arXiv subjects

Liang Shan

Publications and source records attributed to Liang Shan.

7 recordsLinked to original sources

arXiv2026

Escaping the Context Bottleneck: Active Context Curation for LLM Agents via Reinforcement Learning

Large Language Models (LLMs) struggle with long-horizon tasks due to the "context bottleneck" and the "lost-in-the-middle" phenomenon, where accumulated noise from verbose environments degrades reasoning over multi-turn interactions. To address this issue, we introduce a symbiotic framework that decouples context management from task execution. Our architecture pairs a lightweight, specialized policy model, ContextCurator, with a powerful frozen foundation model, TaskExecutor. Trained via reinforcement learning, ContextCurator actively reduces information entropy in the working memory. It aggressively prunes environmental noise while preserving reasoning anchors, that is, sparse data points that are critical for future deductions. On WebArena, our framework improves the success rate of Gemini-3.0-flash from 36.4% to 41.2% while reducing token consumption by 8.8% (from 47.4K to 43.3K). On DeepSearch, it achieves a 57.1% success rate, compared with 53.9%, while reducing token consumption by a factor of 8. Remarkably, a 7B ContextCurator matches the context management performance of GPT-4o, providing a scalable and computationally efficient paradigm for autonomous long-horizon agents.

cs.AI↗

arXiv2025

Topological degree for negative fractional Kazdan--Warner equation on finite graphs

Studies on Kazdan--Warner equations on graphs have grown steadily, yet the fractional case remains insufficiently explored. Using topological degree theory, this work investigates the fractional Kazdan--Warner equation in the negative case on connected finite graphs, focusing on the existence and multiplicity of solutions. This work not only extends the earlier result of S. Liu and Yang (2020) to the fractional setting, but also provides a concise proof for the work of Shan and Y. Liu (2025).

math.AP↗

arXiv2025

MENTOR: A Metacognition-Driven Self-Evolution Framework for Uncovering and Mitigating Implicit Domain Risks in LLMs

Ensuring the safety of Large Language Models (LLMs) is critical for real-world deployment. However, current safety measures often fail to address implicit, domain-specific risks. To investigate this gap, we introduce a dataset of 3,000 annotated queries spanning education, finance, and management. Evaluations across 14 leading LLMs reveal a concerning vulnerability: an average jailbreak success rate of 57.8\%. In response, we propose MENTOR, a metacognition-driven self-evolution framework. MENTOR performs metacognitive self-assessment, using strategies such as perspective-taking and consequential reasoning to uncover latent model misalignments. MENTOR couples single-pass rule-guided inference for routine requests with a selectively invoked metacognitive evolution cycle that revises residual unsafe responses, distills successful corrections into a dynamic rule graph, and compiles validated rules into activation-level steering signals for future inference. Experiments demonstrate that MENTOR substantially reduces attack success rates across all tested domains and outperforms existing safety alignment methods. The code and dataset for MENTOR are available at: https://anonymous.4open.science/r/MENTOR-Evo.

cs.AI↗

arXiv2025

AD-GPT: Large Language Models in Alzheimer's Disease

Large language models (LLMs) have emerged as powerful tools for medical information retrieval, yet their accuracy and depth remain limited in specialized domains such as Alzheimer's disease (AD), a growing global health challenge. To address this gap, we introduce AD-GPT, a domain-specific generative pre-trained transformer designed to enhance the retrieval and analysis of AD-related genetic and neurobiological information. AD-GPT integrates diverse biomedical data sources, including potential AD-associated genes, molecular genetic information, and key gene variants linked to brain regions. We develop a stacked LLM architecture combining Llama3 and BERT, optimized for four critical tasks in AD research: (1) genetic information retrieval, (2) gene-brain region relationship assessment, (3) gene-AD relationship analysis, and (4) brain region-AD relationship mapping. Comparative evaluations against state-of-the-art LLMs demonstrate AD-GPT's superior precision and reliability across these tasks, underscoring its potential as a robust and specialized AI tool for advancing AD research and biomarker discovery.

cs.CL↗

arXiv2024

On the Oscillations in Cournot Games with Best Response Strategies

In this paper, we consider the dynamic oscillation in the Cournot oligopoly model, which involves multiple firms producing homogeneous products. To explore the oscillation under the updates of best response strategies, we focus on the linear price functions. In this setting, we establish the existence of oscillations. In particular, we show that for the scenario of different costs among firms, the best response converges to either a unique equilibrium or a two-period oscillation. We further characterize the oscillations and propose linear-time algorithms for finding all types of two-period oscillations. To the best of our knowledge, our work is the first step toward fully analyzing the periodic oscillation in the Cournot oligopoly model.

econ.TH↗

arXiv2024

On Truthful Item-Acquiring Mechanisms for Reward Maximization

In this research, we study the problem that a collector acquires items from the owner based on the item qualities the owner declares and an independent appraiser's assessments. The owner is interested in maximizing the probability that the collector acquires the items and is the only one who knows the items' factual quality. The appraiser performs her duties with impartiality, but her assessment may be subject to random noises, so it may not accurately reflect the factual quality of the items. The main challenge lies in devising mechanisms that prompt the owner to reveal accurate information, thereby optimizing the collector's expected reward. We consider the menu size of mechanisms as a measure of their practicability and study its impact on the attainable expected reward. For the single-item setting, we design optimal mechanisms with a monotone increasing menu size. Although the reward gap between the simplest and optimal mechanisms is bounded, we show that simple mechanisms with a small menu size cannot ensure any positive fraction of the optimal reward of mechanisms with a larger menu size. For the multi-item setting, we show that an ordinal mechanism that only takes the owner's ordering of the items as input is not incentive-compatible. We then propose a set of Union mechanisms that combine single-item mechanisms. Moreover, we run experiments to examine these mechanisms' robustness against the independent appraiser's assessment accuracy and the items' acquiring rate.

cs.GT↗

arXiv2023

Optimal Pricing Schemes for Identical Items with Time-Sensitive Buyers

Time or money? That is a question! In this paper, we consider this dilemma in the pricing regime, in which we try to find the optimal pricing scheme for identical items with heterogenous time-sensitive buyers. We characterize the revenue-optimal solution and propose an efficient algorithm to find it in a Bayesian setting. Our results also demonstrate the tight ratio between the value of wasted time and the seller's revenue, as well as that of two common-used pricing schemes, the k-step function and the fixed pricing. To explore the nature of the optimal scheme in the general setting, we present the closed forms over the product distribution and show by examples that positive correlation between the valuation of the item and the cost per unit time could help increase revenue. To the best of our knowledge, it is the first step towards understanding the impact of the time factor as a part of the buyer cost in pricing problems, in the computational view.

cs.GT↗