KambaAD: Enhancing State Space Models with Kolmogorov–Arnold for time series Anomaly Detection

Dear Reviewer terY,

Thank you for your meticulous review and valuable suggestions on our work. Your feedback has been crucial in guiding the improvement of the paper's quality. During the revision process, we carefully considered your comments and made the following improvements and optimizations:

• Detailed Explanation
  We added an analysis of the reasons behind KambaAD's poor performance on the GECCO dataset under Aff-R in Table 2. Similarly, we have also added an analysis of Table 4.

• Supplementation of CI, CD Analysis
  In the revised Section 4.3.5, we have added corresponding analysis to further explain the model's performance and specific role in related tasks.

• Analysis of Running Speed
  In Appendix K, we have added a detailed analysis of running efficiency, including comparisons of KambaAD with other advanced models on the following metrics:

  • Training time (seconds)
  • GPU usage (MB)
  • Memory consumption (MB)
  • Model size (MB)
  • Parameter count
    Experimental results based on four benchmark datasets (MSL, SMAP, SMD, and PSM) demonstrate KambaAD's performance in terms of running efficiency, proving that its computational overhead is within a reasonable range.

• Ablation Experiments on Mamba
  In Table 5, we have added experimental results using two Mamba layers and further analyzed the characteristics of Mamba and its performance in anomaly detection tasks:

  • Noise and Anomaly Filtering Capability: Mamba excels in long sequence modeling, and its selection mechanism effectively filters noise and outliers, enhancing the difference between anomaly points and reconstructed data.
  • Handling of Local and Dense Anomalies:
    • For local anomalies, Mamba assigns lower weights to these points, reconstructing them as normal data for easier detection.
    • For dense continuous anomalies, Mamba may learn the anomaly pattern, which increases the difficulty of distinction to some extent.
      Based on these characteristics, we believe Mamba is particularly suitable for detecting local anomalies. | Data | KAN | ATT | Mamba | K+ATT | K+MB | K+MB+MB | A+MB | KambaAD | |-------|------|------|-------|-------|-------|---------|------|---------| | SMAP | 97.55| 98.13| 97.80 | 98.25| 97.83 | 97.99 | 97.88| 99.19 | | MSL | 97.32| 96.89| 96.74 | 96.90 | 98.27| 96.68 | 94.14| 99.41 | | SMD | 96.25| 95.05| 95.56 | 94.27 | 95.10 | 96.04 | 89.92| 97.27 | | PSM | 97.29| 97.05| 97.22 | 96.78 | 96.58 | 90.78 | 78.88| 98.06 | | Ccard | 38.52| 37.06| 38.22 | 36.33 | 38.72 | 35.48 | 39.05| 41.83 | | SWAN | 76.20| 75.53| 78.10 | 78.72 | 78.97| 78.70 | 78.30| 83.84 | | Mulv | 78.31| 75.73| 83.37| 70.86 | 63.05 | 64.39 | 56.75| 69.54 | | GECCO | 51.97| 50.05| 52.34| 51.71 | 52.02| 52.02 | 52.02| 52.02 |

• Analysis of KAN
  We have updated Figure 3 to more intuitively demonstrate KAN's specific role in anomaly detection tasks. Additionally, results from ablation experiments without KAN are included in Table 5, further validating KAN's critical contribution to the overall model performance.

• Additional Comparative Experiments
  To comprehensively evaluate model performance, we have added comparative experiments with the same parameter count in Appendix J, exploring the impact of different settings on model performance. These experiments provide a fairer and more detailed perspective for comparing model performance. Through these improvements, we have further refined the experimental analysis and theoretical explanation of the model, enhancing the completeness and persuasiveness of the research. Thank you again for your recognition and support! If you have any further suggestions, we would be grateful to receive them!

Thank you for reviewing our work and providing valuable feedback. Your comments have played an important role in enhancing the scientific rigor and clarity of the paper. Based on your suggestions, we have made the following revisions and improvements:

• Supplementation of Computational Efficiency Evaluation
  In Appendix K, we have added an evaluation of computational efficiency between KambaAD and two advanced baseline models (AnomalyTransformer and DCdetector), providing a comprehensive view of the model's resource requirements and performance in practical applications:
  • Evaluation Metrics: Training time (seconds), GPU usage (MB), memory usage (MB), model size (MB), and parameter count (millions).
  • Experimental Datasets: Evaluations are based on four benchmark datasets (MSL, SMAP, SMD, and PSM). The results indicate that KambaAD's computational overhead is within an acceptable range while achieving high detection performance. The results in the simplified version are shown in the Table.

• Update of Experimental Results Comparison
  To more comprehensively showcase model performance, we have made the following updates to the experimental results section:
  • Removed comparisons with some older models and added recent outstanding works, including GDN, TranAD, MTAD-GAT, Crossformer, PatchTST, itransformer, ModernTCN, and TimeMixer++.
  • Added specific sources for these baseline model results, see Appendix L for details.

• Correction of Hyperparameter Settings
  We have corrected the descriptions of hyperparameters window_size and patch_len in the paper and provided the latest settings in Appendix G. The revised settings are more accurate and include specific parameter adjustment methods and their impact on model performance.

  Regarding the necessity of partition operations, we further verified their contribution through experimental results (see Figure 2):

  • Although the overall impact on results is not significant, in the context where mainstream anomaly detection models generally achieve F1 scores close to 95, a 1-2 point improvement brought by partition operations is still significant.

• Expression Corrections
  Thank you for your attention to the details of the paper's expression. We have made corrections to ensure that the content is clearer and more rigorous.

Through these revisions, we have further optimized the expression and experimental results of the paper, enhancing the integrity and scientific rigor of the research. Thank you again for your support and guidance! If you have any further suggestions, we would be delighted to adopt them and continue improving.

Thank you for reviewing our work and providing valuable feedback. Your comments have played an important role in enhancing the scientific rigor and clarity of the paper. Based on your suggestions, we have made the following revisions and improvements:

• Visualization of Model Workflow
  In Section 4.3.7 (VISUALIZATION), we visualized the workflow of the model, illustrating how each component functions and analyzing the reasons behind their effectiveness.

• Comparison of Computational Efficiency
  Addressing concerns about model efficiency, we have added a comparison of computational efficiency between KambaAD and two advanced baseline models (AnomalyTransformer and DCdetector) in Appendix K:

  • Evaluation metrics include training time, GPU usage, memory consumption, model size, and parameter count.
  • Experimental results based on four benchmark datasets (MSL, SMAP, SMD, and PSM) indicate that KambaAD is within a reasonable range of computational overhead. The results in the simplified version are shown in the Table.

• Supplementation of Parameter Sensitivity Analysis
  In the revised Section 4.3.6, we have added a detailed analysis of model parameter sensitivity, exploring the specific impact of core parameters on model performance, including the effect of window size changes. Additionally, to facilitate the reproduction of our experimental results, we have supplemented more specific parameter selection guidance in Appendix G, including recommended parameter configurations for different datasets and the rationale behind their selection.

• Comprehensive Ablation Experiments
  More comprehensive ablation experiments are presented. | Data | KAN | ATT | Mamba | K+ATT | K+MB | K+MB+MB | A+MB | KambaAD | |-------|------|------|-------|-------|-------|---------|------|---------| | SMAP | 97.55| 98.13| 97.80 | 98.25| 97.83 | 97.99 | 97.88| 99.19 | | MSL | 97.32| 96.89| 96.74 | 96.90 | 98.27| 96.68 | 94.14| 99.41 | | SMD | 96.25| 95.05| 95.56 | 94.27 | 95.10 | 96.04 | 89.92| 97.27 | | PSM | 97.29| 97.05| 97.22 | 96.78 | 96.58 | 90.78 | 78.88| 98.06 | | Ccard | 38.52| 37.06| 38.22 | 36.33 | 38.72 | 35.48 | 39.05| 41.83 | | SWAN | 76.20| 75.53| 78.10 | 78.72 | 78.97| 78.70 | 78.30| 83.84 | | Mulv | 78.31| 75.73| 83.37| 70.86 | 63.05 | 64.39 | 56.75| 69.54 | | GECCO | 51.97| 50.05| 52.34| 51.71 | 52.02| 52.02 | 52.02| 52.02 |

• Updates to the Experimental Results Section
  We have been closely following the latest advancements in the field of time series anomaly detection and noted that recent methods like GDN, TranAD, MTAD-GAT, Crossformer, PatchTST, itransformer, ModernTCN, and TimeMixer++ have shown outstanding performance. During the revision, we made significant updates to the experimental results section:

  • Removed comparisons with some older models and added experimental results for the recent works mentioned above, along with complete source information (see Appendix L).
  • Corrected the error in recording ImDiffusion data.
  • Our work demonstrates excellent F1 scores across current datasets, showcasing the performance advantage of KambaAD.

Currently, the model does not have specific designs for handling noisy, sparse, or incomplete data, as we are using publicly available datasets and general processes. However, these situations are frequently encountered in real-world scenarios and will become a focus of our future research directions.

While I appreciate that the authors have made changes to address some of my previous concerns, the responses remain unsatisfactory and lack depth in many areas. Specifically:

• It lacks of rigorous justification for component integration. The authors addressed concerns about the unique advantages of integrating KAN, attention mechanisms, and MAMBA by visualizing a few embedding features. While it is helpful to see the visualization, it is inadequate for several reasons: (1) there is no clear reasoning provided for the roles of each component. (2) The explanation lacks specificity about how each element contributes to anomaly detection and why these particular components were chosen over alternatives. (3) The visualization focuses on a few selective embedding features without a comprehensive or systematic analysis. (4) The argument in this part is more descriptive of the visualization itself rather than providing convincing insights into the necessity or advantage of these components. Hence, the authors fail to justify why KAN is used instead of other potential network architectures and what specific problems it addresses.

• The authors provide limited study on efficiency. The evaluation of the model's efficiency in terms of time and resource consumption is restricted to small and medium datasets. A broader analysis on larger datasets is missing, which limits the generalizability of the results. Also, the validation of the model on real-world scenarios is missing. Those are the scenarios where data may be incomplete or noisy that are critical for evaluating the robustness and practical applicability of anomaly detection models.

• The parameter sensitivity analysis is also insufficient. While the authors conduct empirical studies on model parameter sensitivity across different datasets, they fail to provide rigorous justification for the observed impacts of specific dataset characteristics. Additionally, there is no clear rationale for parameter selection, leaving readers without guidance on reproducing the experiments. Lastly, without releasing code or pretrained models, it becomes challenging for others to validate or replicate the results, which is a significant concern for this type of research.

• The baseline comparisons also omits TadGAN model. Even though TadGAN is introduced in 2020, it employs a distinct approach using Generative Adversarial Networks that is worth to compared to.

• One of the main concerns I have is the lack of code and pretrained models provided by the authors. The absence of publicly available code, pretrained models, and datasets undermines the transparency and reproducibility of this study. Including a repository with code, pretrained models, and baseline implementations is essential for meaningful evaluation and validation by the research community. Particularly in the context where many ML research is not able to be reproduced.

• Finally, I have significant concerns about the novelty and fit of this paper for ICLR. The combination of different components into a single framework and demonstrating incremental improvements in metrics like accuracy or F1 score is a commendable engineering effort but lacks the level of novelty expected for ICLR. This work might be more suitable for applied conferences such as IEEE ICDE, where the focus is on practical advancements rather than groundbreaking contributions to the field. The limited novelty and lack of a clearly articulated valuable contribution to the field remain major weaknesses of this paper. Hence, I decide to not change my decision, and strongly believe that this type of work does not fit to ICLR.

Dear Reviewer GtmB,

We sincerely appreciate your detailed review and valuable suggestions on our work. Your feedback has played an important role in improving the overall quality of the paper. During the revision process, we carefully considered your comments and made the following updates and improvements:

• Expansion of Related Work
  We have been closely following the latest advancements in the field and noted that research using Mamba for anomaly detection has been increasing in recent years. Therefore, we have added two references in the Related Work section to further enhance the background review:

  • Joint Selective State Space Model and Detrending for Robust Time Series Anomaly Detection
  • SGFM: Conditional Flow Matching for Time Series Anomaly Detection With State Space Models

  These additional references help us more comprehensively showcase the development of Mamba-based anomaly detection methods in this field.

• Supplementation of Parameter Sensitivity Analysis
  In the revised Section 4.3.6, we have added a detailed analysis of model parameter sensitivity, exploring the specific impact of core parameters on model performance. Additionally, to facilitate the reproduction of our experimental results, we have supplemented more specific parameter selection guidance in Appendix G, including recommended parameter configurations for different datasets and the rationale behind their selection. The table below shows the settings for some of the hyperparameters.

• Correction and Improvement of Experimental Results
  We conducted a comprehensive check of the experimental details and made the following corrections and supplements:

  • Corrected the results of ImDiffusion on the MSL dataset in Table 1 to ensure accurate records.
  • Thoroughly verified the results of other models on each dataset and supplemented the source information of the results, see Appendix L for details.

• Update of Experimental Results Comparison
  In the comparison of experimental results, we have added recent outstanding works, including GDN, TranAD, MTAD-GAT, Crossformer, PatchTST, itransformer, ModernTCN, and TimeMixer++. These methods represent the latest advancements in the field of time series anomaly detection. The updated F1 comparison results for various models across these four datasets are shown in the table. The complete comparison of multiple metrics has been updated in the paper.

Through these improvements, our work presents clearer advantages when compared to the latest methods in the field, further enhancing the integrity and credibility of the research. Thank you again for your recognition and support. If you have any further suggestions, we would be grateful to receive them!

Dear Reviewer hniq,

Thank you for your detailed review and valuable suggestions on our work. Your feedback has been crucial in enhancing the quality of our paper. During the revision process, we carefully considered your comments and made the following updates and improvements:

Objective of KAN

We understand your concern regarding the design objectives of KAN. The primary goal of KAN is to swiftly identify anomaly points where physical properties change dramatically. In the revised Section 4.3.7 (VISUALIZATION), we have demonstrated through visualization how KAN accurately identifies significant anomaly points globally, even with a small parameter count. This capability lays a solid foundation for subsequent anomaly detection tasks.

Overall Paper Optimization

1. Adjustments to the Introduction
   To focus more on the research topic, we have removed unnecessary statements related to cloud devices, further clarifying the research background and motivation.

2. Updates to the Experimental Results Section
   We have been closely following the latest advancements in time series anomaly detection and noted that recent methods like GDN, TranAD, MTAD-GAT, Crossformer, PatchTST, itransformer, ModernTCN, and TimeMixer++ have shown outstanding performance. We made significant updates to the experimental results section:

   • Removed comparisons with some older models and added experimental results for the recent works mentioned above, along with complete source information (see Appendix L).
   • Corrected the error in recording ImDiffusion data.
   • Our work demonstrates excellent F1 scores across current datasets, showcasing the performance advantage of KambaAD.

   Model	SMD	MSL	SMAP	PSM
   OmniAnomaly	85.22	87.67	86.92	80.83
   InterFusion	86.22	86.62	89.14	83.52
   THOC	84.99	89.69	90.68	89.54
   ImDiffusion	94.88	87.79	91.75	97.81
   DiffAD	92.75	94.19	96.95	97.95
   ModernTCN	85.81	84.92	71.26	97.23
   GDN	83.42	95.91	85.18	85.64
   TranAD	96.05	94.94	89.15	92.20
   MTAD-GAT	84.63	90.84	90.13	87.44
   Crossformer	79.70	84.19	69.14	93.30
   PatchTST	84.44	85.14	70.91	97.23
   iTransformer	71.15	72.54	66.87	95.17
   TimesMixer++	86.50	85.82	73.10	97.60
   AnomalyTrans	90.33	93.93	96.41	97.37
   DCdetector	87.18	96.60	97.02	97.94
   KambaAD	97.27	99.41	99.19	98.06

3. Expansion of Related Work
   We have added two references related to anomaly detection models using Mamba to further enhance the background review:

   • Joint Selective State Space Model and Detrending for Robust Time Series Anomaly Detection
   • SGFM: Conditional Flow Matching for Time Series Anomaly Detection With State Space Models

4. Addition of Ablation Experiments
   To comprehensively analyze the contributions of various model components, we have added the following in the ablation experiments:

   • Results using only the Encoder and only the Reconstructor, ensuring consistency with the parameter count of the complete KambaAD model (see Appendix J).
   • Added results using only two Mamba layers and experiments excluding KAN, further validating the critical role of KAN.

   Data	KAN	ATT	Mamba	K+ATT	K+MB	K+MB+MB	A+MB	KambaAD
   SMAP	97.55	98.13	97.80	98.25	97.83	97.99	97.88	99.19
   MSL	97.32	96.89	96.74	96.90	98.27	96.68	94.14	99.41
   SMD	96.25	95.05	95.56	94.27	95.10	96.04	89.92	97.27
   PSM	97.29	97.05	97.22	96.78	96.58	90.78	78.88	98.06
   Ccard	38.52	37.06	38.22	36.33	38.72	35.48	39.05	41.83
   SWAN	76.20	75.53	78.10	78.72	78.97	78.70	78.30	83.84
   Mulv	78.31	75.73	83.37	70.86	63.05	64.39	56.75	69.54
   GECCO	51.97	50.05	52.34	51.71	52.02	52.02	52.02	52.02

5. Parameter Sensitivity Analysis
   In Section 4.3.6, we have supplemented a detailed analysis of model parameter sensitivity, exploring the impact of different parameter settings on performance, providing readers with more intuitive experimental evidence.