Source-linked AI summary
Dynamic Key-Value Memory Networks for Knowledge Tracing
Jiani Zhang, Xingjian Shi, Irwin King, Dit-Yan Yeung
TL;DR
Knowledge tracing needs to represent evolving student knowledge while identifying mastery of individual and related concepts. DKVMN uses static concept keys and dynamic mastery values, updating relevant concept states from exercise–response interactions. It consistently outperforms established methods across the evaluated datasets and can discover underlying exercise concepts, while its current representations omit exercise content information and hierarchical concept structure.
Problem
Existing KT methods either model predefined concepts separately or summarize all concepts in one hidden state, limiting precise concept-level tracing.
Method
DKVMN uses a static key matrix for concept representations and a dynamic value matrix that stores and updates each concept’s mastery state.
Results
DKVMN consistently outperforms BKT and DKT on one synthetic and three real-world datasets, including an AUC of 82.8% on Statics2011.
Takeaways & Limitations
The model can discover underlying exercise concepts and trace students’ changing understanding of each concept over time.
Takeaways & Limitations
Future work is needed to incorporate exercise content information and encode hierarchical relationships between concepts.
Abstract
from arXiv · showhide
Knowledge Tracing (KT) is a task of tracing evolving knowledge state of students with respect to one or more concepts as they engage in a sequence of learning activities. One important purpose of KT is to personalize the practice sequence to help students learn knowledge concepts efficiently. However, existing methods such as Bayesian Knowledge Tracing and Deep Knowledge Tracing either model knowledge state for each predefined concept separately or fail to pinpoint exactly which concepts a student is good at or unfamiliar with. To solve these problems, this work introduces a new model called Dynamic Key-Value Memory Networks (DKVMN) that can exploit the relationships between underlying concepts and directly output a student's mastery level of each concept. Unlike standard memory-augmented neural networks that facilitate a single memory matrix or two static memory matrices, our model has one static matrix called key, which stores the knowledge concepts and the other dynamic matrix called value, which stores and updates the mastery levels of corresponding concepts. Experiments show that our model consistently outperforms the state-of-the-art model in a range of KT datasets. Moreover, the DKVMN model can automatically discover underlying concepts of exercises typically performed by human annotations and depict the changing knowledge state of a student.
1. INTRODUCTION
Knowledge tracing aims to model students’ evolving knowledge from exercise performance so practice can be personalized, but existing methods either separate predefined concepts or summarize knowledge in one hidden state. DKVMN addresses this by learning concept relationships while maintaining and updating each concept state, and it outperforms prior models across the evaluated datasets.
- Motivation: KT traces students’ knowledge states from past exercise performance to personalize hints, practice sequences, and learning focus.
- Problem formulation: KT is formulated as sequence prediction: given past exercise interactions, the model predicts the probability of a correct response while treating concept states as hidden.
- Model distinction: DKT uses a summarized hidden vector, whereas DKVMN maintains a separate state for each concept so the full set of states forms the student’s knowledge state.
- Existing limitations: BKT models predefined concepts separately with binary states, limiting its ability to capture concept relationships, undefined concepts, and complex transitions.
- Capabilities: DKVMN automatically learns exercise–concept correlations, updates only related concept states, discovers underlying concepts, and depicts evolving student knowledge.
- Model design: DKVMN combines a static key matrix storing concept representations with a dynamic value matrix that stores and updates students’ concept mastery levels.
- Results: DKVMN consistently outperforms BKT and DKT on one synthetic and three real-world datasets.
2. RELATED WORKS
Related work frames knowledge tracing as a structured or recurrent sequence-learning problem and situates it within memory-augmented neural networks. These approaches differ in how they represent knowledge, store temporal information, and transition between states.
- Knowledge Tracing: KT evaluates student knowledge from binary correctness responses to tagged exercises without incorporating secondary data.
- Knowledge Tracing: BKT models each concept separately as a binary state, while later variants add personalization, exercise diversity, and other information.
- Deep Knowledge Tracing: DKT uses LSTM hidden states to represent continuous knowledge summaries and shares parameters across time steps.
- Memory-Augmented Neural Networks: Memory-augmented neural networks combine an external memory matrix with a controller that reads and writes through attention mechanisms.
- Memory-Augmented Neural Networks: MANNs use external memory for greater storage capacity, local state transitions, and parameter-efficient increases in memory slots compared with conventional RNNs.
3. MODEL
The model uses an external memory architecture for knowledge tracing, then separates immutable concept representations from dynamically updated concept mastery. DKVMN computes exercise–concept correlations to read relevant mastery, predict correctness, and update only related concept states.
- 3.1 Memory-Augmented Neural Network for Knowledge Tracing: MANN treats an N × M external memory matrix as a student’s knowledge state and uses exercise-response embeddings to read and write memory.The read content predicts the probability of answering each exercise correctly at the next timestamp.
- 3.1 Memory-Augmented Neural Network for Knowledge Tracing: MANN’s single matrix is unsuitable for KT because exercise inputs and answer predictions have different types, yet both are embedded into the same memory space.DKVMN addresses this mismatch with separate key and value components.
- 3.2 Dynamic Key-Value Memory Networks: DKVMN attends each exercise to an immutable key matrix storing latent concepts, then reads and writes the corresponding dynamic value matrix storing concept mastery.The value matrix changes over time, while the key matrix represents the latent concepts.
- 3.2.1 Correlation Weight: The model converts an exercise into an embedding, computes softmax correlation weights over key slots, and uses those weights for both reading and writing.The weights represent correlations between the exercise and latent concepts.
- 3.2.2 Read process: DKVMN reads a weighted sum of value slots, combines it with the exercise embedding, and predicts the probability of a correct response through fully connected layers.The read content summarizes mastery relevant to the exercise while the exercise embedding supplies prior difficulty information.
- 3.2.3 Write process: After each answer, DKVMN erases and then adds information to value slots using the exercise’s correlation weights, allowing concept states to be forgotten or strengthened.The erase signal is computed from the embedded exercise-response tuple, and the model is trained with cross-entropy loss using stochastic gradient descent.
4. EXPERIMENTS
Experiments evaluate DKVMN on synthetic and real-world knowledge-tracing datasets, comparing prediction, parameter efficiency, overfitting, concept discovery, and concept-state tracking. DKVMN consistently outperforms comparison methods while discovering exercise concepts and depicting changing student knowledge states.
- Prediction Accuracy: DKVMN outperforms the standard MANN and state-of-the-art method on four datasets.The evaluation covers one synthetic dataset and three real-world datasets.
- Prediction Accuracy: DKVMN achieves 82.7% test AUC on Synthetic-5 and 81.6% on ASSISTments2009, exceeding the listed MANN, DKT, and BKT results.On Synthetic-5, MANN, DKT, BKT, and BKT+ achieve 81.0%, 80.3%, 62%, and 80%, respectively; on ASSISTments2009, the corresponding listed baselines are 79.7%, 80.5%, and 63%.
- Prediction Accuracy: On Statics2011, DKVMN achieves 82.8% AUC, outperforming DKT, MANN, classical BKT, and BKT variants.The dataset has many distinct exercise tags and relatively few answers, while the listed comparison AUCs range from 73% to 80.2%.
- Model Efficiency: DKVMN achieves better prediction accuracy with fewer parameters than DKT, including with lower state dimensions.The comparison varies state dimensions and DKVMN memory sizes; on Statics2011, DKT reaches 80.20% with 200 state dimensions and 1 million parameters.
- Concept Discovery: DKVMN discovers exercise concepts precisely, producing perfect clustering on Synthetic-5 with adjusted mutual information of 1.0 and reasonable clusters on ASSISTments2009.On Synthetic-5, each exercise is assigned to the latent concept with maximum correlation weight; with memory size 50, the model can still recover five clusters.
- Knowledge-State Tracking: DKVMN depicts students’ concept states over time, showing distinct mastery patterns after exercise interactions.The model updates the state of the discovered concept after each response; an example tracks five concepts and shows mastery of three alongside failure to understand another.
5. CONCLUSIONS AND FUTURE WORK
DKVMN is proposed as a sequence-learning model for knowledge tracing that discovers exercise concepts and tracks students’ concept-level knowledge states over time. Future work will enrich representations with content information and hierarchical concept relationships.
- DKVMN discovers underlying concepts for input exercises and traces a student’s knowledge state across concepts.
- The model is intended for online learning platforms to improve students’ study efficiency.
- Future work will incorporate content information into exercise and concept embeddings to improve their representations.
- Future work will investigate hierarchical key-value memory networks for encoding relationships between concepts.
7. APPENDIX
The appendix evaluates concept discovery on synthetic data and describes the memory operations used by DKVMN. Exercises are represented through correlation weights, clustered into concepts, and used to guide dynamic memory writing.
- Concept Discovery: With memory size N=50, direct clustering on synthetic-5 achieves adjusted mutual information of 0.879 against the ground-truth concepts.
- Concept Discovery: 1.0 adjusted mutual information is obtained when synthetic-5 exercises are clustered using t-SNE, indicating perfect clustering against the ground truth.
- Memory Operations: DKVMN computes cosine similarities between an input key and memory, then converts them into read weights using softmax and key strength β_t.
- Memory Operations: Usage weights track memory-access frequency by decaying previous usage and adding current reading and writing weights.
- Concept Discovery: The heat map’s x-axis lists exercises, while its y-axis shows correlation weights between exercises and five latent concepts.
- Memory Operations: Write weights combine previous read weights with previous least-used weights through a convex combination controlled by a scalar gate.