Multi-Agent Debate with Memory Masking

🕒 Published (v1): 2026-01-01 · Source: ICLR · Venue: ICLR 2026 · link

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Memory masking in multi-agent debate improves consistency; addresses echo chambers

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TL;DR

Multi-agent debate (MAD) frameworks are vulnerable to erroneous memories propagated across debate rounds, causing agents that were initially correct to be misled into wrong answers. This paper proposes MAD-M², which inserts a memory evaluation and binary masking step between debate rounds to filter incorrect memories before the next round. Empirical results on math reasoning and language understanding benchmarks show MAD-M² consistently outperforms naive MAD.

Problem

Standard MAD passes all agent responses from round \(r\) as context to round \(r+1\), including incorrect ones. When erroneous memories outnumber correct ones, they act as low-quality in-context demonstrations that corrupt subsequent reasoning — agents that originally answered correctly are steered toward wrong answers. This vulnerability is theoretically formalized: the probability of a correct final answer degrades exponentially as the number of erroneous memories \(N_e\) increases, since each agent's conditional correct-generation probability is modeled as \(e^{-\alpha N_e}\).

Method

MAD-M² inserts two operations between every pair of debate rounds:

1. Evaluation: Each agent (or a shared evaluator, since all agents share the same base model) critically assesses each memory in \(M_r\) and assigns a flag.
2. Masking: A binary mask vector \(M^{(i)} = g^{\text{map}}_{A_{\theta_i}}(M_r) \in \{0,1\}^{N_a}\) is generated; refined memories are \(\tilde{M}^{(i)}_r = M^{(i)} \odot M_r\).

Two masking strategies are defined: - Subjective: LLM agents label each memory YES / NO / NOT SURE; strictness of the NOT SURE rule is a tunable hyperparameter. - Objective: Perplexity of each response is measured; only the single lowest-perplexity response is retained.

Agents then reason over \(\tilde{M}^{(i)}_r\) instead of the full \(M_r\). Final answer is selected by majority voting over the last-round responses.

Key Contributions

• Identifies and formalizes the erroneous-memory vulnerability in MAD via Propositions 2.2 (CoT-SC) and 2.3 (MAD), showing that filtering \(N_e\) consistently improves performance in both easy (\(e^{-\alpha N_e} \geq \frac{1}{2}\)) and hard (\(e^{-\alpha N_e} < \frac{1}{2}\)) reasoning regimes, whereas simply adding agents can hurt performance in the hard regime.
• Proves that CoT-SC is theoretically an upper bound on MAD's performance, explaining empirical findings that MAD often fails to beat CoT-SC.
• Proposes MAD-M² with both subjective (LLM-based) and objective (perplexity-based) masking strategies.
• Quantifies the additional token overhead: MAD-M² consumes at most \(N_a \sum_{r=2}^{N_{\text{round}}} \sum_{i=1}^{N_a} T^o_{r-1,i}\) extra input tokens versus naive MAD.
• Demonstrates empirical improvements on GSM8K, MATH, AIME24&25, and MMLU-Pro.

Results

Specific accuracy numbers are not present in the provided text excerpt. The paper states: - MAD-M² "generally achieves better performance than naive MAD (Du et al., 2023) on various reasoning tasks" across GSM8K, MATH, AIME24&25, and MMLU-Pro. - Theoretical bounds confirm that reducing \(N_e\) improves the lower bound of MAD's success probability in EPR and tightens the upper bound in HPR, in contrast to increasing \(N_a\) (which can worsen HPR performance exponentially).

Limitations

• MAD-M² consumes strictly more input tokens than naive MAD due to the evaluation step; overhead scales with \(N_a \times N_{\text{round}}\).
• The subjective masking strategy relies on the LLM's own ability to correctly identify erroneous reasoning — if the model cannot detect its own errors, masking may be unreliable.
• The objective (perplexity) strategy retains only a single response, potentially discarding diverse correct reasoning paths.
• The theoretical model assumes agent correctness probability is exactly \(e^{-\alpha N_e}\), a simplification that may not hold for all LLM families or task types.
• Analysis is restricted to 2-round MAD for tractability; extension to \(N_{\text{round}} > 2\) is not fully characterized.

Relevance to Agentic AI / LLM Agents

MAD-M² directly addresses a core reliability problem in multi-agent reasoning pipelines: inter-agent information contamination. This is relevant beyond debate specifically — any agentic system where agents share intermediate reasoning (tool-call traces, scratchpads, plan steps) faces analogous erroneous-context propagation. The theoretical result that CoT-SC upper-bounds MAD provides a principled explanation for why naively wiring LLMs into debate loops can regress performance, guiding the design of more robust multi-agent orchestration. The perplexity-based objective masking strategy also points toward inference-time quality signals as lightweight selectors in agent pipelines.