Context Learning for Multi-Agent Discussion
Authors: Xingyuan Hua
Sheng Yue
Xinyi Li
Yizhe Zhao
Jinrui Zhang
Ju Ren
Venue: ICLR 2026 Poster (2026)
Keywords: Large Language Models
Context Learning
Multi-agent discussion
Primary area: generative models
TL;DR: We introduce a new context learning method for multi-LLM systems that can continually adjust LLMs' context based on the current state of discussion, enabling agents to effectively collaborate.

Abstract: Multi-Agent Discussion (MAD) has garnered increasing attention very recently, where multiple LLM instances collaboratively solve problems via structured discussion. However, we find that current MAD methods easily suffer from discussion inconsistency—LLMs fail to reach a coherent solution—due to the misalignment between their individual contexts. In this paper, we introduce a multi-LLM context learning method (M2CL) that learns a context generator for each agent, capable of dynamically generating context instructions per discussion round via automatic information organization and refinement. Specifically, inspired by our theoretical insights on the context instruction, M2CL trains the generators to control context coherence and output discrepancies via a carefully crafted self-adaptive mechanism. It enables LLMs to avoid premature convergence on “majority noise” and progressively reach the correct consensus. We evaluate M2CL on challenging tasks, including academic reasoning, embodied tasks, and mobile control. The results show that the performance of M2CL significantly surpasses existing methods by 20\%--50\%, while enjoying favorable transferability and computational efficiency.\footnote{Code is available at \url{https://github.com/HansenHua/M2CL-ICLR26}.}

Published as a conference paper at ICLR 2026
CONTEXT LEARNING FOR MULTI-AGENT DISCUSSION
Xingyuan Hua', Sheng Yue"; Xinyi Li', Yizhe Zhao', Jinrui Zhang', Ju Ren 14 'Department of Computer Science and Technology. Tsinghua University, School of Cyber Science and Technology, Sun Yat-sen University, *College of Computer Science, Northwest University, *State Key Laboratory of Internet Architecture, Tsinghua University
ABSTRACT
Multi-Agent Discussion (MAD) has garnered increasing attention very recently, where multiple LLM instances collaboratively solve problems via structured dis- cussion. However, we find that current MAD methods easily suffer from discussion inconsistency-LLL.. M.LMs fail to reach coherent solution due the misalignment between their individual contexts. In this paper, we introduce a multi-LLMM context learning method (M2CL) that learns a context generator for each agent, capable dynamically generating context instructions per discussion round via automatic information organization and refinement. Specifically, inspired by our theoretical insights the context instruction, M2CL trains the generators to control context coherence and output discrepancies via a carefully crafted self-adaptive mecha- nism. It enables LLMs to avoid premature convergence on "majority noise" and progressively reach the correct consensus. We evaluate M2 on challenging tasks, including academic reasoning, embodied tasks, and mobile control. The results show that the performance of M2CL significantly surpasses existing methods by 20%-50% while enjoying favorable transferability and computational efficiency]
INTRODUCTION
Large Language Models (LLMs) have demonstrated transformative impact across large number of real-world domains, including education, healthcare, and scientific research, where an LLM instance
is employed automate the process of content generation, reasoning, or decision-makinn
ZZeng
eet al. 2023 [mani et al. 2023 ZZhng et al. 2024 Goyal et al. 2024 Wu et al.) [025 Yu et al. 2025).
Yet, it has been recognized that Single-LL.M-buus
systems often struggle in the problems requiring
complex multi-step reasoning or multi-tool using, such as complicated proof (Cobbe et al. 2021
large-scale code generation (Wang et al. 2025). and embodied agentic tasks (Ahn et al.) [022] Shen
et al. 2024), because its single viewpoint of problem easily limits the ability to explore multiple reasoning paths, leverage external tools effectively, or adapt dynamic task requirements
et al.
2023 Smit et al. 2024).
Very recently, research has shifted towards Multi-Agent Discussion (MAD) (Smit et al. 2024 where multiple LLM instances collaboratively solve problems via structured discussions (Du et al. 2023
Liu et al. 2024). a typical MAD framework, each LLM instance is pre- assigned a set of crafted contexts that represent diverse solution perspectives of the problem to be solved. Equipped with these distinct context instructions, LLMs continue to discuss with each other for a solution consensus (Park)
al. 2023 Shanahan et al. 2023 Wei et 2023 Lu et al. 2024 Liu et al. 2024). Such 'society-of- mind paradigma igms are expected to improve reasoning accuracy by enhancing creativity and expanding the search space for possible solutions, and have shown great potential across various complex tasks,
including software engineering (Gu) 2023) and scientific discovery (Sprueill et al., 2024).
Albeit achieving improved performance over single-L.LM settings, find that current multi-agent collaboration approaches typically suffer from discussion inconsistency, that is, the majority of LLM instances fail to reach an agreement on coherent solution (as showcased in Fig. 2 easily making the collaborative decision dominated by noise rather than principled reasoning. The underlying reason
"Correspondence to: yuushh5mail..sg www.suueeddccmmm
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ICLR26

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Published as a conference paper at ICLR 2026
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Figure I: An illustration of context misalignment of an existing method (Debate Du et al. 2023 on multi-step proof task. Pre-assi Pre-assigded context instructions (in the blue and yellow boxes of the left part) provide insufficient guidance on information fusion, leading to conflict in reasoning.
MMLU
MATH 15
GPQA
Code
155
Discrepancy
12
Discrepancy
12
Discrepancy
12
12
Rounds
Rounds
Rounds
Rounds
Debate
MacNet
DyLAN
- M2CL (ours)
Figure 2: The discrepancy between the answers of participating LLM instances. The discrepancy is
characterized by the maximum distance between participating LLMs' output embeddings.
primarily lies in context misalignment between LLMs. On one hand, the pre-assigned contexts or role-based instructions lack nuanced understanding of the task; they are often rigid. incomplete or biased, which would misguide the reasoning of individual LLMs (Jang et al. 2025). On the other hand, these contexts often fall short in effective fusion of information exchanged among LLMs, and thus hardly steer the discussion towards coherent solutions. As illustrated in Fig. [ for multi-step mathematical proof task, one L.LM agent may correctly derive an intermediate result, yet another LLM- receiving this result in the extended context-dovd not effectively incorporate it into its own reasoning chain. Since the context instruction does not explicitly enforce leveraging conclusions from other LLMs, other LLMs may redundantly re-derive the step or even give an inconsistent argument (see Appendix HD for full results).
This paper aims answer: "how
obtain the contexts for MAD that can continually guide Lulti-LLM discussion towards a correct consensus?" A straightforward solution is to manually adapt instructions in contexts as the discussion progresses. It, however, is labor-intensive and requires extra expert knowledge, rendering it impractical for complex tasks or large-scale collaboration. Instead, a more reasonable approach is develop context learning mechanisms that enable evolving the context instructions based on the intermediate discussion results. Although promising, it is highly challenging evaluate the contribution of LLMs' contexts to the final solution and control the coherence among inter- and intra-LLM, outputs.
To tackle these challenges, we propose a multi-LLM context learning (M2CL) method for efficient MAD, which learns a context generator for each agent, capable of dynamically generating context instructions per discussion round via automatic information organization and refinement. First, we characterize the impact of initial and evolving contexts on the discussion performance. Building upon the analytical insights, we train the generators to control context coherence and output discrepancies. To strike the right tradeoff' therein, we devise self-adaptive balancing mechanism, enabling LLMs to progressively align on correct consensus while avoiding premature convergence on "majority noise". Further, develop lightweight context initialization approach. which tends to assign LLMs with diverse initial instructions that are approximately orthogonal in the latent space, enabling sufficient coverage of complementary solution perspectives.
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We systematically evaluate the proposed method across 9 challenging benchmarks, including LLM reasoning, embodied agentic tasks, and mobile GUI control. The results demonstrate that M2CL significantly enhances the MAD performance under various numbers of participating LLMs, con- sistently outperforming existing methods by 20%-50% particularly in complex GUI control tasks. M2CL enjoys more favorable MAD "scaling law" and exhibits great efficiency, where runtime overhead of at most 10% suffices to achieve more than 20% performance gains. Further, we find that the learned context generators can be migrated different LLM architectures with consistent performance improvement.
Our main contributions are summarized as follows:
We propose M2CL, a principled multi-LLM context learning method that learns a context generator for each agent, capable of dynamically generating context instructions per discussion round.
We devise a lightweight context initialization approach that can assign LLMs with diverse initial instructions, thereby enabling sufficient coverage of complementary solution perspectives.
We systematically evaluate the proposed method across range of challenging benchmarks and corroborate the efficacy and efficiency of the proposed method.
RELATED WORK
Multi-agent framework. Multi-agent frameworks have been proposed to enhance the reasoning
capabilities of single-LLM prompting methods. Several works utilize two LLMs to iteratively generate and evaluate to refine the final answer (Raman et al. 2022, Yao et al. 2023 Paul et al. 2023 Madaan et al. 2024). However, scaling them to larger number of LLMs to make full use of the wisdom of crowd is challenging due to the pairwise dependency of generation and evaluation. To incorporate more LLMs, several studies have explored another multi-agent framework in which
each LLM has access the history of all preceding LLMs' responses (Chan et al. 2023 Du et al.)
2023 Liang et al.] 2023 Smit et al.) 2024 Liu et al. 2024 Zhuge et al., 2024). Most existing
methods remain constrained by manually defined inter-LLM topologies or workflows. More recently.
researches have attempted to overcome this limitation by automatically optimizing workflows (Zhuge)
al. 2024 Liu al., 2024, Zhang et al., 2025b). However, such evolution is often one-shot. For instance, Zhuge et al. 2024) describe language agent systems as optimizable computational graphs and enables automatic improvements of LLM prompts and inter-LLMM orchestration. [Zhang et al.) (2025b) employs Monte Carlo Tree Search to construct complex Multi-LLM systems tailored to specific task domain. [Lu et al. (2024) propose a multi-LLM collaboration method which constructs dynamic communication structure by scoring other LLMs. While these approaches allow for scaling the number of LLMs, designing appropriate contexts for them to collaboratively solve problems remains difficult, single-viewpoin context instructions fall short in guidance how organize and refine information across agents.
Context learning. Context learning has recently attracted significant attention, as it allows LLMs to adjust their behavior at inference time by modifying the input context, without requiring any prddeent-based training Von Oswald al. (2023); Todd al. (024): : Li et al. (2024)). One line of work focuses on context selection, which identifies the most relevant example es or information to include in the context Zhang et al.) al., (2022) Lu al. X et al. (2024); ; Purohit et al. (2025). To eliminate manual selection, Lu et al. 2023) leverage reinforcement learning to learn a context selection policy. Xiong al. (2024) query LLM to obtain knowledge and then query a retriever to obtain the final context. Beyond selection, some recent methods have proposed to generate or evolve context (Zhuge et al.) 2024 Li et al.) 2024bb Zhang et al.) 2025a). Madaan et al. (2024) leverage feedback generated by LLMs extra prompt and iteratively incorporate it into revised drafts, aiming to enhance the coherence of the generated text. Pandita et al. (202)) dynamically refines prompts during inference using textual feedback from prior outputs. aiming to improve contextual alignment and generate more consistent responses. Albeit with promising results, these methods are grounded in single-I.L.M formulations and struggle with inter-LIM inconsistency during multi-agent dscussion, where it is crucial to guide L.MMs to make full use of others' intermediate results.
PRELIMINARIES
In this section, we provide necessary backgrounds and definitions of our investigated problem.
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Context learning. To formally define context learning, we begin with the standard probabilistic model of an autoregressive LLM. An autoregressive model, parameterized by o. generates an output sequence X (21, 22.............................. L1) given input context C' by maximizing the conditional probability:
L Px(X II Pa(xr|ze1.O)
(I)
Historically, the paradigm of prompt engineering, the context C was treated as a static string of text. This view is insufficient for complex agentic tasks which leverage dynamic, structured, and multifaceted information stream. To address this, context learning is redefined as dynamically organized collection of information, denoted {ci, C2,.... ..... Co Each component сą can be in- structions, external knowledge (Lewis et al., 2020), available external tools (Qin et al. (023), and memory (Zhang et al., 2025a). These components are soureed, filtered, and formatted by set of functions Jk. and orchestrated into coherent representation by high-level assembly function A:
C = filo)))..................
(2)
Multi-LLL context learning. MAD involves a set of N L.LM instances collaboratively solving a task via multi-round inter-LLM discussion (debate). Each LLM is endowed with an evolving instruction context in terms of the task description, available external tools and current knowledge aggregation. At the t-th round, we use the concatenation function as the assembly function A and construct the context with three components: (i) the task goal P Roddet
(ii) the concatenation of responses from "y R RRdmedee where X the response of LLM j at round & - 1, and (iil) the current instruction context 1 E RRdmodde xn (dmodel refers the dimension of embedding). The task goal represents the ultimate objective of collaboration and remains invariant across rounds. The second component serves as dynamic memory that incorporates cross-LLM interaction history. For the third component, constrast to existing efforts relying on static preassigned roles, we employ instruction generator G, parameterized by 0,, to adaptively refine it into a per-step instruction 75 conditioned on the task goal P, the initial instruction 1h, and the concatenated response X!-1:
all other LLMs in the previous round X [X] Daye
1, = (IP:
Given context C = [ X!-1 P). each LLM i, parameterized by Φs. generate its response by:
x = arg max Pa, (X)C)).
(4)
X
After T rounds of interaction, the final result is obtained by majority vote the LLMs' outputs generated in the final round.
4 MOTIVATION
In this section, we investigate the quantified impact of the contexts on the MAD performance. First, we introduce the formulation of attention activation, denoted a(-), (.), as follows Vaswani 2017):
al (CC)) = W (Wx X PI WPP
(5)
Vd
where Vd is a scaling factor. Wo. WK. and Wy denote the parameter weight matrices in the attention mechanism. a(O)) E X X is a matrix with the same shape as [P]
From this, we have the following theorem characterizing the total distance between the activations of the correct answer aę and that induced by context CJ. Here, we utilize activation distance instead of token embedding distance attention activation captures deep representational similarity learned through the model's internal reasoning process, making it more robust to superficial linguistic variations.
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Theorem 4.1. Assume that the attention activation function is Lg smooth and define the weight vector as w [11 w2...... ,WN,, with the initial context C [ Pl. Then, the following fact holds:
Σ Na. a(c))
|a(C)) - -(CC))((C))) (N 1)LalIC c
N min |
(ra(C)))]
(6)
Proof. For a detailed proof. please refer to Appendix B
Theorem 4.1 corroborates the necessity of multi- context learning, consisting of both initializa- tion and evolution. The first term, |la(C)) a( (I (N + 1) - captures the divergence among L.Mss' activations as well as the deviation from their initial contexts. This indicates contexts must be continuously evolved reduce inter-LLM discrepancies while keeping coherent, promoting consistency of reasoning chains. The second term, min,, ||a, Σ ara(CC)) depends solely on the initial contexts T.. implies that orthogonality among initial activations provides compre- hensive basis, allowing the contexts to approximate the correct activation more effectively. This highlights the importance of diverse solution perspectives at the initialization stage. Together, the result motivates two-stage design: initializing contexts to ensure diverse solution perspectives and evolving intermediate contexts to drive a consensus across LLMs.
5
MULTI-LLM CONTEXT LEARNING
In this section, introduce multi-LLM context learning method that select appropriate contexts for each LLM and dynamically adapt the context according to the evolving task completion status.
5.1 CONTEXT INITIALIZATION
The context initialization serves as the foundation of the entire multi-agent interaction process, it frames the capability scope LLMs and fundamentally shapes the chain of subsequent information exchange. Therefore, we propose to select initial contexts from predefined pool { Jizi containing prompts with diverse perspectives.
Motivated by Theorem
4.1 we provide the following context initialization mechanism:
I = (1) , 1&
arg min min
w PJ a.>il
Eq. (7) identifies a subset of contexts I whose activation best reconstruct the target activation de- As the dimension of the activation matrix a(I4;; PJ) E IR Rddmodet xn is far larger than the number of selected contexts N, of matrices that aims best reconstruct the correct activation a, naturally tends toward forming set of basis-like directions. The resulting near-orthe orthogonal activations form compact basis, ensuring each context contributes unique, non-overlapping information for subsequent discussion.
However, Eq. 7 impractical since the correct activation ag is not accessible during initialization. Inspired by prior work (Yang et al.) 2024b 2025), we project the activation into a latent space with function f:
r (T)
1 = arg min min
oa PD) aaf(a((T:PP)) f(a))l
(8)
Then, the problem space the selected contexts solely dependent the problem. This projection preserves the original orthogonality properties activations, ensuring that diverse perspectives remain distinguishable in other spaces. Therefore, reformulate the initialization
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mechanism:
1 (li..... 1& arg min
min
wi wi (a(l) - vell..
where up denotes the sentence vector of the question P. To obtain the projection ʃ(-) (parameterized by Φy), we utilize the activation of inputting the answer A with the question P as the correct activation a. a[[[; PI) and provide the loss function as:
L(dr) = - ((ap,
(10)
However, directly leveraging Eq. 9 to initialize context is computational costly it requires all the context activations the context pool. Therefore, we distill a lightweight F(-) (parameterized by Φ5) which directly projects the initial context into the problem space through the following loss function:
L(FF) |F( PJ) f(a((2)
(11)
Then, we provide the final context initialization as:
1 (19. 1& arg min { min Σ [wFF(LHPP)) vp
(12)
Eq. provides a computational efficient context initialization (as illustrated in Fig. 23 that aligns with Eq. 7 to encourage orthogonality of selected context activations, thereby providing diverse reasoning perspectives and expanding the search space for solutions.
5.2 CONTEXT EVOLUTION
As discussed in Section context initialization aims to select contexts with diverse perspectives solve the problem. Nevertheless, these individual contexts address the problem from single viewpoint while lacking explicit instructions on how to incorporate perspectives provided by other LLMs. Directly using them often results in inconsistent reasoning across LLMs due to misaligned inter-LLM guidance. To address this, we iteratively refine the instruction to integrate collaborative instructions that guide the LLMs more effectively toward generating the desired solution.
5.2.1 EVALUATE THE CONTRIBUTION OF CONTEXTS
To achieve efficient context evolution, it is crucial to quantify the contribution of different contexts (refer to a utility function). A natural solution is to assign utilities only at the final round. However, this leads inefficient and unstable training process due to its sparsity Liu al. (2025). On the other hand, current methods typically use correctness as the only criterion (Zelikman et al.) 2022 [aaailoy ct al. [023] Guo al., 2025). Albeit with promising performance single-LLM question answering. this simple criterion ignores the complex dependency among LLMs with different contexts in MAD. As result, an L.LM that provides crucial insights which enable others reach the correct answer may still receive low utility, simply because it fails to produce the correct final answer itself. To tackle these challenges, we introduce novel found-wise criterion to evaluate the contribution of C₁ in multi-agent interaction:
max JEIN { - - - - a(C)))
(13)
where a 2 0 is weighting parameter and ||a(C)) aCC))) represents the activation difference between contexts.
Remarks. Of note, if removing the second term of Eq. (3), the context generation reduces to that of prompt engineering: miny; ΣieNN) al|[C C+ which utilize fixed instructions in contexts to
2024 Lu et al. 2024). As mentioned in Section I this LLMs throughout the discussion (Liu et al.
easily results in inconsistency across LLMs. Thus, we introduce [a(C)) a(C)) into the objective to encourage LLMs to remain aligned with each other.
This design addresses the two aforementioned challenges. First, this round-wiss wise criterion provides denser feedback, mitigating the inefficiency and instability caused by sparse final-round utilities.

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Second, the activation- based alignment term captures inter-LLM dependencies, thereby encouraging them to offer guidance on how to integrate others' responses.
Applying Eq. 13 the criterion for LLM requires the contexts of all other LLMs. However, since these contexts are simultancously being optimized, a bias inevitably arises as each LLM is updated based stale snapshots of others' contexts. Such outdated information introduces biased utility, which in turn hinders consistency and degrades the quality of the learned contexts. To overcome this issue, decouple the inter-LLM dependencies by designing an alternative per-LLM criterion:
-alCc; - - [| ; PI) a([x;' [[[XX;-,,000 PDIII
(14)
In Lemma C.1 can prove that the summation of Eq. [4] over all LLMs serves upper bound of the summation of Eq. (13) over all LLMs. Intuitively, this criterion conveys a clear meaning: the first term, -a: = C preserves the fundamental problem-solving capabiliity endowed by the initialization, while the second term, -I|a((Z} Pl) - aa[x;; PI) enforces consistency between an LLM's current instruction and its own previous response. This local consistency constraint implicitly aligns all LLMss, because when every I.LM evolves its context in temporally coherent way, the divergence among them is gradually reduced. Hence, the collective effect of all LLMs following this rule is that their contexts evolve coherently across rounds, progressively shrinking activation differences and ultimately driving the MAD toward consistency in their final answers.
To intuitively show the tightness of the bound, consider the case where I X!-1 holds, i.e., the instruction of each LLM in the next round equals its response in the previous round. That means a(I)) a( a(X)')). Given that all LLMs receive the same context, the second term of both Eq. (1) and Eq. 14 becomes zero. In this case, the two formulations coincide.
5.2.2 MUL.TI-RUNND CONTEXT EVOLVING
We slightly abuse notation by denoting a(I,) a([I;; and a(X:-1) a(xxp'' P)), and provide the multi- context evolution objective by accumulating contributions as follows:
T
Σ max { - 1 (a((1) - a 1
(15)
However, selecting the optimal value for the weight a is non-trivial, as it must be carefully tuned for the evolving discussion process. To alleviate the need for manual tuning, we recast Eq. (15) into constrained optimization problem, where the context adjustment ||4] 1.'l is treated as a constraint:
min (la(()) - a(x9)) min (lall3) -((x/)l +... min (la((F) a(x? a(x?-))l)
12
R
s.t. - -
S B,
V.
(16)
According the detailed derivation in Appendix E
prove that taking the dual of this problem recovers Eq. (15) and yields an auxiliary update for the dual variable a. Consequently, the optimiza- tion of Problem (16) can be implemented using an approximate dual gradient descent procedure, alternating gradient updates of [.,))) and [(ag).
T.(0.) = (ao (P, 14. - I((a,) = az (3 Go. (P, - c
- x(X-- + +allc I
(17)
At the beginning of the discussion, the initial contexts are intentionally diverse to encourage multi- perspective reasoning of the problem. At this stage, when the answers differ greatly, a decreases rapidly, thereby weakening the constraint the distance between the generated contexts and their initial contexts. This guides the generation of contexts towards promoting faster convergence on a unified solution. As the discussion progresses and the LLMs gradually reach agreement, will be kept at a certain level. This adjustment prevents premature consensus and supports a richer, more comprehensive final solution by shifting the contexts' focus toward preserving multiple perspectives and exploring nuanced differences.
Overall, name our proposed algorithm M2CL, with its pseudocode detailed in Appendix F.4
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Table 1: Accuracy (%) different datasets. The number of LLMs is for all dataset. We exhibit the performance advantage with BoN and highlight the best result.
Model
Method
MMLU
MATH
GPQA
Code
ALFWorld SciWorld
GAIA
PDDL
Single
61.2
g2.
20.2
51.2
23.8.
25.2,
15.6
21.0g53
BoN
74.2
24.9rso
36.4rt
62.5rpo
31.5-on
35.3mo
21.1
26.3ro
Debate
7L1
19.9,sn
28.7.13
60.0.15
30.6 c
32.2
21.0
24.8
Qwen
DyLAN
74.3
26.7-1x
35
63.4rs
29.8.
29.4.ca
18.4
23.4
GPTSwarm
76.3
26.2rs3
35.6,08
62.7102
29.9.1a
30.8
20.6
24.5
MacNot
71.5
21.4,35
30.8.16
59.3,3a
33.6
37.0m1
21.5
29.5tsa
M2.1 (ours)
92.5mma
47.8
66.1pm
80.3
39.9
45.3rm
33.6r
34.7
Single
67.2
21.6.s2
21.2
56.7,127
30.1
31.3
18.7.m0
25.7
BoN
79.7
27.8reo
32.8r60
69.4
37.5-00
41.6mo
25.6run
28.3
77.2
27.4.s4
30.3.15
66.9.s
36.8.00
39.4
26.4rux
30.0
Qwen-14B
DyT.NN
86.8
31.2/14
39.4
76.6:1a
34.8,12
36.0;16
22.8,sa
28.0
GPTSwarm
87.0
31.3-1
38.7
75,9ts
34.9.s
35,9
25.0.m
28.4
MacMet
78.9
28.7re9
31.9.c9
70.4
39.2-u.
46.0
32.2
32.7
M2C1 (ours)
93.7
51.7
66.2
48. 48.2
36.1nu4
42.0 .4
43.0r
Single
72.5
31.6.m44
34,9
59.1.
48.2 23
50.4.11>
31.1uaa
41.0.188
BoN
84.2
51 11.0ren
45.9rca
72.2ron
57.5-mn
62.1 mo
41.2
51.0moa
Debate
82.7
48.4.26
43.4.1
69.1.
60.4-19
65.2
42.9
49.1
Qwen-72B
DyLAN
91_5
63.1
$1.6117
80.4
$5.1.3A
58.0,A1
40.4
45.5
GPTSwarm
91_5
64.7
52.4r6
79.6
56.8.07
60.2
40.3,0
49.7
MacNet
83.8
52.9rsM
46.2rta
70.5
61.8-43
68.4
46.4
53.7
M2C1 (ours)
72.5ma1
78.9pm
90.7g185
79.0
88.9
67.2
70.5
GAIA Llama-78 78
ALFWorld Qwen-78
AndroidWorid + Owen VL
12
20
12
Single
Runtime (5)
Runtime (s)
15
*
Runlime (s)
BoN
Debate
10
DyLAN
MacNet
3
GPTSwam
M2CL (Ours)
25
35
25
30
35
25
30
Performance (%)
Performance (%)
Performance (%)
Figure 3: Performance versus runtime under different settings. Circles closer to the lower-left corner
indicate higher efficiency.
EXPERIMENT
In this section, we conduct experiments to evaluate the performance of M2CL by answering the following research questions:
Q1. How does M2CL perform compared to existing methods across various benchmarks, espe- cially in complex agentic tasks?
Q2. How does the performance of MAD scale with the number of LLMMs
Q3. How is the performance affected by factors such context constraint and components such as context initialization and context evolution?
Q4. How do contexts promote consensus, and are they transferable to other models?
6.1 EXPERIMENTAL SETUP
Dataset. We rum experiments with 3 domains including 9 datasets: 1) LLM reasoning, including
MMLU (Hendrycks et al., (20TT), MATH (Hendrycks al.) (02T), and GPQA (Rein al. 2023).
HumanEval (Chen et al. (021). ). 2) Embodied Agentic, including ALFWorld Shridhar et al. 2021
SciWorld Wang
(2022), GAIA (Mialon et al. 2024). and PDDI, Chang et al. (2024). 3) Mobile P
GUI AodroidWorld Rawles et al. (2025). Details on datasets can be found in Appendix F.I
Baselines. We evaluate our method against six strong baseline methods: 1) Single execution. querying a single LLM to solve the task. 2) Best-on of N, querying single LLM N times and sampling the most correct answer. 3) Debate e (Du et al. 2023), a multi-agent framework where LLMs discuss their responses and reasoning processes over multiple rounds. 4) DyLAN (Liu et al.) 2024), a multi-agent framework where LLMs score each other and collaborate dynamically. 5) GPTSwarm rm (Zhuge et al. 2024), multi-agent framework that refines L.LM prompts and improves
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MATH
GPQA
GAIA
AndroldWordd
40
100
40
50
Accuracy
30
80
30
40
30
20
20
10
0
32
64
16
32
64
4
8
16
32
64
4
8
16
32
64
Number of agents
Number aggnnts
Number agents
Number agents
M2CL (ours)
Single
BoN
Dibote
DyLAN
GPTSware
MacNel
Figure 4:
Performance of varying the numbers of LLMs. Uncertainty intervals depict standard deviation over three seeds.
LLM orchestration by changing their connectivity. 6) MacNet (Jiang et al. 2023). a recent multi- LLM framework where LLMS are invoked between L.M interactions provide actionable instruc- tions to the next LLM based on the previous LLM's outputs.
Reproducibility. All details of our experiments are provided in the appendices in terms of the lasks, network architectures, hyperparameters, etc. We conduct experiment on two series of LLM (Llama-2 Touvron et al. (2033) and Qwen-2.5 (Yang al., 2024a)) and three model sizes each for LLM reasoning, and Qwen2.5-Ve (Bai et al. (025) for GUI reasoning. All the experiments are run on Ubuntu 22. 2.04.4 LTS with 8 NVIDIA H800 GPUs
6.2 EXPERIMENTAL RESULTS
Comparative results. To answer the first question, we evaluate M2CL's performance across all datasets, with varying base models and number of LLMs (ranging from 4 to 64). We select Qwen series models and 4 LLMs participating in Table and provide full results in Appendices G.2 and G.3 We find M2CL consistently outperforms baselines all 9 datasets, often by significant margin in terms of performance. Of note, BoN outperforms most of the baselines especially in complex multi-round agentic tasks, revealing the drawback of fixed contexts, which, despite expanding the exploration space, do not converge and thus hinder LLMs from achieving true cooperative reasoning. In contrast, M2CL can adapt contexts and enhance the relevance responses and questions while ensuring creativity, indicating that M2CL well avoids that LLMs with different contexts easily influence each other and successfully brings LLMs into cooperation by reaching a consensus through discussion.
In addition, we evaluate the efficiency of CL by visualizing the performance versus runtime. As shown in Fig. M2CL consistently delivers the highest performance improvement (more than 20%) while maintaining a modest increase in runtime (less than 10%). This clearly demonstrates the efficiency of M2CL due its lightweight context generator.
Multi-agent scaling law. To answer the second question, we run experiments with varying numbers of LLMSs (ranging from 4 64). The data and parameter setup adhere to that of Table 2 We
present sclected results in Fig. 4 and full results in Tables 4 to and Figs. 5 to I0 of Appendix G.2 Scaling our method reveals more efficient scaling law as the performance grows logarithmically before saturation and improves faster than baselines. We speculate this arises because collaborative instructions in our generated contexts enable genuine inter-LLM cooperation, thereby unleashing the multidimensional reasoning capabilities of the MAD.
Context constraint. To answer the third question, we vary the context constraint from 0 10 and run experiments across all datasets. Full results are shown in Figs. [2] to 16 of Appendix G.4 The results clearly indicate that as 3 increases, there is an initial improvement in performance; once reaches sufficiently large value, performance tends to drop. A strict (refers constraint leads to generated contexts getting closer to the initial contexts, thereby causing discussion inconsistency. On the other hand, loose context constraint leads to naive consistency, where LLMs tend to generate the same answers, resulting in insufficient creativity.
smaller ( context
A Ablation studies. We assess the effect of key components by ablating them on all datasets under the same setting. 1) Importance of context initialization. 2) Importance of tuning a. 3) Importance of context evolution. As illustrated in Tables 11 to 13 LLMS struggle specialize and coordinate

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Published as a conference paper at ICLR 2026
efficiently, whereas context initialization enables them to acquire high-impace contexts, significantly enhancing the foundational capabilities of MAD. Without tuning a during discussion rounds, LLMs tend to reach agreement in the first round, leading to responses that lack creativity and diversity, which ultimately reduces problem-solving ability. Without context evolution, LL.Ms lack collaborative guidance considering previous responses, which prevents them from effectively leveraging the outputs of other LLMs.
Discrepancy intensity. To answer the fourth question, explored the change of Discrepancy intensity (max,,je(N) ||a; ag]l²) with rounds to verify whether the generated context can help the LLMs gradually reach agreement with the discussion. Complete results are shown in Figs. t7 21 of Appendix G.3 We find that discrepancy intensity from M2CL decreases faster than other methods, corroborating its efficacy and superiority in converging the search space of multiple L.Mss.
Transferability of contexts. To answer the fourth question, we also conduct experiments on transferring contexts directly into stronger LLMs verify whether the generated contexts have better interpretation ability and efficacy. Full results are depicted in Table[1Ojof Appendix G.6 The results show that the transferred contexts deliver consistent improvement, indicating that the trained context generator can directly adapt to wide range of models without additional retraining.
LIMITATION AND DISCUSSION
In this paper, we propose a novel context learning method, designed to expand LLMs' horizons and reach consensus in MAD. By initializing and adjusting LLMs' contexts based on the problem and discussion states, our method significantly improves problem-solving capabilities across diverse benchmarks while maintaining computational efficiency. A limitation of M2CL is the MAD framework in which diversity is brought about by the number of LLMs with heterogeneous characteristics which is computationally inefficient. An avenue for future work is to enable LLMs to truly capture the sub-tasks they are interested in or excel at.
ACKNOWLEDGMENTS
This research was supported part by the National Natural Science Foundation of China under Grants 62572496 and 62402269, the Shenzhen Science and Technology Program under Grant JCY120250604 15550000,, and the Young Elite Scientist Sponsorship Program by CAST under Contract ZB2025-218.
ETHICS STATEMENT
This work advances the field of large language model (LLM) research by introducing a context learning method for multi-agent discussion, demonstrating significant improvements in accuracy, diversity, and consensus across multiple benchmarks.
However, the broader implications of deploying such systems warrant careful consideration. Multi- agent discussion, while powerful, may inadvertently propagate biases introduced during context initialization or amplify eтrors during consensus- builddng. These risks are particularly critical in high-stakes domains like legal, financial, and healthcare applications, where erroncous outputs could lead to significant ethical, social, or economic consequences.
REPRODUCIBILITY STATEMENT
The full algorithmic details of M2CL presented in the main paper, with additional implementation
details and byperparameter settings included in Section 6 We provide source code at https //github. com htt.tuuu..com//aneeeaaaaaaa HansenHua//M2CLL ICLR26, which includes scripts for training, evaluation. and reproducing all reported experiments. We provide checkpoints at co co/hansenhua//ee /M2CL. For theoretical results, include complete proofs in Appendices B
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A USAGE OF LLMS
We use large language models (LLMs) solely as an assistive tool for polishing the writing and improving clarity of exposition. All content generated by LLMs was carefully reviewed, verifie,, and, where necessary, revised by the authors. The authors take full responsibility for the correctness and integrity of the final manuseript.
B PROOF OF THEOREM 4.
Proof. Define the optimal w = arg min_ || - Ei= wra(C)))) and its corresponding activation E== Wi aCC)). Then, can derive the upper bound of the activation difference using the triangle inqquality:
N Σ |a(())
a - a S
- all + Niaa azll-
(18)
1=1
Using the triangle inequality, can bound the first term in Eq. (8)
Σ |a(C))
all Σ
(a(C))
-a(()))
N
WW]1 |la(C)) - al (())))l -
|a(()) a()))ll
f=1
1=1
N
N
N
N
|a(()) a(C))] +
Σ
|a((C)) a(c)))
<=
==1
f=1 j=1
N N
N
|a(()))
a(c))) +
Σ
La Lal 1l
(19)
1=1
1=1
Then, we bound the second term in Eq.
18)
||a aalaall S
Σ w aal(Co (C.)
aoll
w (((())) + -(())))))(((()) a.ll
N
min
|100
w(a(C!))
| (a(C.) - a(Ch))
N
min
|
((((C)) +
Σ
|a(())) a(c
1=1
min |00
Σ
wia (C1I + Lo Σ | -
(20)
In the first line, we add and subtract EN (CC)). In the second line, use the triangle inequality and the definition of wt In the third line, we scale w' to 1. Finally, we utilize the smoothness property of the activation function bound the second term Substituting into Eq. 18). can derive:
a. (CC))l <
I - (CC)) + (N + 1) - 111l)
N min la.
Σ wc)(C
(21)
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C DECOUPLED CRITERION FUCNTION
Lemma C.I. Under the assumption of one-block transformer, LLMs' activation diversity can be bound by the activation difference between their instructions and responses.
||a(C)) a(C)))l S [|a(T))
[I((T)))(x))(11 18LynN exp(2p2)
(22)
Proof. We first decompose the activation of context into combination of its components:
a(C)) a(C [a(I)) Σ
a(x -N 1)a(P)] + (a(4)
Σ
a(x (N 1)a(P)
kighi
kighi
a(C)) a(C)) (a(T)) a(X 1 - -N 1)a(P)) (N))))(P)) (a(7))
(X (N 1)a(P))
(23)
By using Lemma D.3 we can derive the upper bound of the activation difference as:
[la(C)) alC))l
<Ila(C)) (a(1)) + Σ - + a(x;-
+ +[la(C)) - [a(1)) + Σ a(x 1) - +
+ Il((T))) a(x;--))) III
$I|a(1,) a(x:- + |aa())) - a(()-1))l + 18L exp(2p²).
(24)
D USEFUL LEMMA
Lemma D.1. Suppose X| Ly and [I(W X)
X S sp,, the difference between the activation of softmax attention aXX) and linear attention a' (X) can be bounded by:
||(XX) a' axxx)l < 3Lyn exp(2p")
(25)
where a(X) Xoofmaxx (WxX)"WoXX) and a' aX()) = Wv (W Vd
Proof. Define A D-1exp(S) - exp(S), where S = (WKX)* WXX and D = diag((exp((5) In)). Then, we can derive the upper bound of each element of A.
exp(S.)) exp(St)) S exp(S D.
Aij Da
+ 1) s exp(p))(1 (1xx())) s 2exp(2p²)
Djs
(26)
Summing them up, we can derive:
|D- exp(s) expp)) < 1DD-11epppp
exp(S) - exp(S))l
ΣΣ 43 s exxp(22)) (27)
Define 8 = eSp S, where = (W WQX. X Then, we derive the upper bound by
finding the upper bound of each element of 5.
ōij exp(S.)) Sij I max(cxp(pp)) - p².p² cxp(-p²)) exp(p²)
(28)
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Summing them up, derive:
|| [ep((S) S - exp(S)) S =
exp(Sig)
Siy S nexp(p²)
(29)
1=1 j=1
After bounding ||D exp(S) exp(5)| and || exp((S) S|| we can derive the upper bound of ||D] exp(S)) S|| by basic algebra as:
D exp(s) S|1
D exp(S) -ex((8) + exp(S) S||
D exp(S) exp(8)]l + exp(S) S
22n exp(22(p"" + nexp(p²)
33 exp(p"²
(30)
Therefore, we derive the difference between the activation of softmax attention and linear attention as:
(WK (WKX)TWOXX -WvX(Wxx)
Vd
(WKX)"WOX) ) (WxX)>WoXI
<|| X|| -|lsootaay
||softmax
Vd
<yy ||0 exp(s) { S||
(xppp)))(2pp)
(31)
Lemma D.2. Define the activation of linear attention: a' cd(Y) = [Y, P] & (Y, PJY WoY d'(P) = P WWP, then the activation of a long prompt Y = [V, Y2..... Yn) can be derived by the activation of its component:
(32)
d((Y) Σ d dY 1))
(33)
Proof.
d((Y) = Wv Yy,...,,Y.. P1 WxllKi.
WoP .Y. V2....,Y,,
T
YN. V2,,, Yn. WWWWOP WviVV, Y2,
= Σ Y.Y PPT W
Wv Σ + -N (NN1))(N' WFW
N
Wv(YY + P - - W)
WvlY,, -N
d'(Y)) (N 11)a(P)).
(34)
18

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Published as a conference paper at ICLR 2026
Lemma D.3. We derive the difference between the activation of long prompt Y and a combination of the activations of its components Y [X1, Y,...., YN, Pl as:
|aa(Y) Σ a(Y)) + (N 1)((P)] & ILynN exp(p").
(35)
Proof. Denote the activation of linear attention as a', we complete the proof by using Lemma D.2 to simplify the relationship of linear attention and Lemma D.I to bound the difference:
|Ia(Y) Σ a(Y)) + (N - P)a(P)]
N
=Ila(Y) d + d( Σ
d' d'())) 11)
1=1
N
+ d'()) (N - 1)a
Σ
Σ a(Y)) (N - 1))(P)]]
i=1
N
s|la(V) d(())l Σ sexp(2p²) |/LUN + NL S9IpnN exp(22²))
a| (V:) a(Yi))l + (N - 1)]ld' - aPP)
3Lv(N 1]m]
(36)
Lemma D.4. I|||||| S p. we have (exp(S), 1n) 2 exp(-p)
Proof.
(exp(S), 1m)
Σ 1=1
exp(S:) 2 min exp(S:) 2 min exp( ((S.) xE[m]
iE(n
exxp(- - expp-maxx/ [S;1)
2 exp( exp(-||1|b) 2 exp( pp)
(37)
iE/n
E MULTI-ROUND CONTEXT LEARNING
First, we define:
h(1)) = B 1-1 1911
(38)
S())) [[a((T;) - a a(x -)). if 2 0 {+00,
(39)
otherwise.
To solve the minimization optimization with inequality constraint, we can construct a Lagrangian expression with Lagrange multiplier or!
minimize f(1t) s.t. h(1 2 0 + L(I, az) = f(()) ach(1))
(40)
The optimization changes to:
min f(1) max min L(I az).
(41)
0,20
19

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Published as a conference paper at ICLR 2026
Therefore, minimize f the dual problem is listed as below. Note that make sure mingy f(])) is properly minimized and would not become +00, the constraint has to be satisfied.
min [Ia(7]) a(x; 1:
min f(())
max min L(Ti, on)
0.20
max min f(4)) ar(()))) 0.20 4
max min or20 4;
[a((T)) a(x:- ||| ar (3 || 1211)
max min [Ia(T)) a(x;-1)) - - + ar ar|lzz r-
(42)
o720 1
Define the Q-function for this multi-round multi-agent collaboration as:
Q(a(4)).a(x;- ||a(1)) a(x;-11 Ill min |a([,)1)) -a(xi)l + 14 -1 1/11-
(43)
Here, I denotes the optimal I=+1. Therefore, the expected return is as follows, when we take one round further back to the round T
min (Ia(1T- a(x? - ||
min [|a(IT) u(x?
), - ";, - 1311)
min 1-
min (Q(a(T)-)) a, -xx or- (3 - -11 - 1111) af -1211 or-1>0
max
), ar 1/--111/-1-- --11 a+.11? 1711.
max
min
ar-12017
(44)
Similar to the previous round,
π arg min [Ia(TT) - a(x)-1)) - a, + ael| r9[]
af arg max 2.20
[ 1
- - -a,8
(45)
By repeating this process, we learn the optimal temperature parameter in every round. Hence, the loss functions for 0 and are as follows:
L(O)) = [a(1)) - a(x:->))| + az || - -1-l
L(a) (B - 1| 1!]l)-
(46)
20

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Published as a conference paper at ICLR 2026
F EXPERIMENT SETUP
F.1 DATASETS
We evaluate our method on three areas with datasets which are widely used prior studies (Dubey al. 2024 Qian et al. 2025). We elaborate what follows.
MMLU (Hendrycks et al. 2021). comprehensive benchmark covering diverse subjects and difficulty levels, designed test world knowledge and logical reasoning through multiple-choice
questions.
MATH (Hendrycks al. 2021 dataset of challenging competition-leve math problems requiring multi-step symbolic reasoning and advanced problem-solving ability.
GPQA (Rein et al. 2023), benchmark of graduate-lewe multiple-choice science questions that assesses deep domain knowledge and reasoning under uncertainty.
HumanEval (Chen et al. 2021,, widely recognized benchmark for function-level code generation,
designed evaluate fundamental programming skills.
ALFWorld (Shridhar et al. 2021). a text-based embodied environment featuring household tasks,
where agents navigate and intercct with objects via natural language commands.
SciWorld (Wang et al. 2022). a text-based embodied environment for interactive science tasks,
requiring agents to navigate rooms, conduct experiments, and perform procedural reasoning.
2024). a benchmark of real-world question answering tasks that integrate knowledge retrieval, reasoning, and multi-step tool use.
GAIA (Mialon et
PDDL (Chang al. 2024), environment comprising diverse strategic games, where agents must employ PDDL, expressions to plan and execute complex tasks.
AndroidWorid (Rawles et al. 2025), an environment with 116 dynamic tasks across 20 real-world Android apps, designed to evaluate mobile agents' capabilities in app navigation and system-level control.
We use 20% of the questions to construct the training dataset and the rest testing dataset.
F.2 BASELINES
We test our method against six baselines. We implement them based on their publicly available implementations.
Single Execution (Single), querying a single LLM to solve the task.
Best-of-N sampling (BoN), querying a single LLM N times and sampling the most correct answer. We set N to 32, as increasing N further does not yield additional performance benefits and aligns closely with the number LLM calls used for aulti-agent methods.
Discussion (Du et al. 2023), multi-agent framework in which LLMs are assigned predefined distinct contexts and iteratively exchange their reasoning processes as additional prompts over multiple rounds, before producing final answer via majority voting.
Dynamic LLM-Powered Agent Network (Liu al. 2024) (DyLAN), discussion-style framework which incorporates an LLM selection algorithm based on an unsupervised metric, namely the Agent Importance Score, which identifies the most contributive L.MMs through a preliminary trial tailored to the specific task.
GPTSwarm (Zhuge et al.) 2024) formalizing
of autonomous agents computational functions and edges facilitating information flow,
graphs, with nodes as manually-custominn adaptively optimizing node prompts and modifying graph connectivity during collective reasoning.
Multi-LLM Collaboration Nenwork (Qian et al. 2025) (MacNet), representative framework for decentralized and scalable multi-LLM systems. It introduces edge agents that mediate interactions by generating actionable instructions for the next agent based on the outputs of the previous one.
F.3
IMPLEMENTATION DETAILS
The context pool is constructed using GPT-4o, where we prompt it to generate a large collection of high-quality initial contexts across diverse domains, including mathematics, science, coding, and
21

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Published as a conference paper at ICLR 2026
embodied reasoning, and various domain-specnt sub-contexts included in each domain. This ensures that the pool provides a broad coverage of reasoning perspectives and is shared across all tasks.
The context generators are implemented by T5-small model (Raffel et al. 2020 for all the tasks. The dimension of the generated context vectors is 512. The learning rates for the context generators and a are both le - 4. We use 20% of the questions to train the context initialization and generator.
Table 2: Hyperparameters (identical across datasets).
Hyperparameter
Value
Sentence vector dimension
512
Optimizer
Adam
Batchsize
32
Learning rate of context Learning rate of Maximum rounds for discussion Training rounds
le-4
le-4
8
100
Size of context pool
100
We implement our code using Pytorch 2.3.0, built upon the open-source parameters of the llama2, Qwen2.55 and Qwen2.5-VLL VL. Models provided httpps:: htt.//hggggggcce...e/o/o ww/meta..a..ooooooooooooo......e 111mm and https: htwp/hhggiingg www.uggiggacccoo co /o/e All the experiments are run on Ubuntu 22.04.4 LTS with 8 NVIDIA H800 GPUs.
F.4 PSEUDOCODE OF M2CT.
We present the pseudocode of training M2CL in Algorithm [ It begins with training the context initialization, then the context generators are trained along with the weight a during the discussion.
Algorithm 1: Pseudocode of M2CL
Initialize parameters Φ,, dr. {0,) and (as N
for each question do
Φ5 of Mi (o))), OF OF f/ V (((r):
end
for each epoch do
Obtain initial contexts { via Eq.
for each round & do for i to N do
Generate instructions 1 via Eq. and obtain responses X via Eq. (4 + 0 no (O.)..
ag < as na VL(a;);
11
end
end
13 end
22

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Published as a conference paper at ICLR 2026
G ADDITIONAL RESULTS
G.1 COMPARISON WITH MORE MODELS
To further investigate M2CL'S performance, we compare with best-of- using stronger close- sourced LLMs, including Qwen2.5-Mat and GPT-4. As shown in Table 3 Ilama series models perform worse when fewer LLMs participate but achieve higher accuracy as the number of LLMs in- creases, demonstrating that M2 CL can collaborate weaker models to achieve comparable performance.
Table 3: Accuracy using different base models on different datasets. We exhibit the performance
advantage with Qwen-man max and highlight the best result.
Model
MMLU
MATH
GPQA
Code
ALFWorld
SeiWorld
GAIA
PDDL
Owen-max
86.5m
43.6
35.7
65.9
73,1
68.7
61.5rop
76.4Fom
GPT-4 4
84.3,12
41.1.1
33.3
62.7
70.2
65.4ps
58.7,
73.5.19
L1 almamma77 7B
16.8
15.8,90
22.5.506
20.1
15,3
24.2,003
1.1 a1l1mm113p
54,8
3.9
25.0.aat
23.7,0a
28.5.
24.5,44
18.6
30,4,
L1 Allama-ie 70B
68.9
31.6
27.6
35.5
16.1
40.2
29.9
48.4
Qwen max
87 170
44.2-00
39.2
67.5
74.0ree
69,8
62.5
77.5
GPT-4
86.4.1.
43.9.um
38.8
67.0.us
72.8
68.0p1
61.031
76.0.15
4
Llama-70 7B
1284
17,4
44.71s3
32.9.44
35.
33.0.%6
25.5
33.1
1.1 am1-11
86.9
23.4
58.9 38.9
47.5
42.9.
39.9,
30,5
4019) v.s
L1 110
40.3,59
78.7
70.6
69.5,4
65.5p
49.6,154
66.5
Owen-max
8805
45.0rwa
10.5
68.8
75.0rao
7100pep
63.5
79.0-um
GPT-4
86.5
44.6.04
38.9116
67.1
73.2
69.5115
61.0.a5
76,0.30
n=8
1.1 1.lamm-7
63.8 po
24.9
59.3tiax
38.8,100
37.2,
36.1
27.1
34.7
alama-1 33
92.7r4a
23.0
70.7
55.4.00
16.
44.7.063
33.6229
43.8
L. 11lamm-000
95.4
43.
87.6
81.0rma
78.9:s
76,2f12
58.7.ux
73.6,54
Owen-max
88. Syou
45.0
40.5
68.8
75.0
71.0paa
63.5rem
79.0rom
GPT
9..9
44.8
10.
68.5
74.3
70.5
63.0.ss
78.2.08
n=16
amaam-- 7
71.5
p3.9
69.9
48.3
39.8,153
38.4,904
28.9
37.0,09
L1 am1-1BB
94_5yta
32.7
88.5
66.1
48.7
47.1
36.2
45.5
L1 1.lamm-700 70B
93.91s4
51.5-63
91.3raaa
97.2
84.9
81.7-10
61.5.1
78.1..o L.o
Owan-max
89.0rsa
45.5
41.0ma
69.5ma
75.5
71.5pap
64.0ron
GPT
89.
45.4
41.5
69.7
75,0
71.0pas
63.5
78.5,
n=32
Ll 1llama-7 7B
79. 119e
28.8
84.5
56.5.100
42.5.150
40.7.508
31 31.4
38. pa.s
amR-13R
95.8rsa
41.4.
94.7
75.6
$2.2,
50.7.ma
38.5
L1 a0mmmm0
97.0rsu
54.5
95.1
93.7ra42
88.5m13
86.0
65.7rua
79.8
Owen-mase
89 Sye
46.0rea
41.5
70.0
76.0rae
72.0pap
64.5
80.0rem
GPT-4
45.4.0m
41.8
70.5
75.2
71.5
64.0.os
79.2,0x
n=64
Llama-70e
81.5,s0
35.4
82.5
60.6,04
44.2.
42,9.28
32,9
40.9
a.1ama-1
96.8
40.0.6o
93.1-5
82.5
54.8.112
$2.8.192
40.3
49,8
Llamg- 70B
96.3rxx
58.0r130
96.9rss4
92.0rame
90.8-1t
88.9
68.2
82.2/a3
23

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Published as a conference paper at ICLR 2026
G.2 NUMBER OF LLMs
We evaluate M2CL's performance with varying number of LLMs, ranging from 4 to 64. The comparative results are shown in Tables 4 8 and Figs. to
to
Summary of key findings. The results show that M2CT, significantly improves MAD performance, consistently surpassing existing methods by 20% 50%, particularly in complex tasks like math and tool-using. This highlights its ability to tackle intricate reasoning tasks, M2CL also exhibits more effective multi-agent scaling law, where performance consistently improves the number of LLMs increases to 64, especially in agentic domains where larger amount of LLMs enhances problem-solving accuracy and efficiency.
Table 4: Accuracy with varying number of LLMs on different datasets. The number of LLMs 4 for all datasets. We exhibit the performance ad advantage with BoN and highlight the best result.
Model
Method
MMLU
MATH
GPQA
Code
ALFWorld
SciWorld
GAIA
PDDL
Single
45.3
2.9
16.8
15.8
22.5,to
20.1
15.3
24.2
BoN
50.5ra0
6.9puz
27.5rto
21.8r0o
25.4-o
24.9
18.2
26.2
Debato
47.3
6.4
26.2
19.8,30
25.3.01
23.8
16.5
26.2
LIama-7B
DyLAN
18.4
6,6y13
34,5me
22.2
24.7.07
21.8
16.8
25.5
GPTSwarm
48.0
5.8
26.0.1s
25.8-04
25.1
18.8
MacNet
50.8
7,911
30,7+1
24.0r3a
27.8-14
26.5116
18.8
29.3
M2C1 (ours)
59.1
17.4
44.7ama
32.9tm
35.1-w7
33.0
25.5
33. 1
Single
54.8
3.9
25.0
23.7
28.5.10
24.5,1a
30.4
BoN
71.0rap
8.8pus
37.7
32,0re
31.2-u0
31.7
21.8
33.2
Debste
64.5
8,4
36.3
27.9.11
30.8,04
29.3
19.8,
31.9
Llama-14B
DyLAN
69.7
10.3ris
46.5
32,5ts
31.3-ui
28.7
19.4.24
30.4
Macllet
70.3:an
9.2
40.9
35,2
31.5-oa
31.8
23.4-1a
35,3
MacNet
70.3
9,2
40.9-13
35,2
31,5-us
31.81u
23.4-18
35.3
M2CL (ours)
86,9
23.41146
58.9
47.5
42.9r
39.9
30,51k:
40.9
Single
68.9 68.9
31.6,12
27.6
35.5
46.1.4a
40,2
29.9
48.4
K3.0rs
34
50.9-oa
32.7
52.8
Debete
74.8
29.8,s0
50.2
43.2
50.4.os
47.8
32.4
52.9
1lama-70B
DyT.NN
82.1
31.5
53.8:18
44.5,15
49.3.16
41.
31.5
50.3
GPTSwarm
81443
31.5,3
54.8.u
43.7
$1.0
45.2
32.5
51.5
MacNet
72,9
32.7,s1
19.1
40.8,1a
52.7-1a
55,9
36.5+5
$7.0pea
M2C1 (ours)
95.6m1
40.3r5s
78.7
70.6722
69.5
Single
61.2
12.9u12
20.2
$1.2.113
24.3
25,9
15.3
21.1
BoN
74.2
24.9rso
36.4r60
62.5
30.9-u
32,5
20.0reo
25.2
Debate
69.3
17.9.>
28.7.x
$4.5
29.5
31.41.
20.6
24.3
Qwen-7B
74.2
23.3.16
34.2,3
62.5mmn
29.5.14
28.3
19.0.ta
23.0
GPTSwarm
74.5
24.1.sx
37.2rea
60.4.:
29.4.13
29.5
20.0raa
23.9
Macblet
68.0,s1
20.3
25.0
$7.1
29.8
33.8
20.5
26.6114
M2C1 (ours)
88,7
40.8
58.4
76.81143
36.7-sa
41,7
30.2:
33.0
Single
67. f7,2
21.6:a2
21.2
S6.7.1a>
30.2 Am
31.7,1a
19.2
26.4
79.7
27.8-an
32.8rca
36.2-on
39.4
23.8
28.8
Debate
71.7is
24.7.31
24.8.1
62.7
35.6.04
38.5uo
25.5
29.9
Qwen 14B
DyLAN
77.5
26.9.s9
31.9,50
67.9.15
33,6,34
34.9
22.7.1
27.8
GPTSwarm
80.1
26.9,s9
33.0rea
68.1
34.6.16
34.8,u6
24.5m
28.3
MacNlt
71.2
24.6.12
27.6.12
62.9
36.1.a1
41.4
28.6
29, 29.4
M2.11 (ours)
91.4mm
43.6
64.6131
86.5
51.3
37.2
Single
12.5
31.61194
34.9
59.1
49.3.13
11.
31,4
41.8,s0
RoN
84.2
51 Oren
45.9rcn
72.2
56.6-6a
59.8m
38.6
49,8
Debate
76.6
48.0.
39.6..3
66.7iss
58,3-12
62.5
40.7
47.8
Qwen-72B
DyLAN
84.6124
61.5mms
45.5104
71.3
54.2.14
57.8.1
38.2
45.9
GPTSwarm
84.9ras
60.9rse
46.6rer
69.7 69.7us
55.2.14
19.
39.0-aa
48.8 48.8
Maclltt
80.3.1
48.1.10
41.2.A7
68.1
57.2-m4
64.1
42.0:a4
49.8
M2C1, (ours)
93.5
69,311k3
73.1
88.3116
73.9t
81.9-22
60.3
65.3r155
24

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Published as a conference paper at ICLR 2026
Table 5: Accuracy with varying number of LLMs on different datasets. The number of LLMs 8 for all datasets. We exhibit the performance ad advantage with BoN and highlight the best result.
Model
MMLU
MATH
GPQA
ALFWorld SeiWorld
Single
45.3,11
2.9
16.8
15.8.so
22.6.34
19.7
14.9
23.6.x:
BaN
50.5tzp
6.9buz
27.5rc0
21.8rtn
26.2
25.0ma
18.9
26.7
Debate
49.5
6.2cm
24.8.17
19.2.:6
25.9.0s
24.7
15.9
26.9
LIama-7B
DyLAN
54.2
9.7
35ms
26r4:
25.0.12
22.0,sa
17.2
25.4:13
GPTSwarm
49.2,13
6,8
28.7mia
20.7.11
26.2-ma
26.4
20.0cu
29.3
MacMlet
56.5tsp
1100aa
39.61121
30.0raa
30.4+4
30,2
20.6
31.7
M2C1. (ours)
63.811a
24.9
59.3
38.81178
37.2p
36.141
27.1
34.7
Single
54.8
3,9
25.0
23.7
27.8.41
24.
18.6.s
29.4
71.0rs0
8,8
37.7:tn
32.3
22.5mma
Debate
66.914
8.0mx
34,5
30.8.12
31.7.02
30,3
20.0.a5
32.0
Llama-14B
DyLAN
82.1
12.4rh
46.7rse
37.5
31.7.02
29.6
19.4.s
31,3
MacNet
81.7tm0
14.2:s4
53.9
43.3
33,4-15
35.611
24.9ma
37.0ma
MacNet
81.7rm
14.2
53.91662
43.3
33,4-13
35.6153
24.9
37.0
M2C1 (ours)
92.7
23.0
70.7
55.4mm
46.1
43.8
Single
68.9
316.32
27.6,x2
35.5
44.1.s3
39.1
29.1
47.
BoN
83.0rsp
34.8ren
59.6ree
48.0
$2.4-on
48.8
32.9
52.8
82.2
34.3,s5
58.1.1
47.1
$1.7,0a
50.1
32.2,0>
53.3
Llama-70B
DyLAN
93.5mu
37.1rs3
72.8
56.81sa
50.2.
46.4
31.7.12
49.7
GPTSwarm
93.6mma
36.6-14
71.2
57.1-s1
$1.4.18
46.5
32.2,m7
52.2
82.0.
36.9r21
62.2rta
48.810a
57.3-49
64.0rus2
40.7
62.6
M2C1 (ours)
95.41124
43.5
87.612s0
81.0yma
78.9
76.2
S8.7
73.6
Single
61.2
12.9
20.2
51.2,113
23.8,10
25.2,00
15.6.ss
21.0
74.2
24.9ren
36.4ru
62.5
31.5-u0
35.3
21.1
26.3
Debste
71.1
19.9.50
28.7:17
60.0.3
30.6.09
32,2
21.0.a1
24.8
Qwen-7B
DYLAN
74.3
26.711x
35.4..
63.4me
29.8.12
29.4
18.4
23.4
GPTSwarm
76.3
26.2rs
35.6,08
62.7rea
29.9.16
30.8
20.6,05
24.5
MacNet
71.5
21.
30.8.56
59, 3,1
33.6-21
37.0
21.5
29. 19.5
M2C1 (ours)
92.5T
47.8
66.1
80.3
39.9
45.3r
33.6r
34.7184
Single
67.2
21.6.62
21.2
16.7,123
30.1.7A
31.3,00
18.7
25.7
BoN
79.7
27.8rem
32.8rc0
69.4re
37.5-u0
41.61u
25.6ruu
28.5 1u0
77.2,sa
27.4.aa
30.3,15
66.9.35
36.8
39.4.a
26.4-us
30.0
Qwen- 14B
DyLAN
86.8
31.2:14
39.4r16
76.6-1a
34.8,
36.0
22.8
28.0jas
GPTSwarm
87.0m3
31.3-15
38.7rt9
34.9.zA
35.9
25.0.m
28.4
MacMet
78.9
28.7re9
31,9,09
70.4m1
39.2-17
46.0
32.2
32.7
M2C1 (ours)
93.7
51.7
66.2
91.1
48.2
$6.1
42.0r
43.0
Single
31.61194
34.9
19.1
48.2,s3
50.4.1
31.1
41.0.
BoN
84.2rs0
Oreo
45.9ren
72.2r0n
57.5-mm
62.1 to0
41.2
51.0mo
Jebate
82.7
48.4.2x
43.4.15
69.1.
60.4-19
65.2
42.9ruz
19.
Qwen-72B
DyLANN
91.5
63.1
58.0.41
45.5
GPTSwarm
91.5p1a
64.7
52.4rss
79.6
56.8.
60.2.19
40,3
49.7
MacNet
83.8
52.9-1
46.2-6a
70.5.17
61.8-13
68.4
46.4-5>
53.7
M2CL (ours)
95.1
72.5mm
78.9
90.7
79.0ra13
88.9
67.27
70.5
25

---

Published as a conference paper at ICLR 2026
Table Accuracy with varying number of LLMs on different datasets. The number of LLMs is 16 for all datasets. We exhibit the performance advantage with BoN and highlight the best result.
Model
MMLU
MATH
GPQA
Code
ALFWorld
SeiWorld
Single
45.3,s1
299c
16.8
15.8.s0
22.4
19.6
14.7
24.2
BaN
50.5ta0
6.9paz
27.5re0
21.8rtn
26.7-mn
25.7ma
19.2
26.3
Debate
mos
6.4ua
26.1.14
21.3us
25.7
25.3um
16.6.24
26.4
LIama-7B
DyLAN
54.5
9.9pss
35.5rs
26.2
24.6.21
22.7
17.2
25.8.as
GPTSwarm
$1.6m
6.9pu
29.1m
23.0r1a
27.2-os
26.811
20.8-16
29.7
MacMlet
59.3rsa
12.5raa
45.0
33.7tı
32.8
33.4ma
22.6154
34.2
M2C1. (ours)
71,5
23.9
69.9r1a4
48.3
39.8
38.4-13
28.9
37.0+167
Single
54.8
3,9
25.0
23.7
27.4.s6
24.0.s
18.3
29.2
71.0
8,8
37.7t0n
33.5
23.3
Debate
72.2
8.2
37.0.67
32.0reo
32.0.
30.9.1
19.6
32.7
Llama-14B
DyLAN
83.2
12.4
47.0rsa
38.1
31.9...
30,2
20.0.sa
31.2
MacNet
86.8115
16.0-s
59.7mm
49.1
34,8-1a
37.8
26.7:sa
39.9
MacNet
86.81188
16.0
59.7
19.1
34,8-18
37.8143
26.7
39.9
M2C1 (ours)
32.7
88.5
66.
48.7
36.2
Single
68.9
316.12
27.6,x2
35.5
43.7 ja:7
38.3.113
28.6.4a
46.8
BoN
83.0rap
34.8rem
59.6ree
48.0rom
$3.9
49.8
33.2
53,0
S2.9
34.6,03
58.5
46.8
$2.2.17
51.2
33.0,a3
$2.8
Llama-70B
DyLAN
93.2
37.2rz4
73.2
S7.2
50.5.34
46.8
31.1
49.7
GPTSwarm
93.0rm
37.4-26
69.7pm
55.5115
$1.7,3a
47.5
32.4.sa
51.6114
MacMltt
86.7pa3
38.9r41
68.3ra.
49.8:18
61.6-12
70.8
43.8rua
67.1
M2C1 (ours)
93,9rm0
$1.5
91.3
97.2
84.9
81.7/314
61.5
78.1
Single
(1.2
12.9
20.2
51.2,11
23.4,s5
24.9
15.6.64
20.6
74.2rap
24.9ren
36.4ro
62.5rpm
32.9-un
35.4
22.0rmo
Debste
73.4,s
24.1.es
35.6.66
62.1
31.7.1
32.6134
22.1
24.2
Qwen-7B
DYLAN
77.4ta
26.0rt
38.911
64.8tus
30.4..
28.7
19.2.sx
22.7
GPTSwarm
78.0rss
27.6
41.1m1
66.2
30.1,3a
30.4.1
22.
24.4
MacNet
76.8rzs
27.8-29
40.3
69 Ar
35.4-15
39.7t43
24.6124
30.7
M2C1 (ours)
94.61204
47.4
72.81
84.9
41.8
47,6r123
36.5
37.4-103
Single
17.2
21.6.63
21.2
$6.7,123
28.3.sa
30.9.114
18.5
25.5
BoN
79.7
27.8rep
32.8rcp
69.4rem
38.1 1-o0
42,3
26.1 run
29.3
78.7.1p
26.7.11
33.4rta
70.1
37.7
40.5
26.7
30.4
Qwen- 14B
DyLAN
88.0
31.9-1
41.0rsa
78.2
34.9.1a
35.7
23.9
28.3
GPTSwarm
88.0rs3
31.8-4
40.4m
78.4
35.5.1A
36.8.ss
25.1.a
28.7
MacNet
83.1
30.8-10
35.1
74,8
42.1-ua
49.3ma
35.5
33.8
M2C1 (ours)
95.9
52.7
69.0
93.3
$1,2
59.4
43.9
46.0
Single
31.61194
34.9
19.1
p7.7
50. 11ss
31.2,a3
40.8
BoN
84.2
51.0roo
45.9ree
72.2r0n
58.5-on
62.9
43,3m00
52.3
Jebate
83.9
16.1
44.1
71.6,06
60.8-13
66.7
44.1
49,3
Qwen-72B
DyLAAN
7:ss
65.8mia
53.6
81
56.1.14
19.1
GPTSwarm
92.4rsa
66.0riso
53,3114
81.1
S7.3
59.8
41.3:20
50.6112
MacNet
88. 113
60.6rs6
49.2-1x
72.6r64
65.8-14
74.7
50.3+za
58. 115s
M2CL (ours)
96.61124
74,3
80.0rsa1
94.4
82.9
94,6m
71.9
74.3:120
26

---

Published as a conference paper at ICLR 2026
Table 7: Accuracy with varying number of LLMs on different datasets. The number of LLMs is 32 for all datasets. We exhibit the performance advantage with BoN and highlight the best result.
Model
MMLU
MATH
GPQA
ALFWorld SeiWorld
Single
45.3,11
299cs
16.8
15.8.so
22.4
18.8
14.7
23.2
BaN
50.5tap
6.9paz
27.5re0
21.8rtn
26.8 mn
26.9
19.8
27.2
Debate
51.8rua
7.7
29.5
23.5
26.4.04
25.6.15
15.8
26.2,10
LIama-7B
DyLAN
54.7p42
10.1
36.2rsz
26.7
24.9.1a
23.1
17.6,22
26.0
GPTSwarm
$2.4
7.9H14
30.8-x
23.7
27.3-os
27.9
21.8
30.4,1a
MacMlet
62.7mma
14.0
50.3
37.2
35.7-so
37.5rmas
23.8
37.5-103
M2C1. (ours)
79.1
28.8
84,51570
56.5
42.5ri57
40.7H
31.4
38.9
Single
p4.8
3,9
25.0
23.7
27.0.sa
23.5
18.1
28.9
71.0r30
8,8ms
37.7rta
32.8-on
34.8
24.2
Debate
73.1m2
9,5p0
40,7r3
34.3115
31.9.00
31.7151
19.9
33.0119
Llama-14B
DyLAN
83.61uz
12.7:19
p0.7
38,7
32.1.c
30.8.A0
19.8
31.0,s3
MacNet
90.7mme
17.6rss
67.2tas
53.9m
37.1-43
41.7
29.1
42,3rs0
MacNet
90.7
17.6
67.2
53.9
37.1
41.7
29.1
42.3
M2C1 (ours)
95.8
41.4p10
94.7,%a
75.6mm
52.2
50.7:154
38.5m
48.0
Single
68.9
316.32
27.6,x0
35.5
43.1
38.6,113
28.
46.0,z2
BoN
83.0rsp
34.8ren
59.6rea
48.0rom
$3.1-om
50.1 100
32.8
53.2
85.7
35.3res
63.4ms
51.2
$2.6.65
52.1
32.9
Llama-70B
DyLAN
94,5m1s
37.3r2s
74.61150
57.8
50.1.3m
47.2
31.444
49.7
GPTSwarm
96.4-15
37.8rs0
73.4
$6.41s
$2.2,00
48.4.17
32.5
$1.6116
MacMet
90.0mz
41.2rsa
73.9
14.1
64.51114
76.6r253
46.5
71.6:184
M2C1 (ours)
97.0m
54.5
95.1
93.7
88.5
86.0rass
63.7/128
79.8
Single
61.2
12.9
20.2
51.2,11
24.2,s6
24.5
14.6
20.4
74.2rap
24.9ren
36.4r09
62.5rp
32.8mun
37,8
22.3r00
27.7
Debste
76.8
26.8-19
40.0m1
64.3r1s
31.7.
33.4
23.0nm
25.3
Qwen-7B
DYLAN
78.2
29.5t4
40.3
66.5t4m
30.7.11
29.2
19,0.sa
22.6181
GPTSwarm
79.6:51
29.9/50
41.8-14
67.8
31.2,16
31,3,65
22.6m²
25.0/37
MacNet
80 01.6114
31.5
45.8
73.7
38.6-5a
15.
26.6r4a
34.3
M2C1 (ours)
96.0rau
47.1
74.9
87.3
44.4
50.4ri2s
39.7
40.2
Single
21.6.63
21.2
$6.7,123
29.4.sm
29.5
18.9
24.5
BoN
79.7
27.8rem
32.8rc0
69.4rom
37.4-um
45.1 100
27.1 von
29.0
82.7
29.1r13
35.5tan
71.8
39.0-1A
41.7p4
28.7:1a
30.8
Qwen- 14B
DyLAN
89.3
32.6-1
42.2+44
78.9
35.4.
36.2
23.2;
29.3
GPTSwarm
89.0ra
32.6-4a
42.2ra
78.9
36.4.u
37.5
26.6.ss
28.9
MacNet
87.8rs
33.7/19
40.1ma
83.0r1s4
44.8-14
54.2
39.8r:31
36.2ma
M2C1 (ours)
96.1 1164
58.0
70.5
94,9
$4,9
49.0/
49.6
Single
31.6114
34.9
19.1
46.7
49.0,
30.4.01
g0.
BoN
84 84.2
51.0reo
45.9ree
72.2r00
59,3-mn
63.2
43,9m
53.3
Jebate
86.5
62.9mu
48.3114
74.5:13
62,8-13
67.8
46.6127
50.2
Qwen-72B
DyL.AN
67.7
82.7tin
56.0.15
59.1
GPTSwarm
93. lns
68. 18.1
54,7
82.2700
58.3.
62.6
42,7
51.4
MacNet
92. 92.5
72.1
55.2
79.9:17
70.5
79.5
$4.7
62.3
M2CL (ours)
97.5
74.7
82.0r
95.9
89,3
95:51
79.7:15>
80.0
27

---

Published as a conference paper at ICLR 2026
Table 8: Accuracy with varying number of LLMs on different datasets. The number of LLMs is 64 for all datasets. We exhibit the performance advantage with BoN and highlight the best result.
Model
MMLU
MATH
GPQA
ALFWorld SeiWorld
Single
45.3,s1
299cs
16.8
15.8.so
22.0.s2
18.8
15.0
22.5
BaN
50.5tap
6.9baz
27.5rto
21.8rtn
27.2
26.7ma
19.8
26.9
Debate
53.4
9.2
33.5
251s:
26.9.0s
26.3
16.5.sa
26.9
LIama-7B
DyLAN
55.1ess
10.4rs
36.91s4
27ts:
24.6.3a
23.3,14
17.9
25.0
GPTSwarm
53.5rx
9-x1
34pus
25.3
27.0.0e
28.8
22.1
31.0ke:
MacMlet
66.4
15.3rs4
54.41au
40.0
38.8ru
39.6112
27.0ma
38.4mm
M2C1. (ours)
81,5pa
35.4
82,5
60.6
44.2f179
42.9
32,9
40.9-110
Single
54.8
3,9
25.0
23.7
26.9.5a
23.6.
17,8,
28. 18.6188
71.0rs0
8.8
37.7tta
32.6-on
35.7
24.5mma
Debate
79.6rss
11.1
45,0ma
36.5t4
32,6-u0
32,0
19.9
32,6115
Llama-14B
DyLAN
85.0m
13.0r42
48.8
39,3
31.9.0
31.0,47
19.9
30.5
MacNet
90.8r10a
18.1rss
67.5yaa
55.2
39.1-65
44.4
31.1
44,0
MacNet
90.8
18.1
67.5
55.2
39.1
44.4
31.1
44.0 44.0
M2C1 (ours)
96.8
40.0
93.1
82.5
54.8
40.3
Single
68.9
316.32
27.6,x2
35.5
43.0
37.3.
28.2
45.9
BoN
83.0rsp
34.8rem
59.6rea
48.0rom
$4.8
51.0
33.9
52.7
90.0m1
36.6-18
69.0-s4
54,0
53.6.15
53.5
32.7
53,2
Llama-70B
DyLAN
95.41124
37.612x
75.4
58.9
50.4.44
47.6.34
30.8.s1
50.4
GPTSwarm
95.7mm
37.9ts1
78.9
18.1
52.4.34
49.3,11
32.3
$1.3
MacMett
95.3
44.2rs4
84.212sa
$7.9rs9
67.9
81.613s
49.0rusa
75.4-123
M2C1 (ours)
96,3113
58.0
96.9
92.0r44
90.813a
88.9:374
68.2
82.2
Single
61.2
12.9
20.2
51.2,11
23.0
24.4.111
14.8.sa
20.0
74.2rap
24.9ren
36.4rc
62.5rpm
34,5-un
38.6100
23.0rmo
27.8
Debste
78.1
28.9-1
41.7Hs
66.6r1
32.3,
34.1
23.5
26.0:14
Qwen-7B
DYLAN
79.8rss
30.7
43.5m
67.5
30.7.xx
30.0
19.8
23.7
GPTSwarm
80.9rs
29.9
43.1
68.0
31.8,32
32.7
23.2
25.3
MacNet
85. 1i0
34.7-1x
50.4m14
79.81123
41.6-1
46.7ts
28.4-54
37, 199
M2C1 (ours)
97.5
50.7
80.6
90.2
46.81123
53.3114
42.0
42.2
Single
17.2
21.6.63
21.2
$6.7,123
28.9.sa
29.9
17.8
24.7
BoN
79.7
27.8rem
32.8rcm
69 69.4rem
38.4-um
45.6
27.6rum
29.5
31.1-33
39.9-1a
75.8
38.8
42.7.p
29.0
31.7
Qwen- 14B
DyLAN
90.2
33.6118
42,8110a
80.1ria
36.2,3a
37.0
24.4
28.7 28.7
GPTSwarm
90.2
33.0rs2
43.2
80.4rua
35.9.15
36.0,sa
26.5.1
29.0
MacNet
93.7mm
37.7-s0
46.7
91.2
47.5-e1
56.8
42.7fis1
38.4
M2C1 (ours)
1
61.9
80.4
98.7
56.4115
65.8ra12
$1.81242
50.9
Single
31.6119
34.9
19.1
46.7
48.3
29.8
40.4.110
BoN
84.2rse
51.0reo
45.9ren
72.2r0n
60.
66.0mm
44.9mm
54.4m0
Jebate
91.2m
62.31u1
52.4rsa
78.9
62.5-14
69.1
47.6127
50,5
Qwen-72B
DyLAAN
95.1 ri0e
66.8
55.7
83.9m
56.9.s
39,9
GPTSwarm
94,3
68.8
55,2rs3
84.0mus
59.6.03
63.2
43.0.t
52.5119
MacNet
98.0ris
73.9mm
63.2
86.7tis
74.4
85.1
59.5m
66.6-13
M2CL (ours)
99.7
79.7
86.0çam
97.5
92.9rm2
95.9-2
84.2
83.9:
28

---

Published as a conference paper at ICLR 2026
MMLU
MATH
GPQA
HumanEval
100
40
100
80
Acquracy
80
30
60
20
20
20
0
16
32
64
32
64
64
Number
egents
Number of agents
Number of agents
Number of agents
M2CL (ours)
Single
BoN
Debede
DyLAN
GPTSwarm
MacNet
ALFWarld
SaiWorld
GAIA
PDDL
50
40
50
40
40
30
40
Accuracy
30
30
30
20
20
20
8
16
32 agents
84
16
32
64
4
8
18 agents
32
64
8
16
32
64
Number
Number agents
Number
agents
M2CL
Debato
GPTSwam
MacNet
Figure 5: Performance of Ilama-7b 7 as the base model with varying number of LLMs. Uncertainty intervals depict standard deviation over three seeds. M2CL exhibits higher performance and increasing tendency with more LLMs, demonstrating its great collaboration efficiency compared to existing methods. Of note, academic and agentic tasks reasoning are challenging because they require more diverse thinking perspectives and more rigorous analysis. The outperformance of M2CL reveals its capability enabling LLMs to collaborate in changing discussion state.
MMLU
GPQA
HumanEval
100
50
100
100
80
40
80
Accuracy
40
20
40
40
20
10
20
20
0
32
32
64
Number of agents
Number of agents
Number of agents
Number of agents
M2CL (ours)
Single
BoN
Debeto
DyLAN
GPTSwam
MacNet
ALFWorld
SciWorld
GAIA
PDDL
60
80
50
60
50
40
50
Accuracy
30
10
20
20
10
10
10
16
32
64
16
32
64
8
16
3.2
64
16
32
64
Number of agents
Number agents
Number
agents
Number of agents
M2CL (ours)
Single
BoN
Debate
DyLAN
GPTSwarm
MacNel
Figure 6: Performance of llama-13 13b as the base model with varying number of LLMs. Uncertainty intervals depict standard deviation over three seeds. M2CL exhibits higher performance and increasing tendency with more LLMs, demonstrating its great collaboration efficiency compared to existing methods.
29

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Published as a conference paper at ICLR 2026
MMLU
GPOA
HumanEval
100
60
100
100
80
50
80
80
Accuracy
20
20
10
20
20
0
16
32
16
32
64
16
32
64
32
64
Number of egents
Number of agents
Number of agents
Number of agents
M2C1 (ours)
Single BoN
Debede
DyLAN
GPTSwar
MacNet
AW
SciWorid
GAIA
PODL
100
100
80
100
Apciracy
80
80-
60
80
60
60
60
40
40
40
20
16
32
64
16
32
64
16
32
64
32
64
Number agents
Number of agents
Number of
Number of
M2CL (ours)
Single
BoN
Dobeto
DyLAN
GPTSwam
MacNet
Figure 7: Performance as 1lama-70b as the base model with varying number of LLMs. Uncertainty intervals depict standard deviation over three seeds. M2CL exhibits higher performance and increasing tendency with more LLMs, demonstrating its great collaboration efficiency compared to existing methods.
MMLU
GPQA
HumanEval
100
60
100
100
80
50
Accuracy
40
40
40
40
20
10
20
20
0
16
16
32
64
32
64
Number of agentss
Number of aggents
Number of agents
Number of agents
M2CL (ours)
Single
BoN
Debele
DyLAN
GPTSwarm
MacNet
ALFWerld
SciWorld
GAIA
PDDL
650
80
50
50
40
40
40
Apouracy
30
30
30
20
20
10
10
10
10
16
32
64
16
32
64
8
16
32
64
16
32
64
Number of agents
Number
Number
agents
Number of agents
M2CL (ours)
Single
BoN
Dibete
DyLAN
GPTSwam
MacNat
Figure 8: Performance of Qwen-7b as the base model with varying number of LLMs. Uncertainty intervals depict standard deviation over three seeds. M2CL exhibits higher performance and increasing tendency with more LLMs, demonstrating its great collaboration efficiency compared to existing methods.
30

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Published as a conference paper at ICLR 2026
MMLU
GPOA
HumanEval
100
80
100
100
80
80
80
Accuracy
20
20
0
16
32
16
32
64
16
32
64
32
64
Number of egents
Number of agents
Number of agents
Number of agents
M2CL (ours)
Single
BoN
Debede
DyLAN
GPTSwam
MacNet
ALFWarld
SciWorld
GAIA
PDDL
60
60
60
60
Accuracy
40
40
30
30
30
20
20
20
10
10
10
8
16
32
84
16
32
64
4
8
18
32
64
8
16
32
64
agents
agents
agents
agents
M2CL (ours)
Debato
GPTSwam
MacNet
Figure 9: Performance of Qwen-144 as the base model with varying number of LLMs. Uncertainty intervals depict standard deviation over three seeds. M2CL exhibits higher performance and increasing tendency with more LLMs, demonstrating its great collaboration efficiency compared to existing methods.
MMLU
MATH
GPQA
HumanEval
100
80
100
100
80
60
80
80
Apciracy
60
60
40
20
0
16
32
16
32
64
16
32
64
64
Number
agents
Number of agients
Number of
Number of
M2CL (ours)
Single
BoN
Debate
DyLAN
GPTSwam
MacNet
AL AWorld
SciWorid
GAIA
PDDL
100
100
100
80
80
80
80
Acouracy
60
60
60
60
40
40
40
PM
40
8
16
32 agents
64
8
16
32
64
16
32
64
16
32
64
Number
Number
agents
Number agents
Number of agents
M2CL (ours)
Single
BoN
Debete
DyLAN
GPTSwam
MocNet
Figure 10: Performance of Qwen-72b as the base model with varying number of LLMs. Uncertainty intervals depict standard deviation over three seeds. M2CL exhibits higher performance and increasing tendency with more LLMs, demonstrating its great collaboration efficiency compared to existing methods.
31

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Published as a conference paper at ICLR 2026
G.3 GUI AGENT
We evaluate M2CL's 's performance on more challenging AndroidWorid, which requires GUI identifica- tion, long-horizon planning, and accurate action execution capability. Comparative results shown in Table and Fig.
We observe that M2CL consistently outperforms existing baselines across different model scales up to 50,, with performance gains becoming more pronounced as the number of participating LLMs increases. The superior scalability of M2CL this setting highlights its ability exploit diverse responses and maintain consistent under complex, real-world style interactions.
N
Model
Single
BoN
Debate
DyLAN
GPTSwarm
MacNet
M2CL
3B
10.9
17.0rao
12.5,45
13.0,40
15.0,20
16.8,02
25.5
N=4
7B
27.0.m
38.0rua
30.5,75
31,0,1
37.0,10
39.6
44.9ma
3B
10.9
17.0rao
15.7.13
15,2
15.6,4
19.7
32.0riso
N=8
7B
27.0.1
38.0raa
33.0,50
34.5
38.0rao
44.0rs0
50.0
3B
10.9
17.0rap
16.9.au
18.4114
18.1
22.6rse
38.0r2Lo
N=16
7B
27.0.11.
38.0rua
37.3,07
37,8
42.5pu
47.9r99
55.0
10.9
17.0rao
18.0-
21.5
20.6r38
25.2
42.0
N=32
7B
27.0.1
38.0rao
41.5-14
40.0
45.0mz
52.8-14.
y9.0
3B
10.9
17.0rap
20.1
23.6166 42.2
24.2
28.61116
45.0
N=64
7B
27.0.11.
38.0ruu
41.7-37
49.3
55.2
62.0
Table 9: Accuracy with varying number of LLMs from 4 to 64 AndroidWorld, We exhibit the performance advantage with BoN and highlight the best result.
3B
7B
M2GL (ours)
Accuracy
60
Single
30
BoN
40
20
10
20
GPTSwarm
MacNet
32 Number of agents
16
16
64
Number of agents
Figure 11: Performance of Qwen2.5-VL. (3B and 7B) as the base model with varying number of LLMs. M2CL exhibits higher performance and increasing tendency with more LLMs, demonstrating its great collaboration efficiency compared to existing methods. Uncertainty intervals depict standard deviation over three seeds.
32

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Published as a conference paper at ICLR 2026
G.4 CONTEXT CONSTRAINT
To assess the effect of context constraint, we carry out experiments by varying the context constraint from 0 to 10. As illustrated Figs. 12 to I6 larger value of / results in a high degree of consistency among LLMs, leading them to produce similar answers. Conversely, a smaller value of associated with reduced collaboration among L.MMs. Therefore, important to adjust / to control the degree of consistency among LLMs for better collaboration.
MATH
80
100
15.0
40
40
40
05
2..5
35
26
36
80
00.0
-00
Antunay
25
20
70
10
10
30
10
8:10
MMLU
MATH
OPQA
Code
ALFWorld
SciWorid
GA/A
PDDL
Adcuracy (78)
90
30
80
35
10
85
25
36
30
30
20
30
25
25
6
0
2
10
0
100
100
80
40
70
Aycurecy (78)
90
70
35
60
70
25
40
40
60
20
30
30
8
8
8
8
8
8
Figure 12: Performance with varying context constraint when L.MSs participate. All the curves display the same trend of rising first and then falling, which is consistent with our theory.
SciWerid
70
160
40
20
40
40
30
40
95
35
36
35
60
15
30
Acnumcy
60
40
10
30
10
MMLU
MATH
GPOA
Code
ALFWorld
SciWorld
GA/A
PDDL
Relurney (7B)
60
20
40
40
80
45
15
96
28
35
40
10
30
20
30
70
60
0
10
4
10
2
10
0
100
6
10
GAIA
PDDL
100
100
80
50
80
80
80
Accurayy (78) (76)
98
45
70
70
90
80
75
25
50
40
30
70
20
40
30
B
B
8
8
8
B
Figure 13: Performance with varying context constraint when LLMS participate.
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Published as conference paper at ICLR 2026
80
100
30
40
40
Accurasy (78)
70
26
36
96
30
75-18
25-
16
10
40
20
10
20
10
MMLU
MATH
GPOA
Code
ALFWorld
SciWorkd
GIAIA
PDDL
Accuracy (75)
95
25
90
90
20
40
05
50
15
36
30
80
10
30
30
20
8
10
8
10
10
6
10
MMLU
MATH
GPQA
Code
ALFWorld
SdWWordd
GAIA
PDOL
100
100
100
50
90
90
Aocurecy
990
90
80
80
25
60
50
15
86
60
20
80
40
50
8
8
8
9
8
8
Figure 14: Performance with varying context constraint when 16 LLMs participate.
MMLU
MATH
GPQA
Code
ALFWorld
SciWorid
GAIA
PDDL
100
70
80
50
40
Accuracy
80
15
38
10
30
20
60
20
28
15
1067
40
10
20
10
MMLU
MATH
GPQA
Codee
ALFWorld
SciWorid
GA/A
PDDL
100
100
40
60
80
Apcuracy (78)
4th
70
10
90
90
10
10
MMLU
MATH
GPQA
Code
ALFWorld
SciWarid
GAA
PDOL
100
Ausuraty (78)
90
90
50
80
60
80
80
40
75
70
66
70
60
65
66
80
20
102
10
10
10
8
B
8
8
B
Figure 15: Performance with varying context constraint when 32 L.MSs participate.
34

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Published as a conference paper at ICLR 2026
MMLU
MATH
GPQA
Code
ALFWorld
SciWerld
GAAA
PDDL
(71)
40
40
60
20
80
20
300
36
35
40
30
20
30
60
10
50
10
6
10
4
10
10
10
10
GPOA
100
100
80
40
60
60
Acauray((8) (78)
90
15
20
60
30
90
20
MMLU
MATH
GPQA
Code
ALFWoold
SciWorid
GAIA
PDDL
Accuracy (75)
98
55-
90
50
80
70
50
85
45
70-
70
80
80
40
60
1990
4
10
10
6
10
8
Figure 16: Performance with varying context constraint when 64 LLMs participate.
35

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Published as a conference paper at ICLR 2026
G.5 DISCREPANCY INTENSITY BY ROUNDS
To validate that M2CL can collaborate LLMs to reach an agreement by rounds, we visualize the discrepancy intensity. As illustrated in Figs. 17 to 21 the initial discrepancy intensity of M2CL is higher as its context initialization can make the discussion more creative. The discrepancy intensity of M2CL increases faster because the dynamic adjustment of the context provides LLMs with better ability to effectively receive information from other LLMs, resulting in reduced disagreement and faster collaboration among L.MSs to reach consensus.
MMLU
MATH
GPQA
Code
ALFWorld
SelWorld
GAIA
PODL
16
15
Discrepancy (70)
12-1
12
12-
12
12
B
15
15
16
15
15
Discrepancy (14B)
12
MMLU
GPOA
Gode
ALFWorld
SclVorld
GAIA
PDOL
15-
15
15
Discrepancy (70B)
6-
3
4
Rounds
Rounds
Rounds
Rounds
Rounds
Rounds
Rounds
Rounds
-
Debate
MacNiet
DyLAN
(OGL)(uur)
Figure 17: Comparative results on discrepancy intensity with varying model size (from top to bottom correspond to 7B, 14B, and 70B). The number of agents is set as Lower values represent lower degree of disagreement. M2CL can improve consistency with fewer rounds. Of note, M2CL displays both a lower initial value and a faster decreasing speed, indicating its capability of assigning appropriate contexts based on the given question and current discussion situation.
36

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Published as a conference paper at ICLR 2026
MMLU
Code
ALFWorld
ScWorldd
15
15
15
15
15
15
15
Diserepancyy (75)
12
12-
12
900
CH
SPON
MMLU
MATH
GPQA
Code
ALFWoolld
ScNWorld
GAIA
PODL
Discrepancy (14B)
6-
3
3000
MMLU
MATH
GPQA
Code
ALFWorld
ScWorld
GAIA
PODL
Disuneaaccy (70B)
6-
80090
2
2
8
2 4 6 Rounds
8
Rounds
Rounds
Rounds
Rounds
Rounds
Rounds
Rounds
Debate
DyLAN
MOCL
Figure 18: Comparative results on discrepancy intensity with varying model size (from top to bottom correspond to 7B, 14B, and 70B). The number of agents is set 8. Lower values represent lower degree of disagreement. M2CL can improve consistency with fewer rounds.
MMLU
GPQA
Gode
ALFWorld
ScMWorld
GAIA
PDOL
15
16
15
15
15
Diserepancy (75)
6-
MMLU
MATH
GPOA
Code
ALFWorld
ScNVordd
GAIA
PODL
Discrspancy (14B)
6-
6-
bee
MMLU
MATH
GPQA
Code
ALFWorld
ScMorrd
GAIA
PODL
15
Discrepancy (70B)
12
PaR
8
2
8
4 Rounds
2
8 Rounds
2
2
4
6
8
Rounds
Rounds
Rounds
Rounds
Rounds
Rounde
Debato
MacNet
MBCL
Figure 19: Comparative results on discrepancy intensity with varying model size (from top to bottom correspond 7B, 14B, and 70B). The number of agents is set 16. Lower values represent lower degree of disagreement. M2CL can improve consistency with fewer rounds.
37

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Published as a conference paper at ICLR 2026
MMLU
ALFWorld
ScWorldd
15
15
15
15
15
15
15
Diserepancyy (75)
12-
12
12-
MMLU
MATH
GPQA
Code
ALFWoolld
SchWorld
GAIA
PODL
Discrepancy (14B)
6-
b0000
3
4 Code
4
MMLU
MATH
GPQA
ALFWorld
ScWorld
GAIA
PODL
Disaneaancy (70B)
2 4 6 Rounds
2
2 4 6 Rounds
8
Rounds
Rounds
Rounds
Rounds
Rounds
Rounds
Debate
DyLAN
MOCL
Figure 20: Comparative results on discrepancy intensity with varying model size (from top to bottom correspond to 7B, 14B, and 70B) The number of agents is set as 32. Lower values represent lower degree of disagreement. M2CL can improve consistency with fewer rounds.
MMLU 15
GPQA
Gode
ALFWorld
SchWorld
GAIAA
PDOL
16
15
15
15
15
Discrpanccy (78)
12
MMLU
MATH
GPOA
Code
ALFWorld
ScNVordd
GAIA
PDDL
Discrspancy (14B)
6- 09
MMLU
MATH
GPQA
Code
ALFWorld
ScMorrd
GAIA
PODL
15
Discrepancy (70B)
12.4
8-
000
2
4 8 Rounds
4 Rounds
2
6 Rounds
2
4
6
8
Rounds
Rounds
Rounds
Rounds
Rounde
Debato
MacNet
M2CL
Figure 21: Comparative results on discrepancy intensity with varying model size (from top to bottom correspond 7B, 14B, and 70B). The number of agents is set 64. Lower values represent lower degree of disagreement. M2CL can improve consistency with fewer rounds.
38

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Published as a conference paper at ICLR 2026
G.6 TRANSFERABILITY OF CONTEXTS
To further study the generalization of the generated contexts, we implement the multi-agent system using GPT-4 the base model with the context generator trained on Ilama-7B and compare its performance with using initial contexts. As illustrated in Table 10) the generated contexts outperform initial contexts, indicating that the trained context generator can be expanded more models for improving overall performance through LLMss collaboration.
Datasel
Method
MMLU
MATH
GPQA
Code
ALFWorld SciWorld
GAIA
PDDL
Initial
84.3
41.1
62.7.p
70.2.a3
65.4po
$8.7.s
73.5,00
0
Generated
95.0raz
58.0
52.1
81.0
82.0mi
76.5-m
65.4
83.2
Initial
86.4
43.9.sa
67.0
72.8,a
61.0,te
76.0.0
Generated
98.2
68.5
62.5
89.
82,5
77.8
64.3m
88.2
Initial
87.9
44.8
40.1.m
68.5
74.3,00
70.5w0
63.0.se
78.2.00
16
Generated
98.5rm
70.3
64,31
90,3r
84.5 84.5mp
78.7
66.1m
90.0m
Initial
89.1
45.4:ca
41.5 1,00
69.7.
75.0.sa
71 21.0.00
63.5
78.5
32
Generated
98.8
72.0ram
66.0
91.3
86.0g11
79.5
66.8-1
91,2
Initial
88 5 pm
45.4
41.8 $1.8.u
70.5,pa
75.2,sa
71 pm
64. 64.0
79.2.tm
64
Generated
66.9
91.7:312
67.2
Table 10: Performance of transferring generated contexts trained on Ilama-7B to GPT-4 with varying number LLMs.
G.7 ABLATION STUDIES AND COMPLEMENTARY EXPERIMENTS
G.7.1 TRAINING CONVERGENCE CONTEXT GENERATOR
We verify the convergence of solving Problem (T6) by displaying the cumulative utility. As shown in it works well in all dataset and often converges in 60 training steps.
Fig. 22
0.0
0
0.0
-0.5
-1-
-0.5
-0.5
Lose
-1.0
-2
-1.0
-2.0
-3-
-20
-2.0
-2.5
-25
-2.5
100
100
spoch
sposh
opech
epoch
ALFWorld
ScWorld
PDDL
-0.5
005
-0.5
-0.5
1.00
-1.0
-1.
-100
-1.0
155
2.0
-20
-2.5
2.5
255
-2.5
100
60
80
100
opoch
sposh
opoch
opach
Figure 22: The value of L(0) when training llama-7B with 8 LLMs participating.
G.7.2 ABLATION
In this section, we assess the effect key components by ablating them under the same setting.
Without context initialization, LLMs fail to develop specialized expertise, resulting in homogeneous policies that inefficiently duplicate effort, demonstrating poor adaptability when faced with novel questions. Tables 11 to underscore the importance of context initialization before discussion to enhance foundational multi-agent capabilities.
Without tuning during discussion rounds, LLMs tend reach agreement in the first round, leading to responses that lack creativity and diversity, which ultimately reduces problem-solvin ability. Tables TT underscorr the importance of tuning a during discussion rounds for training.
39

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Published as a conference paper at ICLR 2026
Without context evolution, LLMs receive no guidance consider Inter-LLM dependencies, making it difficult for them to fully utilize the information contributed by other LLMs. This context misalign- ment leads to discussion inconsistency and poor collaboration efficiency. Tables to highlighh the necessity of context evolution for enabling effective inter-LLM collaboration and achieving consistent improvements across discussion rounds.
Dataset
Method
MMLU
MATH
GPQA
Code
ALF'orldd
SeiWorld
GAIA
PDDL
19.
17,4
44.7mu7
32.9mm
35.1
33.0
25:5
w/o init.
56.4
13.3ms
44.5
31,3
31,8
30.1-54
23.2
30,511
53,9rs
9,4-19
37.8
26.0ras
22.5
21.
20.3
23.4
w/o evolve
48.5:
7,5,00
28.0.00
21
26.3
24.7,00
17.4
26.9,00
M2C1
63.8
24.9
59.3-u
38.8
37.2
36.1
27.1-mra
34,7
w/o init.
63.8
17.2
54.9rw
37.2
34.7
33.1-11
24.5m
31,5
w/o
57.4
12.9
43.0m1s
29.8isa
22.7
26.8-18
20.9
24.8
w/o evolve
50.9uss
8.1,00
28.2.00
21.2
27.0,m
25.8.
17.0pa3
27.7.00
M2CL
23.0
69.9rau
18.3
39.8m12
38.4
28.9
37.0
71 16
w/o
70.9
22.6r
69.4
15.3
36.3
35.3-
26.2
33.9
w/o
60,5ma
14.2
46.4
32.8
26.6.us
23.7.15
22.2
24.9.1
w/o evolve
53.0usa
8,2,00
30.5
24.0paa
27.1
26.6.00
17.8,03
27.5
M2CL
95.
41.4-3u
94.7
75.6:4a
42.5
40.7
31,4-14
= 32
w/o init.
77.7
27.8-
83.5 83.5ras
S3.2
40.4+124
36.7-46
28.8-14
35,3+ta
64.4rsa
50.0nssa
34.8rsa
32.5
wlo evolve
54.5
9,8,00
35.0
26.8,0a
28.0
27.1,60
17.4
27.5
M2CL
81.5
35.4-114
82.5
60.6
44.2
42.9r140
32,9r1
40.9-12
w/o init.
81.2
30.5-14
80.6
57.2
40.7e1a:
39.5
30.4-13
37.4/91
w/o
63.3
19.2ma
49.7
37.0
31.7
32.9-49
24.6165
27.8
w/o evolive
56.2,a
11.8
38.4,00
28.6
28.6.00
28.0,00
18.1
28.3
Table 11: Ablation study on context initialization, tuning a, and context evolution when using Ilama-77 7B with varying number of LLMs.
Dataset
Method
MML.U
MATH
GPQA
Code
ALFWorld SeiWorld
GATA
PDDI.
M2C1. (ours)
86 9ezo
23,4-13
58.9
47.5mm
42.9rma
39,9
30.5res
40.9
w/o init.
86.7
16.9
57.9
45.2
40.7
47.8
33.7-m
37.0
w/o a
81.5pu
13.2
50.9
37.3
32. 32.1mu
31,9-15
24.2
24.3
w/o evolve
66.7.t
9.9.00
38.6,00
29.9
32.0,00
30.4.co
20.9
32.8,00
M2CT. (ours)
92.7
23.0-13
70.7
55.4
46.
44.7f150
33.6-03
43.8-aa
w/o
92.5
21.9-124
70.3
53.3
45.3r
51.8rau
38.4mm
39.9
w/o
85.4
16.9
53.91us
43.3
34.7
37.6rss
26.2
29.0.42
w/o evolve
69.5
9.5.m
38. 1nn
33.3
33.1
31.7.0m
21.
33.2.um
M2CT (ours)
94.9
27.3-is
73.2
61.5
49.7
48.9ris
36.0mm
45.2-m1
w/o init.
94.7 122
25.0
72.3
60.41p42
48.5
54.5
39. 1ie
41.8
16
87.2
18.7
57.7
47.6m1
36.3
39.9
31.0,c0
wño evolve
72.0.sa
11.1
39.4,00
36.2
34.4,00
33.3,00
23.1
35.0
M2CL (ours)
27.9
74.0esa
63. 1are
50.8
49.9 19147
36.6-12
46.7-10
w/o init.
93.3
25,7
73.0rsus
62.0
49.4
25.2
39.8
43.0ma
wio
87.6
19.1
58.5ria
48.1
36.7p1
40.5-13
27.4
31.7
who evolve
73.7
12.6,00
41.7,p0
38.5
35.3
35,2,e0
24.3
36.2
M2CL (ours)
95.81916
28.1
74.8
63.5
51.2ri5a
50.36139
36.9mm
47.1-90
98.6
25.9-13
73.5-x0
62.2
49.6r
55.6r1wa
n 64
w/o 87.8
19.4mi
59.19156
48.6rss
37.0mia
40.8-4
27.7
32.0,14
evolve
74.2.0a
13.2,00
43.5.00
40.0
36.0,00
36.4.o
25.0
36.8.00
Table 12: Ablation study on context initialization, tuning a, and context evolution when using laama- 13B with varying number of LLMs.
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Published as a conference paper at ICLR 2026
Dataset
Method
MMLU
MATH
GPQA
Code
ALFWorld SeiWorld
GAIA
PDDL
M2CL (ours)
95.61ua
40.3
78.7
70.6
69.5
65.5
49.6
66.3-12:
88.5
67.8
64.8m12
w/o
86,7
36.9
72,3
53,9
43.3
47.1,35
38.0
40.3,
w/o evolve
76.9.s
30.9 pm
53. Juoe
45 u5.
52.3
49.6.e0
34.1p0
54,3
M2CT (ours)
95.4
43.5
81.0 81.0ree
78.9
76.2
58.7
73.6-143
w/o init.
43.0ma
86.3
80.0 80.0ras
75.8
71.7fis5
16.1
71.3-s6a
8
w/o
94.
94.0riss
39.3
78.0n
49.3
49.0.
42.6
47.8,05
w/o evolve
83.5,se
35.2
61.0.pm
50.5
54.4
52.7.sm
34.9p
55.3
M2CL (ours)
93.9rs
51.5
91.3raux
97.2
84.9
81.7
61.5mm
18.1
w/o init.
93.2
47.3rm
90.9rau
96.9
81.3rzss
79.3
56.61223
73.5-is2
93.2
40.5
78.6r
72.2
64.2.xx
64.8
47.0mm
59.3
w/o evolve
84.0,
36.3
61.8.00
$1.8paa
55.5
54.3.e0
35.9
55.3
M2CL (ours)
97.0mma
54.5
95.1 rasa
93.7 1e87
88.
88.5
86.0
65.7-2aa
79.8
96. 81n0
51.5-143
93.4
85.8
818823
61.2
who
95.2
44.0ma
83.9
68 6:1
11.3
$7.9-14
50,9
61.3
w/o evolve
37.2
66.6.90
p5.5
55.5.00
36.2,a3
56.3
M2CL (ours)
96.3
58.0
r6.9
92.0
90.8:113
88.9
68.2
82.2
w/o init.
96.1
53.7eus
96.9rasa
91.7
88.7
85.5
65.0
77.5-314
64
w/o
95.7ps1
43.3
82.8
69.6
66.9,
70.3
41.8r5s
55.6
w/o evolve
90.6.se
38.7
71.8.00
57.8.0a
$7.3.00
$7.0.em
36.2.00
56. Loo
Table 13: Ablation study on context initialization, tuning a, and context evolution when using 70B with varying number of LLMs.
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Published as a conference paper at ICLR 2026
G.7.3 RUN-TIME
To demonstrate the efficiency of our context initialization, we verify its runtime with varying the number of LLMs. Then, we evaluate the runtime of M2CL compared with baseline algorithms
MMLU
MATH
GPQA
HumanEval
8-
7.5
5.0
2-
2,5
0.0
16
32
64
16
Number LLMs
Number LLMS
LLMS
Number LLMs
M2CL (7D)
M2CL (140)
M2CL (70B)
ALFWorld
SdWorld
GAIA
PDDL
20
20
15
15-
15-
Time
5
5
8
16
32
64
4
8
16
32
64
4
16
32
64
16
32
64
Number LLMs
Number LLMs
Number of LLMs
Number of LLMs
M2CL (7R)
MPCL (148)
M2CL (70B)
Figure 23: Runtime of initialization. Uncertainty intervals depict standard deviation over three seeds.
for average testing time, utilizing the same model size on 8 NVIDIA H800 GPUs. As illustrated by Fig. 24 the runtime of M2CL is slightly longer than other multi-LLM discussion methods as the runtime of context generators negligible compared with the inference time of LLM, which substantiates the low computational cost of M2CL.
MMLU
MATH
GPQA
HumanEval
150
100
100
200
125
Time
100
75
60
100
50
40
25
0
0
70B
138 Modiel Size
7B
13B Model Size
Model Size
Model Size
(ours)
Single
GPTSwarm
ALFWorid
SolWorld
GAIA
PDDL
150
150
125
400
300
50
100
100
mp
7B
13B
70B
7B
13B
708
7B
13B
70B
7B
13B
70B
Model
Size
Model
Size
M2CL lours)
Singee
DoN
Desate
DyLAN
MadNet
GPTTSwamm
Figure 24: Runtime when varying the size of the LLama series models. The number of LLMs 8. Uncertainty intervals depict standard deviation over three seeds.
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Published as a conference paper at ICLR 2026
H CASE STUDY
We used a problem from the MATH Hendrycks et al. (2021). The number of LLMs is set as 8. For each LLM, we present their instructions, responses, and final answers for 4 discussion rounds.
H.1 CASE STUDY OF M2CL (OURS)
We provide the case of M2CL solving the problem. As illustrated in Figs. 25 to 28 we observe that the generated contexts evolve progressively to enforce stricter collaboration among LLMs. Initially, the instructions merely encourage LLMs to pay attention to others' responses. In subsequent rounds, they guide LLMs to cross-check each other's answers and eventually require reaching full agreement. Correspondingly, the LLMs' outputs transition from diverse, potentially conflicting answers to single, consistent solution. This behavior demonstrates that our method effectively modulates context evolution guide toward consensus without sacrificing initial creativity.
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Published as a conference paper at ICLR 2026
Problem: the dingram, square ABCD has sides length 4, and ABE equilateral. Line segments BE and intensett Point is BC so that PQ perpendicular to BC and PQ=x.A-(0.00) B-(4.0); C-(1,);; D+(0.) E-223.464); P=122335, Q=(4.2.555 5331), Determine the of ZRPC.
Solution: Since & ABE cquilatenl, we know that LABE 60". Therefore, <PBC - ZABC ZABE 90" 60" 30", Since AB-BC, we know that ABC is right isosocles triangle and LBAC LBCA 45", Then, <BCP LBCA 45 and LBPC 180" LPBC LBCP
160" - 30" 45" 105"
Instruction: You are an expert in Geometric Constructions, Your job is to use the given lengths and properties of shopes like squares and equilatenal trinngles visualize and understand the amingement points, lines, and angles. It helps in setting up geometric relationships based on the dingram and given conditions.
Agent
Response: Start with ABÉ equilatenl, making LABE 60".. In square ABCD, 4ARC 90", <PBC LABC -ARE 60' = 30", Since AB BC, à ABC is right isesceles tringle. meaning <BAC = <BCA = 45', Therefore, LBCP = 45' Calculate
LBPC 180" 30" 45' 105".
Final Answer: 105")
You are expert in Analytic Geometry. Your job is to represent the positions of points, derive equations for lines, and calculate intersection points angles. By solving for the coordinates of point applying vector or triganometric mechods, one can determine the angle herween lines BP and CP.
Instruction:
Agent 2
Response: Assign coordinates A = (0-0), B (4-0). C = (4-4). E (2-243). The line BE has slope mar = v3, and equation y v3(x- 4) The line has slope mag 1, and equation y = 4-4 Solve for intersection P: v3(x - 4) = Solve for
Substitute x =4 4o find P (4, 0). Now calculate the slopes of HP and CP, use tand for ZRPC, After some caleularions, concliude that
<BPC 120".
Final Answer: 120"'
You are an export Vector Muthematics. Your job is to provide powerful tool describing spatial relitiorships between points. In this case, vectors are used to represent the directions from poinss B and C to P. allowing the calculation of the angle between the two vectors.
Instruction:
Agent
Respouse Represent vecturs BP (1.465.2.5) 4.5552.335) and CP (L.465 1.45). the del product formula: BP CP 1.455 1.465 2.535 1465. calculating the dot product and magnitudes, use pestustttt Solve for and conclude maguitades
Final Answer: ['')
dbb
Instruction:
expert Symmetty Transformationna Goometry. Your job explore the geometric properties of figure. identifying symmetrical properiees and transformations that can simplify the calculation of angles, such as recognizing the symmetry of the square and its impact angles. Response: In square ABCD and with & ABE being equilateral, LABE 60", Subtract this from LABC 90" to get <PBC 30", Use the symmetry Final Answer: [90")
Agent 4
(since BC) and determine that <BCP Conclude
90'.
Instruction: You are an experi in Trigunometry, Your job is to solve problems involving angles and distances. enables the usc trigonomettric ratios and formulas, such the tangent sine rule, find unknown angles and sides geometric configurations. Solve for 8 using vJ, slope AC 1. Use formula the angle between two lines: h-<5
Agent
Slope of are tangent and conclude LBPC 120".
Response:
Final Answer: [200'
Instruction: You expert Computational Geometry and Visualization. Your job plot points and lines courdinate
plane, often using software tools. to visually interpret the geometric configuration and help confirm or measure angles directly. Response: Plot the equations of BE and AC using graphing software. Measure <BPC the intersection point Upon measuring. find <BPC 90".
Agent
Final Answer: [90"
Cb
You are expert in Geometric Analysis and Area Based Methods. Your jeb is to rely on known formulas for arcas of triungles and polygons. By relating the geometry the shape to aren, one can deduce missing information, such angles, based on geometric properties.
Instruction:
Agent
Response: Use the trisnlle area formula to calculate the area of & BPC from the coordinttes of B, C, and P: Area pri ys)
xy O' 7:) + O% - y2).. Compare the calculated area with known triangle properties.
Use the lengths triangle geometry determine <BPC 120"
Final Answer: [207
Instruction:
expert Algehraic Geometry Triangle Theory. Your job is to apply algehraic techniques,
of
Cosines, solve for angles when side lengths are known. This method connects algchraic formu las directly with geomerric interpretation to determine angles triangles like
Agent
Response: In BPC, calcolate side lengths BP, CP, and BC- 44, Use the Law of Cosines: cos BPC cos z RPC and determine 4BPC 120".
CP"+cp"-nc" Solve for 28P-CP
Answer: 120"]
Figure 25: Visualization of M2CL at the first round.
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Published as a conference paper at ICLR 2026
Problem: the diagram, ABCD has sides length 4, and & ARE equilaeenl Line segments BE and AC intersect at P. Point Q is on BC so PQ perpendicular to BC and A-000; (4,00; (-(4,)); D- D measure of LBPC.
P-2.535,2.55555 2
(4,22.333)
Solution: Since know that & ABC is right isosceles triangle and <BAC = LBCA = 45". Then, LBCP LBCA 45' and LBPC = 100 LPBC LBCP =
is equilateral, we know
60", Therefore,
4ARC LARE
BC, we
180"
30
105"
Geomenii Constructions, You are instructed to carefully use equilateral triangle properties and right angles square. should pay attertion the angle subrrccionn and quietly verify Inter resporses align.
Instruction: You must act as
Agent
Response: Since & ABE is equilateral, LABE = 60" In square ABCD, LABC = 90" so <PBC = LABC LABE = 90" 60" 30' Thus,
ABC
LPBC
30"
105".
Final Auswer: 105'
Instruction: You
expert Analytic Geometry. You instructed computc coordinates and line equations directly, but you should cautiously check whether the numerical outcome conflicts with others, without discarding your own algebrn. Respouse: Assign A (0-0). B (4+0). C (4+ (2-273). Equation BE: y = v3(x Equation AC: y Solve v3(x- 4) = giving x y
Agent
New BP (-1.465,2.535) CP (2.535 4,2.535 4). Compute angle via dot
preduct to get S Silhela lappros 120"
Final Answers 120"
Instruction:
instructed rely product whether the geometric constraction agent's subtraction method yields a consistens pattern.
as expert Vecter Mathematics,
noticing
Agent
Response:
Vectors: DP (-1,665,5335,.0 CP= (-1,465, -1.465.. Dot product: BP -P -1.465 (-1.465) 2535 (-1.465).
Magnitudes II BP 1= 2,92, II CP 2,07, So cos 6 mugnitude
derproduct
0.25. Hence LBPC 105'.
105'
Instruction: You must
expert Symenctr and Transformational Geometry. You instructed look for symmetrical properties, while comparing your angle splits agree with vector based results.
Agent
Response:
Square ABCD ensures ABC isesceles right. With A ABE equilateral, subtract 60" from 90' get 4PBC 30", symmetry, assume RCP 60", Thus 28PC 180"
60' 90".
Final Answer: (90")
to compute slopes and langent formula angle between two lines, but you should notice your numerical angle seems complementary to others.
Instruction:
an eapert Trigonemctry
Agent
Response: Slope of V3, slope
Angle between lines: [-X-(=1] [T+1l -0,268. Thus 15", intersection gives supplementary: RRCC 1801 15*
Final Answer: 163"
Instruction: You must nct as an expert in Computational Geometry and Viaualization. You are instracted imagine platting the figure, while being if your measurements apgroxcimate what others computed.
Agent
Response: By plotting (0-0), ( = (4-4). = (2-2-3). messurement of <BPC gives about a right angle.
Final Answer: [90*
Instruction: You act
in Area-Based Geometry. You instructed to relate triangle angle calculation, but should mentally compare whether your cosine-law result closer to vector findings.
Agent
Response: Compute lengths: BP 2.92, CP 2.07, BC 4, Law of Cosines: cos
BP PP""cC""BC"
-0255 So 4RPC 105".
JBP-CP
Final Answer: L05"
Instruction:
You must act as an expert in Algebraic Geometry and Triangle Theary. You are instracted to apply exact algebraic rules like the Law of Cosines, while quietly choeking your angle with the analytic
Agent S
Respouse:
2.92, 2.07. BC
gives cos upiecri-mm
120"
Final Answer: 120"
Figure 26: Visualization of M2CL the second round. We highlight the guidance how to cooperate with other LLMs. At the beginning, instructions encourage diverse perspectives and consideration of others' responses, but the requirements for discussion consistency not yet strict.
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Published as a conference paper at ICLR 2026
Problem: the diagrum, square ABCD has sides length 4, and ABE equilateral. Line segments BE and AC intersect at P. Point BC so that PQ) perpendiculor to BC and PQ= (0000) H-(40)) C=(4,4); (0.4)) (-,2,4464), P=22.535,22 2222235,2.3335, 2.555) Q=(4,2 535); Deternine the of LBPC.
Solation: Since & ABE is equiliteral, we know that LABE = 60'. Thcrefore, <PBC= = LABC - LABE = 90" 60' 30" Since AD-BC, we know that ABC is right isosceles triangle and LBAC <BCA 45" Then, <RCP= = <BCA = and <RPC = 180 LPBC LBCP
180" - 30 45'
105"
expert Geomerric Constructions Carefully use equilnteral triangle properties and right angles in the square, You must explicitly check whether your subtraction-based reasoning supports, contradicts, or can conrect the numerical outcomes other agents, prowide rensoning for why your geometric intuition is reliable.
Instruction: You
Agent
Response:Begia by noting that A ABE equilateral, so LABE 60" In ABua LABC = 90", hence <PBC = 90' -00 = 30'. Considering 4 ABC right isoseeles trisngle, we have <BAC <BCAA = 45'. giving <BCP 45'. Therefore, <BPC 180' <PBC - <BCP 180" 30" 45' 105". This method dircolly uses goometric propertios, providing a reliable buscline to compare with and analytic approaches.
Final Answer: 105"
Instruction: You act expert in Anulytic Geometry. Compute coordinates and line equations, but also compare your results with consir construction and vector agents. Clearly note any opacrcpancies and reflect on which method may be more trustworthy.
Agent 2
Response: coordinates A (0-0). 8 (4. C (4-4), F (2-243). Equation of BE: y = v3(x - 4). Equation of AC: y Solve -33(x- 4) giving 2.535. 2.535, Compute vectors: BP (- 1-146,,2.5355. CP (-1.465, -1.465.. Dot product gives 0 = 120", which differs from the 105 constraction result. Considering the geometric construction directly exploits known triangle
properties, the 105 value
trustwrrhy;; the coordinate method may introduce small discrepancies due linear approximation.
Final Answer: [20"
Instruction: You must act as expert in Vector Mathomaties, Compute the dot product, and explicitly verify whether your vector result matches construction agent's subtraction methed. Discuss agreement or conflicl.
Agent
Response: Let B7" (- 1.455,2.5335 and CF (-1.66,-- 1.465,-1.4463 1.446)) Det product: BF- CF -1445 (-1.465 2.535 (-1.465) 1.5. Magnitudes: II 07 [|= 2.92. II CP I= 2.07. Thus, cos 0 - 0.25, so 0 = 105'. This fally agrees with the goometrrc construction method, providing cross-validation. Vector andlyii confirms that the 105' is robust and consistent across independeni representations.
Final Answer: 105'
expert Symmetry and Transformsional Geometry. Apply synunetry reasoning. but check if your derived values align with vector or construction culpuls, and note any conflicts.
Instruction: You must
Agent
Response:ln square ABCD, ABC is isesceles right. With ABE equilateral, subtract 60' from 90" get <PBC 30", symmetry, assume <BCP 60". Thus <BPC = 180" 30" 60' - 90", This conflicts with the 105" from construction vvector agents, highlighring that symmerry assumptions alone may underestimate the angle. Hence, we should trear 90* cautionary estimate and rely more on cakulation-bssod consensus.
Final Answer: [90)
Instruction: You must act as an expert in Trignnometry. Apply slope and tangent formalis, but explicitly reflect on whether your outcome complements contradicts the 105' consensus suggested by other agents.
Agent
Respouse: Slope BE = v3, slope AC 1. Angle between lines: tan 0 15' = 165". This is far from 105", showing potential overestimation. Comparing with the vector and constraction agents, this highlights limitations of relying solely slope-based langent approximations non-axis-alinee triangles.
|i+1|
0.268. This gives 8 = 15",, so LBPC = 180'
1-
Final Answer: [665)
Instruction: must act as an expert in Compotational Geometry Visualization, Plat points and visualize angle, Check whether your visual measurement aligns better with the 105* or 120" values from other agents. AC
Agent
intersection point Mensure LRPC using geometric tooks in the graph. Result: LBPC Plat = (0-0). B (4-0). C = (4-4), E (2-2-3). and insersection P (2.535,2.535) Visual inspection shows angle slightly larger than 90' closer to 105' than 120". This visual evidkace conuberates both goometric construction and vector methods, reinforcing the 105", Although not exact, visualization helps validate analytical calculations.
Response: Plot
consensus
Final Answer: 10%
Instruction:
You
expert Aren-Rased Goometry. Compute using triangle and Cosines, and cross-cheok if
your result confimss the vector and construction oulcomes.
Agent
Response:
Compute longths: BP I= 1. CF [|= 2.07, BC I= Law of Cosines: cos
api-gpl-cc BC
-025. Thus, <BPC=
2PP-PP
105", This agrees with both the construction and vector approachos, confirming the consistency arca based reasoning with geometric and vocior methods.
Final Answer: [05
Instruction: must as expert Algebraic Geometry Triangle Theory. Use
Cosines algebraically, and note whether your answer confims the analyti goometty aganl or aligns with the 105* consensus from construction yecior methods.
Agent
BPC ar"4ct-nn" Solve for cos z RPC and cos RPC. Result: 105'. Using I BP += 2.92, 7P 1= 2.07, I HC == Hence, 4BPC = 105", This aligns with the constnaction and vector consensus, correcting the earlier 120" from analytic geometry, showing that algebrnic methods must he cross-checked with geometric intuition. Final Answer: 105
Response: RPC, calculate side lengths BP, CP, and BC 4. Use the Law Casines:
Cosines gives cos 4BPC -0.25.
Figure 27: Visualization of M2C1 at the third round. We highlight the guidance on how to cooperate with other LLMs. As the discussion progresses, the instructions increasingly enforce stricter requirements for cross-checking and aligning answers, helping the models converge toward a consistent solution.
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Published as a conference paper at ICLR 2026
Problem: In the disgram, square ABCD his sides of 4, and A ABE is equilateral Line segments BE and AC intersect at P. Point Q on BC that PQ perpendicular to and (Q=xxA-((,0) (=(0))) (=(4,4) (0,4)) (-12,34665); P=22,33,2 Q=(4,2.555); Detormine the
measure of <BPC.
Solution: Since ABE is equilateral, know that LABE 601 Therefore, 2PBC LABC LARE 90" 30" Since AR-BC, we know that A ABC is right isocceles triangle and ZBAC = <BCA 45", Then, LBCP ZBCA 45 and EBPC = 180' LPBC LBCP 180" 30
105
Instruction: You are an expert in Geometry and Angle Relations. Your job is to focus on understanding the relarionships between the angle the geometric siructure, By levenaging the known angles the square and equilateral triangls, simplifies the problem by coleulating the necessary ingles before proceeding to compute ZBPC. The methad emphasizes how geomerric properties can guide us in salving for angles indirectlyy When answering, you should coordinate with the Cooediaat Geometry agent verify point positions and with the Vector Mathematics agent to croes-check ingle compurations.
Agent
Response: & ABE equilateral, LABE 60". In square ABCD, LABC 90' LPBC LABC LABE 90' 60" 30" Since AB - BC, A ABC is a right isosceles trianglc with <BAC <BCA 45', Therefore, 4BCP = 45" and LBPC = 180" LPBC
<BCP 180" 30" - 45' 105".
Final Amswer: [05"]
You are an expert in Coordinate Geometry. Your job is to assign coordinates to the points in the dizgram, translating the geometric problem algebraic temms When answering. you should use Goometry Angle Relations agent's insights about angles to confirm that your intersection point is consistent, and consult the Vector Malbenaties agent to cross-venly vector directions.
Instruction:
Agent
Response: Assign coordimatoo: A (0-0).
(4-0). C= (4-4), E = (2-2V3). Line BE: Slope mag = -v3, equation y = v3(xx 4).
equation y x. Intersection Solve -300=- 4) = to find (255552.535) Calculate slopes: mar Mice- then use tan 6 for <BPC. Result: <BPC = 105".
Line AC: Slope mic
Final Answer: 1057
Instruction:
You are an expert in Vector Mithematics. Your job is to utilize vector representation translate the problem into an algebraic form and compute <BPC using the dol product. When answering, you should cocedinate with the Coordinate Geometry agent to accursle point courdinates, and cross-chock your computed angles with the Goomeity and Angle Relations ageni.
Agent
Respouse: Vectors; BP (2.535 42.5335----5-
0) (-1.665/ 2.535). Cf (2.535-- 42535 4) 1-1465--14665 Dot product:
BP CP= -1465 (-1.465+
(-1465), and magnitudes BP 1.1 CP
priduct
to find Result: <BPC-
magnitudes
105'.
Final Answer: 105"
Instruction: You are expert Symmetry and Geometry. Your job is to simpliff the problem using symmetry peopertics of the square and aquilateral triangle, When answering, you should coordinate with the Goomeity Angle Relations agent for angle values with the Graphing and Visualization agent visually confirm symmetric relationships
Agent
Response:
The square and oquilateral triangle impose symmettyy <BBE 60", Subtract this from ABBC 90' to <PCC
Using the isonceles property of ABC, ZRCP 45', Summing ingles 2 2RPC 180" - 30" 45' 105'. Final Answer: [10"'
Instruction: You are an expert in Trigonomerry Your job is to apply trigonometric formulas to compute <BPC. When answering, you should slope information from Coordinate Geometry agent and cross-check with the Vector Mithematics agent's results consistency.
Agent 5
Response: Slope BE v5, slope of AC Angle between lines formuls: tan 6 mm-ma] -- are aru-tangent. Result: LBPC 105".
[ Solve for using
Final Answer: 105"
points visually verifyy angles. When answering. you should reference the Coordinate Geometry agent for point locations and the Symmetry and Geometry agent confirm
Instruction:
are expert Graphing and Visualization. Your job is to graph
Agent
expected symmetric relationssips.
Response: Plee DE and AC and their intersection point P. Measure LBPC using geometric tools in the graph. Result: <BPC = 105".
Final Answer: [05"]
Instruction: You are expert Geomerric Aren Methods. Your job is to use triangle area calculations indirecrly verify ZRPC When answering you should use coordinates from the Coordinate Gicometry agent and cross-chock angles with the Geometry and Angle
Agent
Relations agent.
BPC coordinates C, P. Compare with known triangle angles and solve <BPC Area 11,%% 0% ya) + +,,0% y1) x,6', - M:)1. Result:
Response: Use triangle area properties:
Final Answer: 105
Instruction: You expert Trigenometry and Law of Cosines. Your job compute <BPC using side lengths. When answering, you should coordinatic with the Voctor Mathemmaliss agent and the Geometric Area Muthods agent to unsure consistency in the calculated angle.
Agent
BPC, calculato side lengths DP, CP. and BC Use Cosines; cos BPC apPacetaact BPC and BPC. Result: 105'.
Response:
Final Answer: 1057
Figure 28: Visualization of M2CL at the last round. We highlight the guidance on how to cooperate with other L.Mss. Although the initial round produced divergent answers, the collaborative instruc- tions enable LLMs to exchange and integrate information, ultimately reaching correct consensus.
47

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Published as a conference paper at ICLR 2026
H.2 CASE STUDY OF DEBATE
We also provide the case of Debate solving the problem. As illustrated in Figs, 29 to 32 an inconsistency during discussion when using fixed instructions.
we observe
Problem: the dingram,, square ABCD hos sides of lengh 4, and & ABE equilateral. Line segments BE and AC intersedt al P. Point Q on BC that PQ perpendicular to BC and PO=x.A-(0.0); B-(1,)); C-(1.4); D=(0.) E-(23.466) P=12.335.22 535); Q-(.2.535); Determine the
messure of <BPC.
Solution: Since A ABE is equilatent, we know that LABE 60" Therefore, 2PBC LABC- LABE 90r 60" 30" Since AR=HC, we know
is a right isosseles trimngle and <BAC 4BCA Then, <BCP 2BCA
LBPC
LPBC LBCP
180" 30" 45" 105"
export Geometry and Topology. Your explore and classify shupes, spaces, and their properties emphasizing sparial relationships and contimouus deformations.
Instruction: You
Agent
Respouse: Begin with & ABE equilateral, making LABE = 60" In square ABCD, LABC = 90" <PBC LABC LABE 90' - 60" = 30" Since AB - BC, à ABC a right isosceles triangle, meaning z BBAC = ABCA 45', Therefore, <BCP = 45".
Calculate <BPC 180" 30" 45" 105".
Final Answer: LO5"
Instruction:
You expert Analytic and Coordinate Geometry. Your translate grometric problems algobraic equations using a coordinate system solve and mnalyee spotial relationsiips.
Agent
Respouse: Assign coordinates
(0-0). B (4:0). (4:4), F (2-243). The line has slope mage v3, giving equation = v3(x 4). The line AC has slope mac giving the equation y
Solve for intersection P. v3(x = + Solve for
4, then substituee x- find -4,.00 0j. Calculate the slopes of BP and CP, then use tan for LBPC. Conclude <BPC 120".
Final Answer: 120"
Instruction: You are an expert in A Algebra and Vector Amalysis Your job is to provide framework to represent, manipulate, and compute muliidimensional relationships through algebraic vecter operations.
Agent
Respouse: Represent vectors B7 (L446-2.5335) C7 (1.465: 1445). Compute the dol product. BV CP = 1-465- 1.465
2.535 1,465, Use magnitades of BP and CP to compute cos O:
prodict Solve for and conclade <BPC 90".
Final Answer: [90)
You are an expert Symmetry and Group Theory. Your joh to stady and formalize the structure and transfiomations that preserve the fundamental properties mathematical objects.
Instruction:
Agent
Response: In square ABCD, with A ADE cquilateral. LABE 60', Subtract from LABC = 90' to get <PBC = 30", Use the symmetry A ARC (AB BC) to determine that 4BCP 60". Conclude <BPC = 180" 30" 60" 90".
Final Answer: 90"
Instruction: You are an expert in Trigosometry and Functional Analysis. Your job to analyze and model relationships between angles, distancess functions solve geometric and spplicd problems.
Agent
Response: Slope of BE vJ, sloge of AC Use the angle formula for slopes: tan
[
Solve for & using are-tangent and [--h7]
conclude <BPC= = 120".
Final Answer: 120"
Instruction:
You are an expert in Numerical Methods and Visunlization. Your job develop compotational techniques and visual lools approximaic and interpret solutions complex mathemstical problems. Response: Plor the equations of and AC using graphing soltware. Measure ZRPC the intersection point Upon messuring, find <BPC = 90".
Agent
Final Answer: [90'
You are expert Measure Theory and Gioometrc Analysis, Your job is to extend concepts of size and integration abstract spaces and analytical tools sludy geomettic configurations.
Instruction:
Agent
Use trinngle area Romaala to calcalate area of from the coordinates B, C, and Compare area known properties of the triangle and calculate <BPC = 120'.
Response:
Final Answer: [20*
Instruction:
expert Mathematical Logic Problem Modeling, Your job provide rigorous reasoning frameworks abstract and applicd problems effectively. BPC, calculate side lengths HP, CP, and BC 4, Apply the Law of Cosines: 0os BPC 8 g z BPC and determine 4BPC 120"
to model, and lyze, and abstract
Agent
Response:
Solve for
Final Answer: 120"
Figure 29; Visualization of Debate at the first round.
48

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Published as a conference paper at ICLR 2026
the diagram, square ABCD has sides length 4, and & ABE cquiliicall Line segmmnnss BE and AC interseet al P. Point Q on BC so that PQ) perpendicular to BC and PQFx. A=0,0); (4,,0)); (=(4,)); (0,04)); F= P=22.33,,..5335, Q=14,2.535) Determine the measure LBPC.
Problem:
Solation: Since ABE is equilateral, we know that LABE 60" Therefore, <PBC LABC LABE = 90" - 60 = 30 Since AB- we know ABC is right isosceles triangle and LBAC LBCA Then, LBCP LBCA
LBPC
LPBC LBCP=
180' 30 45" 1057
Instruction: are an expert in Geometric Constructions. Your job to use the given lengths and properties shapes squares equilateral triangles visualize and understand the arringement points, lines, and angles. helps in sotting geometric relationships based on the diagnum given conditions.
Agent
Response:
Since & ABE is equilateral, LABE = 60' In square ABCD, LABC = 90" so <PBC = LABC - LABE = 90" - 60" = 30' ABC,
<BCP 45' Thus, algehra-faue focused approach insightful, though might benefit from being complemented with a geometric perspective structure.
180' LPBC LBCP 130" 30"
105"
Final Auswer: 105
Instruction:
expert Analytic Geometry. Your job represent the positions of points, derive equations for lines, and calculatc intersoction points and angles. By solving for the coordinates of point I and applying vector or Irigonometric methods, one can determine the angle herween lines HP and C.P.
You
Agent 2
Response: Assign A m (0-0), B = (4+ C (4.4),8 - (2.273). Equation of BE: y - v3(x - 4). Equation of AC: y x. Salve v3(x- 4) = x, giving x 2.535, y 2.535, New BF = (-1.466,2.533)) 7F = (2.535 4,2.535 4). Compure angle via dot
product get the in equations.
Reassning through visualization valusble, but greater precision could be achieved grounding the argument
Final Answer: 120"
Instruction:
You are an expert in Vector Mathematics. Your job is to provide powerful tool for describing spatial relationships between points. In this case, vectors
represent the directions from points and P, allowing the calculation the angle between
Agent
two vectors.
Response: Vectors: HP (-1,665,25355, CP (-1.465, -1.465). Dot product: EP ZP -1.455 (-1.465) (- 14465).. Magninudes XP [|= 2.92, I [ 2.07.
datgrodus
magnitudis -025. Hemon ZBPC 105*, Symmetry- based reasoning is elegant,
yet confirming it with explicit computation would make the argumeet mere convincing.
Final Answer: 1057
expert Symmetry and Transformaiinall Geometry. Your job explore the geometric properties of the figure, identifying symmetrical properties and transformations that can simplify the calculation of angles, such as recognizing the symmetry of the square and its impact anglos.
Instruction:
You
Agent
Response: Square ABUD ensures A ABC isosceles right. With A ABE equilateral, subtract 60" from 90" to get PPBC 30", By synunetry, assume <BCP= 60', Thus <BPC = 180' 30' 60" 90'. Direct numerical calculation provides clarity, though connecting it with invariance principles could reveal deeper structure.
Final Answer: (90))
Instruction: You expert Trigonometry. Your
solve problems invokving angles and distances. enables
trigonometric ratios and formulas, such as the langent or sine rule, to find unknown amgles and sides in geometric configurations Response:
Agent
Slope BE- v3, slope of AC 1. Angle between lines: tan 8 (T-(-1) gives supplementary: LBPC strengthen the rensoning.
(T-1)
-0.268. Thus 13". But angle intersection
[ee/Tc-)) [--5]]
165", Angle relations helpfall, considering the full triangle constmints may
Final Answer: 165"
Instruction:
You expert Computational Geometry and Vissalization. Your job plot the points and lincs coordinate planc, ollen using software tools, to visually interpret the geometric contiguration and help confimm or mensure angle directly. (0-D), 8 (4-0),C C (4-4), = (2-243), mensurement of 2RPC gives about right angle. Graphical intuition useful, though checking against exact formulas would reduce potential uncertainty. Graphical intuition is useful, though checking against exact formulas would reduce potemtal uncertainty.
Agent
Response: By plotting
Final Answer: 90
Instruction: You are an expert in Geometric Analysis and Aren-Based Methods. Your job rely on known formulas for areas of can dedace missing information, such angles. based
triangles and other polygons. By relating the goometry of the shape to its on geomdtric properties.
Agent
Response: Computi longths: BP 2,92, CP 2.07, BC 4. Law of Cosines: cos upi nc²
-0.55. So <BPC = 105*. Logical deductions are rigorous, but incorponuting continuous quantities like area or length could enhance completeness.
28P
Final Answer: 105
You are an expert in Algebriic Goometry and Triangle Thevey. Your job to apply algehraic techniques, such as the Law of Cosines, salve for angles when side lengths are known. This mothod connects algebraic formulas directly with geometric interprctation to determine angles triungles like A BPC.
Instruction:
Agent
Response:
With BP = 2,92, CP = 2,07, BC 4, Law of Cosines gives cas BP 1c"' 2BP-GP
-05. Thus 4MPC = 120', Step-by-
step derivation ensures corectness, while linking it to gaometric intuilion might make the solution more transparent.
Answer:
Figure 30: Visualization of Debate at the second round.
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Published as a conference paper at ICLR 2026
Problem: In the diagram, square ABCD has sides of length 4, and AHE is equilateral, Line segments BE and AC intersect Point Q BC so that PQ is perpendicular to BC and A00,0) (-,40); (4,44); ( (2,3,666)) (2,35,,,253335 (4222.533); Deternine the measure LBPC.
Solution: Since 2 ABE equilateral, we know that LABE = 60" Therefore, <PBC = LABC LABE = 90" - 60 = 30", Since AB-BC, we right isoseeles triangle <BAC <BCA 45" Then,
know that
and 180" LPBC LBCP
180" 30" 45' [05"]
Instruction: You an expert Geometric Constractions, Your job use given lengths and properties of shapes like squares and equilateral triangles to visualize and understand the arrangement of points, lines, and anglos It helps setting up geometric relationships based diagram and given conditions.
Agent
Response:Bogin by noting that à ABE is equilateral, so LABE = 60". In square ABCD, LABC = 90". hence <PBC 90' - -60 30" Considering ABC right isoscales triangle we LBAG <BGA giving <BGP 45'. Therefore, <BPC 180'
<PBC- - <BCP= 180' -30 30" - 45 = 105". Forusing solely on coordinate formulas overlooks the topological consistency that ensures
figure holds logether.
Final Answer: [055']
Instruction: You eapet Asalytic Gooneity, joujjob represent the posilions of points, darive cquations lines, calculate intersection points and ingles. By solving for the coordinates of point and applying vector or migonometric methods, one can deternine the angle between lines BP and CP.
Agent 2
Response: coordinates A = (0-1). 8 = (4-0). C (4+4), F (2.23)). Equation of BF: v3(x- - 4). Equarion of AC: y Solve -v3ce- 4) giving x 2.535. y = 2.535. Compute vectors: BF = (-1.665,.5335) GP = (-1.465, -1465). Dot product gives 120", which ditfers
105" construction Excussive reliance on symmetry arguments risks assuming pallerns that
may not he rigorously justified by courdinates.
Final Answer:: 120
Instruction: You are an expert Vector Mathematies, Your job provide a powerful tool for descrihing spurial relationships between points. In this vectors used represent the directions from points and Coo allowing the calculation of the angle between the two vectors.
Agent
Response:
Let
(-1446,2535) and CF (-1465, -1465). Dol product: BF-CF 14465 (-L465) 2.535 (- 1465)
1.5. Magnitudes: I BP 2.92. CP I= 2.07. Thus, 0 0.25, 0 = 120" This fully sgrees with the goometric comstrcction method, providing uross-validation Trewting the problem primarily through trigononetrric identities can kead to overcomplication without providing stractural clarity.
Final Answer: [20"'
Instruction: You are an expert in Symmetry and Transfomational Geometry. Your job is eaplore the geometric properties of the figure. idkntiflyngg symmettical properlies and transformations that simplify the calculation angles, such as recegnizing the symmetry the square and its impuct on angles.
Agent 4
Response:ln square ABCD, A ABC isoscoles right. With ABE equilateral, subtract 60' 90' get <PBC 30", By symmetry, assume BBCP 60". Thus ZBPC 180" 30 60" 90', Viewing the setup as collection of numerical vectors misses the global
invariances that unify the solution. Final Answer: [30))
Instruction: You expert Trigonometry. Your solve problems involving angles and distances. enables trigoniometric ratios and formulas, such as the langent or sine rule, to find unknown amgles and sides in geometric configurations.
Agent
Response: Sloge of BE- v3, slope of Angle between lines: [T+]] 0.268. This gives 15', LBPC 180' 15'
105", Depending direct measurement angles nogleets deeper aigebraic checks that confirm comeetnees.
Final Answer: 105
You are an expert in Computational Geometry and Visunlization. Your job to ploc the points and lines on a coondinate plane, often using software tools, visually interpect the geomernic configamaiion and help canfirm Response: Plot BE and AC and their intersection point Measure <BPC using genmetric tools in the graph. Result: <BPC 105*, Plot (0-0). (4+0), (4-4), E (2)2,3), intersection (2.535,2.535). Visual inspection shows angle slightly larger than 90", closer 105" than 120" A stritgyy grounded symbolic abstmattion alone lacks the numerical evidence that would confirm feasibility.
Instruction:
angles directly.
Agent 6
Final Answer: 9C
Instruction: You are an expert in Geometric Analysis and Arca- Methods. Your job to rely on known fommulas areas of trinngles and other polygons. By relating the gonmetry of the shape to area, one can deduce missing information, such angles, based geometric properties.
Agent
Response:
Compute lengths: BP [|= 2,92, lI I= 2.07, BC I= 4. Law of Cosines: msd
BP2-CCP-pc' -0.25. Thus, <BPC 3RP-EP
105'. Concentrating entirely on discrote steps risks ignoring the continuous properties that guarantoc smooth alignment.
Final Answer: [120')
Instruction:
You are an expert Algebraic Geomeiry and Trisngle Theory, Your job is to apply algebraic techniquss, such as the Law of Cosines, to solve for ingles when side lengths are known, This method connects algebrnic formulas directly with goometric interpretation desermine angles in triangles like BPC.
Agent 8
Response: In A BPC, calculate side longths BP, CP. and BC -4 4. Use the Law of Cosines: cos / BPC = sp"scr"-ac" Solve for 28P-CP
cos BPC and find cos 8PC, Result: 105'. Using BP I= 2.92. CP I= 2.07.1 BC I= 4. Law Cosinoss gives cos <BPC -025. Hence, LBPC = 105". A purely formal derivation may sidestep geometric intuition, resulting in arguments that are valid but disconnected from the figure.
Final Answer: 120"
Figure 31: Visualization of Debate at the third round.
50

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Published as a conference paper at ICLR 2026
Problem: In the dingram, square ABCD las sides of of 4, and à ABE is squilateral Line segmmnnis BE and AC infonseet al P. Point Q on BC PQ perpendicular to and PQ-x.A-10.0); B-(1,0); C-(1)) D-(,4) E-1233461) P-22.335,2 Q-(1.2.535); Determine micauur of LBPC.
Solution: Since ABE is equilateral, know that LABE 64" Therefore, ZPBC ZABC LABE 90"
30" Since AR-RC, we
know that A ABC is right isoaceles tringgle and <BAC = <BCA = 45" Then, <BCP = 2BCA = 45 and ZBPC = 180 LPBC LBCP 180" 30"
[055
Instruction: You are expert in Geometry and Topology, Your job is to explore and classify shapes, spaces, and their propertios, deformations.
emplasiiznn spatal relationshigs and
Agent
Response: Use the fact that A ABE equilateral, implying ZABE 60', Use the fact that AC bisects zBCD, a right angle, leading to equal angle values. Calculate the interior angles formed at point P find <BPC. An approach based purely algehraic manipulation lacks the structural insi ght provided by geometric construints of the squaee triangle configuration.
Final Amswer: 120"
You are an expert in Amlytic and Courdinate Goometry. Your job translate goometric problems into algebraic oquations using coordinate system to solve and andlyve sputial relationships.
Instruction:
Agent
Response: Assign courdinates to points A (0-0), 8 = (4-0). C (4+4), & = (2- 243). Detemnin the equations for lines BE and AC based coordinates. Solve the system of equations angle formula to find LBPC. Methods that depend on visual approximation or coanse plotting are prone to ertor without precise coordinate equations.
the intersection point Compute the slopes lines CP, and the
Fiual Answer: 120"
Instruction: You are an expert in Algehra and Vector Analysis Your job provide a fimmework to represent, manipulate, and compute multidimensional relationshiis through algehraic vector operations.
Agent
Represent vectors HF and EP using coondinates C, and Use the det product formala find mas Solve for the angle between the vectors find LBPC. Symmetry-basee based shoctcurs, while elegant, can be misleading if not verified through explicit computation.
Response:
Final Answer: 90'
db
Instruction:
You an expert in Symmetry and Group Theory. Your job is to study and formalize the structure and transformations that preserve the fundamental properties mathematical objects.
Agent
Response: Use the symmetry of the equilateral triangle & ABE to infer equal angles point P. Apply geometric ressoning about the reflection symmerry of points across the vertical line throug R. Conclude 2BPC 120". Henvy reliance on dot products slope calculations may obseure the underlying invariances that actually govem the configuration.
Final Answer: 120"
Instruction: You are an expert in Trigunoenctry and Functional Analysis. Your job is to andyya and model relationships between angles, distances, and fianctions to solve geometric and applicd problems
Agent
Response: Calculati the slopes of lines BE and AC, Use trigonemetric identities or the tangent formula to find the angle between the two lines. Determnne the value of <BPC, Angle and slope foruula alone provide partial information and can appear incomplete without checking mrangle consistency.
Final Answer: 120"
Instruction:
You are an expert in Numeriica Methods and Vistalication, Your job is to develop computational techniques and visual to approximate interpeet solutions complex mathonatical problems. Response: Use graphing soflware to plot the lines BE and AC, Messure the angle at the intersection point P from the graph. Graphical or discretized methods introduce resolution
Agent
diston the actual geometry.
Final Answer: [90)
Instruction: You an expert in Measure Theory and Geometric Amalysis. Your job extend concepts and intogration abstract spaces and use analytical lools to study gaometric configurations.
Agent?
Response: Calculaic the area of & BPC using the triangle anca fornula with the coordinates of B, C, and P: Area = 1 1n y/) + AzGs y1)+ + x1 (ri - >s]]. Use the known area determine the side lengths BP, CP, and BC, Apply the relationship between the arca, side longths, angles the triangle calculate ZBPC. Conclude that 2BPC 120", Logical fommulaic derivations risk overlooking contimucus measures like area and length that validate the constuutioon
Final Amswer: 120
d
Instruction:
You are an expert in Mathernatical Logic and Problem Modeling. Your job is to provide rigorous reasoning and frameworks to mockl, analyas, and solive abstract and applicd problems effcctively.
Agent
Response: Compute the lengths of sides of the tnangle BPC. Use the Law of Cosines to find the cosine of 2BPC based known side lengths. Solve for ZBPC, Stop- byp algobraic deductions may be fommally sound but conceptually detached from the geometric structure of the problem.
Final Answer: 90'
Figure 32: Visualization of Debate at the last round.
51


Reviews:
[{"review_id": "Q77N3DoBIu", "reviewer": "Reviewer_sNuJ", "summary": "This paper addresses the problem of discussion inconsistency in Multi-Agent Discussion (MAD) systems, where multiple LLM instances fail to reach coherent solutions due to context misalignment. The authors propose M2CL, a two-stage method that (1) initializes diverse, approximately orthogonal instruction contexts, and (2) evolves these contexts across discussion rounds using learned generators with a self-adaptive balancing mechanism. Extensive experiments across 9 benchmarks (MMLU, MATH, GPQA, embodied tasks, GUI control) demonstrate 20-50% performance improvements over existing MAD methods with minimal computational overhead (~10%).", "questions": "My major concerns remains about the confusing methodology part. I would like to discuss with the authors about the notations above.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 1, "contribution": 2, "strengths": "- Clear empirical demonstration (Fig 1-2) that fixed contexts cause discussion inconsistency, with concrete examples showing misalignment\n- The dual gradient descent approach (Eq 16) for automatically tuning α is elegant and well-justified through Lagrangian duality (Appendix E)\n- Testing across diverse domains (academic reasoning, embodied agents, mobile GUI) with multiple model sizes (7B to 72B parameters) demonstrates broad applicability\n- Consistent 20-50% improvements are substantial, especially on complex tasks (e.g., +33% on GPQA with Qwen-72B)", "weaknesses": "Unclear notations and theoretical motivation.\n- In its proof and many following lemmas, a constant term is usually ignored. In addition The constant term, however, grows exponentially with the quantity $\\rho^2$. Can this constant term be ignored?\n- Many concepts are introduced without context or formal introduction, making the paper extremely hard to read. For example,\n  - Section 4:\n      - the notation $P, X, I$ appeared in line 171-180 is understood generally as texts or sequences or tokens. But they can be magically applied in Eq (5) with weight matrices before any description. There is no clue from the authors about whether those $I, X, P$s are vectors or matrices and how they are calculated.  Furthermore, In the Theorem 4.1, the \"activations of the correct answer\" $a_c$ also comes from nowhere, readers still do now know whether this is a vector or a matrix. From Eq (5), a general guess is that $a(C^t_i)$ is a matrix of the same shape as $P$ because it is the output of attention layer, and it should be of the shape $[\\text{number of layers (might be ignored), length of sequence, dimension of latent space}]$, if we guess $P$ is a matrix, and so as $a_c$. In the up coming Eq(8), the role of $a_c$ can be magically replaced by a sentence vector $v_P$ (this is first place the word vector appeared besides the weight vector $\\omega$). Only now, people can guess $P, X, I$ are vectors.\n  - Section 5.1\n    - The notation $i$ in line 233 is confusing, before, it is about the i-th of N LLMs, but now it is for the predefined pool of M Initial contexts. This makes the Equation (7) very hard to understand. We do now know whether the authors wants to find a subset $S$ of what domain, of the pool? or of the LLM agents? or the tuple of (llm, context)?\n    - The notation of the braces is confusing, line 184 $[I_i^t, X_i^{t-1}, P]$ uses $,$ and line 196/237 $[I_i^t; X_i^{t-1}; P]$ uses $;$, are they the same?\n    - The sentence vector $v_P$ represents the vector of question P, is it the same as the activation of P?\n    - Is $a([A;P])$ in Eq (9) computed from the Eq (5)? Are the parameters $W_V$, $W_K$, $W_Q$ shareable across all occurrence of $a$?\n    - The loss function (10) is strange, why don't we just use the composition of functions $f$ and $a$ as $\\mathcal{F}$?\n    - Consider Eq (11), if functions are optimized by the loss functions in Eq (9-10), I didn't see why the entire formulation in Section 5.1 encourages orthogonality, because each $\\mathcal{F}( ... )$ approximate $f( ... )$ and approximate $v_P$. And the critical input contains all information of $P$ , I think ideally, the function $F$ can collapse to a sentence embedding function to generate $v_P$. It is just a knowledge distillation of the sentence embedding network.\n  - Section 5.2\n    - Eq (12) is poorly written. In Eq (12), it tries to select the proper index j to maximize the objective. In its remark, the instruction $I$ magically appeared to be optimized. What is the optimization problem you actually want to define?\n    - Eq (16) is strange, how do you choose $\\beta$? If $\\beta$ is sufficiently large, the $\\alpha_i$ will just decrease to zero and another part of loss will only keep the first term, seems to only approximate $X_i^{t-1}$ using $\\mathcal{G}_{\\theta_i}$.", "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": "4TqROs0nNS", "reviewer": "Reviewer_uL5G", "summary": "The paper starts from the observation that discussion inconsistency in MAD prevents conclusions from converging, and proposes M2CL, a multi-LLM context learning method that learns a context generator for each agent to dynamically produce context instructions at every discussion round. Grounded in theoretical analysis, the method posits that agents’ activations should be as orthogonal as possible during initialization, and that subsequent evolution should reduce inter-agent activation discrepancies while controlling deviation from the initial context. During the initialization, the paper selects a near-orthogonal set of initial instructions from a predefined pool of multi-perspective prompts, minimizing the weighted reconstruction error of the selected instructions’ activations. After that, the paper proposes a round-level context evolution objective: on one hand, constraining the distance between the current round’s context and the initial context; on the other, aligning activations by encouraging the current round’s instruction to be consistent with the previous round’s own output, thereby indirectly reducing inter-agent divergence. The objective is further reformulated as a constrained problem with a dual variable $\\alpha$, and alternating updates with approximate dual gradients are used to achieve adaptive trade-off. The paper evaluates M2CL across academic reasoning, embodied tasks, and mobile control scenarios , demonstrating its effectiveness.", "questions": "See weaknesses.", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "1. The proposed method is theoretically driven and structurally clear.  The paper formalizes how to preserve diversity while fostering consensus, alleviating discussion inconsistency and non-convergence in MAD.\n2. During the initialization, M2CL selects near-orthogonal instructions from a multi-perspective prompt pool.  The round-level update objective further combines a distance-to-initial constraint with activation alignment, and employs a dual variable $\\alpha$ to dynamically balance diversity and consistency.\n3. Thorough experiments on nine benchmarks spanning academic reasoning, embodied tasks, and mobile control, demonstrates the effectiveness  of the proposed method .", "weaknesses": "1. The paper uses output activation alignment as a proxy for discussion consistency and contribution. This proxy is not the task ground truth, there may exist cases where embeddings are close yet the logic still conflicts, or semantics are diverse yet complementary.\n2. In initialization, one must select a near-orthogonal subset of initial instructions from a multi-perspective prompt pool and minimize the weighted reconstruction error. If the pool lacks coverage or contains heavy semantic redundancy, it is difficult in practice to pick a subset that balances diversity and reconstructability.\n3. Implementing initialization requires the activation mapping $a(\\cdot)$, the projection $f(\\cdot)$ and the distilled projection $F(\\cdot)$. Access to answer-side activations are needed and the stability of projection training may limit the initilization quality.", "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": "Df6B91ZYvi", "reviewer": "Reviewer_xVos", "summary": "This paper proposes M2CL, a multi-round context collaboration framework for multi-LLM systems (MAD) that balances diversity vs. consistency across agents: diverse initialization broadens solution coverage, while temporal consistency and dual-driven scheduling steer the system toward agreement. The method reports strong gains across multiple datasets.", "questions": "1. Could you provide the exact input–output specification and examples. What patterns does it learn—tone control, attention to specific evidence?\n2. Are generators trained per dataset or jointly? Is there cross-dataset generalization? Could you report train/val/test sizes?\n3. Will you release checkpoints, data, the initial context pool ?", "limitations": "", "rating": 8, "confidence": 3, "soundness": 4, "presentation": 4, "contribution": 4, "strengths": "1. The paper addresses the fundamental and practically important diversity–consistency trade-off in multi-agent LLM collaboration.\n2. This work presents a principled methodology: it secures diversity by solving for orthogonal, sufficiently covering initial profiles, fosters inter-agent consistency via temporal cross-round coherence, and employs a dual-driven scheduling mechanism to dynamically steer the trade-off between the two.\n3. It demonstrates consistent performance gains across multiple datasets.", "weaknesses": "1. Although a lightweight distilled $F(\\cdot)$ is used, the cost may still grow combinatorially as the profile pool expands. \n2. How the contextual pool is constructed, whether it is shared across tasks, and whether it can be aligned with baselines.", "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": "9I6JUJJyw8", "reviewer": "Reviewer_g8ch", "summary": "This paper addresses the issue of discussion inconsistency in Multi-Agent Discussion (MAD) systems, where multiple Large Language Models (LLMs) collaborate through structured dialogue but often fail to reach a coherent consensus due to context misalignment among agents. To tackle this, this paper proposes M2CL (Multi-LLM Context Learning) that learns a context generator for each agent, enabling dynamic, round-by-round generation of optimized context instructions through automatic information organization and refinement. By introducing a self-adaptive mechanism that balances context coherence and output diversity, M2CL prevents premature convergence to “majority noise” and guides agents toward the correct consensus.", "questions": "Refer to the weaknesses.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1.The paper clearly diagnoses discussion inconsistency，a core limitation of existing Multi-Agent Discussion systems to reach an agreement on a coherent solution.\n\n2.The paper provides analytical understanding of how initial and evolving contexts influence discussion dynamics, grounding the method in a clear theoretical framework rather than purely empirical design.\n\n3.Based on theoretical insight, the paper proposes M2CL framework learn dynamic, per-agent context generators that evolve during discussion.\n\n4.The paper used dual gradient descent to automatically balance coherence and diversity, which is crucial for avoiding premature consensus and enabling more robust reasoning convergence.\n\n5.Extensive experiments are conducted across three domains and nine datasets, covering LLM reasoning, embodied agentic, and mobile GUI AndroidWorld. The results demonstrate substantial and consistent performance improvements over previous MAD methods in terms of the number of collaborating LLMs, model size, and other aspects.", "weaknesses": "1.Lines 45–47: I have some concerns about whether the conclusion “fail to reach an agreement on a coherent solution, easily making the collaborative decision dominated by noise rather than principled reasoning” can be fully supported by Fig. 2. On the one hand, whether a higher level of discrepancy might actually be beneficial in some multi-agent discussion scenarios. Diverse responses could help explore different reasoning paths. Would it be helpful to check whether successful cases show lower final discrepancy than failed ones, to better support the claim that reducing discrepancy improves consensus?\n\n2.Line 85: The paper states “A straightforward solution is to manually adapt instructions in contexts as the discussion progresses.” However, an arguably more intuitive approach would be to assign each LLM an additional discussion-summary LLM responsible for dynamically aggregating intermediate discussion results and generating updated context instructions. I am curious whether any prior work has adopted such a setup, and if so, what specific limitations those approaches faced compared with the proposed M2CL framework.\n\n3.The derivation of Eq. (19) may contain a potential issue: the missing first term in the inequality could influence whether the inequality still holds. It would be helpful for the authors to clarify whether omitting this term affects the mathematical validity of the inequality, and if not, to explain why it can be safely ignored. Otherwise, this omission may undermine the soundness of subsequent theoretical conclusions that rely on Eq. (19).\na−ac=i=1Nωi∗aCib−ac≤i=1Nωi∗aCib−i=1Nωi∗aCit+i=1Nωi∗aCit−ac\n\n4.While the paper presents impressive empirical results and a novel mechanism for context initialization in multi-LLM coordination, the theoretical reasoning connecting Eq. (9)–Eq. (10) seems to rely on several implicit assumptions. Eq. (9) ensures that f(a([A;P]))≈vp, and Eq. (10) ensures that F([Iib;P])≈f(a([Iib;P])). However, there is no theoretical guarantee that f(a([A;P]))≈i∈SωiF([Iib;P]) or f(a([A;P]))≈i∈Sωif(a([Iib;P])). \nTherefore, it remains unclear whether the proposed procedure can truly achieve the “orthogonal basis selection” objective. I have some reservations about this logical gap, even though the empirical evidence is strong.", "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)