cs.AIOct 12, 2026
SaveHeterogeneous 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
Figure 1: From human-directed optimization to heterogeneous agentic coevolution. HACE brings together specialized foundation models and LLM agents into a shared learning process, where each helps determine how the other improves. Across rounds, both learners and their interaction harness evolve, creating new opportunities for reciprocal improvement.
Figure 2: Overview of HACE. Agent exploration selects specialist training experience. Joint validation retains the specialist and harness, after which fresh verified responses train the agent and shape later exploration. The on-policy agent optimization step uses reinforced self-training.
| 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} |
Table 1: Main results on recommendation across five datasets and three architectures. Entries report HR@10 with standard deviations in subscript. Bold marks the best mean in each row.
| 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} |
Table 2: Main results on protein function prediction (CAFA) and material discovery (WBM). Higher is better for all metrics. Full scientific metrics appear in Tables 5 and 6 .
| 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} |
Table 3: Ablation studies on recommendation (Toys/SASRec), protein function prediction (CAFA/ESM-2 650M), and material discovery (WBM/CHGNet). Metrics are HR@10 for Toys and mean NDCG for CAFA and WBM.
| 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 | |||
Table 4: Scaling experiment on protein function prediction task. NDCG averages cutoffs 5 and 10. Base denotes the initial specialists, which are already trained to convergence before coevolution; Appendix C.3 states the criterion we use. Agent variants use a shared 30-round configuration. Subscripts report standard deviations of within-run gains on three random seeds.
Figure 3: Evolution dynamics of three domains. Best recorded scores during evolution, measured by HR@10, Recall@10, and mean NDCG@3 and NDCG@5. Dashed lines mark the frozen specialist.
Figure 4: Illustrations on events during coevolution. Upper panels compare specialist and combined predictions. Lower panels show recorded selection scores and their running maxima from one run in each domain, with selected updates annotated.
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} |
Table 5: Protein function prediction on CAFA with two frozen backbones.
| 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} |
Table 6: Material discovery task on WBM with CHGNet.
| 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 |
Table 7: HACE is agnostic to specialist architectures and adaptation on different learning components.
| 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 |
Table 8: How exploration guides the two learners. Relative improvement determines eligibility for different learning objectives.
| 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 |
Table 9: Recommendation harness fields. “Fixed” denotes a value outside the search space.
| 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 |
Table 10: Presentation fields of the protein harness. Experience selection is described in Appendix B.3 .
| 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 |
Table 11: Presentation fields of the crystal stability harness. Prototype lengths are measured in characters.
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