arXiv subjects

Rui Jia

Publications and source records attributed to Rui Jia.

7 recordsLinked to original sources

arXiv2026

The subsonic limit of the 3D Zakharov system

We obtain the optimal convergence rates in the subsonic limit of the three-dimensional Zakharov system for initial data belonging to the low-regularity Sobolev space $\HH^s=H^s\times H^{s-1}\times H^{s-1}$. For the Schr\"odinger component, we prove first-order convergence in $L^2$ for initial data in $\HH^3$, and second-order convergence under the compatibility condition for data in $\HH^4$. For the wave component, we obtain first-order convergence in $L^2$ for data in $\HH^3$ and second-order convergence for data in $\HH^4$. The obtained rates are optimal and coincide with those predicted by the formal asymptotic expansion. No localization assumptions, smallness or high-order regularity hypotheses are required. This improves all previous results on the subsonic limit of the Zakharov system and resolves the optimality issue at the Sobolev regularity level. The proof relies on a uniform local well-posedness theory that remains valid in the subsonic limit. A key ingredient is a refined normal form analysis combined with bilinear Strichartz estimates in atomic function spaces, which allows us to fully exploit the dispersive structure of the Zakharov system at low regularity and to overcome the derivative losses arising from the singular coupling.

math.AP↗

arXiv2026

CASTLE: A Comprehensive Benchmark for Evaluating Student-Tailored Personalized Safety in Large Language Models

Large language models (LLMs) have advanced the development of personalized learning in education. However, their inherent generation mechanisms often produce homogeneous responses to identical prompts. This one-size-fits-all mechanism overlooks the substantial heterogeneity in students cognitive and psychological, thereby posing potential safety risks to vulnerable groups. Existing safety evaluations primarily rely on context-independent metrics such as factual accuracy, bias, or toxicity, which fail to capture the divergent harms that the same response might cause across different student attributes. To address this gap, we propose the concept of Student-Tailored Personalized Safety and construct CASTLE based on educational theories. This benchmark covers 15 educational safety risks and 14 student attributes, comprising 92,908 bilingual scenarios. We further design three evaluation metrics: Risk Sensitivity, measuring the model ability to detect risks; Emotional Empathy, evaluating the model capacity to recognize student states; and Student Alignment, assessing the match between model responses and student attributes. Experiments on 18 SOTA LLMs demonstrate that CASTLE poses a significant challenge: all models scored below an average safety rating of 2.3 out of 5, indicating substantial deficiencies in personalized safety assurance.

cs.CL↗

arXiv2026

Logic-Oriented Retriever Enhancement via Contrastive Learning

Large language models (LLMs) struggle in knowledge-intensive tasks, as retrievers often overfit to surface similarity and fail on queries involving complex logical relations. The capacity for logical analysis is inherent in model representations but remains underutilized in standard training. LORE (Logic ORiented Retriever Enhancement) introduces fine-grained contrastive learning to activate this latent capacity, guiding embeddings toward evidence aligned with logical structure rather than shallow similarity. LORE requires no external upervision, resources, or pre-retrieval analysis, remains index-compatible, and consistently improves retrieval utility and downstream generation while maintaining efficiency. The datasets and code are publicly available at https://github.com/mazehart/Lore-RAG.

cs.CL↗

arXiv2025

EduAgentQG: Multi-Agent Personalized Mathematics Question Generation with Explicit Diversity and Objective-Aware Evaluation

In intelligent education, personalized mathematics question generation aims to produce mathematics questions that satisfy educational requirements while supporting adaptive assessment and learning. Existing LLM-based single-agent and multi-agent methods improve generation flexibility, but they still tend to rely on aggregated feedback or model randomness, making it difficult to jointly ensure dimension-wise objective alignment and controllable diversity. To address these challenges, we propose EduAgentQG, a multi-agent collaborative framework for personalized mathematics question generation with explicit diversity and objective-aware evaluation. EduAgentQG organizes question generation as a closed-loop process of planning, writing, evaluation, refinement, and checking: structured generation plans and multiple generation directions guide candidate generation, while fine-grained evaluation verifies logical correctness, solvability, and objective alignment in knowledge concepts, difficulty, grade level, and core competencies. We first construct a mathematics question generation benchmark containing 10,273 questions across Grades 1-9, covering 634 knowledge concepts, 16 core competencies, and three difficulty levels; for evaluation, it is organized into two subsets: MathChoice, with 489 educational objectives for multiple-choice question generation, and MathBlank, with 500 educational objectives for fill-in-the-blank question generation. Experiments show that EduAgentQG consistently outperforms COT, COT$_N$, ReAct, and EQPR in diversity, Objective Consistency, and Win Rate.

cs.CY↗

arXiv2025

DiaCDM: Cognitive Diagnosis in Teacher-Student Dialogues using the Initiation-Response-Evaluation Framework

While cognitive diagnosis (CD) effectively assesses students' knowledge mastery from structured test data, applying it to real-world teacher-student dialogues presents two fundamental challenges. Traditional CD models lack a suitable framework for handling dynamic, unstructured dialogues, and it's difficult to accurately extract diagnostic semantics from lengthy dialogues. To overcome these hurdles, we propose DiaCDM, an innovative model. We've adapted the initiation-response-evaluation (IRE) framework from educational theory to design a diagnostic framework tailored for dialogue. We also developed a unique graph-based encoding method that integrates teacher questions with relevant knowledge components to capture key information more precisely. To our knowledge, this is the first exploration of cognitive diagnosis in a dialogue setting. Experiments on three real-world dialogue datasets confirm that DiaCDM not only significantly improves diagnostic accuracy but also enhances the results' interpretability, providing teachers with a powerful tool for assessing students' cognitive states. The code is available at https://github.com/Mind-Lab-ECNU/DiaCDM/tree/main.

cs.CL↗

arXiv2024

The Advancement of Personalized Learning Potentially Accelerated by Generative AI

The rapid development of Generative AI (GAI) has sparked revolutionary changes across various aspects of education. Personalized learning, a focal point and challenge in educational research, has also been influenced by the development of GAI. To explore GAI's extensive impact on personalized learning, this study investigates its potential to enhance various facets of personalized learning through a thorough analysis of existing research. The research comprehensively examines GAI's influence on personalized learning by analyzing its application across different methodologies and contexts, including learning strategies, paths, materials, environments, and specific analyses within the teaching and learning processes. Through this in-depth investigation, we find that GAI demonstrates exceptional capabilities in providing adaptive learning experiences tailored to individual preferences and needs. Utilizing different forms of GAI across various subjects yields superior learning outcomes. The article concludes by summarizing scenarios where GAI is applicable in educational processes and discussing strategies for leveraging GAI to enhance personalized learning, aiming to guide educators and learners in effectively utilizing GAI to achieve superior learning objectives.

cs.AI↗

arXiv2023

Instability of the solitary waves for the Generalized Benjamin-Bona-Mahony Equation

In this work, we consider the generalized Benjamin-Bona-Mahony equation $$\partial_t u+\partial_x u+\partial_x( |u|^pu)-\partial_t \partial_x^{2}u=0, \quad(t,x) \in \mathbb{R} \times \mathbb{R}, $$ with $p>4$. This equation has the traveling wave solutions $\phi_{c}(x-ct), $ for any frequency $c>1.$ It has been proved by Souganidis and Strauss \cite{Strauss-1990} that, there exists a number $c_{0}(p)>1$, such that solitary waves $\phi_{c}(x-ct)$ with $1 c_{0}(p), $ $\phi_{c}(x-ct)$ is orbitally stable. The linear exponential instability in the former case was further proved by Pego and Weinstein \cite{Pego-1991-eigenvalue}. In this paper, we prove the orbital instability in the critical case $c=c_{0}(p)$.

math.AP↗