Semantic Consensus: Process-Aware Conflict Detection and Resolution for Enterprise Multi-Agent LLM Systems

The shift from monolithic LLMs to distributed multi-agent architectures demands new frameworks for verifying and securing autonomous coordination. Unlike traditional multi-agent systems focused on cooperative state alignment, modern LLM patterns: multi-agent debate, constitutional oversight, helper-critic loops-rely on adversarial critique for error correction and reasoning refinement. Since LLMs are dynamical systems whose latent states are imperfectly observable from verbalized outputs, securing these networks requires understanding both macroscopic topology and microscopic agent observability. This paper establishes a rigorous graph-theoretic framework for analyzing consensus in signed, directed interaction networks, bridging graph theory and LLM reasoning by formally mapping Transformer cross-entropy log-odds to the signed Laplacian. We characterize agreement stability through structural balance theory, showing how unbalanced critique cycles produce logical frustration and persistent reasoning oscillations, and prove that unobservable latent states from hidden system prompts act as topological Trojan horses that destabilize cooperative consensus. To resolve unobservable deadlocks, we restrict interaction topologies to chordal graphs and apply matrix decomposition with Gram-Schmidt orthogonalization, proving that rank-one spectral edge perturbations deterministically break expertise symmetry by shifting eigenvalues into the stable left-half plane. Core contributions include consensus theorems, polynomial-time Perfect Elimination Ordering verification algorithms, and large-scale empirical validation on clustered ensembles of LLaMA-3, Mistral, and Gemma agents.

Large language model (LLM) agents are increasingly expected to operate in enterprise environments, where work is distributed across specialized roles, permission-controlled systems, and cross-departmental procedures. However, existing enterprise benchmarks largely evaluate single agents with broad tool access, while existing multi-agent benchmarks rarely capture realistic enterprise constraints such as role specialization, access control, stateful business systems, and policy-based approvals. We introduce EntCollabBench, a benchmark for evaluating enterprise multi-agent collaboration. EntCollabBench simulates a permission-isolated organization with 11 role-specialized agents across six departments and contains two evaluation subsets: a Workflow subset, where agents collaboratively modify enterprise system states, and an Approval subset, where agents make policy-grounded decisions. Evaluation is based on execution traces, database state verification, and deterministic policy adjudication rather than natural-language response judging. Experiments with representative LLM agents show that current models still struggle with end-to-end enterprise collaboration, especially in delegation, context transfer, parameter grounding, workflow closure, and decision commitment. EntCollabBench provides a reproducible testbed for measuring and improving agent systems intended for realistic organizational environments.

Large language model (LLM) based multi-agent systems enable complex problem solving through coordinated reasoning and action, but their distributed structure also introduces new challenges in diagnosing system-level failures. When an execution fails, identifying which agent is responsible and at what point the trajectory first becomes irreversibly misdirected is difficult due to long-horizon interactions and tightly coupled agent behaviors. In this paper, we study the problem of failure localization in LLM-based multi-agent systems and present AgentLocate, a framework that attributes failures to both a specific agent and the earliest decisive step. AgentLocate combines an LLM-based judging mechanism with multi-perspective verification by independent evaluators, whose assessments are aggregated using a confidence-aware strategy. The resulting feedback is further used to adapt the judge through lightweight fine-tuning, improving attribution quality. We evaluate AgentLocate on two complementary benchmarks covering diverse tasks, agent configurations, and trajectory lengths. Experimental results show that AgentLocate consistently outperforms existing failure localization methods in identifying both responsible agents and failure steps, while remaining efficient in terms of token usage and running time.