Heterogeneous Agentic Coevolution
Organizations: Meta AI · University of Virginia
Abstract
Recent advances in self-improving LLM agents have demonstrated the potential of AI systems that drive their own intelligence. However, many domain-specific applications rely on specialized foundation models that possess strong domain expertise but remain dependent on human-designed improvements. Extending recursive self-improvement to these models presents a key challenge: as a specialist improves, the strategies used to advance it must also adapt. To address this challenge, we propose Heterogeneous Agentic CoEvolution (HACE), a framework that jointly evolves specialized foundation models and LLM agents through reciprocal learning. HACE improves the specialist through supervised learning while training the agent with on-policy reinforced self-training, guided by verified performance gains on the current specialist. The agent's exploration, in turn, informs subsequent specialist training, enabling both models to adapt to each other's progress. To sustain this reciprocal learning, HACE further employs evolutionary search to optimize their interaction harness, adapting how the models exchange information and select training experiences as their capabilities evolve. We evaluate HACE across three challenging domains: recommendation systems, protein function prediction in biology, and crystal stability prediction in material discovery. We show that HACE outperforms the evaluated self-improving methods on the primary task metrics across all three domains. These results shed light on heterogeneous coevolution as a universal approach to improving specialized foundation models through reciprocal interaction with a learning agent.
Figures & tables
| Dataset | Base | ReST-EM | Meta-Harness | OpenEvolve | DGM | TTT-Discover | HACE |
|---|---|---|---|---|---|---|---|
| SASRec | |||||||
| ML-1M | 0.2557_{\color[rgb]{0.4,0.4,0.4}\pm.0012} | 0.2492_{\color[rgb]{0.4,0.4,0.4}\pm.0022} | 0.2491_{\color[rgb]{0.4,0.4,0.4}\pm.0017} | 0.2421_{\color[rgb]{0.4,0.4,0.4}\pm.0004} | 0.2488_{\color[rgb]{0.4,0.4,0.4}\pm.0018} | 0.2473_{\color[rgb]{0.4,0.4,0.4}\pm.0013} | \mathbf{0.2632}_{\color[rgb]{0.4,0.4,0.4}\pm.0013} |
| Beauty | 0.0599_{\color[rgb]{0.4,0.4,0.4}\pm.0004} | 0.0597_{\color[rgb]{0.4,0.4,0.4}\pm.0010} | 0.0631_{\color[rgb]{0.4,0.4,0.4}\pm.0007} | 0.0638_{\color[rgb]{0.4,0.4,0.4}\pm.0003} | 0.0634_{\color[rgb]{0.4,0.4,0.4}\pm.0005} | 0.0633_{\color[rgb]{0.4,0.4,0.4}\pm.0004} | \mathbf{0.0672}_{\color[rgb]{0.4,0.4,0.4}\pm.0004} |
| CDs | 0.0576_{\color[rgb]{0.4,0.4,0.4}\pm.0005} | 0.0587_{\color[rgb]{0.4,0.4,0.4}\pm.0010} | 0.0604_{\color[rgb]{0.4,0.4,0.4}\pm.0004} | 0.0611_{\color[rgb]{0.4,0.4,0.4}\pm.0002} | 0.0592_{\color[rgb]{0.4,0.4,0.4}\pm.0008} | 0.0587_{\color[rgb]{0.4,0.4,0.4}\pm.0007} | \mathbf{0.0647}_{\color[rgb]{0.4,0.4,0.4}\pm.0006} |
| Sports | 0.0315_{\color[rgb]{0.4,0.4,0.4}\pm.0003} | 0.0325_{\color[rgb]{0.4,0.4,0.4}\pm.0001} | 0.0323_{\color[rgb]{0.4,0.4,0.4}\pm.0002} | 0.0331_{\color[rgb]{0.4,0.4,0.4}\pm.0004} | 0.0333_{\color[rgb]{0.4,0.4,0.4}\pm.0003} | 0.0323_{\color[rgb]{0.4,0.4,0.4}\pm.0002} | \mathbf{0.0356}_{\color[rgb]{0.4,0.4,0.4}\pm.0003} |
| Toys | 0.0596_{\color[rgb]{0.4,0.4,0.4}\pm.0001} | 0.0648_{\color[rgb]{0.4,0.4,0.4}\pm.0007} | 0.0657_{\color[rgb]{0.4,0.4,0.4}\pm.0008} | 0.0662_{\color[rgb]{0.4,0.4,0.4}\pm.0008} | 0.0661_{\color[rgb]{0.4,0.4,0.4}\pm.0009} | 0.0646_{\color[rgb]{0.4,0.4,0.4}\pm.0008} | \mathbf{0.0706}_{\color[rgb]{0.4,0.4,0.4}\pm.0003} |
| CAFA / ESM-2 | CAFA / ProtT5-XL | WBM / CHGNet | ||||
|---|---|---|---|---|---|---|
| Method | NDCG | NDCG | NDCG | |||
| Base | 0.6285_{\color[rgb]{0.4,0.4,0.4}\pm.0019} | 0.2218_{\color[rgb]{0.4,0.4,0.4}\pm.0014} | 0.6241_{\color[rgb]{0.4,0.4,0.4}\pm.0011} | 0.2221_{\color[rgb]{0.4,0.4,0.4}\pm.0005} | 0.6388_{\color[rgb]{0.4,0.4,0.4}\pm.0011} | 0.5159_{\color[rgb]{0.4,0.4,0.4}\pm.0003} |
| ReST-EM | 0.6286_{\color[rgb]{0.4,0.4,0.4}\pm.0018} | 0.2219_{\color[rgb]{0.4,0.4,0.4}\pm.0014} | 0.6242_{\color[rgb]{0.4,0.4,0.4}\pm.0011} | 0.2221_{\color[rgb]{0.4,0.4,0.4}\pm.0005} | 0.6496_{\color[rgb]{0.4,0.4,0.4}\pm.0006} | 0.5508_{\color[rgb]{0.4,0.4,0.4}\pm.0004} |
| Meta-Harness | 0.6309_{\color[rgb]{0.4,0.4,0.4}\pm.0015} | 0.2224_{\color[rgb]{0.4,0.4,0.4}\pm.0013} | 0.6261_{\color[rgb]{0.4,0.4,0.4}\pm.0017} | 0.2229_{\color[rgb]{0.4,0.4,0.4}\pm.0006} | 0.6513_{\color[rgb]{0.4,0.4,0.4}\pm.0008} | 0.5510_{\color[rgb]{0.4,0.4,0.4}\pm.0004} |
| OpenEvolve | 0.6320_{\color[rgb]{0.4,0.4,0.4}\pm.0018} | 0.2230_{\color[rgb]{0.4,0.4,0.4}\pm.0012} | 0.6254_{\color[rgb]{0.4,0.4,0.4}\pm.0014} | 0.2230_{\color[rgb]{0.4,0.4,0.4}\pm.0003} | 0.6486_{\color[rgb]{0.4,0.4,0.4}\pm.0008} | 0.5463_{\color[rgb]{0.4,0.4,0.4}\pm.0003} |
| DGM | 0.6325_{\color[rgb]{0.4,0.4,0.4}\pm.0019} | 0.2219_{\color[rgb]{0.4,0.4,0.4}\pm.0014} | 0.6273_{\color[rgb]{0.4,0.4,0.4}\pm.0016} | 0.2235_{\color[rgb]{0.4,0.4,0.4}\pm.0006} | 0.6496_{\color[rgb]{0.4,0.4,0.4}\pm.0007} | 0.5508_{\color[rgb]{0.4,0.4,0.4}\pm.0003} |
| Leave-one-out component | Toys | CAFA | WBM |
|---|---|---|---|
| HACE | \mathbf{0.0706}_{\color[rgb]{0.4,0.4,0.4}\pm.0003} | \mathbf{0.6745}_{\color[rgb]{0.4,0.4,0.4}\pm.0016} | \mathbf{0.6541}_{\color[rgb]{0.4,0.4,0.4}\pm.0010} |
| w/o harness optimization | 0.0658_{\color[rgb]{0.4,0.4,0.4}\pm.0005} | 0.6307_{\color[rgb]{0.4,0.4,0.4}\pm.0019} | 0.6500_{\color[rgb]{0.4,0.4,0.4}\pm.0012} |
| w/o specialist optimization | 0.0641_{\color[rgb]{0.4,0.4,0.4}\pm.0005} | 0.6310_{\color[rgb]{0.4,0.4,0.4}\pm.0022} | 0.6395_{\color[rgb]{0.4,0.4,0.4}\pm.0012} |
| w/o agent optimization | 0.0622_{\color[rgb]{0.4,0.4,0.4}\pm.0006} | 0.6520_{\color[rgb]{0.4,0.4,0.4}\pm.0016} | 0.6502_{\color[rgb]{0.4,0.4,0.4}\pm.0011} |
| w/o joint selection | 0.0650_{\color[rgb]{0.4,0.4,0.4}\pm.0006} | 0.6531_{\color[rgb]{0.4,0.4,0.4}\pm.0020} | 0.6497_{\color[rgb]{0.4,0.4,0.4}\pm.0013} |
| w/o agent-guided experience | 0.0662_{\color[rgb]{0.4,0.4,0.4}\pm.0005} | 0.6575_{\color[rgb]{0.4,0.4,0.4}\pm.0026} | 0.6507_{\color[rgb]{0.4,0.4,0.4}\pm.0012} |
| Model | Base | HACE | Reported |
|---|---|---|---|
| Specialist size Fixed agent Gemma-4 E4B | |||
| ESM-2 35M | +0.0409_{\color[rgb]{0.5,0.5,0.5}\pm 0.0007} | ||
| ESM-2 150M | +0.0422_{\color[rgb]{0.5,0.5,0.5}\pm 0.0004} | ||
| ESM-2 650M | +0.0460_{\color[rgb]{0.5,0.5,0.5}\pm 0.0006} | ||
| ESM-2 3B | +0.0424_{\color[rgb]{0.5,0.5,0.5}\pm 0.0007} | ||
| Agent variant Fixed specialist ESM-2 650M | |||
Appendix figures & tables7 assets
Supplementary material from the paper’s appendix.
Appendix
| Method | AUPR | NDCG | Recall@10 | ||
|---|---|---|---|---|---|
| ESM-2 | |||||
| Base | 0.2218_{\color[rgb]{0.5,0.5,0.5}\pm 0.0014} | 0.1078_{\color[rgb]{0.5,0.5,0.5}\pm 0.0012} | 12.557_{\color[rgb]{0.5,0.5,0.5}\pm 0.060} | 0.6285_{\color[rgb]{0.5,0.5,0.5}\pm 0.0019} | 0.7179_{\color[rgb]{0.5,0.5,0.5}\pm 0.0014} |
| ReST-EM | 0.2219_{\color[rgb]{0.5,0.5,0.5}\pm 0.0014} | 0.1079_{\color[rgb]{0.5,0.5,0.5}\pm 0.0012} | 12.557_{\color[rgb]{0.5,0.5,0.5}\pm 0.060} | 0.6286_{\color[rgb]{0.5,0.5,0.5}\pm 0.0018} | 0.7180_{\color[rgb]{0.5,0.5,0.5}\pm 0.0012} |
| Meta-Harness | 0.2224_{\color[rgb]{0.5,0.5,0.5}\pm 0.0013} | 0.1076_{\color[rgb]{0.5,0.5,0.5}\pm 0.0012} | 12.553_{\color[rgb]{0.5,0.5,0.5}\pm 0.059} | 0.6309_{\color[rgb]{0.5,0.5,0.5}\pm 0.0015} | 0.7245_{\color[rgb]{0.5,0.5,0.5}\pm 0.0007} |
| OpenEvolve | 0.2230_{\color[rgb]{0.5,0.5,0.5}\pm 0.0012} | 0.1087_{\color[rgb]{0.5,0.5,0.5}\pm 0.0011} | 12.549_{\color[rgb]{0.5,0.5,0.5}\pm 0.060} | 0.6320_{\color[rgb]{0.5,0.5,0.5}\pm 0.0018} | 0.7222_{\color[rgb]{0.5,0.5,0.5}\pm 0.0016} |
| DGM | 0.2219_{\color[rgb]{0.5,0.5,0.5}\pm 0.0014} | 0.1075_{\color[rgb]{0.5,0.5,0.5}\pm 0.0012} | 12.557_{\color[rgb]{0.5,0.5,0.5}\pm 0.060} | 0.6325_{\color[rgb]{0.5,0.5,0.5}\pm 0.0019} | 0.7261_{\color[rgb]{0.5,0.5,0.5}\pm 0.0016} |
| Method | NDCG | DAF | MAE | ||
|---|---|---|---|---|---|
| Base | 0.6388_{\color[rgb]{0.5,0.5,0.5}\pm 0.0011} | 0.5159_{\color[rgb]{0.5,0.5,0.5}\pm 0.0003} | 1.644_{\color[rgb]{0.5,0.5,0.5}\pm 0.003} | 0.1049_{\color[rgb]{0.5,0.5,0.5}\pm 0.0002} | -1.289_{\color[rgb]{0.5,0.5,0.5}\pm 0.001} |
| ReST-EM | 0.6496_{\color[rgb]{0.5,0.5,0.5}\pm 0.0006} | 0.5508_{\color[rgb]{0.5,0.5,0.5}\pm 0.0004} | 2.172_{\color[rgb]{0.5,0.5,0.5}\pm 0.005} | 0.0756_{\color[rgb]{0.5,0.5,0.5}\pm 0.0002} | -0.323_{\color[rgb]{0.5,0.5,0.5}\pm 0.001} |
| Meta-Harness | 0.6513_{\color[rgb]{0.5,0.5,0.5}\pm 0.0008} | 0.5510_{\color[rgb]{0.5,0.5,0.5}\pm 0.0004} | 2.171_{\color[rgb]{0.5,0.5,0.5}\pm 0.003} | 0.0754_{\color[rgb]{0.5,0.5,0.5}\pm 0.0003} | -0.281_{\color[rgb]{0.5,0.5,0.5}\pm 0.001} |
| OpenEvolve | 0.6486_{\color[rgb]{0.5,0.5,0.5}\pm 0.0008} | 0.5463_{\color[rgb]{0.5,0.5,0.5}\pm 0.0003} | 2.193_{\color[rgb]{0.5,0.5,0.5}\pm 0.004} | 0.0755_{\color[rgb]{0.5,0.5,0.5}\pm 0.0002} | -0.264_{\color[rgb]{0.5,0.5,0.5}\pm 0.001} |
| DGM | 0.6496_{\color[rgb]{0.5,0.5,0.5}\pm 0.0007} | 0.5508_{\color[rgb]{0.5,0.5,0.5}\pm 0.0003} | 2.183_{\color[rgb]{0.5,0.5,0.5}\pm 0.003} | 0.0748_{\color[rgb]{0.5,0.5,0.5}\pm 0.0003} | -0.251_{\color[rgb]{0.5,0.5,0.5}\pm 0.001} |
| TTT-Discover | 0.6474_{\color[rgb]{0.5,0.5,0.5}\pm 0.0007} | 0.5504_{\color[rgb]{0.5,0.5,0.5}\pm 0.0003} | 2.203_{\color[rgb]{0.5,0.5,0.5}\pm 0.003} | 0.0748_{\color[rgb]{0.5,0.5,0.5}\pm 0.0002} | -0.284_{\color[rgb]{0.5,0.5,0.5}\pm 0.001} |
| Domain | Model | Architecture | Updated parameters |
| Recommendation | SASRec | Causal self-attention Transformer | Model parameters |
| HSTU | Causal sequential transducer with pointwise aggregated attention | Model parameters | |
| Wukong | Stacked factorization-machine network | Model parameters | |
| Protein | ESM-2 | Encoder-only protein Transformer | Prediction head |
| ProtT5-XL | Protein T5 with encoder-decoder pretraining | Prediction head | |
| Materials | CHGNet | Charge-informed graph neural potential | Model parameters |
| Exploration outcome | Agent learning | Specialist learning |
|---|---|---|
| At least one sampled ranking improves the specialist | Best positive response is eligible for the agent curriculum | Instance is eligible for the verified curriculum |
| No sampled ranking improves the specialist | No response from this instance enters the agent update | Instance is eligible for the unsuccessful curriculum |
| Field | Initial | Candidate values | Role |
|---|---|---|---|
| n_candidates | 50 | Fixed | Specialist shortlist size |
| n_history | 15 | 5, 10, 15, 25, 40 | Number of history entries |
| top_k | 5 | 1, 3, 5, 10 | Requested ranking length |
| promote_from | 10 | 0, 5, 10, 20 | Leading candidates shown separately |
| n_promote | 1 | Fixed | Promotion count when |
| show_year | True | True, False | Release year metadata |
| Field | Initial | Candidate values | Role |
|---|---|---|---|
| n_candidates | 50 | Fixed | Specialist shortlist size |
| n_known | 10 | 0, 5, 10, 20 | Number of known annotations |
| top_k | 5 | 1, 3, 5, 10 | Requested ranking length |
| promote_from | 10 | 0, 5, 10, 20 | Leading candidates shown separately |
| def_chars | 120 | 0, 120, 300 | Definition length, zero for name only |
| show_aspect | True | True, False | Target ontology aspect |
| Field | Initial | Candidate values | Role |
|---|---|---|---|
| n_candidates | 20 | Fixed | Specialist shortlist size |
| top_k | 3 | 1, 2, 3, 5 | Requested ranking length |
| promote_from | 2 | 0, 1, 2, 3 | Leading candidates shown separately |
| proto_chars | 24 | 0, 24, 48 | Structure prototype length |
| show_elements | True | True, False | Element set |
| show_rank | True | True, False | Specialist rank per candidate |
LLM Agent Self-Improvement
Large language model agent self-improvement studies how agents use experience and feedback to improve their behavior, tools, and workflows.
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