MELD: Recursive Self-Improvement via Hierarchical Coordination for Multi-Agent Scientific Discovery

Multi-agent scientific discovery with large language models raises a coupled learning problem: research assignments determine both which experiments are pursued and the experiences from which agents adapt. We introduce MELD, a unified hierarchical test-time training framework that jointly adapts a team-level Coordinator policy and agent-level individual Scientist policies within a single discovery process. The Coordinator generates a joint portfolio of search branches and research directives over a shared derivation tree, while Scientists develop hypotheses and execution plans implemented by a shared frozen Executor. Both levels receive alternating GRPO-style parameter updates under a shared smooth best-of-budget objective, allowing team organization and individual research behavior to co-evolve in a recursive self-improvement loop. Our analysis establishes objective alignment for the hierarchy, characterizes conditions for coordination gains over independent parallel discovery and the first-order benefit of private adaptation, and derives a finite-budget regret bound for adapted models. On 22 MLGym and MLE-bench tasks, MELD is best on 20 of them and achieves the highest aggregate normalized scores on MLGym, using a 4B backbone for coordination and research. Most baselines use proprietary Scientists, and all systems share one frozen Executor.