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Dynamic Trust-Aware Sparse Communication Topology for LLM-Based Multi-Agent Consensus

Wanshuang Gou, Zihan Liu

Year: 2026Venue: arXiv preprintArea: cs.MAType: PreprintEmbeddings: 45

Intelligence

Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 93%

Last extracted: 7/9/2026, 12:06:45 AM

Summary

The paper introduces DySCo (Dynamic Sparse Consensus), a dynamic trust-aware sparse consensus mechanism for LLM-based multi-agent systems. It addresses the quadratic scaling of fully connected communication by dynamically selecting high-value communication edges based on agent reliability, answer divergence, confidence, and task relevance under a budget constraint. DySCo reduces token costs and latency while preserving cross-validation information, achieving superior reasoning performance on mathematical, logical, and factual tasks compared to fully connected and fixed sparse topologies.

Entities (10)

DySCo · method · 98%GSM8K · dataset · 95%LogiQA · dataset · 95%StrategyQA · dataset · 95%Token cost · metric · 93%Fully connected communication · communication-pattern · 92%Trust weights · mechanism · 91%GPT-3.5-Turbo · model · 90%Random-k · topology · 88%Static Ring · topology · 88%

Relation Signals (8)

DySCo → evaluatedon → LogiQA

confidence 95% · evaluate the performance of DySCo on logical reasoning... LogiQA

DySCo → evaluatedon → StrategyQA

confidence 95% · evaluate the performance of DySCo on factual question-answering tasks... StrategyQA

DySCo → evaluatedon → GSM8K

confidence 95% · evaluate the performance of DySCo on mathematical reasoning... GSM8K

DySCo → mitigates → Fully connected communication

confidence 94% · This mechanism replaces universal broadcasting with on-demand communication, thereby reducing communication overhead

DySCo → reducescomplexityto → O(Rnk)

confidence 93% · communication complexity can be reduced from O(Rn^2) to O(Rnk)

DySCo → utilizes → Trust weights

confidence 92% · aggregates the answers of different agents through dynamic trust weights and terminates the discussion early once consensus stabilizes

DySCo → outperforms → Static Ring

confidence 89% · compared with fully connected multi-agent debate, DySCo achieves superior reasoning performance with lower token costs

Answer divergence → influences → Edge selection

confidence 87% · estimates the value of communication edges based on agent reliability, answer divergence, and task relevance

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Abstract

Abstract:Large language model-driven multi-agent systems enhance the reliability of complex reasoning tasks through multi-round deliberation, role specialization, and cross-validation. However, existing multi-agent debate and collaboration frameworks typically adopt fully connected communication, causing the number of messages, token costs, and end-to-end latency to grow approximately quadratically with the number of agents; although fixed sparse topologies reduce overhead, they cannot adapt communication relationships to different task instances or intermediate reasoning states, making them prone either to preserving low-value interactions or to losing critical error-correction information. To address this problem, this paper proposes DySCo (Dynamic Sparse Consensus), a dynamic trust-aware sparse consensus mechanism. In each round of reasoning, DySCo estimates the value of communication edges based on agent reliability, answer divergence, and task relevance, and selects a small number of high-value edges for message exchange under budget constraints; it then aggregates the answers of different agents through dynamic trust weights and terminates the discussion early once consensus stabilizes. This mechanism replaces universal broadcasting with on-demand communication, thereby reducing communication overhead while preserving essential cross-validation information. We further present analyses of communication complexity and consensus stability, and evaluate the performance of DySCo on mathematical reasoning, logical reasoning, and factual question-answering tasks.

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Dynamic Trust-Aware Sparse Communication Topology for LLM-Based Multi-Agent Consensus Wanshuang Gou 1 , Zihan Liu 1 1 Chengdu University Abstract Large language model–driven multi-agent systems enhance the reliability of complex reasoning tasks through multi-round deliberation, role specialization, and cross-validation. However, existing multi-agent de- bate and collaboration frameworks typically adopt fully connected communication, causing the number of mes- sages, token costs, and end-to-end latency to grow ap- proximately quadratically with the number of agents; although fixed sparse topologies reduce overhead, they cannot adapt communication relationships to differ- ent task instances or intermediate reasoning states, making them prone either to preserving low-value in- teractions or to losing critical error-correction infor- mation. To address this problem, this paper proposes DySCo (Dynamic Sparse Consensus), a dynamic trust- aware sparse consensus mechanism. In each round of reasoning, DySCo estimates the value of communica- tion edges based on agent reliability, answer diver- gence, and task relevance, and selects a small num- ber of high-value edges for message exchange under budget constraints; it then aggregates the answers of different agents through dynamic trust weights and terminates the discussion early once consensus sta- bilizes. This mechanism replaces universal broadcast- ing with on-demand communication, thereby reduc- ing communication overhead while preserving essen- tial cross-validation information. We further present analyses of communication complexity and consensus stability, and evaluate the performance of DySCo on mathematical reasoning, logical reasoning, and factual question-answering tasks. Introduction In recent years, LLM-based multi-agent systems have emerged as an important paradigm for enhancing the capacity to solve complex tasks. Representative ap- proaches include Multi-Agent Debate (MAD)(Du et al. 2023), ChatDev(Qian et al. 2024), AutoGen(Wu et al. 2023), and MetaGPT(Hong et al. 2024). These systems typically organize multiple LLM instances into agents endowed with distinct roles, perspectives, or tool-use capabilities, enabling collaborative reasoning or task planning through the exchange of natural-language messages. Compared with a single LLM, multi-agent 0123 Communication Round (t) 0.25 0.50 0.75 1.00 1.25 1.50 Consensus Entropy Dense MAD DySCo (Ours) Early Stop Threshold (a) 0.02.55.07.510.012.515.0 Token Cost per Query (Thousands) 72 74 76 78 80 82 84 Accuracy on GSM8K (%) Single-Agent CoT Static Ring Random-k Trust-Only Dense MAD DySCo (Ours) (b) Figure 1: A schematic illustration of the core motivation and overall effect of DySCo. The left panel depicts the process of consensus convergence under different com- munication mechanisms, where DySCo more rapidly reduces consensus entropy among agents through dy- namic sparse communication and can terminate early once a stable threshold is reached. The right panel il- lustrates the trade-off between accuracy and communi- cation cost: compared with fully connected multi-agent debate, DySCo achieves superior reasoning performance with lower token costs, demonstrating the advantage of dynamic sparse communication in balancing eﬀiciency and quality. mechanisms can mitigate answer instability in complex reasoning by drawing upon diverse perspectives. However, multi-agent collaboration is often accompa- nied by substantial communication overhead. For a sys- tem comprisingnagents and running forRrounds of in- teraction, if fully connected communication is adopted in each round, the number of messages isO(Rn 2 ). Since each message often contains intermediate reasoning or answer explanations, this overhead is directly trans- lated into token cost and end-to-end latency. As the number of agents scales, fully connected communication can readily become a system bottleneck and may fur- ther amplify the propagation of flawed reasoning among agents. Existing work has demonstrated that communication topology is a crucial factor shaping the eﬀiciency and ef- fectiveness of LLM-based multi-agent debate. Li et al. (2024b) systematically investigated a range of sparse communication topologies and found that sparse com- arXiv:2606.01828v1 [cs.MA] 1 Jun 2026 munication can preserve, or even enhance, reasoning performance while reducing message exchange and com- putational cost. This indicates that multi-agent systems do not always require fully connected interaction, and that appropriately constraining the scope of communi- cation can diminish the propagation of redundant in- formation. However, existing methods primarily rely on fixed sparse topologies, such as ring graphs, star graphs, random graphs, or predefined graph structures. Such methods address the excessive cost of fully con- nected communication, but they do not resolve the mis- match between communication relationships and rea- soning states. During multi-round reasoning, agents’ re- liability, confidence, answer divergence, and task rele- vance continually evolve; a fixed topology may preserve low-value messages while also missing critical error- correction information. Therefore, how to dynamically select communication edges according to the current reasoning state constitutes a central problem in build- ing an eﬀicient consensus mechanism for LLM-based multi-agent systems. To address the aforementioned problem, this paper proposes DySCo (Dynamic Sparse Consensus), a dy- namic trust-aware sparse consensus mechanism. Rather than relying on a fixed communication graph, DySCo dynamically assesses the value of communication edges in each round of reasoning according to agent reliabil- ity, answer divergence, confidence, and task relevance, and selects a small number of high-value neighbors for information exchange under budget constraints. Af- ter receiving feedback, agents update their answers by integrating local reasoning with neighboring opinions, while the system forms a final consensus through trust- weighted aggregation and terminates early once consen- sus becomes stable. In this way, DySCo replaces fully connected broadcasting with dynamic sparse communi- cation, preserving critical error-correction information while reducing token consumption and latency. The contributions of this paper are as follows: •We propose a dynamic sparse communication frame- work for LLM-based multi-agent reasoning, extend- ing communication topology from a fixed structure into an adaptive decision variable driven by task states. •We design a trust-aware edge selection mecha- nism that jointly considers historical reliability, cur- rent confidence, answer complementarity, and task dependencies, selecting high-value communication edges under a given token budget. •We provide analyses of communication complexity and abstract consensus stability, showing that when each agent connects to at mostkneighbors in each round, the communication complexity can be re- duced fromO(Rn 2 )toO(Rnk). •We establish a reproducible experimental protocol for comparing fully connected communication, mul- tiple static sparse topologies, and DySCo in terms of reasoning accuracy, token cost, latency, and consen- sus stability. Related Work LLM-Based Multi-Agent Collaboration and Debate LLM-based multi-agent systems enhance complex task- solving capabilities by organizing multiple model in- stances for role specialization, cross-agent discussion, or collaborative task execution. Unlike single-model sampling-aggregation methods, such as self-consistency, which improve answer stability through multiple rea- soning paths, LLM-based multi-agent approaches fur- ther introduce explicit mechanisms for interaction, cri- tique, and revision across agents(Wang et al. 2023). Multi-Agent Debate enables multiple LLMs to indepen- dently propose answers and critique one another over multiple rounds, thereby improving accuracy in math- ematical reasoning, strategic reasoning, and factual question-answering tasks(Du et al. 2023). Subsequently, ChatEval applied multi-agent debate to text evaluation in LLM-as-a-judge scenarios(Chan et al. 2024), while ReConcile enhanced consensus quality in complex rea- soning through round-table discussions among hetero- geneous LLMs and confidence-weighted voting(Chen, Saha, and Bansal 2024). In addition, CAMEL demon- strated that role-playing-based multi-agent dialogue can be used for task decomposition and collaborative exploration(Li et al. 2023). AutoGen(Wu et al. 2023), ChatDev(Qian et al. 2024), and MetaGPT(Hong et al. 2024) further reveal the application potential of LLM- based multi-agent systems in tool use, software develop- ment, and structured workflows. However, these meth- ods typically rely on fully connected communication, manually specified communication links, or fixed col- laborative procedures, and therefore lack explicit con- trol over the trade-off between communication cost and reasoning quality. Sparse Communication Topology Communication topology is a crucial factor shap- ing the eﬀiciency, stability, and quality of collec- tive decision-making in multi-agent systems. In tra- ditional multi-agent reinforcement learning, CommNet learns information exchange among agents through differentiable communication(Sukhbaatar, Szlam, and Fergus 2016), while subsequent studies further intro- duce attention mechanisms, targeted message pass- ing, and communication-triggering mechanisms to learn “with whom to communicate” and “when to commu- nicate”(Jiang and Lu 2018; Das et al. 2019; Singh, Jain, and Sukhbaatar 2019). These studies demonstrate that communication links need not always be fully con- nected; through selective communication, systems can reduce the propagation of redundant information and enhance collaborative eﬀiciency. In the context of LLM-based multi-agent debate, existing studies have likewise shown that communi- Agent PoolAgent Pool Phase 1: Initial Reasoning Solve the task and collaborate under a limited communication budget Phase 2: Dynamic Edge SelectionPhase 3: Trust-Aware UpdatePhase 4: Weighted Consensus Task input Answer A (steps 1 to 3) Maybe B (Need more info) Check step 2 Answer C (looks promising) Learn A (based on fact X) Not sure yet Agents reason independently Edge Scoring Cues trusttrustdisagreementcostcost confidencetask relevance critique evidence evidence critique revise revise B ? A √ Uncertain ? A √ Compressed feedback + trust weights (sender, receiver, summary, weight) A A A A Most Agents converge to A Weighted vote (by trust) Early stop? Yes Final Consensus Answer: A Figure 2: Overview of the DySCo framework. Given a task input and an agent pool, each LLM agent first reasons independently and generates an initial answer. Subsequently, DySCo evaluates the value of candidate communication edges according to historical trust, current confidence, answer divergence, task relevance, and communication cost, selecting a small number of high-value edges under budget constraints. Agents exchange compressed feedback only through the selected edges and update their own answers by incorporating trust weights. Finally, the system aggre- gates the outputs of all agents through trust-weighted voting and terminates early once consensus becomes stable. cation topology significantly influences reasoning eﬀi- ciency and effectiveness. Li et al. (2024b) systematically compared multiple sparse communication topologies and found that sparse topologies can preserve, or even enhance, reasoning performance while reducing compu- tational cost. Recent work on sparse mixture-of-agents has also explored sparse information flow in multi-agent LLMs from the perspectives of response selection and early stopping mechanisms(Li et al. 2024a). Unlike the aforementioned studies, which primarily compare fixed topologies or sparsify communication based on candi- date responses, this paper focuses on dynamic topol- ogy selection: communication edges are no longer de- termined by predefined graph structures, but are adap- tively generated during the reasoning process according to agent confidence, answer divergence, task state, and historical reliability. Consensus and Trust Modeling Traditional consensus algorithms in multi-agent sys- tems typically examine weighted averaging of agent states over communication graphs, neighbor interac- tions, and convergence conditions(DeGroot 1974; Jad- babaie, Lin, and Morse 2003; Olfati-Saber, Fax, and Murray 2007). The consensus problem in LLM-based multi-agent reasoning is more intricate, because agent states encompass natural-language reasoning trajecto- ries, discrete answers, and imperfectly calibrated confi- dence estimates. Existing studies have shown that the confidence of modern neural networks may suffer from systematic calibration issues(Guo et al. 2017); in the context of LLMs, although models can express or esti- mate their own uncertainty to some extent, such self- assessment is not always reliable(Kadavath et al. 2022; Lin, Hilton, and Evans 2022). Therefore, this paper does not directly assume that LLM outputs satisfy the con- ditions of classical linear systems, but instead models answer updates and trust-weighted aggregation within an abstract confidence-vector space, and verifies the ef- fectiveness of the dynamic sparse consensus mechanism through experiments with real LLMs. Problem Definition Given a taskxto be solved, such as a mathemati- cal problem, a logical reasoning question, or a factual question-answering task, the system comprisesnLLM agentsA=a 1 , . . . , a n . Each agent maintains a state at roundt: z t i = (y t i , r t i , c t i ),(1) wherey t i denotes the current answer,r t i denotes the natural-language reasoning or explanation, andc t i ∈ [0,1]denotes the self-reported or calibrated confidence. In fully connected multi-agent debate, the commu- nication graph at roundtisG t = (V, E t ), where V=AandE t = (i, j) :i̸=j. Thus, each round con- tainsn(n−1)directed messages. This paper considers sparse communication under budget constraints: each agent receives information from at mostkneighbors, wherek≪n. The objective is to maximize the qual- ity of the final answer under a communication budget B, while reducing token consumption and end-to-end latency: max E t t=1 R ;E[Q(ˆy, y ∗ )]s.t. ∑ t= 1 R |E t |≤B,(2) whereˆydenotes the final consensus answer,y ∗ denotes the ground-truth answer, andQdenotes a task-quality metric, such as exact match or correctness. Method DySCo comprises four modules: individual initial rea- soning, dynamic edge selection, trust-aware state up- dating, and final consensus aggregation. The overall procedure is presented in Algorithm 1. Individual Initialization At round 0, each agent independently solves the taskx: (y 0 i , r 0 i , c 0 i ) =LLMi(Psolve(x)),(3) whereP solve denotes a unified task-solving prompt. The agents may be different sampling instances of the same LLM, or heterogeneous agents instantiated through dif- ferent models, different system prompts, or distinct role specifications. Dynamic Communication Edge Selection At the beginning of roundt, DySCo computes a communication-value scores t ij for each potential di- rected edge(j→i), representing the prospective bene- fit for agentiof receiving information from agentjin the current round: s t ij =αT t j +βc t j +γD t ij +δH ij (x)−ηL t j .(4) Here,T t j denotes the historical trust weight of agentj, c t j denotes its current confidence,D t ij represents the de- gree of answer or reasoning divergence betweeniand j,H ij (x)represents the degree of task dependency or role complementarity, andL t j denotes the estimated to- ken cost incurred by receiving the message fromj. The coeﬀicientsα, β, γ, δ, ηare hyperparameters. The divergence scoreD t ij can be obtained from an- swer agreement, the cosine distance between reason- ing embeddings, or judgments produced by a critique prompt. For multiple-choice questions, it can be defined as D t ij =I[y t i ̸=y t j ].(5) For open-ended reasoning tasks, sentence-vector dis- tance may be used to approximate reasoning comple- mentarity. The task-dependency termH ij (x)can be specified by role relationships or a task-dependency graph. For example, in code review, a testing agent may have a high dependency weight with respect to a coding agent; in mathematical reasoning, a verification agent may offer high feedback value to a solving agent. Under the budget constraint, each receiveriselects theksenders with the highest scores: Ni t =TopKj̸=i(s t ij , k),(6) and setsE t = (j, i) :j∈N t i . Therefore,|E t |≤nk. Message Compression and Critique Generation To further control communication costs, the sender does not directly broadcast the complete reasoning trajec- tory, but instead generates a structured, compressed message: m t j→i =LLMj(Pcritique(x, y t i , r t i , y t j , r t j )).(7) The message contains three components: the current answer, the single most critical supporting reason, and a potential counterexample or revision suggestion for the receiver’s answer. This structure constrains the propa- gation of redundant long-form text, reduces the token budget, and preserves information valuable for consen- sus. Trust-Aware State Update Receiveriupdates its answer according to its local state and the messages received from its neighbors: (y t+1 i , r t+1 i , c t+1 i ) =LLMi(Previse(x, z t i , m t j→i , T t j j∈N t i )). (8) The prompt requires the agent to explicitly distinguish among three cases: “retaining the original answer,” “making a partial revision,” and “completely changing the answer,” while also providing the rationale for any change in confidence. To prevent erroneous agents from dominating the discussion, neighbor messages are pre- sented with weights according toT t j ; the opinions of low-trust agents are required to be treated only as coun- terexamples awaiting verification, rather than as direct evidence. Trust weights are updated according to historical per- formance, current consistency, and verifier feedback: T t+1 i =λT t i + (1−λ)(ρV t i + (1−ρ)A t i ),(9) whereV t i denotes the score assigned by a lightweight verifier to agenti’s current reasoning,A t i denotes its degree of agreement with the final or provisional ma- jority consensus, andλcontrols historical smoothing. If the task admits an executable verifier, such as mathe- matical answer checking, code unit testing, or retrieval- evidence matching, thenV t i can be provided by an ex- ternal tool; otherwise, it can be supplied by an inde- pendent judge LLM. Algorithm 1DySCo: Dynamic Sparse Consensus Require:Taskx, agentsA, roundsR, neighbor budget k, stopping thresholdε 1:Each agent independently generates(y 0 i , r 0 i , c 0 i ) 2:Initialize trust weightsT 0 i ←1/n 3:fort= 0toR−1do 4:foreach receiver agentido 5:Compute edge scoress t ij for allj̸=i 6:Select neighborsN t i ←TopK j̸=i (s t ij , k) 7:end for 8:foreach selected edge(j, i)do 9:Generate compressed critique messagem t j→i 10:end for 11:foreach agentido 12:Update local state(y t+1 i , r t+1 i , c t+1 i ) 13:Update trust weightT t+1 i 14:end for 15:ifweighted consensus entropy< εthen 16:break 17:end if 18:end for 19:returnweighted consensus answerˆy Consensus Aggregation and Early Stopping After at mostRrounds, DySCo adopts trust-weighted aggregation: ˆy=argmax y n ∑ i=1 T R i c R i I[y R i =y].(10) For open-ended answers, a normalizer may first be used to map equivalent responses into the same candidate set before weighted aggregation is performed. To reduce un- necessary communication, DySCo introduces an early- stopping criterion. When the entropy of the weighted answer distribution falls below the thresholdε, or when the consensus answer remains unchanged for two con- secutive rounds and the increase in average confidence is smaller than a predefined threshold, the system ter- minates communication. Complexity and Consensus Analysis Communication Complexity.In fully connected communication, the number of messages in each round isn(n−1), and the total number of messages is Rn(n−1). If the average length of each message is ̄ ℓ, then the communication token cost can be approxi- mated as C dense =O(Rn 2 ̄ ℓ).(11) DySCo restricts each agent to receiving at mostkmes- sages per round; therefore, the total number of messages is at mostRnk, and the communication token cost is C sparse =O(Rnk ̄ ℓ c ),(12) where ̄ ℓ c denotes the length of the compressed critique message. Sincek≪nand ̄ ℓ c ≤ ̄ ℓ, DySCo can substan- tially reduce communication costs. Abstract Consensus Stability.To analyze the consensus behavior of DySCo, we abstract each agent’s discrete answer as a confidence vectorp t i ∈∆ |Y| over the candidate answer setY. If the communication up- date at roundtcan be approximated as p t+1 i =w t i p t i + ∑ j∈Ni t wij t p t j +ξ t i ,(13) wherew t ij ≥0, ∑ j w t ij = 1, andξ t i denotes the non- linear update error of the LLM, then, under the con- dition thatξ t i is ignored or bounded, this process may be viewed as weighted consensus over a time-varying graph. Proposition 1 (Weak Consensus Condition un- der a Communication Budget).If there exists an integerB >0such that the union graph of any consec- utiveBrounds of communication is strongly connected, and all nonzero weights satisfyw t ij ≥μ >0, then, when the perturbation termsξ t i are bounded and have zero mean, the confidence vectors of all agents converge in expectation toward a common consensus neighborhood. Proof Sketch.In the absence of perturbations, this re- sult corresponds to the classical consensus convergence property of products of time-varying stochastic matri- ces. If DySCo’s Top-kedge selection preserves suﬀicient cross-cluster connectivity over time, it can satisfy joint strong connectivity. In the presence of bounded pertur- bations, the system does not necessarily converge to a single point, but rather to a neighborhood determined by the magnitude of the perturbations. Since real LLM updates are not linear systems, this proposition serves only as an abstract interpretation; its ultimate effective- ness must be established through empirical evaluation. 4812 Number of Agents (n) 20 40 60 Token Cost (Thousands) (a) Communication Cost Scaling Dense MAD DySCo (Ours) 4812 Number of Agents (n) 82 84 86 Accuracy (%) (b) Performance Scaling Dense MAD DySCo (Ours) Figure 3: Comparison of communication cost and rea- soning performance under different agent scales. The left panel shows that, as the number of agentsnin- creases, the token cost of fully connected Multi-Agent Debate rises rapidly, whereas DySCo exhibits a more gradual increase in cost by limiting the number of com- munication neighbors in each round. The right panel shows that DySCo maintains high accuracy across dif- ferent agent scales, indicating that dynamic sparse com- munication can improve scalability while preserving ef- fective multi-agent collaboration. Experiment Experimental Setup The experiments cover three categories of tasks: math- ematical reasoning, logical and commonsense reason- ing, and factual question answering. GSM8K (math- ematics), LogiQA (logic), and StrategyQA (common- sense question answering) are selected as the evalua- tion datasets, respectively. We randomly sample 300 test instances from each dataset for evaluation. The base model is uniformly set togpt-3.5-turbo, and the number of agents in the multi-agent framework is set ton= 6(except in the scalability experiments), with a maximum communication round number ofR= 3. For DySCo and the other sparse topologies, the maximum number of receiving neighbors is set tok= 2. We compare DySCo with the following baseline meth- ods: single-agent chain-of-thought reasoning (Single- Agent CoT), self-consistency (Self-Consistency,n= 6 sampling aggregation), fully connected multi-agent de- bate (Dense MAD), a fixed ring topology (Static Ring), random selection ofkneighbors (Random-k), and a sparse topology based solely on historical trust (Trust- Only Sparse). The evaluation metrics include task accu- racy (Accuracy), the average total token consumption per question (in thousands), end-to-end average latency (Latency), and consensus entropy (Consensus Entropy, where a lower value indicates smaller disagreement). Main Results The main experimental results are shown in Table 1. The experiments demonstrate that multi-agent meth- ods, including Dense MAD and DySCo, substantially outperform single-agent CoT across all three datasets. However, Dense MAD incurs considerable token con- sumption and latency. Compared with Dense MAD, DySCo not only reduces token consumption by ap- proximately 70% and latency by nearly half, but also achieves consistently superior accuracy, reaching 84.3% on GSM8K, for example. Although fixed topologies, such as Static Ring, and random topologies, such as Random-k, effectively reduce overhead, their accuracy gains remain limited because they lose high-value error- correction information. By dynamically matching high- quality neighbors and performing weighted aggregation, DySCo successfully achieves the best trade-off between performance and cost. Ablation Study Module Ablation.Ablation experiments were con- ducted on the datasets, and the results are shown in Table 2. Removing trust awareness (w/o Trust Weight) and removing divergence evaluation (w/o Diversity Score) both lead to a marked decline in accuracy, demonstrating that selecting neighbors who are both reliable and endowed with complementary perspec- tives is essential for error correction. Removing mes- sage compression (w/o Message Compression) yields a slight accuracy improvement of 0.2%, but causes to- ken consumption to surge by 82.2%. Removing the early-stopping mechanism (w/o Early Stopping) intro- duces unnecessary communication rounds, increasing cost without delivering any gain in accuracy. Scalability with Agent Count.The central chal- lenge faced by existing multi-agent frameworks is the explosion of communication cost brought about by scaling. Table 3 presents the performance of different frameworks on GSM8K when the number of agents isn∈4,8,12. Asnincreases, the token consump- tion of Dense MAD grows quadratically and sharply, reaching a striking 58.4k whenn= 12; moreover, be- cause erroneous opinions propagate indiscriminately, its accuracy improvement tends to plateau and even decline whenn >8. In contrast, DySCo maintains linear communication-cost growth ofO(Rnk)and, by precisely distilling high-quality opinions, enables sys- tem accuracy to rise steadily with agent scale, reaching 86.8%. Consensus Dynamics Analysis.To investigate the effect of dynamic topology on the consensus- convergence process, we tracked the system’s average consensus entropy and accuracy across different com- munication rounds, as shown in Table 4. At round 0, corresponding to initial independent answers, the sys- tem exhibits a relatively high entropy value of 1.54 be- cause no communication has yet occurred. After en- tering the first communication round, DySCo’s con- sensus entropy rapidly declines to 0.62, substantially lower than the 0.88 observed for Dense MAD. This in- dicates that trust-based opinion aggregation in DySCo can quickly eliminate salient erroneous disagreements. By round 2, DySCo has largely reached the conver- gence threshold and triggers extensive early stopping, effectively suppressing the propagation of noise while achieving a higher final accuracy than Dense MAD at round 3. Hyperparameter Analysis.Table 5 presents the sensitivity of DySCo to key hyperparameters. Overall, DySCo maintains relatively stable performance under different settings, indicating that its effectiveness does not depend on any particular set of manually tuned pa- rameters. For the neighbor budgetk, whenkincreases from 1 to 2, the average accuracy rises from 81.4% to 82.7%, while consensus entropy decreases from 0.34 to 0.25, suggesting that a moderate increase in commu- nication neighbors helps agents perform effective er- ror correction. However, whenkis further increased to 3, accuracy improves only marginally, whereas token consumption increases substantially, indicating dimin- ishing marginal returns from denser communication. For the maximum number of communication rounds R, the default setting ofR= 3achieves a favor- able balance between performance and cost; further increasing it toR= 4yields only a slight accuracy gain while introducing higher communication cost. The Table 1: Main performance comparison on GSM8K, LogiQA, and StrategyQA datasets (n= 6, k= 2, R= 3). Token usage is measured in thousands (k) per query. Latency is the average end-to-end response time in seconds. Results are reported as mean and standard deviation (subscript) across 3 random seeds. Dark-red annotations in the DySCo row indicate absolute improvements over the strongest dense multi-agent baseline, Dense MAD. Method GSM8KLogiQAStrategyQA Avg Latency (s) Acc (%)↑Tokens (k)↓Acc (%)↑Tokens (k)↓Acc (%)↑Tokens (k)↓ Single-Agent CoT72.3 ±0.8 0.4 ±0.0 68.1 ±0.9 0.5 ±0.0 75.6 ±0.7 0.3 ±0.0 3.2 ±0.3 Self-Consistency78.5 ±0.5 2.5 ±0.1 72.4 ±0.7 3.1 ±0.1 80.2 ±0.5 1.9 ±0.1 4.5 ±0.4 Dense MAD82.0 ±1.2 14.8 ±0.8 76.8 ±1.1 16.2 ±0.9 83.5 ±1.0 12.4 ±0.7 18.6 ±2.1 Static Ring80.1 ±1.1 4.2 ±0.2 74.3 ±1.2 4.8 ±0.2 82.0 ±0.9 3.6 ±0.1 9.4 ±0.8 Random-k80.5 ±1.5 4.2 ±0.2 74.5 ±1.4 4.8 ±0.2 81.8 ±1.3 3.6 ±0.1 9.5 ±0.9 Trust-Only Sparse81.8 ±0.9 4.2 ±0.2 75.6 ±0.8 4.8 ±0.2 83.1 ±0.7 3.6 ±0.1 9.6 ±0.8 DySCo (Ours)84.3 ±0.4 ↑2.34.5 ±0.3 ↓10.378.5 ±0.6 ↑1.75.0 ±0.3 ↓11.285.4 ±0.4 ↑1.93.8 ±0.2 ↓8.69.8 ±1.0 ↓8.8 Table 2: Ablation study on the GSM8K dataset. Token Delta indicates the percentage change in token usage compared to the full DySCo model. Variant Acc (%) Token Delta Consensus Entropy Full DySCo84.3–0.21 w/o Trust Weight81.5+1.2%0.45 w/o Diversity Score82.1-0.5%0.38 w/o Task Dependency 83.2+0.0%0.25 w/o Msg Compression 84.5+82.2%0.20 w/o Early Stopping84.3+25.4%0.18 Table 3: Scalability performance on GSM8K with vary- ing number of agents (n). Metrickis dynamically scaled as⌊n/3⌋for DySCo. Agents (n) DySCok Dense MADDySCo (Ours) Acc (%) Tokens (k) Acc (%) Tokens (k) n= 4180.56.281.83.1 n= 6282.014.884.34.5 n= 8282.426.585.56.8 n= 12481.858.486.810.5 early-stopping thresholdεreflects the trade-off between quality and eﬀiciency: a smaller threshold can achieve lower consensus entropy but requires more communica- tion, whereas a larger threshold can reduce token con- sumption at the cost of a slight decrease in accuracy. Finally, when the edge-scoring weightsα, β, γ, δ, ηare varied, the changes in accuracy, token consumption, and consensus entropy remain modest. This suggests that DySCo’s performance primarily arises from the joint modeling of historical trust, current confidence, answer divergence, task relevance, and communication- cost penalties, rather than from an excessive reliance on any single scoring term or any fixed set of weights. Discussion The central assumption of DySCo is that communi- cation edges in multi-agent collaboration have non- uniform value. Neighbors that exhibit high confidence, strong historical reliability, and meaningful disagree- ment with the current agent are usually more valuable communication partners than neighbors that are unre- liable or merely provide redundant information. A dy- Table 4: Evolution of Consensus Entropy and Accuracy over communication rounds on LogiQA. Round (t) Dense MADDySCo (Ours) Entropy↓Acc (%) Entropy↓Acc (%) t= 0(Init)1.5472.41.5472.4 t= 10.8874.5 0.6276.8 t= 20.5176.10.2878.2 t= 30.4076.8 0.2578.5 namic sparse topology can therefore not only reduce communication cost, but also potentially mitigate the indiscriminate diffusion of erroneous reasoning. Nevertheless, the method still faces several risks. First, LLM self-reported confidence may be poorly cal- ibrated, and directly usingc t i may amplify overconfi- dent errors. A possible remedy is to introduce an exter- nal verifier or calibrate confidence based on historical task performance. Second, trust weights may produce an early rich-get-richer effect, causing some agents to be marginalized over time. This issue can be alleviated by incorporating an exploration term into edge selec- tion, such asε-greedy exploration or an upper confi- dence bound. Third, overly sparse communication may lead the system to form local opinion clusters, resulting in a failure to reach global consensus. Therefore, DySCo needs to maintain long-term graph connectivity, for ex- ample by periodically introducing random cross-cluster edges. Limitation The effectiveness of DySCo relies on the premise that the value of a communication edge can be approxi- mately estimated from signals such as historical reli- ability, current confidence, answer divergence, and task relevance. This assumption is relatively reasonable for mathematical reasoning, logical reasoning, and verifi- able question-answering tasks, where candidate answers are usually comparable and some errors can be iden- tified through a verifier, a reference answer, or con- sistency checks. However, in open-ended generation, value-laden judgment, or tasks with multiple valid so- Table 5: Hyperparameter sensitivity analysis of DySCo. Except for the hyperparameter shown in the current row, all other settings remain consistent with the main experiments; the gray row indicates the default setting used in the main experiments of this paper. Here,kdenotes the neighbor budget,Rdenotes the maximum number of communication rounds,εdenotes the early-stopping threshold, andα,β,γ,δ, andηdenote the historical trust, current confidence, answer divergence, task relevance, and communication-cost penalty terms, respectively. The results show that DySCo maintains stable performance under different hyperparameter settings, indicating that its effectiveness does not depend on any particular set of manually tuned parameters. Setting Avg. Acc. (%)↑Tokens (k)↓Entropy↓ k= 181.43.210.34 k= 282.74.430.25 k= 383.05.860.22 R= 282.03.720.31 R= 382.74.430.25 R= 482.85.180.23 ε= 0.2082.84.910.21 ε= 0.3082.74.430.25 ε= 0.4082.33.960.32 α= 0.3082.74.430.25 α= 0.4082.54.410.26 β= 0.2082.74.430.25 β= 0.3582.34.390.28 γ= 0.2582.74.430.25 γ= 0.4082.94.480.24 δ= 0.1582.74.430.25 δ= 0.3082.44.440.27 η= 0.1082.74.430.25 η= 0.2582.13.910.30 lutions, these signals do not always reflect answer qual- ity. For example, high confidence may result from model overconfidence, and large answer divergence may reflect only differences in expression rather than substantive complementarity. Therefore, DySCo should be under- stood as a reasoning coordination mechanism for reduc- ing communication overhead, rather than as a general mechanism for determining factual correctness. Another limitation arises from the dynamic update of trust weights. Although trust-aware aggregation can suppress the propagation of low-quality opinions, it may also amplify agents that are accidentally correct or more confidently expressed in early rounds, causing subse- quent communication to concentrate around a small number of nodes. This mechanism improves eﬀiciency, but it may reduce the continued visibility of minority reasoning paths. For scenarios that require the preser- vation of dissenting views, evidence-chain inspection, or accountability, DySCo should be combined with ex- plicit exploration edges, human review, or external veri- fication modules, rather than being used as a standalone final adjudication procedure. References Chan, C.-M.; Chen, W.; Su, Y.; Yu, J.; Xue, W.; Zhang, S.; Fu, J.; and Liu, Z. 2024. ChatEval: Towards Better LLM-based Evaluators through Multi-Agent Debate. In International Conference on Learning Representations. Chen, J. C.-Y.; Saha, S.; and Bansal, M. 2024. 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Reproducible Prompt Templates To facilitate reproducibility, we provide the core prompt templates used by DySCo. The templates are written in a model-agnostic form and can be instanti- ated with different LLM backbones. In all experiments, the prompts should be fixed across methods except for communication-specific fields required by each baseline. Solve Prompt.This prompt is used in the initializa- tion stage, where each agent independently solves the task without observing other agents’ outputs. You are an independent reasoning agent. Task: question Instructions: 1. Solve the task independently. 2. Do not refer to other agents or assume that other agents exist. 3. Provide a concise but sufficient reasoning process. 4. If the task is mathematical, show the key intermediate steps. 5. If the task is multiple-choice, select exactly one option. 6. If the task is open-ended, provide the shortest answer that is still complete. 7. Estimate your confidence in the final answer as a number between 0 and 1. Output format: Final Answer: <your final answer> Key Reasoning: <the key reasoning steps> Confidence: <a number between 0 and 1> Critique Prompt.This prompt is used when an agent sends compressed feedback to a selected neigh- bor. The goal is not to repeat the full reasoning, but to provide a short critique that may help the receiver revise its answer. You are a critique agent in a multi-agent reasoning system. Original Task: question Your Current Answer: sender_answer Your Reasoning: sender_reasoning Neighbor's Current Answer: receiver_answer Neighbor's Reasoning: receiver_reasoning Your trust weight in the current round: sender_trust_weight Instructions: 1. Compare your answer with the neighbor's answer. 2. State whether you agree, partially agree, or disagree. 3. Identify the most important reason supporting your judgment. 4. Point out at most one possible error, missing step, or counterexample in the neighbor's reasoning. 5. Do not repeat your full reasoning. 6. Keep the feedback concise and actionable. 7. Use no more than 120 words. Output format: Agreement: <agree / partially agree / disagree> Key Reason: <one concise reason> Possible Issue: <one possible error or counterexample, or " None"> Suggested Revision: <what the neighbor should reconsider> Revise Prompt.This prompt is used when an agent updates its answer after receiving sparse feedback from selected neighbors. Neighbor messages are accompanied by trust weights, so the agent should treat high-trust and low-trust feedback differently. You are a reasoning agent revising your answer after receiving feedback from selected neighboring agents. Original Task: question Your Previous Answer: current_answer Your Previous Reasoning: current_reasoning Your Previous Confidence: current_confidence Neighbor Feedback Messages: neighbor_feedback_list Each feedback message contains: - neighbor id - neighbor trust weight - neighbor answer - critique message Instructions: 1. Re-examine your previous answer using the received feedback. 2. Give more consideration to feedback from agents with higher trust weights. 3. Do not automatically follow the majority opinion. 4. Revise your answer only if the feedback exposes a real reasoning error, missing evidence, or stronger alternative solution. 5. If you keep your original answer, explain why the feedback is insufficient. 6. If you revise your answer, explain which feedback message was most useful. 7. Output a new confidence score between 0 and 1. Output format: Decision: <keep / revise> New Final Answer: <your updated final answer> Revision Reason: <why you kept or changed the answer> Adopted Feedback: <ids of the main feedback messages used, or "None"> New Confidence: <a number between 0 and 1> Consensus Normalization Prompt.For open- ended tasks where exact matching is diﬀicult, we use an optional normalization prompt before trust-weighted voting. This step groups semantically equivalent an- swers without changing their original meaning. You are an answer normalization judge. Original Task: question Candidate Answers: candidate_answers Instructions: 1. Group candidate answers that are semantically equivalent . 2. Do not judge which answer is correct unless equivalence requires it. 3. Preserve important distinctions between different numerical values, options, entities, or factual claims. 4. Return a canonical answer for each equivalence group. Output format: Group 1: Canonical Answer: <canonical form> Equivalent Answers: <list of answer ids> Group 2: Canonical Answer: <canonical form> Equivalent Answers: <list of answer ids>

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