Title: MambaAD: Exploring State Space Models for Multi-class Unsupervised Anomaly Detection
Venue: NeurIPS 2024
Accepted: yes
Keywords: Mamba

State Space Models

Anomaly Detection

Unsupervised Learning
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.

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

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 .

1 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:

Weintroduce 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

2.1 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

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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.

2.2 State Space Models

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. VLMamba [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.

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3.1 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):

where 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 :

After the discretization, the discretized model formulation can be represented as:

At last, from the perspective of global convolution, the output can be defined as:

where ∗ represents convolution operation, L is the length of sequence x , and K ∈ R L is a structured convolutional kernel.

3.2 MambaAD

The MambaAD framework is proposed for multi-class anomaly detection as illustrated in Fig. 2(a). It consists of three main components: a pre-trained CNN-based encoder, a Half-FPN bottleneck, and a Mamba-based decoder. During training, the encoder extracts feature maps at three different

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scales and inputs them into the H-FPN bottleneck for fusion. The fused output is then fed into the Mamba Decoder with a depth configuration of [3,4,6,3]. The final loss function is the sum of the mean squared error (MSE) computed across feature maps at three scales. Within the Mamba Decoder, we introduce the Locality-Enhanced State Space (LSS) module. The LSS can be configured with different stages M i , where each stage represents the number N of Hybrid State Space (HSS) blocks within the module. In this experiment, we employ LSS with M i = 3 and M i = 2 as the primary modules. The LSS module processes the input X i through HSS blocks that capture global information and through two different scales of Depth-Wise Convolution (DWConv) layers that capture local information. The original input feature dimension is restored through concatenation and convolution operations. The proposed HSS block features a Hybrid Scanning (HS) Encoder and an HS Decoder, which accommodates five distinct scanning methods and eight scanning directions.

3.3 Locality-Enhanced State Space Module

Transformers excel in global modeling and capturing long-range dependencies but tend to overlook local semantic information and exhibit high computational complexity when processing high-resolution features. Conversely, CNNs effectively model local semantics by capturing information from adjacent positions but lack long-range modeling capabilities. To address these limitations, we propose the LSS module in Fig. 2 (b), which incorporates both Mamba-based cascaded HSS blocks for global modeling and parallel multi-kernel depth-wise convolution operations for local information capture.

Specifically, for an input feature X i ∈ R H × W × C , global features G i ∈ R H × W × C enter the HSS blocks while local features L i ∈ R H × W × C proceed through a convolutional network. The global features G i pass through a series of N HSS blocks to obtain global information features G o .

where n ∈ N is the number of HSS blocks. In this study, we primarily use N = 2 and N = 3 , with further ablation experiments presented in Sec. 4.3.

Local features L i are processed by two parallel DWConv blocks, each comprising a 1 × 1 Conv block, an k × k DWConv block, and another 1 × 1 Conv block.

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.

3.4 Hybrid State Space Block

Following 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.

Hybrid 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:

where H 1 = ( 1 2 4 3 ) and 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.

4 Experiments

4.1 Setups: Datasets, Metrics, and Details

MVTec-AD [3] encompasses a diverse collection of 5 types of textures and 10 types of objects, 5,354 high-resolution images in total. 3,629 normal images are designated for training. The remaining 1,725 images are reserved for testing and include both normal and abnormal samples.

VisA [58] features 12 different objects, incorporating three diverse types: complex structures, multiple instances, and single instances. It consists of a total of 10,821 images, of which 9,621 are normal samples, and 1,200 are anomaly samples.

Real-IAD [42] includes objects from 30 distinct categories, with a collection of 150K high-resolution images, making it larger than previous anomaly detection datasets. It consists of 99,721 normal images and 51,329 anomaly images.

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.

4.2 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 Results. As shown in Tab. 1, on MVTec-AD dateset, our MambaAD outperforms all the comparative methods and reaches a new SoTA to 98.6 / 99.6 / 97.6 and 97.7 / 56.3 / 59.2 / 93.1 in multi-class anomaly detection and segmentation. Specifically, compared to DiAD [18], our proposed MambaAD shows an improvement of 1 . 4 ↑ / 0 . 6 ↑ / 1 . 3 ↑ at image-level and 0 . 9 ↑ / 3 . 7 ↑ / 3 . 7 ↑ / 2 . 4 ↑ at pixel-level. Notably, for overall metric mAD of a model, our MambaAD improves by 2 . 0 ↑ , compared with SoTA DiAD. The VisA dataset is more complex and challenging, yet our method still

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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.

4.3 Ablation and Analysis

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.

Local/Global Branches of the LSS Module. We conducted three ablation experiments to verify the impact of branches in the LSS module as shown in Tab. 3. The Local branch represents the use of only the parallel CNN branch, without the Mamba-based HSS branch. The Global branch represents the use of only the Mamba-based HSS branch, without the parallel CNN branch, making the decoder in this structure purely Mamba-based. Finally, Global+Local represents the proposed LSS structure used in MambaAD, which combines the serial Mamba-based HSS with parallel CNN branches of different kernel sizes. The experimental results are shown in the table below. The Local branch, which uses only CNNs, has the lowest parameter count and FLOPs but also the lowest mAD metric, indicating high efficiency but suboptimal accuracy. The Global method, based on the pure Mamba structure, consumes more parameters and FLOPs than the Local method but shows a significant improvement in performance (+2.7%). Finally, the combined Global+Local method, which is the LSS module used in MambaAD, achieves the best performance with a notable improvement of (+1.6%) over the individual methods.

Effectiveness comparison of different pre-trained backbone and Mamba decoder depth. First, we compared various pre-trained feature extraction networks, focusing on the popular ResNet series

as shown in Tab. 4. When maintaining a consistent Mamba decoder depth, we observed that ResNet18 performed the poorest, despite its minimal model size and computational complexity. ResNet50, with approximately 8 times more parameters and computations. Although WideResNet surpassed ResNet34 in certain metrics, it required nearly 10 times the parameters and computational cost. Consequently, after considering all factors, we elected to use ResNet34 as the backbone feature extractor. Then, we examined the impact of different Mamba decoder depths while keeping the backbone network constant. The depths [2,2,2,2] and [3,4,6,3] corresponded to ResNet18 and ResNet34 depths, respectively, while [2,9,2,2] was the prevalent choice in other methods. Our experiments revealed that the [3,4,6,3] depth, despite a slight increase in parameters and computations, consistently outperformed the other configurations.

Efficiency comparison of different SoTA methods. In Tab. 6, we compared our model with five SoTA methods in terms of model size and computational complexity. MambaAD exhibits a minimal increase in parameters compared to UniAD. However, MambaAD outperforms it by 4 . 3 ↑ on the comprehensive metric mAD. Moreover, MambaAD significantly outperforms these other approaches, demonstrating its effectiveness in model

lightweight design while maintaining high performance. Particularly, our method MambaAD has achieved about 2 . 0 ↑ improvement with only 1/50 the parameters and flops of DiAD .

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 and k = 7 , complemented by 1 × 1 convolutions before and after.

5 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.

Acknowledgments and Disclosure of Funding

This work was supported by Jianbing Lingyan Foundation of Zhejiang Province, P.R. China (Grant No. 2023C01022).

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Appendix

Overview

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.

Method

→

RD4AD [12]

UniAD [47]

SimpleNet [30]

DeSTSeg [55]

DiAD [18]

MambaAD

Category

↓

CVPR'22

CVPR'23

CVPR'23

AAAI'24

ours

Objects

Bottle

99.6/99.9/98.4

99.7/

100.

/

100.

100.

/

100.

/

100.

98.7/99.6/96.8

99.7/96.5/91.8

100.

/

100.

/

100.

Cable

84.1/89.5/82.5

95.2/95.9/88.0

97.5/98.5/94.7

89.5/94.6/85.9

94.8/98.8/95.2

98.8

/

99.2

/

95.7

Capsule

94.1/96.9/

96.9

90.7/97.9/93.5

82.8/95.9/92.6

89.0/97.5/95.5

94.4

/

98.7

/94.9

60.8/69.8/86.4

99.8/

100.

/99.3

99.9/

100.

/99.3

98.8/99.2/98.6

99.5/99.7/97.3

100.

/

100.

/

100.

Metal Nut

100.

/

100

./

99.5

99.2/99.9/

99.5

96.9/99.3/96.1

92.9/98.4/92.2

99.1/96.0/91.6

99.9/

100.

/

99.5

Pill

97.5

/

99.6

/

96.8

93.7/98.7/95.7

88.2/97.7/92.5

77.1/94.4/91.7

95.7/98.5/94.5

97.0/99.5/96.2

Screw

97.7

/99.3/95.8

87.5/96.5/89.0

76.7/90.5/87.7

69.9/88.4/85.4

90.7/

99.7

/

97.9

94.7/97.9/94.0

Toothbrush

97.2/99.0/94.7

94.2/97.4/95.2

89.7/95.7/92.3

71.7/89.3/84.5

99.7

/

99.9

/

99.2

98.3/99.3/98.4

Transistor

94.2/95.2/90.0

99.8/98.0/93.8

99.2/98.7/97.6

78.2/79.5/68.8

99.8/99.6/97.4

100.

/

100.

/

100.

Zipper

99.5

/

99.9

/

99.2

99.0/99.7/98.3

88.4/96.3/93.1

95.1/99.1/94.4

99.3/99.8/97.5

Textures

Carpet

98.5/99.6/97.2

99.8

/

99.9

/

99.4

95.7/98.7/93.2

95.9/98.8/94.9

99.4/

99.9

/98.3

99.8

/

99.9

/

99.4

Grid

98.0/99.4/96.6

98.2/99.5/97.3

97.6/99.2/96.4

97.9/99.2/96.6

98.5/99.8/97.7

100.

/

100.

/

100.

Leather

100.

/

100.

/

100.

100.

/

100.

/

100.

100.

/

100.

/

100.

99.2/99.8/98.9

99.8/99.7/97.6

100.

/

100.

/

100.

Tile

98.3/99.3/96.4

99.3

/99.8/98.2

99.3

/99.8/

98.8

97.0/98.9/95.3

96.8/

99.9

/98.4

98.2/99.3/95.4

Wood

99.2/99.8/98.3

98.6/99.6/96.6

98.4/99.5/96.7

99.9

/

100.

/99.2

99.7/

100.

/

100.

98.8/99.6/96.6

Mean

94.6/96.5/95.2

96.5/98.8/96.2

95.3/98.4/95.8

89.2/95.5/91.6

97.2/99.0/96.5

98.6

/

99.6

/

97.8

Method

→

RD4AD [12]

UniAD [47]

SimpleNet [30]

DeSTSeg [55]

DiAD [18]

MambaAD

Category

↓

CVPR'22

CVPR'23

CVPR'23

AAAI'24

(ours)

Objects

Bottle

97.8/68.2/67.6/94.0

98.1/66.0/69.2/93.1

97.2/53.8/62.4/89.0

93.3/61.7/56.0/67.5

98.4/52.2/54.8/86.6

98.8

/

79.7

/

76.7

/

95.2

Cable

85.1/26.3/33.6/75.1

97.3

/39.9/45.2/86.1

96.7/42.4/51.2/85.4

89.3/37.5/40.5/49.4

96.8/

50.1

/

57.8

/80.5

95.8/42.2/48.1/

90.3

Capsule

98.8

/43.4/

50.1

/

94.8

98.5/42.7/46.5/92.1

98.5/35.4/44.3/84.5

95.8/

47.9

/48.9/62.1

97.1/42.0/45.3/87.2

98.4/43.9/47.7/92.6

97.9/36.2/51.6/92.7

98.1/55.2/56.8/94.1

98.4/44.6/51.4/87.4

98.2/65.8/61.6/84.5

98.3/

79.2

/

80.4

/91.5

99.0

/63.6/64.4/

95.7

Metal Nut

93.8/62.3/65.4/91.9

94.8/55.5/66.4/81.8

98.0

/

83.1

/

79.4

/85.2

84.2/42.0/22.8/53.0

97.3/30.0/38.3/90.6

96.7/74.5/79.1/

93.7

Pill

97.5

/63.4/65.2/

95.8

95.0/44.0/53.9/95.3

96.5/

72.4

/

67.7

/81.9

96.2/61.7/41.8/27.9

95.7/46.0/51.4/89.0

97.4/64.0/66.5/95.7

Screw

99.4/40.2/44.7/96.8

98.3/28.7/37.6/95.2

96.5/15.9/23.2/84.0

93.8/19.9/25.3/47.3

97.9/

60.6

/

59.6

/95.0

99.5

/49.8/50.9/

97.1

Toothbrush

99.0

/53.6/58.8/92.0

98.4/34.9/45.7/87.9

98.4/46.9/52.5/87.4

96.2/52.9/58.8/30.9

99.0

/

78.7

/

72.8

/

95.0

99.0

Transistor

85.9/42.3/45.2/74.7

97.9

/59.5/64.6/

93.5

95.8/58.2/56.0/83.2

73.6/38.4/39.2/43.9

95.1/15.6/31.7/90.0

96.5/

69.4

/

67.1

/87.0

Zipper

98.5

/53.9/60.3/94.1

96.8/40.1/49.9/92.6

97.9/53.4/54.6/90.7

97.3/

64.7

/59.2/66.9

96.2/60.7/60.0/91.6

98.4/60.4/

61.7

/

94.3

Textures

Carpet

99.0/58.5/60.5/95.1

98.5/49.9/51.1/94.4

97.4/38.7/43.2/90.6

93.6/59.9/58.9/89.3

98.6/42.2/46.4/90.6

99.2

/

60.0

/

63.3

/

96.7

Grid

99.2

/46.0/47.4/

97.0

96.5/23.0/28.4/92.9

96.8/20.5/27.6/88.6/

97.0/42.1/46.9/86.8

96.6/

66.0

/

64.1

/94.0

99.2

/47.4/47.7/

97.0

Leather

99.3/38.0/45.1/97.4

98.8/32.9/34.4/96.8

98.7/28.5/32.9/92.7

99.5

/

71.5

/

66.5

/91.1

98.8/56.1/62.3/91.3

99.4/50.3/53.3/

98.7

Tile

95.3/48.5/60.5/85.8

91.8/42.1/50.6/78.4

95.7

/60.5/59.9/90.6

93.0/

71.0

/

66.

2/87.1

92.4/65.7/64.1/

90.7

93.8/45.1/54.8/80.0

Wood

95.3/47.8/51.0/90.0

93.2/37.2/41.5/86.7

91.4/34.8/39.7/76.3

95.9

/

77.3

/

71.3

/83.4

93.3/43.3/43.5/

97.5

94.4/46.2/48.2/91.2

Mean

96.1/48.6/53.8/91.1

96.8/43.4/49.5/90.7

96.9/45.9/49.7/86.5

93.1/54.3/50.9/64.8

96.8/52.6/55.5/90.7

97.7

/

56.3

/

59.2

/

93.1

B More Quantitative Results for Each Category on The VisA Dataset.

Tab. A3 and Tab. A4 respectively present the results of image-level anomaly detection and pixel-level anomaly localization quantitative outcomes across all categories within the VisA dataset. The results further demonstrate the superiority of our method over various SoTA approaches.

Method

→

RD4AD [12]

UniAD [47]

SimpleNet [30]

DeSTSeg [55]

DiAD [18]

MambaAD

Category

↓

CVPR'22

CVPR'23

CVPR'23

AAAI'24

(ours)

pcb1

96.2

/

95.5

/

91.9

92.8/92.7/87.8

91.6/91.9/86.0

87.6/83.1/83.7

88.1/88.7/80.7

95.4/93.0/91.6

pcb2

97.8

/

97.8

/

94.2

87.8/87.7/83.1

92.4/93.3/84.5

86.5/85.8/82.6

94.2/93.7/89.3

pcb3

96.4

/

96.2

/

91.0

78.6/78.6/76.1

89.1/91.1/82.6

93.7/95.1/87.0

86.2/87.6/77.6

93.7/94.1/86.7

pcb4

99.9

/

99.9

/

99.0

98.8/98.8/94.3

97.0/97.0/93.5

97.8/97.8/92.7

99.6/99.5/97.0

99.9

/

99.9

/98.5

75.9/61.5/76.8

79.9/79.8/72.7

85.9/82.5/73.1

76.6/69.0/71.0

85.7/85.2/78.8

91.6

/

89.8

/

81.6

macaroni2

88.3

/

84.5

/

83.8

71.6/71.6/69.9

68.3/54.3/59.7

68.9/62.1/67.7

62.5/57.4/69.6

81.6/78.0/73.8

capsules

82.2/90.4/81.3

55.6/55.6/76.9

74.1/82.8/74.6

87.1/93.0/84.2

58.2/69.0/78.5

91.8

/

95.0

/

88.8

candle

92.3/92.9/86.0

94.1/94.0/86.1

84.1/73.3/76.6

94.9/94.8/89.2

92.8/92.0/87.6

96.8

/

96.9

/

90.1

cashew

92.0/95.8/90.7

92.8/92.8/

91.4

88.0/91.3/84.7

92.0/96.1/88.1

91.5/95.7/89.7

94.5

/

97.3

/91.1

chewinggum

94.9/97.5/92.1

96.3/96.2/95.2

96.4/98.2/93.8

95.8/98.3/94.7

99.1

/

99.5

/

95.9

97.7/98.9/94.2

fryum

95.3

/

97.9

/

91.5

83.0/83.0/85.0

88.4/93.0/83.3

92.1/96.1/89.5

89.8/95.0/87.2

95.2/97.7/90.5

pipe_fryum

97.9/98.9/96.5

94.7/94.7/93.9

90.8/95.5/88.6

94.1/97.1/91.9

96.2/98.1/93.7

98.7

/

99.3

/

97.0

Mean

89.6

85.5/85.5/84.4

87.2/87.0/81.8

88.9/89.0/85.2

86.8/88.3/85.1

94.3

/

94.5

/89.4

Method

→

RD4AD [12]

UniAD [47]

SimpleNet [30]

DeSTSeg [55]

DiAD [18]

MambaAD

Category

↓

CVPR'22

CVPR'23

CVPR'23

AAAI'24

(ours)

pcb1

99.4/66.2/62.4/

95.8

93.3/

3.9/

99.2/

86.1

/

78.8

/83.6

95.8/46.4/49.0/83.2

98.7/49.6/52.8/80.2

99.8

/77.1/72.4/92.8

pcb2

98.0/

22.3

/

30.0

/

90.8

93.9/

4.2/

9.2/66.9

96.6/

8.9/18.6/85.7

97.3/14.6/28.2/79.9

95.2/

7.5/16.7/67.0

98.9

/13.3/23.4/89.6

pcb3

97.9/26.2/35.2/

93.9

97.3/13.8/21.9/70.6

97.2/

31.0

/

36.1

/85.1

97.7/28.1/33.4/62.4

96.7/

8.0/18.8/68.9

99.1

/18.3/27.4/89.1

pcb4

97.8/31.4/37.0/

88.7

94.9/14.7/22.9/72.3

93.9/23.9/32.9/61.1

95.8/

53.0

/

53.2

/76.9

97.0/17.6/27.2/85.0

98.6

/47.0/46.9/87.6

99.4/

2.9/

6.9/

95.3

97.4/

3.7/

9.7/84.0

98.9/

3.5/

8.4/92.0

99.1/

5.8/13.4/62.4

94.1/10.2/16.7/68.5

99.5

/

17.5

/

27.6

/95.2

macaroni2

99.7

/

13.2

/

21.8

/

97.4

95.2/

0.9/

4.3/76.6

93.2/

0.6/

3.9/77.8

98.5/

6.3/14.4/70.0

93.6/

0.9/

2.8/73.1

99.5/

9.2/16.1/96.2

capsules

99.4

/60.4/

60.8

/

93.1

88.7/

3.0/

7.4/43.7

97.1/52.9/53.3/73.7

96.9/33.2/39.1/76.7

97.3/10.0/21.0/77.9

99.1/

61.3

/59.8/91.8

candle

99.1

/25.3/35.8/94.9

98.5/17.6/27.9/91.6

97.6/

8.4/16.5/87.6

98.7/

39.9

/

45.8

/69.0

97.3/12.8/22.8/89.4

99.0/23.2/32.4/

95.5

cashew

91.7/44.2/49.7/86.2

98.6/51.7/58.3/

87.9

98.9

/

68.9

/

66.0

/84.4

87.9/47.6/52.1/66.3

90.9/53.1/60.9/61.8

94.3/46.8/51.4/87.8

chewinggum

98.7/59.9/61.7/76.9

98.8

/54.9/56.1/

81.3

97.9/26.8/29.8/78.3

98.8

/

86.9

/

81.0

/68.3

94.7/11.9/25.8/59.5

98.1/57.5/59.9/79.7

fryum

97.0/47.6/51.5/

93.4

95.9/34.0/40.6/76.2

93.0/39.1/45.4/85.1

88.1/35.2/38.5/47.7

97.6

/

58.6

/

60.1

/81.3

96.9/47.8/51.9/91.6

pipe_fryum

99.1/56.8/58.8/

95.4

98.9/50.2/57.7/91.5

98.5/65.6/63.4/83.0

98.9/

78.8

/

72.7

/45.9

99.4

/72.7/69.9/89.9

99.1/53.5/58.5/95.1

Mean

98.1/38.0/42.6/

91.8

95.9/21.0/27.0/75.6

96.8/34.7/37.8/81.4

96.1/

39.6

/43.4/67.4

96.0/26.1/33.0/75.2

98.5

/39.4/

44.0

/91.0

C More Quantitative Results for Each Category on The MVTec-3D Dataset.

Tab. A5 and Tab. A6 respectively present the results of image-level anomaly detection and pixel-level anomaly localization quantitative outcomes across all categories within the MVTec-3D dataset. The results further demonstrate the superiority of our method over various SoTA approaches.

Method

→

RD4AD [12]

UniAD [47]

SimpleNet [30]

DeSTSeg [55]

DiAD [18]

MambaAD

Category

↓

CVPR'22

CVPR'23

CVPR'23

AAAI'24

(ours)

98.6/39.0/45.1/91.3

97.6/30.4/35.8/84.4

93.2/23.6/30.9/70.4

98.7

/

53.0

/52.9/77.6

98.5/49.6/

54.2

/

93.8

98.5/38.3/41.1/92.1

cable gland

99.4

/37.9/43.2/98.2

98.9/26.4/34.8/96.3

95.2/14.4/23.1/86.8

97.8/

46.0

/

49.8

/64.1

98.4/25.2/32.0/94.5

99.4

/39.5/43.9/

98.4

carrot

99.4

/27.5/33.7/97.2

98.0/12.2/19.3/93.4

96.4/13.8/21.2/84.4

86.9/26.5/21.7/14.2

98.6/20.0/26.9/94.6

99.4

/

30.1

/

35.4

/

98.1

cookie

96.6/27.5/32.9/86.6

97.5

/

40.4

/

45.6

/88.7

90.5/26.7/31.4/66.6

93.3/34.0/35.6/40.9

94.3/14.0/23.8/83.5

96.8/39.0/41.9/83.6

dowel

99.7

/47.7/

50.8

/

98.8

99.1/32.1/37.7/96.1

95.3/17.4/25.6/83.0

97.3/43.1/44.5/31.2

97.2/31.4/40.1/89.6

99.6/

49.9

/50.4/97.1

foam

94.2/15.0/26.4/79.9

82.2/

6.8/18.9/55.8

87.8/15.7/26.7/66.7

95.7

/

43.7

/

49.3

/63.6

89.8/

9.6/23.5/69.1

95.1/23.4/32.8/

82.7

peach

98.5/15.5/22.7/93.2

97.4/11.7/17.9/90.4

92.9/

8.1/15.0/74.8

95.9/35.7/41.2/48.2

98.4/27.6/31.3/94.2

99.4

/

43.2

/

45.1

/

97.1

potato

99.1

/14.9/22.5/

95.9

97.6/

5.1/

8.9/91.1

91.0/

4.3/10.9/72.8

89.2/

8.7/12.2/

6.2

98.0/

8.6/17.8/93.9

99.0/

17.6

/

22.6

/94.8

rope

99.6

/50.3/55.9/

97.9

99.0/34.5/40.7/94.3

99.3/51.1/52.9/92.8

98.8/

64.5

/

62.1

/90.4

99.3/61.0/59.9/96.5

99.4/52.1/50.9/95.5

tire

99.2/23.2/31.1/96.4

98.0/11.9/20.3/90.6

93.8/

8.1/15.3/77.9

97.0/25.8/30.0/27.3

91.8/

5.9/13.7/68.8

99.5

/

42.0

/

46.9

/

97.0

Mean

98.4/29.8/36.4/93.5

96.5/21.2/28.0/88.1

93.6/18.3/25.3/77.6

95.1/

38.1

/39.9/46.4

96.4/25.3/32.3/87.8

98.6

/37.5/

41.1

/

93.6

D More Quantitative Results for Each Category on The Uni-Medical Dataset.

Tab. A7 and Tab. A8 respectively present the results of image-level anomaly detection and pixel-level anomaly localization quantitative outcomes across all categories within the Uni-Medical dataset. The results further demonstrate the superiority of our method over various SoTA approaches.

E More Quantitative Results for Each Category on The COCO-AD Dataset.

Tab. A9 and Tab. A10 respectively present the results of image-level anomaly detection and pixellevel anomaly localization quantitative outcomes across all categories within the COCO-AD dataset. The results further demonstrate the superiority of our method over various SoTA approaches.

F More Quantitative Results for Each Category on The Real-IAD Dataset.

Tab. A11 and Tab. A12 respectively present the results of image-level anomaly detection and pixellevel anomaly localization quantitative outcomes across all categories within the Real-IAD dataset. The results further demonstrate the superiority of our method over various SoTA approaches.

Method

→

RD4AD [12]

UniAD [47]

SimpleNet [30]

DeSTSeg [55]

DiAD [18]

MambaAD

Category

↓

CVPR'22

CVPR'23

CVPR'23

AAAI'24

(ours)

audiojack

76.2/63.2/60.8

81.4/

76.6

/64.9

58.4/44.2/50.9

81.1/72.6/64.5

76.5/54.3/65.7

84.2

/76.5/

67.4

bottle cap

89.5/86.3/81.0

92.5/91.7/81.7

54.1/47.6/60.3

78.1/74.6/68.1

91.6/

94.0

/

87.9

92.8

/92.0/82.1

button battery

73.3/78.9/76.1

75.9/81.6/76.3

52.5/60.5/72.4

86.7

/

89.2

/

83.5

80.5/71.3/70.6

79.8/85.3/77.8

end cap

79.8/84.0/77.8

80.9/

86.1

/78.0

51.6/60.8/72.9

77.9/81.1/77.1

85.1

/83.4/

84.8

78.0/82.8/77.2

eraser

90.0/88.7/79.7

90.3

/

89.2

/

80.2

46.4/39.1/55.8

84.6/82.9/71.8

80.0/80.0/77.3

87.5/86.2/76.1

fire hood

78.3/70.1/64.5

80.6/74.8/66.4

58.1/41.9/54.4

83.3

/

81.7

/

80.5

79.3/72.5/64.8

mint

65.8/63.1/64.8

67.0/66.6/64.6

52.4/50.3/63.7

58.4/55.8/63.7

76.7

/

76.7

/

76.0

70.1/70.8/65.5

mounts

88.6

/

79.9

/74.8

87.6/77.3/77.2

58.7/48.1/52.4

74.7/56.5/63.1

75.3/74.5/

82.5

86.8/78.0/73.5

pcb

79.5/85.8/79.7

81.0/88.2/79.1

54.5/66.0/75.5

82.0/88.7/79.6

86.0/85.1/

85.4

89.1

/

93.7

/84.0

phone battery

83.6/80.0/71.6

51.6/43.8/58.0

83.3/81.8/72.1

82.3/77.7/75.9

90.2

/

88.9

/

80.5

plastic nut

80.3/68.0/64.4

80.0/69.2/63.7

59.2/40.3/51.8

83.1/75.4/66.5

71.9/58.2/65.6

87.1

/

80.7

/

70.7

plastic plug

81.4/75.9/67.6

48.2/38.4/54.6

71.7/63.1/60.0

88.7

/

89.2

/

90.9

85.7/82.2/72.6

porcelain doll

86.3/76.3/71.5

85.1/75.2/69.3

66.3/54.5/52.1

78.7/66.2/64.3

72.6/66.8/65.2

88.0

/

82.2

/

74.1

regulator

66.9/48.8/47.7

56.9/41.5/44.5

50.5/29.0/43.9

79.2

/63.5/56.9

72.1/

71.4

/

78.2

69.7/58.7/50.4

rolled strip base

97.5/98.7/94.7

98.7

/

99.3

/

96.5

59.0/75.7/79.8

96.5/98.2/93.0

68.4/55.9/56.8

98.0/99.0/95.0

sim card set

91.6/91.8/84.8

89.7/90.3/83.2

63.1/69.7/70.8

95.5

/

96.2

/

89.2

72.6/53.7/61.5

94.4/95.1/87.2

switch

84.3/87.2/77.9

85.5/88.6/78.4

62.2/66.8/68.6

90.1/92.8/83.1

73.4/49.4/61.2

91.7

/

94.0

/

85.4

tape

96.0/95.1/87.6

97.2

/

96.2

/

89.4

49.9/41.1/54.5

94.5/93.4/85.9

73.9/57.8/66.1

96.8/95.9/89.3

terminalblock

89.4/89.7/83.1

87.5/89.1/81.0

59.8/64.7/68.8

83.1/86.2/76.6

62.1/36.4/47.8

96.1

/

96.8

/

90.0

toothbrush

82.0/83.8/77.2

78.4/80.1/75.6

65.9/70.0/70.1

83.7/85.3/79.0

91.2

/

93.7

/

90.9

85.1/86.2/80.3

toy

69.4/74.2/75.9

68.4/75.1/74.8

57.8/64.4/73.4

70.3/74.8/75.4

66.2/57.3/59.8

83.0

/

87.5

/

79.6

toy brick

63.6/56.1/59.0

77.0

/

71.1

/

66.2

58.3/49.7/58.2

73.2/68.7/63.3

68.4/45.3/55.9

70.5/63.7/61.6

transistor1

91.0/94.0/85.1

93.7/95.9/88.9

62.2/69.2/72.1

90.2/92.1/84.6

73.1/63.1/62.7

94.4

/

96.0

/

89.0

u block

89.5/85.0/74.2

88.8/84.2/

75.5

62.4/48.4/51.8

75.2/68.4/67.9

89.7

/

85.7

/75.3

usb

84.9/84.3/75.1

78.7/79.4/69.1

57.0/55.3/62.9

87.8/88.0/78.3

58.9/37.4/45.7

92.0

/

92.2

/

84.5

usb adaptor

71.1/61.4/62.2

76.8/71.3/64.9

47.5/38.4/56.5

80.1

/74.9/

67.4

76.9/60.2/67.2

79.4/

76.0

/66.3

vcpill

85.1/80.3/72.4

87.1/84.0/74.7

59.0/48.7/56.4

83.8/81.5/69.9

64.1/40.4/56.2

88.3

/

87.7

/

77.4

wooden beads

81.2/78.9/70.9

78.4/77.2/67.8

55.1/52.0/60.2

82.4/78.5/

73.0

62.1/56.4/65.9

82.5

/

81.7

/71.8

woodstick

76.9/61.2/58.1

80.8

/

72.6

/

63.6

58.2/35.6/45.2

80.4/69.2/60.3

74.1/66.0/62.1

80.4/69.0/63.4

zipper

95.3/97.2/91.2

98.2/98.9/95.3

77.2/86.7/77.6

96.9/98.1/93.5

86.0/87.0/84.0

99.2

/

99.6

/

96.9

Mean

82.4/79.0/73.9

83.0/80.9/74.3

57.2/53.4/61.5

82.3/79.2/73.2

75.6/66.4/69.9

86.3

/

84.6

/

77.0

G More Quantitative Results for Each Category on The MVTec-AD Dataset for Single-class Anomaly Detection.

Tab. A13 and Tab. A14 respectively present the results of image-level anomaly detection and pixel-level anomaly localization quantitative outcomes for single-class anomaly detection of the MVTec-AD dataset.

Method

→

RD4AD [12]

UniAD [47]

SimpleNet [30]

DeSTSeg [55]

DiAD [18]

MambaAD

Category

↓

CVPR'22

CVPR'23

CVPR'23

AAAI'24

(ours)

audiojack

96.6/12.8/22.1/79.6

97.6/20.0/31.0/83.7

74.4/

0.9/

4.8/38.0

95.5/

25.4

/

31.9

/52.6

91.6/

1.0/

3.9/63.3

97.7

/21.6/29.5/

83.9

bottle cap

99.5/18.9/29.9/95.7

99.5/19.4/29.6/96.0

85.3/

2.3/

5.7/45.1

94.5/25.3/31.1/25.3

94.6/

4.9/11.4/73.0

99.7

/

30.6

/

34.6

/

97.2

button battery

97.6/33.8/37.8/

86.5

96.7/28.5/34.4/77.5

75.9/

3.2/

6.6/40.5

98.3

/

63.9

/

60.4

/36.9

84.1/

1.4/

5.3/66.9

98.1/46.7/49.5/86.2

end cap

96.7/12.5/22.5/89.2

95.8/

8.8/17.4/85.4

63.1/

0.5/

2.8/25.7

89.6/

14.4

/

22.7

/29.5

81.3/

2.0/

6.9/38.2

97.0

/12.0/19.6/

89.4

eraser

99.5

/30.8/36.7/

96.0

99.3/24.4/30.9/94.1

80.6/

2.7/

7.1/42.8

95.8/

52.7

/

53.9

/46.7

91.1/

7.7/15.4/67.5

99.2/30.2/38.3/93.7

fire hood

98.9

/

27.7

/35.2/

87.9

98.6/23.4/32.2/85.3

70.5/

0.3/

2.2/25.3

97.3/27.1/

35.3

/34.7

91.8/

3.2/

9.2/66.7

98.7/25.1/31.3/86.3

mint

95.0/11.7/23.0/72.3

94.4/

7.7/18.1/62.3

79.9/

0.9/

3.6/43.3

84.1/10.3/22.4/

9.9

91.1/

5.7/11.6/64.2

96.5

/

15.9

/

27.0

/

72.6

mounts

99.3/30.6/37.1/94.9

99.4

/28.0/32.8/

95.2

80.5/

2.2/

6.8/46.1

94.2/30.0/

41.3

/43.3

84.3/

0.4/

1.1/48.8

99.2/

31.4

/35.4/93.5

pcb

97.5/15.8/24.3/88.3

97.0/18.5/28.1/81.6

78.0/

1.4/

4.3/41.3

97.2/37.1/40.4/48.8

92.0/

3.7/

7.4/66.5

99.2

/

46.3

/

50.4

/

93.1

phone battery

77.3/22.6/31.7/94.5

85.5/11.2/21.6/88.5

43.4/

0.1/

0.9/11.8

79.5/25.6/33.8/39.5

96.8/

5.3/11.4/85.4

99.4

/

36.3

/

41.3

/

95.3

plastic nut

98.8/21.1/29.6/91.0

98.4/20.6/27.1/88.9

77.4/

0.6/

3.6/41.5

96.5/

44.8

/

45.7

/38.4

81.1/

0.4/

3.4/38.6

99.4

/33.1/37.3/

96.1

plastic plug

99.1

/20.5/28.4/

94.9

98.6/17.4/26.1/90.3

78.6/

0.7/

1.9/38.8

91.9/20.1/27.3/21.0

92.9/

8.7/15.0/66.1

99.0/

24.2

/

31.7

/91.5

porcelain doll

99.2

/24.8/34.6/

95.7

98.7/14.1/24.5/93.2

81.8/

2.0/

6.4/47.0

93.1/

35.9

/

40.3

/24.8

93.1/

1.4/

4.8/70.4

99.2

/31.3/36.6/95.4

regulator

98.0

/

7.8/16.1/

88.6

95.5/

9.1/17.4/76.1

76.6/

0.1/

0.6/38.1

88.8/18.9/23.6/17.5

84.2/

0.4/

1.5/44.4

97.6/

20.6

/

29.8

/87.0

rolled strip base

99.7

/31.4/39.9/98.4

99.6/20.7/32.2/97.8

80.5/

1.7/

5.1/52.1

99.2/

48.7

/

50.1

/55.5

87.7/

0.6/

3.2/63.4

99.7

/37.4/42.5/

98.8

sim card set

98.5/40.2/44.2/

89.5

97.9/31.6/39.8/85.0

71.0/

6.8/14.3/30.8

99.1

/

65.5

/

62.1

/73.9

89.9/

1.7/

5.8/60.4

98.8/51.1/50.6/89.4

switch

94.4/18.9/26.6/90.9

98.1/33.8/40.6/90.7

71.7/

3.7/

9.3/44.2

97.4/

57.6

/

55.6

/44.7

90.5/

1.4/

5.3/64.2

98.2

/39.9/45.4/

92.9

tape

99.7/42.4/47.8/

98.4

99.7/29.2/36.9/97.5

77.5/

1.2/

3.9/41.4

99.0/

61.7

/

57.6

/48.2

81.7/

0.4/

2.7/47.3

99.8

/47.1/48.2/98.0

terminalblock

99.5/27.4/35.8/97.6

99.2/23.1/30.5/94.4

87.0/

0.8/

3.6/54.8

96.6/

40.6

/

44.1

/34.8

75.5/

0.1/

1.1/38.5

99.8

/35.3/39.7/

98.2

toothbrush

96.9/26.1/34.2/88.7

95.7/16.4/25.3/84.3

84.7/

7.2/14.8/52.6

94.3/

30.0

/

37.3

/42.8

82.0/

1.9/

6.6/54.5

97.5

/27.8/36.7/

91.4

toy

95.2/

5.1/12.8/82.3

93.4/

4.6/12.4/70.5

67.7/

0.1/

0.4/25.0

86.3/

8.1/15.9/16.4

82.1/

1.1/

4.2/50.3

96.0

/

16.4

/

25.8

/

86.3

toy brick

96.4/16.0/24.6/75.3

97.4

/17.1/27.6/

81.3

86.5/

5.2/11.1/56.3

94.7/

24.6

/

30.8

/45.5

93.5/

3.1/

8.1/66.4

96.6/18.0/25.8/74.7

transistor1

99.1/29.6/35.5/95.1

98.9/25.6/33.2/94.3

71.7/

5.1/11.3/35.3

97.3/

43.8

/

44.5

/45.4

88.6

7.2/15.3/58.1

99.4

/39.4/40.0/

96.5

u block

99.6

/40.5/45.2/

96.9

99.3/22.3/29.6/94.3

76.2/

4.8/12.2/34.0

96.9/

57.1

/

55.7

/38.5

88.8/

1.6/

5.4/54.2

99.5/37.8/46.1/95.4

usb

98.1/26.4/35.2/91.0

97.9/20.6/31.7/85.3

81.1/

1.5/

4.9/52.4

98.4/

42.2

/

47.7

/57.1

78.0/

1.0/

3.1/28.0

99.2

/39.1/44.4/

95.2

usb adaptor

94.5/

9.8/17.9/73.1

96.6/10.5/19.0/78.4

67.9/

0.2/

1.3/28.9

94.9/

25.5

/

34.9

/36.4

94.0/

2.3/

6.6/75.5

97.3

/15.3/22.6/

82.5

vcpill

98.3/43.1/48.6/88.7

99.1

/40.7/43.0/

91.3

68.2/

1.1/

3.3/22.0

97.1/

64.7

/

62.3

/42.3

90.2/

1.3/

5.2/60.8

98.7/50.2/54.5/89.3

wooden beads

98.0

/27.1/34.7/

85.7

97.6/16.5/23.6/84.6

68.1/

2.4/

6.0/28.3

94.7/

38.9

/

42.9

/39.4

85.0/

1.1/

4.7/45.6

98.0

/32.6/39.8/84.5

woodstick

97.8/30.7/38.4/

85.0

94.0/36.2/44.3/77.2

76.1/

1.4/

6.0/32.0

97.9

/

60.3

/

60.0

/51.0

90.9/

2.6/

8.0/60.7

97.7/40.1/44.9/82.7

zipper

99.1/44.7/50.2/96.3

98.4/32.5/36.1/95.1

89.9/23.3/31.2/55.5

98.2/35.3/39.0/78.5

90.2/12.5/18.8/53.5

99.3

/

58.2

/

61.3

/

97.6

mean

97.3/25.0/32.7/89.6

97.3/21.1/29.2/86.7

75.7/

2.8/

6.5/39.0

94.6/

37.9

/

41.7

/40.6

88.0/

2.9/

7.1/58.1

98.5

/33.0/38.7/

90.5

Method

→

RD4AD [12]

UniAD [47]

SimpleNet [30]

DeSTSeg [55]

PatchCore [36]

MambaAD

Category

↓

CVPR'22

CVPR'23

CVPR'23

CVPR'22

ours

Objects

Bottle

100.

/

100.

/

100.

100.

/

100.

/

100.

99.9/

100.

/99.2

100.

/

100.

/

100.

100.

/

100.

/

100.

100.

/

100.

/

100.

Cable

94.8/97.0/89.7

97.9/98.7/93.8

99.6/99.7/97.3

97.1/98.4/93.3

99.8

/

99.9

/

98.9

98.5/99.1/95.1

Capsule

98.4

/

99.7

/97.3

87.1/95.3/95.2

97.2/99.2/

98.6

97.4/99.5/96.8

97.4/99.4/98.2

97.8/99.5/97.2

100.

/

100.

/

100.

99.7/99.8/98.6

99.0/99.4/97.2

99.7/99.8/99.3

100.

/

100.

/

100.

100.

/

100.

/

100.

Metal Nut

99.9/

100.

/99.5

98.7/99.7/98.4

99.9/

100.

/99.5

99.7/99.9/98.9

99.9/

100.

/99.5

100.

/

100.

/99.5

Pill

97.5/99.6/97.1

96.0/99.3/95.8

98.6

/

99.7

/

97.9

96.2/99.3/95.7

96.6/99.4/96.5

95.3/99.1/95.3

Screw

97.7/99.2/95.9

87.7/93.0/93.1

97.5/99.2/95.1

92.3/97.5/90.9

98.1

/

99.3

/

97.

5

97.6/99.1/97.1

Toothbrush

93.3/97.2/95.2

88.1/94.8/93.8

99.4/99.8/98.4

100.

/

100.

/

100.

96.1/98.4/95.2

Transistor

98.4/97.7/93.8

100.

/

100.

/

100.

98.5/98.2/94.7

100.

/

100.

/

100.

100.

/

100.

/

100.

Zipper

98.3/99.5/97.9

90.6/96.5/93.9

99.8/99.9/99.6

100.

/

100.

/

100.

99.6/99.9/98.7

98.6/99.6/97.5

Textures

Carpet

99.7/99.9/98.3

99.4/99.8/98.9

99.1/99.7/98.3

99.3/99.8/97.7

98.5/99.6/97.1

100.

/

100.

/

100.

Grid

100.

/

100.

/

100.

97.6/99.3/96.6

100.

/

100.

/

100.

100.

/

100.

/

100.

99.7/99.9/99.1

100.

/

100.

/

100.

Leather

100.

/

100.

/

100.

100.

/

100.

/

100.

100.

/

100.

/

100.

100.

/

100.

/

100.

100.

/

100.

/

100.

100.

/

100.

/

100.

Tile

100.

/

100.

/

100.

95.8/98.2/95.8

99.9/99.9/98.8

100.

/

100.

/99.4

99.0/99.7/98.8

97.5/99.1/94.7

Wood

99.5/99.8/98.3

97.9/99.4/95.9

99.9/

100.

/99.2

99.3/99.8/98.4

99.1/99.7/97.5

99.6/99.9/99.2

Mean

98.5/99.3/97.5

95.8/98.9/96.7

99.3

/

99.8

/98.5

98.6/99.5/97.6

99.2/

99.8

/

98.8

98.7/99.6/98.1

Method

→

RD4AD [12]

UniAD [47]

SimpleNet [30]

DeSTSeg [55]

PatchCore [36]

MambaAD

Category

↓

CVPR'22

CVPR'23

CVPR'23

CVPR'22

(ours)

Objects

Bottle

98.6/75.9/74.1/95.8

98.3/73.6/70.7/94.4

98.0/70.4/72.7/88.8

99.3

/

91.0

/

84.3

/94.0

98.5/77.7/75.2/94.9

98.8/79.7/76.6/

96.1

Cable

96.8/51.3/57.3/88.8

97.4/54.8/56.9/87.7

97.4/

66.8

/60.0/87.7

95.8/55.0/52.8/82.4

98.4

/66.3/

65.1

/92.5

98.0/54.4/61.7/

93.4

Capsule

98.9/48.1/49.9/95.3

98.0/35.2/40.1/86

98.9/42.5/49.1/92.8

98.8/

52.4

/

57.9

/71.6

99.0

/44.7/50.9/91.7

98.6/45.0/47.5/

94.3

98.8/59.6/60.8/

96.5

98.3/55.0/56.1/92.8

97.9/46.2/50.3/78.9

99.4

/

84.5

/

79.0

/90.6

98.7/53.5/59.2/89.7

99.0/61.8/63.9/95.8

Metal Nut

96.9/75.3/79.5/

94.1

94.4/55.8/68.8/77.8

98.8/91.6/86.6/84.0

99.2

/

95.0

/

88.7

/95.0

98.3/86.9/85.1/91.4

97.1/78.3/80.6/93.6

Pill

97.6/66.6/66.7/

95.9

95.2/45.9/51.9/92.2

98.5/79.5/72.6/92.5

98.9

/

87.9

/

79.6

/56.6

97.8/77.8/72.9/94.1

97.3/64.5/66.0/95.8

Screw

99.5

/44.6/47.2/96.9

98.4/15.5/23.6/91.3

99.3/35.0/38.8/95.2

97.3/

54.2

/

53.3

/53.6

99.5

/36.5/40.1/96.6

99.5

/52.2/51.7/

97.6

Toothbrush

99.0/51.8/60.9/92.0

98.5/42.6/52.1/84.6

98.5/41.7/52.9/

92.4

99.5

/

78.2

/

73.7

/90.8

98.6/38.3/52.3/92.3

99.0/51.1/60.7/92.3

Transistor

90.6/52.8/54.9/80.8

98.8

/

79.5

/

75.8

/

94.5

96.8/67.4/62.1/91.1

88.1/63.6/60.0/80.9

96.2/66.4/61.5/89.8

96.8/69.7/67.5/91.6

Zipper

98.7/53.0/59.0/94.6

96.5/35.5/43.4/89.3

98.9/64.3/65.4/

95.5

99.2

/

85.7

/

77.4

/84.3

98.9/62.9/66.1/94.3

98.1/55.6/58.8/94.8

Textures

Carpet

99.1/60.1/60.9/95.6

98.5/52.1/53.3/94.9

98.0/43.2/47.8/87.9

98.2/

77.5

/

72.5

/94.9

99.1/64.1/63.0/94.8

99.2

97.0

Grid

99.3/45.2/47.7/96.3

94.3/24.3/31.5/85.8

98.8/34.7/39.3/93.9

99.5

/

62.5

/

63.5

/93.8

98.8/31.0/35.3/94.2

99.2/48.9/48.8/

97.3

Leather

99.3/44.7/46.7/97.9

99.1/38.5/41.9/98.1

99.2/41.7/45.6/95.7

99.8

/

74.9

/

69.6

/96.9

99.3/46.3/46.7/96.8

99.3/47.5/49.5/

98.6

Tile

95.1/48.6/59.7/85.1

90.2/40.4/48.7/77.1

97.2/69.8/68.8/89.7

99.4

/

94.6

/

87.1

/89.1

95.8/55.0/64.7/

90.0

93.1/42.8/52.3/80.3

Wood

94.8/48.6/49.5/91.6

93.5/38.6/43.9/85.2

94.0/45.6/48.1/82.5

98.4

/

84.5

/

77.5

/90.9

95.0/50.2/50.9/85.3

93.9/44.2/47.7/

92.1

Mean

97.5/55.1/58.3/93.1

96.6/45.8/50.6/88.8

98.0/56.0/57.3/89.9

98.1

/

76.1

/

71.8

/84.4

98.1

/57.2/59.3/92.6

97.8/57.2/59.8/

94.0

H More Quantitative Results for Each Category on The VisA Dataset for Single-class Anomaly Detection.

Tab. A15 and Tab. A16 respectively present the results of image-level anomaly detection and pixel-level anomaly localization quantitative outcomes for single-class anomaly detection of the VisA dataset.

Method

→

RD4AD [12]

UniAD [47]

SimpleNet [30]

DeSTSeg [55]

PatchCore [36]

MambaAD

Category

↓

CVPR'22

CVPR'23

CVPR'23

CVPR'22

(ours)

pcb1

95.9/95.6/92.8

91.9/90.9/87.2

98.9

/

98.9

/

96.0

94.9/92.5/92.0

97.7/97.1/94.9

96.0/95.1/93.8

pcb2

96.5/96.2/92.1

92.2/92.3/84.8

98.8

/

98.8

/

93.9

96.6/94.7/93.4

97.7/98.2/93.3

97.1/96.8/91.9

pcb3

96.2/96.1/91.1

90.9/91.3/86.2

98.9

/

98.8

/

95.1

97.0/97.3/91.7

98.5/98.5/93.5

97.8/98.0/92.7

pcb4

100.

/

100.

/

99.5

98.8/98.6/96.1

99.3/99.0/97.6

99.3/99.3/94.8

99.8/99.8/97.5

99.7/99.7/97.5

92.1/90.2/85.4

87.5/83.3/79.6

94.8

/

92.7

/

89.0

82.8/75.1/77.2

91.3/85.9/87.0

91.2/88.4/84.1

macaroni2

86.1

/80.3/

80.2

83.1/

82.5

/76.4

83.4/77.0/70.4

75.2/60.6/59.4

81.8/78.9/77.7

capsules

89.7/94.2/87.7

79.1/88.7/79.0

90.1/93.3/86.4

85.3/91.5/83.6

77.7/83.2/74.4

91.4

/

94.6

/

90.5

candle

94.6/94.7/89.4

96.5/96.5/89.3

92.3/85.6/86.9

94.6/95.1/87.2

92.2/85.3/84.4

97.7

/

97.7

/

92.1

cashew

96.9

/

98.6

/93.4

91.9/96.1/90.3

94.1/96.2/90.9

73.8/87.2/81.3

91.2/93.5/89.2

95.7/97.6/

93.7

chewinggum

98.8/99.4/96.3

97.4/98.8/94.8

98.6/99.3/

96.9

97.1/98.8/95.9

97.9/98.8/95.4

99.0

/

99.5

/96.1

fryum

94.8/97.7/91.7

85.5/92.6/86.0

96.4/98.0/

93.5

91.7/96.0/88.6

95.0/96.7/89.8

96.5

/

98.3

/92.5

pipe_fryum

99.7/99.8/98.5

91.9/95.4/90.8

99.8

/

99.9

/

99.0

99.3/99.6/97.5

99.1/99.5/97.5

99.2/99.6/97.6

Mean

95.1/95.2/91.5

90.6/92.3/86.7

95.4

/94.8/91.3

90.4/91.1/87.7

92.8/91.4/88.0

95.3/

95.3

/

91.7

Method

→

RD4AD [12]

UniAD [47]

SimpleNet [30]

DeSTSeg [55]

PatchCore [36]

MambaAD

Category

↓

CVPR'22

CVPR'23

CVPR'23

CVPR'22

(ours)

pcb1

99.7/71.2/68.4/94.8

99.2/53.0/56.2/86.7

99.6/87.7/78.4/89.6

99.4/61.5/62.8/76.9

99.8

/

91.8

/

85.9

/94.7

99.8

/72.5/67.4/

94.9

pcb2

98.8/16.2/24.0/90.1

97.1/

5.8/13.0/80.8

98.2/11.9/22.2/87.7

98.9/

20.0

/

30.1

/

91.5

98.7/12.5/22.8/89.9

98.9

/10.1/19.5/90.7

pcb3

99.2/26.4/29.6/92.0

98.2/14.9/23.0/80.3

99.3/45.5/45.4/92.5

98.7/31.3/33.1/40.4

99.4

/

48.1

/

47.3

/89.2

99.3/25.7/27.9/

92.8

pcb4

98.4/39.7/40.9/89.1

97.5/20.8/29.4/82.0

97.5/40.6/45.5/80.6

96.7/27.5/37.5/66.2

98.2/42.1/45.8/82.2

98.7

/

47.6

/

47.0

/

90.9

99.6/

21.0

/

31.1

/95.4

99.0/ 6.8/13.5/95.8

99.6/

7.0/11.1/98.5

98.7/17.3/25.3/53.4

99.7

/

99.6/18.7/27.8/

96.8

macaroni2

99.5

/

10.9

/

18.7

/

95.9

98.2/

3.8/10.3/95.3

98.4/

3.9/

8.8/94.8

99.0/

8.6/18.2/68.8

98.8/

4.9/

7.6/94.5

99.3/10.8/16.2/

95.9

capsules

99.6

/61.1/59.5/92.8

98.4/44.8/49.4/76.6

98.8/52.8/56.2/89.6

98.9/49.6/51.0/90.0

99.4/

65.2

/

65.6

/89.8

99.3/

65.2

/62.5/

93.1

candle

98.9/22.6/33.7/94.5

98.9/16.7/26.2/94.9

98.4/13.1/22.2/90.2

99.0/

31.1

/

36.7

/78.7

99.3

/18.7/27.2/96.7

98.7/19.9/30.5/

95.1

cashew

95.4/53.0/56.2/89.8

99.2/64.6/64.3/85.5

98.9/62.3/62.6/78.5

99.0

/

80.1

/

74.9

/89.2

98.7/58.8/60.0/

91.8

97.5/58.9/59.3/86.9

chewinggum

98.8/54.5/

59.1

/82.6

98.7/48.0/48.5/81.2

98.4/19.5/35.7/

86.0

98.8/24.6/38.8/82.9

98.9

/43.0/44.2/81.1

98.4/

56.5

/56.2/80.6

fryum

96.6/44.2/49.5/90.3

97.1/43.4/51.5/73.8

91.1/37.9/46.0/85.0

95.0/

51.8

/52.3/70.2

92.6/38.3/45.9/89.1

97.0

/48.1/

52.9

/

91.1

pipe_fryum

99.0/51.0/55.5/93.7

99.3/56.9/63.7/90.7

98.9/59.6/60.4/91.5

99.7

/

89.2

/

82.6

/50.7

98.9/58.7/58.8/

96.4

98.9/51.1/54.7/94.0

Mean

98.6/39.3/43.8/91.7

98.4/31.6/37.4/85.3

98.1/36.8/41.2/88.7

98.5/

41.1

/

45.3

/71.6

98.5/40.8/43.7/91.1

98.8

/40.4/43.5/

91.9

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Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe 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.\n\nSTRENGTHS:\nThis paper is the first to explore Mamba in the anomaly detection field. \n\nThe proposed MambaAD achieves state-of-the-art multi-class anomaly detection performance with lower computational demand and fewer parameters than other multi-class anomaly detection alternatives. \n\nThe experiments are extensive, featuring six distinct AD datasets with seven metrics.\n\nWEAKNESSES:\n1. 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?\n\n2. 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.\n\n3. 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.\n\n4. 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?\n\n5. 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?\n\nQUESTIONS:\nSee the weakness.\n\nLIMITATIONS:\nSee the weakness.", "TITLE": "Official Review", "RECOMMENDATION": 8, "REVIEWER_CONFIDENCE": 5, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2024-07-09"}

comments: 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.

STRENGTHS:
1. As far as I am concerned, MambaAD is the first attempt to use Mamba in the anomaly detection domain.
2. The experimental results are SOTA.
3. The representation is clear and easy to follow.

WEAKNESSES:
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:
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:
The limitation and broader societal impacts are mentioned in the last paragraph.
TITLE: Official Review
SOUNDNESS_CORRECTNESS: 3
DATE: 2024-07-13

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe 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.\n\nSTRENGTHS:\n1. The use of Mamba-based models for multi-class anomaly detection and the innovative LSS module are novel contributions.\n2. The theoretical foundations are robust, and the empirical validation is comprehensive.\n3. The paper is clearly written, with well-structured sections and effective use of visual aids.\n4. The approach addresses a critical gap in anomaly detection research and demonstrates significant performance improvements, making it highly relevant and impactful.\n\nWEAKNESSES:\n1. The sensitivity of the method to the selection of scanning methods and directions could be explored further.\n2. While the experimental results are compelling, additional validation on more diverse and challenging datasets would further strengthen the claims.\n3. 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.\n\nQUESTIONS:\n1. Could the authors provide more insights into the selection of scanning methods and the impact of different numbers of directions on the detection performance?\n2. Have the authors considered the robustness of the method under different environmental conditions, such as varying lighting and occlusions?\n3. Could additional experiments on other industrial or medical datasets help to further validate the generalizability of the proposed method?\n\n===== post rebuttal ======\n\nThe authors' rebuttal solve most of my concerns, hence I raise my score to 7.\n\nLIMITATIONS:\nThe 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.", "TITLE": "Official Review", "RECOMMENDATION": 7, "REVIEWER_CONFIDENCE": 3, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2024-07-13"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis 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.\n\nSTRENGTHS:\n1. This study represents a novel exploration in using Mamba for anomaly detection. As far as I understand, this is the first research endeavor to apply Mamba in the context of anomaly detection.\n2. Extensive experiments are presented in the paper.\n\nWEAKNESSES:\n1. From a methodological standpoint, the anomaly detection approach essentially implements RD4AD, with the CNN decoder replaced by a Mamba decoder.\n2. Several key ablations are absent from the experimentation:\n(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.\n(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.\n\nQUESTIONS:\nPlease refer to the comments in the Weakness Section.\n---------------\nPost-rebuttal review: \nWhile 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.\n\nLIMITATIONS:\nMinimal discussion. Although the section labeled \"limitations\" includes some wording, it does not actually discuss any perspectives on real limitations on the methods.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 5, "SOUNDNESS_CORRECTNESS": 2, "DATE": "2024-07-17"}