cs.CLOct 28, 2026

HEDGE: Gated Hypergraph Memory for Scalable Multi-Agent Debate

Authors: Amirhossein Abaskohi, Mahdi Mostajabdaveh, Zirui Zhou

Organizations: University of British Columbia · Huawei Technologies Canada

Read PDF
Ask AI
Cite

Copy citation

DOINot available for this paper

Abstract

Multi-agent debate systems require agents to retain and revisit arguments across multiple rounds, yet limited context windows and unstructured memories make relevant information increasingly difficult to recover. Existing flat and pairwise-graph memories also struggle to capture higher-order relations, including multi-agent agreement, conflicting evidence, and evolving consensus. We introduce HEDGE, a selective memory framework that represents debate trajectories as semantic hypergraphs. Hyperedges connect related claims across agents, while intra-hyperedge relational graphs preserve fine-grained argumentative structure. A learned memory selection module (MSM), trained through supervised learning and reinforcement learning, routes each memory candidate to STORE, BACKUP, or OMIT, retaining useful information while limiting redundancy. Across seven diverse benchmarks, HEDGE consistently outperforms strong single-agent, multi-agent, and memory baselines, improving accuracy by 5.0 points on average over the strongest multi-agent system with GPT-4o-mini. The gains reach 8.2 points on conflict-heavy tasks, while HEDGE reduces memory usage by 48% and the number of debate rounds by 34%.

Figures & tables

Figure 1: Trajectory-level memory in HEDGE during multi-agent debate. Without memory ( left ), agents revisit a rejected founder hypothesis; with HEDGE ( right ), the stored rationale avoids redundant reasoning and reaches the correct answer in 3 instead of 4 rounds.
Figure 2: Overview of HEDGE ’s memory update pipeline. The current debate is organized as a semantic hypergraph, while the memory selection module uses candidate features and cross-attention over hyperedge centroids to route new information to store , backup , or omit .
MethodMATH500GPQAFaithEvalConflictQANovelQAHotpotQAMMLU-Pro
Single-Agent (Vanilla)
GPT-5.457.1_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.2}}56.2_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.4}}72.7_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.3}}48.9_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.5}}62.4_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.4}}45.3_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.3}}85.2_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.2}}
GPT-4o53.2_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.3}}44.2_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.5}}66.4_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.4}}41.5_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.6}}58.1_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.3}}38.9_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.4}}77.6_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.3}}
GPT-4o-mini49.8_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.4}}33.8_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.6}}61.4_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.5}}29.2_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.7}}53.3_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.4}}29.4_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.5}}66.8_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.4}}
Qwen3.5-27B51.4_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.3}}48.9_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.4}}69.2_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.3}}36.8_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.6}}57.6_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.5}}39.8_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.4}}83.4_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.2}}
Single-Agent (Advanced) ( GPT-4o-mini )
Table 1: Accuracy (%) across seven benchmarks. Each value reports the mean over three runs , with red subscripts indicating the corresponding error. All multi-agent methods use a three-agent topology. HEDGE performs best under both backbone models, with particularly strong gains on FaithEval, ConflictQA, and NovelQA.
MemoryMATH500GPQAFaithEvalConflictQANovelQAHotpotQAMMLU-Pro
AutoGen 2024
No-memory55.5_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.5}}38.9_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.6}}68.0_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.4}}36.5_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.7}}56.3_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.5}}32.7_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.4}}74.7_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.3}}
Voyager57.3_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.4}}40.7_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.5}}69.8_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.6}}38.6_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.8}}58.1_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.4}}34.2_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.5}}76.3_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.3}}
Memory Bank54.9_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.6}}38.2_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.7}}67.3_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.5}}37.2_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.6}}57.1_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.6}}33.5_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.4}}75.3_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.4}}
Generative57.8_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.5}}41.4_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.6}}70.5_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.4}}39.3_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.7}}58.9_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.5}}34.7_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.6}}77.1_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.3}}
MetaGPT-M58.4_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.4}}42.1_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.5}}71.1_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.5}}40.2_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.6}}59.6_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.4}}35.3_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.5}}77.9_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.3}}
Table 2: Comparison of memory mechanisms under AutoGen and DyLAN. Values are mean accuracy over three runs, with red subscripts indicating standard deviation. HEDGE achieves the best performance across all benchmarks. See Appendix I for the results on MacNet and G-Designer.
Figure 3: Performance–efficiency trade-offs across representative benchmarks and orchestration frameworks. Top: performance versus total token usage, with bubble size indicating the average number of reasoning rounds. Bottom: performance versus persistent memory footprint. See Appendix J for full results across benchmarks.
ConfigurationConflictQAHotpotQA
 Acc.RTMAcc.RTM
No MSM51.78.144.8K30.6K37.58.046.3K32.1K
Stage I only55.26.539.6K22.7K40.66.641.2K23.8K
Stage I + Stage II57.85.736.9K18.2K42.35.838.1K19.6K
Table 3: Effect of MSM and its training stages on accuracy, rounds (R), token usage (T), and memory footprint in tokens (M).
Appendix figures & tables23 assets

Supplementary material from the paper’s appendix.

Appendix

BenchmarkCapability probedSplit / subset#EvalContext scaleAnswer format
MATH500Symbolic reasoningtest500short problem statementfree-form
GPQAExpert scientific knowledgemain448short question4-way multiple choice
FaithEvalContextual faithfulnesscounterfactual1,000single passageshort-form extractive
ConflictQAEvidence conflict resolutionpopQA (gpt4)9,544two conflicting passagesshort-form
NovelQALong-context comprehensionfull2,305>> 200K tokens per novelfree-form (generative)
HotpotQAMulti-hop retrievaldev (fullwiki)7,4055.2M-passage corpusshort-form extractive
Appendix
Table 4: Statistics of the seven evaluation benchmarks. Context scale refers to the evidence available at inference time rather than to the question length.
HyperedgeNodes (Claims)Connections
H1: Film and Castn 1 : Kiss and Tell stars Shirley Temple as Corliss Archer n 2 : Shirley Temple portrayed Corliss Archer in Kiss and Telln 1 →EVIDENCE\mbox−FOR\xrightarrow{\mathrm{EVIDENCE\mbox{-}FOR}} n 2
H2: Government Positionn 3 : Shirley Temple served as U.S. Chief of Protocol n 4 : Chief of Protocol is a U.S. government position n 5 : Shirley Temple held the government position of Chief of Protocoln 3 →EVIDENCE\mbox−FOR\xrightarrow{\mathrm{EVIDENCE\mbox{-}FOR}} n 5 n 4 →SUPPORTS\xrightarrow{\mathrm{SUPPORTS}} n 5
H3: Actress–Government Role Linkingn 2 : Shirley Temple portrayed Corliss Archer in Kiss and Tell n 5 : Shirley Temple held the government position of Chief of Protocol n 6 : The actress portraying Corliss Archer held the position of Chief of Protocoln 6 →DEPENDS\mbox−ON\xrightarrow{\mathrm{DEPENDS\mbox{-}ON}} n 2 n 6 →DEPENDS\mbox−ON\xrightarrow{\mathrm{DEPENDS\mbox{-}ON}} n 5
Appendix
Table 5: Hypergraph memory constructed by HEDGE . Nodes represent atomic claims, while typed directed relations encode evidential support and argumentative dependencies within each hyperedge. Nodes n 2 and n 5 belong to multiple hyperedges, connecting entity-specific reasoning with the final conclusion through overlapping membership.
MemoryMATH500GPQAFaithEvalConflictQANovelQAHotpotQAMMLU-Pro
G-Designer 2025b
No-memory55.3_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.5}}38.6_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.6}}67.5_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.4}}36.1_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.7}}55.8_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.5}}32.6_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.4}}74.2_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.3}}
Voyager57.0_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.4}}40.4_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.5}}69.3_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.6}}38.2_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.7}}57.6_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.4}}33.9_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.5}}75.9_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.3}}
Memory Bank54.8_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.6}}37.9_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.7}}66.9_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.5}}36.8_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.6}}56.5_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.6}}33.1_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.4}}74.6_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.4}}
Generative57.3_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.5}}41.1_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.6}}70.1_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.4}}38.9_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.8}}58.2_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.5}}34.3_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.6}}76.4_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.3}}
MetaGPT-M57.7_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.4}}41.8_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.5}}70.7_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.5}}39.6_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.6}}58.8_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.4}}34.8_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.5}}77.0_{{\color[rgb]{1,0,0}\scriptscriptstyle\pm 0.3}}
Appendix
Table 6: Additional results under the G-Designer and MacNet multi-agent frameworks. Values report the mean over three runs, with red subscripts indicating the standard deviation. EquiMem consistently improves G-Memory, while HEDGE achieves the strongest performance across all benchmarks with lower run-to-run variability.
MethodMATH500GPQAFaithEvalConflictQANovelQAHotpotQAMMLU-Pro
 RTRTRTRTRTRTRT
Single-Agent (Vanilla)
GPT-4o-mini18566173121548918235157911914716623
Single-Agent (Advanced) ( GPT-4o-mini )
Self-Refine21427321315829276315342314895316211211367
Self-Consistency422491420358314872524137523705525164417628
Appendix
Table 7: Average number of reasoning rounds (R) and total token usage (T) for non-memory systems built on GPT-4o-mini . Methods are grouped into single-agent, advanced single-agent, and multi-agent settings.
MethodMATH500GPQAFaithEval
 RTMRTMRTM
ChatDev-M5.23018561246.12846257834.3201374215
MacNet-M6.33398281426.83217476855.1226485562
MetaGPT-M6.136125102847.33441896815.4241027025
MAD-M 25.42916464875.82754660384.2194824476
MeMAD7.238261184727.836847173656.12597312498
Appendix
Table 8: Average reasoning rounds (R), average total token usage (T), and average memory footprint (M) for memory-based multi-agent systems implemented with AutoGen using GPT-4o-mini .
MethodMATH500GPQAFaithEval
 RTMRTMRTM
ChatDev-M7.237210112458.135590103846.2248307412
MacNet-M7.539185136728.437421127556.5261949156
MetaGPT-M8.341562168419.239873158927.12794511237
MAD-M 26.935984117367.834327109425.9239167798
MeMAD8.143218214959.041576201847.32916314122
Appendix
Table 9: Average reasoning rounds (R), average total token usage (T), and average memory footprint (M) for memory-based multi-agent systems implemented with DyLAN using GPT-4o-mini .
BenchmarkMethodRAtomic callsRelation callsAux. tokensTotal tokensMemory tokensLatency (s)
ConflictQAG-Memory+EquiMem9.227.604,31243,61535,86449.3
ConflictQAHEDGE5.717.126.88,74636,89118,21441.2
HotpotQAG-Memory+EquiMem8.525.504,58745,18738,74251.1
HotpotQAHEDGE5.817.429.69,38138,14519,62843.5
Appendix
Table 10: End-to-end efficiency comparison under AutoGen with GPT-4o-mini on ConflictQA and HotpotQA. Values are per-question averages. R denotes debate rounds; atomic and relation calls count auxiliary LLM invocations; auxiliary tokens include atomic-fact and relation-extraction usage. Total tokens include auxiliary LLM calls, while memory tokens measure the persistent memory footprint. Latency is end-to-end wall-clock time.
Scaling factorSettingAccuracy (%)Total tokensMemory tokensRelation callsLatency (s)
Agent count3 agents57.836,89118,21426.841.2
Agent count4 agents58.543,27621,63737.147.9
Agent count5 agents58.950,41825,48349.655.8
Agent count6 agents58.657,96229,74163.464.1
Debate length3 rounds56.125,28413,47216.329.4
Debate length6 rounds57.937,42618,60828.742.3
Appendix
Table 11: Scaling analysis of HEDGE on ConflictQA under AutoGen with GPT-4o-mini. The agent-count sweep uses the default debate-stopping procedure; the debate-length sweep keeps three agents fixed. All token, memory, call, and latency measurements are averages per question.
Embedding ModelMATH500GPQAFaithEvalConflictQANovelQAHotpotQAMMLU-Pro
text-embedding-ada-00260.345.276.552.663.739.980.2
text-embedding-3-small61.046.177.654.164.640.881.3
text-embedding-3-large61.646.978.755.465.441.782.1
Qwen3-Embedding-0.6B60.845.878.254.665.041.281.5
Qwen3-Embedding-4B62.247.779.856.066.042.482.7
Qwen3-Embedding-8B62.447.980.156.366.242.683.0
Appendix
Table 12: Sensitivity of HEDGE to the embedding model. Performance remains stable across models, with only modest gains from increasing embedding-model scale. Qwen3-Embedding-4B is the default.
MMMATH500GPQAConflictQANovelQA
257.841.947.658.5
459.243.950.661.9
862.948.357.867.2
1262.647.957.166.7
1661.947.155.865.6
Appendix
Table 13: Effect of the number of retrieved nodes per group MM on HEDGE with GPT-4o-mini, keeping the number of retrieved groups fixed at K=3K=3 .
KKMATH500GPQAConflictQANovelQA
160.845.953.163.8
262.147.256.065.9
362.948.357.867.2
462.547.857.066.5
561.746.955.465.1
Appendix
Table 14: Effect of the number of retrieved groups kk on HEDGE with GPT-4o-mini, keeping the number of retrieved nodes per group fixed at M=8M=8 .
Relation Extraction ModelMATH500GPQAFaithEvalConflictQANovelQAHotpotQAMMLU-Pro
Qwen3-32B ( Yang et al., 2025 )62.147.679.755.865.942.382.6
GPT-4o-mini62.247.779.856.066.042.482.7
GPT-4o62.347.879.956.266.142.582.8
GPT-5.462.447.980.056.366.242.682.9
Claude-Sonnet-4.6 ( Anthropic, 2026 )62.447.980.156.466.242.783.0
Appendix
Table 15: Sensitivity of HEDGE to the relation extraction model. Performance remains stable across models, with only marginal gains from larger relation extractors. GPT-4o-mini is used by default.
BenchmarkAccuracyAvg. Number of Hyperedges
 Signature + EmbeddingEmbedding OnlySignature + EmbeddingEmbedding Only
MATH50062.260.85.23.8
GPQA47.746.05.74.1
FaithEval79.877.36.54.6
ConflictQA56.054.27.35.1
NovelQA66.063.26.94.8
Appendix
Table 16: Effect of combining sparse signatures with dense embeddings for hyperedge matching. The embedding-only variant removes the Jaccard signature gate.
Figure 20
Figure 21
Figure 22
Figure 23
Figure 24
Figure 25
Figure 26
Figure 27
Figure 28
Figure 29
More in this topic

Memory Management for LLM Agents

See all 92 papers

Explore similar work

CardsList

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

    Sep 3, 2026Xuanfa Jin, Zhijian Ma, Yongcheng Zeng +3AI Agent ReliabilityMulti-Agent Debate

    Institute of Automation, Chinese Academy of Sciences · University of Chinese Academy of Sciences · University College London

  2. Hear Both Sides: Efficient Multi-Agent Debate via Diversity-Aware Message Retention

    Mar 21, 2026Manh Nguyen, Anh Nguyen, Dung Nguyen +2Multi-Agent DebateMulti-Agent Reasoning

    Applied Artificial Intelligence Initiative Deakin University, Australia

  3. EquiMem: Calibrating Shared Memory in Multi-Agent Debate via Game-Theoretic Equilibrium

    May 10, 2026Yuqiao Meng, Luoxi Tang, Sakshi Sunil Narvekar +4Multi-Agent DebateAgent Memory Poisoning

    Binghamton University, State University of New York, Binghamton, NY, USA · University of Iowa, Iowa City, IA, USA