{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,4]],"date-time":"2026-08-04T15:22:11Z","timestamp":1785856931621,"version":"3.56.0"},"reference-count":51,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,6,26]],"date-time":"2025-06-26T00:00:00Z","timestamp":1750896000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62207013"],"award-info":[{"award-number":["62207013"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Knowledge tracing (KT) models learners\u2019 evolving knowledge states to predict future performance, serving as a fundamental component in personalized education systems. However, existing methods suffer from data sparsity challenges, resulting in inadequate representation quality for low-frequency knowledge concepts and inconsistent modeling of students\u2019 actual knowledge states. To address this challenge, we propose Dual-Encoder Contrastive Knowledge Tracing (DECKT), a contrastive learning framework that improves knowledge state representation under sparse data conditions. DECKT employs a momentum-updated dual-encoder architecture where the primary encoder processes current input data while the momentum encoder maintains stable historical representations through exponential moving average updates. These encoders naturally form contrastive pairs through temporal evolution, effectively enhancing representation capabilities for low-frequency knowledge concepts without requiring destructive data augmentation operations that may compromise knowledge structure integrity. To preserve semantic consistency in learned representations, DECKT incorporates a graph structure constraint loss that leverages concept\u2013question relationships to maintain appropriate similarities between related concepts in the embedding space. Furthermore, an adversarial training mechanism applies perturbations to embedding vectors, enhancing model robustness and generalization. Extensive experiments on benchmark datasets demonstrate that DECKT significantly outperforms existing state-of-the-art methods, validating the effectiveness of the proposed approach in alleviating representation challenges in sparse educational data.<\/jats:p>","DOI":"10.3390\/e27070685","type":"journal-article","created":{"date-parts":[[2025,6,27]],"date-time":"2025-06-27T03:33:25Z","timestamp":1750995205000},"page":"685","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Dual-Encoder Contrastive Learning Model for Knowledge Tracing"],"prefix":"10.3390","volume":"27","author":[{"given":"Yanhong","family":"Bai","sequence":"first","affiliation":[{"name":"Laboratory of AI for Education, East China Normal University, Shanghai 200062, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xingjiao","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Pharmacy, East China Normal University, Shanghai 200062, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tingjiang","family":"Wei","sequence":"additional","affiliation":[{"name":"Laboratory of AI for Education, East China Normal University, Shanghai 200062, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4723-5486","authenticated-orcid":false,"given":"Liang","family":"He","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, East China Normal University, Shanghai 200062, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"100110","DOI":"10.1016\/j.caeai.2022.100110","article-title":"AI-based learning content generation and learning pathway augmentation to increase learner engagement","volume":"4","author":"Diwan","year":"2023","journal-title":"Comput. Educ. Artif. Intell."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1186\/s40561-020-00140-9","article-title":"A systematic literature review of personalized learning terms","volume":"7","author":"Shemshack","year":"2020","journal-title":"Smart Learn. Environ."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"108766","DOI":"10.1016\/j.engappai.2024.108766","article-title":"UIFRS-HAN: User interests-aware food recommender system based on the heterogeneous attention network","volume":"135","author":"Forouzandeh","year":"2024","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"127326","DOI":"10.1016\/j.neucom.2024.127326","article-title":"A novel healthy food recommendation to user groups based on a deep social community detection approach","volume":"576","author":"Rostami","year":"2024","journal-title":"Neurocomputing"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"100025","DOI":"10.1016\/j.caeai.2021.100025","article-title":"AI technologies for education: Recent research & future directions","volume":"2","author":"Zhang","year":"2021","journal-title":"Comput. Educ. Artif. Intell."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1007\/s40593-021-00270-2","article-title":"Education for AI, not AI for education: The role of education and ethics in national AI policy strategies","volume":"32","author":"Schiff","year":"2022","journal-title":"Int. J. Artif. Intell. Educ."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"6483","DOI":"10.1007\/s10489-024-05509-8","article-title":"A survey of explainable knowledge tracing","volume":"54","author":"Bai","year":"2024","journal-title":"Appl. Intell."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3569576","article-title":"Knowledge tracing: A survey","volume":"55","author":"Abdelrahman","year":"2023","journal-title":"ACM Comput. Surv."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1007\/BF01099821","article-title":"Knowledge tracing: Modeling the acquisition of procedural knowledge","volume":"4","author":"Corbett","year":"1994","journal-title":"User Model. User-Adapt. Interact."},{"key":"ref_10","unstructured":"Pandey, S., and Karypis, G. (2019, January 2\u20135). A Self-Attentive Model for Knowledge Tracing. Proceedings of the 12th International Conference on Educational Data Mining, Montreal, QC, Canada."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Zhang, J., Shi, X., King, I., and Yeung, D.Y. (2017, January 3\u20137). Dynamic Key-Value Memory Networks for Knowledge Tracing. Proceedings of the 26th International Conference on World Wide Web, Perth, Australia.","DOI":"10.1145\/3038912.3052580"},{"key":"ref_12","first-page":"2236","article-title":"Deep knowledge tracing","volume":"28","author":"Piech","year":"2015","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Yang, Y., Shen, J., Qu, Y., Liu, Y., Wang, K., Zhu, Y., Zhang, W., and Yu, Y. (2021, January 13\u201317). GIKT: A Graph-Based Interaction Model for Knowledge Tracing. Proceedings of the Machine Learning and Knowledge Discovery in Databases: European Conference, Bilbao, Spain.","DOI":"10.1007\/978-3-030-67658-2_18"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Nakagawa, H., Iwasawa, Y., and Matsuo, Y. (2019, January 14\u201317). Graph-Based Knowledge Tracing: Modeling Student Proficiency Using Graph Neural Network. Proceedings of the IEEE\/WIC\/ACM International Conference on Web Intelligence, Thessaloniki, Greece.","DOI":"10.1145\/3350546.3352513"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Liu, Y., Yang, Y., Chen, X., Shen, J., Zhang, H., and Yu, Y. (2020). Improving knowledge tracing via pre-training question embeddings. arXiv.","DOI":"10.24963\/ijcai.2020\/219"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2012","DOI":"10.1002\/int.22763","article-title":"Knowledge structure enhanced graph representation learning model for attentive knowledge tracing","volume":"37","author":"Gan","year":"2022","journal-title":"Int. J. Intell. Syst."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Zhang, T., He, S., Dai, T., Wang, Z., Chen, B., and Xia, S.T. (2024, January 20\u201327). Vision-Language Pre-Training with Object Contrastive Learning for 3D Scene Understanding. Proceedings of the AAAI Conference on Artificial Intelligence, Vancouver, BC, Canada.","DOI":"10.1609\/aaai.v38i7.28559"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Liu, J., and Chen, S. (2024, January 20\u201327). Timesurl: Self-Supervised Contrastive Learning for Universal Time Series Representation Learning. Proceedings of the AAAI Conference on Artificial Intelligence, Vancouver, BC, Canada.","DOI":"10.1609\/aaai.v38i12.29299"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Xu, X., Dong, H., Qi, L., Zhang, X., Xiang, H., Xia, X., Xu, Y., and Dou, W. (2024, January 14\u201318). Cmclrec: Cross-Modal Contrastive Learning for User Cold-Start Sequential Recommendation. Proceedings of the 47th International ACM SIGIR Conference on Research and Development in Information Retrieval, Washington, DC, USA.","DOI":"10.1145\/3626772.3657839"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"108274","DOI":"10.1016\/j.knosys.2022.108274","article-title":"Bi-CLKT: Bi-graph contrastive learning based knowledge tracing","volume":"241","author":"Song","year":"2022","journal-title":"Knowl. Based Syst."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Lee, W., Chun, J., Lee, Y., Park, K., and Park, S. (2022, January 25\u201329). Contrastive Learning for Knowledge Tracing. Proceedings of the ACM Web Conference 2022, Lyon, France.","DOI":"10.1145\/3485447.3512105"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1016\/j.ins.2022.12.075","article-title":"Self-supervised heterogeneous hypergraph network for knowledge tracing","volume":"624","author":"Wu","year":"2023","journal-title":"Inf. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2838","DOI":"10.1109\/TCE.2023.3293953","article-title":"Weighted heterogeneous graph-based three-view contrastive learning for knowledge tracing in personalized e-learning systems","volume":"70","author":"Sun","year":"2023","journal-title":"IEEE Trans. Consum. Electron."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Yin, Y., Dai, L., Huang, Z., Shen, S., Wang, F., Liu, Q., Chen, E., and Li, X. (May, January 30). Tracing Knowledge Instead of Patterns: Stable Knowledge Tracing with Diagnostic Transformer. Proceedings of the ACM Web Conference 2023, Austin, TX, USA.","DOI":"10.1145\/3543507.3583255"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"He, K., Fan, H., Wu, Y., Xie, S., and Girshick, R. (2020, January 14\u201319). Momentum Contrast for Unsupervised Visual Representation Learning. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Seattle, WA, USA.","DOI":"10.1109\/CVPR42600.2020.00975"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Ghosh, A., Heffernan, N., and Lan, A.S. (2020, January 23\u201327). Context-Aware Attentive Knowledge Tracing. Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, Online.","DOI":"10.1145\/3394486.3403282"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1109\/TLT.2024.3521898","article-title":"AAKT: Enhancing Knowledge Tracing with Alternate Autoregressive Modeling","volume":"18","author":"Zhou","year":"2024","journal-title":"IEEE Trans. Learn. Technol."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"125988","DOI":"10.1016\/j.eswa.2024.125988","article-title":"csKT: Addressing cold-start problem in knowledge tracing via kernel bias and cone attention","volume":"266","author":"Bai","year":"2025","journal-title":"Expert Syst. Appl."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Pandey, S., and Srivastava, J. (2020, January 19\u201323). RKT: Relation-Aware Self-Attention for Knowledge Tracing. Proceedings of the 29th ACM International Conference on Information & Knowledge Management, Online.","DOI":"10.1145\/3340531.3411994"},{"key":"ref_30","unstructured":"Tong, H., Zhou, Y., and Wang, Z. (2020). HGKT: Introducing problem schema with hierarchical exercise graph for knowledge tracing. arXiv."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"117681","DOI":"10.1016\/j.eswa.2022.117681","article-title":"SGKT: Session graph-based knowledge tracing for student performance prediction","volume":"206","author":"Wu","year":"2022","journal-title":"Expert Syst. Appl."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"510","DOI":"10.1016\/j.ins.2021.08.100","article-title":"Jkt: A joint graph convolutional network based deep knowledge tracing","volume":"580","author":"Song","year":"2021","journal-title":"Inf. Sci."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2108","DOI":"10.1109\/JAS.2023.123678","article-title":"GraphCA: Learning from graph counterfactual augmentation for knowledge tracing","volume":"10","author":"Wang","year":"2023","journal-title":"IEEE\/CAA J. Autom. Sin."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2967","DOI":"10.1109\/TKDE.2023.3329238","article-title":"Dynamic Graph Embedding via Meta-Learning","volume":"36","author":"Mao","year":"2023","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"126838","DOI":"10.1016\/j.eswa.2025.126838","article-title":"Learning states enhanced Knowledge Tracing: Simulating the diversity in real-world learning process","volume":"274","author":"Wang","year":"2025","journal-title":"Expert Syst. Appl."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Wang, J., Tang, Q., and Zheng, Z. (2025). A knowledge tracing approach with dual graph convolutional networks and positive\/negative feature enhancement network. PLoS ONE, 20.","DOI":"10.1371\/journal.pone.0317992"},{"key":"ref_37","unstructured":"Lee, U., Yoon, S., Yun, J.S., Park, K., Jung, Y., Stratton, D., and Kim, H. (2024, January 20\u201325). Difficulty-Focused Contrastive Learning for Knowledge Tracing with a Large Language Model-Based Difficulty Prediction. Proceedings of the 2024 Joint International Conference on Computational Linguistics, Language Resources and Evaluation (LREC-COLING 2024), Torino, Italy."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Guo, Y., Shen, S., Liu, Q., Huang, Z., Zhu, L., Su, Y., and Chen, E. (2024, January 21\u201325). Mitigating Cold-Start Problems in Knowledge Tracing with Large Language Models: An Attribute-Aware Approach. Proceedings of the 33rd ACM International Conference on Information and Knowledge Management, Boise, ID, USA.","DOI":"10.1145\/3627673.3679664"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Fu, L., Guan, H., Du, K., Lin, J., Xia, W., Zhang, W., Tang, R., Wang, Y., and Yu, Y. (2024, January 21\u201325). Sinkt: A Structure-Aware Inductive Knowledge Tracing Model with Large Language Model. Proceedings of the 33rd ACM International Conference on Information and Knowledge Management, Boise, ID, USA.","DOI":"10.1145\/3627673.3679760"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"113396","DOI":"10.1016\/j.knosys.2025.113396","article-title":"Harnessing code domain insights: Enhancing programming knowledge tracing with large language models","volume":"317","author":"Sun","year":"2025","journal-title":"Knowl. Based Syst."},{"key":"ref_41","unstructured":"Chen, T., Kornblith, S., Norouzi, M., and Hinton, G. (2020, January 13\u201318). A Simple Framework for Contrastive Learning of Visual Representations. Proceedings of the International Conference on Machine Learning, Online."},{"key":"ref_42","unstructured":"Velickovic, P., Fedus, W., Hamilton, W.L., Li\u00f2, P., Bengio, Y., and Hjelm, R.D. (2019, January 6\u20139). Deep Graph Infomax. Proceedings of the ICLR 2019, New Orleans, LA, USA."},{"key":"ref_43","unstructured":"Zhu, Y., Xu, Y., Yu, F., Liu, Q., Wu, S., and Wang, L. (2020). Deep graph contrastive representation learning. arXiv."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"128366","DOI":"10.1016\/j.neucom.2024.128366","article-title":"Self-paced contrastive learning for knowledge tracing","volume":"609","author":"Dai","year":"2024","journal-title":"Neurocomputing"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Xu, L., Guo, L., Wu, X., Wang, X., and Guo, L. (2024, January 5\u20138). Knowledge Tracing with Contrastive Learning and Attention-Based Long Short-Term Memory Network. Proceedings of the International Conference on Intelligent Computing, Tianjin, China.","DOI":"10.1007\/978-981-97-5591-2_3"},{"key":"ref_46","unstructured":"Arora, S., Liang, Y., and Ma, T. (2019, January 9\u201315). A Theoretical Analysis of Contrastive Unsupervised Representation Learning. Proceedings of the ICML, Long Beach, CA, USA."},{"key":"ref_47","unstructured":"Yeung, C.K. (2019). Deep-IRT: Make deep learning based knowledge tracing explainable using item response theory. arXiv."},{"key":"ref_48","unstructured":"Vie, J.J., and Kashima, H. (February, January 27). Knowledge Tracing Machines: Factorization Machines for Knowledge Tracing. Proceedings of the AAAI Conference on Artificial Intelligence, Honolulu, HI, USA."},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Wang, C., Ma, W., Zhang, M., Lv, C., Wan, F., Lin, H., Tang, T., Liu, Y., and Ma, S. (2021, January 8\u201312). Temporal Cross-Effects in Knowledge Tracing. Proceedings of the 14th ACM International Conference on Web Search and Data Mining, Online.","DOI":"10.1145\/3437963.3441802"},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Dai, H., Yun, Y., Zhang, Y., Zhang, W., and Shang, X. (2022, January 27\u201331). Contrastive Deep Knowledge Tracing. Proceedings of the International Conference on Artificial Intelligence in Education, Durham, UK.","DOI":"10.1007\/978-3-031-11647-6_54"},{"key":"ref_51","unstructured":"Forouzandeh, S., DW, P.M., and Jalili, M. (2025, January 24\u201328). DistillHGNN: A Knowledge Distillation Approach for High-Speed Hypergraph Neural Networks. Proceedings of the Thirteenth International Conference on Learning Representations, Singapore."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/7\/685\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:59:32Z","timestamp":1760032772000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/7\/685"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,26]]},"references-count":51,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2025,7]]}},"alternative-id":["e27070685"],"URL":"https:\/\/doi.org\/10.3390\/e27070685","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,6,26]]}}}