arXiv:2602.02050v3 Announce Type: replace Abstract: Tool-using agents based on Large Language Models (LLMs) excel in tasks such as mathematical reasoning and multi-hop question answering. However, in long trajectories, agents often trigger excessive and low-quality tool calls, increasing latency and degrading inference performance, making managing tool-use behavior challenging. In this work, we conduct entropy-based pilot experiments and observe a strong positive correlation between entropy reduction and high-quality tool calls. Building on this finding, we propose using entropy reduction as a supervisory signal and design two reward strategies to address the differing needs of optimizing tool-use behavior. Sparse outcome rewards provide coarse, trajectory-level guidance to improve efficiency, while dense process rewards offer fine-grained supervision to enhance performance. Experiments across diverse domains show that both reward designs improve tool-use behavior: the former reduces tool calls by 72.07% compared to the average of baselines, while the latter improves performance by 22.27%. These results position entropy reduction as a key mechanism for enhancing tool-use behavior, enabling agents to be more adaptive in real-world applications.

arXiv:2506.11087v3 Announce Type: replace-cross Abstract: Supervised Fine-Tuning (SFT) empowers Large Language Models (LLMs) with exceptional performance on specialized tasks, but it yields dense, high-dimensional delta parameters that pose severe storage and distribution challenges. Singular Value Decomposition (SVD)-based compression offers a compact representation for such delta parameters, but existing methods adopt heuristic quantization without clarifying underlying mechanisms, leading to poor generalizability. In this work, we propose PrinMix, a rigorous SVD-based framework that models quantization as an optimization problem, grounding the design in mathematical mechanisms. We first theoretically derive quantization error and identify a key singular-value-dominated scaling mechanism, which mathematically proves the necessity of mix-precision quantization. We then model the quantization scheme as a 0/1 Integer Linear Programming (ILP) problem, which yields optimal bit-budget-constrained solutions without empirical assumptions. Furthermore, PrinMix integrates a Reconstruction Target Correction (RTC) method to compensate for errors from the $\mathbf{V}$-then-$\mathbf{U}$ sequential quantization process. Extensive experiments confirm PrinMix performs well: for 7B LLMs, PrinMix outperforms SOTA Delta-CoMe on challenging benchmarks by 22.3% on AIME2024 and 6.1% on GQA.