The benchmarks are fine, however the evaluation metrics don't seem to make sense (see next section for my doubts, please). Also, the authors fail to show whether they do any sort of cross-validation after they split the series in windows, or whether they use the time component to define the train, validation, and tests sets. In other words, are you using time, say first 10 windows for training, the 11th and 12th window for validation, and from the 13th window you test? Or are you mixing these windows, say 80% of all windows goes to training, 2% to validation, and the rest to test? If the former is the case, then how many $k$-cross validations are you doing?

The authors don't make any theoretical claims, which haven't been shown/proven before: i.e., using Fourier transformata instead of B-splines when wanting to capture periodic patterns, or having more local smoothness.

I don't know why the authors are proposing different evaluation strategies. All of the F1 variants adopted seem to misrepresent the performances of KAN-AD. Sure, the delay penalizes KAN-AD, but why do you need to penalize it? Here's an example.

$\times$ is true anomaly; T = detected anomaly; TP = True Positive; FN = False Negative; TN = True Negative; FP = False Positive.

So, my doubt is on the evaluation itself. Since the authors treat univariate series only, this is even clearer. Each $x_i$ at any timestamp $t_i$ can be either normal or anomalous. Therefore, the predictor can be evaluated for each $t_i$ as shown above: i.e., timestep-based. In these conditions, the authors report $F1_d = 0.2857, F1_e = 0.5714$ - since it doesn't consider the length of the detected anomalies nor false positives. Nevertheless, the real F1 score should be that for each time-step: i.e., $F1_t = 0.5$. The authors claim that they use the event-based calculation - i.e., $F1_e$ - which smears false negatives as being true positives (see the point-wise PA and Figure 4 in the paper). The authors were self-critical with the delay in the beginning and then decide to use the event-based one. It's very confusing, and the reason the authors provide is "For the sake of convenience [...] use Event F1 [...] as it is more alignment (typo) with the need for real-time anomaly detection in real-world situations." Who says that event F1 is more aligned with real-time anomaly detection? Is there any other work that argues this? If not, this statement is unfounded, and actually harmful, since, again, event F1 obfuscates false negatives, a critical aspect in critical domains, especially healthcare: e.g., if you miss an anomaly in neurodegenerative patients, they might die.

If we take the example in Figure 4 of the paper, we have $F1_d = 0.1429$, and $F1_e = 0.5714$, which is an overestimate of the true performance according to the timestep-based approach proposed above $F1_t = 0.2667$. Therefore, $F1_t$ emulates quite closely the "self-harming" $F1_d$. Again, $F1_e$ is an overestimate of the true performances.

The only sound metric here is AUPRC, which doesn't actually show that KAN-AD is way better than the second-best (i.e., KAN in KPI and WSD). So, in KPI you're comparable to KAN (difference of .029 which is statistically insignificant) and in WSD you underperofm by .013 (which again is statistically insignificant). Let's agree that in 2/4 datasets you're comparable to SoTA, and you win in 2 others. Therefore, across the board KAN-AD is not the best. Moreover, as per my comment in Sec. Methods And Evaluation Criteria, we can't even be sure that these metrics make sense since we don't know the number of folds you tested this on and what is the train-validation-test split you used.

Moreover, the average $F1_e$ reported in Table 2 isn't indicative of KAN-AD's overall performance. There are statistical tests that showcase how much better is one method compared to others. For example the Friedmann test with a post-hoc Bonferroni-Dunn could actually show if KAN-AD is better than KAN in the previous two edge cases, which I doubt it would. However, these tests work if you have multiple runs/folds for each of the detectors compared.

In Table 3, why isn't SAND's resource consumptions reported? It has the second-best $F1_e$ score according to Table 2! Even though you can execute it on CPU, the reader still should have these values reported. What does the justification you provided "SAND’s CPU-only execution requirement and SubLOF’s limited multi-core utilization capabilities preclude fair comparison in modern hardware acceleration contexts" mean? You're using most of the other methods on GPU which actually accelerate the methods. What fair comparison are you doing then here by excluding SANDS or SubLOF? Also, how come KAN-AD has a lower execution time on CPU rather than on GPU? Are you doing a lot of I/O transfer operations? Actually this happens for all methods with 1k or less parameters.

The scope of the paper seems shortsighted. Nowadays, especially foundational models [1], treat multivariate time-series [2]. KAN-AD treats only univariate ones. Real-world scenarios usually have multiple variables which makes detecting anomalies more complicated especially if one wants to produce an explanation/interpretation of why the anomaly happened. I'm sceptical about KAN-AD's usage in broader TSAD. The overall experiments (especially the evaluation) raises a lot of question about KAN-AD's utility (see Experimental Designs Or Analyses)

[1] Gao et al. Units: A unified multi-task time series model. NeurIPS'25

[2] Flaborea et al. Are we certain it's anomalous?. Workshops CVPR'23.

Why are the authors only considering forecasting approaches? AD has also reconstruction-based approaches. This neglection hinders the generalizability of KAN-AD. Therefore, the authors have missed a lot of important competitors in TSAD. Here are a few that should be discussed and, perhaps, compared against. Most importantly, the comparison against UniTS [11] is paramount since they are SoTA in all time-series problems. I'm aware that some of these are >5 years old, however [1,9,11] should definitely be considered in the experiments.

[1] Flaborea et al. Are we certain it's anomalous?. Workshops CVPR'23.

[2] Audibert et al. Usad: Unsupervised anomaly detection on multivariate time series. KDD'20

[3] Bieber et al. Low sampling rate for physical activity recognition. PETRA'14

[4] Geiger et al. Tadgan: Time series anomaly detection using generative adversarial networks. Big Data'20

[5] Hundman et al. Detecting spacecraft anomalies using lstms and nonparametric dynamic thresholding. KDD'18

[6] Li et al: Mad-gan: Multivariate anomaly detection for time series data with generative adversarial networks. ICANN'19

[7] Su et al. Robust anomaly detection for multivariate time series through stochastic recurrent neural network. KDD'19

[8] Zhang et al. A deep neural network for unsupervised anomaly detection and diagnosis in multivariate time series data. AAAI'19

[9] Zhang et al. Unsupervised deep anomaly detection for multi-sensor time-series signals. IEEE TKDE'21

[10] Zhao et al. Multivariate time-series anomaly detection via graph attention network. ICDM'20

[11] Gao et al. Units: A unified multi-task time series model. NeurIPS'25 (however, the arxiv was published since February 2024, so this cannot be considered simultaneous and concurrent paper, and the authors should've included it in their discussion, especially since it can be used also in forecasting modality to detect anomalies). I'm mostly interested to see KAN-AD compared against UniTS, the latter beign a foundational model for time-series problems. I suggest the authors look at [12] to see how to adapt it for anomaly detection.

[12] Gabrielli et al. Seamless Monitoring of Stress Levels Leveraging a Universal Model for Time Sequences. arXiv preprint arXiv:2407.03821. 2024 Jul 4.

The proposed method is designed for only univariate time series, and experimented only in univariate datasets, making it impossible to be used in multivariate time series, which is the case in many cases in real life. I assume that the proposed method can be extended to multivariate time series, and I wonder if there is any specific reason for KAN-AD not applied to multivariate time series in the paper.

The paper does not contain any theoretical claims.

The paper does not clarify how TODS benchmark is synthesized, which can affect the performance highly. The authors should clarify detailed information about the benchmark for its validity.

The key contribution of the paper that it adopts KAN backbone for efficient TSAD is related to recent advent of KAN network. The paper adequately adopted Kolmogorov-Arnold representation theorem that it decomposes multivariate continuous function into a finite sum of univariate functions to time series data.

The paper cited the related works appropriately.

KAN-AD definitely makes sense. With respect to evaluation, the metrics Event F1 and Delay F1 align with real world use cases of detecting sustained as well as varied length anomalus segments in the time series.

The paper doesn’t introduce a new theory/theorems, instead relies on the Kolmogorov-Arnold representation theorem as the theoretical foundation. Though I haven’t verified it, I think the correctness of the Kolmogorov-Arnold theorem is well established in the literature.

I’d answer yes. Experimental setup is clearly described, with details on datasets, training and testing setup, baselines and evaluation metrics as well as ablation studies (Section 4 as well as appendix C). I do not find issues with designs as such.

The paper draws on KAN networks, and clearly points to overfitting phenomena in deep anomaly detection models. I actually like the paper, and find that it provides a new perspective on TSAD approach, overcomes the overfitting issues of existing methods, and cleverly uses Fourier transform to improve current KANs for time series anomaly detection, which is an extremely relevant problem to study.

I think the paper references related literature.

While the range of benchmark datasets needs broadening, as I mentioned in the claims and evidence section, the metrics that they use for evaluation are quite appropriate.

There are no proofs provided, which is reasonable given the nature of this paper, which is more algorithmic and experimental.

I did check the soundness of the experimental designs and analysis. The analysis provided is fairly thorough and appropriate. I have a few questions/comments on this:

1. In figure 4, it appears that the 5-delay PA and Point-wise PA rows are swapped.
2. What are the differences in the types of anomalies detected by the different methods?
3. In 4.4.2, the authors state "In contrast, Taylor series exhibited persistent bias due to non-zero function values in most cases, hindering optimal model performance." Is this true specifically in the context of this ablation study? I can't see this being an issue in general, since Taylor series, like the other methods, allows for constant term elimination.

This paper yields an anomaly detection method that has greater robustness to anomalies in the training set, is smaller in terms of the number of patterns, and runs faster; relative to recent methods that have a large number of parameters.

I cannot think of any essential references that were not discussed in this paper.