Sparse Binary Representation Learning for Knowledge Tracing
Yahya Badran, Christine Preisach
TL;DR
The paper tackles the problem that knowledge tracing models rely on potentially incomplete human-defined KCs. It proposes SBRKT, which learns a sparse binary vector $\mathbf{a} \in \{0,1\}^A$ of auxiliary KCs for each exercise, and integrates these with existing KCs through an RNN to predict future student performance. A binarization-based, fully trainable encoder yields discrete auxiliary KCs that are compatible with both Bayesian (e.g., BKT with forgetting, $P(F)$) and deep learning (e.g., DKT) KT models. Empirical results on multiple datasets show that auxiliary KCs improve predictive accuracy across baselines and consistently bolster BKT performance, highlighting the method's practical value for augmenting traditional KT frameworks without relying solely on human-labeled concepts.
Abstract
Knowledge tracing (KT) models aim to predict students' future performance based on their historical interactions. Most existing KT models rely exclusively on human-defined knowledge concepts (KCs) associated with exercises. As a result, the effectiveness of these models is highly dependent on the quality and completeness of the predefined KCs. Human errors in labeling and the cost of covering all potential underlying KCs can limit model performance. In this paper, we propose a KT model, Sparse Binary Representation KT (SBRKT), that generates new KC labels, referred to as auxiliary KCs, which can augment the predefined KCs to address the limitations of relying solely on human-defined KCs. These are learned through a binary vector representation, where each bit indicates the presence (one) or absence (zero) of an auxiliary KC. The resulting discrete representation allows these auxiliary KCs to be utilized in training any KT model that incorporates KCs. Unlike pre-trained dense embeddings, which are limited to models designed to accept such vectors, our discrete representations are compatible with both classical models, such as Bayesian Knowledge Tracing (BKT), and modern deep learning approaches. To generate this discrete representation, SBRKT employs a binarization method that learns a sparse representation, fully trainable via stochastic gradient descent. Additionally, SBRKT incorporates a recurrent neural network (RNN) to capture temporal dynamics and predict future student responses by effectively combining the auxiliary and predefined KCs. Experimental results demonstrate that SBRKT outperforms the tested baselines on several datasets and achieves competitive performance on others. Furthermore, incorporating the learned auxiliary KCs consistently enhances the performance of BKT across all tested datasets.