
27.9
20.7
19.2
26.8
2
30.1
27.8
23.6
27.3
23.5
19.2
28.7
0
60.1
72.5
51.2
49.8
67.1
65.4
64.5
Gemini-1.5-Fii
1
34.9
49.5
32.7
37.9
41.3
60.8
38.1
2
31.9
45.6
22.6
30.1
36.5
53.8
34.4
65.8
81.8
61.0
65.9
71.9
94.2
72.0
GPT-4o
1
67.5
86.3
66.0
68.6
80.0
91.9
73.2
Table 23: Distributions of the accuracy changes of Self-Refine on MILLS and L.LMs.
Type
Model
Maintain Right
Wrong Wrong
Right Wrong
> Wrong Accuracy Variation
LLaVA
36.24
38.77
14.28
10.71
-24,49
MLLM
Gemini
36.49
48.44
8.28
6.79
-40.16
GPT-4o
66.00
25.00
4.00
5.00
-21.00
LLaMA GPT-4o-mini
38.86
14.43
8.71
38.00
-5.71
LLM
79.14
4.29
4.71
11.86
+0.43
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Table 24: Distributions of the accuracy changes of Self-Judge on MILMS and LLMs.
Type
Model
Maintain Right -> Wrong Wrong + Right Wrong + Wrong Accuracy Variation
LLaVA Gemini
66.83
17.95
9.02
6.20
-8.93
MLLM
67.01
20.38
7.27
5.34
-13.14 14
LLaMA
30.71
20.00
9.14
40.14
-10.86
LLM
GPT-4o-mini
86.57
1.57
4.00
7.86
+2.43
Question:
C
Think about the magnetic force between the magnets in each pair. Which of the following statements is true?
903 mmh
--.77
Context:
The images below show two pairs of magnets. The magnets different pairs not affect each other. All the magnets shown made of the material.
Options:
(A) The magnitude of the magnetic force is smaller in Pair 2.
(B) The magnitude the magnetic force is smaller in Pair 1.
(C) The magnitude of the magnetic force the same in both pairs.
Initial Response
The answer is C. Because the magnetic force between the magnets in each pair the same. In pair the same magnetic properties. The distance between also the same, which means the magnetic force will be the same. The only difference between the two pairs the orientation of the magnets, but this does not affect the magnetic force between them. Therefore, the magnetic force between the magnets in each pair the
image, the magnets
and made of the material, which magnets in each pair
means they
1st Round
Upon reviewing my previous answer, realize that incorrect. correct answer Because the magnitude the magnetic force between the magnets in Pair smaller than the magnetic force between the magnets in Pair 2. This is because the magnets in Pair 2 are closer to each other than the magnets Pair 1. According to the inverse square law of magnetism, the magnetic force between
magnets decreases the distance between them increases. Pair 2, the magnets are closer together, so the magnetic force between them stronger than the magnetic force between the magnets in Pair 1, which are farther apart. Therefore, the correct answer is
2rd Round
Upon reviewing my previous answer, realize that is incorrect. The correct answer Because the magnetic force between magnets
image, the magnets each pair are the same size and made the same material, which means they have the same magnetic properties. The distance between the magnets in each pair is also the same, which means the magnetic force will be the orientation of magnets, this does affect magnetic force between them. Therefore, the magnetic force between the magnets each pair is the same.
pair same.
The only difference between the pairs is
Figure 10: Example of Self-Refine on ScienceQA.
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F COMPUTATIONAL OVERHEAD
Analyzing computational overhead is important to real-world applications. We use a word as token calculate the tokens overhead DMAD and traditional MAD, Le., MAD (All IO) during the debate rounds with Gemini on ScienceQA, as shown in T5 We can see that (DMAD tokens / MAD tokens) becomes larger as the debate round increases. This is because the selected diverse strategies generate more tokens. The diverse solutions are added to each agent's 's debate history in each round. The accumulated history of diverse solutions will cause more and more overhead. Nonetheless, DMAD in 2 rounds gets better performance and needs lower overhead and calls than MAD when MAD achieves its best performance and cost for each method with GPT-4o-mini MATH, as shown in Table 26 DMAD balances the overhead MAD (All CoT), MAD (All SBP), and MAD (All PoT), and can achieve the best performance than other methods.
rounds. We also report the token overhead
Table 25: Comparison of performance and tokens of DMAD and MAD across different rounds.
Accuracy DMAD
Tokens MAD
Round
MAD
DMAD
DMAD / MAD
84.58
84.24
1,169,209
721,800
1.61985
85.57
84.84
4,114,780
2,059.791
1.99767
85.62
85.34
7,753,647
3,585,669
2.16240
85.52
85.34
11,517.726
5,215.068
2.20855
85.52
85.44
15,364,227
6,905,985
2.22486
Table 26: Tokens and cost overhead of different methods on MATH.
Methods
Tokens
Cost ($)
Accuracy
CoT-SC
1,494,692
0.7801
68.57
SBP-SC
3,933,134
1.8876
66.43
PoT-SC
1,015,705
0.3441
56.14
Self-Refine
2,871,764
1.0271
67.71
Self-Contrast
6,159,049
2.4389
62.14
MRP
4,298,926
2.0293
65,00
MAD-persona-D D
5,156,017
1.2743
62.43
MAD-persona-E
2,680,871
0.6824
62.43
MAD (All CoT)
4,445,066
1.5077
69.86
MAD (All SBP)
11,076,792
3,5419
66.14
MAD (All PoT)
3,113,716
1.0215
67.76
DMAD (Ours)
6,331,316
2.0449
70.38
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G CASE EXAMPLES
In this section, we list many case examples to illustrate the effectiveness of DMAD. Some comple- tion prompts and solving processes are omitted. MAD easy to be trapped by the mental set, which always gets wrong answers in all rounds. Instead, DMAD can utilize diverse reasoning methods to refine each agent's solution collectively arrive at the optimal solution.
Figure I Using DMAD to solve Problem 1. In the 1st round, Agent with CoT and Agent with SBP get wrong answers, while Agent with PoT calculates the right answer. In the 2nd round, Agent 1 and Agent refine their answers and all agents obtain the correct answer.
Figure
Using MAD (All CoT) to solve Problem 1. All agents get wrong answers in all rounds.
Figure 13
Using MAD (All SBP) to solve Problem 1. All agents get wrong answers in all rounds.
Figure 14
Using DMAD to solve Problem 2. In the 1st round, Agent with CoT and Agent with SBP get right answers, while Agent 3 with PoT calculates the wrong answer. In the 2nd round, Agent 3 refines answer and all agents obtain the correct answer.
Figure 15
Using MAD (All PoT) to solve Problem 2. All agents get wrong answers in all rounds.
Figure
LLaVA-1.6- generates more nonsense sentences as the debate round increases.
Figure 17
Using MAD (All I0) to solve the same problem as Figure All agents get wrong
answers in all rounds.
Figure 18
Using MAD (All CCoT) to solve the same problem as Figure All agents get wrong rounds.
answers in
Using DMAD to solve Problem 3. In the 1st round, Agent 1 with 10 and Agent 3 with DDCoT get wrong answers, while Agent with CCoT gives the right answer. In the 2nd round, Agent 1 and Agent refine their answers and all agents obtain the correct answer.
Figure 19
Figure
Using MAD (All IO) to solve Problem All agents get wrong answers in all rounds.
Figure 21
Using MAD (All DDCoT) to solve Problem 3. All agents get wrong answers in all
rounds.
Figure 22 Using DMAD to solve Problem 4. All agents give wrong answers in the 1st round while reaching the correct solutions in the 2nd round. In the round, all agents get wrong answers, but they provide useful messages from different perspectives. All agents provide the correct rationale "the magnetic force between two magnets is inversely proportional to the square of the distance between them". Agent 2 with CCoT focuses more image understanding, it gives the distances of two pairs of magnets, while Agent and Agent 3 do not. All agents provide partially useful messages but draw wrong conclusions. In the 2nd round, Agent 1 and Agent 3 gain insights from Agent 2. Agent 1 revises its original judgment " Thee magnets in Pair are closer to each other than the magnets in Pair 2" to "The magnets in Pair are further apart than the magnets in Pair 2", Agent 3 introduces the sub-question and sub-answer about distances to solve the problem step by step- Agent 2 reflects itself according to other agents' solutions. All agents reach the correct solutions including the right rationales and results in the 2nd round.
Failed case of DMAD, All agents get wrong answers in all rounds. This is because no agent can provide effective messages, they all believe the image does not provide information about whether is organic or not. However, the label on the paper indicates organic.
Figure 23
33

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Published as a conference paper at ICLR 2025
Problem:
Find all real numbers Sx$ such that httpe///wwhhhhccc///////////////
1st Round
Agent 1:
think with CoT.
Directly solve the problem step by step.
First, we need simplify the right-hand side the equation:\V225 + 2(5)(3) + 9[1]Calculatiin WV 2(5)33 W) gives
W 30 W. Therefore:\\/25 +0 (Now, we rewrite the original equation:
NWVVeftt(ydfrassk/il//vrrgggg 3x^2 81x 729 64\ySubrracting 64 from both sides:
NINVeft(\\dffacck////VVvvvv 3x*2 81x 729 64 O/ simplifies
3x^2 811-88xx-220 793 [1 we convert /ftVee/tth//fraaa////////g//////
inta a more usable form. We
this into the equation, we 793 OVJTo eliminate the fraction, we multiply the entire equation by find the of this polynomial equation. using the Rational Root Theorem, which suggests testing possible rational roots. Next, Thus, the only real number satisfying the original equation is MM Agent 2: think with SBP.
get:i[llidffaacxx-1122-- 3x*2
27 81x*2 2187x 21411 OWUNow,
First, extract the mathematics concepts and principles involved in solving the problem. To solve the given problem, we will break it down into several mathematical concepts and principles involved in
the solution: *Alggbbraic Manipulation :"... **..
*CCbic Equations** ... 3. "Pooynommil Equivalence**
**Setting the Equation**: **
Finding Techniques**: ...
steps in detail solve the
problem: 1. * **Simplify the right-hand side"*: "Rearrange the equation**: *MMllippy by 27
eliminate the fraction**:
4. *Investtiaate possible rational roots**; 5. **Finding and testing roots**; *
6. *Furthrr factorization"* * 7. "Coonclud"*.
Then slove the problem step by step according to the concepts and principles.
Thus, the real solution Wooxed
Agent think with PoT.
Write Python Code solve the following mathematics problem. the result variable named \'ans\". The Python program:/nnynans NoneYnfrom sympy import symbols, Eq, solvelninx pymbols/x//neeuutton Eq((x/ 3)**3-3 3 x=*2+ #1 x 729, 25 (5) (3) +9 V)soluution solvelequation, x/\mans = [s.evalf(] for
solutioons] result: (39 139.00000000000000
221.0 11.00-10.300 10.9923048454133"| 21.00
10.3923088454133"1
2nd Round
Agent think with COT.
Directly solve problem step by step.
Let's solve the equation step step. focusing extracting the real solutions. in\nGiven the http://////eeeee(///aaaaaa///e//
3x*2 81x 729 = 25 2(5)3) 9WniVVnn Simplify the right-hand side* *InFirst, calculate the right-hand side:An\\/1125 30 64)ntW//nnTThus the equation
becomes: (ilea/nllel(((//rriilllle.. equation Rnearrangigg gieesiowwelliileeeerrrra////eeer
3x*2 81x 729 64nnWinn ** Step Rearranging the 3x*2 B1x 793 Dini)/nn "Step
Thus, merging results from all methods confirms the only real number solution bownl////noooodd3333) Agent 2: think with SBP.
3x*2 + 81x 729 First, extract the mathematics concepts and principles involved in solving the problem. To find all real numbers WXX that satisfy the equation (enna//nWeettdddraxxiiilVVWW
+ 2(5)(3) 9, 9.An\/lmmmwee will apply various mathematical concepts and principles. Below is structured approach to solving problem, integrating concepts such algebraic simplification, use of the polynomial, and rational
theorem. 1. "Simplification the Right-Hand Side**: "dd...... 2. *RRerrrnnging the Equation**: ... 3.* Expressing the Cubic Term** 4, **Clearing Fractions**: * ... .. **Finding Roots Using the Rational Root Theorem** :... 6. **Using Synthetic Division"* 7. *"Solving the Quadratic Equation **:
Concepts and Principles Involved:\n- Alggebricc Simplification* f... **Cubic Polynomial Functions*
"aRational Root Theorem** **: :... "*Synthetic Division** :... "Quadratic Formula** **: **Comples plemppex Numbers Then slove the problem step by step according concepts principles.
Thus, the only real solution to the original equation \nin\Vin (oooeWin An\] Agent 3: think with PoT.
(oxed(39)
Write Python Code to solve the following mathematics problem. Store the result variable named \'ans)". import sympy as spininnt Define the variablelnx = no..symbols('"))ii Define the equstionlnequation
3 3*x**2 81*x 729 (25 -25- 2"5*3 9/vnnn Solve the equationiysoluttins sp sp.solve(equation,
xjynknn Filter solutions)/real solutiions (sol.vvalf() for sol in solutions mool.is_reel])m)ntt Store resultynans real_ solutions VninExecution result
Figure 11: Example of DMAD. The agents actually receive raw markdown text on MATH.
34

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Published as a conference paper at ICLR 2025
Problem:
Find real numbers Sx$ such that wtt.ee//....e.aaaaaaaa/////////2
1st Round
Agent 1: think with Co
First, we need to simplify the right-hand side of the equation:\ninl//Wzz 2[5)(3) #intW//nnnnCalcuaatingg
W 2(5H3) W gives \M 30 W. Therefore:enlnWV//255--- 9 64/11/////nnnn//// we rewrite the original
3x*2 81x 729 641nn\/lninSubbraccinn 64 from both
3x^2 81x 729 64 O'vikillnnTThis simplifies
to: leckonl(DnlleelllffasstkivWe
3x*2
DinW//ollnNext convert
MMlleeng\eefraas////MMM3m3333 into
usable form. We peeeetiiinlpolleelllaaaa/vvviiie
this into the equation, we
3x22
3x*2 81x 793
= OVnVV//nnnTT eliminate the fraction, we multiply the entire equation by 27:ln)o\W/ -
21411 DinoW we want to find the roots this polynomial equation.
Thus, only real number satisfying original equation is: (8x nV| Agent think with CoT.
the problem, first simplify right of the given equation \n1nn///225555 2[5](3)
@lnWW\nnnCalcuuattng the multiplication first:innnnW//22255533 30inl\/n'vnNow Oogether:inln\(//m255 30 64/nn\//nhnTThu, the original equation simplifies
add everything
to: tcchon/luullleff//fffasssseeeeen
3x*2 81x 729 64)n1\))nnNNeet, we move M164N to the left side
3x*2 81x 729 64 O'nii/ininThis further simplifies WlnWWWnnnTo eliminate fraction, multiply through \127WW (since W271) (s) WW3-3/ W/3-s /Jettt/ddracc/////iiii/// 27[3x* 27(B1x)
eww.toowwcnlllllleeeeee/aaaaaaan 3x*2
27[793) = wwii:: simplfies to:in//1/[[m/>> (ttpa/mmmmmmmmm2--2-00 2187x 21411 Olel)/Vn we have cubic
polynomiaallnbbll000mm>>33 81x'2 2187x 21411 [[n\i]
Thus, Agent think with CoT.
(boxed(81
2[5)(3) 9.InUJlnynle''s the right side, have:()nnn\(((22(()33)) Do..n\\WinnnThuus,nviiil 90 9 WnW rewrite the
the equation oonNUhnWuft((frresk333laaaar 3x*2
first simplify the side the equation. Calculating the
3x"2 3x*2 81x 729 64. Ne..nneneeeeeet we move 64 to the left
sieel/ooww//llllfffff////hhhhein 3x*2 81x 793 O.Inn\//rnnNoww let us simplify the term
VVfracx*3) Wn/onw/eWWW can rewrite d.IniV/onnnTo eliminate the fraction, multiply D.I.nW//nnnWoWww need find real roots of this cubic
the equation Beteeln/W/iir/rrress///-222--2-
through
21311
equation.
We then can conclude withlnlnnlsW Mboved
bW
2nd Round
Agent 1: with CoT.
Let's solve equation step by step.
Lastly, after extensive evaluation, will finalize that the sole identified real value from practical evaluations and confirmed vields to: Mbbxxdd88 W. Agent 2: think with COT.
Since we are looking for real solutions only, we conclude that the only real salution to the original equation NoooWeds \nW
Agent 3: think with CoT.
To solve equation
resolved forms checks, only satisfying
Inhn|Win [83 AnWi
3rd Round
Agent 1: think with CoT.
To solve equation
only solution thus identified is Wix -1WV-nnnnni (boxed/81 InlyT verifies aligning against other promising rational roots sought.
Agent 2: think with CoT.
To solve the problem Therefore, the only real number WxV) that satisfies the equation (clptn/lViielllbxeeeee An|V
Agent 2: think with CoT.
To solve the equation... Thus, the only real number satisfying the original equation is: eoo 1bowed8811
\n\Vin
Figure 12: Mental of MAD (All CoT).
35

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Published as a conference paper at ICLR 2025
Problem:
Find all real numbers Sx$ such that Stt.eftt\/rrrrrc/////eeeee/e///e
1st Round
Agent think with SBP.
First, extract the mathematics concepts and principles involved in solving the problem.
To solve the given problem, will break it down into several mathematical concepts and principles invo ved
the solution: 1. *AAlgebraic Manipulation .... 2. C*Cubic Equations*":
3. *"Polynomial Equ ivalence " 5. Root Finding Techniques** * Here are the steps in detail to solve the right-hand
4. **Setting the Equation**:
problem: 1. "Simplify right hand side" .. Rearrange the equation*
""Multiply by
elim fraction**; .. **Investigate possible rational roots**; ... **Finding and testing roots**: 7. "****one"" *Cnncluee**:
6. Further factorization**
Then slove the problem step by step according to the concepts and principles.
Thus, the only solution (boved(9))
Agent think with SBP. First, extract the mathematics concepts and principles involved solving the problem.
solve the equation step by step, Equation),nGiven the equation on MinnUhnnieefllfffaa///////iiee 9 3x^2 81x 729 25 2(5)(3)
from the beginning:Ininnuz 1: Simalify the Right Side the
9, R.ln//ewwwe first simplify the right side IinCalcccaai Wa21ss39NW-bo///00225333333 this to 25 and 9:Ininl\(\m255 30 9 64/nn///rn,,,,, now the equation becomes
301//\//rhnkdddng SidelnWe now rearrange the equation set http://wwwwiillo/eeeeee////a/aaa
3x*2 81x 729 64. 64. Step 2: Move Terms
-3x22
729 64 D.InI\//rnwhhie simplifies hww.:///wiiieee//aaaaaallll.. - 3x"2 81x 793
0.Ink///nnn@eu Step 3: Substitute the Cubic Term\nNow, we expand the term
WV this into the equation alvesstoorV//niiieedde33333 3x*2 81x 793 0.1r\\//nlomm
#** Final AnswerknThus, the solution is:In)n\\/V Vn (oooedr81 \nW... Agent think with SBP.
First, extract the mathematics concepts and principles involved solving the problem.
Let's through the steps hand side:\nin1. **aalculate \W2[5H33NV*** Win Vitimes 5 Vitimes 30.vn W/Vvln2. Combining everything" *:An Whn 25 30 = 64.1n WinlasS the equation now 3x*2 + 81x 729 64. 64A1n\/\rnnnee Step Move All Terms to One 3x*2 81x 793 O.in)//rvnnm* Step 3:
this:kninse Step Simplifying the Right SideknFirst, simplify right-
(nVV///nllef(((/ddrrriik//// SidelnRearrangiing ht Elim nnte FractioninTo eliminate the fraction, multiply the equation (since 11277 3+3VV)Ammm))
Thus, the solution Wn 22xedd27 Alli
2nd Round
Agent 1: think with SBP.
solve given problem, we start the www.uuuiwirilllllll/effeaaaaaaee
2(5(3) 9.nn)]]nnnees Step Simplifying the Right SideinijnHiss,, calculate the right side:\ninV1 bide:vrrn'\\nn2255i33 30Wnn/inngg this W/25W and WW91AAnbnn the equation now /tw.:///wwww///le///////aasaeas
30 6ntinnnnno
-xx/))))))3333-----0 81x 729 64.Ini][innnHuul Step 2:
3x"2
Rearranging the Equation WnWWe now rearrange the equation to set
3x*2 81x 793 0.3n)Ulnnn
Thus, the final result is:nn/WW/ [27xed[22] Nooooess222 AnW
Agent 2: think with SBP.
Let's work through the problem carefully find correct salution. solution..n/nneeeee (nYnee Step Simplifying the Right ShdelynThe original equation
3x*2 81x 729 25 2(5)3)
23nnW/VnkoFirss let's simplify the right-hand side:\nn11. Calculate WM255)///\A W/In \itimes 5 Vitimes A0 1/1n2. Combine:)n
W/In 25 + 30 = 64.vv
the only number VxV sat'sfying the original equation Is: V [boxed IntV
Agent 3: think with SBP To solve equation (afnl///WWlee(llffffa////WMMee
3v*2
2(5)(3) + Wn
proceed htte-bby-tte::nnnniitt Step Simplify the Right Side\nCalculating
N2255/97NAAnmnn/(00022533/ 30. S0.nn\/innnddi this to 25 and givess:nn/nn//2225 30 64.
ConclusionVnReeiistiie and assessing detail once more, the only feasible real solution isAnn Aboxed(8
AnW
Figure 13: Mental of MAD (All SBP).
36

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Published as a conference paper at ICLR 2025
Problem:
Zach three bags and bunch of pencils placed into the bags. He told place the greatest number pencils possible into each the three bags while also keeping the number of pencils in each bag the same. What is the greatest number of pencils he could have left over?
1st Round
Agent 1: think with Co
Directly solive the problem step by step determine the greatest number of pencils Zach could have left over after placing the greatest number of equal pencils into each of the three bags,
represent this situation mathem mathematicallyy/v atiically.nninnteel W P W be the total number of pencils Zach has. When he divides these pencils among the three bags, he can place MM Weltt Wrrac(H)3) Wright\\yfloor W pencils in each bag, where W (flot /rright W denotes the greatest integer less than or equal to Wi The pencils Is used bags can then calculated as:\n\\(vn3 Vtimes Weft\V/floor (Mrrc(PH)) \rightt)rlloor/n))) (atoooorrrnnn//////n find out how many pencilss left over, we need subtract the used pencilss from the total pencils W P WAAn
left over) = P-3 Wtimes Weftt/ W/rra(PP[3) www.ghhhwroooo/nnilliinnoooo by the properties es of division and floor functions, we know that the possible remainders when dividing W P W by 3 can either be 1, or 2. SpecificallyAn- WP Vequiv (lmod 3 W: then W P WV for some integer WM k W and the remainder WO W/An- If W Wequiv 1 Vmodd Wi then WP 3k + 1 W and the remainder is W. WJAn- If W Veeuiv 2 Wmmdd W: then WP 3k W and remainder is
greatest number of pencils Zach could have left over oecurs when WV Veequv 2 Vimad 3VU, which gives remainder of 2. 2.An'TTuus, the maximum leftover pencils Zach can end with, when distributing as stated,
W-AnynClearly,
is Is number of pencils left over) = 2nnWillnnTTTeeefeee the answer is W MMcceed W..
Agent 2:/ think with SBP.
To solve the problem, let's Identify the mathematical concepts and principles involved: 1. *Division"* :.....
Remaiiner"** ... 3. *Madular Arithmetic** :... 4, "Iteeger Divisian"":... :..55. **Maximization" ... To solve the problem step by step, we'll apply concepts and principles identified elniie:
"* Unde rstanding the total quantity**: 2. ** "Dividing the pencils**:... 3. *"Finding the remainder**:
** "oosiible remainders** :..... **aaxiization""..
Therefore, the greatest number of pencils Zach cauld have left over is:An/al (arnn///////aaannn Abcxed kn)))
Agent 3: think with PoT.
Write Python Code to solve the mothematics problem. Store the result as variable named \'ans)". The Python program/nnnpeecce 100 # example total number of pencilslnbags = 3\nans = pencils % bogssnnynExecution result:
2nd Round
Agent 1: / think with COT.
Directly salve the problem step by step.AnTa determine the greatest number of pencils Zach could have left over, we need to analyze
divis the total number of pencils W () by the number of bags (which is 3).In)nWhhn dividing WM P by can express total number of pencils
of remainders Inkn- If
W Veeuui 0 Wmod WJ Remainder is 0.An- If W Veequiv 1 Vmmod WV: Remainder is 1.An- If \M P Veeuuv WWmad 3 Wi Remainder S.icce the goal to maximize the number of pencils left over after distributing them evenly into the three bags, we find that the maximum remainder possible when dividing by
3 2.Any, the greatest number pencils Zach could have left over Setnnnnnnnlllbeeeeeoo [1 vnW Agent 2:/ think with SBP.
To extract the mathematics concepts and principles involved in solving the problem about Zach and the pencils, we can summarize
following key elements:Anyn1. **Division" ... Remaiinde and Modulo Operation **; ... 3. ** **Fooor Function** + ... **Popperties of Modular Arithmetic** 6. **Integer Solutions**: ... **Examples and Illustrations** ....
*Maxxiization"*: **...
To solve the problem step by step according to the concepts and principles mentioned, we will use the concepts of division and remainder calculations. calculations.nnnnitk \n)nids Step 1: Define the Problem)nlet WM MMPPM (V) be the total
number of pencils Zach has wants distribute these pencils evenly into three bags Vnlyne Step
Calculate Pencils Each BaginTo find out how many pencils can go each bag, we perform integer division of /M P W W. Mi--ir//DDittextPPeeen in each bug)= = Wleft/Vfoorr Wrra((P)3
means we are determining how many full sets of can be formed from VM P W. innnttt Step 3: Determine the Total Used Pencils\nNext we calculate how many pencils are actually placed into the bags, which given MyAAmiiM/n/tttttttTT pencils used] =3 \itmes Woott Wrar[(H33
Step 4:
number of pencilk left over after distributing them into the bags, subtrrct the used sencils from the total number (nwniiss//Wiiiittteetttee pencils used)(n\ /nnn//nnnnnuin the division properties, this also be simplified using the modulo pencils) P Vmmod Vei exp expression directly provides the remainder when \M W div ded by VM 3 W.A...
Calculate the Leftover Pencilk)
penc Is} Votext[Total
operation:yn//M/W bri////\texxx(Lefooo
Thus, the greatest number of pencils Zach could have left over after distributing them into the three bags
(ookerr [nW)
Agent 3: / think with PoT.
Write Python Code
the mathermatics problem. Store result variable named V Vansl". The
Python program:\niynass 2'n\nExecution result: 2.0
Figure 14: Example of DMAD on MATH.
37

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Published as a conference paper at ICLR 2025
Problem:
Zach has three bags and bunch pencils to be placed into the bags. He is told to place the greatest number of pencils possible into each of the three bags while also keeping the number of pencils in each bag the same. What is the greatest number of pencils he could have left over?
1st Round
Agent / think with PoT.
Write Python Code to solve the following mathematics problem. Store the result as variable named \'ans\".
The Python program:
pencils 100
# example total number of pencils
bags=
ans pencils % bags Execution result:
Agent 2: think with PoT.
Write Python Code solve the following mathematics problem. Stare the result as variable named \"ans\".
The Python program:
pencils
# You can change this number to test different scenarios
bags 3
pencils % hags
Execution result:
Agent 3: J think with PoT.
Write Python Code solve the following mathematics problem. Store the result as variable named \"ans\".
The Python program:
bags 3
total_pencils= 100
# Example total number of pencils
total pencils % bags
Execution result:
2nd Round
Agent 1: think with PoT.
Write Python Code to solve the following mathematics problem. Store the result a variable named \lans"".
The Python program:
pencils 100
Example number of pencils
b ans pencils % bags
Execution result: 1.0
Agent 2: think with PoT.
Write Python Code to solve the following mathematics problem. Store the result as a variable named \"ans\".
The Python program:
pencils 100
You change this value other scenarios
bags=
ans = pencils % bags Execution result: 1.0
Agent 3: think with
Write Python Code to solve the following mathematics problem. Store the result as a variable named \"ans)".
The Python program:
pencils 100
Example total number pencils
bags 3
max_per b_g = pencils // bags
ans = pencils (max per_ per_bag bags) Execution result:
Figure 15: Mental of MAD (All PoT).
38

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Published as a conference paper at ICLR 2025
Question:
What occasions would someone use this meme?
1st Round
This meme features cat with its mouth wide open, and the text " ! "which is Chinese for "cry" or "weep." The meme is often used to express strong emotions, such as sadness, frustration, or disappointment. It can be used various contexts where someone wants convey sense of overwhelming emotion, such
response a heartbreaking story or news.
2. When someone has experienced significant loss setback.
3. During a heated argument or disagreement.
When expressing sympathy empathy for someone else's misfortune.
5. In a humorous context to exaggerate one's emotional state for comedic effect.
The meme is versatile and can be used in wide range of situations where strong emotional reaction is warranted.
2nd Round
The meme features cat with its mouth wide open, and the text "M
M U1 U UC) (C, IC, (I)) (I) UC) UC) (C) (I) (E) uC) uC)
15 TİL 16 T6L D6 D6 DE D6 1C
DC
ng
3rd Round
un un ug un un
Figure 16: Failed MAD case of LLaVA-1.6-138 on MM-Vet. nonsense sentences the debate round increases.
LLaVA-1.6-13B generates more
39

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Published as a conference paper at ICLR 2025
PORK BELLY
Question:
30%
9.80
What the original price pork belly before discount?
1st Round
O
The original price
O
The original price was 9.80
The original price for pork belly before discount was 9.80
KTP
was 9.80
ATD
Agent 1
Agent
Agent
2nd Round
The original price for pork belly before
The original price for pork belly before discount was 9.80
The original price for pork belly before discount was 8.80
Agent
discount was 9.80
Agent
Agent
3rd Round
The original price for
The original price for pork belly before discount was 9.80
The original price for pork belly before discount was 80
pork belly before
Agent
discount was 9.80
Agent
Agent
4th Round
The original price for
The original price for
The original price for pork belly before discount
pork belly before
pork belly before discount 9.80
AEED
CLDD
Agent
discount 9.80
Agent 2
Agent 3
5th Round
The original for pork belly before
The original price for pork belly before discount was
The original price belly before discount was
O
O O CTT
QTD
LTD
Agent
discount was
Agent 2
Agent
Figure 17: Mental set of MAD (All IO), All agents fail correctly answer the question even in multiple rounds.
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Published as a conference paper at ICLR 2025
PORK
Question:
30%
9.80
What is original price pork belly before discount?
Round
['abject"; "price".
("abject": "text",
O
"atribbtes": [*9.80"]],
O
[t ['oojocc": "price".
CTD
"attributes":
('object": "discount".
"attributes": ["9.80"]
Agent
["9,80"] "relation"""BEFO RE DISCOUNT",
Agent
"attributes:: ["30%]]] { "attributes": ["pork belly"]].
Agent
("object"" "discount", "attribures": ["30%"]],
("abjcct": "preduct",
("ubject"; "product",
("relation": "FOR",
"attributes": ["pork belly"
('abject": "pork belly", "relation":
"subjoct": "prico". "object":
("relation": "on", "subject";
"product"), ("relation":
"discount", "object": "product"), ("relation",
"HAS PRICE") The original price pork belly before the discount
"OF", "subject": "discount", "object": "price"]]
"subject": "price", "object": "product")]
The original price was You
The original price of the pork belly was 50180
discount shown 30%
and the price now 8.80
2nd Round
[""bbjec"" "price",
Hoobjects":
oobjectt" "price",
"atributes": ["9,80"]]
l"price", "pork belly"I.
"attributes:: ["9.80"]].
:"object": "discoun"",
Agent
Agent 2
("object": "discount"
Agent
"attributes;; ["30%]] J.
"attributes": ["9.80", "30%",, "relationships":
"attributes" ["30%"]] }].
('objcet": "product".
("object":
"product",
"attributes:: ["pork belly")
"attributes" ("pork
("relation" "FOR", "subjoct":
('the price of belly 9.80", "the price of pork belly is discounted 30%
belly"]]. ("relation":
"price" "object":
"product").
"FOR". "subjocr":
("relation": "OF", "subject";
"price", "object": "product"), ("relation": "OF".
"discount". "object": "price"),
("relation" "BEFORF DISCOUNT", "subjocr":
"subject": "discount",
"price". "object": "product")) The original price for pork belly before the discount is B.sll price
The original price is is 80. This is indicated bay the
"object": "price"!]
The original price was
8.80 You can tell because discount
number the
prace after the discount. We know this because the discount
right-hand side of the screen.
shown 30% and
the price now
displayed as 30% and the price displayed
Thus,
the original price was 9.80
Figure 18: Mental set of MAD (All CCoT). All agents fail to correctly answer the question even in multiple rounds.
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Question:
Which statement describes the
Kaeng Krachan National Park ecosystem?
Context:
Figure:
Kaeng Krachan National Park.
Kaeng Krachan National Park tropical rain forest ecosystem in western Thailand. It Thailand's largest national park has many animals, including elephants.
Options:
(A) It has soil that is poor in nutrients.
(B) It has mostly small plants.
1st Round
Agent think with
The answer is B Because Kaeng Krachan National Park is tropical rain forest ecosystem, it is characterized by rich biodiversity with variety of plant and animal species. Tropical rain forests are known for their lush vegetation and abundant plant life, which includes a wide range tree species, shrubs, and herbs. soil in ecosystems typically rich nutrients, which supports growth of diverse plant community The image provided shows a dense forest with variety of plants, including large trees and smaller plants, which is consistent with the type of vegetation found in tropical rain forests. The presence of a river also indicates that the park has water source, which is essential for the survival the flora fauna the ecosystem. CCoT.
Agent think
The answer is Because Kaeng Krachan National Park tropical rain forest ecosystem, which typically has soil that is poor in nutrients due to the high evapotranspiration rates of the vegetation. This leads to humid and humid climate, with abundant rainfall, which supports the growth diverse range plant species, including large trees and variety small plants. presence of elephants the park also suggests diverse ecosystem that support their needs.
Agent 3: think with DDCOT.
The answer is Because the image shows a dense forest with a stream, which characteristic tropical rain forest ecosystem. These ecosystems are known their high levels biodiversity, including a wide variety plant and animal species. While
that there may many plants tropical rain forest, the statement does not accurately describe the overall characteristics of the ecosystem, as also includes large mammals such as elephants, which are present in the image.
2nd Round
Agent 1: think with 10.
The answer is A, Because Kaeng Krachan National Park is tropical rain forest ecosystem, it characterized by rich biodiversity with variety of plant and animal species. Tropical rain forests are known for their lush vegetation and abundant plant life, which includes a wide range of tree species, shrubs, and herbs. The soil in these ecosystems typically rich in nutrients, which supports the growth of diverse plant community. The image provided shows dense forest with variety of plants, including large trees and smaller plants, which is consistent with the type of vegetation found in tropical rain forests. The presence river also indicates that source, which is essential the survival the flora and fauna soil that poor nutrients.
the park statement that describes the Kaeng Krachan National is because tropical rain forests are known for their high evapotranspiration rates, which can lead a humid humid climate, with abundant rainfall. This high evapotranspiration rate can result soil is poor nutrients, as the plants quickly take up the available nutrients, leaving little for the soil retain. However, despite the poor sail quality, tropical rain forests are able to support diverse range of plant and animal species due to the high levels of rainfall and the availability of sunlight. Agent 2: think with CCoT.
ecosystem. The
ecosystem
The answer is A Because Kaeng Krachan National Park is tropical rain forest ecosystem, which typically has soil that is poor in nutrients due to the high evapotranspiration rates of the vegetation. This leads to humid and humid climate, with abundant rainfall, which supports the growth of diverse range of plant specles, including large trees and variety of small plants. The presence of elephants in the park also suggests diverse ecosystem that support their needs. The image provided shows dense forest with variety of plants, including large and smaller plants, which is consistent the type of vegetation found tropical rain source, which is essential for the survival
forests. The presence river also indicates that the park the flora fauna the ecosystem.
Agent think with DDCoT.
The answer is A Because Kaeng Krachan National Park a tropical rain forest ecosystem, it is characterized by rich biodiversity with variety of plant and animal species. Tropical rain forests are known for their lush vegetation and abundant plant life, which includes a wide range of tree species, shrubs, and herbs. The soil in these ecosystems is typically rich in nutrients, which supports the growth of diverse plant community. The image provided shows a dense forest with variety of plants, including large trees and smaller plants, which is consistent with the type of vegetation found in tropical rain forests. The presence of river also indicates that the park has water source, which is essential for the survival of the flora and fauna in the ecosystem.
Figure 19: Example of DMAD.
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Question:
Which statement describes the
Kaeng Krachan National Park ecosystem?
Context:
Figure:
Kaeng Krachan National Park.
Kaeng Krachan National Park a tropical rain forest ecosystem western Thailand. Thailand's largest national park many animals, including elephants.
Options:
(A) has soil that is poor nutrients.
(B) has mostly small plants.
1st Round
Agent 1: think with IO.
The answer is Because Kaeng Krachan National Park is tropical rain forest ecosystem, it is characterized by specles. Tropical
variety of plant vegetation and abundant plant life, which includes wide
for their of tree species, shrubs, and herbs. The soil in these ecosystems is typically rich nutrients, which supports the growth of diverse plant community,Ini Ane
biodiversity
image provided shows dense forest with variety plants, including large trees and smaller plants, which is also indicates that the park has water source, which essential for the survival of the flora and fauna in the ecosystem.
consistent with the type of vegetation found tropical rain forests. The presence of
Agent think with IO.
The answer Because Kaeng Krachan National Park tropical forest ecosystem, which characterized by rich biodiversity, including wide variety of plant species. Tropical rain forests are known for their high levels of plant species diversity, with mix of large and small plants, as well as variety tree types and other vegetation. The presence of large number plant species provides habitat including elephants, which are found in the park. The soil tropical rain forest ecosystem is typically rich nutrients due to the high levels of rainfall and the decomposition of plant matter, which creates a nutrient-rich environment for plant growth.
wide range animals,
Agent think with
The answer is Because Kaeng Krachan National Park is tropical rain forest ecosystem, which typically has rich and diverse plant life, including a variety trees, shrubs, and herbs. The forest floor is often covered with dense layer of vegetation, including many small plants. The soil such ecosystems usually rich nutrients due to the high levels of rainfall and the decomposition organic matter, which supports the growth of wide
range of species.
2nd Round
Agent think with 10.
The answer Based on the information provided by other agents, Kaeng Krachan National Park tropical
forest ecosystem characterized by rich biodiversity, including wide variety of plant species. The forest floor
often covered with dense layer vegetation, including many small plants. The in such ecosystems
usually rich nutrients due the high levels rainfall the decomposition of organic matter, which supports the growth of wide range plant species. Therefore, the correct answer is option as accurately describes the ecosystem of Kaeng Krachan National Park.
Agent think with IO.
The answer Because Kaeng Krachan National Park is a tropical rain forest ecosystem, which is characterized by a rich biodiversity with a variety of plant and animal species. Tropical rain forests are known for their lush vegetation and abundant plant life, which includes a wide range of tree species, shrubs, and herbs. The soil in these ecosystems is typically rich in nutrients, which supports the growth of diverse plant community. \nThe image provided shows dense forest with variety of plants, including large trees and smaller plants, which is consistent with the type of vegetation found in tropical rain forests. The presence of a river also indicates that the park has water source, which essential for the survival of the flora and fauna the ecosystem.
Agent 3: / think with IO.
The answer is Because Kaeng Krachan National Park is tropical rain forest ecosystem, which is characterized by rich biodiversity, including wide variety of plant species. Tropical rain forests are known for their high levels of plant species diversity, with mix of large and small plants, as well as variety of tree types and other vegetation. The presence of large number of plant species provides habitat for wide range of animals, including elephants, which are found in the park. The soil in tropical rain forest ecosystem is typically rich in nutrients due to the high levels of rainfall and the decomposition of plant matter, which creates nutrient-rich environment for plant growth. The image provided shows dense forest with variety of plants, including large trees and smaller plants, which consistent with the type of vegetation found in tropical rain forests. The presence of river also indicates that the park has a water source, which is essential for the survival of the flora and fauna in the ecosystem.
3rd Round
4th Round
5th Round
Agent The
Agent
Agent 1:
Agent The answer
Agent The
Agent 2:
Agent The answer
Agent The answer
Agent
Figure 20: Mental set of MAD (All IO). All agents fail to correctly answer the question even in multiple rounds.
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Question:
Which statement describes the
Kaeng Krachan National Park ecosystem?
Context:
Figure:
Kaeng Krachan National Park.
Kaeng Krachan National Park is tropical rain forest ecosystem in western Thailand. It Thailand's largest national park and has many animals, including elephants.
Options:
(A) It has soil that is poor in nutrients.
(B) It has mostly small plants.
1st Round
Agent 1: think with DDCoT.
The answer Because image shows dense forest stream, which characteristic of tropical rain forest ecosystem. These ecosystems are known for their high levels of biodiversity, including wide variety of plant and animal species. While true that there may be many small plants in a tropical rain forest, the statement does not accurately describe the overall characteristics of the ecosystem, it also includes large mammals such elephants, which present in the image.
Agent 2: think with DDCoT.
The answer B, Because the image shows dense forest with variety plants, including a large tree with thick trunk and roots, which is characteristic of tropical rain forest ecosystem. The presence of river and the lush greenery suggest that the the park likely to nutrients, supporting the growth of diverse range of plant species. While Kaeng Krachan National Park indeed home to variety of animals, including elephants, image not provide enough information to determine the specific characteristics of the soil or the types of animals commonly found in the park.
Agent 3: think with DDCoT.
The answer Because the image shows dense forest with stream, which is characteristic of tropical rain forest ecosystem. These ecosystems are known for their high levels of biodiversity, including wide variety of plant and animal species. While is true that there may be many small plants in a tropical rain forest, the statement does not accurately describe the overall characteristics of the ecosystem, it also includes large mammals such elephants, which present in the image.
2nd Round
Agent think with DDCoT.
The answer is B. Because the image shows dense tropical rain forest environment with variety plants, including large trees, which characteristic the Kaeng Krachan National Park ecosystem. Tropical rain forests are known for their high biodiversity and the presence of wide range of plant species, including both large and small plants. Therefore, the statement that describes the Kaeng Krachan National Park ecosystem is: (B) It has mostly small plants.
Agent 2: think with DDCoT.
The answer B Because the image shows a dense forest with a variety of plant life, including large tree with many roots and stream, which indicates that the park has lush ecosystem with rich biodiversity suggest that the park is tropical rain forest ecosystem, which typically has variety of plant species, including large trees.
diverse range of plant species, not just small plants. presence of water source
Agent 3: think with DDCoT.
tropical rain forest ecosystem, which characterized by dense vegetation and wide variety of plant species. While it is possible that there are some small plants the park, likely that there are also larger plants, given the high levels biodiversity in tropical rain forests.
answer Because Kaeng Krachan National
Figure 21: Mental set of MAD (All DDCoT). All agents fail correctly answer the question even in multiple rounds.
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Par
Question:
Think about the magnetic force between the magnets in each pair. Which the following statements is true?
Context:
The images below show two pairs of magnets. The magnets different pairs do not affect each other. All the
magnets shown made of the same material.
Options:
(A) The strength of the magnetic force is the same in both pairs.
(B) The magnetic force weaker in Pair 2.
(C) The magnetic force weaker Pair 1.
1st Round
Agent 1: think with IO.
Directly answer the question. The answer is Because the magnetic force between two magnets is inversely
proportional the square the distance between them. The magnets In Pair are closer to each other than the
Inagnets Pair Therefore, the magnetic force weaker in Pair
Agent 2: think with CCoT.
[["ojject": "magnet", "attributes": ("north", "south", "pair1", apart"]
Probjctt"="mannee"" "attributes": ("north", "south", "pair2", apart"]
force", "attributes": ("stronger in pair 1 I"relation": "next to", "subject": "magnet", "ougnet".""bb""" "object": "magnet]]
The answer is Because the magnetic force between twa magnets is inversely proportional to the square the distance between them. The distance between the magnets Pair 1 is inches, while the distance between the magnets Pair is inch, Therefore, the magnetic
weaker Pair
Agent 3: think with DDCoT.
Sub-questions:
1. What determines the strength of the magnetic force between two magnets?
2. How does the distance between two magnets affect the strength of the magnetic force?
Sub-answers:
1. The strength of the magnetic force between two magnets is determined by the strength of the individual
magnets and distance between them,
2. The closer the magnets are each other, the stronger the magnetic force
The answer
Because the magnetic force weaker Pair because magnets are further apart in
2nd Round
Agent 1: think with 1O.
The answer Because the magnetic force is inversely proportional to the square of the distance between the magnets. This means that as the distance between the magnets increases, the magnetic force decreases, The magnets in Pair 1 are further apart than the magnets in Pair 2, so the magnetic force between them is weaker
Agent 2: think with CCoT.
[[object":
"pair", "attributes": ["1"], "relationships": [["object": "distance", "relation": ": "has", "attributes": 2 inch IH],,
{ ("object": pair", "attributes": ["2"], "relationships": (""ojject": "distance", "relation": "has", "attributes": | I'1 inch 1H},
("object": "force", "attributes": "relationships": [("object": "distance", "relation": : "is inversely proportional to".
"attributes": ('weaker in pair 1" 1"])
The answer is Because the magnetic force between two magnets is inversely proportional to the square of the distance between them. The magnets Pair 1 are inches apart, while in Pair 2, they are 1 inch apart. Therefore, the
magnetic force in Pair weaker
Agent 3: think with DDCoT.
Sub-questions:
1. What is the relationship between magnetic force and distance between magnets?
How does the distance between the magnets Pair 1 compare the distance between the magnets in Pair 2?
3. Considering the answers to questions and 2, which pair would experience stronger magnetic force?
Sub-answers:
1. The magnetic force between two magnets is inversely proportional to the square of the distance between them.
This means that as the distance between the magnets increases, the magnetic force decreases,
2. The distancce between the magnets in Pair 1 is inches, while the distance between the magnets Pair 2 Inch
3. Pair would experience stronger magnetic force because the magnets are closer together
The answer (C) The magnetic force weaker Pair
Because the magnetic force between two magnets inversely propertional to square of the distance between
them. This means that the distance between the magnets increases, the magnetic force decreases, The magnets Pair are further apart than the magnets in 2, so the magnetic between weaker,
Figure 22: Example of DMAD. All agents get wrong answers in the 1st round while reaching the right solutions in the 2nd round.
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1st Round
Agent 1: think with 10.
The image shows an apple with sticker on it. The sticker includes barcode and some text, but it does not provide information about whether the apple is organic not. To determine the apple organic, one would typically look for label or certification mark indicating that meets organic standards. If such label not visible, it not possible to definitively whether the apple
organic not based salely on the image
Agent 2: think with CCoT.
("scene": ("objects": [["type": "apple", , "attributes": : ("calor": "red", "texture"; "smooth", "label": "PUIA 94131 USA"), "ralti"ittioosshpp"""""
Question:
Is this apple organic?
[["type": "label", "label", "laael", "PUJA 94131 USA ",( "ttptt"":: "texture", "texture";
"smooth",."type" ""color"""cooor""" "osolorr""red"" "IH," "relationships". [("type"; "label", "label",," "PUJA 94131 USA"),(" "Stpe""" "t""ypp""""eexture" "texture,, "eexturr"""exture""" "texture": "smooth"), "tttppe" "color",, "alorr,"colo""" "color": "red"H))" use the image and scene graph as context to answer the question.The image shows an apple with a sticker on it. The sticker
typically contains information about the apple, including its variety, origin, and sometimes whether it is organic not. In this case, the sticker indicates that the apple is "PUIA 94131 USA," but does not provide information about whether is organic or not To determine if the apple is organic, one would need to look for specific organic certification logo text on the sticker, which is not visible this image.
Agent 3: think with DDCoT.
Sub-questions:
1. What is the label on the apple?
2. What does the label indicate about the apple?
3. What is the significance of the label indicating "PUJA 94131 USA"?
Sub-answer answers:
1. The label on the apple reads "PUJA 94131 USA."
2. The label indicates that the apple is product of the United States.
3. The significance of the label "PUJA 94131 USA" is that it provides information about the origin of the apple.
It suggests that the apple was grown, harvested, and packaged in the United States. However, does no
provide information about whether the apple organic or not
Then, according to the sub-questions and sub-answers to answer the question. No, the apple is not organic 2nd Round
Agent 1: think with
Directly answer question. Based on the image and the information provided, is not possible to definitively determine the apple organic or not. The sticker on the apple indicates that it is a product of the United States, but does not provide any information about whether organic, one would need to look for a specific organic certification logo or text on the sticker, which is not visible in this image. Therefore, the answer to the question is cannot tell if the apple is organic based on the image and the information provided
organic or not. To determine the apple is
Agent 2: think with CCoT.
("scene": ("objects": [("type": "apple", "aoplee,""tttinnn "'attributes": ("color": "red", "texture": "smooth" "labbll: "PUJA 94131 USA"), "relaiisssii [["type": "label", "label': "PUJA 94131 USA"), USt"M'"t:"e":: "texture", "ttettur": "smooth") t""tpee" "calor", "colar": "red")]]I, "relationshiss" [[" [["type": ": "label", "label": "PUJA 94131 USA"), (""ttee"" "texture" " "texture": "smooth") ",(" typy""" "color", "color": "red")]]) Based on image the scene graph provided, we can see that the apple provide any information about the apple being organic. To determine look label or certification mark indicating that it meets organic standards. Since such label not visible in the image, not possible to definitively say whether the apple is organic or not based solely on the image.
sticker on it with the text "PUJA 94131 USA. The sticker does not
apple is organic, one would need to
Agent 3: think with DDCoT.
sub-questions:
1. What is the label on the apple?
What does the label indicate about the apple?
3. What is the significance of the label "PUJA 94131 USA"?
Sub-answers:
The label on the apple reads "PWAA 94131 USA."
The label indicates that the apple product of United States.
3. significance the label "PUJA 94131 USA" that provides information the origin the apple. It suggests that the apple was grown, harvested, and packaged in United States, However, does not provide information about whether the apple is organic or not.
determine if the apple organic, one would typically look label or certification mark indicating that meets organic standards. If such label is not visible, is not possible to definitively say whether the apple is organic not based solely on the image.
Therefore, the answer to the original question is: No, the apple is not organic
Figure 23: Failed case of DMAD.
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H PROMPTS
We display the prompts all methods in this section, ie., CoT (Figure 24 SBP (Figure 25 PoT
(Figure 26). IO (Figure 27j. CCoT (Figure 28). DDCoT (Figure 29.. Self-Refine (Figure 30 the contrast stage of Self-Contrast (Figure the reflection stage of Self-Contrast (Figure 32) MRP for LLMs (Figure 33). MRP for MLLMs (Figure 34), MAD-persona (Figures 33 38 MAD (Figure
39) and DMAD (Figure 40p. The part colored yellow represents prompts that need to be filled, and
the part colored green represents the responses of the assistant.
CoT prompt
User:
<problem description>
Problem:
<problem>
Answer:
Assistant:
konswer>
Figure 24: CoT prompt.
SBP prompt
User:
You are an expert at <subject>. Your task is to extract the <subject> concepts and principles involved in solving the problem.
Probiem:
<problem>
Assistant:
<concepts>
User:
Slove the problem step by step according to the concepts and principles.
Assistant:
kanswer>
Figure 25: SBP prompt.
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PoT prompt
User:
Write Python Code solve following mathemotics problem. Store your result o variable named "ons". You can only output Python program that can be executed by the Python function exec(). Do not say ony other words.
Problem:
<problem>
Assistant:
<codea
Figure 26: PoT prompt.
10 prompt
User:
<image>
Question:
<question>
Assistant:
kanswer
Figure 27: 10 prompt.
CCoT prompt
User:
<image>
Question:
<question>
For the provided image and its associated question, generate scene graph JSON format that includes the following:
1. Objects that are relevant to answering the question.
2. Object attributes that are relevant answering the question.
3. Obect relationships that are relevant to answering the question.
Just generate the scene groph in JSON format. Do not say extra words.
Assistant:
<scene graph>
User:
Use the image ond scene graph as context and answer the following question. <question>
Assistant:
<answer>
Figure 28: CCoT prompt.
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DDCoT prompt
User:
<imoge>
Question:
<question>
Given the image and question, please think step-by-step about the preliminary knowledge to answer the question, deconstruct the problem as completely as possible down to necessary sub sub-questions. Then with the aim of helping humans onswer the original question, try answer the sub-questions. The expected answering form is as follows:
Sub-questions:
1. <sub-question 1>
<sub-question
sub-answers:
1. <sub-answer 1>
<sub-answer 2>
Assistant:
ksub-questions
<sub-answers>
User:
Give your answer of the question according to the sub subb-iussions and sub- aub-answers.
Assistant:
conswer>
Figure 29: DDCoT prompt.
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Self-Refine prompt
User:
CoT prompt (LLM) or 10 prompt (MLLM)
Assistant:
<previous answer>
User:
Review your previous answer and find problems with your answer.
Assistant:
<feedback>
User:
Based the problems of your previous answer, imprave your answer.
Assistant:
<revised onswer>
Figure 30: Self-Refine prompt.
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Self-Contrast prompt Contrast
User:
You are specialist who specializes in <subject>, Given some condidate solutions for question, you should carefully compare difference for each two solutions their solving steps. When you compare, need to consider the following questions: Are the two solutions have different final answers and expressions? 2: Where the differences their solution steps and expressions?
3: Why are the answers of the two solutions different?
After contrasting, you should generate checklist based these differences between candidate solutions. You should carefully consider each discreponcy and the reasons behind it, summorizing them into few checking instructions in the checklist. This checklist con guide others re-exomine the input question and these candidate solutions to eliminate these discrepancies.
Input Format:
The question <guestion>
All solutions:
Solution1: [Solution1]
Solution2: [Solution2]
Solution3: [Solution3)
Output Format:
For Solution1 and Solution2: (Differencei)
For Solution1 and Solution3: (Difference2) For Solution2 and Solution3: (Difference3) Checklist: (Directive1, Directive2,...)
Assistant:
<Differencesa
<Checklists
Figure 31: Prompt of the contrast stage of
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Self-Contrast prompt- Reflection
User:
Given question, multiple inconsistent solutions, their differences their solving processes, and a checklist. You should revise the inconsistent solving step for each solution, eliminate the differences, and output a new solving process for each solution. Guidance Rules for Reflection:
1. Please check carefully according to the requirements on the checklist. It helps you to resolve conflicts between different solutions.
2. When you finish revising inconsistent solutions, please ensure all revised solutions should have the same answer. If not, please revise again until all inconsistencies are removed, and all candidates are consistent.
3. Please output all revised solutions in ISON format as input, without any other text.
The question (question). The candidate solutions and their discrepancy are as follows:
"Candidate":
"result 1": ""solution": : "[solution1]") "),
"result 2": ("solution": : "[solution2]") )
"result 3": ("solution": "[solution3]"]
"Discrepancy":
"difference_ 1_2":
"source": "result_ 1",
"torget": "result_ 2";
"relation": "[differencel 2)"
"difference 3":
"source": "result_ 1"
"torget": "result 3",
"relation": "[difference1 3)"
J
"difference_223 3"
"source": "result_2 2",
"torget": "result 3",
"relation": "(difference2 3)"
Checklist: [Checklist)
Please revise each inconsistent solution.
Assistant:
<onswer>
Figure 32: Prompt of the reflection stage of Self-Contras
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MRP prompt- LLM
User:
Instructions:
You are an adaptive reasoning method with meto-reasoning abilities, capable of selecting the most oppropriate reasoning method based on the task provided by the user. Please use a meto-reasoning thinking pathway and adhere to the following guidelines when answering questions.
Reasoning method pool:
These reasoning methods are available for your tasks. Understand their applications for various tosks.
1. CaT:
Directly onswer the question step by step.
2. Step back:
First, extract the mathematics concepts and principles involved in solving the problem.
Then, solve problem step by step according to the concepts and principles.
3. PoT:
Write Python Code to solve the mathematics problem. Store the result as a variable nomed "ons".
Analyzing giving tosk:
Evoluate problem's difficuity carefully. Avoid underestimating the complexity make considered decision.
Anticipate the mistakes you might make:
Identify possible errors in method selection, such as underestimating the problem's difficulty.
Meta reasoning:
Apply meta-reasoning to choose the oppropriate pathway.
Grading:
Rate suitability of each solution on scale of 1-3, selecting the method with the highest score as your preferred choice.
Choosing reasoning method:
Proceed methodically, taking deep breath and thinking step by step. Select reasoning method from the provided options only, reflecting on the decision to avoid intuitive errors.
Question:
<question>
The last sentence of your answer should be "So the best reasoning method is xxx",, where "xox" is the name of the best reasoning method.
Assistant:
<answer>
Figure 33: MRP prompt for experiments on LLMs.
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MRP prompt- MLLM
User:
Instructions:
You adaptive reasoning methad with meta-reasoning abilities, capable of selecting the most oppropriate reasoning method bosed on the task provided by the user. Please use meto-reasoning thinking pathway adhere to the following guidelines when answering questions.
Reasoning method pool:
These reasoning methods are available for your tasks. Understand their applications for various tasks.
10:
Directly onswer the question.
2. CCoT:
First, get the scene graph of the image in JSON format.
Then, use the image and scene graph context to answer the question.
3. DDCoT:
First, deconstruct the question down to sub-questions.
Then, accord to the sub-questions and sub-answers to answer the question.
Analyzing giving task:
Evaluate the problem's difficulty carefully. Avoid underestimating the complexity and make considered decision.
Anticipate the mistakes you might make:
Identify possible errors in method selection, such as underestimating the problem's difficulty.
Meto reasoning:
Apply meta-reasoning to choose the oppropriate pathway.
Grading:
Rate the suitability of each solution on a scale of 1-7, selecting the method with the highest score as your preferred choice.
Choosing reasoning method:
Proceed methodically, taking deep breath and thinking step-by-step. Select reasoning method from the provided options only, reflecting on the decision to avoid intuitive errors.
Question:
<question>
The last sentence of your answer should be "So the best reasoning method is xxx", where "xox" is the name of the best reasoning method.
Assistant:
<onswers
Figure 34: MRP prompt for experiments MLLMs.
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MAD-persona prompt Affirmative Side
System:
You are debater. Hello and welcome the debote. it's not necessary to fully ogree with each other's perspectives, as our objective is to find the correct onswer.
The debate topic is stated as follows: <question>
User: You think the correct
Restate it and provide your reasons.
Assistant:
<answer>
User:
<negative answer>
Assistant:
<answer>
User:
Assistant:
Figure 35: Prompt of the affirmative side of MAD-persona.
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MAD-persona prompt- Negative Side
System:
You are debater. Hello and welcome to the debote. it's not necessary to fully agree with each other's perspectives, as our objective to find the correct answer. The debate topic is stated follows: <question>
User: <affirmative answer>
You disagree with my onswer. Provide your answer and reasons.
Assistant:
<answer>
User:
<affirmative answer>
Do you agree with my perspective? Please provide your reasons and answer.
Assistant:
<answera
User:
Assistant:
Figure 36: Prompt of the negative side of MAD-persona.
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MAD-persona prompt Discriminative Mode
System:
You are moderator. There will be two debaters involved in debate. They present their onswers and discuss their perspectives on the following topic: <question>
At the end each round, you will evaluate onswers and decide which is correct.
User:
Now the <number> round of debate for both sides has ended.
Affirmative side arguing: <affirmative answer>
Negative side arguing: <negative answer>
You, the moderator, will evaluate both sides' onswers and determine if there clear preference for an answer candidate. If so, please summorize your reasons for supporting offirmative/negatin and give the final answer
you think correct, debate will continue to the next round. Now please output your answer in json format, with the format as follows: { ("Whether there is preference": "Yes or No", "Supported Side": "Affirmative or Negative", "Reason": "debate onswer": ""). "debate onswer" in the format should only be the right answer. Please strictly output in json format, do not output irrelevant content.
debote conclude. If not, the
Assistant:
<answer>
User:
Assistant:
Figure 37: Prompt of the discriminative mode of MAD-persona.
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---

Published as a conference paper at ICLR 2025
MAD-persona prompt- Extractive Mode
System:
You are moderotor. There will be two debaters involved in debate. They will present their onswers and discuss their perspectives on the following topic: <question>
At the end of each round, you will evaluate onswers and decide which is correct.
User:
Affirmative side arguing:
<affirmative answer>
Negative side arguing: <negative answer>
Now, what candidate answers do we have? Present them without reasons.
Assistant:
kanswerz
User:
Therefore, what is the correct onswer the following question?
<question>
Please summarize your reasons and give the final answer that you think is correct. Now please output your answer in json format, with the format as follows: !"Reason": " "debate, answer": ""). "debate answer" in the formot should only be the right answer. Please strictly output in json format, do not output irrelevant content.
Assistant:
kanswer>
Figure 38: Prompt of the extractive mode of MAD-persona.
58

---

Published as a conference paper at ICLR 2025
MAD prompt
User:
<prompt of one reasoning method> (All agents think with the same method.)
Assistant:
<solving process>
<answer>
User:
These are the answers to the question from other agents:
One agent answer: ""(solving process 1, answer 1)"" One agent answer: ""(solving process 2, answer 2)"
Using answers from other agents as additional informotion, can you provide your onswer the question?
<question>
Assistant:
<answer>
User:
Assistant:
Figure 39: MAD prompt.
59

---

Published as a conference paper at ICLR 2025
DMAD prompt
User:
sprompt of one reasoning method> (All agents think with different methods.)
Assistant:
<solving process>
<answer>
User:
These are other answers to the question using different reosoning methods:
One answer: ""ssoling process 1, answer 1)" One answer: [ssolving process answer 2}" "*
Using the answers of different methods as additional information, can you provide your answer the question?
<question>
Assistant:
kanswer>
User:
Assistant:
Figure 40: DMAD prompt.
60


Reviews:
[{"review_id": "jDunk3Jn0K", "reviewer": "Reviewer_PpgF", "summary": "This paper proposes Diverse Multi-Agent Debate (DMAD), an improved version of Multi-Agent Debate (MAD) that leverages agents using different reasoning methods to break \"mental set\" and enhance reasoning performance. In DMAD, each agent adopts a distinct prompting strategy (e.g. chain-of-thought, step-back prompting, program-of-thoughts) to generate solutions. The agents then review each other's solutions, extract insights from the different reasoning approaches, and iteratively refine their own responses. Experiments on both language models and multimodal language models across various benchmarks demonstrate that DMAD outperforms MAD with homogeneous reasoning as well as other baselines like self-reflection methods. Key results include DMAD in 2 rounds surpassing MAD in 5 rounds, and improvements of 7-8% on metrics compared to 5% for standard MAD. The paper provides a systematic analysis of DMAD, showing performance improves with more debate rounds and agents using a greater diversity of reasoning methods.", "questions": "Some questions came up during the analysis:\n\nHow does DMAD perform on tasks that require multi-hop reasoning over longer contexts? Do the gains over baselines hold there as well?\nExpanding on the above,  it would be great to see MMLU results, even if just on a subset of subjects most relevant to reasoning.\nCan the authors comment on the computational overhead of DMAD compared to standard MAD, both at inference time and during the debate rounds?\nSince multimodal models are more computationally intensive in general, were the number of trials/random seeds adjusted for those experiments? Clarifying those details would be helpful.\nFigure 1 is quite interesting - if space permits, visualizing even more of the ablations (number of rounds, removing step output, etc) in this format could provide further insight.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1) The key idea of using diversity in reasoning methods to break mental set and improve multi-agent debate is novel and creative. This can leverage different type of strneghts and activation patternsa of LLMs at inference time to produce diverse outputs. This leverages the ideas from cognitive science - the idea of mental set is interestijng.\n2) The approach is evaluated across a variety of models (multiple open and closed-source language and multimodal models), datasets/tasks (4 language and multimodal benchmarks), and against strong baselines (standard MAD, self-reflection methods, etc). The authors demonstrate that DMAD approach works well.\n3) The ablation studies on number of agents, debate rounds, importance of thought process, etc provide ways to undersstand the robustness of the papers results.", "weaknesses": "While the experiments cover a good range of models and tasks, it would have been nice to see results on more challenging reasoning datasets like MMLU to further validate the approach.\n\nWhile the paper shows that using agents with diverse reasoning strategies is helpful, its not clear on what kind of diversity is most effective. The authors use three pre-defined reasoning methods (chain-of-thought, step-back, program-of-thoughts), but do not explore other possibilities or study the properties of these methods that make them complementary. A more principled analysis of reasoning diversity could be helpful. \n\nThe paper shows the benefits of DMAD with a fixed number of agents (3) and debate rounds (2-5). However, there is no systematic analysis of how the performance and computational cost scale with these parameters. In real-world applications, it may be necessary to use a much larger number of agents and rounds to tackle complex reasoning tasks. Understanding the scalability properties of DMAD is important. \nAlso, for the multimodal experiments, it's unclear if the visual information is playing an important role. Adding experiments on more vision-centric tasks/datasets could strengthen this aspect. \nIts also not well discussed why self-reflection methods struggle on multimodal tasks compared to language-only tasks. Is this an inherent limitation or due to the specific self-reflection approaches used?\n\nThe paper is a good start but stops short on addressing these points.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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": "365jSlfunG", "reviewer": "Reviewer_QNMW", "summary": "The pair introduces Diverse Multi-Agent Debate (DMAD), a new method that encourages AI agents to employ different reasoning approaches when debating to solve problems. Unlike traditional MAD, in which agents use the same reasoning method, DMAD assigns distinct reasoning strategies to each agent. DMAD consistently outperformed other methods across multiple benchmarks, demonstrating that diverse reasoning approaches can help break mental sets - the tendency to approach problems in fixed ways based on past experience. This work provides a promising direction for enhancing AI reasoning capabilities without requiring model retraining.", "questions": "1: Is there a reason you chose the 3 reasoning strategies (CoT, SBP, PoT)? How about others like least-to-most prompting (Zhou et al., 2023)?\n\n2: Could the system dynamically adjust its reasoning methods during the debate process? For instance, could agents switch reasoning strategies based on the progress of the debate or the nature of disagreements that emerge? \n\n3: Why do you focus on mathematical reasoning and visual understanding? How about other tasks?\n\n4: What criteria determine the ideal number of debate rounds?  Examining Figure 4 (Performance with increased rounds), there's an interesting pattern where DMAD sometimes achieves better performance in 2 rounds than MAD does in 5 rounds, however would a smarter stopping criteria can help mitigate the problem?\n\n\nReference:\n\nZhou, Denny, Nathanael Schärli, Le Hou, Jason Wei, Nathan Scales, Xuezhi Wang, Dale Schuurmans, Claire Cui, Ed Chi, Yun-Hsuan Sung, Daphne Ippolito, and Claire Cassidy. 2023. \"Least-to-most Prompting Enables Complex Reasoning in Large Language Models.\" In International Conference on Learning Representations (ICLR).", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 1, "strengths": "1: The solution is simple since it doesn't require model retraining or additional data collection, making it immediately applicable.\n2: The research provides extensive experimental validation across multiple dimensions and shows consistent improvements.", "weaknesses": "1:Resource Efficiency Analysis\n\nThe paper lacks a critical discussion on computational efficiency and practical costs. A detailed analysis comparing token usage, API costs, and computational overhead between DMAD and simpler reasoning strategies would better demonstrate its practical value. This is particularly important for real-world applications where resource constraints must be balanced against performance gains.\n\n2: Weak Theoretical Foundation and Empirical Evidence\n\nWhile the paper draws motivation from psychology's \"mental set\" phenomenon, the connection appears tenuous. Traditional MAD with a single reasoning method (e.g., CoT) achieves comparable performance to DMAD (as shown in Table 1), suggesting that method diversity might not be the key driver of improvement (Or statistical significance should be provided). This weakens the paper's central thesis that diverse reasoning methods are necessary to break mental set, as even fixed methods can yield different problem-solving approaches through debate. This raises questions about whether the gains are truly from method diversity or simply from the debate process itself (which also encourages some sort of \"divergent thinking\").\n\n3: Model Capability Scaling\n\nThe paper's focus on large, capable models leaves an important question unexplored: could smaller models using DMAD potentially outperform larger models using simpler reasoning methods? This comparative analysis would better demonstrate the method's value proposition, especially for scenarios where using large models isn't feasible. Understanding how DMAD's effectiveness scales with model size could provide valuable insights for practical applications.\n\n4:Limited Implementation Guidelines\n\nDespite DMAD's potential impact on engineering workflows, the paper lacks concrete guidance on implementation decisions. Critical questions remain unanswered; See Questions blow for more.\n\n5: Incremental Rather Than Novel Contribution:\n\nWhile the paper effectively implements diverse reasoning in a MAD framework, the core concept builds on existing ideas. Similar approaches of leveraging diverse perspectives for improved reasoning have been explored in recent work (Zhang et al., 2024). Although DMAD shows impressive results, its primary contribution appears to be an incremental improvement (applying diversity to MAD) rather than introducing a fundamentally new concept to the field.\n\nReference:\nZhang, W., Shen, Y., Wu, L., Peng, Q., Wang, J., Zhuang, Y., & Lu, W. (2024). Self-Contrast: Better Reflection Through Inconsistent Solving Perspectives. 2024 ACL.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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": "ce8owtRf1B", "reviewer": "Reviewer_pspo", "summary": "The paper presents a new method, Diverse Multi-Agent Debate (DMAD), for enhancing the reasoning capabilities of large language models (LLMs) by incorporating diverse approaches to problem-solving within a debate framework. The approach builds on the Multi-Agent Debate (MAD) method by requiring each agent—represented by an LLM—to employ a unique reasoning strategy in order to address a shared problem. Traditional techniques, such as self-reflection, are limited by the model's fixed patterns of reasoning, and MAD likewise suffers when agents adopt similar approaches due to inherent limitations in reasoning diversity. By (manually) instructing each agent to use a distinct reasoning approach, DMAD seeks to enhance solution accuracy across problem-solving scenarios. In each debate round, agents independently solve a problem and then iteratively refine their solutions using insights from other agents' approaches. DMAD is tested on multiple models, including GPT-4o-mini, LLaMA-3-70B, LLaVA-1.6-13B, Gemini-1.5-Flash, and GPT-4o-2024-05-13, demonstrating overall positive, though incremental, performance gains across benchmarks.", "questions": "## General Questions\n1. In Table 1, for the Alg. column and the LLaMA model, the value 72 achieved by DMAD is not the highest (c.f. MAD (All CoT) and CoT - SC); is this a typo or a correct results (in the latter case, please correct the text bolding)?\n2. Do you believe there would be merit in attempting to set up another LLM to propose reasoning strategies, instead of having them fixed? I understand this is a feat warranting a paper on its own, though I'm quite curious about such applications, as it would allow one to close the loop — having reasoning strategies being proposed and directly “evaluated” by the agents;\n3. Have you examined setups with more than 3 agents? Building on my previous question, I assume it's not as straight forward to find additional reasoning strategies that would be assigned to new debaters? Do you believe, given more reasoning strategies, that the performance of the method would scale up with the number of agents, or would it plateau, similar to what happens with the number of rounds?\n4. I got confused when reading Eq. 3 and Eq. 4; namely, history $\\mathbb{H}$ is defined as a set of tuples, one per agent, each of which containing information pertaining to a particular agent (question, solving process, answer). Perhaps I am missing something obvious, but in Eq. 4, wouldn't it be sufficient to simply define $h_i \\equiv \\mathbb{H}$ because $\\mathbb{H}$ by definition contains the information tuple for the agent $i$, but also for all other agents? To quote the paper “*$h_i$ represents the history of messages for $M_i$, extended with messages from other agents*”, which to me looks exactly like $\\mathbb{H}$?\n5. Regarding the MATH benchmark, could you provide some intuition on why the performance degrades after 3 rounds (for GPT-4o-mini) compared to 2 rounds? Additionally, why does the LLaMA model's performance improve linearly with more rounds using the MAD method, but drops after the third round with DMAD? Do you have any insights into what kinds of mistakes are being made with additional rounds when using DMAD?\n\n## Minor Comments\n- Line 157: Did you mean to write $h_i$ instead of $A_{i,1}$? The variable $A_{i,1}$ is not referenced in Eq. 1;\n- Line 314: Shouldn't this be \"DMAD\" instead of \"MAD\"?\n- Appendix Figures (e.g., 9, 10, 11, etc.): The figures are difficult to interpret due to the formatting characters. You may want to include pre-formatted versions for clarity and consider adding a footnote explaining that the agents actually receive raw markdown text, if necessary.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "The paper contributes meaningfully to the ongoing exploration of multi-agent debate in LLMs by proposing a straight forward extension of the MAD approach that encourages diverse reasoning within the debate process. DMAD's design is simple and builds logically upon MAD, representing an incremental advance. The experiments are comprehensive and cover multiple relevant benchmarks, which gives a well-rounded view of DMAD’s performance. The inclusion of evaluations across various LLMs, both uni- and multimodal, is particularly nice, as it demonstrates the method's effectiveness across different architectures and contexts. The results show that reasoning techniques enforced by DMAD enhance performance on most tasks, confirming that diversity in reasoning approaches can be advantageous even if the cumulative improvement is moderate. Overall, the paper is clearly written and presents a straightforward extension to the multi-agent debate approaches in LLMs, supported by compelling experimental results.", "weaknesses": "While DMAD is a nice addition to the multi-agent debate line of work, its novelty is limited. The method represents an incremental improvement rather than a fundamentally new concept. The debate setup in DMAD may be perceived as a minor extension of the MAD framework, as it mainly focuses on modifying agents’ reasoning patterns. I would have liked to see additional investigations that more deeply alter the default setup of the debate, even if it was as “simple” as running an ablation study with different number of agents. Additionally, while DMAD shows an overall improvement, some gains are marginal or even negative, raising questions about the method’s broader applicability. Though the authors attempt to reason about cases where DMAD's performance lags behind other approaches, the study could benefit from a more thorough investigation of typical mistakes made during debating with DMAD.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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:

Decision: Accept (Poster)