Zhiguo Yang

Suchuan Dong, Zhiguo Yang, Lianlei Lin

We focus on the numerical approximation of the Cahn-Hilliard type equations, and present a family of second-order unconditionally energy-stable schemes. By reformulating the equation into an equivalent system employing a scalar auxiliary variable, we approximate the system at the time step $(n+θ)$ ($n$ denoting the time step index and $θ$ is a real-valued parameter), and devise a family of corresponding approximations that are second-order accurate and unconditionally energy stable. This family of approximations contains the often-used Crank-Nicolson scheme and the second-order backward differentiation formula as particular cases. We further develop an efficient solution algorithm for the resultant discrete system of equations to overcome the difficulty caused by the unknown scalar auxiliary variable. The final algorithm requires only the solution of four de-coupled individual Helmholtz type equations within each time step, which involve only constant and time-independent coefficient matrices that can be pre-computed. A number of numerical examples are presented to demonstrate the performance of the family of schemes developed herein. We note that this family of second-order approximations can be readily applied to devise energy-stable schemes for other types of gradient flows when combined with the auxiliary variable approaches.

Jieting Xiao, Yun Lin, Huizhen Qiu et al.

While Large Language Models have achieved remarkable integration in various vertical scenarios, their deployment in the telecommunications domain remains exploratory due to the lack of a standardized evaluation framework. Current telecom benchmarks primarily focus on static, foundational knowledge and isolated atomic skills, neglecting the equipment-specific documentation and end-to-end industrial workflows essential for real-world production systems. To bridge this gap, we present TeleCom-Bench, a comprehensive benchmark comprising 12 evaluation sets with 22,678 curated samples, which evaluates LLMs across a synergistic hierarchy: (1) Multi-dimensional Knowledge Comprehension, which integrates telecommunication fundamentals, 3GPP protocols, and 5G network architecture with proprietary product knowledge across wired, core, and wireless networks via knowledge graph-driven synthesis; and (2)End-to-End Knowledge Application, which formalizes six core tasks on authentic trajectories from live network agent workflows, including intent recognition, entity extraction, event verification, tool invocation, root cause analysis, and solution generation-across network optimization and fault maintenance scenarios. Evaluations of eight state-of-the-art LLMs reveal a universal Execution Wall: while models achieve 90% accuracy in linguistic interface tasks such as intent recognition and entity extraction, performance collapses to approximately 30% in procedural execution tasks like solution generation. This capability gap demonstrates that current LLMs function competently as diagnosticians but fail as field engineers. TeleCom-Bench provides standardized diagnostics to precisely pinpoint this deficit, offering actionable guidance for domain-specific alignment toward production-ready telecom agents. The dataset and evaluation code have been released at https://github.com/ZTE-AICloud/TeleCom-Bench.

Zhiguo Yang, Suchuan Dong

We present a set of effective outflow/open boundary conditions and an associated algorithm for simulating the dynamics of multiphase flows consisting of $N$ ($N\geqslant 2$) immiscible incompressible fluids in domains involving outflows or open boundaries. These boundary conditions are devised based on the properties of energy stability and reduction consistency. The energy stability property ensures that the contributions of these boundary conditions to the energy balance will not cause the total energy of the N-phase system to increase over time. Therefore, these open/outflow boundary conditions are very effective in overcoming the backflow instability in multiphase systems. The reduction consistency property ensures that if some fluid components are absent from the N-phase system then these N-phase boundary conditions will reduce to those corresponding boundary conditions for the equivalent smaller system. Our numerical algorithm for the proposed boundary conditions together with the N-phase governing equations involves only the solution of a set of de-coupled individual Helmholtz-type equations within each time step, and the resultant linear algebraic systems after discretization involve only constant and time-independent coefficient matrices which can be pre-computed. Therefore, the algorithm is computationally very efficient and attractive. We present extensive numerical experiments for flow problems involving multiple fluid components and inflow/outflow boundaries to test the proposed method. In particular, we compare in detail the simulation results of a three-phase capillary wave problem with Prosperetti's exact physical solution and demonstrate that the method developed herein produces physically accurate results.

Naxian Ni, Zhiguo Yang, Suchuan Dong

We present a set of new energy-stable open boundary conditions for tackling the backflow instability in simulations of outflow/open boundary problems for incompressible flows. These boundary conditions are developed through two steps: (i) devise a general form of boundary conditions that ensure the energy stability by re-formulating the boundary contribution into a quadratic form in terms of a symmetric matrix and computing an associated eigen problem; and (ii) require that, upon imposing the boundary conditions from the previous step, the scale of boundary dissipation should match a physical scale. These open boundary conditions can be re-cast into the form of a traction-type condition, and therefore they can be implemented numerically using the splitting-type algorithm from a previous work. The current boundary conditions can effectively overcome the backflow instability typically encountered at moderate and high Reynolds numbers. These boundary conditions in general give rise to a non-zero traction on the entire open boundary, unlike previous related methods which only take effect in the backflow regions of the boundary. Extensive numerical experiments in two and three dimensions are presented to test the effectiveness and performance of the presented methods, and simulation results are compared with the available experimental data to demonstrate their accuracy.

Taojie Zhu, Dongyang Xu, Ding Zou et al.

Post-training paradigms for Large Language Models (LLMs), primarily Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL), face a fundamental dilemma: SFT provides stability (low variance) but suffers from high fitting bias, while RL enables exploration (low bias) but grapples with high gradient variance. Existing unified optimization strategies often employ naive loss weighting, overlooking the statistical conflict between these distinct gradient signals. In this paper, we provide a rigorous theoretical analysis of this bias-variance trade-off and propose \textbf{DYPO} (Dynamic Policy Optimization), a unified framework designed to structurally mitigate this conflict. DYPO integrates three core components: (1) a \textit{Group Alignment Loss (GAL)} that leverages intrinsic group dynamics to significantly reduce RL gradient variance; (2) a \textit{Multi-Teacher Distillation} mechanism that corrects SFT fitting bias via diverse reasoning paths; and (3) a \textit{Dynamic Exploitation-Exploration Gating} mechanism that adaptively arbitrates between stable SFT and exploratory RL based on reward feedback. Theoretical analysis confirms that DYPO linearly reduces fitting bias and minimizes overall variance. Extensive experiments demonstrate that DYPO significantly outperforms traditional sequential pipelines, achieving an average improvement of 4.8\% on complex reasoning benchmarks and 13.3\% on out-of-distribution tasks. Our code is publicly available at https://github.com/Tocci-Zhu/DYPO.

Jianyu Qi, Ding Zou, Wenrui Yan et al.

Recent advances in Multimodal Large Language Models (MLLMs) have spurred significant progress in Chain-of-Thought (CoT) reasoning. Building on the success of Deepseek-R1, researchers extended multimodal reasoning to post-training paradigms based on reinforcement learning (RL), focusing predominantly on mathematical datasets. However, existing post-training paradigms tend to neglect two critical aspects: (1) The lack of quantifiable difficulty metrics capable of strategically screening samples for post-training optimization. (2) Suboptimal post-training paradigms that fail to jointly optimize perception and reasoning capabilities. To address this gap, we propose two novel difficulty-aware sampling strategies: Progressive Image Semantic Masking (PISM) quantifies sample hardness through systematic image degradation, while Cross-Modality Attention Balance (CMAB) assesses cross-modal interaction complexity via attention distribution analysis. Leveraging these metrics, we design a hierarchical training framework that incorporates both GRPO-only and SFT+GRPO hybrid training paradigms, and evaluate them across six benchmark datasets. Experiments demonstrate consistent superiority of GRPO applied to difficulty-stratified samples compared to conventional SFT+GRPO pipelines, indicating that strategic data sampling can obviate the need for supervised fine-tuning while improving model accuracy. Our code will be released at https://github.com/qijianyu277/DifficultySampling.

Xiaojun Wu, Xiaoguang Jiang, Huiyang Li et al.

Large language models (LLMs) demonstrate remarkable reasoning capabilities in tasks such as algorithmic coding and mathematical problem-solving. Recent methods have improved reasoning through expanded corpus and multistage training combining reinforcement learning and supervised fine-tuning. Although some methods suggest that small but targeted dataset can incentivize reasoning via only distillation, a reasoning scaling laws is still taking shape, increasing computational costs. To address this, we propose a data-efficient distillation framework (DED) that optimizes the Pareto frontier of reasoning distillation. Inspired by the on-policy learning and diverse roll-out strategies of reinforcement learning, the key idea of our approach is threefold: (1) We identify that benchmark scores alone do not determine an effective teacher model. Through comprehensive comparisons of leading reasoning LLMs, we develop a method to select an optimal teacher model. (2) While scaling distillation can enhance reasoning, it often degrades out-of-domain performance. A carefully curated, smaller corpus achieves a balanced trade-off between in-domain and out-of-domain capabilities. (3) Diverse reasoning trajectories encourage the student model to develop robust reasoning skills. We validate our method through evaluations on mathematical reasoning (AIME 2024/2025, MATH-500) and code generation (LiveCodeBench), achieving state-of-the-art results with only 0.8k carefully curated examples, bypassing the need for extensive scaling. Our systematic analysis demonstrates that DED outperforms existing methods by considering factors beyond superficial hardness, token length, or teacher model capability. This work offers a practical and efficient pathway to advanced reasoning while preserving general capabilities.

Dengfeng Liu, Jucai Zhai, Xiaoguang Jiang et al.

Code completion technology based on large language model has significantly improved the development efficiency of programmers. However, in practical applications, there remains a gap between current commonly used code completion evaluation metrics and users' actual perception. To address this issue, we propose two evaluation metrics for code completion tasks--LCP and ROUGE-LCP, from the perspective of probabilistic modeling. Furthermore, to tackle the lack of effective structural semantic modeling and cross-module dependency information in LLMs for repository-level code completion scenarios, we propose a data processing method based on a Structure-Preserving and Semantically-Reordered Code Graph (SPSR-Graph). Through theoretical analysis and experimental validation, we demonstrate the superiority of the proposed evaluation metrics in terms of user perception consistency, as well as the effectiveness of the data processing method in enhancing model performance.