We prove that the root lattice $D_4$ uniquely minimizes the normalized second moment among four-dimensional lattices, up to similarity. The minimum is $13/(120\sqrt{2})$. The proof reduces the problem to polynomial inequalities on three secondary cones. We derive the second-moment formulas geometrically and give explicit polynomial certificates that can be checked by coefficient comparison. We also derive a lower bound for lattice quantizers in every dimension at least two from the number of Voronoi facets, using a comparison with circular cones and concavity in the solid angle. This bound strictly improves the sphere bound and recovers the hexagonal value in dimension two.
Yu Zhao, Fan Jiang, Tianle Liu, Bo Zeng, Xintong Wang, Jiaxuan Teng, Yu Liu, Yichao Du
Recent advancements in Large Reasoning Models (LRMs), exemplified by DeepSeek-R1, have underscored the potential of scaling inference-time compute through Group Relative Policy Optimization (GRPO). However, GRPO frequently suffers from gradient signal attenuation when encountering problems that are either too trivial or overly complex. In these scenarios, the disappearance of inter-group advantages makes the gradient signal susceptible to noise, thereby jeopardizing convergence stability. While variants like DAPO attempt to rectify gradient vanishing, they do not alleviate the substantial computational overhead incurred by exhaustive rollouts on low-utility samples. In this paper, we propose Difficulty-Estimated Policy Optimization (DEPO), a novel framework designed to optimize the efficiency and robustness of reasoning alignment. DEPO integrates an online Difficulty Estimator that dynamically assesses and filters training data before the rollout phase. This mechanism ensures that computational resources are prioritized for samples with high learning potential. Empirical results show that DEPO achieves approximately 1.86x faster rollouts than DAPO in the profiled configuration, while improving benchmark performance over GRPO at comparable training cost. Our approach significantly lowers the computational barrier for training high-performance reasoning models, offering a more sustainable path for reasoning scaling.
Tianle Liu, Zhiliang Tian National University of Defense Technology, Zhen Huang National University of Defense Technology, Tianlun Liu National University of Defense Technology, Jingyuan Huang, Zhaoning Zhang National University of Defense Technology, Chengcheng Shao, Dongsheng Li National University of Defense Technology
As the text generated by large language models (LLMs) increasingly resembles human-written text (HWT), detecting LLM-generated text (LGT) is crucial to avoid malicious use of LGT. Recent research treats LGT detection as an out-of-distribution (OOD) detection problem and views HWT as the OOD. However, existing OOD detection methods assume that LGT is a single homogeneous distribution. In practice, LGT exhibits different characteristics under different generation conditions. Text from weaker LLMs tends to form distinct clusters and is easy to detect, whereas text from stronger models significantly overlaps with HWTs and is hard to detect. To address the issue, in this paper, we propose an LGT detection framework based on density-aware manifold learning and the construction of hybrid Mahalanobis energy. We apply density-aware manifold learning with Laplacian smoothness and density regularization in embedding space, amplifying differences between LGT and HWT. We further propose a density-adaptive hybrid Mahalanobis metric that combines global and local covariance via density weighting, enabling adaptation to the manifold-aware embedding space. Finally, based on the metric, we define the distribution energy as a measure of distribution discrepancy, and we employ energy learning and contrastive learning to separate distributions hierarchically, establishing a clear OOD decision boundary. Experiments show that our method outperforms strong baselines.
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cs.CL
Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) · 2026 · 正式发表
Tianlun Liu National University of Defense Technology, Zhiliang Tian National University of Defense Technology, Zhen Huang National University of Defense Technology, Xingzhi Zhou Huawei Technologies Ltd., Wanlong Yu, Tianle Liu, Feng Liu National University of Defense Technology, Dongsheng Li National University of Defense Technology
Text understanding application often suffers from domain shifts. To handle testing domains, domain adaptation (DA) is trained to adapt to a fixed and observed testing domain; a more challenging paradigm, test-time adaptation (TTA), cannot access the testing domain during training and online adapts to the testing samples during testing, where the samples are from a fixed domain. We aim to explore a more practical and underexplored scenario, continual test-time adaptation (CTTA) for text understanding, which involves a sequence of testing (unobserved) domains in testing. Current CTTA methods struggle in reducing error accumulation over domains and enhancing generalization to handle unobserved domains: 1) Noise-filtering reduces accumulated errors but discards useful information, and 2) accumulating historical domains enhances generalization, but it is hard to achieve adaptive accumulation. In this paper, we propose a CTTA-T (continual test-time adaptation for text understanding) framework adaptable to evolving target domains: CTTA-T adopts a teacher-student framework, where the teacher is equipped with domain awareness and generalization for evolving domains. To improve teacher predictions, we propose a refine-then-filter based on dropout-driven consistency, which calibrates predictions and removes unreliable guidance. For the adaptation–generalization trade-off, we construct a domain-aware teacher by dynamically accumulating cross-domain semantics via incremental PCA, which continuously tracks domain shifts. Experiments show CTTA-T excels baselines.
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cs.CL
Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) · 2026 · 正式发表