arXiv subjects

Dongdong Xiang

Publications and source records attributed to Dongdong Xiang.

2 recordsLinked to original sources

arXiv2026

Space-filling foldover designs for order-of-addition experiments under Kendall tau distance criteria

Order-of-addition experiments arise when the response depends on the order in which a set of components is added. Since the number of possible orders increases factorially with the number of components, full permutation designs are rarely feasible except for small problems. This paper studies space-filling fractional designs for order-of-addition experiments based on the Kendall tau distance, a natural metric for comparing permutations through pairwise ordering disagreements. We consider the maximin Kendall tau distance criterion and related dispersion criteria, and establish their connections with statistical optimality under the pairwise ordering model and a Gaussian process model with the Mallows kernel. To construct such designs, we propose an efficient foldover simulated annealing algorithm, denoted by FSA-KD, based on swap moves in the permutation space, together with foldover and incremental updating strategies. Numerical studies show that the resulting FSA-KD designs have large minimum pairwise Kendall tau distances, denoted by k_min(D), and stable pairwise distance distributions, and perform well in surrogate modeling and permutation-based optimization tasks.

stat.ME↗

arXiv2025

ToolExpander: Extending the Frontiers of Tool-Using Reinforcement Learning to Weak LLMs

Training Large Language Models (LLMs) with Group Relative Policy Optimization (GRPO) encounters a significant challenge: models often fail to produce accurate responses, particularly in small-scale architectures. This limitation not only diminishes performance improvements and undermines the potential of GRPO but also frequently leads to mid-training collapse, adversely affecting stability and final efficacy. To address these issues, we propose ToolExpander, a novel framework that advances tool-oriented reinforcement learning for resource-constrained LLMs through two key innovations:(1) Dynamic Multi-Round Hard Sampling, which dynamically substitutes challenging samples(those without correct outputs over 10 rollouts) with high-quality few-shot demonstrations during training, coupled with an exponential learning rate decay strategy to mitigate oscillations;(2) Self-Exemplifying Thinking, an enhanced GRPO framework that eliminates KL divergence and incorporates adjusted clipping coefficients, encouraging models to autonomously generate and analyze few-shot examples via a minimal additional reward (0.01).Experimental results demonstrate that ToolExpander significantly enhances tool-using capabilities in LLMs, especially in weaker small-scale models, improving both training stability and overall performance.

cs.CL↗