BaRe-Mem: Bayesian Reliability Memory for Robust and Adaptive Agent Consultation

Memory is central to long-horizon LLM agents, yet existing memory systems primarily preserve interaction content rather than modeling which agents can be trusted and under what conditions. This limitation is particularly important in multi-agent systems, where a central model may be unable to directly verify plausible or correlated peer responses. We introduce $Σ$-Mem, an online reliability memory that records historical competence evidence for individual peers and peer relationship evidence across the peer set. Both forms of evidence are maintained as real symmetric states and updated from post-decision correctness feedback. By Weyl's inequality, the spectral change caused by each event-level update is bounded, enabling stable online adaptation without retraining the underlying models. $Σ$-Mem provides a general write-and-read interface: the same memory can be used for residual steering of a central model, response-free peer routing, or reliability-weighted voting. Across five Qwen-family models, $Σ$-Mem adapts to counterfactual reliability shifts and generalizes to unseen peers and task domains. Direct memory readouts also outperform majority voting and the best fixed peer over the full OOD evaluation set. Moreover, performance improves consistently as more correctness feedback becomes available, indicating that $Σ$-Mem progressively accumulates actionable reliability information. These results establish reliability memory as a reusable foundation for adaptive coordination in LLM-based multi-agent systems.

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.

Multi-agent debate (MAD) systems increasingly rely on shared memory to support long-horizon reasoning, but this convenience opens a critical vulnerability: a single corrupted entry can contaminate the downstream memory-augmented reasoning, and debate alone fails to filter such errors. Existing safeguards filter entries via heuristics or LLM-based validation, yet they rely on AI judgments that share the same failure modes and overlook the cross-agent dynamics of MAD. We address this gap by formulating memory updating in MAD as a zero-trust memory game, in which no agent is assumed reliable and the game's equilibrium motivates a principled objective for calibrating memory influence. Guided by this objective, we propose EquiMem, an inference-time calibration mechanism that evaluates each update against the shared memory state and the memory already being used by other agents, using their existing retrieval queries and traversal paths as evidence of calibration. EquiMem instantiates this calibration for both embedding- and graph-based memory, and across diverse benchmarks, MAD frameworks, and memory architectures, it consistently outperforms existing safeguards, remains robust under adversarial agents, and incurs negligible inference overhead.