Process reward models (PRMs) score intermediate reasoning steps and are widely used for search, ranking, and training, but optimization can exploit these learned proxies by increasing reward while turning correct reasoning into incorrect reasoning. We formulate PRM stress testing as a quality-diversity search problem using MAP-Elites, retaining the most severe correctness-flipping edit in each behavior-space region while separating search coverage from exploit coverage. We characterize what such archives certify: finite-cell repair bounds covered-cell tail risk and average residual severity but cannot bound the worst remaining cell from covered fraction alone; under Lipschitz post-repair loss and metric-cover auditing, the residual is bounded by archive fitting error plus the Lipschitz constant times the covering radius. A controlled landscape validates this certificate and the impossibility of any fraction-only worst-case guarantee. On real PRMs, the search reveals an aggregation-dependent vulnerability in Qwen2.5-Math-PRM-7B: padding yields 44 strict exploits with maximum gain 0.294 under mean pooling versus one exploit under minimum readout; a matched syntactic control isolates the mechanism, and an RLHFlow value-head model shows the same qualitative effect with maximum gain 0.005. A predeclared paired LoRA repair protocol reduces exploit rates from 0.148 to 0.037 to 0.074, lowers the worst attack from 0.333 to 0.177 to 0.212, improves ranking AUROC without degrading best-of-4 accuracy, attributes gains to adversarial fine-tuning rather than archive diversity, and is confirmed by independent unpaired replications (44 to 1, clean-split worst gain 0.0092, MATH-500 41 to 0, clean ranking 40/40).
Large Language Models (LLMs) have significantly automated the process of scientific discovery over the past few years. However, existing systems share one core limitation: they generate and optimize ideas independently for either Quality or Diversity. This often leads to the generation of ideas in close proximity to one another or to a large set of trivial, unsound, or unclear concepts. In this work, we instead argue that research ideation should be treated as a conjunction of both objectives and framed as a Quality-Diversity (QD) search. In line with this perspective, we introduce IDEAgent, a multi-agent framework that manages the evolution of ideas through lineages. We jointly drive Quality using multi-objective feedback for dedicated repair and refinement, while Diversity is achieved through lightweight sequential memory and explicit comparison against completed ideas, their historical ancestors, and rejected proposals. To systematically evaluate this QD conjunction, we develop Yield, a joint metric that computes the largest set of mutually diverse ideas that satisfy a predetermined quality threshold. Finally, through evaluations across 32 topics spanning 8 domains of Computer Science, we show that IDEAgent outperforms the best baseline by 3.89x on Yield, while achieving non-zero Yield on 8x more topics. We further corroborate these findings through an analysis of quality improvements, showing that repair and refinement are crucial for building logical rigor and clarity while preserving non-obviousness. To encourage future research on QD-search-based ideation, we open-source IDEAgent at https://github.com/declare-lab/IDEAgent.