This paper presents the Entropy-Driven Unified Process Reward Model (EDU-PRM), a novel framework that approximates state-of-the-art performance in process supervision while drastically reducing training costs. EDU-PRM introduces an entropy-guided dynamic step partitioning mechanism, using logit distribution entropy to pinpoint high-uncertainty regions during token generation dynamically. This self-assessment capability enables precise step-level feedback without manual fine-grained annotation, addressing a critical challenge in process supervision. Experiments on the Qwen2.5-72B model with only 7,500 EDU-PRM-generated training queries demonstrate accuracy closely approximating the full Qwen2.5-72B-PRM (71.1% vs. 71.6%), achieving a 98% reduction in query cost compared to prior methods. This work establishes EDU-PRM as an efficient approach for scalable process reward model training.

NP-hard problem-solving traditionally relies on heuristics, but manually crafting effective heuristics for complex problems remains challenging. While recent work like FunSearch has demonstrated that large language models (LLMs) can be leveraged for heuristic design in evolutionary algorithm (EA) frameworks, their potential is not fully realized due to its deficiency in exploitation and exploration. We present UBER (Uncertainty-Based Evolution for Refinement), a method that enhances LLM+EA methods for automatic heuristic design by integrating uncertainty on top of the FunSearch framework. UBER introduces two key innovations: an Uncertainty-Inclusive Evolution Process (UIEP) for adaptive exploration-exploitation balance, and a principled Uncertainty-Inclusive Island Reset (UIIS) strategy for maintaining population diversity. Through extensive experiments on challenging NP-complete problems, UBER demonstrates significant improvements over FunSearch. Our work provides a new direction for the synergy of LLMs and EA, advancing the field of automatic heuristic design.

We establish an open framework for developing plan optimization models for knowledge-based planning (KBP) in radiotherapy. Our framework includes reference plans for 100 patients with head-and-neck cancer and high-quality dose predictions from 19 KBP models that were developed by different research groups during the OpenKBP Grand Challenge. The dose predictions were input to four optimization models to form 76 unique KBP pipelines that generated 7600 plans. The predictions and plans were compared to the reference plans via: dose score, which is the average mean absolute voxel-by-voxel difference in dose a model achieved; the deviation in dose-volume histogram (DVH) criterion; and the frequency of clinical planning criteria satisfaction. We also performed a theoretical investigation to justify our dose mimicking models. The range in rank order correlation of the dose score between predictions and their KBP pipelines was 0.50 to 0.62, which indicates that the quality of the predictions is generally positively correlated with the quality of the plans. Additionally, compared to the input predictions, the KBP-generated plans performed significantly better (P<0.05; one-sided Wilcoxon test) on 18 of 23 DVH criteria. Similarly, each optimization model generated plans that satisfied a higher percentage of criteria than the reference plans. Lastly, our theoretical investigation demonstrated that the dose mimicking models generated plans that are also optimal for a conventional planning model. This was the largest international effort to date for evaluating the combination of KBP prediction and optimization models. In the interest of reproducibility, our data and code is freely available at https://github.com/ababier/open-kbp-opt.