CARD: Towards Conditional Design of Multi-agent Topological Structures

Tongtong Wu; Yanming Li; Ziye Tang; Chen Jiang; Linhao Luo; Guilin Qi; Shirui Pan; Gholamreza Haffari

cs.CLMar 1, 2026

CARD: Towards Conditional Design of Multi-agent Topological Structures

Authors: Tongtong Wu, Yanming Li, Ziye Tang, Chen Jiang, Linhao Luo, Guilin Qi, Shirui Pan, Gholamreza Haffari

Organizations: Monash University · Southeast University · Griffith University

Abstract

Large language model (LLM)-based multi-agent systems have shown strong capabilities in tasks such as code generation and collaborative reasoning. However, the effectiveness and robustness of these systems critically depend on their communication topology, which is often fixed or statically learned, ignoring real-world dynamics such as model upgrades, API (or tool) changes, or knowledge source variability. To address this limitation, we propose CARD (Conditional Agentic Graph Designer), a conditional graph-generation framework that instantiates AMACP, a protocol for adaptive multi-agent communication. CARD explicitly incorporates dynamic environmental signals into graph construction, enabling topology adaptation at both training and runtime. Through a conditional variational graph encoder and environment-aware optimization, CARD produces communication structures that are both effective and resilient to shifts in model capability or resource availability. Empirical results on HumanEval, MATH, and MMLU demonstrate that CARD consistently outperforms static and prompt-based baselines, achieving higher accuracy and robustness across diverse conditions. The source code is available at: https://github.com/Warma10032/CARD.

Figures & tables

Figure 1: Agent attributes and corresponding communication topologies under two environmental configurations, illustrating that topology is determined by both task requirements and the capabilities of the model base and available resources.

Figure 2: Overview of the Conditional Agentic Graph Designer (CARD) framework. Agent profiles and dynamic environment conditions are encoded into embeddings, which a conditional graph-generation module (Encoder $\rightarrow$ Condition Adaptation $\rightarrow$ Decoder) uses to produce an adaptive communication topology. CARD then performs environment-aware training, iteratively refining graphs under changing resource configurations, and deploys runtime adaptation to automatically update the multi-agent topology in response to new environmental states.

Method	Mul.	Auto.	Cond.	gpt4o-mini	deepseek-v3	llama3-70B	gpt4o	qwen-72B	Avg.
				HumanEval
Vanilla	✗	✗	✗	85.83	92.50	76.66	85.83	86.66	85.50
CoT	✗	✗	✗	88.33	93.33	78.33	90.00	8 8.33	87.66
Random-graph	✓	✗	✗	87.50	94.16	73.33	90.00	85.00	86.00
LLM-Debate	✓	✗	✗	9 1.66	9 5.00	75.83	87.50	80.00	86.00
GPTswarm	✓	✓	✗	89.16	92.50	78.33	91.66	81.66	86.66

Table 1: Evaluation of multi-agent and topology design methods on HumanEval, MATH, and MMLU. "Mul.", "Auto.", and "Cond." indicate support for multi-agent collaboration, automated topology design, and conditional configuration, where ✓ indicates "Yes" and ✗ indicates "No". For automated methods, CYAN cells denote in-domain adaptation (trained and tested on the same LLM), GREEN cells denote out-domain adaptation (generalization to unseen LLMs), and YELLOW cells denote the average performance.

Figure 3: Performance and gains of w/o Cond., w/ Cond.p, and CARD on HumanEval, MATH, and MMLU across LLM bases (M1–M5, same to Table 1 ). Top: absolute accuracy (%). Bottom: $\Delta$ accuracy (%) over the w/o Cond. baseline.

Figure 4: Visualization of CARD topology matrices (See Appendix D for matrices and correlation analysis details.) under different conditions. Edge thickness reflects the communication probability between agents. Configurations 1 to 4 (Table 10 ) are shown from left to right.

Appendix figures & tables13 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 5: Left : Accuracy on MATH and HumanEval across LLMs with different reasoning capabilities. Right : Accuracy across different model sizes within the same LLM family.

Figure 6: Left : Performance comparison using different external knowledge sources. Central : Performance across various available tools (search engines). Right : Impact on multi-agent performance on HumanEval, when only a single node’s condition is updated instead of the global agent condition.

Figure 7: MMLU performance of CARD vs G-Designer across varying agent counts. CARD consistently outperforms G-Designer in both (a) in-domain and (b) out-of-domain settings, with larger gains under domain shift; shaded areas denote 95% confidence intervals.

Figure 8: Left : Accuracy comparison before and after adversarial attacks across different methods. Right : The inference cost (USD per instance) across methods and LLMs.

	Knowlegable Expert	Searcher	Philosopher	Mathematician	Critic
Knowlegable Expert	Masked	0.79	0.88	0.81	0.5
Searcher	0.17	Masked	0.79	0.69	0.34
Philosopher	0.11	0.17	Masked	0.81	0.5
Mathematician	0.15	0.21	0.15	Masked	0.37
Critic	0.25	0.22	0.25	0.23	Masked

Appendix

Table 2: Adjacency Matrix 1: gpt-4o-mini + Google

	Knowlegable Expert	Searcher	Philosopher	Mathematician	Critic
Knowlegable Expert	Masked	0.54	0.15	0.4	0.14
Searcher	0.25	Masked	0.53	0.81	0.5
Philosopher	0.13	0.25	Masked	0.39	0.13
Mathematician	0.24	0.15	0.24	Masked	0.36
Critic	0.12	0.25	0.11	0.23	Masked

Appendix

Table 3: Adjacency Matrix 2: gpt-4o + Google

	Knowlegable Expert	Searcher	Philosopher	Mathematician	Critic
Knowlegable Expert	Masked	0.73	0.86	0.73	0.46
Searcher	0.2	Masked	0.76	0.57	0.3
Philosopher	0.12	0.18	Masked	0.75	0.5
Mathematician	0.2	0.25	0.19	Masked	0.29
Critic	0.25	0.21	0.25	0.21	Masked

Appendix

Table 4: Adjacency Matrix 3: gpt-4o-mini + Wiki

	Knowlegable Expert	Searcher	Philosopher	Mathematician	Critic
Knowlegable Expert	Masked	0.84	0.73	0.8	0.5
Searcher	0.13	Masked	0.67	0.75	0.42
Philosopher	0.2	0.22	Masked	0.6	0.27
Mathematician	0.16	0.19	0.24	Masked	0.35
Critic	0.25	0.24	0.2	0.23	Masked

Appendix

Table 5: Adjacency Matrix 4: Llama-3-70B + Wiki

Comparison	$r$	$p$	Strength	Sig.
Matrix 1 vs 2	0.32	0.54	Weak	No
Matrix 1 vs 3	0.98	0.001	Very strong	Yes
Matrix 1 vs 4	0.78	0.07	Strong	Marginal

Appendix

Table 6: Pearson correlation between matrix pairs with corresponding strength and significance.

	Configuration	LLM	Role
Train & Test	Configuration 1	gpt-4o-mini	Project Manager
		gpt-4o-mini	Algorithm Designer
		gpt-4o-mini	Programming Expert
		gpt-4o-mini	Test Analyst
		gpt-4o-mini	Bug Fixer
	Configuration 2	deepseek-v3	Project Manager

Appendix

Table 7: HumanEval Environment Configuration Set

	Configuration	LLM	Role
Train & Test	Configuration 1	gpt-4o-mini	Math Solver
		gpt-4o-mini	Mathematical Analyst
		gpt-4o-mini	Mathematical Analyst
		gpt-4o-mini	Programming Expert
		gpt-4o-mini	Inspector
	Configuration 2	deepseek-v3	Math Solver

Appendix

Table 8: MATH Environment Configuration Set

	Configuration	LLM	Role
Train & Test	Configuration 1	gpt-4o-mini	Mathematician
		gpt-4o-mini	Programmer
		gpt-4o-mini	Critic
		gpt-4o-mini	Doctor
		gpt-4o-mini	Psychologist
	Configuration 2	deepseek-v3	Mathematician

Appendix

Table 9: MMLU Environment Configuration Set

	Configuration	LLM	Role	External Tool (search engine)
Train & Test	Configuration 1	gpt-4o-mini	Knowlegable Expert
		gpt-4o-mini	Searcher	Google
		gpt-4o-mini	Psychologist
		gpt-4o-mini	Mathematician
		gpt-4o-mini	Critic
Only Test	Configuration 2	gpt-4o	Knowlegable Expert

Appendix

Table 10: MMLU Environment Configuration Set with External Tools

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Multi-agent systems driven by large language models (LLMs) rely on structured communication topologies to facilitate information exchange and collaborative reasoning. However, effectively scheduling these topologies to dynamically determine who talks to whom and when to communicate remains a fundamental challenge in balancing collective reasoning performance against exponential token overhead. Existing topology scheduling approaches either enforce static communication graphs that cannot adapt to dynamic problem-solving states, or overlook agent role complementarity while failing to explicitly incorporate the synthesized graph structure into team-level decision evaluation. To tackle these limitations, we propose ACTS, a role-aware adaptive communication topology scheduling framework for efficient LLM multi-agent collaboration. Orchestrated within a Centralized Training with Decentralized Execution (CTDE) paradigm, ACTS introduces a novel dual-attention mechanism. Specifically, a Role-conditioned Relational Attention module dynamically selects variable-cardinality interaction partners based on agent roles and evolving execution states, while a Topological Attention Mixer explicitly embeds the directed communication topology into team value decomposition for precise credit assignment. Comprehensive evaluations across 9 challenging benchmarks covering code generation, multi-step reasoning, general knowledge, and competitive mathematics demonstrate that ACTS consistently outperforms state-of-the-art baselines, boosting average accuracy by up to 6.19 percentage points while reducing token consumption by over 15%. The project website is available at https://acts-mas.github.io/ACTS/.

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