The easy-hard-easy pattern in the difficulty of combinatorial search problems as constraints are added has been explained as due to a competition between the decrease in number of solutions and increased pruning. We test the generality of this explanation by examining one of its predictions: if the number of solutions is held fixed by the choice of problems, then increased pruning should lead to a monotonic decrease in search cost. Instead, we find the easy-hard-easy pattern in median search cost even when the number of solutions is held constant, for some search methods. This generalizes previous observations of this pattern and shows that the existing theory does not explain the full range of the peak in search cost. In these cases the pattern appears to be due to changes in the size of the minimal unsolvable subproblems, rather than changing numbers of solutions.
Local Optima Networks of the Quadratic Assignment Problem
University of Lausanne（洛桑大学）；INRIA Lille - Nord Europe（法国国家信息与自动化研究所里尔-北欧分所）；University of Nice Sophia-Antipolis（尼斯索菲亚·安提波利斯大学）；CNRS（法国国家科学研究中心）；University of Nottingham（诺丁汉大学）
Easy2Hard-Bench: Standardized Difficulty Labels for Profiling LLM Performance and Generalization
University of Maryland（马里兰大学）；University of Waterloo（滑铁卢大学）；Carnegie Mellon University（卡内基梅隆大学）；California Institute of Technology（加州理工学院）；Microsoft（微软）；Capital One
Mechanistically Interpreting the Role of Sample Difficulty in RLVR for LLMs
Beijing Jiaotong University（北京交通大学）；AntGroup（蚂蚁集团）；Northwestern Polytechnical University（西北工业大学）；University of Leeds（利兹大学）；University of Southampton（南安普顿大学）
DIVA-GRPO: Enhancing Multimodal Reasoning through Difficulty-Adaptive Variant Advantage
State Key Laboratory of AI Safety, Institute of Computing Technology, CAS, Beijing, China（人工智能安全国家重点实验室，计算技术研究所，中国科学院，北京，中国）；University of Chinese Academy of Sciences, Beijing, China（中国科学院大学，北京，中国）；Kuaishou Technology, Beijing, China（快手科技，北京，中国）
