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Xu Xia

Xu Xia contributes to research discovery and scholarly infrastructure.

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Published work

4 published item(s)

preprint2026arXiv

SkillMaster: Toward Autonomous Skill Mastery in LLM Agents

Skills provide an effective mechanism for improving LLM agents on complex tasks, yet in existing agent frameworks, their creation, refinement, and selection are typically governed by external teachers, hand-designed rules, or auxiliary modules. As a result, skills remain external resources to be invoked, rather than capabilities that agents can develop, adapt, and internalize through experience. To endow LLM agents with autonomous skill mastery, we propose SkillMaster, a training framework that teaches agents to create new skills, refine existing skills, and select accumulated skills during task solving. This capability is achieved through three key designs. First, we train agents through trajectory-informed skill review, teaching agents to propose, update, or retain skills based on evidence from completed episodes. Second, each candidate skill edit is designed to be evaluated by its counterfactual utility on related probe tasks, providing a direct learning signal for training skill-editing decisions. Third, we introduce DualAdv-GRPO, which separately estimates advantages for task-solving actions and skill-editing decisions, stabilizing joint training across task solving and skill management. Experiments on ALFWorld and WebShop show that SkillMaster improves the overall success rate over state-of-the-art baselines by 8.8% and 9.3%, respectively, achieving the best performance among all compared methods. Further analysis reveals a marked shift in agent capability: agents trained with SkillMaster can identify skill failures, refine procedural knowledge from trajectory evidence, and transfer improvements to future tasks with limited skill-bank edits. Overall, SkillMaster moves LLM agents beyond mere skill use toward self-improving agents capable of developing, adapting, and applying their own skill repertoires.

preprint2022arXiv

Anomalous mobility edges in one-dimensional quasiperiodic models

Mobility edges, separating localized from extended states, are known to arise in the single-particle energy spectrum of disordered systems in dimension strictly higher than two and certain quasiperiodic models in one dimension. Here we unveil a different class of mobility edges, dubbed anomalous mobility edges, that separate bands of localized states from bands of critical states in diagonal and off-diagonal quasiperiodic models. We first introduce an exactly solvable quasi-periodic diagonal model and analytically demonstrate the existence of anomalous mobility edges. Moreover, numerical multifractal analysis of the corresponding wave functions confirms the emergence of a finite band of critical states. We then extend the sudy to a quasiperiodic off-diagonal Su-Schrieffer-Heeger model and show numerical evidence of anomalous mobility edges. We finally discuss possible experimental realizations of quasi-periodic models hosting anomalous mobility edges. These results shed new light on the localization and critical properties of low-dimensional systems with aperiodic order.

preprint2022arXiv

Eigenvalues restricted by Lyapunov exponent of eigenstates

We point out that the Lyapunov exponent of the eigenstate places restrictions on the eigenvalue. Consequently, with regard to non-Hermitian systems, even without any symmetry, the non-conservative Hamiltonians can exhibit real spectra as long as Lyapunov exponents of eigenstates inhibit imaginary parts of eigenvalues. Our findings open up a new route to study non-Hermitian physics.

preprint2021arXiv

Dual-mapping and quantum criticality in off-diagonal Aubry-André models

We study a class of off-diagonal quasiperiodic hopping models described by one-dimensional Su-Schrieffer-Heeger chain with quasiperiodic modulations. We unveil a general dual-mapping relation in parameter space of the dimerization strength $λ$ and the quasiperiodic modulation strength $V$, regardless of the specific details of the quasiperiodic modulation. Moreover, we demonstrated semi-analytically and numerically that under the specific quasiperiodic modulation, quantum criticality can emerge and persist in a wide parameter space. These unusual properties provides a distinctive paradigm compared with the diagonal quasiperiodic systems.