Sequence Denoising with Self-Augmentation for Knowledge Tracing

We thank the reviewer for their feedback and address their questions below.

W1:The algorithm design has not been fully explained. In equation (8), the principle of quantifying noise in real data sets has not been thoroughly explained. Direct comparison of singular values does not seem reasonable enough and may not provide a meaningful noise measurement.

Thank the reviewers for their valuable comments. In the formula, we used the binary norm of the singular value matrix to represent the difference between the problem and the interaction sequence before and after denoising, and the larger the difference value, the lower the similarity between the features, indicating that the part of data may contain noise. In this way, we detected noise and classified the data. Regarding the direct comparison of singular values mentioned by the reviewers, we acknowledge that this method may raise questions, but we emphasize that the calculation of this difference is to effectively evaluate the impact of noisy data, not to directly make a simple comparison of singular values, and we will further clarify this point to make the description more rigorous. Thanks again to the reviewers for their careful review and valuable comments.

W2:The algorithm's performance is unconvincing, with modest improvement gains. While it integrates explicit and implicit denoising mechanisms, Table 1 shows no significant advantage over using either strategy alone. This fusion, a key innovation, fails to demonstrate clear practical benefits.

Thank you for the reviewer’s comments. Our explanation is as follows:

While Table 1 shows relatively limited performance gains, we would like to emphasize that the main advantage of this combination lies not only in the improvement in performance but also in the enhancement of interpretability. In the paper, we have outlined the limitations of using explicit or implicit denoising alone. Explicit denoising helps identify and handle obvious noise points in the data, while implicit denoising better captures differences in students’ response patterns, thereby improving the overall robustness of the data. Moreover, we conducted robustness experiments on using a single denoising strategy, as shown in Table 2, where the results indicate greater instability with a single approach. We will further elaborate on the motivation behind this strategy in the paper.

W3:The paper has a number of writing and presentation problems, including formatting inconsistencies and language inaccuracies. For example, in equations (6) and (7), the embedding vector was improperly affected by singular value decomposition when matrix form should have been used, the citation format in line 196 was incorrect, and the reference format was inconsistent. In addition, there is a mismatch between the description and equation (4), where the text refers to the original sequence, while the formula uses the denoised sequence.

Thank you for the reviewer’s suggestions. We will thoroughly review the paper’s formatting and language to ensure consistency and accuracy. Regarding the equations, we acknowledge that our expression and descriptions may lack precision, and we will make the necessary improvements. For the discrepancy between the text description and equation (4), we combined the original and denoised sequences to create a new sequence, which might not have been clearly explained in the text. We will clarify this in the revised version. Once again, we sincerely thank you for your detailed review and valuable feedback, which will greatly help us improve the quality and readability of our paper.

Thanks to the reviewers for their in-depth attention to our method, we explain the question about maximizing the maximum singular value to reduce noise as follows:

The core idea of maximizing the maximum singular value is to remove low-information noise components by preserving the most important information in the data. In singular value decomposition (SVD), the data matrix is decomposed into the product of three matrices: U, Σ, and V^⊤. The size of the singular value Σ reflects the importance or information of the data, where larger singular values correspond to the most representative part of the data, while smaller singular values usually represent noise and unimportant components. By maximizing the maximum singular value, we are actually selecting the primary components that best represent the data, and by compressing or ignoring smaller singular values, removing those low-frequency components that might add to the noise. This processing method can effectively reduce the influence of noise, and improve the quality of data and the robustness of the model. We will add a detailed explanation of this theoretical background in the revised version to help readers better understand the role of maximizing the maximum singular value. Thank you again for your valuable questions.

We thank the reviewers for their valuable feedback. We address these issues below and add to the manuscript by adding more clarifications and new research.

W1:As Table 1 shows, DKT-ED performs much worse than DAT, and the combination of explicit and implicit denoising is not as good.

In the field of knowledge tracking (KT), due to the relatively sparse student interaction data, explicit denoising alone may cause excessive denoising problems and affect model performance. In this case, explicit de-noising can mistakenly delete normal interactive data, especially in base models such as DKT that do not use additional information, and the risk of performance degradation is more significant. We have detailed the reasons for this performance degradation in our analysis in Table 1. In addition, for the understanding of excessive Denoising, we refer to the related research SSDRec: Self-Augmented Sequence Denoising for Sequential Recommendation. Specifically, explicit denoising can effectively reduce noise interference to the data, while implicit denoising helps the model automatically adapt to different noise patterns during the inference process. Through this combination, our model not only improves the accuracy, but also enhances the interpretability of the model.

W2:Why SVD vectors, as shown in formulas 6 and 7? The first three wrong answers to q1 and the last two correct answers are inconsistent with the contents in Figure 1. Why can f_{den} play the role of denoising? This paper does not introduce why data enhancement is needed for denoising?

1.(6) and (7) use SVD to decompose problem vectors and interaction vectors to reduce noise effects in data representation. By retaining the main singular values, we can effectively reduce the noise component, and thus more clearly identify and distinguish the noisy data that may be present in the original sequence.

2.Thanks to the reviewer for pointing out that Figure 1 is inconsistent with the description of "q1 answer wrong for the first three times and correct for the last two times". We will make corrections to Figure 1 to ensure that the example is consistent with the diagram and to avoid confusion for the reader.

3.For the denoising mechanism of f_{den}, we refer to SSDRec: Self-Augmented Sequence Denoising for Sequential Recommendation and Hierarchical Item Inconsistency Signal Learning for sequential recommendation Sequence Denoising in Sequential Recommendation, and some denoising modules are used for optimization. The revised draft will add a detailed introduction to the mechanism and principle of f_{den) denoising.

4.In addition, given the prevalence of data sparsity in the field of knowledge tracking (KT), there are existing methods to mitigate this problem through data enhancement. But in our study, there was noise in the original data set, and doing data enhancement directly could amplify that noise. Therefore, while improving the diversity of data, we de-noised the original data and enhanced data to further improve the data quality on the basis of rich data.

W3:Some important details are missing. What is the meaning of q_d? Figure 2 is not clear. How to calculate the influence weights in “in traditional KT methods, the influence weights” is not explained and the references are not mentioned. The effect of lambda is not very reasonable, as shown in Figure 5.

Thank the reviewers for their detailed review of our work and constructive comments. In response to these questions, we provide the following responses, which will be supplemented in the revised draft.

1.q_{d} represents the new feature representation vector of the problem sequence after denoising, and v_{d} represents the new feature representation vector of the interaction sequence after denoising. We will explain these symbols in detail in the revised draft to ensure that the symbols are more clearly defined.

2.Regarding the clarity of Figure 2, we will describe Figure 2 in more detail, adding comments and annotations to convey the information more intuitively.

3.As for the calculation of influence weights, we have demonstrated them in visualizations and referred to relevant literature. Tracing Knowledge Instead of Patterns: Stable Knowledge Tracing with Diagnostic Transformer to illustrate the effectiveness of our method for weight analysis. Through the analysis of experimental results, we further explain why our method is more efficient in weight calculation. 4.Regarding the design of the λ parameter, we have designed this parameter to adjust the ratio of the original sequence to the enhanced sequence. Since the model is more reliable to the original sequence, we explore four different λ values in the experiment. Based on the results in Figure 5, we find that the best performance is achieved on average across the four data sets when λ is 0.01. These values obtained in the experiment will help to better understand the role of λ.

We are grateful for the strong evaluation and detailed feedback on our analyses.

W1:This article ignores some important benchmarks. For example, HD-KT is not discussed or compared, and, as mentioned in the related work section, more sequence denoising work should be considered as a benchmark to better validate the effectiveness of the proposed methods.

Thank the reviewers for their valuable comments. We will expand the related work section to cover more research and methods in sequence denoising. Thanks again for the reviewer's suggestions, we will improve the manuscript according to the comments.

W2:The main technical contribution of the paper is the use of SVD decomposition to analyze informative signals. However, this approach is relatively simple and has been applied in other fields. Additionally, the paper lacks a thorough discussion on computational overhead, particularly the time-intensive nature of SVD calculations, which could impact real-time feasibility in large-scale applications.

Thank you for your questions. We acknowledge that SVD decomposition is a classical method and has been widely used in other fields. However, the use of SVD for KT domain recognition and noise reduction has been less explored. As for the computational overhead, our research focuses on educational data sets, which are usually relatively small in size, so no significant time overhead problem is seen in this study. We will explore the impact of time overhead on datasets of different sizes in future studies, and make specific analysis for large-scale datasets.

W3:There are minor writing issues: Missing punctuation at the end of the formula; inconsistent of reference format and so on.

Thank you for the questions raised by the reviewer. I am very sorry for this mistake. We will carefully review and correct handwriting and formatting problems in the manuscript to improve the overall quality and readability of the article. Thanks to the reviewers for their careful review and valuable feedback.

We are grateful for the strong evaluation and detailed feedback on our analyses.

W1:The motivation for noise in KT interaction sequences is poorly defined. The paper doesn't clearly quantify the extent of noise in real KT datasets or demonstrate its impact empirically.

Thank the reviewers for their valuable comments. We reply as follows:

In the KT field, noise often comes from student guesswork, slips, or occasional wrong reactions, factors that are often present in the actual data but difficult to quantify accurately. Therefore, we did not directly quantify the degree of noise in the experiment, but only manually injected different degrees of noise and observed its impact on the accuracy of the model prediction.

W2:This article was unable to find comparison results for other baselines.

Thank the reviewers for their valuable comments. We reply as follows:

We understand the reviewers' concern with baseline comparison results. Since our proposed approach is a plug and play module, in our study we aim to be compatible with the existing KT model, focusing on the effectiveness of the module, without presenting more baseline model comparisons in the paper.

W3:The artificial noise injection experiments only use Gaussian noise, which may not reflect realistic noise patterns in educational data.

Thanks to the reviewer for his comments on the artificial noise injection experiment. We explain as follows:

In the experiment, we chose to use Gaussian noise for noise injection in order to evaluate the robustness of the model under common noise conditions. We understand the reviewer's point of view that the real noise pattern in education data may be more complex, not limited to Gaussian noise. In order to further verify the model's performance in more realistic scenarios, we plan to introduce other types of noise such as random guess or systematic bias in future studies, so as to reflect the noise characteristics in education data more comprehensively.

W4:There may be confusion between the model names SDAKT and CL4KT-DA.

Thanks to the reviewer for pointing out possible confusion between SDAKT and CL4KT-DA. In order to avoid confusion among readers, we will explicitly and uniformly use CL4KT-DA as the abbreviation of the model in the paper, and make clarifications and adjustments in relevant parts to ensure consistency and clarity of terms.

W5:Limited analysis of computational overhead introduced by the denoising module.

Thanks for the reviewer's concern about the computational cost of denoising model, we reply as follows:

In our study, due to the small dimension of the input data of the model, the introduction of the denoising module does not significantly increase the computing overhead. At this data scale, the impact of the denoising module on the overall training and reasoning time is negligible.