FlowMAS: Learning Multi-Agent Workflow Topology via Information-guided Generative Flow Network

Haitao Wang; Chenjing Liang; Haipeng Zhang; Jiawei Hu; Sicheng Wang; Songzhu Mei; Chenglu Wen; Siqi Shen

cs.MASep 29, 2026

FlowMAS: Learning Multi-Agent Workflow Topology via Information-guided Generative Flow Network

Authors: Haitao Wang, Chenjing Liang, Haipeng Zhang, Jiawei Hu, Sicheng Wang, Songzhu Mei, Chenglu Wen, Siqi Shen, +1 more

Organizations: Fujian Key Laboratory of Urban Intelligent Sensing and Computing, Xiamen University, Xiamen, China · School of Computer, National University of Defense Technology, China

Abstract

Automated multi-agent systems offer clear advantages over manually designed ones in scalability and adaptability, but existing workflow topology methods still face important limitations. Search-based methods are often computationally expensive, textual-gradient-based methods rely on coarse-grained feedback, and existing generation-based methods are not well suited to discrete workflow topologies with complex dependencies. To address these limitations, we propose FlowMAS, a multi-agent workflow topology method based on Generative Flow Networks (GFlowNets). FlowMAS models workflow generation as reward-guided flow over the topology space and introduces three components: a GFlowNet-based topology generation backbone, a curiosity-driven module for structure-aware exploration, and an information-guided optimization module for evaluating intermediate topologies. Concretely, the curiosity-driven module encourages exploration of structurally novel workflows, while the information-guided module measures both the information contribution and the communication efficiency of different operators to favor more informative and effective collaboration patterns. Experiments on six benchmark datasets with three LLM backbones show that FlowMAS consistently outperforms multiple baselines.

Figures & tables

Figure 1: Experiments with Llama-3.1-8B-Instruct on HumanEval. Left: the quality of the generated workflow for solving specific test problems. Middle: the number of executable workflows discovered during topology exploration on the training set. Right: Total token consumption.

Figure 2: The overall framework of our proposed FlowMAS.

Method	HumanEval	GSM8K	MATH	MBPP	HotpotQA	DROP	Avg.
IO	50.1 $\pm 1.4$	73.7 $\pm 1.4$	18.9 $\pm 1.5$	67.1 $\pm 1.3$	60.5 $\pm 1.6$	68.8 $\pm 2.1$	56.52
CoT [ 27 ]	51.2 $\pm 1.5$	75.6 $\pm 1.1$	21.0 $\pm 1.7$	69.4 $\pm 1.4$	64.0 $\pm 1.9$	73.1 $\pm 1.9$	59.05
CoT-SC [ 28 ]	52.4 $\pm 0.8$	77.5 $\pm 0.9$	22.1 $\pm 0.0$	66.8 $\pm 0.8$	66.0 $\pm 0.9$	75.4 $\pm 1.3$	60.03
ReAct [ 29 ]	51.9 $\pm 1.9$	75.2 $\pm 1.7$	28.1 $\pm 2.0$	65.4 $\pm 1.5$	63.7 $\pm 1.7$	71.9 $\pm 1.7$	59.37
Reflexion [ 30 ]	50.5 $\pm 1.7$	79.1 $\pm 1.1$	22.0 $\pm 2.1$	65.7 $\pm 1.4$	57.6 $\pm 1.5$	64.6 $\pm 2.0$	56.58
LLM-Majority [ 9 ]	56.6 $\pm 0.0$	76.7 $\pm 1.2$	22.4 $\pm 1.6$	67.3 $\pm 0.9$	62.0 $\pm 1.1$	71.4 $\pm 1.2$	59.40

Table 1: Main results on Llama-3.1-8B-Instruct. We bold the best results and underline the second-best results. Each experiment is run five times to record the mean and standard deviation.

Method	HumanEval	GSM8K	MATH	MBPP	HotpotQA	DROP	Avg.
GPT-4o-mini
IO	86.3 $\pm 0.6$	86.3 $\pm 0.5$	45.0 $\pm 0.7$	71.2 $\pm 0.4$	66.7 $\pm 0.6$	73.2 $\pm 0.9$	71.45
ADAS [ 13 ]	83.4 $\pm 1.2$	84.9 $\pm 0.9$	42.7 $\pm 1.2$	67.3 $\pm 0.8$	63.9 $\pm 0.9$	75.5 $\pm 1.2$	69.62
AgentNet [ 34 ]	86.8 $\pm 0.9$	91.8 $\pm 0.0$	47.5 $\pm 0.1$	71.1 $\pm 0.2$	64.5 $\pm 0.2$	80.8 $\pm 0.0$	73.75
SELFORG [ 35 ]	86.0 $\pm 2.0$	92.7 $\pm 0.1$	50.7 $\pm 0.7$	71.7 $\pm 0.3$	68.9 $\pm 0.0$	84.3 $\pm 0.1$	75.72
AFlow [ 14 ]	89.6 $\pm 0.7$	90.5 $\pm 0.7$	50.5 $\pm 0.9$	81.0 $\pm 0.6$	72.6 $\pm 0.9$	79.7 $\pm 0.5$	77.32

Table 2: Results of IO and selected automated MAS-design methods on Gemma-4-26B-A4B-it and GPT-4o-mini backbones. We bold the best results and underline the second-best results.

Method	Acc. (%)	Training tokens	Train $\times$	Inference tokens	Infer $\times$
DyLAN [ 32 ]	51.9	5,842,507	15.2 $\times$	25,064,472	27.8 $\times$
ADAS [ 13 ]	59.5	84,526,998	220.0 $\times$	97,526,460	108.3 $\times$
AgentNet [ 34 ]	50.8	792,775	2.1 $\times$	451,047	0.5 $\times$
SELFORG [ 35 ]	61.9	853,528	2.2 $\times$	2,755,046	3.1 $\times$
AFlow [ 14 ]	65.1	6,253,861	16.3 $\times$	13,690,205	15.2 $\times$
MaAS [ 3 ]	62.7	223,042	0.6 $\times$	1,151,392	1.3 $\times$

Table 3: Efficiency comparison between FlowMAS and state-of-the-art baselines on the HumanEval. Train

\times

and Infer

\times

are relative to FlowMAS

Method	HumanEval	GSM8K	HotpotQA
ADAS [ 13 ]	59.5	79.5	60.9
FlowMAS	69.6	86.2	73.6
FlowMAS (VAE)	62.6	81.6	46.1
FlowMAS (Graph Diffusion Model)	55.7	80.8	50.6
FlowMAS (Transformer)	58.8	82.5	53.2
FlowMAS (MLP)	60.3	81.1	62.9

Table 4: Q1. Generator backbone ablation.

Variant	HE Acc.	G8K Acc.	HQ F1.	Avg. Topo. Count
ADAS [ 13 ]	59.5	79.5	60.9	31
w/o CDM	67.3	84.9	72.0	68
w/o CDM, w/ Graph Edit Distance [ 42 ]	66.8	85.2	72.1	73
w/o CDM, w/ Intrinsic Curiosity Module [ 43 ]	67.9	85.4	72.7	73
w/o IOM	65.0	84.2	69.3	60
w/o IOM, w/ Embedding Similarity	62.0	84.2	68.5	56

Table 5: Q2. Method-component ablation. HE, G8K, and HQ denote accuracy on HumanEval, GSM8K, and HotpotQA, respectively. “Avg. Topo. Count” denotes the average number of executable topologies discovered during training across the three benchmarks.

Appendix figures & tables10 assets

Supplementary material from the paper’s appendix.

Appendix

r_{\text{step}}^{(t)}\leftarrow\alpha\cdot r_{\text{cur}}^{(t)}+\beta\cdot\sum_{D_{i}}(r_{\text{pid}}^{(t)}+r_{\text{ch}}^{(t)})

Appendix

Algorithm 1 FlowMAS

Figure 3: Case study of the workflow topologies designed by AFlow, MaAS, and FlowMAS on DROP Benchmark.

Domain	Dataset	#Train/Val	#Test	Metric
Code Generation	HumanEval	33	131	pass@1
Code Generation	MBPP	86	341	pass@1
Math Reasoning	GSM8K	264	1,055	Solve rate
Math Reasoning	MATH	119	486	Solve rate
Reading Comprehension	HotpotQA	200	800	F1
Reading Comprehension	DROP	200	800	F1

Appendix

Table 6: Dataset statistics used in our experiments.

Method	HumanEval	GSM8K	MATH	MBPP	HotpotQA	DROP	Avg.
IO	86.3 $\pm 0.6$	86.3 $\pm 0.5$	45.0 $\pm 0.7$	71.2 $\pm 0.4$	66.7 $\pm 0.6$	73.2 $\pm 0.9$	71.45
CoT [ 27 ]	86.6 $\pm 0.7$	86.4 $\pm 0.5$	45.8 $\pm 0.6$	72.6 $\pm 0.6$	66.4 $\pm 0.9$	77.0 $\pm 0.8$	72.47
CoT-SC [ 28 ]	87.6 $\pm 0.0$	86.5 $\pm 0.3$	46.5 $\pm 0.0$	74.2 $\pm 0.5$	67.4 $\pm 0.6$	77.5 $\pm 0.7$	73.28
ReAct [ 29 ]	87.0 $\pm 0.8$	86.5 $\pm 0.7$	43.3 $\pm 0.9$	77.7 $\pm 0.6$	71.0 $\pm 0.8$	73.8 $\pm 0.9$	73.22
Reflexion [ 30 ]	88.7 $\pm 0.7$	87.5 $\pm 0.4$	45.9 $\pm 0.9$	76.8 $\pm 0.6$	66.2 $\pm 0.7$	77.1 $\pm 0.8$	73.70
LLM-Majority [ 9 ]	87.9 $\pm 0.3$	86.5 $\pm 0.6$	46.8 $\pm 0.0$	74.4 $\pm 0.0$	68.3 $\pm 0.6$	74.6 $\pm 0.5$	73.08

Appendix

Table 7: Detailed results on GPT-4o-mini. The best result in each column is boldfaced, and the second-best is underlined. Each experiment is run five times to record the mean, standard deviation.

Method	HumanEval	GSM8K	MATH	MBPP	HotpotQA	DROP	Avg.
IO	90.8 $\pm 0.8$	90.5 $\pm 0.7$	61.3 $\pm 0.9$	73.3 $\pm 0.6$	74.9 $\pm 0.8$	83.9 $\pm 1.0$	79.12
CoT [ 27 ]	91.6 $\pm 0.9$	91.6 $\pm 0.6$	61.7 $\pm 1.0$	76.7 $\pm 0.7$	79.3 $\pm 1.1$	87.4 $\pm 0.9$	81.38
CoT-SC [ 28 ]	87.6 $\pm 0.0$	91.2 $\pm 0.5$	61.7 $\pm 0.3$	78.0 $\pm 0.4$	78.3 $\pm 0.6$	87.8 $\pm 0.7$	80.77
ReAct [ 29 ]	90.0 $\pm 1.0$	90.3 $\pm 0.9$	60.0 $\pm 1.1$	77.4 $\pm 0.8$	78.6 $\pm 1.0$	88.2 $\pm 0.9$	80.75
Reflexion [ 30 ]	91.8 $\pm 0.9$	92.1 $\pm 0.6$	62.2 $\pm 1.2$	76.2 $\pm 0.7$	73.5 $\pm 0.8$	85.1 $\pm 1.0$	80.15
LLM-Majority [ 9 ]	91.7 $\pm 0.8$	91.2 $\pm 0.4$	61.3 $\pm 0.4$	78.5 $\pm 0.0$	79.3 $\pm 0.7$	88.2 $\pm 0.6$	81.70

Appendix

Table 8: Detailed results on Gemma-4-26B-A4B-it. The best result in each column is boldfaced, and the second-best is underlined. Each experiment is run five times to record the mean, standard deviation.

# Operators	Method	Training Tokens	GPU Hours	Wall-clock Time (min)	Accuracy
10	AFlow	6,253,861	1.61	97	65.1
	MaAS	223,042	0.52	31	62.7
	FlowMAS	384,278	0.65	39	69.6
15	AFlow	9,746,315	2.90	174	61.8
	MaAS	493,110	0.78	47	61.8
	FlowMAS	427,057	0.70	42	68.7

Appendix

Table 9: Scalability comparison on HumanEval with different numbers of candidate operators.

Backbone	Method	Accuracy
Llama-3.1-8B-Instruct	AFlow	43.7
	MaAS	60.0
	FlowMAS	69.0
GPT-4o-mini	AFlow	75.7
	MaAS	81.6
	FlowMAS	85.0

Appendix

Table 10: Generalization results on BIG-Bench Hard across different LLM backbones.

$\alpha$	0.1	0.2	0.3	0.4	0.5
Accuracy	67.9	69.6	69.6	68.7	67.9
$\beta$	0.6	0.7	0.8	0.9	1.0
Accuracy	66.4	68.7	69.6	67.9	67.9

Appendix

Table 11: Hyperparameter sensitivity analysis on HumanEval with Llama-3.1-8B-Instruct.

Method	Training Time (min)	Inference Time (min)	Accuracy
ADAS	200	91	59.5
AFlow	97	66	65.1
MaAS	31	22	62.7
FlowMAS	39	13	69.6

Appendix

Table 12: End-to-end training and inference wall-clock time on HumanEval with Llama-3.1-8B-Instruct. All experiments are measured on a single NVIDIA GeForce RTX 5090.

Method	Total Training	IOM Time	CDM Time	Embedding Time
	Time (min)	(min)	(min)	(min)
FlowMAS	39	1.81	0.74	2.89

Appendix

Table 13: Detailed training-time overhead of FlowMAS on HumanEval. IOM Time includes the embedding computation required for the IOM reward, while Embedding Time denotes the total embedding-model computation throughout training.

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EvoMAS: Learning Execution-Time Workflows for Multi-Agent Systems

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Multi-Agent Workflows Multi-Agent Coordination Agentic Workflow Design Single-Agent Baselines Smooth Execution Single Trajectory+1

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Large language model (LLM)-based multi-agent systems have shown strong potential on complex tasks through agent specialization, tool use, and collaborative reasoning. However, most automated multi-agent system design methods still follow a one-shot paradigm: a workflow is optimized or selected before execution and then reused unchanged throughout the task. This static coordination strategy is ill-suited for long-horizon tasks whose subgoals, intermediate evidence, and information needs evolve over multiple execution stages. We propose EvoMAS, a framework for execution-time multi-agent workflow construction. EvoMAS formulates workflow construction as a meta-level sequential decision problem along a single task trajectory. At each stage, it constructs an explicit task state through a Planner-Evaluator-Updater pipeline and uses a learned Workflow Adapter to instantiate a stage-specific layered workflow from a fixed pool of candidate agents. The adapter is trained with policy gradients using sparse, verifiable terminal task success as the main supervision signal, while evaluator-based process reward is analyzed separately under very-hard sparse-reward settings. Experiments on GAIA, HLE, and DeepResearcher show that EvoMAS outperforms single-agent baselines and recent automated multi-agent workflow design methods. Our analyses further show that explicit task-state construction and learned workflow adaptation provide complementary benefits. Additional results indicate that process reward is most useful when terminal success is extremely sparse, and qualitative case studies illustrate that EvoMAS adapts agent coordination as the task state evolves.

Abstract

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