{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T09:15:15Z","timestamp":1774862115941,"version":"3.50.1"},"reference-count":29,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T00:00:00Z","timestamp":1774396800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Morocco\u2019s Ministry of Education, Ministry of Industry, and the Digital Development Agency","award":["451\/2020"],"award-info":[{"award-number":["451\/2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Knowledge Tracing (KT) is a fundamental task in intelligent education systems, designed to track students\u2019 evolving knowledge states and predict their future performance. While Deep Learning-based Knowledge Tracing (DLKT) models have advanced the field, they often face significant limitations in jointly capturing short-term performance fluctuations and long-term knowledge retention, which restricts their predictive precision in complex learning trajectories. This paper proposes the Extended Deep Knowledge Tracing (xDKT) model, which integrates the Extended Long Short-Term Memory (xLSTM) architecture to enhance multi-scale temporal learning representations. Specifically, through rigorous ablation studies over extended learning sequences (up to 1000 steps), our analysis indicates that the exponential gating and advanced scalar memory of sLSTM units are the primary drivers of performance. This architecture effectively captures both short-term performance shifts and long-term knowledge retention without the vanishing gradient degradation inherent to standard LSTMs. We evaluate xDKT across six diverse benchmark datasets, including Synthetic, Algebra2005\u20132006, Statics2011, and the ASSISTments series, covering over 22,000 learners. Experimental results show that xDKT yields improved Area Under the ROC Curve (AUC) scores on Statics2011 (0.8562) and ASSISTments2009 (0.8318) compared to baseline models such as DKT, DKVMN, and AKT. Finally, through extensive validation, these findings suggest that xDKT architecture provides a robust and promising framework for accurate and adaptive learning environments.<\/jats:p>","DOI":"10.3390\/a19040251","type":"journal-article","created":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T13:57:34Z","timestamp":1774447054000},"page":"251","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Extended LSTM to Enhance Learner Performance Prediction"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6280-3058","authenticated-orcid":false,"given":"Adel","family":"Ihichr","sequence":"first","affiliation":[{"name":"Engineering Sciences Laboratory, National School of Applied Sciences, Ibn Tofail University, Kenitra 14000, Morocco"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5877-818X","authenticated-orcid":false,"given":"Soukaina","family":"Hakkal","sequence":"additional","affiliation":[{"name":"Engineering Sciences Laboratory, National School of Applied Sciences, Ibn Tofail University, Kenitra 14000, Morocco"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9666-2583","authenticated-orcid":false,"given":"Omar","family":"Oustous","sequence":"additional","affiliation":[{"name":"Engineering Sciences Laboratory, National School of Applied Sciences, Ibn Tofail University, Kenitra 14000, Morocco"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4018-437X","authenticated-orcid":false,"given":"Youn\u00e8s El Bouzekri El","family":"Idrissi","sequence":"additional","affiliation":[{"name":"Engineering Sciences Laboratory, National School of Applied Sciences, Ibn Tofail University, Kenitra 14000, Morocco"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8739-3369","authenticated-orcid":false,"given":"Ayoub Ait","family":"Lahcen","sequence":"additional","affiliation":[{"name":"Engineering Sciences Laboratory, National School of Applied Sciences, Ibn Tofail University, Kenitra 14000, Morocco"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,3,25]]},"reference":[{"key":"ref_1","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_2","unstructured":"Bai, S., Kolter, J.Z., and Koltun, V. (2018). An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling. arXiv."},{"key":"ref_3","unstructured":"Cortes, C., Lawrence, N., Lee, D., Sugiyama, M., and Garnett, R. (2015). Deep Knowledge Tracing, Stanford University."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"917","DOI":"10.1007\/s10618-019-00619-1","article-title":"Deep Learning for Time Series Classification: A Review","volume":"33","author":"Forestier","year":"2019","journal-title":"Data Min. Knowl. Discov."},{"key":"ref_5","unstructured":"Ribeiro, A.H., Tiels, K., Aguirre, L.A., and Sch\u00f6n, T. (2020, January 26\u201328). Beyond Exploding and Vanishing Gradients: Analysing RNN Training Using Attractors and Smoothness. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, online."},{"key":"ref_6","unstructured":"Gil, G.L., Duhamel-Sebline, P., and McCarren, A. (2024). An Evaluation of Deep Learning Models for Stock Market Trend Prediction. arXiv."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Barbre, Z., and Li, G. (2025). Enhanced Wind Energy Forecasting Using an Extended Long Short-Term Memory Model. Algorithms, 18.","DOI":"10.3390\/a18040206"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"137540","DOI":"10.1109\/ACCESS.2025.3595176","article-title":"xLSTMKT: xLSTM for Knowledge Tracing","volume":"13","author":"Aderghal","year":"2025","journal-title":"IEEE Access"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Zhou, Y., Han, W., and Chen, J. (2025). Revisiting Applicable and Comprehensive Knowledge Tracing in Large-Scale Data. Proceedings of the Joint European Conference on Machine Learning and Knowledge Discovery in Databases, Springer.","DOI":"10.1007\/978-3-032-06109-6_14"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"110036","DOI":"10.1016\/j.knosys.2022.110036","article-title":"A Survey on Deep Learning Based Knowledge Tracing","volume":"258","author":"Song","year":"2022","journal-title":"Knowl.-Based Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1109\/72.279181","article-title":"Learning Long-Term Dependencies with Gradient Descent Is Difficult","volume":"5","author":"Bengio","year":"1994","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Yeung, C., and Yeung, D. (2018). Addressing Two Problems in Deep Knowledge Tracing via Prediction-Consistent Regularization. Proceedings of the Fifth Annual ACM Conference on Learning at Scale, Hong Kong University of Science & Technology.","DOI":"10.1145\/3231644.3231647"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Lyu, L., Wang, Z., Yun, H., Yang, Z., and Li, Y. (2022). Deep Knowledge Tracing Based on Spatial and Temporal Representation Learning for Learning Performance Prediction. Appl. Sci., 12.","DOI":"10.3390\/app12147188"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1007\/978-3-030-30952-7_3","article-title":"BiRNN-DKT: Transfer Bi-Directional LSTM RNN for Knowledge Tracing","volume":"Volume 11817","author":"Ni","year":"2019","journal-title":"Proceedings of International Conference on Web Information Systems and Applications"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Zhang, L., Xiong, X., Zhao, S., Botelho, A., and Heffernan, N. (2017). ACM Incorporating Rich Features into Deep Knowledge Tracing, Worcester Polytechnic Institute.","DOI":"10.1145\/3051457.3053976"},{"key":"ref_16","unstructured":"Bittencourt, I., Cukurova, M., Muldner, K., Luckin, R., and Millan, E. (2020). Deep Knowledge Tracing with Transformers, ACT Inc."},{"key":"ref_17","first-page":"1","article-title":"FDKT: Towards an Interpretable Deep Knowledge Tracing via Fuzzy Reasoning","volume":"42","author":"Liu","year":"2024","journal-title":"ACM Trans. Inf. Syst."},{"key":"ref_18","unstructured":"Sonkar, S., Waters, A.E., Lan, A.S., Grimaldi, P.J., and Baraniuk, R.G. (2020). qDKT: Question-centric deep knowledge tracing. arXiv."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"112384","DOI":"10.1016\/j.knosys.2024.112384","article-title":"MLC-DKT: A Multi-Layer Context-Aware Deep Knowledge Tracing Model","volume":"303","author":"Zhang","year":"2024","journal-title":"Knowl.-Based Syst."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"104210","DOI":"10.1016\/j.ipm.2025.104210","article-title":"A Novel Framework for Deep Knowledge Tracing via a Dual-State Joint Interaction Mechanism","volume":"62","author":"Zhang","year":"2025","journal-title":"Inf. Process. Manag."},{"key":"ref_21","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_22","unstructured":"Pandey, S., and Karypis, G. (2019). A Self-Attentive Model for Knowledge Tracing. arXiv."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Ghosh, A., Heffernan, N., and Lan, A.S. (2020). Context-Aware Attentive Knowledge Tracing. Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, Virtual Event, CA USA, 6\u201310 July 2020, ACM.","DOI":"10.1145\/3394486.3403282"},{"key":"ref_24","unstructured":"Beck, M., P\u00f6ppel, K., Spanring, M., Auer, A., Prudnikova, O., Kopp, M., Klambauer, G., Brandstetter, J., and Hochreiter, S. (2024). xLSTM: Extended Long Short-Term Memory. arXiv."},{"key":"ref_25","first-page":"43","article-title":"A Data Repository for the EDM Community: The PSLC DataShop","volume":"43","author":"Koedinger","year":"2010","journal-title":"Handb. Educ. Data Min."},{"key":"ref_26","first-page":"31","article-title":"When Is Deep Learning the Best Approach to Knowledge Tracing?","volume":"12","author":"Gervet","year":"2020","journal-title":"J. Educ. Data Min."},{"key":"ref_27","unstructured":"Khajah, M., Lindsey, R.V., and Mozer, M.C. (2016). How deep is knowledge tracing?. arXiv."},{"key":"ref_28","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_29","doi-asserted-by":"crossref","unstructured":"Zhao, W., Xu, Z., and Qiu, L. (2025). BPSKT: Knowledge Tracing with Bidirectional Encoder Representation Model Pre-Training and Sparse Attention. Electronics, 14.","DOI":"10.3390\/electronics14030458"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/19\/4\/251\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T08:30:54Z","timestamp":1774859454000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/19\/4\/251"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,25]]},"references-count":29,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2026,4]]}},"alternative-id":["a19040251"],"URL":"https:\/\/doi.org\/10.3390\/a19040251","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,25]]}}}