Learning path recommendation aims to provide learners with a reasonable order of items to achieve their learning goals. Intuitively, the learning process on the learning path can be metaphorically likened to walking. Despite extensive efforts in this area, most previous methods mainly focus on the relationship among items but overlook the difficulty of items, which may raise two issues from a real walking perspective: (1) The path may be rough: When learners tread the path without considering item difficulty, it's akin to walking a dark, uneven road, making learning harder and dampening interest. (2) The path may be inefficient: Allowing learners only a few attempts on very challenging items before switching, or persisting with a difficult item despite numerous attempts without mastery, can result in inefficiencies in the learning journey. To conquer the above limitations, we propose a novel method named Difficulty-constrained Learning Path Recommendation (DLPR), which is aware of item difficulty. Specifically, we first explicitly categorize items into learning items and practice items, then construct a hierarchical graph to model and leverage item difficulty adequately. Then we design a Difficulty-driven Hierarchical Reinforcement Learning (DHRL) framework to facilitate learning paths with efficiency and smoothness. Finally, extensive experiments on three different simulators demonstrate our framework achieves state-of-the-art performance.

Student knowledge profile is the basis for adaptive learning applications in online learning resulting from modeling the student mastery of knowledge concepts. In recent years, typical works based on knowledge tracing (KT) expect to profile students and have achieved significant success for the next performance prediction. However, in practical online learning scenarios, current methods tend to suffer from the following challenges: 1) Prediction inconsistency: The accuracy of the next performance prediction is inconsistent with the accuracy of student knowledge profile prediction, which is the more required result. 2) Cold start of knowledge: In online learning scenarios, it is often necessary to profile some knowledge concepts without learning records in advance. In this paper, we propose a novel Graph-based Student Knowledge Profile Model (GSKPM), along with a new end-to-end training objective, to tackle these challenges. We first define a new training objective to ensure the model is capable of inferring consistent student knowledge profiles. Then in this model, a two-stage hyper-aggregation process is employed to make full use of the topological relations between knowledge concepts and knowledge domains to provide information during profiling, especially for cold start knowledge concepts. Finally, through extensive experiments on real-world datasets, we will show that GSKPM achieves better prediction performances on student knowledge profiles and well deals with the cold start problem.

Unsupervised semantic hashing has emerged as an indispensable technique for fast image search, which aims to convert images into binary hash codes without relying on labels. Recent advancements in the field demonstrate that employing large-scale backbones (e.g., ViT) in unsupervised semantic hashing models can yield substantial improvements. However, the inference delay has become increasingly difficult to overlook. Knowledge distillation provides a means for practical model compression to alleviate this delay. Nevertheless, the prevailing knowledge distillation approaches are not explicitly designed for semantic hashing. They ignore the unique search paradigm of semantic hashing, the inherent necessities of the distillation process, and the property of hash codes. In this paper, we propose an innovative Bit-mask Robust Contrastive knowledge Distillation (BRCD) method, specifically devised for the distillation of semantic hashing models. To ensure the effectiveness of two kinds of search paradigms in the context of semantic hashing, BRCD first aligns the semantic spaces between the teacher and student models through a contrastive knowledge distillation objective. Additionally, to eliminate noisy augmentations and ensure robust optimization, a cluster-based method within the knowledge distillation process is introduced. Furthermore, through a bit-level analysis, we uncover the presence of redundancy bits resulting from the bit independence property. To mitigate these effects, we introduce a bit mask mechanism in our knowledge distillation objective. Finally, extensive experiments not only showcase the noteworthy performance of our BRCD method in comparison to other knowledge distillation methods but also substantiate the generality of our methods across diverse semantic hashing models and backbones. The code for BRCD is available at https://github.com/hly1998/BRCD.

Although pre-trained language models~(PLMs) have recently advanced the research progress in mathematical reasoning, they are not specially designed as a capable multi-task solver, suffering from high cost for multi-task deployment (e.g. a model copy for a task) and inferior performance on complex mathematical problems in practical applications. To address these issues, we propose JiuZhang 2.0, a unified Chinese PLM specially for multi-task mathematical problem solving. Our idea is to maintain a moderate-sized model and employ the cross-task knowledge sharing to improve the model capacity in a multi-task setting. Specially, we construct a Mixture-of-Experts (MoE) architecture for modeling mathematical text, to capture the common mathematical knowledge across tasks. For optimizing the MoE architecture, we design multi-task continual pre-training and multi-task fine-tuning strategies for multi-task adaptation. These training strategies can effectively decompose the knowledge from the task data and establish the cross-task sharing via expert networks. To further improve the general capacity of solving different complex tasks, we leverage large language models (LLMs) as complementary models to iteratively refine the generated solution by our PLM, via in-context learning. Extensive experiments have demonstrated the effectiveness of our model.

This paper aims to advance the mathematical intelligence of machines by presenting the first Chinese mathematical pre-trained language model (PLM) for effectively understanding and representing mathematical problems. Unlike other standard NLP tasks, mathematical texts are difficult to understand, since they involve mathematical terminology, symbols and formulas in the problem statement. Typically, it requires complex mathematical logic and background knowledge for solving mathematical problems.