Recent advancements in graph learning have revolutionized the way to
understand and analyze data with complex structures. Notably, Graph Neural
Networks (GNNs), i.e. neural network architectures designed for learning graph
representations, have become a popular paradigm. With these models being
usually characterized by intuition-driven design or highly intricate
components, placing them within the theoretical analysis framework to distill
the core concepts, helps understand the key principles that drive the
functionality better and guide further development. Given this surge in
interest, this article provides a comprehensive summary of the theoretical
foundations and breakthroughs concerning the approximation and learning
behaviors intrinsic to prevalent graph learning models. Encompassing
discussions on fundamental aspects such as expressiveness power,
generalization, optimization, and unique phenomena such as over-smoothing and
over-squashing, this piece delves into the theoretical foundations and frontier
driving the evolution of graph learning. In addition, this article also
presents several challenges and further initiates discussions on possible
solutions.

图形学习的理论基础、突破和挑战以及可能的解决方案的综合概述。

图学习理论的基础与前沿

Foundations and Frontiers of Graph Learning Theory

Student simulation presents a transformative approach to enhance learning
outcomes, advance educational research, and ultimately shape the future of
effective pedagogy. We explore the feasibility of using large language models
(LLMs), a remarkable achievement in AI, to simulate student learning behaviors.
Unlike conventional machine learning based prediction, we leverage LLMs to
instantiate virtual students with specific demographics and uncover intricate
correlations among learning experiences, course materials, understanding
levels, and engagement. Our objective is not merely to predict learning
outcomes but to replicate learning behaviors and patterns of real students. We
validate this hypothesis through three experiments. The first experiment, based
on a dataset of N = 145, simulates student learning outcomes from demographic
data, revealing parallels with actual students concerning various demographic
factors. The second experiment (N = 4524) results in increasingly realistic
simulated behaviors with more assessment history for virtual students
modelling. The third experiment (N = 27), incorporating prior knowledge and
course interactions, indicates a strong link between virtual students' learning
behaviors and fine-grained mappings from test questions, course materials,
engagement and understanding levels. Collectively, these findings deepen our
understanding of LLMs and demonstrate its viability for student simulation,
empowering more adaptable curricula design to enhance inclusivity and
educational effectiveness.

利用大型语言模型模拟学生学习行为，揭示学习行为与测试问题、课程材料、参与度和理解水平之间的关联，加深我们对大型语言模型的理解，展示其对学生模拟的可行性，从而为更具适应性的课程设计提供支持，增强包容性和教育效果。