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simpleKT: A Simple But Tough-to-Beat Baseline for Knowledge Tracing

Zitao Liu, Qiongqiong Liu, Jiahao Chen, Shuyan Huang, Weiqi Luo

arXiv:2302.06881v2cs.LGcs.AI

TL;DR

KT predicts students’ future outcomes from learning interactions, but increasingly complex DLKT methods and inconsistent baseline results complicate comparisons. SIMPLEKT models question-specific differences and uses ordinary dot-product attention; it performs strongly across datasets, supporting its use as a KT baseline.

  • Problem

    DLKT methods have become increasingly complex, while published baseline results are inconsistent, including DKT AUC scores ranging from 0.721 to 0.821 on ASSISTments2009.

    Source: §1 · p. 2

  • Method

    SIMPLEKT combines KC embeddings with question-specific variation and uses ordinary dot-product attention to model student interactions.

    Source: §1 · p. 2, §3.2.1 · p. 4, §3.2.3 · p. 5

  • Results

    55 wins, 3 ties and 18 losses against 12 baselines on 7 datasets; SIMPLEKT almost always ranks in the top 3 by AUC.

    Source: §4.4 · p. 7

  • Takeaways & Limitations

    The authors conclude that SIMPLEKT is a strong baseline for future KT research.

    Source: §5 · p. 9

Abstract

from arXiv · show

Knowledge tracing (KT) is the problem of predicting students' future performance based on their historical interactions with intelligent tutoring systems. Recently, many works present lots of special methods for applying deep neural networks to KT from different perspectives like model architecture, adversarial augmentation and etc., which make the overall algorithm and system become more and more complex. Furthermore, due to the lack of standardized evaluation protocol \citep{liu2022pykt}, there is no widely agreed KT baselines and published experimental comparisons become inconsistent and self-contradictory, i.e., the reported AUC scores of DKT on ASSISTments2009 range from 0.721 to 0.821 \citep{minn2018deep,yeung2018addressing}. Therefore, in this paper, we provide a strong but simple baseline method to deal with the KT task named \textsc{simpleKT}. Inspired by the Rasch model in psychometrics, we explicitly model question-specific variations to capture the individual differences among questions covering the same set of knowledge components that are a generalization of terms of concepts or skills needed for learners to accomplish steps in a task or a problem. Furthermore, instead of using sophisticated representations to capture student forgetting behaviors, we use the ordinary dot-product attention function to extract the time-aware information embedded in the student learning interactions. Extensive experiments show that such a simple baseline is able to always rank top 3 in terms of AUC scores and achieve 57 wins, 3 ties and 16 loss against 12 DLKT baseline methods on 7 public datasets of different domains. We believe this work serves as a strong baseline for future KT research. Code is available at \url{https://github.com/pykt-team/pykt-toolkit}\footnote{We merged our model to the \textsc{pyKT} benchmark at \url{https://pykt.org/}.}.

1 INTRODUCTION

The introduction motivates a simpler KT baseline amid increasingly complex methods and inconsistent benchmark results. It presents SIMPLEKT’s question-specific modeling and attention-based approach, reporting strong performance against existing DLKT models.

1 INTRODUCTION

  • KT predicts student outcomes over questions by modeling their knowledge states, while knowledge components describe mental structures or processes used to complete task steps.The introduction situates this work alongside probabilistic graphical, factor-analysis, and deep-learning approaches to KT.Source: §1 · pp. 1–2
  • Reported DKT AUC on ASSISTments2009 ranges from 0.721 to 0.821, while AKT ranges from 0.747 to 0.835 across cited studies.The introduction also notes conflicting assessments of DKT’s performance and attributes substantial variation to hyperparameters and preprocessing.Source: §1 · p. 2
  • SIMPLEKT represents each question using the average of its KC embeddings plus a question-specific variation, and applies ordinary dot-product attention to student interactions.The approach is motivated by the Rasch model and evaluated through the PYKT benchmark against 12 DLKT methods on 7 datasets.Source: §1 · p. 2
  • SIMPLEKT beats a wide range of modern neural KT models, including graph-, memory-, and adversarial-based models.The authors propose it as a baseline for future KT research.Source: §1 · p. 3

2 RELATED WORK

Related DLKT work includes sequential, memory, adversarial, graph, and attention-based approaches. These categories can overlap; SIMPLEKT is categorized as attention-based and uses ordinary dot-product attention.

2 RELATED WORK

  • Deep sequential models use autoregressive architectures, memory-augmented models use memory networks, and adversarial models generate perturbations to improve generalization.Examples include DKT, a sequential model using an LSTM, and an adversarially trained attentive-LSTM model.Source: §2 · p. 3
  • Graph-based models use graph neural networks to represent relations among questions, knowledge components, and interactions, while attention-based models capture dependencies between interactions.Cited attention approaches include self-attention and monotonic attention mechanisms.Source: §2 · p. 3
  • The categories are not exclusive, and SIMPLEKT is classified as attention-based because it models student interactions with ordinary dot-product attention.A sequential key-value memory network is given as an example of combining categories.Source: §2 · p. 3

3 A SIMPLE METHOD FOR KNOWLEDGE TRACING

simpleKT predicts a student’s response to a question from their past interactions, representing questions through their associated knowledge components (KCs) while retaining question-specific variation. It extracts knowledge states with ordinary dot-product attention and distinguishes its design from other attention-based KT models.

3.1 PROBLEM STATEMENT

  • simpleKT estimates the probability that a student will answer an arbitrary question correctly from the student’s chronologically ordered historical interactions.Each interaction records a question, its associated KC set, a binary response, and a response time step.Source: §3.1 · p. 3

3.2.1 REPRESENTATIONS OF QUESTIONS, KCS AND RESPONSES.

  • Each question-level interaction is expanded into multiple KC-level interactions when the question is associated with a set of KCs.The transformation converts question-response data into KC-response data.Source: §3.2.1 · p. 4, Figure 2 · p. 4
  • Question and interaction representations combine KC representations with question-specific variation and response information, preserving differences among questions that cover the same KCs.The design is motivated by the observation that questions sharing KCs can have different difficulty levels and student outcomes.Source: §3.2.1 · p. 4

3.2.2 PREDICTION WITH ORDINARY DOT-PRODUCT ATTENTION.

  • The model uses ordinary dot-product attention over past KC and interaction representations to retrieve a knowledge state, then refines it with a two-layer fully connected network.The retrieved state is computed from the current KC representation and the past KC and interaction representations.Source: §3.2.2 · p. 4

3.2.3 RELATIONSHIP TO EXISTING DLKT MODELS.

  • Compared with AKT, simpleKT omits self-attentive encoders and time-decayed monotonic attention; compared with SAKT and SAINT, it models question-specific difficulty among questions sharing KCs.SAINT uses an encoder-decoder Transformer architecture, while simpleKT uses dot-product attention.Source: §3.2.3 · pp. 4–5

4 EXPERIMENTS

The experiments evaluate SIMPLEKT on seven datasets, against 12 deep-learning knowledge-tracing baselines, using standard training procedures and overall and multi-step prediction tests. SIMPLEKT ranks near the top overall, while the ablation and qualitative analyses examine question-difficulty modeling.

4.1.1 DATASETS CONTAINING INFORMATION OF BOTH QUESTIONS AND KCS

  • The D1 datasets contain both question and KC information, including ASSISTments2009, Algebra2005, Bridge2006, and NIPS34.The paper evaluates four D1 datasets with question and KC information.Source: §4.1 · p. 5, §4.1.1 · p. 5

4.1.2 DATASETS CONTAINING INFORMATION OF EITHER QUESTIONS OR KCS

  • The D2 datasets contain either question or KC information, including Statics2011, ASSISTments2015, and POJ.Together, the D1 and D2 groups comprise the seven datasets used in the experiments.Source: §4.1 · p. 5, §4.1.2 · pp. 5–6

4.3 EXPERIMENTAL SETUP

  • Sequences shorter than three attempts are removed, history length is capped at 200, and evaluation withholds 20% of students' sequences before five-fold cross-validation.The study uses Adam, early stopping, and AUC as its main metric, with accuracy as a secondary metric.Source: §4.1.2 · p. 6, §4.3 · pp. 6–7

4.2 BASELINES

  • The comparison covers 12 DLKT baselines, including recurrent models, memory networks, adversarial models, graph models, and attention-based models.The listed baselines include DKT, DKVMN, ATKT, GKT, SAKT, SAINT, and AKT.Source: §4.2 · p. 6

4.4 EXPERIMENTAL RESULTS

  • SIMPLEKT almost always ranks in the top three by AUC, with 55 wins, 3 ties, and 18 losses against 12 baselines across seven datasets.The overall comparison reports average AUC and accuracy; win/tie/loss counts use paired t-tests at the 0.01 significance level.Source: Table 2 · p. 7, §4.4 · p. 7
  • In non-accumulative multi-step prediction, SIMPLEKT achieves the best AUC on BD2006 and NIPS34; AUC predictions improve with more history in most cases.The study varies observed interaction history from 20% to 90% in 10% increments and reports results for AUC and accuracy.Source: Figure 3 · p. 8, §4.4 · pp. 8–9
  • For questions sharing the same KCs, SIMPLEKT's predicted correctness probability decreases as the question's historical error rate increases.The analysis uses historical error rate as a surrogate for question difficulty.Source: §4.4 · p. 9, Figure 5 · p. 9
  • Removing question-difficulty modeling lowers performance by more than 2% on every D1 dataset, while replacing its vector with a scalar has minimal effect.The D2 variants are mathematically unidentifiable because those datasets contain only question information or KC information.Source: §4.4 · p. 9, Table 4 · p. 9

5 CONCLUSION

The conclusion presents SIMPLEKT as a strong baseline that models question-specific differences and uses ordinary dot-product attention for student knowledge-state estimation.

5 CONCLUSION

  • SIMPLEKT uses ordinary dot-product attention to simplify student knowledge-state estimation.Source: §5 · p. 9
  • Motivated by the Rasch model, SIMPLEKT captures differences among questions sharing the same knowledge components.Source: §5 · p. 9
  • Experiments show SIMPLEKT beats a wide range of recent DLKT models across datasets from different domains.Source: §5 · p. 9
  • The authors present SIMPLEKT as a strong baseline for future knowledge-tracing research.Source: §5 · p. 9

REPRODUCIBILITY STATEMENT

The statement identifies where to obtain the model and comparison-model code and how the experiments align with PYKT data partitions.

REPRODUCIBILITY STATEMENT

A.1 DATA STATISTICS OF 7 DATASETS

Table 5 reports statistics for seven datasets, distinguishing original from preprocessed data and defining the average-KC measure.

A.1 DATA STATISTICS OF 7 DATASETS

  • Table 5 presents data statistics for seven datasets.Source: Table 5 · p. 13
  • The table distinguishes initial data statistics from statistics after preprocessing.Source: Table 5 · p. 13
  • The table's “avg KCs” measure is the average number of knowledge components per question.Source: Table 5 · p. 13

A.2 MORE VISUALIZATION OF SIMPLEKT

The appendix adds SIMPLEKT prediction visualizations for students 2, 3, and 4.

A.2 MORE VISUALIZATION OF SIMPLEKT

  • Figure 6 visualizes SIMPLEKT prediction results for student 2.Source: Figure 6 · p. 13
  • Figure 7 visualizes SIMPLEKT prediction results for student 3.Source: Figure 7 · p. 13
  • Figure 8 visualizes SIMPLEKT prediction results for student 4.Source: Figure 8 · p. 13

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