# Uncertainty-preserving deep knowledge tracing with state-space models

arXiv: https://arxiv.org/abs/2407.17427 · HTML: https://mlsanity.com/paper/2407.17427/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 25 references that are in the map.
- First posted on arXiv 9 Jul 2024.

## Builds on (most cited first, 11 of 11)

- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Deep Knowledge Tracing](https://mlsanity.com/paper/1506.05908/) (2015)
- [A Self-Attentive model for Knowledge Tracing](https://mlsanity.com/paper/1907.06837/) (2019)
- [Towards an Appropriate Query, Key, and Value Computation for Knowledge Tracing](https://mlsanity.com/paper/2002.07033/) (2020)
- [pyKT: A Python Library to Benchmark Deep Learning based Knowledge Tracing Models](https://mlsanity.com/paper/2206.11460/) (2022)
- [Knowledge Query Network: How Knowledge Interacts with Skills](https://mlsanity.com/paper/1908.02146/) (2019)
- [Item Response Theory -- A Statistical Framework for Educational and Psychological Measurement](https://mlsanity.com/paper/2108.08604/) (2021)
- [pyBKT: An Accessible Python Library of Bayesian Knowledge Tracing Models](https://mlsanity.com/paper/2105.00385/) (2021)
- [An Elementary Introduction to Kalman Filtering](https://mlsanity.com/paper/1710.04055/) (2017)
- [Is Your Model "MADD"? A Novel Metric to Evaluate Algorithmic Fairness for Predictive Student Models](https://mlsanity.com/paper/2305.15342/) (2023)
- [Bayes Nets in Educational Assessment: Where Do the Numbers Come From?](https://mlsanity.com/paper/1301.6722/) (2013)

## Built on by (most cited first, 1 of 1)

- [UNVaMP: Neural Knowledge Tracing with Variational Regularization of Latent Knowledge Dynamics](https://mlsanity.com/paper/2608.03811/) (2026)

## Abstract (arXiv)

A central goal of both knowledge tracing and traditional assessment is to quantify student knowledge and skills at a given point in time. Deep knowledge tracing flexibly considers a student's response history but does not quantify epistemic uncertainty, while IRT and CDM compute measurement error but only consider responses to individual tests in isolation from a student's past responses. Elo and BKT could bridge this divide, but the simplicity of the underlying models limits information sharing across skills and imposes strong inductive biases. To overcome these limitations, we introduce Dynamic LENS, a modeling paradigm that combines the flexible uncertainty-preserving properties of variational autoencoders with the principled information integration of Bayesian state-space models. Dynamic LENS allows information from student responses to be collected across time, while treating responses from the same test as exchangeable observations generated by a shared latent state. It represents student knowledge as Gaussian distributions in high-dimensional space and combines estimates both within tests and across time using Bayesian updating. We show that Dynamic LENS has similar predictive performance to competing models, while preserving the epistemic uncertainty - the deep learning analogue to measurement error - that DKT models lack. This approach provides a conceptual bridge across an important divide between models designed for formative practice and summative assessment.