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

Sizhe Tang; Zuyuan Zhang; Zeyu Fang; Tian Lan

cs.AIOct 17, 2026

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

Authors: Sizhe Tang, Zuyuan Zhang, Zeyu Fang, Tian Lan

Organizations: George Washington University

Abstract

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.

Figures & tables

MLGym
		Prior Works				Ours
Task	Baseline	CORAL	AIRA	MLEvolve	ARTS ∗	Meld	Human Best
Titanic (acc $\uparrow$ )	0.766	0.947	0.921	0.947	0.952	0.972	0.830
CIFAR-10 (acc $\uparrow$ )	0.497	0.962	0.963	0.955	0.959	0.960	0.994
Fashion-MNIST (acc $\uparrow$ )	0.848	0.943	0.947	0.937	0.945	0.957	0.968
House Prices ( $R^{2}$ $\uparrow$ )	0.880	0.924	0.929	0.929	0.931	0.943	0.990

Table 1: Best held-out scores within the nominal evaluator-call budget on 12 MLGym and 10 MLE-bench tasks, averaged over three independent seeds. All baseline values are our same-harness reruns with the shared Executor and evaluator. Baseline is the starting solution of each task, and Human Best is our independently measured task-specific reference for MLGym (Appendix B.1 ) and the Kaggle top-1 score for MLE-bench. Dark and light purple mark the best and second-best automated methods.

Figure 1: Fashion-MNIST

Figure 6: Median, IQM, Mean, and Optimality Gap of normalized scores (Baseline

{}=0

, Human Best

{}=1

) over the 12 MLGym tasks, with 95% bootstrap intervals. Meld is best on all four.

Appendix figures & tables4 assets

Supplementary material from the paper’s appendix.

Appendix

Task	Metric	Timeout	Baseline	Human best
Titanic	accuracy	1800 s	0.766 (0.943)	0.830
House Prices	$R^{2}$	1800 s	0.880	0.990
Fashion-MNIST	accuracy	1800 s	0.848	0.968
CIFAR-10	accuracy	1800 s	0.497	0.994
MNLI	accuracy (%)	2400 s	52.51 (50.81)	92.5
Language Modeling	validation loss	2400 s	4.238	3.280

Appendix

Table 2: Tasks, metrics, timeouts, and reporting anchors. Human-best references are independently measured as described below; for Titanic and MNLI, re-measured baseline values are shown in parentheses.

Backbone	Qwen3-4B-Instruct-2507 (frozen, bfloat16)
Adapters	1 Coordinator + 3 Scientist LoRA, $r{=}32$ , $\alpha{=}64$ , dropout 0
Research units $N$ / forks per group $G$	3 / 8
Candidates per group	$G{\times}N=24$
Optimizer steps per group	1
Clipping range $[1-\epsilon_{\mathrm{lo}},1+\epsilon_{\mathrm{hi}}]$	$[0.8,\,1.28]$
KL coefficient $\beta_{\mathrm{KL}}$ (to task-start policy)	$0.01$

Appendix

Table 3: Test-time adaptation hyperparameters for Meld .

	PD		CB
Variant	Median	Hits / 24	Median	Hits / 24
Full Meld	$2.35\rightarrow 2.57$	$2\rightarrow 10$	$0.000\rightarrow 0.010$	$2\rightarrow 6$
Coordinator-only	$2.35\rightarrow 2.44$	$2\rightarrow 5$	$0.000\rightarrow 0.004$	$2\rightarrow 3$
Scientist-only	$2.35\rightarrow 2.48$	$2\rightarrow 6$	$0.000\rightarrow 0.006$	$2\rightarrow 4$
Frozen	$2.35\rightarrow 2.37$	$2\rightarrow 3$	$0.000\rightarrow 0.002$	$2\rightarrow 2$

Appendix

Table 4: Adaptation ablation on Prisoner’s Dilemma (PD) and Colonel Blotto (CB), averaged over three independent seeds. Each entry reports

b_{\mathrm{pre}}\!\rightarrow b_{\mathrm{post}}

: the initial 24-candidate batch and a fresh 24-candidate batch generated after all enabled updates in one scheduled Coordinator–Scientist cycle. “Median” is the mean of the per-seed medians over valid candidates; “hits” is the mean number of threshold hits (score at least

2.62

on PD or

0.245

on CB) per 24 attempted evaluations.

Task	MLEvolve	AIRA	CORAL	ARTS ∗	Meld
Titanic	1.00	1.00	1.00	1.00	1.00
House Prices	0.45	0.45	0.40	0.46	0.57
Fashion-MNIST	0.74	0.82	0.79	0.81	0.91
CIFAR-10	0.92	0.94	0.94	0.93	0.93
MNLI	0.79	0.79	0.79	0.79	0.79
Language Modeling	0.49	0.58	0.60	0.59	0.60

Appendix

Table 5: Normalized, clipped scores

z

behind Figure 6 .

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