Counterfactual Graph for Multi-Agent LLM Calibration

Multi-agent LLM systems improve reasoning by combining outputs from multiple agents, but interaction-heavy methods can introduce error propagation and high communication overhead. When agents exchange raw responses or reasoning traces, incorrect intermediate reasoning may be adopted and amplified, leading to confident but wrong consensus; multi-round communication also increases token consumption, latency, and inference cost. In this paper, we propose a controlled-communication coordination framework named DarkForest. DarkForest first keeps agents independent, so each agent produces an answer without seeing the others' outputs. It then parses the raw responses into structured candidate records, groups semantically equivalent candidates into clusters, and estimates a calibrated belief distribution over these clusters using agent reliability, confidence, parse quality, support-pattern reliability, and independence corrections. A coordinator receives only policy-permitted evidence from this belief state with controlled communication. Experiments on six reasoning benchmarks show that DarkForest achieves leading overall quality, improves the strongest baseline by up to 30.7% on benchmark metrics, and reduces token consumption by up to $6.5\times$ compared with communication-heavy baselines.

Practitioners deploying multi-agent large language model (LLM) systems must currently choose between communication topologies such as chain, star, mesh, and richer variants without any pre-inference diagnostic for which topology will amplify drift, converge to consensus, or remain robust under perturbation. Existing evaluation answers these questions only post hoc and only for the task measured. We introduce a structural diagnostic for multi-agent LLM communication graphs based on the successor representation $M = (I - γP)^{-1}$ of the row-stochastic communication operator, and we connect three of its spectral quantities, the spectral radius $ρ(M)$, the spectral gap $Δ(M)$, and the condition number $κ(M)$, to three distinct failure modes. We derive closed-form spectra for the chain, star, and mesh under row-stochastic normalization, and validate the predictions on a 12-step structured state-tracking task with Qwen2.5-7B-Instruct over 100 independent trials. The condition number is a perfect rank-order predictor of empirical perturbation robustness ($r_s = 1.0$); the spectral gap partially predicts consensus dynamics ($r_s = 0.5$); and the spectral radius is perfectly \emph{inverted} with respect to cumulative error ($r_s = -1.0$). We trace this inversion to a regime in which linear spectra are blind to non-contracting bias drift, and we propose an affine-noise extension of the predictive map that recovers the empirical ordering. We read this as a first step toward representational, drift-aware structural diagnostics for multi-agent LLM systems, sitting alongside classical spectral and consensus theory.

With an ever-growing zoo of LLMs and benchmarks, the need to orchestrate multiple models for improved task performance has never been more pressing. While frameworks like Mixture-of-Agents (MoA) attempt to coordinate LLMs, they often fall short in terms of (1) selecting relevant agents, (2) facilitating effective intra-agent communication, and (3) integrating responses efficiently. In this work, we propose Graph-of-Agents (GoA), a new graph-based framework for modeling multi-agent LLM communication. Our approach begins with node sampling, selecting only the most relevant agents by leveraging model cards that summarize each model's domain, task specialization, and other characteristics. Next, we construct edges between the selected agents by evaluating their responses against one another to determine relevance ordering. Directed message passing is then performed from highly relevant agents to less relevant ones to enhance their responses, followed by reverse message passing to refine the original responses of the more relevant agents. Finally, the updated responses are aggregated via graph-based pooling (e.g., max or mean pooling) to produce a single, unified answer. We evaluate GoA on diverse multi-domain benchmarks (MMLU, MMLU-Pro, GPQA) and domain-specific benchmarks (MATH, HumanEval, MedMCQA), with an agent pool of 6 LLMs spanning multiple domains. Surprisingly, GoA achieves superior performance using only 3 selected agents, outperforming recent multi-agent LLM baselines that utilize all 6 agents simultaneously. By adopting a graph structure, GoA offers both scalability and effectiveness through structured message passing-positioning it as a strong candidate for navigating the challenges of the ever-growing LLM zoo. Code is available at: https://github.com/UNITES-Lab/GoA.