Tiancheng Zhang

Hengyu Liu, Qiang Fu, Lun Du et al.

Learning rate is one of the most important hyper-parameters that has a significant influence on neural network training. Learning rate schedules are widely used in real practice to adjust the learning rate according to pre-defined schedules for fast convergence and good generalization. However, existing learning rate schedules are all heuristic algorithms and lack theoretical support. Therefore, people usually choose the learning rate schedules through multiple ad-hoc trials, and the obtained learning rate schedules are sub-optimal. To boost the performance of the obtained sub-optimal learning rate schedule, we propose a generic learning rate schedule plugin, called LEArning Rate Perturbation (LEAP), which can be applied to various learning rate schedules to improve the model training by introducing a certain perturbation to the learning rate. We found that, with such a simple yet effective strategy, training processing exponentially favors flat minima rather than sharp minima with guaranteed convergence, which leads to better generalization ability. In addition, we conduct extensive experiments which show that training with LEAP can improve the performance of various deep learning models on diverse datasets using various learning rate schedules (including constant learning rate).

Hengyu Liu, Tiancheng Zhang, Fan Li et al.

Knowledge tracing aims to track students' knowledge status over time to predict students' future performance accurately. Markov chain-based knowledge tracking (MCKT) models can track knowledge concept mastery probability over time. However, as the number of tracked knowledge concepts increases, the time complexity of MCKT predicting student performance increases exponentially (also called explaining away problem. In addition, the existing MCKT models only consider the relationship between students' knowledge status and problems when modeling students' responses but ignore the relationship between knowledge concepts in the same problem. To address these challenges, we propose an inTerpretable pRobAbilistiC gEnerative moDel (TRACED), which can track students' numerous knowledge concepts mastery probabilities over time. To solve \emph{explain away problem}, we design Long and Short-Term Memory (LSTM)-based networks to approximate the posterior distribution, predict students' future performance, and propose a heuristic algorithm to train LSTMs and probabilistic graphical model jointly. To better model students' exercise responses, we proposed a logarithmic linear model with three interactive strategies, which models students' exercise responses by considering the relationship among students' knowledge status, knowledge concept, and problems. We conduct experiments with four real-world datasets in three knowledge-driven tasks. The experimental results show that TRACED outperforms existing knowledge tracing methods in predicting students' future performance and can learn the relationship among students, knowledge concepts, and problems from students' exercise sequences. We also conduct several case studies. The case studies show that TRACED exhibits excellent interpretability and thus has the potential for personalized automatic feedback in the real-world educational environment.

Hui Chen, Hengyu Liu, Longbing Cao et al.

Bayesian personalized federated learning (BPFL) addresses challenges in existing personalized FL (PFL). BPFL aims to quantify the uncertainty and heterogeneity within and across clients towards uncertainty representations by addressing the statistical heterogeneity of client data. In PFL, some recent preliminary work proposes to decompose hidden neural representations into shared and local components and demonstrates interesting results. However, most of them do not address client uncertainty and heterogeneity in FL systems, while appropriately decoupling neural representations is challenging and often ad hoc. In this paper, we make the first attempt to introduce a general BPFL framework to decompose and jointly learn shared and personalized uncertainty representations on statistically heterogeneous client data over time. A Bayesian federated neural network BPFed instantiates BPFL by jointly learning cross-client shared uncertainty and client-specific personalized uncertainty over statistically heterogeneous and randomly participating clients. We further involve continual updating of prior distribution in BPFed to speed up the convergence and avoid catastrophic forgetting. Theoretical analysis and guarantees are provided in addition to the experimental evaluation of BPFed against the diversified baselines.

Wangyue Lu, Lun Du, Sirui Li et al.

Interactive theorem provers (ITPs) require manual formalization, which is labor-intensive and demands expert knowledge. While automated formalization offers a potential solution, it faces two major challenges: model hallucination (e.g., undefined predicates, symbol misuse, and version incompatibility) and the semantic gap caused by ambiguous or missing premises in natural language descriptions. To address these issues, we propose CRAMF, a Concept-driven Retrieval-Augmented Mathematical Formalization framework. CRAMF enhances LLM-based autoformalization by retrieving formal definitions of core mathematical concepts, providing contextual grounding during code generation. However, applying retrieval-augmented generation (RAG) in this setting is non-trivial due to the lack of structured knowledge bases, the polymorphic nature of mathematical concepts, and the high precision required in formal retrieval. We introduce a framework for automatically constructing a concept-definition knowledge base from Mathlib4, the standard mathematical library for the Lean 4 theorem prover, indexing over 26,000 formal definitions and 1,000+ core mathematical concepts. To address conceptual polymorphism, we propose contextual query augmentation with domain- and application-level signals. In addition, we design a dual-channel hybrid retrieval strategy with reranking to ensure accurate and relevant definition retrieval. Experiments on miniF2F, ProofNet, and our newly proposed AdvancedMath benchmark show that CRAMF can be seamlessly integrated into LLM-based autoformalizers, yielding consistent improvements in translation accuracy, achieving up to 62.1% and an average of 29.9% relative improvement.

Hengyu Liu, Yushuai Li, Minghe Yu et al.

Intelligent Tutoring Systems (ITS), such as Massive Open Online Courses, offer new opportunities for human learning. At the core of such systems, knowledge tracing (KT) predicts students' future performance by analyzing their historical learning activities, enabling an accurate evaluation of students' knowledge states over time. We show that existing KT methods often encounter correlation conflicts when analyzing the relationships between historical learning sequences and future performance. To address such conflicts, we propose to extract so-called Follow-up Performance Trends (FPTs) from historical ITS data and to incorporate them into KT. We propose a method called Forward-Looking Knowledge Tracing (FINER) that combines historical learning sequences with FPTs to enhance student performance prediction accuracy. FINER constructs learning patterns that facilitate the retrieval of FPTs from historical ITS data in linear time; FINER includes a novel similarity-aware attention mechanism that aggregates FPTs based on both frequency and contextual similarity; and FINER offers means of combining FPTs and historical learning sequences to enable more accurate prediction of student future performance. Experiments on six real-world datasets show that FINER can outperform ten state-of-the-art KT methods, increasing accuracy by 8.74% to 84.85%.