Remember and Reweight: Enhancing Multi-Agent Debate with Experience Memory and Confidence Estimation

Multi-agent debate (MAD) improves the reasoning capabilities of large language models by having multiple agents iteratively refine their responses through discussion. However, MAD suffers from a critical vulnerability known as shared misconception: when a majority of agents initially converge on an incorrect answer, the debate process tends to amplify rather than correct the error. Existing methods primarily address peer skew but leave the agents' inherently biased concept priors unaddressed. To mitigate this systematic weakness, we propose R$^2$-MAD (Remember and Reweight for Multi-Agent Debate), a framework that equips agents with an experience memory accumulated from past debates. R$^2$-MAD intervenes on both failure modes through two complementary mechanisms: A debate-state-aware retrieval policy dynamically calibrates the concept prior by retrieving relevant historical evidence based on the current consensus level. Then these retrieved experiences provide a basis for estimating per-agent reliability, yielding confidence weights to modulate peer influence. Experiments on various benchmarks show that R$^2$-MAD achieves consistent improvements over existing single-agent and MAD baselines.

Meta-Moderator: Empowering Multi-Agent Debate with Meta-Cognition

Multi-agent debate can improve large language model reasoning by eliciting diverse hypotheses and critiques, yet its performance is often constrained by weak moderation. Common pipelines rely on fixed budgets, agreement-based stopping, or untrained judges, leading to redundant deliberation and unreliable evidence aggregation. We cast moderation as a meta-cognitive process, monitoring debate utility, controlling deliberation, and adjudicating a final answer, and introduce Meta-Moderator, a learnable framework that dynamically regulates debate and decides when to finalize an answer. Meta-Moderator is trained independently of the debaters via outcome-driven policy optimization, making debate regulation an explicit capability rather than an incidental effect of prompting. Across five benchmarks, Meta-Moderator outperforms widely used decision layers and transfers across tasks and system configurations. Further analyses show that it allocates debate more selectively and reduces mis-aggregation after informative hypotheses appear.

CLAIR-Fin: An Adversarial Multi-Agent Framework for Claim-Level Verification and Adaptive Debate in Cross-Modal Financial QA

Existing defenses against hallucination in retrieval-augmented and multi-agent pipelines remain partial: evidence is trusted despite modality disagreement, debate verifies an aggregate report rather than individual claims, and such verification occurs only after drafting, leaving inter-agent errors undetected until the final text. To close this gap, we present CLAIR-Fin, a nine-agent framework that decomposes each question into atomic claims maintained in a typed Financial Claim Ledger. Each claim is resolved through Asymmetric Evidence Authority, which conditions evidence trust on claim type rather than treating all modalities as equally reliable; Chain-of-Custody Verification, which checks grounding at the hand-off between drafting and adversarial review rather than only at the pipeline's exit; an Adaptive Rebuttal Cycle, which routes contested claims through adversarial debate whose depth scales with what that debate finds; and a terminal entailment audit paired with a continuous Hallucination Risk Index that distinguishes claims that passed scrutiny from claims never contested. We evaluate CLAIR-Fin on BB-FinQA-X, a 500-question cross-modal financial evaluation set built from Bangladesh Bank Annual Report material, stratified by query type, format, and difficulty. Relative to a single-pass retrieval-augmented generation baseline, it raises faithfulness ($0.780 \rightarrow 0.889$) while abstaining on 5.4% of questions when evidence is insufficient rather than forcing an unsupported response, and it exceeds stronger retrieval-strategy baselines such as HyDE and Graph-RAG on faithfulness ($\leq 0.874$).

Where Reasoning Diverges: Localized Multi-Agent Debate for Multi-Hop Question Answering

Multi-agent debate commonly exchanges complete rationales even when disagreements concern only a few intermediate claims. We introduce Localized Multi-Agent Debate (LMAD), an inference-time protocol that represents agent rationales as nodes, locates their earliest conflict, and restricts debate to the corresponding local segments. Guarded resolution extends a shared committed state so that later conflicts can be addressed without reopening accepted steps. We evaluate LMAD on four multi-hop question-answering benchmarks using ten backbones from four model families. Our method achieves the highest macro-averaged judge accuracy across all ten backbones, outperforming the strongest conventional baseline by up to 7.20 percentage points.

More Debate, Same Evidence: Structural Limits of Homogeneous Multi-Agent Groundedness

Large language model (LLM) judges are increasingly organized as multi-agent panels under the assumption that exchanging critiques improves judgment quality. We test this assumption for \emph{groundedness verification}, where a judge must determine whether a claim is supported by the supplied evidence. We evaluate a homogeneous three-agent panel on six public fact-verification and hallucination-detection benchmarks. Relative to a fixed single-agent reference, the panel's system-level accuracy difference ranges from $+8.5$ to $-4.4$ percentage points: two datasets show reliable gains, one shows a reliable loss, and three are statistically inconclusive. Because the reference and panel use different model variants, these differences characterize the complete systems rather than isolate a causal debate effect.

MADA-RL: Multi-Agent Debate-Aware Reinforcement Learning for Parameter-Efficient Reasoning in Compact Models

Large language models achieve strong reasoning performance, but often at prohibitive training cost - a challenge that is especially acute for compact models ($\leq 4 \, \mathrm{B}$ parameters) trained under limited budgets. We introduce MADA-RL, a post-training framework that specializes compact models into generator and critic roles and trains them with a debate-aware learning signal, fine-tuning only a small subset of parameters via LoRA adapters. Our central contribution is a counterfactual critic advantage: a dynamic, role-conditioned baseline that redefines the critic's advantage as its reward minus the generator ensemble's per-instance accuracy. This explicitly optimizes critics to improve over generator consensus rather than to merely reproduce a correct answer, yielding more targeted credit assignment than static mean-reward normalization. At deployment, the specialized agents are composed in a lightweight multi-round protocol. Across five mathematical reasoning benchmarks, MADA-RL raises the accuracy of the DeepSeek-R1-Distill-Qwen-1.5B model from $39.9 \, \%$ to $41.9 \, \%$ ($+2.0$ points, $p < 0.001$) using $16$ times fewer trainable parameters than fully fine-tuned baselines, placing it on the accuracy-trainable-parameter Pareto front. It approaches, but does not surpass, the strongest baselines (DeepScaleR, STILL-3), which are trained on substantially larger datasets; we analyse this gap and the associated inference-time cost directly. A controlled study isolates the source of MADA-RL's gains: the counterfactual advantage produces the highest critic improvement rate of any model evaluated, indicating that trained critics learn to correct generator errors rather than to imitate them.

Debate-on-Graph: Reliable and Adaptive Reasoning of Large Language Model on Uncertain Knowledge Graph

Large language models (LLMs) have demonstrated remarkable capabilities in natural language processing. However, LLMs often suffer from hallucinations and lack of relevant knowledge when dealing with question answering (QA) tasks. To mitigate these issues, knowledge graphs (KGs) have been utilized to enhance LLM reasoning. Nevertheless, KGs often contain noise and errors, while existing KG-enhanced LLM approaches are generally unable to identify and filter such noisy and erroneous content, which can instead amplify hallucinations and pose challenges for reliable reasoning. Uncertain knowledge graphs (UKGs), which associate each triple with a confidence score to quantify uncertainty, offer a promising direction to address this challenge. Compared with prior work, we investigate how to leverage UKGs to support LLMs for QA. We propose Debate-on-Graph (DoG), a new framework that enables LLMs and UKGs to collaborate adaptively for reliable reasoning. Specifically, we first design a heuristic search algorithm tailored for UKGs to extract reliable and question-relevant subgraphs, thereby reducing noise and errors in retrieved knowledge. We then introduce a Multi-Agent Debate mechanism, which yields reliable answers through adaptive adversarial debates, aiming to fully exploit the knowledge in UKGs while preserving the reliability of retrieved evidence. Extensive experiments on four benchmark QA datasets show that DoG achieves state-of-the-art performance over existing LLM reasoning methods and KG-based baselines, while enabling reliable and adaptive reasoning. Our code is available at https://github.com/seucoin/Debate-on-Graph.

Does Multi-Agent Debate Improve AI Feedback on Research Papers?

Probably not, at least for meta-analyses in economics. In a pre-registered, identity-masked, within-paper experiment, the authors of 44 meta-analyses ranked three AI reports on their own paper by usefulness for improving it: a single pass by a frontier model against two multi-agent debate tools we built and expected to win. All reports were held to a common length and template. The authors preferred the single pass, by 0.66 rank points over mad-research (95% CI 0.32 to 1.00) and 0.57 over paper-workshop (0.16 to 0.95), though paper-workshop spent roughly thirty times the tokens. Authors who recalled their journal referee report usually placed it first and never last; in a separate exercise, three AI judges almost always placed the real journal referee report last. Among the three AI reports, Gemini (the judge whose model family wrote none of the reports) would have ranked paper-workshop first in the authors' place, reversing the single-pass preference. The reversal warns against substituting an AI judge for the author. We measure perceived usefulness for finished papers; whether AI should referee papers is a separate question.

L-MAD: A Systematic Evaluation of Multi-Agent Debate Structures in Legal Reasoning

While multi-agent debate (MAD) frameworks have shown significant potential in general reasoning, their effectiveness in highly structured, knowledge-heavy legal domains remains under-explored. In this work, we introduce the Legal Multi-Agent Debate (L-MAD) framework to systematically evaluate different debate structures and aggregation methods within Legal Textual Entailment. By assigning distinct expert personas to multiple agents, L-MAD improves upon strong single-agent baselines by up to 8\%. Furthermore, analyzing how debate scales reveals a clear trade-off: increasing the agent population reduces inconsistency and improves accuracy, whereas extending discussion rounds induces a detrimental \textit{over-deliberation drift} where agents reinforce each other's mistakes. Ultimately, our findings outline the practical boundaries and safety margins of deploying collaborative multi-agent systems in high-stakes legal reasoning environments.

What LLM Agents Say When No One Is Watching: Social Structure and Latent Objective Emergence in Multi-Agent Debates

LLM agents will increasingly act in socially structured settings where role, audience, and relational context can shape what is advantageous or costly to say. We study whether such social structure, without any explicit objective in the prompt, changes what an agent expresses publicly relative to an off-the-record (OTR) channel elicited under the same condition. We introduce a dual-channel debate framework in which agents produce public utterances that enter the shared history alongside OTR responses that are recorded but never shown to the other participant. Across 10 models, 3 scenarios, and 5 variations within each scenario, alignment-inducing settings produce systematic public-OTR divergence in the targeted agent, with its decision divergence rising from a $\sim$3% baseline to roughly 40%. The effect is consistent across four aggregate analyses: stance, semantic similarity, natural language inference, and survey responses. In some cases, the OTR response explicitly attributes public accommodation to relational pressures, such as career risk or sponsorship obligation. The findings suggest that agent evaluation should extend beyond explicit goals and detect emergent objectives. We present a dual-channel evaluation framework and complementary behavioral measures that operationalize this assessment.

Mixture of Debaters: Learn to Debate at Architectural Level in Multi-Agent Reasoning

Existing multi-agent debate frameworks suffer from two critical limitations: they rely on static architectures where agent roles and coordination patterns are fixed at design time, and they require instantiating multiple model copies, incurring substantial computational overhead. We propose Mixture of Debaters (MoD), a unified framework that enables dynamic self-debate within a single model by leveraging the Mixture-of-Experts paradigm. We address three key challenges in adapting MoE for dialectical reasoning: (1) dual-routing that decouples role allocation from process flow, dynamically determining when to debate versus when to synthesize; (2) momentum switching that smooths token-level routing with local context, reducing expert-switch jitter; and (3) unified self-debate that encapsulates diverse debating personas into lightweight expert modules, eliminating inter-agent communication while preserving behavioral diversity. Extensive experiments on multimodal benchmarks demonstrate that MoD outperforms both single-model baselines and conventional multi-agent systems, achieving superior accuracy with 3.7x lower latency and 87% reduction in token consumption.The source code can be accessed at https://github.com/YongLD/MoD.

Diagnosing and Mitigating Compounding Failures in Agentic Persuasion via Taxonomic Strategy Retrieval

Foundation-model agents in multi-step, open-ended environments frequently suffer from compounding errors, where early mistakes contaminate long-horizon trajectories. While Multi-Agent Debate (MAD) succeeds in deterministic domains, agents in subjective tasks like persuasion experience severe problem drift and sycophantic conformity. We identify semantic leakage in standard Retrieval-Augmented Generation (RAG) as a reproducible trigger for these failures, as standard RAG prioritizes vocabulary overlap over logical necessity. To eliminate this leakage, we introduce Taxonomic Strategy RAG (TS-RAG), a systems intervention that routes strategies through a discrete categorical bottleneck to decouple argumentative structure from topical content. Zero-shot, cross-domain evaluations demonstrate that TS-RAG significantly improves the transfer of abstract logic where standard semantic retrieval collapses. Crucially, TS-RAG acts as a "capability bridge" in asymmetric deployments, empowering lightweight persuaders to consistently defeat parametrically superior opponents (improving win rates from 70.5 to 78.5) and accelerating argumentative efficiency. Finally, we introduce trace-level diagnostics via a turn-by-turn Debate State Representation (DSR), demonstrating the necessity of strict constraints to prevent evaluation collapse via default agentic sycophancy.

ExpertIVS: Sociological Expert Driven Individual Value Simulation in Large Language Models

Large Language Model (LLM) agents have demonstrated considerable potential for social simulation, yet struggle to accurately model individual value systems. Most existing methods mechanically stitch survey responses into prompts, which suffer from semantic fragmentation, failing to capture the internal coherence of human value systems. The value systems of LLMs are typically assessed using static multiple-choice questions, which fail to evaluate the value orientation in real-world dialogue interactions. To address these issues, we propose ExpertIVS, a framework employing 14 Sociological Expert Agents to interpret World Values Survey (WVS) responses through structured professional perspectives, rather than direct responses concatenation. These expert agents perform deep semantic reconstruction to generate robust and internally consistent individual profiles. To evaluate the consistency between LLMs and individual value systems during dynamic interactions, we further introduce a multi-agent debate mechanism. Extensive experiments across 480 individuals from 12 countries demonstrate that ExpertIVS achieves 90.78% value restoration fidelity and significantly outperforms baselines in value generalization (+5.3%). Moreover, ExpertIVS exhibits strong personality discriminability and behavioral consistency, enabling a shift from mere response concatenation to genuine sociological role-playing.

LegalHalluLens: Typed Hallucination Auditing and Calibrated Multi-Agent Debate for Trustworthy Legal AI

AI systems deployed in legal workflows hallucinate at rates that aggregate metrics report at ~52%, but this average conceals where errors concentrate and in which direction they run, leaving compliance officers without an actionable signal for trustworthy deployment. We present LegalHalluLens, an auditing framework with three components: typed hallucination profiles across four legally-motivated claim categories (numeric, temporal, obligation/entitlement, factual) over CUAD (Hendrycks et al., 2021); a Risk Direction Index (RDI) that reduces omission-versus-invention bias to a single deployment-comparable scalar; and a typed debate pipeline calibrated to both magnitudes and directions. Across 510 contracts and 249,252 clause-level instances we measure a within-model gap of approximately 38-40 pp between obligation/numeric and temporal claims that aggregate reporting hides, and show that two systems with matched 52% rates can carry opposite RDIs. The debate pipeline reduces fabricated detections by 45% with per-category gains tracking the diagnosis, matching commercial APIs with a substantially smaller backbone (4B active parameters). Typed profiles and RDI surface failure modes that aggregate metrics hide; we further show these diagnostics serve as calibration inputs for multi-agent debate pipelines, where Skeptic challenges and asymmetric gates targeted at measured failure modes outperform generically-tuned debate. The framework supports direction-aware procurement, accountability, and agent design for legal AI deployed in the wild.

Misinformation Propagation in Benign Multi-Agent Systems

Multi-agent systems, in which multiple large language model agents solve problems through turn-based interaction, are increasingly deployed in high-stakes settings such as medical diagnosis, legal analysis, and forensic decision-making. Their reliability can be at risk when single agents reason from incorrect or misleading context, e.g., from tool calls, since errors may propagate through agent interactions. This work studies this risk by injecting intent-based misinformation into benign single-agent and multi-agent systems across reasoning, knowledge, and alignment tasks. We find that misinformation can degrade single-agent performance and persists across multi-agent debate, with agents often retaining answers introduced by misinformed peers. Nevertheless, multi-agent debate reduces the resulting performance degradation compared to single-agent prompting, especially when most agents are not exposed to misinformation. Robustness depends on group composition and decision protocol. Consensus can be more stable than voting under peer pressure, while majorities can often steer misinformed agents back toward correct answers. Our results show that misinformation robustness in multi-agent systems depends on the underlying model and also on how agents exchange information and aggregate decisions.

ARMOR-MAD: Adaptive Routing for Heterogeneous Multi-Agent Debate in Large Language Model Reasoning

Multi-agent debate (MAD) can improve large language model reasoning, but fixed debate pipelines often waste computation and can amplify correlated errors among similar agents. We propose ARMOR-MAD, a training-free heterogeneous MAD framework that treats debate as conditional computation. ARMOR-MAD combines three components: Pre-debate Agreement Routing (PAR) decides whether independently generated Round-0 answers require debate; Early Agreement Stopping Evaluator (EASE) stops debate after convergence; and Semantic Outlier Detection (SOD) down-weights abnormal final answers during aggregation. Across MATH Level 5, GSM8K, MMLU, and MMLU-Pro, ARMOR-MAD consistently improves over fixed-round heterogeneous debate with the same model pool, reaching 65.5\%, 96.5\%, 90.0\%, and 81.5\% accuracy, respectively. The results suggest that genuine model heterogeneity and agreement-based control are both important for making MAD more accurate and efficient.

Decoupling Thought from Speech: Knowledge-Grounded Counterfactual Reasoning for Resilient Multi-Agent Argumentation

Multi-agent debate frameworks have been shown to improve large language model performance in convergent tasks, but they are currently optimized in a way that heavily favors final output accuracy rather than stability of the process. During long-horizon exchanges reactive systems under sustained perturbations often experience logic degradation, argument repetition, and role drift. To structurally prevent the identity loss and maintain the process fidelity, we introduce Knowledge-Grounded Counterfactual Reasoning (KG-CFR), a dual-stage architecture that enforces a strict separation of concerns between a private, retrieval-augmented planning buffer, and a public execution layer. We assess this system in Dynamic Resource Allocation under Uncertainty (DRAU), a dedicated 1v1v1 environment, introducing diversity as distinct from standard debate settings. Over 270 completely factorial crisis simulation trajectories with stochastic environmental shocks, KG-CFR prevents judge-detected critical post-shock degradation (defined as a quality shift, $Δ\le -0.20$) in more than 95% of perturbed runs, increasing the overall argument quality from 0.694 to 0.822. Our primary contribution is the demonstration of architectural decoupling being an important factor of systemic resilience enhancement under sustained pressure without quality loss. Furthermore, we introduce custom vector metrics for discourse divergence and plan-execution alignment that provide strong, directionally consistent evidence of operational stability. Our ablation experiments suggest that the proper doctrinal grounding can be an equally important factor for argument quality, as the prospective planning. KG-CFR, according to our initial metric evaluations, reduces semantic looping, by preserving the agent's consistency with the original plan.

Early-Token Confidence Predicts Reasoning Quality in Multi-Agent LLM Debate

Evaluating reasoning quality in multi-agent LLM systems is challenging, especially for open-ended tasks without reference answers. We investigate whether intrinsic confidence signals, token-level log-probabilities from decoding, can predict reasoning quality as assessed by LLM-as-judge evaluation. Using a debate-based essay scoring framework, we compare confidence proxies against rubric-based judge scores across two ASAP essay sets. We find that early-token confidence, particularly within the first few generated tokens, is consistently the strongest predictor of reasoning quality, outperforming full-sequence statistics. Analysis of log-probability trajectories shows that the opening phase of generation is the most heterogeneous and therefore most informative. We also observe a systematic asymmetry between agent roles, with stronger alignment between confidence and quality for supportive reasoning than for adversarial critique. These results suggest that early decoding dynamics provide a lightweight and effective signal for estimating reasoning reliability in multi-agent LLM systems.

The Confident Liar: Diagnosing Multi-Agent Debate with Log-Probabilities and LLM-as-Judge

Multi-agent debate systems are typically evaluated only on whether the final answer is correct, overlooking the quality of the intermediate reasoning that debate is designed to produce. This paper studies the relationship between three signals in multi-agent debate: token-level log-probability distributions over reasoning tokens, LLM-as-judge rubric scores assigned to those tokens, and final task accuracy. We examine whether internal confidence signals predict externally evaluated reasoning quality, and whether either signal aligns with task correctness, across three domains: rubric-based scoring, mathematical reasoning, and factual question answering. Our framework pairs a two-agent debate architecture -- a Constructor and an Auditor -- with an LLM-as-judge that scores each agent's reasoning along instruction following, justification quality, and evidence grounding, together with a critical-failure flag. Experiments in the rubric-scoring domain reveal a consistent four-phase confidence trajectory and a substantial role asymmetry: confidence aligns with judged reasoning quality roughly twice as strongly for the Constructor as for the Auditor, and confidence-based detection of critical reasoning failures is markedly more reliable for the Constructor (AUROC 0.804) than for the Auditor (0.634). These findings motivate the broader cross-domain investigation proposed in this paper.

SMADE-IE: Sparse Multi-Agent Framework with Evidence-Driven Debate for Zero-Shot Information Extraction

Zero-shot information extraction (IE) with large language models (LLMs) has attracted increasing attention due to its flexibility in adapting to new schemas and domains without task-specific training. Existing approaches mainly rely on monolithic prompting, each-type prompting, or multi-agent debate. However, monolithic prompting often suffers from boundary and type errors, while each-type prompting and multi-agent debate introduce cross-type conflicts, redundant agent interactions, and substantial token overhead. To address these challenges, we propose SMADE-IE, a sparse and evidence-driven multi-agent framework for zero-shot IE. SMADE-IE first employs an Adaptive Mode Selector to dynamically route inputs into either a lightweight Global Extraction Mode or a Type-Centric Extraction Mode, reducing unnecessary type selection and reasoning noise. For conflicting predictions, we further introduce an Evidence-Driven Debate mechanism that structures arguments into Toulmin-style components and performs confidence aggregation through external evidence scoring and Bayesian updates. Experimental results on 9 benchmark datasets across NER, RE, and JERE tasks show that SMADE-IE consistently outperforms existing zero-shot IE baselines while also improving token efficiency through sparse agent selection and early-stopping debate.

When Helping Hurts and How to Fix It: Multi-Agent Debate for Data Cleaning

When does multi-agent debate help data cleaning, and when does it hurt? Across three benchmarks, four model families, and over 6,000 task-condition pairs, we find debate's effect reverses sign: it degrades generation across all four models (-1.6 to -15.5pp) through critique-induced confusion (CIC), hallucinated Critic feedback that the Generator accepts uncritically, yet improves error detection (+27.4pp F1, d=1.0). We derive a debate benefit condition: debate helps when the probability of rescuing a wrong output (Critic verification odds weighted by fixability) exceeds the probability of destroying a correct one. A factorial experiment proves adversarial separation is essential: self-verification with identical tools fails, while a separate Critic with code-execution grounding and evidence-gated generation produces the first debate configuration to significantly exceed single-agent on a generative task (+5.3pp, p<0.05). The condition correctly predicts all nine task types and generalizes with zero false positives across 19 published comparisons in seven domains.

MM-StanceDet: Retrieval-Augmented Multi-modal Multi-agent Stance Detection

Multimodal Stance Detection (MSD) is crucial for understanding public discourse, yet effectively fusing text and image, especially with conflicting signals, remains challenging. Existing methods often face difficulties with contextual grounding, cross-modal interpretation ambiguity, and single-pass reasoning fragility. To address these, we propose Retrieval-Augmented Multi-modal Multi-agent Stance Detection (MM-StanceDet), a novel multi-agent framework integrating Retrieval Augmentation for contextual grounding, specialized Multimodal Analysis agents for nuanced interpretation, a Reasoning-Enhanced Debate stage for exploring perspectives, and Self-Reflection for robust adjudication. Extensive experiments on five datasets demonstrate MM-StanceDet significantly outperforms state-of-the-art baselines, validating the efficacy of its multi-agent architecture and structured reasoning stages in addressing complex multimodal stance challenges.

A Systematic Comparison of Prompting and Multi-Agent Methods for LLM-based Stance Detection

Stance detection identifies the attitude of a text author toward a given target. Recent studies have explored various LLM-based strategies for this task, from zero-shot prompting to multi-agent debate. However, existing works differ in data splits, base models, and evaluation protocols, making fair comparison difficult. We conduct a systematic comparison that evaluates five methods across two categories -- prompt-based inference (Direct Prompting, Auto-CoT, StSQA) and agent-based debate (COLA, MPRF) -- on four datasets with 14 subtasks, using 15 LLMs from six model families with parameter sizes from 7B to 72B+. Our experiments yield several findings. First, on all models with complete results, the best prompt-based method outperforms the best agent-based method, while agent methods require 7 to 12 times more API calls per sample. Second, model scale has a larger impact on performance than method choice, with gains plateauing around 32B. Third, reasoning-enhanced models (DeepSeek-R1) do not consistently outperform general models of the same size on this task.

From Soliloquy to Agora: Memory-Enhanced LLM Agents with Decentralized Debate for Optimization Modeling

Optimization modeling underpins real-world decision-making in logistics, manufacturing, energy, and public services, but reliably solving such problems from natural-language requirements remains challenging for current large language models (LLMs). In this paper, we propose \emph{Agora-Opt}, a modular agentic framework for optimization modeling that combines decentralized debate with a read-write memory bank. Agora-Opt allows multiple agent teams to independently produce end-to-end solutions and reconcile them through an outcome-grounded debate protocol, while memory stores solver-verified artifacts and past disagreement resolutions to support training-free improvement over time. This design is flexible across both backbones and methods: it reduces base-model lock-in, transfers across different LLM families, and can be layered onto existing pipelines with minimal coupling. Across public benchmarks, Agora-Opt achieves the strongest overall performance among all compared methods, outperforming strong zero-shot LLMs, training-centric approaches, and prior agentic baselines. Further analyses show robust gains across backbone choices and component variants, and demonstrate that decentralized debate offers a structural advantage over centralized selection by enabling agents to refine candidate solutions through interaction and even recover correct formulations when all initial candidates are flawed. These results suggest that reliable optimization modeling benefits from combining collaborative cross-checking with reusable experience, and position Agora-Opt as a practical and extensible foundation for trustworthy optimization modeling assistance. Our code and data are available at https://github.com/CHIANGEL/Agora-Opt.

BARRED: Synthetic Training of Custom Policy Guardrails via Asymmetric Debate

Deploying guardrails for custom policies remains challenging, as generic safety models fail to capture task-specific requirements, while prompting LLMs suffers from inconsistent boundary-case performance and high inference costs. Training custom classifiers achieves both accuracy and efficiency, yet demands substantial labeled data that is costly to obtain. We present BARRED (Boundary Alignment Refinement through REflection and Debate), a framework for generating faithful and diverse synthetic training data using only a task description and a small set of unlabeled examples. Our approach decomposes the domain space into dimensions to ensure comprehensive coverage, and employs multi-agent debate to verify label correctness, yielding a high-fidelity training corpus. Experiments across diverse custom policies demonstrate that small language models finetuned on our synthetic data consistently outperform state-of-the-art proprietary LLMs (including reasoning models) and dedicated guardrail models. Ablation studies confirm that both dimension decomposition and debate-based verification are critical for ensuring the diversity and label fidelity required for effective fine-tuning. The BARRED framework eliminates the reliance on extensive human annotation, offering a scalable solution for accurate custom guardrails.