MambaAD: Exploring State Space Models for Multi-class Unsupervised Anomaly Detection

Authors: haoyang  he
yuhu  bai
jiangning  zhang
†  qingdong he
hongxu  chen
zhenye  gan
chengjie  wang
xiangtai  li
guanzhong  tian
lei  xie
Venue: NeurIPS_cc_2024_Conference
Published: 2024-05-06 13:30:42

Abstract: Recent advancements in anomaly detection have seen the efficacy of CNN- and transformer-based approaches. However, CNNs struggle with long-range dependencies, while transformers are burdened by quadratic computational complexity. Mamba-based models, with their superior long-range modeling and linear efficiency, have garnered substantial attention. This study pioneers the application of Mamba to multi-class unsupervised anomaly detection, presenting MambaAD, which consists of a pre-trained encoder and a Mamba decoder featuring (Locality-Enhanced State Space) LSS modules at multi-scales. The proposed LSS module, integrating parallel cascaded (Hybrid State Space) HSS blocks and multi-kernel convolutions operations, effectively captures both long-range and local information. The HSS block, utilizing (Hybrid Scanning) HS encoders, encodes feature maps into five scanning methods and eight directions, thereby strengthening global connections through the (State Space Model) SSM. The use of Hilbert scanning and eight directions significantly improves feature sequence modeling. Comprehensive experiments on six diverse anomaly detection datasets and seven metrics demonstrate state-of-the-art performance, substantiating the method's effectiveness. The code and models are available at https://lewandofskee.github.io/projects/MambaAD.

Main paper: 
 introduction: 
 The advent of smart manufacturing has markedly increased the importance of industrial visual Anomaly Detection (AD) in production processes. This technology promises to enhance efficiency, diminish the costs of manual inspections, and elevate product quality along with the stability of production lines. Presently, most methods predominantly utilize a single-class setting [12, 30, 55] , where a separate model is trained and tested for each class, leading to considerable increases in training and memory usage. Despite recent progress in introducing multi-class AD techniques [47, 18] , there is still significant potential for advancement in terms of both accuracy and efficiency trade-off.The current unsupervised anomaly detection algorithms can be broadly categorized into three approaches [50, 9, 51] : Embedding-based [36, 11, 4, 12, 8] , Synthesizing-based [48, 24, 55, 30] , and Reconstruction-based [27, 18, 6] . Despite the promising results of both Synthesizing and Embeddingbased methods in AD, these approaches often require extensive design and inflexible frameworks. Reconstruction-based methods, such as RD4AD [12] and UniAD [47] , exhibit superior performance and better scalability. RD4AD, as depicted in Fig. 1 (a), employs a pre-trained teacher-student model, comparing anomalies across multi-scale feature levels. While CNN-based RD4AD captures local context effectively, it lacks the ability to establish long-range dependencies. UniAD, the first multiclass AD algorithm, relies on a pre-trained encoder and transformer decoder architecture as illustrated in Fig. 1 (b ). Despite their superior global modeling capabilities, transformers are hampered by quadratic computational complexity, which confines UniAD to anomaly detection on the smallest feature maps, potentially impacting its performance.Recently, Mamba [15] has demonstrated exceptional performance in large language models, offering significantly lower linear complexity compared to transformers while maintaining comparable effectiveness. Numerous recent studies have incorporated Mamba into the visual domain, sparking a surge of research [29, 57, 40, 22, 37, 43] . This paper pioneers the application of Mamba into the anomaly detection area, introducing MambaAD, as illustrated in Fig. 1 (c ). MambaAD combines global and local modeling capabilities, leveraging its linear complexity to compute anomaly maps across multiple scales. Notably, it boasts a lower parameter count and computational demand, making it well-suited for practical applications.Specifically, MambaAD employs a pyramid-structured auto-encoder to reconstruct multi-scale features, utilizing a pre-trained encoder and a novel decoder based on the Mamba architecture. This Mamba-based decoder consists of Locality-Enhanced State Space (LSS) modules at varying scales and quantities. Each LSS module comprises two components: a series of Hybrid State Space (HSS) blocks for global information capture and parallel multi-kernel convolution operations for establishing local connections. The resulting output features integrate the global modeling capabilities of the mamba structure with the local correlation strengths of CNNs. The proposed HSS module investigates five distinct scanning methods and eight scanning directions, with the (Hybrid Scanning) HS encoder and decoder encoding and decoding feature maps into sequences of various scanning methods and directions, respectively. The HSS module enhances the global receptive field across multiple directions, and its use of the Hilbert scanning method [19, 23] is particularly suited to the central concentration of industrial product features. By computing and summing anomaly maps across different feature map scales, MambaAD achieves SoTA performance on several representative AD datasets with seven different metrics for both image-and pixel-level while maintaining a low model parameter count and computational complexity. Our contributions are as follows:• We introduce MambaAD, which innovatively applies the Mamba framework to address multiclass unsupervised anomaly detection tasks. This approach enables multi-scale training and inference with minimal model parameters and computational complexity.• We design a Locality-Enhanced State Space (LSS) module, comprising cascaded Mambabased blocks and parallel multi-kernel convolutions, extracts both global feature correlations and local information associations, achieving a unified model of global and local patterns.• We have explored a Hybrid State Space (HSS) block, encompassing five methods and eight multi-directional scans, to enhance the global modeling capabilities for complex anomaly detection images across various categories and morphologies.• We demonstrate the superiority and efficiency of MambaAD in multi-class anomaly detection tasks, achieving SoTA results on six distinct AD datasets with seven metrics while maintaining remarkably low model parameters and computational complexity.2 Related Work 
unsupervised anomaly detection: 
 Unsupervised Anomaly Detection. Existing AD methods can be mainly categorized into three types: 1) Embedding-based methods focus on encoding RGB images into multi-channel features [36, 11, 4, 12, 10, 38] . These methods typically employ networks per-trained on ImageNet [13] .PatchCore [36] extracts nominal patch features with a memory bank for measuring the Mahalanobis distance. [4] is based on a student-teacher framework where student networks are trained to regress the output of a teacher network. However, the datasets used for these pre-trained models have a significant distribution gap compared to industrial images. 2) Synthesizing-based methods synthesize anomalies on normal images [48, 24, 39, 20] . The pseudo-anomalies in DREAM [48] are generated utilizing Perlin noise and texture images. DREAM, taking anomaly mask as output, consists of a reconstruction network and a discriminative network. Despite the decent performance of such methods, the synthesized anomalies still have a certain gap compared to real-world anomalies. 3) Reconstruction-based methods [12, 27, 52, 7] typically focus on self-training encoders and decoders to reconstruct images, reducing reliance on pre-trained models. Autoencoder [35] , Transformers [33] , Generative Adversarial Networks (GANs) [27, 46] and diffusion models [18, 45] can serve as the backbone for reconstruction networks in anomaly detection. While the model's generalization can occasionally lead to inaccuracies in pinpointing anomalous areas.Multi-class Anomaly Detection. Most current works are trained individually on separate categories, which leads to increased time and memory consumption as the number of categories grows, and they are uncongenial to situations with large intra-class diversity. Recently, to address these issues, multiclass unsupervised anomaly detection (MUAD) methods have attracted a lot of interest. UniAD [47] firstly crafts a unified reconstruction framework for anomaly detection. DiAD [18] investigates an anomaly detection framework based on diffusion models, introducing a semantic-guided network to ensure the consistency of reconstructed image semantics.ViTAD [50] further explores the effectiveness of vanilla Vision Transformer (ViT) on multi-class anomaly detection.State space models (SSMs) [17, 16, 41, 32, 14] have gained considerable attention due to their efficacy in handling long language sequence modeling. Specifically, structure state-space sequence (S4) [16] efficiently models long-range dependencies (LRDs) through parameterization with a diagonal structure, addressing computational bottlenecks encountered in previous works. Building upon S4, numerous models have been proposed, including S5 [41] , H3 [14] , and notably, Mamba [15] . Mamba introduces a data-dependent selection mechanism into S4, which provides a novel paradigm distinct from CNNs or Transformers, maintaining linear scalability of long sequences processing.The tremendous potential of Mamba has sparked a series of excellent works [29, 57, 37, 21, 22, 40, 44, 43, 31, 54, 26] in the vision domain. Vmamba [29] proposes a cross-scan module (CSM) to tackle the direction sensitivity issue between non-causal 2D images and ordered 1D sequences. Moreover, Mamba has found extensive use in the domain of medical image segmentation [37, 28, 44, 43, 25] , incorporating Mamba blocks to UNet-like architecture to achieve task-specific architecture. VL-Mamba [34] and Cobra [56] explore the potential of SSMs in multimodal large language models. Besides, ZigMa [21] addresses the spatial continuity in the scan strategy, and it incorporates Mamba into the Stochastic Interpolation framework [1] .In this work, we develop MambaAD to exploit Mamba's long-range modeling capacity and linear computational efficiency for multi-class unsupervised anomaly detection. This approach innovatively combines SSM's global modeling capabilities with CNNs' detailed local modeling prowess. 3 MethodQuestion: Does the paper discuss the limitations of the work performed by the authors?Answer: [Yes] Justification: The authors have discussed the limitations of the work at the end of the Conclusion section.Guidelines:• The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper. • The authors are encouraged to create a separate "Limitations" section in their paper.• The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be. • The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on a few datasets or with a few runs. In general, empirical results often depend on implicit assumptions, which should be articulated. • The authors should reflect on the factors that influence the performance of the approach.For example, a facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting. Or a speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon. • The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size. • If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness. • While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an important role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations. 
preliminaries: 
 State Space Models [16] , inspired by control systems, map a one-dimensional stimulation x(t) ∈ R L to response y(t) ∈ R L through a hidden state h(t) ∈ R N , which are formulated as linear ordinary differential equations (ODEs):EQUATIONwhere the state transition matrix A ∈ R N ×N , B ∈ R N ×1 and C ∈ R 1×N for a state size N .S4 [16] and Mamba [15] utilize zero-order hold with a timescale parameter ∆ to transform the continuous parameters A and B from the continuous system into the discrete parameters A and B:EQUATIONAfter the discretization, the discretized model formulation can be represented as:EQUATIONAt last, from the perspective of global convolution, the output can be defined as:EQUATIONwhere * represents convolution operation, L is the length of sequence x, and K ∈ R L is a structured convolutional kernel.The MambaAD framework is proposed for multi-class anomaly detection as illustrated in Fig. EQUATIONEQUATION)where k is the kernel size for the DWConv. k = 5 and k = 7 are used in this experiment with further ablations in Sec. 4.3. Each convolutional module includes a Conv 2D layer, an Instance Norm 2D layer, and a SiLU as illustrated in Fig. 2 (d) . Local and global features are aggregated by concatenation along the channel dimension. The final output X o of this block is obtained by a 1 × 1 2D convolution to restore the channel count to match that of the input and a residual connection.EQUATIONFollowing the method outlined in [29, 37] , the HSS block is designed for hybrid-method and hybriddirectional scanning and fusion, as depicted in Fig. 2 (c ). The HSS block primarily comprises Layer Normalization (LN), Linear Layer, depth-wise convolution, SiLU activation, Hybrid Scanning (HS) encoder E HS , State Space Models (SSMs), HS decoder D HS , and residual connections.EQUATIONHybrid Scanning methods. Inspired by space-filling curves [49, 53] , as shown in Fig. 3 , this study explores five different scanning methods: (I) Sweep, (II) Scan, (III) Z-order, (IV) Zigzag, and (V) Hilbert, to assess their impact on the SSM's modeling capabilities. The Hilbert scanning method is ultimately selected for its superior encoding and modeling of local and global information within feature sequences, particularly in mitigating the challenges of modeling long-range dependencies.Further experimental results will be presented in the ablation study. Assuming A is a matrix, A T is the transpose of A, A lr is the left-right reversal of A, A ud is the up-down reversal of A. The Hilbert curve can be obtained by an n-order Hilbert matrix:EQUATIONwhereH 1 = 1 2 4 3and E n is all-one matrix for n-order.Hybrid Scanning directions. Following the setup of previous scanning directions, this study supports eight Hilbert-based scanning directions: (i) forward, (ii) reverse, (iii) width-height (wh) forward, (iv) wh reverse, (v) rotated 90 degrees forward, (vi) rotated 90 degrees reverse, (vii) wh rotated 90 degrees forward, and (viii) wh rotated 90 degrees reverse, as illustrated in Fig. 3 (a). Multiple scanning directions enhance the encoding and modeling capabilities of feature sequences, enabling the handling of various types of anomalous features with further ablations in Sec. 4.3.The HS encoder aims to combine and encode input features according to different scanning methods and directions before feeding them into the SSM to enhance the global modeling capacity of the feature vectors. The HS decoder then decodes the feature vectors output by the SSM back to the original input feature orientation, with the final output obtained by summation. More results on MVTec-3D [5] , as well as newly proposed Uni-Medical [50, 2] and COCO-AD [52] datasets, can be viewed in Appendix 5.Metrics. For anomaly detection and segmentation, we report Area Under the Receiver Operating Characteristic Curve (AU-ROC), Average Precision [48] (AP) and F1-score-max [58] (F1_max). Additionally, for anomaly segmentation, we also report Area Under the Per-Region-Overlap [4] (AU-PRO). We further calculate the mean value of the above seven evaluation metrics (denoted as mAD) to represent a model's comprehensive capability [50] .Implementation Details. All input images are resized to a uniform size of 256 × 256 without additional augmentation for consistency. A pre-trained ResNet34 acts as the feature extractor, while a Mamba decoder of equivalent depth [3, 4, 6, 3] to ResNet34 serves as the student model for training.In the Mamba decoder, the number of cascaded HSS blocks in the second LSS module is set to 2, while all other LSS modules employ 3 cascaded HSS blocks. This experiment employs the Hilbert scanning technique, utilizing eight distinct scanning directions. The AdamW optimizer is employed with a learning rate of 0.005 and a decay rate of 1 × 10 -4 . The model undergoes a training period of 500 epochs for the multi-class setting, conducted on a single NVIDIA TESLA V100 32GB GPU.During training, the sum of MSE across different scales is employed as the loss function. In the testing phase, the sum of cosine similarities at various scales is utilized as the anomaly maps.Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material?Answer: [Yes]Justification: The authors have submitted all the codes in Supplementary Material which provided sufficient instructions to faithfully reproduce the main experimental results.Guidelines:• The answer NA means that paper does not include experiments requiring code. • Providing as much information as possible in supplemental material (appended to the paper) is recommended, but including URLs to data and code is permitted. 
comparison with sotas on different ad datasets: 
 We compared our method with current SoTA methods on a range of datasets utilizing both imagelevel and pixel-level metrics (c.f., Sec. 4.1). This paper primarily compares with UniAD [47] and DiAD [18] dedicated to MUAD. In addition, we also compare our MambaAD with Reconstructionbased RD4AD [12] and Embedding-based DeSTSeg [55] /SimpleNet [30] .Quantitative demonstrates excellent performance. As shown in Tab. 1, our MambaAD exceeds the performance of DiAD [18] by 7.5 ↑/6.2 ↑/4.3 ↑ at image-level and by 2.5 ↑/13.3 ↑/11.0 ↑/15.8 ↑. Meanwhile, we achieve an enhancement of 8.7 ↑ compared to advanced DiAD on the mAD metric. In addition, the SoTA results on Real-IAD datasets, shown in Tab. 1, illustrate the scalability, versatility, and efficacy of our method MambaAD. We also compared the results of MambaAD with state-of-the-art (SoTA) methods for single-class anomaly detection in Tabs. A13 to A16 in the Appendix. In the single-class tasks, we included a comparison with the PatchCore [36] method. On the MVTec-AD dataset, SimpleNet and PatchCore achieved the best results at the image level, while our method achieved the second-best results. At the pixel level, DeSTSeg achieved the best results in most metrics, whereas our method achieved the best results in AUPRO. For the VisA dataset, our method achieved the best results in two metrics each at both the image and pixel levels. This demonstrates that our multi-class anomaly detection method can also achieve optimal or near-optimal results in single-class tasks, indicating its effectiveness and robustness. In contrast, existing single-class SoTA methods like SimpleNet and DeSTSeg, although effective in single-class tasks, show a significant performance drop in multi-class tasks. The PatchCore method can only operate in single-class tasks; for multi-class tasks, it encounters issues such as GPU and memory overflow due to the need to store all features in the Memory Bank. In summary, MambaAD exhibits strong robustness and effectiveness. More detailed results for each category are presented in the Appendix.Qualitative Results. We conducted qualitative experiments on MVTev-AD and VisA datasets that substantiated the accuracy of our method in anomaly segmentation. Fig. 4 demonstrates that our method possesses more precise anomaly segmentation capabilities. Compared to DiAD, our method delivers more accurate anomaly segmentation without significant anomaly segmentation bias.Components IncrementalAblations. The ablation experiments for the proposed components are summarized in Tab. 2. Using the most basic decoder purely based on Mamba and employing only the simplest two-directional sweep scanning method, we achieve an mAD score of 82.1 on the MVTec-AD dataset. Subsequently, by incorporating the proposed LSS module, which integrates the global modeling capabilities of Mamba with the local modeling capabilities of CNNs, the mAD score improves by +2.8%. Finally, replacing the original scanning directions and methods with HSS, which combines features from different scanning directions and employs the Hilbert scanning method, better aligns with the data distribution in most industrial scenarios where objects are centrally located in the image. This results in an additional +1.1% point improvement in the mAD score. Overall, the proposed MambaAD achieves an mAD score of 86.0 on the MVTec-AD dataset and 78.9 on the VisA dataset, reaching the SoTA performance. Effectiveness and efficiency comparison of different scanning methods and directions. In the initial stage, we compared five distinct scanning methods with an 8-direction scan as shown in Tab. 5.The results indicated that the other four methods produced similar outcomes as Index 1-4, albeit marginally inferior to the Hilbert scanning technique at the image level. Subsequently, we examined the impact of varying scan directions. As the number of scan directions increased as Index 5-7, image-level metrics improved gradually, while pixel-level metrics remained consistent. This suggests that augmenting the number of scan directions enhances the global modeling capability of SSM, thereby decreasing the likelihood of image-level misclassification. Ultimately, our analysis revealed that combining various scanning techniques while maintaining a total of eight scan directions led to a decline in performance as as Index 8-12. This decrement could be attributed to the significant disparities among the scanning approaches employed. Consequently, we opted for the Hilbert scanning method, as it demonstrated better suitability for real-world industrial products.Effectiveness comparison of different LSS designs. In Tab. 7, the design focuses on three distinct design directions: the number of M i in the LSS module, the configuration of parallel multi-kernel convolution modules, and the kernel size selection for Depth-Wise Convolutions (DWConv). Initially, we compare scenarios where M i = 1, meaning each LSS module contains a single HSS block, and we experiment with different kernel sizes for DWConv alone and configurations flanked by 1 × 1 convolutions. Subsequently, we contrast the results without residual connections against those with identical settings but with M i = 1. Finally, we examine the outcomes when M i = 2 and M i = 3 under otherwise consistent settings. Analysis reveals that with M i = 1, regardless of the presence of residual connections, the results are inferior to those with M i = 2 and M i = 3. Moreover, using only DWConv blocks with M i = 1, a comparison of parallel depth-wise convolutions with varying kernel sizes indicates that smaller kernels, such as k = 1, significantly degrade performance. Therefore, subsequent comparative experiments focus on larger convolution kernels. In the absence of residual connections, some metrics may surpass those with residual connections, but the longer training time and difficulty in convergence preclude their use in further experiments. In configurations with M i = 2 and M i = 3, we find that DWConv blocks augmented with 1 × 1 convolutions exhibit superior performance. Additionally, kernels sized k = 5 and k = 7 are more suitable for extracting local features and establishing local information associations. Consequently, in this study, we opt for a quantity of HSS blocks with M i = 2 and M i = 3, and we employ parallel DWConv blocks with kernels sized k = 5 andk = 7, complemented by 1 × 1 convolutions before and after. 
conclusion: 
 This paper introduces MambaAD, the first application of the Mamba framework to AD. MambaAD consists of a pre-trained encoder and a Mamba decoder, with a novel LSS module employed at different scales and depths. The LSS module, composed of sequential HSS modules and parallel multi-core convolutional networks, combines Mamba's global modeling prowess with CNN-based local feature correlation. The HSS module employs HS encoders to encode input features into five scanning patterns and eight directions, which facilitate the modeling of feature sequences in industrial products at their central positions. Extensive experiments on six diverse AD datasets and seven evaluation metrics demonstrate the effectiveness of our approach in achieving SoTA performance.Limitations, Broader Impact and Social Impact. The model is not efficient enough and more lightweight models need to be designed. This study marks our initial attempt to apply Mamba in AD, laying a foundation for future research. We hope it can inspire lightweight designs in AD. MambaAD exhibits significant practical implications in enhancing industrial production efficiency. 
experimental setting/details: 
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experiment statistical significance: 
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 Appendix: The supplementary material presents the following sections to strengthen the main manuscript:-Sec. A shows more quantitative results for each category on the MVTec-AD dataset.-Sec. B shows more quantitative results for each category on the VisA dataset.-Sec. C shows more quantitative results for each category on the MVTec-3D dataset.-Sec. D shows more quantitative results for each category on the Uni-Medical dataset.-Sec. E shows more quantitative results for each category on the COCO-AD dataset.-Sec. F shows more quantitative results for each category on the Real-IAD dataset.-Sec. G shows more quantitative results for single-class results on the MVTec-AD dataset.-Sec. H shows more quantitative results for single-class results on the VisA dataset.A More Quantitative Results for Each Category on The MVTec-AD Dataset.Tab. A1 and Tab. A2 respectively present the results of image-level anomaly detection and pixel-level anomaly localization quantitative outcomes across all categories within the MVTec-AD dataset. The results further demonstrate the superiority of our method over various SoTA approaches. Justification: The abstract and introduction have clearly included the motivations, important assumptions, and contributions made in the paper.Guidelines:• The answer NA means that the abstract and introduction do not include the claims made in the paper. • The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers. • The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings. • It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper.Justification: The authors conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics.Guidelines:• The answer NA means that the authors have not reviewed the NeurIPS Code of Ethics.• If the authors answer No, they should explain the special circumstances that require a deviation from the Code of Ethics. • The authors should make sure to preserve anonymity (e.g., if there is a special consideration due to laws or regulations in their jurisdiction). 


Decision: This paper proposed a Mamba-based autoencoder approach for multi-class anomaly detection. The main novelty is adapting the Mamba architecture for anomaly detection. All reviewers recognized this, as well as the extensive experiments demonstrating improved performance over CNN architectures. The paper is also well written and contains attractive diagrams. All reviewers recommended acceptance. 

The AC is concerned the paper did not compare to PatchCore and other standard AD approaches. Indeed, there are some doubts if this approach outperforms standard AD approaches. The lack of comparison is an issue with many multi-class/unified AD works. Still, given the reviewer consensus and as this was not raised during the discussion, the AC gives the paper the benefit of the doubt and recommends acceptance. Please include a comparison with SoTA one-class methods in the camera-ready version.

Reviews: review: paper_summary: paper_summary: This paper introduces a method for multi-class unsupervised anomaly detection utilizing a CNN-based encoder and a Mamba-based decoder. It incorporates an LSS module and a HSS block within the Mamba decoder to enhance performance. The effectiveness of the method is validated through experiments conducted on three image anomaly detection datasets.
strength_weakness: strength_weakness: 1. From a methodological standpoint, the anomaly detection approach essentially implements RD4AD, with the CNN decoder replaced by a Mamba decoder.
2. Several key ablations are absent from the experimentation:
(a) It would be nice to conduct a comparison study using the same RD4AD architecture with CNN-based decoder, transformer-based decoder, and Mamba-based decoder. This comparison would validate the effectiveness of Mamba compared to other decoder architectures.
(b) Ablations of model components should be included, which compares the proposed method, the proposed method without the HSS block, and the proposed method without the LSS module. This ablation study would provide insights into the functionality of these components.
questions: questions: Please refer to the comments in the Weakness Section.
---------------
Post-rebuttal review: 
While I still have some reservations about the methodological novelty of this study, the performance and generalizability of the method appear to be strong. After reviewing the authors' response and considering the feedback from other reviewers, I have decided to raise my initial rating.
limitations: limitations: Minimal discussion. Although the section labeled "limitations" includes some wording, it does not actually discuss any perspectives on real limitations on the methods.
paper_summary: paper_summary: The paper "MambaAD: Exploring State Space Models for Multi-class Unsupervised Anomaly Detection" introduces MambaAD, a novel framework for multi-class unsupervised anomaly detection using Mamba-based models. The framework consists of a pre-trained encoder and a Mamba decoder that integrates Locality-Enhanced State Space (LSS) modules at multiple scales. The LSS module combines Hybrid State Space (HSS) blocks and multi-kernel convolution operations to capture both long-range and local information. The proposed method is evaluated on six diverse anomaly detection datasets, demonstrating state-of-the-art performance and significant improvements in efficiency and accuracy.
strength_weakness: strength_weakness: 1. The sensitivity of the method to the selection of scanning methods and directions could be explored further.
2. While the experimental results are compelling, additional validation on more diverse and challenging datasets would further strengthen the claims.
3. The discussion of potential limitations and future work could be expanded to provide a more comprehensive view of the method's applicability and areas for improvement.
questions: questions: 1. Could the authors provide more insights into the selection of scanning methods and the impact of different numbers of directions on the detection performance?
2. Have the authors considered the robustness of the method under different environmental conditions, such as varying lighting and occlusions?
3. Could additional experiments on other industrial or medical datasets help to further validate the generalizability of the proposed method?

===== post rebuttal ======

The authors' rebuttal solve most of my concerns, hence I raise my score to 7.
limitations: limitations: The authors have adequately addressed some limitations, including potential issues with scanning method selection and environmental conditions. Constructive suggestions for improvement include exploring the sensitivity to scanning parameters and validating the method under different environmental conditions.
paper_summary: paper_summary: This paper employs a pyramid-structured auto-encoder to reconstruct multi-scale features, utilizing a pre-trained encoder and a decoder based on the Mamba architecture. The experimental results show SoTA performances on several commonly used datasets.
strength_weakness: strength_weakness: 1. My major concern is the efficiency comparison shown in Table 4. UniAD is a transformer-based method, but leading to the smallest params and FLops. The advantage of Mamba should be the efficiency, however, which is not as good as transformer-baed methods.
2. The backbone model is WideResNet50. The backbone model of the other method is not WideResNet50. For example, UNIAD use the efficient-net. I am not sure about wether the improvements in this model imply in different backbone model.
questions: questions: 1. Why the params and FLOPs are higher than the transformer-based model?
2. Why the evaluation metrics on the pixel level is lower? Is the anomaly localization worse?
limitations: limitations: The limitation and broader societal impacts are mentioned in the last paragraph.
paper_summary: paper_summary: The paper pioneers the utilization of Mamba in the anomaly detection field. Specifically, the core contribution of the proposed MambaAD is a Locality-Enhanced State Space module, which utilizes Mamba for global information and CNN for local information. Whereas the motivation and the core technical contribution of this paper are similar to other works like U-Mamba, VMamba, and MedMamba, the proposed MambaAD is the first to extensively explore Mamba in the anomaly detection field and achieve state-of-the-art multi-class anomaly detection performance with a low parameter count and computational demand, making this paper acceptable for me.
strength_weakness: strength_weakness: 1. The motivation for using Mamba for visual anomaly detection should be strengthened. e.g., what’s the core challenge for multi-class anomaly detection? why long-range modeling is important for multi-class anomaly detection?

2. It would be better to report the performance with only global/local branches in Table 5, which can better show the influence of individual branches.

3. While the proposed MambaAD achieves better detection performance in most metrics on the evaluated datasets, for some metrics, like AUPRO on VisA, the proposed MambaAD is not the best one. It would be better to offer some analysis on this issue.

4. The current MambaAD framework appears to still rely on a pre-trained CNN encoder, utilizing the Mamba model only in the decoder. Why is this design chosen? What would be the implications if the entire structure were based on the Mamba model?

5. It seems that only the Hilbert scanning method is ultimately used out of the five proposed hybrid scanning methods. How should we further interpret the ablation study in Table 3?
questions: questions: See the weakness.
limitations: limitations: See the weakness.

Comments: title: Any more comments or concerns?
Please let us know whether we address all the issues
Thanks and response to resolutions.
Uni-Medical dataset reference.
Supplementary Ablation Experiments on VisA dataset.
Response to Reviewer FXx2 about mAD.
Thanks.
Response to Reviewer gwhg about FLOPs and FPS
Thanks for the rebuttal
Question on the Uni-Medical dataset
Response
comment: Dear reviewers,

Thanks a lot for your effort in reviewing this submission! We have tried our best to address all the mentioned concerns/problems in the rebuttal. Feel free to let us know if there is anything unclear or so. We are happy to clarify them.

Best regards!

Authors of MambaAD.
Dear reviewer,

Thank you for the comments on our paper.

We have submitted the response to your comments. Please let us know if you have additional questions so that we can address them during the discussion period. We hope that you can consider raising the score after we address all the issues.

Thank you!

Best Regards!

Authors of # Mamba AD
Dear Reviewer wfnx,

**Thank you for recognizing our work and your valuable suggestions to help us improve the manuscript.** We commit to *including ablation experiments based on Transformer methods corresponding to Tab. 1, 7, and 8 in the revised version*. Additionally, we will incorporate the *mIoU evaluation metric results across six datasets to further validate the effectiveness of our approach in anomaly localization*.

**Q: Different Input Resolutions**

***(1)*** Regarding the impact of different resolutions, particularly on long-term information acquisition capability, we compared MambaAD's performance on the **MVTec-AD and VisA datasets at $256^2$ and $512^2$ resolutions**, as shown in the table below. For the MVTec-AD and VisA datasets, the **RD4AD method shows a significant decline in all metrics as the resolution increases**, indicating that *purely convolutional approaches struggle with long-distance modeling*.

***(2)*** For the Transformer-based UniAD method, increasing the resolution on the MVTec-AD dataset results in a **decline in image-level metrics, while pixel-level metrics such as P-AP, P-F1_max, P-AUPRO, and P-mIoU improve**. A similar trend is observed in MambaAD. This outcome may be due to the enhanced and clearer detailed information in higher resolutions, which **aids the model in more accurately identifying and distinguishing different regions for pixel-level tasks**, thereby improving anomaly localization metrics. However, for image-level classification tasks, **excessive detail may introduce noise and increase model complexity, leading to a decline in performance**. The decrease in the P-AUROC metric could be attributed to AUROC's nature as a measure of a classifier's overall performance across different thresholds, *reflecting the model's ability to distinguish between positive and negative samples*. *Higher resolution might cause instability in the model's performance at certain thresholds, especially for borderline samples, leading to a decrease in AUROC*. Overall, on the MVTec-AD dataset, the **MambaAD model outperforms both the CNN-based RD4AD and the Transformer-based UniAD at $512^2$ resolution**.

***(3)*** On the VisA dataset, the **UniAD method shows a general decline in performance at $512^2$ resolution compared to $256^2$ resolution**. This could be due to the *smaller anomaly areas in the VisA dataset, where Transformers may introduce noise during high-resolution global modeling and lack local region modeling capability*. For the **MambaAD** method, **increasing the resolution significantly improves all metrics except P-AUROC**. This improvement is attributed to the **effective long-distance modeling capability of Mamba and the integration of the proposed Locality-Enhanced LSS module. *The decline in P-AUROC might be due to changes in the distribution of positive and negative samples caused by the increased detail, affecting AUROC*. Overall, on the **VisA** dataset, **increasing the resolution significantly enhances MambaAD's performance compared to CNN and Transformer-based models**.

In the future, we will continue to explore the impact of different resolutions, particularly higher resolutions such as $1024^2$ and $2048^2$, to demonstrate the effectiveness of the Mamba model in high-resolution anomaly detection.

***MVTec-AD Dataset***
| Resolution | Method  | I-AUROC | I-AP   | I-F1_max | P-AUROC | P-AP   | P-F1_max | P-AUPRO | P-mIoU |
| ---------- | ------- | ------ | ---- | ------ | ------ | ---- | ------ | ------ | ---- |
| $256^2$ | RD4AD | 94.6   | 96.5 | 95.2   | 96.1   | 48.6 | 53.8   | 91.1   | 37.0 |
| $256^2$ | UniAD   | 96.5   | 98.8 | 96.2   | 96.8   | 43.4 | 49.5   | 90.7   | 32.5 |
| $256^2$ | MambaAD | 98.6   | 99.6 | 97.8   | 97.7   | 56.3 | 59.2   | 93.1   | 41.2 |
|$512^2$| RD4AD | 86.0   | 91.9 | 90.3   | 92.9   | 45.4 | 49.1   | 88.2   | 33.5 |
|$512^2$ | UniAD   | 96.3   | 98.5 | 95.5   | 95.6   | 46.9 | 50.1   | 91.5   | 33.7 |
| $512^2$ | MambaAD | 97.7   | 99.0 | 96.3   | 96.8   | 60.4 | 60.9   | 93.1   | 44.5 |

***VisA Dataset***
| Resolution | Method  | I-AUROC | I-AP   | I-F1_max | P-AUROC | P-AP   | P-F1_max | P-AUPRO | P-mIoU |
| ---------- | ------- | ------ | ---- | ------ | ------ | ---- | ------ | ------ | ---- |
| $256^2$ | RD4AD | 92.4   | 92.4 | 89.6   | 98.1   | 38.0 | 42.6   | 91.8   | 27.9 |
|$256^2$ | UniAD   | 88.8   | 90.8 | 85.8   | 98.3   | 33.7 | 39.0   | 85.5   | 25.7 |
| $256^2$| MambaAD | 94.3   | 94.5 | 89.4   | 98.5   | 39.4 | 44.0   | 91.0   | 29.5 |
| $512^2$| RD4AD | 89.1   | 90.2 | 86.9   | 93.8   | 29.8 | 37.0   | 89.7   | 23.2 |
| $512^2$| UniAD   | 87.4   | 88.5 | 84.8   | 96.6   | 26.7 | 35.2   | 87.2   | 22.0 |
| $512^2$| MambaAD | 95.7   | 97.0 | 92.5   | 96.1   | 40.1 | 46.1   | 92.0   | 31.0 |

Best regards!

Authors of MambaAD.
Thank you for your response. The file **./data/README.md in the official code directory** provided in the abstract of paper [46] documents that **Uni-Medical originates from [A]**. After extracting the Uni-Medical dataset and comparing it with the BMAD dataset proposed in [A], we found that the authors of **[46] selected 3 out of the 6 medical anomaly detection datasets mentioned in [A]. These selected datasets contain both pixel-level and image-level ground truth and were formatted to conform to the MVTec-AD dataset standard**. We have also identified this issue and *attempted to contact the authors of [46] via email to point out the discrepancies between the code and the paper*. **In the revised version, we will cite both [46] and [A] for the Uni-Medical dataset**. Once again, thank you for your efforts in improving the quality of the manuscript.

[A] Bmad: Benchmarks for medical anomaly detection. Bao *et al.*. CVPRW’24.
**Q: Dataset Ablations**

To further validate the reliability of the ablation experiments, we have added ablation experiments on the **VisA dataset on mAD** evaluation metric. Due to time constraints, we only conducted ablation experiments on **Tab. 1, 2, 3, 9, and 10 from the PDF on the VisA dataset**. The results on the **VisA dataset are consistent with the conclusions drawn from the MVTec-AD dataset**. We will provide more detailed and comprehensive experiments as supplementary material in the final version.


***Tab. 1 Decoder Ablations***
| Method                    | Params | FLOPs | MVTec-AD | VisA |
| ------------------------- | --------- | -------- | -------- | ---- |
| CNN-based       | 13.0M        | 5.0G        | 81.7     | 72.5 |
| Transformer-based  | 27.1M      | 8.4G      | 80.2     | 67.4 |
| Mamba-based        | 22.5M      | 7.5G      | 82.1     | 72.9 |


***Tab. 2 Scaning Directions Ablations***
| Scan Directions | Params | FLOPs | Training Time | Training Memory | MVTec-AD | VisA |
| --------------- | --------- | -------- | ------------- | --------------- | -------- | ---- |
| 2               | 21.8M     | 7.2G     | 2h1m          | 6230            | 85.8     | 78.5 |
| 4               | 23.1M     | 7.5G     | 2h56m         | 7974            | 85.9     | 78.6 |
| 8               | 25.7M     | 8.3G     | 5h39m         | 11802           | 86.0       | 78.9 |

***Tab. 3 Components Ablations***
| Basic Mamba | LSS | HSS | MVTec-AD | VisA |
| ------------------- | --- | --- | -------- | ---- |
| √                   |     |     | 82.1     | 72.9 |
| √                   | √   |     | 84.9     | 78.0   |
| √                   | √   | √   | 86.0       | 78.9 |

***Tab. 9 Branches Ablations***
| Method       | Params | FLOPs | MVTec-AD | VisA |
| ------------ | --------- | -------- | -------- | ---- |
| Local        | 13.0M      | 5.0G      | 81.7     | 72.5 |
| Global       | 22.5M      | 7.5G      | 82.1     | 72.9 |
| Global+Local | 25.7M      | 8.3G      | 86.0     | 78.9 |

***Tab. 10 Mamba-based Backbone Ablations***
| Backbone          | Params | FLOPs | MVTec-AD | VisA |
| ----------------- | ------ | ----- | -------- | ---- |
| EfficientVMamba-T | 6.3M   | 1.0G  | 72.7     | 71.2 |
| VMamba-T          | 30.2M  | 6.0G  | 82.9     | 76.2 |
| ResNet34          | 8.2M   | 4.0G  | 86.0     | 78.9 |
Dear reviewer FXx2:

Thank you for your comments. The ablation experiments in the three tables mentioned in the rebuttal were all conducted on the **MVTec-AD** dataset. **In the PDF, only Tab. 4 and 6** include experiments conducted on **multiple datasets**, as indicated in the first row of the respective tables. **All other tables' ablation experiments** were performed on the standard **MVTec-AD dataset**.

Best regards!

Authors of MambaAD.
Dear reviewer aMDx:

Thank you for recognizing our work. We commit to incorporating the content you suggested in the revised version. Thank you again for your effort in the review and the discussion!

Best regards!

Authors of MambaAD.
Dear Reviewer gwhg:

Thank you for your comments.

**Q: FLOPs**

(1) As shown in Fig. 1 of the main text, UniAD is a single-scale method, whereas our Mamba-based MambaAD is a multi-scale method. UniAD **concatenates features from the four stages of the encoder** and uses a Transformer to model **only the smallest scale feature map**. In contrast, MambaAD gradually **increases the resolution of the feature maps** during the decoder stage and performs modeling and reconstruction at four different scales. This difference in framework leads to MambaAD consuming more parameters and FLOPs **on high-resolution feature maps**. Additionally, the WideResNet-50 backbone network, with its higher number of channels at each scale, further increases the parameter and FLOP differences between the two methods.

(2) The Mamba-based model offers **better interpretability and performance**. The model's FLOPs are also related to the implementation method. For instance, Mamba's **FLOPs could be reduced if the state transition is implemented using a vanilla for-loop**. However, the authors of Mamba chose to double the FLOPs to achieve a more parallel and efficient implementation.

**Q: FPS**

We evaluated the FPS of UniAD and MambaAD on ResNet-34 and WideResNet-50 backbones to demonstrate inference speed. The results show that MambaAD still lags behind UniAD in terms of inference speed. The following are possible reasons and directions for optimization:

(1) Model framework: As mentioned in ***Q: FLOPs***, the MambaAD model requires more FLOPs, which affects inference speed to some extent.

(2) Code implementation: The MambaAD code currently uses the initial Mamba implementation with mamba_ssm and causal-conv1d for SSM, which suffers from suboptimal algorithmic efficiency. Using the latest CUDA-accelerated selective_scan_cuda_core algorithm could improve computational efficiency by **40%**.

(3) Number of scanning directions: The current method uses eight different scanning directions to ensure optimal performance. Using only **two different scanning directions** on the ResNet-34 backbone can still achieve an **mAD of 85.8 and an FPS of 574.6**, representing a **258% increase in FPS** compared to using eight scanning directions.

(4) Code implementation of scanning methods: The current Hybrid Scan method is implemented solely in PyTorch, resulting in low efficiency. Our observations indicate that the HS encoder and HS decoder **occupy more than 60% of the time**. We plan to use **Triton or CUDA to accelerate** this process in the future.

In summary, while MambaAD shows **significant performance improvements** over UniAD, its inference speed is affected by the aforementioned issues. We will continue to optimize the model and algorithms to surpass the inference speed of Transformer-based frameworks.

| UniAD | Params(M) | FLOPs(G) | FPS | mAD |
| ------------ | --------- | ----- | ---- | ---- |
| ResNet-34 | 16.1 | 6.1 | 1119.9 | 78.2 |
| WideResNet-50 | 33.5 | 14.4 | 582.7 | 78.9 |

| MambaAD | Params(M) | FLOPs(G) | FPS | mAD  |
| ----------- | --------- | ------ | ---- | ---- |
| ResNet-34 | 25.7 | 8.3 |  222.5 | 86.0 |
| WideResNet-50 | 268  | 68.1 | 44.6 | 86.6 |


Best regards!

Authors of MambaAD.
I appreciate the authors' rebuttal and their engagement with my comments. Given that the experiments were conducted on multiple datasets, could the authors clarify which specific dataset was used to obtain the ablation mAD in the table above?
Thank you for the clarification. I noticed that the authors referenced [46] for the Uni-Medical dataset. However, the paper in [46] neither includes experiments on medical anomaly detection nor references any medical anomaly dataset. Could the authors please confirm the accuracy of this citation for the Uni-Medical dataset?
Thanks for your detailed response. Some of my issues have been addressed. But why does the MambaAD with the backbone ResNet-34 and WideResNet-50 result in more parameters and Flops (compared to UNIAD)? Moreover, could you please list the inference time or FPS to show the inference speed of MambaAD and UniAD?
After considering the author's responses to all reviewers during the rebuttal phase, I believe that the contribution and quality of this paper fully meet the high standards of NeurIPS. I strongly recommend accepting this paper and will modify my rate from 6 to 8. Here are my reasons:

The authors are the first to apply Mamba to the field of anomaly detection, which represents a significant innovation. The introduction of the LSS and HSS modules demonstrates unique approaches and technical advantages in handling multi-class anomaly detection tasks. The experimental section is very detailed and convincing. The rebuttal provided extensive theoretical and experimental analyses that addressed most of my concerns.

However, there is still some room for minor improvements. I suggest including the comparative experimental analysis with Transformer-based methods in the main text. Additionally, incorporating the pixel-level evaluation metrics in the main text would further substantiate the effectiveness of the approach in anomaly localization. Also, it will be interesting to study the influence of different input resolutions, since Mamba should have better long-term information acquisition capability.