ST-EVO: Towards Generative Spatio-Temporal Evolution of Multi-Agent Communication Topologies
Organizations: East China Normal University
Abstract
LLM-powered Multi-Agent Systems (MAS) have emerged as an effective approach towards collaborative intelligence, and have attracted wide research interests. Among them, ``self-evolving'' MAS, treated as a more flexible and powerful technical route, can construct task-adaptive workflows or communication topologies, instead of relying on a predefined static structue template. Current self-evolving MAS mainly focus on Spatial Evolving or Temporal Evolving paradigm, which only considers the single dimension of evolution and does not fully incentivize LLMs' collaborative capability. In this work, we start from a novel Spatio-Temporal perspective by proposing ST-EVO, which supports dialogue-wise communication scheduling with a compact yet powerful flow-matching based Scheduler. To make precise Spatio-Temporal scheduling, ST-EVO can also perceive the uncertainty of MAS, and possesses self-feedback ability to learn from accumulated experience. Extensive experiments on nine benchmarks demonstrate the state-of-the-art performance of ST-EVO, achieving about 5%--25% accuracy improvement.
Figures & tables
| PE | VE | System State Description |
| Low ( ) | Low ( ) | High Confidence (Deterministic) |
| High ( ) | High ( ) | Conflicting Uncertainty (Branching) |
| High ( ) | Low ( ) | Uniform Ignorance (Cluelessness) |
| Low ( ) | High ( ) | Overconfident Anomaly (Rare state) |
| Method | MMLU | GSM8K | MultiArith | SVAMP | AQuA | HumanEval | DS-1000 | HotpotQA | DDXPlus | Avg. |
| Vanilla | 80.47 | 87.15 | 93.40 | 87.25 | 69.27 | 73.28 | 38.40 | 82.35 | 56.40 | 74.22 |
| Single-Agent Systems | ||||||||||
| CoT | 81.85 ↑1.38 | 87.35 ↑0.20 | 93.60 ↑0.20 | 87.90 ↑0.65 | 72.40 ↑3.13 | 74.05 ↑0.77 | 42.35 ↑3.95 | 81.04 ↓1.31 | 64.22 ↑7.82 | 76.08 |
| SC | 82.95 ↑2.48 | 87.66 ↑0.51 | 94.40 ↑1.00 | 87.40 ↑0.15 | 71.85 ↑2.58 | 75.82 ↑2.54 | 37.66 ↓0.74 | 82.24 ↓0.11 | 66.43 ↑10.03 | 76.27 |
| Multi-Agent Systems | ||||||||||
| Chain | 82.40 ↑1.93 | 87.23 ↑0.08 | 92.88 ↓0.52 | 87.16 ↓0.09 | 69.85 ↑0.58 | 73.40 ↑0.12 | 38.25 ↓0.15 | 80.77 ↓1.58 | 65.28 ↑8.88 | 75.25 |
| Variant | MMLU | HumanEval | SVAMP | GSM8K |
| ST-EVO | 89.9 | 94.4 | 94.7 | 97.6 |
| w/o Scheduling | 84.7 | 89.6 | 88.6 | 92.5 |
| w/o | 84.9 | 88.2 | 90.3 | 93.7 |
| w/o Node Encoder | 82.0 | 84.8 | 87.5 | 94.8 |
Appendix figures & tables40 assets
Supplementary material from the paper’s appendix.
Appendix
| Entropy Estimator | Avg. Acc. | PE Corr. | Extra Calls |
| Logprob-based | 94.15 | 1.00 | 0 |
| Sample-based ( ) | 92.95 | 0.85 | |
| Sample-based ( ) | 92.23 | – | |
| Confidence probe | 92.40 | 0.78 | 0 |
| w/o PE/VE | 91.80 | – | 0 |
| Category | Dataset | Answer Type | Metric | #Test | License |
| General reasoning | MMLU | Multi-choice | Acc. | 153 | MIT License |
| HotpotQA | Span | F1 | 7,405 | CC BY-SA 4.0 | |
| Math reasoning | GSM8K | Number | Acc. | 1,319 | MIT License |
| MultiArith | Number | Acc. | 600 | Unspecified | |
| SVAMP | Number | Acc. | 1,000 | MIT License | |
| AQuA | Multi-choice | Acc. | 254 | Apache-2.0 |
| Method | SWE-Bench | Terminal-Bench | MLE-Bench | WebArena |
| Vanilla (single) | 37.4 | 32.6 | 9.2 | 15.7 |
| Chain (4 agents) | 39.1 | 34.8 | 10.6 | 17.9 |
| Complete Graph | 40.8 | 36.3 | 12.1 | 20.3 |
| G-Designer | 44.2 | 39.7 | 15.8 | 24.6 |
| SafeSieve | 45.6 | 40.9 | 16.4 | 25.8 |
| STEER | 46.3 | 41.5 | 17.2 | 26.7 |
| Backbone | Architecture | Vanilla | Best Baseline | ST-EVO | Gain |
| gpt-oss-120b | 120B Dense | 74.22 | 83.91 | 88.42 | |
| Qwen3.5-122B-A10B | 122B MoE (10B active) | 71.99 | 81.75 | 86.48 | |
| Qwen3.6-27B | 27B Dense | 70.05 | 79.88 | 84.83 | |
| Qwen3.6-35B-A3B | 35B MoE (3B active) | 64.16 | 75.18 | 81.14 | |
| Qwen3-30B-A3B | 30B MoE (3B active) | 62.71 | 73.74 | 79.59 | |
| Qwen3-Coder-30B-A3B | 30B MoE (3B active) | 61.67 | 72.50 | 78.29 |
| #Agents | 5 | 10 | 20 |
| Random Graph | |||
| Accuracy (%) | 82.7 | 83.3 | 83.6 |
| Time (min) | 14.2 | 31.4 | 59.7 |
| #Tokens | 431,064 | 1,317,148 | 4,245,925 |
| GPTSwarm | |||
| Accuracy (%) | 83.6 | 84.2 | 84.8 |
| #Iterations | 3 | 6 | 12 |
| Random Graph | |||
| Accuracy (%) | 82.7 | 83.1 | 83.3 |
| Time (min) | 14.2 | 27.4 | 52.5 |
| #Tokens | 431,064 | 816,266 | 1,425,295 |
| GPTSwarm | |||
| Accuracy (%) | 83.6 | 84.0 | 84.2 |
| Variant | MMLU | HumanEval | SVAMP | GSM8K | Avg. |
| ST-EVO | 89.9 | 94.4 | 94.7 | 97.6 | 94.15 |
| w/ LLM Scheduler | 86.8 | 91.2 | 91.5 | 94.9 | 91.10 |
| w/o Scheduling | 84.7 | 89.6 | 88.6 | 92.5 | 88.85 |
| w/ Random Scheduler | 83.8 | 88.7 | 87.9 | 91.6 | 88.00 |
| Variant | MMLU | HumanEval | SVAMP | GSM8K | Avg. |
| ST-EVO | 89.9 | 94.4 | 94.7 | 97.6 | 94.15 |
| w/ Diffusion Scheduler | 87.6 | 92.0 | 92.4 | 95.5 | 91.88 |
| w/ VAE Scheduler | 87.1 | 91.6 | 91.8 | 95.0 | 91.38 |
| Variant | MMLU | HumanEval | SVAMP | GSM8K | Avg. |
| ST-EVO (full) | 89.90 | 94.40 | 94.70 | 97.60 | 94.15 |
| w/o Entropy Reward | 87.23 | 91.76 | 92.41 | 95.82 | 91.81 |
| w/o Retrieval | 84.86 | 88.24 | 90.31 | 93.72 | 89.28 |
| w/o Both | 83.17 | 86.43 | 87.94 | 91.76 | 87.33 |
| MMLU | HumanEval | SVAMP | GSM8K / Avg. | ||
| 0.3 | 0.7 | 88.17 | 92.68 | 93.14 | 96.33 / 92.58 |
| 0.5 | 0.5 | 89.85 | 94.36 | 94.72 | 97.60 / 94.13 |
| 0.7 | 0.3 | 89.06 | 93.51 | 93.85 | 96.92 / 93.34 |
| 1.0 | 0.0 | 87.43 | 91.74 | 91.96 | 95.48 / 91.65 |
| 0.0 | 1.0 | 86.72 | 91.15 | 91.37 | 94.93 / 91.04 |
| Capacity | MMLU | HumanEval | SVAMP | GSM8K | Avg. |
| 0 | 84.86 | 88.24 | 90.31 | 93.72 | 89.28 |
| 25 | 87.74 | 91.93 | 92.76 | 95.81 | 92.06 |
| 50 | 88.93 | 93.47 | 93.85 | 96.74 | 93.25 |
| 100 | 89.90 | 94.40 | 94.70 | 97.60 | 94.15 |
| 200 | 89.82 | 94.31 | 94.63 | 97.54 | 94.08 |
| 500 | 89.79 | 94.28 | 94.58 | 97.51 | 94.04 |
| MMLU | HumanEval | SVAMP | GSM8K | Avg. | Time (ms) | |
| 10 | 86.53 | 90.74 | 91.18 | 94.46 | 90.73 | 12 |
| 25 | 88.19 | 92.83 | 93.41 | 96.23 | 92.67 | 24 |
| 50 | 89.24 | 93.79 | 94.05 | 96.98 | 93.52 | 38 |
| 100 | 89.85 | 94.36 | 94.72 | 97.60 | 94.13 | 65 |
| 200 | 89.91 | 94.38 | 94.74 | 97.62 | 94.16 | 125 |
| 500 | 89.94 | 94.42 | 94.79 | 97.65 | 94.20 | 305 |
| Method | Jaccard | Std. | Oscillation Rate |
| Random Scheduler | 0.31 | 0.22 | 78.4% |
| G-Designer (fixed) | 1.00 | 0.00 | 0.0% |
| ST-EVO w/o smoothing | 0.72 | 0.15 | 22.3% |
| ST-EVO w/ smoothing | 0.81 | 0.09 | 12.8% |
| Variant | MMLU | HumanEval | SVAMP | GSM8K | Jaccard |
| w/o smoothing | 89.85 | 94.36 | 94.72 | 97.60 | 0.72 |
| 89.78 | 94.29 | 94.64 | 97.53 | 0.78 | |
| 89.71 | 94.18 | 94.51 | 97.42 | 0.81 | |
| 89.32 | 93.81 | 94.03 | 97.06 | 0.88 | |
| 87.46 | 91.53 | 92.18 | 95.27 | 0.95 |
| Transfer Setting | Target Domain | Original on Target | Transfer Acc. | Drop |
| GSM8K SVAMP | Math Math | 94.72 | 93.85 | 0.87 |
| HumanEval DS-1000 | Code Code | 58.65 | 57.42 | 1.23 |
| GSM8K HumanEval | Math Code | 94.36 | 88.54 | 5.82 |
| HumanEval GSM8K | Code Math | 97.60 | 90.71 | 6.89 |
| Transfer Setting | Domain | Target-Trained | Zero-Shot | Drop |
| GSM8K SVAMP | Math Math | 94.72 | 91.38 | 3.34 |
| GSM8K MultiArith | Math Math | 99.05 | 96.73 | 2.32 |
| HumanEval DS-1000 | Code Code | 58.65 | 53.07 | 5.58 |
| GSM8K HumanEval | Math Code | 94.36 | 81.92 | 12.44 |
| HumanEval GSM8K | Code Math | 97.60 | 84.17 | 13.43 |
| GSM8K MMLU | Math General | 89.85 | 80.26 | 9.59 |
| Hyperparameter | Value |
| Backbone LLM | gpt-oss-120b |
| Prompt template | Same as ST-EVO |
| Decoding temperature | |
| Optimization target | Graph edges and prompts |
| Graph optimizer | REINFORCE |
| Initial edge probability |
| Hyperparameter | Value |
| Backbone LLM | gpt-oss-120b |
| Prompt template | Same as ST-EVO |
| Decoding temperature | |
| Communication rounds | |
| Node encoder | all-MiniLM-L6-v2 |
| Node embedding dimension |
| Hyperparameter | Value |
| Backbone LLM | gpt-oss-120b |
| Prompt template | Same as ST-EVO |
| Decoding temperature | |
| Search algorithm | Monte Carlo Tree Search |
| Workflow representation | Code-represented workflow |
| Optimized components | Workflow edges and node prompts |
| Hyperparameter | Value |
| Backbone LLM | gpt-oss-120b |
| Prompt template | Same as ST-EVO |
| Decoding temperature | |
| Routing granularity | Reasoning step |
| Draft model | gpt-oss-120b |
| Verifier model | gpt-oss-120b |
| Hyperparameter | Value |
| Backbone LLM | gpt-oss-120b |
| Prompt template | Same as ST-EVO |
| Decoding temperature | |
| Routing granularity | Reasoning step |
| Routing signal | Logit-based confidence |
| Confidence estimator | Maximum logit confidence |
| Hyperparameter | Value |
| Backbone LLM | gpt-oss-120b |
| Prompt template | Same as ST-EVO |
| Decoding temperature | |
| Initial topology | Fully connected graph |
| Pruning granularity | Communication edge |
| Initial edge scoring | Semantic compatibility |
| Hyperparameter | Value |
| Backbone LLM | gpt-oss-120b |
| Prompt template | Same as ST-EVO |
| Decoding temperature | |
| Topology generation paradigm | Autoregressive graph generation |
| Graph initialization | Empty graph |
| Node generation strategy | Role selection from agent pool |
| Method | Attack Ratio | MMLU | SVAMP | HumanEval | Avg. |
| Random Graph | Clean | 83.20 | 87.10 | 84.14 | 84.81 |
| Attack | 76.48 ( 6.72) | 79.72 ( 7.38) | 77.73 ( 6.41) | 77.98 ( 6.83) | |
| Attack | 72.36 ( 10.84) | 75.64 ( 11.46) | 73.97 ( 10.17) | 73.99 ( 10.82) | |
| Attack | 67.83 ( 15.37) | 70.82 ( 16.28) | 68.52 ( 15.62) | 69.06 ( 15.75) | |
| SafeSieve | Clean | 84.65 | 90.10 | 90.15 | 88.30 |
| Attack | 80.93 ( 3.72) | 85.15 ( 4.95) | 84.31 ( 5.84) | 83.46 ( 4.84) |
| Method | Metric | 5 Agents | 10 Agents | 20 Agents | 40 Agents |
| Random Graph | Accuracy (%) | 82.7 | 83.3 | 83.6 | 83.8 |
| Time (minutes) | 14.2 | 31.4 | 59.7 | 118.5 | |
| #Tokens | 431,064 | 1,317,148 | 4,245,925 | 13,184,762 | |
| GPTSwarm | Accuracy (%) | 83.6 | 84.2 | 84.8 | 85.1 |
| Time (minutes) | 67.8 | 201.8 | 422.5 | 825.0 | |
| #Tokens | 1,672,201 | 5,103,328 | 14,054,825 | 39,487,316 |
| Method | Metric | 5 Agents | 10 Agents | 20 Agents | 40 Agents |
| Random Graph | Accuracy (%) | 83.6 | 84.1 | 84.6 | 84.9 |
| Time (minutes) | 3.8 | 7.5 | 15.2 | 31.4 | |
| #Tokens | 158,426 | 316,917 | 641,382 | 1,296,745 | |
| GPTSwarm | Accuracy (%) | 86.5 | 87.1 | 87.8 | 88.2 |
| Time (minutes) | 8.9 | 17.6 | 35.9 | 73.8 | |
| #Tokens | 189,742 | 381,653 | 776,438 | 1,592,817 |
| Method | Metric | 5 Agents | 10 Agents | 20 Agents | 40 Agents |
| Random Graph | Accuracy (%) | 86.6 | 87.1 | 87.5 | 87.8 |
| Time (minutes) | 10.6 | 21.4 | 43.8 | 89.7 | |
| #Tokens | 648,372 | 1,294,816 | 2,631,457 | 5,382,904 | |
| GPTSwarm | Accuracy (%) | 86.7 | 87.3 | 87.8 | 88.1 |
| Time (minutes) | 25.8 | 52.6 | 108.4 | 223.7 | |
| #Tokens | 1,006,481 | 2,018,736 | 4,126,592 | 8,482,317 |
| Method | Metric | 3 Iterations | 6 Iterations | 12 Iterations |
| Random Graph | Accuracy (%) | 82.7 | 83.1 | 83.3 |
| Time (minutes) | 14.2 | 27.4 | 52.5 | |
| #Tokens | 431,064 | 816,266 | 1,425,295 | |
| GPTSwarm | Accuracy (%) | 83.6 | 84.0 | 84.2 |
| Time (minutes) | 67.8 | 112.5 | 199.4 | |
| #Tokens | 1,672,201 | 3,025,162 | 5,925,102 |
| Method | Metric | 3 Iterations | 6 Iterations | 12 Iterations |
| Random Graph | Accuracy (%) | 84.1 | 84.5 | 84.8 |
| Time (minutes) | 5.6 | 10.8 | 20.9 | |
| #Tokens | 246,382 | 467,915 | 834,276 | |
| GPTSwarm | Accuracy (%) | 87.1 | 87.5 | 87.8 |
| Time (minutes) | 18.4 | 32.7 | 60.8 | |
| #Tokens | 381,624 | 704,892 | 1,326,517 |
| Method | Metric | 3 Iterations | 6 Iterations | 12 Iterations |
| Random Graph | Accuracy (%) | 86.6 | 87.0 | 87.2 |
| Time (minutes) | 10.6 | 20.5 | 39.2 | |
| #Tokens | 648,372 | 1,227,762 | 2,143,815 | |
| GPTSwarm | Accuracy (%) | 86.7 | 87.1 | 87.3 |
| Time (minutes) | 25.8 | 42.8 | 75.9 | |
| #Tokens | 1,006,481 | 1,820,815 | 3,566,259 |
| Methods | MMLU | GSM8K | MultiArith | SVAMP | AQuA | HumanEval | DS-1000 | HotpotQA | DDXPlus | Avg. |
| LLM-Debate | 83.28 | 89.95 | 95.45 | 88.30 | 73.52 | 85.24 | 49.26 | 84.55 | 71.33 | 80.10 |
| G-Designer | 84.63 | 93.35 | 97.60 | 89.52 | 76.30 | 89.40 | 54.82 | 87.66 | 76.42 | 83.30 |
| ST-EVO (10 Queries) | 85.35 | 93.85 | 97.45 | 89.85 | 77.60 | 89.70 | 55.05 | 88.10 | 76.95 | 83.77 |
| ST-EVO (20 Queries) | 87.10 | 95.20 | 98.20 | 91.35 | 81.10 | 91.55 | 56.35 | 89.75 | 79.15 | 85.53 |
| ST-EVO (40 Queries) | 89.85 | 96.85 | 99.05 | 93.70 | 84.90 | 93.30 | 57.65 | 91.55 | 81.40 | 87.58 |
| ST-EVO (60 Queries) | 90.10 | 97.60 | 99.12 | 94.72 | 86.10 | 94.10 | 58.30 | 92.20 | 82.25 | 88.28 |
| Component | Time (ms) | Percentage |
| LLM inference (4 agents) | 8,500 | 93.9% |
| Entropy computation | 45 | 0.5% |
| Flow-Matching scheduling | 65 | 0.7% |
| Cache retrieval | 12 | 0.1% |
| Topology parsing and routing | 8 | 0.1% |
| Inter-agent message passing | 420 | 4.6% |
| Metric | Value |
| Scheduler parameters | 2.8M |
| Training hardware | 1 NVIDIA 3090 (24 GB) |
| Training GPU memory | 4.2 GB |
| Training time (40 queries) | 35 min |
| Training time (80 queries) | 68 min |
| LLM calls for training (80 queries) | 2,400 |
| Method | Training Time | GPU Memory | Parameters |
| G-Designer | 45 min | 3.8 GB | 2.1M |
| ARG-Designer | 55 min | 4.5 GB | 3.2M |
| SafeSieve | 50 min | 3.5 GB | 1.8M |
| ST-EVO | 68 min | 4.2 GB | 2.8M |
| MMLU | GSM8K | MultiArith | SVAMP | AQuA | |
| ST-EVO | 89.82 0.18 | 97.55 0.21 | 99.01 0.12 | 94.68 0.24 | 86.48 0.36 |
| HumanEval | DS-1000 | HotpotQA | DDXPlus | ||
| ST-EVO | 94.29 0.31 | 58.72 0.42 | 92.49 0.27 | 82.43 0.39 |