Knowledge Tracing (KT) aims to assess students'dynamic knowledge states from their learning histories. While most existing KT methods focus on single-domain learning with notable success, real-world learning scenarios often involve multiple domains simultaneously, introducing two critical factors: 1) Cognitive load, arising from managing learning across domains in both temporal and knowledge dimensions. 2) Knowledge transfer, where knowledge states in one domain influence related states both within and across domains. In this paper, we focus on exploring these factors to improve students'knowledge state assessment in multi-domain learning scenarios and propose a novel method incorporating cognitive Load and knowledge Transfer for Multi-domain Knowledge Tracing (LT-MKT). Specifically, to bridge isolated domains, LT-MKT first integrates textual information from questions and their associated concepts to construct a Multi-domain Hierarchical Graph, leveraging the advanced representational capabilities of large language models (LLMs). Then, cross-domain features in both the temporal and knowledge dimensions are explicitly modeled to capture the effects of cognitive load. Additionally, a knowledge transfer module is designed to model the propagation of knowledge states within and across domains. By jointly modeling these factors, LT-MKT enables more accurate prediction of students'future performance. Finally, extensive experiments on real-world datasets demonstrate that our method achieves state-of-the-art performance.
Haotian Zhang, Shucun Wang, Jinze Wu et al.· 0 citations
Existing LLM-based theorem provers have achieved impressive results on formal mathematics benchmarks, yet they remain confined to acting as autonomous agents that prove a stated proposition. In this paper, we propose MathCoPilot, a human-in-the-loop system that embodies a new human--AI symbiotic paradigm for mathematical research, in which the mathematician steers the high-level mathematical direction while AI agents carry out the detailed formalization and proof work under continuous human guidance. MathCoPilot unifies three core capabilities: (1) an interactive workbench where the mathematician and AI agents collaborate through a living proof blueprint that decomposes a proof into navigable steps the human can directly inspect, direct, and refine; (2) automated proving skill orchestration with adaptive knowledge base search and Lean-integrated iterative verification; and (3) topic-driven paper retrieval and automated formalization into a verified Lean knowledge base. Using MathCoPilot, we systematically compare four state-of-the-art LLMs, including Gemini~3.1~Pro, GPT-5.4, and Claude~Opus~4.7, on a FormalMATH subset and on two real PDE theorems requiring deep domain expertise, evaluating their ability to produce verified Lean~4 proofs and to identify errors in deliberately incorrect proofs. Our results show that while current models can handle undergraduate-level problems with high success rates under favorable autoformalization conditions, substantial challenges remain for domain-specific theorems requiring genuine mathematical understanding.
Junjie Zhang, Jia-Yin Liu, Wenbin Liu et al.· 1 citation
