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 2024 poster (2024)
Keywords: Mamba
State Space Models
Anomaly Detection
Unsupervised Learning
Primary area: machine_vision
TL;DR: The first to utilize the Mamba model to address multi-class anomaly detection tasks.

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
Haoyang Hel*
Yuhu Bail* Jiangning Zh
Qingdong He² Hongxu Chen
Zhenye Gan Chengjie Wang? Xiangtai Li Guanzhong Tian' Lei Xie
'Zeejiang University Youtu Lab, Tencent "Nanyang Technological University (haoyanghe.yhbaii (0066..chehoongxu.zziiin (yingcaihe, wingzygan, jasoncjwang) @ttencent.com xiangtai94 @ gmail.com, leix @iipe.zju.edi edu.cu.ceennn
zju.edu.ccn
Abstract
Recent advancements in anomaly detection have seen the efficacy of CNN- and transformer-based approaches. However, CNNs struggle with long-range depen- dencies, while transformers are burdened by quadratic computational complex- ity. namba-based models, with their superior long-range modeling and linear efficiency, have garnered substantial attention. This study pioneers the applica- tion of Mamba multi-class unsupervised anomaly detection, presenting Mam- baAD, which consists of a pre-trained encoder and a Mamba decoder featuring ELohaliy-Enhanced State Space) LSS modules 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 se- quence modeling. Comprehensive experiments on six diverse anomaly detec- tion datasets and seven metries demonstrate state-of-the-are performance, sub- stantiating the method's effectiveness. The code and models are available at https://leeandoffkkee github. io/projects//ambaalt
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 single-class setting [12, 30, 55], where 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 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 ap- proaches [50. 9. 51]: Smbedding-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 Embedding- based methods in AD, these approaches often require extensive design and inflexible frameworks. Reconstruction-basse methods, such as RD4AD [12] and UniAD [47], exhibit superior performance
"qqual contributions. Coorespponding author.
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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and better scalability. RD4AD, as depieted 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 multi- class 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 ef- fectiveness. 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. (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 reconstruct multi-scale fea- tures, utilizing a pre-trained encoder and a novel decoder based on the Mamba architecture. This Mamba-based decoder consists of Locality-Enhann 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 estab- lishing 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 multi- class unsupervised anomaly detection tasks. This approach enables multi-scale training and inference with minimal model parameters and computational complexity.
We design a Locality-Enhanee based blocks and parallel multi-kernel convolutions, extracts both global feature correlations and local information associations, achieving unified model of global and local patterns.
State Space (LSS) module, comprising cascaded Mamba-
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 detec- tion 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: Z) Embedding-basee
methods focus on encoding RGB images into multi-channel fea- tures [36, 11, 4, 12, 10, 38]. These methods typically employ networks per-trained on ImageNet [13]. PatchCore [36] extracts nominal patch features with 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 teacher network. However, the datasets used for these pre-trained models have significant distribution gap compared to industrial images. 2) Synthesizing-baase methods synthesize anomalies normal images [48, 24, 39, 20). The pseudo-anomalies in DREAM [48] are generated

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(a) RD4AD
(b) UniAD
(c) MambaAD
(1)
(Nv2)
((N)
CNN- Decoeee 2
CNN- MWN-Decoder
Taastormn
Treraformet
N Sheeddr
Mambo Decoder
Mamba-Decoder
Encoder
Encoder
Emooiee
Encoder
Encoder
Encoder
Enoodera
Nook
Decoder
Encoder
Encoder
Enoccer
Anomaly Map
Anomaly Map
Anomaly Map
Receptive Field:
Local
Global
Global Local
Anomaly map:
Multi-Scale
Single-Soale
Multi-Scale
Compared with (a) local CNN-based RD4AD [12] and (b) global Transformer-based UniAD [47], ours MambaAD with linear complexity capable of integrating the advantages of both global and local modeling, and multi-scale features endow it with more refined prediction accuracy.
Figure I:
utilizing Perlin noise and texture images. DREAM, taking anomaly mask 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-basse methods [12, 27, 52, 7] typically focus on self-training encoders and decoders reconstruct images, reducing reliance on pre-trane 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 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 uncongenial to situations with large intra-class diversity. Recently, to address these issues, multi- class unsupervised anomaly detection (MUAD) methods have attracted 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 reconstructed image semantics. ViTAD [50] further explores the effectiveness of vanilla Vision Transformer (VTT) on multi-class anomaly detection.
2.2 State Space Models
State space models (SSMs) [17, 16, 41, 32, 14] have gained considcrable 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 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 data- deta-dependent selection mechanism into S4, which provides novel paradigm distinct from CNNs or Transformers, maintaining linear scalability of long sequences processing.
The tremendous potential of Mamba has sparked 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 ID sequences. Moreover, Mamba has found extensive use in the domain 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, Ma [21] addresses the spatial continuity in the scan strategy, and incorporates Mamba into the Stochastic Interpolation framework [1].
In this work, we develop MambaAD to exploit Mamba's '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

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Pre-troined
Encodor
W
Conv
Encoder
Encoder
Encoder
H-FPN BottleNeck
W xca
Global
Local
R2
Concat
Block
1x1
1
Add
Loss
HSS block
Mul
DWVConv Block
DWCo Block
LSS Module x2
LSS Module M, x2
N
5x5
7
SILU
Module
Module x1
Frozen
HSS block
Cony Block
Conv Block
x1
1x1
1x1
H
Mamba Decoder
X,
MambaAD
LSS Module (Sec. 3.3).
EX6 CUDo
MM
Ippost
SH
SH
Linear Layer
Conv
& x A
InstanceNNrm220
G
SiLU
Linear Layer
HSS Block (Sec. 3.4)
Conv Block
Figure Overview of the proposed MambaAD, which employs pyramidal auto-encoder framework to reconstruct multi-scale features by the proposed efficient and effective Locality-Enhancer State Space (LSS) module. Specifically, each LSS consists of: /) cascaded Hybrid State Space (HSS) blocks to capture global interaction; and 2) parallel information. Aggregated multi-scale reconstruction error serves as the anomaly map for inference.
convolution operations to replenish local
Method
3.1 Preliminaries
State Space Models [16], inspired by control systems, map one-dimensional stimulation xx() E RL response y(f) RR through hidden state h(t) E R. which are formulated as linear ordinary differential equations (ODEs):
M'(t) Ah(l) + Bx((), D(1) Ch((), where the state transition matrix A NNN BE R and C IRIN for state size N. S4 [16] and Mamba [15] utilize zero-order hold with timescale parameter A transform the continuous parameters A and B from the continuous system into the discrete parameters A and B:
(1)
A AA)(AA), B (AA) AA) - I) AB.
(2)
After the discretization, the discretized model formulation can be represented as:
A Brg y/- Clty
At last, from the perspective of global convolution, the output can be defined as:
K = (CB, CAB CAL-'B) x=x* K.
(4)
where represents convolution operation, L is the length of sequence x, and K R4 is structured convolutional kernel.
3.2 MambaAD
The MambaAD framework is proposed for multi-class anomaly detection as illustrated in Fig. 2(a). consists of three main components: pre-trained CNN-based encoder, Half-FPN bottleneck, and Mamba-bau based decoder. During training, the encoder extracts feature maps at three different

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(8)
(86)
(i)
(H) Sean
(XI))
(Vi6)
[in] Z-Order
(IV) Zigau
(a) Hilbert scamning method with 8 directions
Other scanning meLhods
Figure 3: Hybrid Scanning directions and methods. (a) The Hilbert scanning method with scanning directions is used for HS Encoder and Decoder. (b) The other four scanning methods for comparison.
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 the sum of the mean squared error (MSE) computed across feature maps three scales. Within the Mamba Decoder, State Space (LSS) module. The LSS can be configured with
we introduce the Locality-Enhanee different stages M4. where each stage represents the number N of Hybrid State Space (HSS) blocks within the module. In this experiment, we employ LSS with M, = 3 and M, = 2 as the primary modules. The LSS module processes the input X, 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 Hybrid Scanning (HS) Encoder and an HS Decoder, which accommodates five distinct scanning methods and eight scanning directions.
3.3 Locality-Enhancee State Space Module
Transformers excel global modeling and capturing long-range dependencies but tend to overlook lo- cal semantic information and exhibit high computational complexity when processing high-reso resoluoooo features. Conversely, CNNs effectively model local semantics by capturing information from adjacent positions but lack long-range modeling capabilities. To address these limitations, propose the LSS module in Fig. (b), which incorporates both Mamba-base 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, E RHxW global features G, H enter HSS blocks while local features L, E IR H X proceed through convolutional network. The global features G2 pass through series of HSS blocks to obtain global information features Go.
Ge
(HSS (HSS, (C))
(5)
where n E 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 Li are processed by two parallel DWConv blocks, each comprising 1 x Conv block, k x k DWConv block, and another 1 Conv block.
Lm = ConvB1x1 (AIBBiixDDOoooe (DWConvBes (ConvBIx1(L.)
(6)
where is the kernel size for the DWConv. = 5 and = are used in this experiment with further ablations in Sec. 4.3. Each convolutional module includes Conv 2D layer, an Instance Norm 2D layer, and a SiLU as illustrated in Fig. (d). Local and global features are aggregated by concatenation along the channel dimension. The final output X, of this block is obtained by a x 1 2D convolution to restore the channel count to match that the input and a residual connection.
X. Conv2D 1x1 (Concat (Go, Lks Lxy)) + X,-
3.4 Hybrid State Space Block
Following the method outlined in [29,37], the HSS block is designed for hybrid-method and hybrid- directional scanning and fusion, depicted in Fig. 2 (c). The HSS block primarily comprises Layer
5

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Normalization (LN), Linear Layer, depth-wise convolution, SiLU activation, Hybrid Scanning (HS)
encoder Ens, State Space Models (SSMs), HS decoder Dus, and residual connections.
G¹ = LL
(8)
G Linear(C,; L o(Lineer(LNN())))) +G;
Hybrid Scanning methods. Inspired by space-filling curves [49, 53], shown in Fig. 3, this study explores five different scanning methods: (I) Sweep, (II) Scan, (III) Z-order, (IV) Zigzag, and (V) Hilbert, assess their impact the SSM's modeling capabilities. The Hilbert scanning method is ultimately selected for its superior encoding and modeling 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 matrix, A" is the transpose of A, A is the left-right reversal of A, Aud is the up-down reversal of A. The Hilbert curve can be obtained by an n-order Hilbert matrix:
Hn (4u+1 +1)En Hn En + H² (3x + En - (H2
4 E, + HT
{
Had (3 x3 4th + 1n (H!r)²
if is even,
Hat1=
(4u+1 + +1 - H
if n is odd.
1 2
where Hi
and E, is all-one matrix for n-order.
4 3
Hybrid Scanning directions. Following the setup of previous scamning directions, this study supports eight Hilbert-based scanning directions: (i) forward, (ii) reverse, (ii) 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 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 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 diverse collection of 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 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 collection of 150K high-resolution images, making larger than previous anomaly detection datasets. It consists of 99,721 normal images and 51,329 anomaly images.
More results on MV [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 Fl-score-mar [58] (F1 (F1_max). Additionally, for anomaly segmentation, also report Area Under the PurrRReiinn--ve [4] (AU-PRO). We further calculate the mean value of the above seven evaluation metrics (denoted as m.AD) represent a model's comprehensive capability [50].
Implementation Details. input images are resized to a uniform size of 256 x 256 without additional augmentation for consistency, A pre-trained ResNet34 acts the feature extractor, while

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Table 1: Quantitative Results on different AD datasets for multi-class setting.
Image-lovel
PiscHHevel
Dateset
Method
mAD
AU-ROC
AU-ROC
AU-PRO
RDVAD [12]
54.6
96.3
95.2
96.1
15.6
51.3
y1,1
82.3
UniAD [47]
96.5
98.8
96.2
96.3
43,4
49.5
90.7
31.7
SimpleNet [90]
98
95.8
49.7
DeSTSeg [55]
89.2
95.5
91.6
93.1
$4.3
50.9
64.8
77.1
DiAD [18]
97.2
99.0
96.5
96.8
52.6
55.5
90.7
%4.0
RDXAD
92.4
92.4
89.6
98.1
38.0
42.6
91.8
22.8
UniAD> [47]
88.8
90.8
85.8
98.1
33.7
39.0
85.5
74.6
SimpleNet
VisA [88]
DeSTSeg [55]
88.9
89.0
85.2
96.1
39.6
43.4
67.4
72.8
DiAD [18]
$6.8
$8.3
85.1
96.0
26.1
33.0
75.2
70.1
(Oun)
RI4AD [12]
82.4
79.0
73.9
V1.3
25.0
32.7
89.6
68.6
UniAD [47]
83.0
$0.9
24.3
97.3
21.1
29.2
86.7
67.5
Real-TAD [42]
SimpleNet [50]
57.22
75.7
2.8
39.0
DeSTSeg [55]
82.3
79.2
73.2
94.6
37,9
41.7
40.6
61.2
DiAD [18]
75.6
66.4
69.9
88.0
2.9
7.1
58.1
52.6
MambnAD (Ours)
0.1
33.0++06
38.7
Mamba decoder of equivalent depth [3,4,6,3] to ResNet34 serves as 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 cascaded HSS blocks. This experiment employs the Hilbert scamning technique, utilizing cight distinct scanning directions. The AdamW optimizer is employed with learning rate of 0,005 and a decay rate of 10 The model undergoes a training period of 500 epochs for the multi-class setting, conducted single NVIDIA TESLA V100 32GB GPU. During training, the sum MSE across different scales is employed as the loss function. In the testing phase, the sum of cosine similarities various scales is utilized as the anomaly maps.
4.2 Comparison with SoTAs Different AD datasets
We compared our method with current SoTA methods on a range of datasets utilizing both image- level and pixel-level metries (c.f., Sec. 4.1). This paper primarily compares with UniAD [47] and DiAD [18] dedicated to MUAD. addition, we also compare our MambaAD with Reconstruction- based RD4AD [12] and Embedding- DeSTSeg [55]/SimpleNet [30].
Quantitative Results. As shown Tab. 1, on MVTec-AD dateset, our MambaAD outperforms all the comparative methods and reaches
So'A to 98.6/99.6//99 /97.6 and 97.7 /...///.//// 956.3/59.2/99 in multi-class anomaly detection and segmentation. Specifically, compared to DiAD [18], our proposed MambaAD shows improvement of 1.4 1/0.6 f/1.3 1 at image-level and 0.9 1/3.7 1/3.7 1/2.4 4 at pixel-level. Notably, for overall metric mAD of a model, our MambaAD improves by 2.0 f. compared with SoTA DiAD. The VisA dataset is complex and challenging, yet method still
Un30
0-D
Tnothbrash
Nut
Cancle
froum
Pipe Fryum
Figure Qualitative visualization for lexel-level anomaly segmentation on MVTec and VisA datasets.

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demonstrates excellent performance. As shown in Tab. 1. our MambaAD exceeds the performance of DiAD [18] by 7.5 1/6.2 1/4.3 1 at image-level and by 2.5 f/13.3 1/11.0 t/15.8 f. 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 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 pecrementalAblationn 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. 111%% % 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.
Table 2: Incremental Ablations.
Table 3: Ablation Study on the LSS Module.
Basic Mamba
LSS
HSS
MVT
VisA
Method
Params(M)
FLOPs(G)
MVTec-AD
VisA
82.1
72.9
Local
13.0
5.0
81.7
72.5
84.9
78.0
Global
22.5
7.5
82.1
72.9
86.0
78.9
Local + Global
25.7
8.3
86.0
78.9
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 only the Mamba-based HSS branch, without the parallel CNN branch, making the decoder in this structure purely Mamba-based. Finally, Global+ represents the proposed LSS structure used in MambaAD, which combines the serial Mamba-basch 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
8

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Table 4: Ablation studies on the pre-trainee backbone and Mamba decoder depth.
Image-levd
Piscl-lovel
Backbone
Decoder Depth
Parums(M)
GLOPs()
AU-ROC
AP
F1, Fl_max
AP
Fl.mat
AL-PRO
ResNeti8
[34.6.3]
(22.222
98.6
98.8
19.1
91.8
30.3
[2..2.3]
99.3
97.0
10.0
ResNec34
(29.2.3]
97.6
99.3
97.3
$6.4
93.2
36.1
[34.6.3]
99.6
27.8
07.2
59.2
93.1
25.7
Ro
(34.6.3]
99.4
07.2
92.3
251.0
WideResNee50
[34.6.3]
98.6
00.5
98.0
57.9
93.8
268.0
as shown in Tab. 4. When maintaining 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, elected to use ResNet34 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.
Table 5: Ablations on different scanning methods and directions.
HS Methods
Directions
Image-Jevel
Pixel-level
Index
Sweep
Sean
Zigzag
AU-ROC
Fl_max
AU-ROC
8
98.1
99.4
97.2
97.5
56.8
58.8
92.9
98.0
99.4
97.2
97.6
56.6
59.0
93.4
8
98.1
99.4
97.4
97.6
56.6
59.0
93.0
96.2
99.1
97.6
97.6
56.3
58.8
93.1
97.9
97.1
97.3
56.5
59.2
59.1
98.6
97.8
56.3
96.8
99.0
97.0
97.4
54.4
57.0
928
97.5
99.2
97.4
97.5
$5.0
57.4
93.1
10
97.4
99.1
96.8
97.5
55.5
57.9
03.1
96.0
99.3
97.4
97.6
56.2
58.5
Efficiency comparison of different SoTA methods. In Tab. 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 by 4.3 1 on the comprehensive metric mAD. More- over, MambaAD significantly outperforms these other approaches, demonstrating its effectiveness in model lightweight design while maintaining high performance. Particularly, method MambaAD has achieved about 2.0 improvement with only 1/50 the parameters and flops of DIAD.
Table 6: Efficiency comparison of SoTA methods.
Method
Parums(M)
FLOPx(G)
mAD
RD4AD[12]
80.6
28.4
UniAD [47]
24.5
3.6
81.7
DeSTSeg [55]
35.2
122.7
81.2
SimpleNet [30]
72.8
16.1
77.1
DiAD [18]
1331.3
451.5
84.0
MambaAD (Ours)
25.7
8.3
86.0
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 Tab. 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 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 total of eight scan directions led to a decline in performance as as Index 12. This decrement could be attributed to the significant disparities among the scanning approaches employed. Consequently, scanning method, as it demonstrated better suitability for real-world industrial products.
opted for the Hilbert
Effectiveness comparison of different LSS designs. In Tab. 7, the design focuses on three distinct design directions: the number of Mj in the LSS module, the configuration of parallel multi-kernel convolution modules, and the kernel size selection for Depth-Wise Convolutions (DWConv). Initially,

---

Table 7: Ablation studies on LSS module's designs.
Image level
Pixel Pixet-level
LSS Design
Local Con
Kernel AU ROC
[[_ma [1_maxx
AL ROC
AP
Fl_max
PRO
k=l.3
96.6
98.0
96.2
96.7
49.5
52.4
91.3
k-1.5
94.6
96.0
96.4
96.6
50.1
53.5
91.3
Only DWCConv
k=1.3,5
kvd,7
94.8
96.5
98.9
98.2
96.7
96.
96.6
95.9
47.7
51.0
51.6
53.8
89.8
91.4
Mr
kx3,5,7
96.5
98.3
96.5
97.2
51.5
55.2
92.2
1,3577
95.2
96.3
96.5
96.5
49.1
$2.6
90.8
k-1.5
96.1
96.7
96.7
07.2
$2.2
55.6
92.5
DWConv 1 Conv
k-5,7
95.8
95.6
96.3
97.3
51.7
54.5
92.0
k-3,577
96.0
98.6
96.7
97.3
52.4
55.4
92.2
k-3.5
97.3
96.9
53.4
55.9
91.5
Only DWCCsnv
kvd.7
95.0
k=3,57
M. noskip
k=0.5
95.4
DWCCov Conv
ked.7
k-3,5,7
96.0
52.3
55.4
k=1.5
08.2
97.4
58.2
Only DWCConv
k-5.7
08.3
99.4
$6.1
59.0
k-1,5,7
98.2
99.3
97.3
90.5
53.9
57.5
92.9
M. 2. 2, 33
k-0,5
98.6
99.5
97.6
90.5
55.3
58.3
92.7
DWCCov
L-5.7
98.6
99.6
97.8
97.7
$6.3
59.2
93.1
k-3,5,7
98.1
99.3
97.4
22.5
55.1
57.5
92.8
compare scenarios where M, 1, meaning each LSS module contains single HSS block, and we experiment with different kernel sizes for DWConv alone and configurations flanked by x 1 convolutions. Subsequently,
contrast the results without residual connections against those with identical settings but with M, = 1. Finally, we examine the outcomes when M, = 2 and M, = 3 under otherwise consistent settings. Analysis reveals that with M, 1, regardless of the presence of residual connections, the results are inferior to those with M, = 2 and M; = 3. Moreover, using only comparison of parallel depth-wise convolutions with varying kernel
DWConv blocks with M, 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 metries may surpass those with residual connections, but the longer training time and difficulty in convergence preclude their use further experiments. In configurations with M, and MM = 3. we find that DWConv blocks augmented with 1 x 1 convolutions exhibit superior performance. Additionally, kernels sized 5 and ie are more suitable for extracting local features and establishing local information associations. Consequently, in this study, we opt for quantity of HSS blocks with M, and M; 3, and we employ parallel DWConv blocks with kernels sized l = 5 andk 7, complemented by 1 x convolutions before and after.
5
Conclusion
This paper introduces MambaAD, the first application of the Mamba framework to AD. MambaAD consists of pre-trained encoder and a Mamba decoder, with novel L.S module employed at different scales and depths. The LSS module, composed of sequential HSS modules and parallel multi-core convolutional networks, combines Mamba's '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 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 AD, laying a foundation for future research. We hope it can inspire lightweight designs in AD. MambaAD exhibits significant practical implications 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).
10

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13

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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 the MVTec-AD dataset.
Sec. 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 the Uni-Medical dataset.
Sec. 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.
Table A1: Comparison with SoTA methods on MVTec-AD dataset for multi-class anomaly detection with AU-ROC/AP/FI __ma metrics.
Method -
RD4AD [12]
UniAD [47]
SimpleNet [30]
DeSTSeg [55]
DIAD [18]
MambaaD
Category 4
CVPR'22
NeurIPS'22
CVPR'22 23
CVPR'25
AAAI'24
Bottle
99.6/99.9/98.8 4
99.7/100./100.
100./100/110..
08.7/99.699..
99.7/96.5/91.8 8
100//10./100.
Cable
(1.1//995/82.3
95,2/95 9/88.0
75.2/95.9/88.0
97.5/98.5/94
89.5/94.60 99.5//9.6/85.9
94,8/98 8/9522
98.8/99.//95.7
Capsule
94.1/96.9/96.
86.9/97 8/94.4
00.7/97.9/933
82.8/95.99 9/969/9992.6
$9.0/97.5/955
94.4/98.7/94.9
Hazelnut
60.8/69.8886 4
89,8/100//99 3
99,9/100./99.3
99.5/99.7/97.
100//100.100.
Metal Nut
100//100//9.55
99.2/99 9/99.5
96.9/99.3/98
92. 92.9/98.4/99
99. 1/96.0/91.6 6
99.9/100./99.
Pill
97.5/99.6/96.8
93.7/98.7/98
28.2//7.7/922.
77.1/94.4 7/94//9//91.
95.7/98.5/94.5
97.0/9995/96.2
Screw
(1.7/99.3/95..
77.5//6.5/89
7t.7/99.5/87.
69.9/88, 4/85,4
90.7/99.7/97.9
94,7/97 799944440
Toothbrush
97.2/99.0/44.7
94.2/97.A/9 A/95.2
99.7/95.7/922
99.7/99.9/99
98, 2/993/99. 3/98
Transistor
94,2/95 2/90.0
8/98. 3.99.8
99.2/98.7/977
27.27/9.5/68.8
99 8/9966//
100./100/100.
Zipper
99,5/99.//99.2
95, 8/99 5/97.1
12.00999777 7/98.3
88.4/96.3/99
1/99. 1/94,
99,3/99 8/97.5
Carpet
98.5/99.6W9F
99.8//9.9/99.4
95.7/98.7/99 7/93.2
95. 9/98.8/9944...
99.4//9.9/98.
99.8/9999999
Grid
98.06/99//96.6
98.2/99 5/97.3
97.6/99.2/96.
97, 99.99/9999...
78.55/998/977 8/97.7
100./100./100.
Leather
100./100/100.
100./100//000.
100./100.1000
2/99 8/98.9
9/98 8/997/99777 7/97.6
100./000./00.
Tile
28.3/99.3/96 .4
99.3/99 8/98.2
99.3/99
97. 9995.9995.3
96. 8/99.9/98.8.
98. 98.22/993/955 3/55.4
Wood
99,2999./98
98. 6..9999.0 6/96.6
98.4/99
99.9/100./99.2
99. 10.0//00./100.
98. 99..//9.6/966
94.6/66559522
96.5/98.8/96.2
95.3/98.4/95.8
89.2/95.5/91.6
97.2/99.0/96.5
98.6/99.697.88
Table A2: Comparison with SoTA methods on MVTec-AD dataset for multi-class anomaly localiza-
tion with AU-ROC/AP/F1 max/AU-PRO metrics.
Method
RD4AD [12]
UniAD (47)
SimpleNet [30)
DeSTSeg [55]
DiAD (18)
MambaAD
Chiegary
CVPR
NeurIPS
CVPRR23
CVPR 23
(curs)
Boitle
77.8/68:266.6/940
9772/53.862 4/89.0
91.3161.75660077..
98.4/2 25547855
98.879.7776.7955.
Cable
85. $5.1/26.3:3.6//55
97,3/39 (01.99555.2200 2/86.
96.7682.4/51
2/85.4
89,3/37.5448 5/955999
96.8/50.1/57.8/00
95 95.8/42.244 1/90.3
Caponle
98.8/334:140.100
98.5/42 7146, 5/12.1
98. 4/44 3/94.5
95.8/47.9153
97.1:42.0/45 3/87.2
96. 46.43//4//3 7/92.66
Hazelnut
97.9//6.2/51.69999
2/56.8/94 8/941
95.4/44
4/87.4
98.3779.28004911.
99.0/63.6/64
Metal Nut
94,8/55 5/66.
95.0/83.1179.4/85.
2..244..0/2.886 2/533.00
97.3/30.0/38,3990
96.7/74.5/79. 1/93339999.
Pill
97.5/63 /16...//.5.... 2/95.8
95.0/M 0V53 9/95 3
96. 05.5772.466.7781
96.2/61
1/227
95 95.7/66.0/51. 19166.0/51.4/944
97. 07.4/61.D/66 5.95.
Surew
99.4/40, 2444, 7/96.8 8
98. 3/28 7/37 6/95. 2
96.5/15.9/23 9/23 .2/84.0
93.8/19 9/25.3447 3
97 9/6666/99669955
99.5-99 8/50 9,97.1
Toothbrush
99.153 8/92.0
4/34
2/91 .7
Transistor
2/74.7
97,955
8:88
73.6/38
7/000
96.5669.666.1.87..
Zipper
98.5/53.9990.55
3/94
96.8/40
1/99 9/92.66
9/53.4/444 6/90.7
97. 97.3164.7/99.220 26669
95
Carper
99.0U58 5/61 5/U5.1
98.1149
9/51, 1 4
VT A558, 7/43 22/00.6
93 6/19 9/58 929.3
VN 6/42 2/46. 4/90
99.2/6n.1M53 3/6
Grid
99.2/46. 01..6..0444..99 4/97.0
96.5733 (V28 4M929
97.0/42 1/46, 9/868
29.2/47.4/47 7/97.0
Leather
1/97.4
98.8/2290
49668
72.8//28.
99.5/71.5
8:56 1/62
99
Tile
91.842 1/50.678..
25.7/60.//99.999 99999999.6
93.0/71.0/66,/8887
92. 22.465.77/6 7967
93.5 1/5.8
Wood
95.3/17.8/55
LV90000
93.2/37
5186..7
91 21//31.8/5 7/76.3
95.9 95.9/77.3/77 3/1.3831
92 23.3/1333/115.997
91. 31.4/16.2/ 2/15 2/91.2
Mean
96.8/43.
5990
96.945 9/999/9999//88.
96.8/52./5555990
97.7796.1199229.1
14

---

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.
Table A3: Comparison with SoTA methods on VisA dataset for multi-class anomaly detection with AU-ROC/AP/FI_nn max metrics.
Method +
RD4AD [12]
UniAD [47]
SimpleNet [30]
DeSTSeg [55]
DiAD [18]
MambaAD
Category
CVPR'22
NeuriPS'22
CVPR 23
CVPR
AAAI'24
(ours)
pebl
96.2/95.5/991.9
92.8/92.7887.8
9166/1199/66 O
87.6/83 17.6/3
35.4993.0/91.
peb2
779997.8/94.2
87.8/87.7/33.1
92.4/93.3/84.5
86.5/85.8/82..
91.4/91.//44.
94.2/93.7/89.3
peb3
96.4/96.2/91, 1.0
78.6/78.6/761
89.1/91.1/822
93.1/95.1/87.0
86.2/87 6/77.6
93.7/94, 1/86,7
pcb4
99.9/99.//99.0
8/88/9
97 97.0997.0/93.5
9/.8/99.
99.6/99.5/97.0
99.9/99.9/98 S
macaronil
75.9/61.5776.
79.9779.8722.7
85.9/82.5733.1
76.6/69.0/1100
85. 2/78.8
91.6/89.8/816
macaroni2
88.3/84.5/833.8
7166716666
68.3/54.3/99.7
68,9/62.1/67.7
62.5/57 4/69.6
81.6/78.0773.
capsules
82.2/90.4/81.3
55.6/55.676.9
74.1/82.8/74. 8/74.6
87.1/93.0/84..2
58,2/69.0/78.
91.8/95.0/88.8
candle
92.3//2.9/86.00
94,16
84.1/73.3/7.66
9499/
92.8/92.0/87..
96.8/96.9/90.1
cashew
8/90.7
92.8/92.//1.44
88.0/91
92.0/96. 1/88..
91.5/95.7/89.7
94.5/97.3/1..
chewinggum
94.9/97.5/92.1
2/95..2
96,4/98.2/99
95, 05.8//8.3/944
99.1/99.5/95.9
97.7/98. 9/94,2
fryum
95/9/
03.0833.08850
88 4/9.0/888833
92.1/99.1 1/89.5
89 99.8/95.008 0/87.2
95.22/7.7/990.
pipe fryum
97.9/98.9/96
9/96.5
94.7/94.7/99.9
90.8/95.5/88.6
14.1/97.1N 1/91.9
16.2/7
98.7/99.3/97.0
Mean
92.4/92.4/89.6
85.3785.5/84.4
87.2/87.08188
88,9/89.0/55.2
86.8/88.3/85.1
94.3/94.5/99.4
Table A4: Comparison with SoTA methods on VisA dataset for multi-class anomaly localization with AU-ROC/AP//I max/ AROOPO metrics.
Method
RD4AD [12]
UniAD (47] NeurIPS'22
SimpleNet [30] CVPR'23
DeSTSeg [55] CVPR
DiAD [18]
MambuAD (ours)
Category
CVPR'22
AAAAI24
pebl
99.4666.2 4/958
93.3/ 3.9/ 8.3/64.1
99.2/661/78888888
1/78.883..6
95.8//96444 4M496,4499.0 DV83.2
98,7449
8//00
99 W/7. 1/72 4/2
peh2
0K.0/22..3/000//900
93.97 4.2/ 9. 9.2/66.9
96.6 8.9/8 6/85.7
97.3/14.6/28 2/79.9
95.2/
7.5/16. 7/67.0
98.9/13. 3/23 ANY 6
pch3
97.9/26.2/35 2/339
97.3/13.8/2119009
97.7/28.
1/3.44.133.4
99.1/18.3/27
pch4
97.8/31 4/37.0888
9/.//14//22//72
93.9/23.9/22 9/61.
95.8/53.0/53.2766
97.0/17.6/27.2/855
98.6/47 0/46 9/87.
macaronil
99.6/ 2.5/ 6,9/95.3
97.4/ 3.7/ 9,7/84.0
98.9/ 3.5/ 8,49200
99.1/ 5.8/13 4/62.4
94.1/10,2/16 2/6.55
2P.5/17.5/27.44
99.7/13.2/21
4.3/16.6
D&W 3,9777.8
41444447700.0
0.9V 2.8/78.1
9.2/16,
capsales
99.4950.0600.893..
88.7/ 3.0/ 7.4/3.77
97. 97.1/52
9/5333/333.7 3/7.77
96.9/33.2/39,
1/76.7
97.3/10.0/21
10777.9
99.1/61.3/99
8/9)
candle
99, 99,1/25,3/35 8/94.9
98.5/1 9/117///27///91..
97.6/ 8.4/16.5/874
98. 98.773999/45.8869.
97,3//2.8/22.88 8/89.4
99.0/23, 2/32 A/9555
casbew
91.7/44,
98.6/51 7/58, 3/87.9
98.9688
87.9 6/52, 1/66.3
90.9/53 1/60 9161 88
3/46, 8/51 4M87.8
chewinggum
98.8/54
1/81_3
9/26 8/78.3
98.866.9/11.0
94.
9/25 8/59.5
1/57 5/59 9/79.7
fryum
97.0/47.645 (4446//511.. 5.93.4
95.9/34 6/7.6666666666
93 0139. 4/8.1
88. 2/5.2/388.5/47...
77.6/58.6/60. 1/811111111.
96 9/17 8/51 9991 6
pipe_fry fryum
90.1/56.8/58.8/95
95.9750.257..71.55
98. 53.5665.60 4/830
98.9777..77..744599
99.4/72.718999788 9/999/99///
99, 99.1/53.5/58 5/95_1
Mean
98. 08.1/59.0042.6/91..8
95.9/21 4/27.0/75.6
964.83477/37
888.4
96.1V26. 1...2261/33.075...
ww.5739.4/44.00111
C More Quantitative Results for Each Category on The MVTeec-DD Dataset.
Tab. A5 and Tab. A6 respectively present the results of image- 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.
Table A5: Comparison with SoTA methods on MeTTec- dataset for multi-class anomaly detection
with AU-ROC/AP/F1 max metrics.
Method -
RD4AD [12]
UniAD [47]
SimpleNet [30]
DeSTSeg [55]
DiAD [18]
MambaAD
Category 4
CVPR'22
2e
CVPR'23 23
CVPR 23
AAAI'24
(ours)
bagel
82.5/95.4/89.6
82.7/95.8/89.3
76.2/93.3/89.3
89.7/99.4/92..6
100//100/100.
87.7/96.7/92.2 7/92.2
cable gland
90.1/97.5/92.6
89,8/9 8/97.2/93.9
70.3/91.0/90
84.9/99.7/91.5
68.1/91.000 0/92.3
94.3/98.6/93.5
carrot
87.3/96.7/93.2
8/3.8/988
71.4/92.6/91.2
79.1/94.7/91.0
94.4/99.3/98.0
90.7/97. 7/95.0
cookie
46.0/77.4/88.0
77.3/93.5/88.0 0
66.7/89.6/88.4
67.4/89.8/88.0
19.4//8.8/90.
61.2/87. 5/8884
dowel
96.7/98.9/97.6
96.7/99.3/96
83,7/95.1/91.7
77.3/94.3/88.9
98.0/99.3/97.3
77.6/99.5/96.6
foam
74.3/92.9/90.6
70.5/92.4/88) 4/88.9
77.4/94.2/89
77.9/94.7/88.9
100./100./00.
84.0/95. 8/90.4 44
peach
64.3/84.8/90.6
62.0/86.9/8)
82.2/95.3/9007
58.0/91.30 1,3/94.3
02.8/98.1/94.
polato
5/990.
8/89.3
56. 56.7/82.2/89 2/89.8
62.9/87 8/90.
76.3/94.3/95.0
66.8/88 6/90.5
rope
96.3/98.5/93.2
97.4/99009555
95.6/98.4944,
93.5/97.4/92.55
89.2/95 4/91.9
97.4/98. 9/94.7
tire
79.2/93.0/88.4
75.7/90.7/89.7
65.3/86.8/87 8/87.9
80.8/93.6/91.5
92.7/98.9/95.8
90.0/97.00 99999
Mean
77.9/92.4991.4
78.9/93.4791.4
2..//9.0/90003
19.6/94.179066
8/.6//4
86.2/95.8/92.8
15

---

Table A6: Comparison with SoTA methods MVTec-3D dataset for multi-class anomaly localiza-
tion with AU-ROC/AP/FI max/AU-PRO metrics.
Method
RD4AD [12]
Un7A
SimpleNet (30)
DeSTSog [55]
DiAD [18]
MambaaA
Casegary..
CVPR'22
NeurIPS'22
CVPR'23
CVPR'22
hagel
95.6/39)0/45.110 1891.1
97.830.4335
8844
98.7/53052 9/77.
98.5749.65542221.3
98,5738 1/92
cable gland
99,4/37,9/43 2996 2
98.926, 4/34 896.3
4/2/144//281/866
37,844660//999888
98. 95.4725../52..0944
99,4/39 5443 9/98.4
сarrot
29.427.9/33.799222
98.0/12.2/19
3934
86.9/26.5/11.7/11
96.6/20.62269995 9/996.
99.4:30.1/35.4%%6
cookie
96.6/27.5/52.99966
97.540..4455.488
93.3/34.0/55 8/40.99
94.3/14.0/3.8883.5
06.8/39.0411 9/83.6
dowel
99.7/47.7:50.8/900
99.1/52. 1/37 7966.
95.
4/.3/17.4/25.66 6.83.D
97.3/43, 1/44 S/31.2
V7.2/51,44400 (1.1,,44001/000 1/4601//89.6
99.6449.9/50 4/97.
foam
9/55.
87.8/15.7/26.
95.7:43.7/49
89.8/ 9.6/23.5/66
25.1/23.4/22 8/8.7
peach
97.4111.7/11.99900
92.9/ 8.1/15.0/74.8
95.9/35 7/41 2/48.2
98,4/27.6/31.3288
99,4-43.2/45,110 1/97.1
potato
99.1/14.9/22.11995
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 99.0/11.6/22.662
rope
99.6/50. 3/55003//559/97.
99. 39,0034.3/40 7/94.
99. 19..951.1/22./922.
99. 1...3/0.0/9999999 99999
99,4/52. 9/50.9/98.5
tire
99.2/25.2331
98. 98.0011 9920 3/906
93.8/ 8.1715.3777.9
97.0755 8/30 0/27.3
91. 5,9/13.7/68
99.5542.00466999997
Mean 98.4729.88564491..
96.5/21.2288000 0088
94.0/18,
95, 1/38, 1/39.//66.4
2w.4225,3732.1887.
98.6/37.5/41.1/93.66
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.
Table A7: Comparison with SoTA methods on Uni-Medical dataset for multi-class anomaly detection with AU-ROC/AP/FI max metrics.
Method +
RD4AD [12]
UniAD [47]
SimpleNet [30]
DeSTSeg [55]
DiAD [18]
MamhaAD
Category
CVPR'22
NeurlPS'22
CVPR'23
CVPR'23
AAA1'24
(ours)
brain
82.4/94.4/91.5
89.9/97.5/92.6
82.3/95.6/90 6/90.9
84.5/95.0/92.1
93.7/98. 1/95.0
94.2/98.6/994.5
35.1/46.3/64.1
61.0/48 8/63.2
55.8/47 6/60.9
69.2/60.6/64.7
59.2/55.6/60.9
63.2/53. 1/64.7
retinal
89,2/86.7/78.5
84.6/79.4/73.9
6/78.6
88.3/83.8/79.2
88.3/86.6/77.7
93.6/88.7/86.6
Mean
75.6/75.8/78.0
78.5/75.2/7.66
75.6/76.9/76.8
80.7/79.8/78.7
80.4/80.1/77.8
83.7/80.1/82.0
Table A8: Comparison with SoTA methods on Uni-Medical dataset for multi-class anomaly localiza- tion with AU-ROC/AP/FI max/AU-PRO metrics.
Mothod +
RD4AD [12)
UmiAD [47]
SimpleNet [30]
DeSTSeg [55]
DIAD [18]
MambaAD
Culegory
CVPR'22
NeurIPS'22
CVPR 23
CVPR'23
AAAI24
brain
96 286
97.4/5..755
823.3
93.491299336 7/8.3
08.1162.7762.2288766
liver
96.6/ 5,7/10.3/85
97.1/ 7.8/1377/2.77
97/413.2/22 1/86.33320//88633
79.4/21./28.5/20
97.1/13.7/
7.3991,4
96.9/ 9.1/16. 3/96
retinal
96.4/64.7/v. 9/86.5
94.8499
379.99
95.3/59.5/66.555 1921
91.099900466 8/31.7
95.3/57.5/62
8/8.11
95.7664.56. 4/33.493.
Mean
5/38.77740.11886
96.4/37.6/4022885
95.9/38.3/39.6900
86.6/8.0/37.5/55,
95.9/38.0/35.668
96.9445.444.333777
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 pixel- level 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.
Table A9: Comparison with SoTA methods on COCO-AD dataset for multi-class anomaly detection with AU-ROC/AP/F1 max metrics.
Method >
RD4AD [12]
UmiAD [47]
SimpleNet [30]
DeSTSeg [55]
DiAD [18]
MambaAD
Category
CVPR'22
NeurlPS'22
CVPR'23
CVPR 23
AAATT24
(ours)
65.7/81.9785.
66. 66.1/84.078.1
57.8/77.4784.7
09.7/79.1785.1
57.5/77.5/85.3
05.3/89.8/85
54.9/46.8/61. 8/611
56.1/47 8
51.2/42.3/59.0
55.6/47./661
54.4/49.8/62.2
55.00 55.0/48.14 1/61.0
59.6/39
52.3/30.8/49
8/49.5
60.1./3.5/50.7
55.8/37.6/50
63.8/43.4/52.5
66. 46.9/46.4/54.6
53.5/36.4/51.5
50.1/33.5/51.2
59.2/39.2/52.2
53.5/36.5/51.2
60.1/41.4/2.99
58. 58.4/40.5/51
Mean
1/64.3
56.2/49.0/61.7
47.1/49
56.2/50.3/61.9
58.9/53.0/63.2
63.9/56.2/63.2
16

---

Table A10: Comparison with SoTA methods COCO-AD dataset for multi-class anomaly localiza-
tion with AU-ROC/AP/FI max/AU-PRO metrics.
Method
[13
UniAD [47]
SimpleNet [30]
DeSTSeg [55]
DiAD [18]
MamibAAD
Calegory
CVPR'22
NeurIPS'22
CVPR'23
CVPR'23
AAAI24
(ours)
0
72. 8/30,8888 245.9
70.8/29.4/66
7/36.5
61.0/7.4/34111266
61.8221.//2..2222
67.0/33.4/26.2223
75.6/38.6441.7444
70.77 6,2711 2/40.6
70.0 6,2/1 3/31
61 4,9 8.9/33.0
69.3/ 6/871.
71.3/11.8/ 7 7.8/28.8
71.2/ 6.6/11. 3/366
68.4/11 1/8.9999
7.2714
61.1/
68.0/19.2:12222322
71.2113.9/22.644444
58.3 2/3314
59.81 8.3/48311
55.3/ 8,2/13.9210
$1.2/ 6.9/12,4/16.88
68.9117.5511663323.
59.0/ 446/4444/34.77
Mcan
65,4122:99944 4/3177
59.3/12.211.:22755
00.9111.316.3236
68.020.5/1442220 2/330.
69.3:16.//2.2244.5
F More Quantitative Results for Each Category on The Real-IAD Dataset.
Tab. All and Tab. A12 respectively present the results of image-level anomaly detection and pixel- level 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.
Table All: Comparison with SoTA methods on Real-IAD dataset for multi-class anomaly detection with AU-ROC/AP/FI max metrics.
Method
RDAAD [12]
UniAD [47]
SimpleNet [30]
DeSTSeg [55]
DiAD [18]
MamiaaD
Category
CVPR'22
NeurlPS 22
CVPR 23
CVPR 23
2AAI'24
(ours)
audiojack
76,2/63.2/60.8
81.476.6/6499
58.4/44.2/50.9
81.177.66/4.5
76.3/54.3/65.7
84.2/76.5/6..4
bottle cap
89.5/86.3/81.0
12.5//1.7/811.7
04.1/47.6/0...
78.1/74.6/68.
91.6/94.0/87.9
92.8/92.0/82.1
button battery
73.3/78.9/76.1
75.9/81.66 16766.3
52.5/60.5/72.4
86.7/89.2/83.5
80.5/71.3/7066
79.8/85.3/77
end cap
79,8/84.0/77.5 8
80.9/86.1778.0
51.6/60.8/72.9
1777.1
85.1/83.4/84.8
78.0/82.8/77.
craser
90.0/88.7/79.7
90.3/89.2/80.22
84.6/82.977 9/71.8
80.0/80.0/777.3
87.5/86.2/D8
fire hood
78.3/70. 1/64.5
80.6/74.8/66.4
18.1/41.9/54.4
81,2772.4/67.7
83.3/81.7/80.5
79.3/72.5/64.8
minl
65.8/63. 8
67.0/66 6/64.6
52.4/50.3/63.7
$8.4/55 8/63.7
76.7/76.7/76.0
70.1/70.88 8/65.5
mounts
88.6/79.9/44.8
87.6/77 3/77.2
$8.7/48. 1/52.4
5/63,
5/.3.
86.8/78 0/733.5
peb
79,5/85.8/77 8/79.7
81.0/88
1
44.5/66.0/75.
82.0/88.7/79.6
86.0/5.1188 1/85.4
89.1/93,7/84.0
phone buttery
37.5//3.3/77..1
83.6/80.0/11.6
$1.6/43 8/58.0
8372/
82.3/77.7778
90.2/88.9/80.3
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
81.9/74./668.8
814475.9/67.6
48.2/38 4/54,66
71.7/63.
1/6000
28.7/89.2/90.99
15.7782.2/726
porcelain doll
86.3/76.3711.5
15.1//5///69
66.3/54.5/52.
78.7/66. 2/676
72.6/66.8/65
88.0/82.2/74.J
regulator
66.9/48 8/47.7
56,9/4 L5444.5
00.5/29.0/43.9
79.2/63. 5/56.9
42.1/21/77..2
69.7/55 7/50.7
rolled strip base
97.5/98.7/94.7
98.7/99.3/96.55
19.0/75.7/79.
96.5/98.2/99
68.4/55. 9/56.8
98.0/99.0/95.00
card xet
91.6//188888 8/84.8
89.7/90.8 3/83,2
1/69 7/70.8
95.5/96.2/89.2
72.6/53.7/6 7/61.5
94, 94.4/95.1/87
switch
84.3/87.2/77.9
85.5/88 6//88.6/78.4
22.2/66.8/68.
80.1//9.8/83., 8/83.1
73.4/49.4/11
91.7/94.0/85.
lape
96.0/95.1/87.6
97.2/96.2/89.4
11.9/111/54.3
94.5/93.4/85.
73.9/57 8/696
96.8/95 9/89./9/8...
terminalblock
89.4/89.7883.1
87.5/89. 1/81.0
59.8 $9.8/ 7/68.8
1/86/86.22 1/76.2/76.6
62, 1/37 8
96.1/96.8/90.
toothbrush
82.0/838877.2
78.4/80. 1/7561
65.9/70.0/70.
83.7/85.3/70 3/79.0
91.2/93.7/9009
8/81 2/80.3
toy
69.4774.2/55.9
68.4/75.1/7488
57.8/64.4/73.
70.3/74
66.2/57.3/59.
83.0/87.5/79
toy brick
63.6/56.1/500 1/59.0
77.6/1.1/66.22
08.3/49.7/58.
73.2/68.7/66
68.4/45.3/53
70.5/63.7/6
transistorl
91.0 91.0//4.0/85.1 1
93. 73.7/95 9/888. 9
1/T2.1
90,2/92. 1/84.6
73.1/63. 1/62.7
94,4/96.0/89.
block
09,5/85.0/44.
88, 2/8../5
62.4/48, 4/51.8
80,1/73 9/64.3
75.2/68 4/67.9
399.7/85.7755.3
usb
78.7/79.4/66 14.998
57.0/55.3/625 3/62.9
87.8/88 0/78.3
58.9/37.A/43 A/45.7
92.0/92.2/84455
ush adaptor
71.1/614462.22
76.8/71 33/44
47.5/38.4/56.
80.1/74.9/67.4
76.9/60.2/61
79.4/76.0/66
vepill
85. 1/80//2.3/72.
87.1/84.0/74.7
59.0/48.7/56
83.8/81. 5/699.
6/4.//404/56.2
88.3/87.7 77777.
wooden beads
81.2/78.9/70.9
78.4/77.22 2/67.8
SS. 55.1/52.006 152.00/60.
82, 5/73.0
62, 1/w.1/66444 4/65, 9
82.5/81..771 1.771.
woodstick
76.9/61.2/58.1
80.8/7.6/66.6
$8,2/35 6/45.2
80.4/69.2/611 2/60.3
74. 1/66 0/62.1
80 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
06.0/87.0V84)
99.2/99.6/96.9
Mean
82.4/79.0/33.9
83.0/80.//44.3
57.2/53.4/61.5
82.3/79.2/3..2
75.6/66.4/69.9
86.3/84.6777.0
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.
17

---

Table A12: Comparison with SoTA methods on Real-IAD dataset for multi-class anomaly localization
with AU-ROC/AP/FI _max/AU-PRO
CAOO//PPFLLmaX/AA-PRRO metrics.
Method ->
RD4AD [12]
UniAD [47)
SimpleNer [30]
DeSTSeg [55]
DIAD (18)
MambaAD
Category_
C2PR'22
NeuriPS 22
CVPR223
CVPR 23
2AAI22
(ours)
andiojack
ww.612..22211999
97.6/20 1VX3.7
74.4/
0.5/ 4.8/88D
91 1.V 3.966.3
97.7721 6/2.//99/.00 5/83.9
bottle cap
99.5/18999999999
99.5/19 4/29 6/266696.0
85.3/
5
94.5/25.22 1/2551
94.8/ 4.9/144773
99.7:3906/3466999
batton batery
97.6/33.835.888655
96.7/28.5534
534.4775
75.9/
3.21 6.6/40.5
98.3661.96604466699
84.1/ 1.4l 5.3/56.9
98.1/46
2/995//6.2
end cap
96.2/12/5/22.1992 5/99 2
95.8 8.8/17 4185,4
63.17 0.5/ 2.8/25.7
89.41144422.7729
81 2/00 6.9188.2
97.0/12.0/11 6489,4
99.5/30.8/36. 7/96.0
23.3/244330.900
80.6/
2.7/ 7.1/42.8
25.77577733.9
91.1/ 7.7715.4867.5
99.2/30
2/2. 28.3/93.7
haod
95.9/77.7/35.2/57..
98.6/23 4/32 2/8..3
70.5/
2:2/25.3
97.
91.8/ 3.2/ 9,2/96.7
98.2/25 3/$6.3
mint
95.0/11.//25.00222
94 7 1/6..3
79.9/ 0.9/ 3.6/3.33
1/10.3/22 A/ 9.9
91.1/ 1.74166
9/..7115.9/77.772.
mounts
99.3/20.6/55 1/9. 9
99,4/28 033 8/952
80.5/ 2.2/ 6.8/46.1
94
24222300044133442.
84.3 OZA1 1 1,1988.8
99. 4/15 4,93.5
peb
97.5/15./24../88.
97.0/18 5/88.1888
76.0/ 1.4/ 4.3/41.3
272/37.1/40./485 8
92.0V 177 7-406-5
99.2:46. 49994...
phone battery
77.322.633.7/511.
85.5/11
43/4/
0./1188
5/25 6/33 8/99
96.8
99.4436.3/41.33
plastic nut
1/29//1//99//911/ O
98.4/20 627. 1188.9
77.41 0.6/ 3.6/4155
96.
96.5/448445778884 4
81 1P 3,433.6
99,4233 3/96.
plastic
99.1 20.120.5/28.//44.
98.6/17 122..199..
78.6/ 0.7/ 19/38.8
91 1/9 0
92
1711509611
99 99.0224.233..7911
porcelain doil
09.2/211./341.69995
96.7/14 1/21.5/93.2
81.8/ 2.0/ 6.4/1.00
93 1/35 940.
99.2:31 6995.
regulatir
1/886
76.6/
0.6/8.11
8118 9133
67.6:20.6/ 2/.887
rolled strip base
99.7/31.4/39.0998 4
99.6/20 7/2.297.8
80.5/ 1.2/ 5.1/52.1
99.248.7/50.185
69 17 A0980
77 A20 4
99.7/37 4/1../442255988. 5/988
sim card set
switch
98.5/4..2441
94,4/18 (13.99966666900 6/999 9
96. 1/33 840.6
97 833 8/850
71.0 6.8/14 3/30.8
71.7/ 5.7/ 9. 9.3/44.2
90.5 MAL S $.16--
95. 9145 4,92.9
98. M5. 6/89/
tape
99.2/42.4447.8998
99, 2/96
77.51 1.2/ 3.9/144
99.066L7157
80- 1/18 2/98.0
kerminalblock
39.5/27.4335 6
99.2/23 5/3
87.07 0.8/ 3.6/51.8
66.660064444133 1/34
75 LTO SEETTT
990- 3/39, 7,98.2
toothbrush
96.91/6. 1/3442288.77 7
95. 4/5
64.7/
7.2/14 8/522.
94 3330033,
A72N MSW 565449
57.5237 8C16 7/91.
toy
95.2/ 5. 3/12.2/222.3
93.4/ 4 4/7LS
67.7/ 0.1/ 0.4/25 D
86. V 9/16
9
KET AL 4.75511
3
96.006..4255 8/86.1
toy brick
96///16.0/21.677
974417 127.681
86.51
5.2/1 1/566.
886 7.2/1 3AS1SAA
86 06-631505 8/74,7
transistor]
99 19.1/29 6/35.5/05
98 9/25 633 204.3
71.71
5.1/11 1 3/35.
99-4229 AND 0'96.5
u block
99.6/40.5/4X 2/49//
99 322 N29 644.3
76.21 2.8/122//44.
96 W6..5.718...7.
99-1257 8-46 1995,
usb
98.
97.9/2007 &3L 288.33
81.1/ 1.5/ 4.9/52.4
9% 444.3477777
78 AT 3 1728.0
99,2739 4/952
adaptor
94.55 9.8/77.57777
96. 6616/10 ST9007T
67.9%
1.3/28
3/22 6/82.5 97.
vepill
98. 648.6877
99.140 091.3
68.2/ 1.1/ 3.3/22.0
1/64776623222
20.27 1. 62244
28. 2/50 2/54 5189.1
wooden heads
1...227./3447/8855
68.1/ 2.47 6.0/28.3
85.0V 1LT1 4.745.6
98.0/32 6/39 3/399 8/54.5
woodslick
97. 8/30 4/85.4
94 94.8/3 2044, 3/7
76.1V 1 6 6.0/32.0
97. W7.9:60.366000511
D
9V 2/6' 8.06617
97. 7400 1/44, 9/82
zipper
2/91
98 98.4/32 $36118511
89.9/5.3/31 2/55..
2/35 3/39
90.2/12.5/188/2
musm
97.3/25.055227899
97.3/21 129.276677
75.77 2.8/ 6.539.
91.637.941.70066
SS.V 2.9 7,175811
08.5/33.008
7/905
Table A13: Comparison with SOTA methods MVTec-AD dataset for single-class anomaly
detection with AU-ROC/APPE max metrics.
Method -
RD4AD [12)
UniAD (47)
SimpleNet [30]
DeSTSeg [55]
PatehCore [36]
MambaAD
Culegory
CVPR 22
22
CVPR'22 23
CVPR 23
CVPR 22
ours
Bottle
100/100/100.
100/100//00.
99.9/100.99922
100./100//000.
100/1000/100.
100./100//000.
Cable
8/97 0/89.7
97.9/98.7/9 7/93
09,6/99.7/97.
97. 17.1//8.0 4/93.
99.8/99.//98.
5/995/9...0 1/95.1
Capsule
98.4/99.7/97.3
87.1 37.9//5.3/95.2
97.2/99.2/98.
97.4/99.5/96.
97.4/99.4998.
Hazelnut
100/110./100.
99.7/99.8/98 6
99.0/99.4/97.
99.7/99.8/99
100//100/100.
100//100./00.
Metal Nut
99.9/100./99.5
98.7/99.799
99.9/100./99.5
99. 99,7/99,90 9/999
99.9/100./99.5
100./100/99.5
Pill
97.5/99.6/97.
96.09993300 3/955 8
98.6/99.7//77.9
26.2//9.3/955
06.6/99.4/966.
1/955/
Screw
77.7/99.2/9553
97.7//3.0/93.
97.5/99.2/98
92.3/97.5/90 99999999
98.1/99.3/97.5
97.6/99. 1/97_
Toothbrush
93.3/97 2/95.2
1.111/48880 8/93.8 8
99, 22,4/99..0 8/98.4 4
99. 70,7799..00 9/98, 4
100./100//00..
96. 1/92.
Transistor
100./100./100.
9/9979998.7
98. 2/..9/98./994.7
100./100.100.
100./100./100.
Zipper
03.33/99//97
90.6/96.5P9 5/93.9
99.8/9999/999
100./100./100.
99.6/9999999 7
98.6/99.6997 6/97.5
Carpet
99,1/99 37918.3
99,4799.878 8798.9
19_1/9977998
99. 87977
98, 1/9777
100//00./100.
Toxtung
Grid
100/110//100.
97. 6/99/99.... 6/9969
100//100/100.
100./100/100.
99,.//999/99
100//100/100.
Leather
100/100./100.
100./100//00..
100./100./100.
100./100./100.
100./100./000.
100./100./000.
Tile
100//10./100.
95, 8/98//8.2 22/5.8 88
99. 9/98.9
100./100./9.. 4
99. 99.0/99.7/98 7/9888
97. 97.5//991/94
Wood
99,5/99 8/98.3
97,9/99 4/95.9
99. 99,99/100/99.2
99.3/99. 3/9998/98.4
99.1/99.7.8 1/99.7/97.5
99. 99966/99999999 9/99.2
Mean
98.5/99.3/97.5
95.8/98.9/96.
99.3/99.8/9885
98.6/99.5/97.6
99.2//9.8/98.8
08.7/99.6/98.
Table A14: Comparison with SoTA methods on MVTec-AD dataset for single-class anomaly localization with AU-ROC/AP/FI max/AU-PRO metrics.
Mothod +
RDMAD (12)
UniAD [17]
SimpleNett [30] CVPR
DeSTScg [55]
PatchCore [36]
MambaaD
Calegory
CVPR 22
Nou
CVPR 23
CVPR
(ours)
Bottle
98.6775.9/7..19553
95.0770.772
19.391.04
58.3777.775
98.879..7766699
Cable
96.8/51.3/57 3/88.8
97/414488/56
9/87.7
97.4166.8/50.0 0V87.7
95.8/55 8/82.8/82.1
08.4466.366.111 1/9..5
98,0154, A/61, 7/93,4
Capsule
9448 1/49 9/95.3
08.0535.2/40.
1/86
9% 9142 5/49 1/92.8
9%
6
99.0444 7/50 9/9 7.7
9X 19.6445 (1/44)444755 5/94,3
Huzelout
98.8/59.6/60.88
8/96.
98.3155,0156.
1/92.8
97.9166.2/5 3/78.
99.48445779.099
98. 78.7553.5/ 2/89.7
99.0/61. 8/63, 9/95.8
Not
96.9/75.3/7999 5.94.1
94.1/5
8/77.8
98.8/9166/56.. 6/81.0
99.295.0088.771 7:9.0
98.3/86.998
1/91.1
1.788.380.6693.6
Pill
97.6/66 6/66, 7/95.9
2455/9151 9/92.2
98. 5/79 5/22 6/92.5
99..987.9/79966966 6
97.8/7 8/77 9994,
97. 71.3364.55 5/66. 0/95 8
Screw
99 09.5444.6/47..0 2296.
9% 0/315.5/33.40 6/911 3
99. 3/550033 8/95
97. 27.3354.2/5..//5..
99.5/36. 5/40 1/96.6
99.5:52.2/5 2/151 7/97.6
Toolibrush
199.0511.86609999 9/92.0
98. 08.5442,6675
1/841.
98. 111.521.7/222 9/92.4
w9.5778.7733./991
98 6/3.3/522 3/92.3
99.0251. 1/1.0110000.00 7/92.3
Transistor
6/52.8/54 SVN00
7A.N79.5/78.8.44
96. A162
8K.
9
5189.8
8/666 7/67. 5:91 1.
Zipper
7/53.0859 6
96 5355555544 4/89.
98 9M64, 3W55 4/95.5
99.2285.777.44443
98 966.9966 1/94.
98. 1:55 6/58 8/94 8
Carpat
99 1760, 180 SP936
3/9T
9% 0743 044.27477 S7TT.
98:377,57235999
99. 1184 0P9T8
99..255.0663. 4:97.
530131
Gird
99 3145.2447 2447 7/96.
94 3/31 3/31 598..8 8
U% 8/34, 7/39 3/93
W9.5562.506355993 8
ux. 8/1 AU35 3/44.2
99, 24..2448.. 91-48, 8/97.3
Leather
99.3/41.7/16.770 7/97.9
113.188811..0
19.2411.7445.. 659.7
99.8/74.9/69
99 3/16. 7/96.8
99,3/17.55 00177.51195. 5/986
Tike
95. 148 6/59 7/85
90 4H4 7/77.1
97. 2769 8/68 8/89.7
99.4994.6/87.1199
95 35.8555.00 0164 7/90.0
93,1 1442 8/52. 3/80.3
Wood
94 3448 6/49 5/91 6
93. 5/58 6/43 9/85.2
94 044555.660 6/48 1/92.5
9N.4414..577.550011
9
95 IV50 2/50 WX5.3
93.9644 2/47 7/92.1
Mem
97. 175.5/553.993111
98.056.037
18,1757,259 3992.6
97.8757.259.899 8/940
18

---

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-Ievel anomaly localization quantitative outcomes for single-class anomaly detection of the VisA dataset.
Table A15: Comparison with SoTA methods on VisA dataset for single-class anomaly detection with AU-ROC/AP/FI max metrics.
Method +
RD4AD [12]
UniAD [47]
SimpleNet [30]
DeSTSeg [55]
PatchCore [36]
MambaAD
Cutegory
CVPR'22
2eur
CVPR
CVPR'23
CVPR
(ours)
pebl
95.9/95.6/921
91.9/90.9/87.2
98.9/98.99960
94.9/92.5792.00
97.7/97.17944
96.0/95.179.
peb2
96.5/96.2/99
22.2/92.3/443
98.8/98.8/93,
96.6/94.7/9 7/93.4
97.7/98.2/93.3
97.1/96./99 .9
peb3
96.2/96. 1/91.1
90.9/91.3/86.2
98.9/98.8/95.
97.099.3//1.7
98.5/98.5/933
0/92.7
peb4
100./100.99.55
98. 8/969/96//6.11
99.3/99.0/97 6
39.9//9.3/94..
00.8/998//77.
99.7/99.7/99 7/99977/97.5
macaronil
92.1/90.2/85.4 4
87 87.5/83.3777 3/79.6
94.8/9.7/89.J
82.8/75.177 1/77.2
91.3/85.9/777
91.2/88 4/84.1
macaroni2
86.1/80.3/80.2
85. 1/82.5///76.
83.4/77 4
72.8/66. 1/69.2
25.2/60.6/59.4
81.8/78 9.77777
capsules
89.7/94.2/87.7
79. 1/81/88.77 7/79.0
90.1/93.3/86.
85.3/91.5/833
77.7/83.2/74.4
91.4/94.6/90.5
cundle
94.6/94.7889.4
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
96.9/98.6/93.44
91.9/96. 1/90.3
94. 1199.2290.99
73. 8787.7778
91.2793.5/89.2
95,7797 6/93.7
chewinggum
98.8/99.4/96.3
97. 77.4//88//94.8 8/94.8
98.6/99.3/96.
97. 8/95,9
97.9/9888/55.
99.0/99.5/96.1
fryum
79.8997.//91.7
85.5/92.6/86..
06.9335
95.0//6.7789.
96.5/98.3/92.5
pipe Jryum
pipe_Iryum
99,7/99.8/98.5
91.9/95.4/90
99.8/99.//99.0
99.3/99.6/97,
99.1/99.5/97/
09.2//9.6/97.66
Mcan
95.1/95.2291.5
90.6/92.3/56.7
93.4994.8/9.3
90.4/91./87.7
92.8/944/8.00
95.3/99.3/91.7
Table A16: Comparison with SoTA methods on VisA dataset for single-class anomaly localization with AU-ROC/AP/FI_maa//A _max/AU-PRO metrics.
Method
RD4AD [12]
UniAD (47)
SimpleNet [30]
DeSTSeg [55) CVPR 23
PatchCore [36]
MambuAD
Category
CVPR'22
NeurIPS22 22
CVPR 23
CVPR 22
tours)
99.7711 2/8 8
99.2/53 2/633/0956.//6-
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19

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26


Reviews:
[{"review_id": "tjGTgGvHRX", "reviewer": "Reviewer_FXx2", "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.", "questions": "Please 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.", "limitations": "Minimal discussion. Although the section labeled \"limitations\" includes some wording, it does not actually discuss any perspectives on real limitations on the methods.", "rating": 5, "confidence": 5, "soundness": 2, "presentation": 2, "contribution": 1, "strengths": "1. 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.", "weaknesses": "1. 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.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Q1: From a methodological perspective**\n\n*(1)* We adopt a **reconstruction-based framework**. Anomaly detection methods based on reconstruction can be broadly categorized into **image reconstruction and feature reconstruction**. Methods such as GAN and diffusion-based approaches primarily fall under image reconstruction, where the similarity between the generated image and the input is calculated. In contrast, feature reconstruction methods compute the similarity between the input features and the reconstructed features. **RD4AD is merely a specific instance within the feature reconstruction methods. Additionally, this framework is not referred to as a contribution in our paper.**\n\n*(2)* Mamba, as a novel global modeling structure, **has not yet been explored for its potential in anomaly detection (AD)**. We found that directly applying it to multi-class anomaly detection tasks does not significantly improve performance compared to the original CNN architecture (+0.4%) in Tab. 1. Therefore, we first combined Mamba's global modeling capability with CNN's local modeling capability in Tab. 3, which significantly improved performance (**+2.8%**), and proposed the **AD-adaptive LSS module**, corresponding to the contribution in the fusion modeling approach. Secondly, we introduced the **AD-adaptive HSS method** to specifically enhance the scanning approach (**+1.1%**) for multi-class anomaly detection data, corresponding to the contribution in the scanning method.\n\n**Q2: More key ablations**\n\n***(1) Decoder Ablations***\n\nWe conducted experiments on different decoder structures **within the same RD4AD framework**, and the results are summarized in the table below. The Mamba-based decoder, which uses only Mamba as the component for each decoder module instead of the proposed LSS module that integrates Mamba with CNN structures, shows a decrease in performance compared to the result of 86.0 reported in the paper. However, compared to decoders based purely on CNN or Transformer architectures, the Mamba-based decoder achieves the highest mAD score of **82.1**. Additionally, **the Mamba-based decoder has fewer parameters and FLOPs compared to the Transformer-based structure.**\n| Decoder | Params(M) | FLOPs(G) | mAD |\n| --- | --- | --- | --- |\n| CNN-based | 13.0 | 5.0 | 81.7 |\n| Transformer-based | 27.1 | 8.4 | 80.2 |\n| Mamba-based | 22.5 | 7.5 | 82.1 |\n\n***(2) Components Ablations***\n\nThe ablation experiments for the proposed components are summarized in the table below. 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, reaching the SoTA performance.\n| Basic Mamba Decoder | LSS | HSS | mAD |\n| --- | --- | --- | --- |\n| ✓ |  |  | 82.1 |\n| ✓ | ✓ |  | 84.9 |\n| ✓ | ✓ | ✓ | 86.0 |\n\n**Q3: More Limitations**\n\n*(1)* Although Mamba has linear computational complexity, the current multi-scale reconstruction-based framework (*c.f.* Fig. 1) is more effective than the single-scale UniAD method (81.7 -> 86.0). However, due to the limitations of the framework, existing methods are still not efficient enough.\n\n*(2)* Moreover, since most industrial anomaly defects are relatively small, as seen in datasets like VisA and Real-IAD, where defects occupy a very low proportion of the entire image, it is necessary to improve detection resolution to identify small target defects. However, increasing the resolution brings additional computational complexity to the model. Therefore, **designing more efficient and lightweight anomaly detection models is urgently needed in industrial scenarios.** We extended the MambaAD method to high-resolution tasks, such as $512^2$, $1024^2$, and even higher $2048^2$ input resolutions. At a resolution of $512^2$, the model's FLOPs reach 33.2G with a throughput of only 45.1. At a resolution of $1024^2$, the FLOPs soar to 133G with a throughput of only 10.3. At a resolution of $2048^2$, we could not measure the corresponding FLOPs due to OOM (Out of Memory) errors. In summary, **there is still much room for improvement in the lightweight design of current models, especially when applied to high-resolution industrial scenarios. The current models do not yet meet the efficiency and real-time requirements of high-resolution industrial applications.**\n\n*(3)* **The existing Mamba-based encoder still has certain deficiencies in terms of efficiency and effectiveness**. In the table below, we replaced the current encoder with two different lightweight pre-trained Mamba encoders. The parameters and FLOPs only represent the results of the encoder. Although EfficientVMamba-T has the highest efficiency, its feature extraction capability is lacking. On the other hand, VMamba-T shows significant improvement in effectiveness but still lags behind the current CNN encoder in terms of real-time performance and overall effectiveness. Therefore, **designing more lightweight, efficient, and accurate Mamba-based encoders for anomaly detection is crucial and will be the focus of our future research.**\n\n| Backbone| Params(M) | FLOPs(G) | mAD  |\n| ------- | ------ | ----- | ---- |\n| EfficientVMamba-T | 6.3   | 1.0  | 72.7 |\n| VMamba-T| 30.2  | 6.0  | 82.9 |\n| ResNet34| 8.2   | 4.0  | 86.0 |", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "uL696eTvT2", "reviewer": "Reviewer_aMDx", "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.", "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?\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.", "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.", "rating": 7, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. 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.", "weaknesses": "1. 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.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Q1: Further Exploration of Scanning Methods and Direction Selection**\n\n***(1) Scan Directions***\n\nFirstly, we further investigate the impact of different scanning directions on Params, FLOPs, training time over 100 epochs, training memory usage, and final performance, as shown in the table below. It is evident that as the number of scanning directions increases, there is a corresponding increase in Params, FLOPs, training time, and training memory usage. Consequently, the performance in terms of mAD also improves. Therefore, for those prioritizing efficiency, scanning with **2 directions offers the lowest Params and FLOPs, while also requiring less training time and memory, yet achieving satisfactory performance**. Conversely, for those aiming for optimal performance and willing to accept increased computational load and training time, scanning with **8 directions yields the best results**.\n| Scan Directions | Params(M) | FLOPs(G) | Training Time | Training Memory | mAD  |\n| --------------- | --------- | -------- | ------------- | --------------- | ---- |\n| 2               | 21.8     | 7.2     | 2h1m          | 6230           | 85.8 |\n| 4               | 23.1    | 7.5     | 2h56m         | 7974           | 85.9 |\n| 8               | 25.7     | 8.3     | 5h39m         | 11802          | 86.0 |\n\n***(2) Scan Methods***\n\nSubsequently, we further explore the impact of different scanning methods and the fusion of multiple scanning methods on the results, as shown in the table below. Different scanning methods exhibit negligible differences in terms of parameters, FLOPs, training time, and memory usage, with variations only observed in the final results. The results indicate that using any of the five different scanning methods individually can achieve satisfactory outcomes. However, combining different scanning methods tends to degrade performance, possibly due to the significant differences between the methods, which may hinder the selective scanning and global modeling convergence of the SSM. Therefore, we ultimately choose to use only the Hilbert scanning method. **This method allows for continuous scanning in the central part of the image, which is advantageous for SSM in learning and modeling the distribution of anomaly detection data, as most data in anomaly detection datasets are centered in the image.**\n|Sweep|Scan|Zorder|Zigzag|Hilbert|mAD|\n|-----|----|------|-----|-----|----|\n|√|||||85.8|\n||√||||85.9|\n|||√|||85.8|\n||||√||85.8|\n|||||√|86.0|\n||||√|√|84.9|\n|||√||√|85.3|\n||√|||√|85.4|\n|√||||√|85.7|\n||√|√|√|√| 85.3 |\n\n**Q2: Additional Datasets**\n\nIn Tab. 1 of the main text, we demonstrate the effectiveness and robustness of our method on three industrial anomaly detection datasets: MVTec-AD, VisA, and Real-IAD. To further validate the effectiveness of our method, we include additional datasets from **medical, 3D, and real-world scenes**. The **Uni-Medical** dataset [1] comprises CT scans from three different anatomical locations. The **MVTec-3D** dataset [2] includes both RGB images and depth maps. Additionally, [3] extends the commonly used COCO dataset for detection and segmentation to anomaly detection, creating a large-scale, general-purpose **COCO-AD** dataset that encompasses complex scenes and diverse distributions. These datasets exhibit significant distributional differences compared to traditional industrial anomaly detection datasets, providing a robust test for our method. The results are summarized in the table below. For more detailed results, please refer to **Appendix C-E**. Our MambaAD method shows improvements over existing SoTA methods, with **+4.2%** on the medical dataset, **+3.7%** on the 3D dataset, and **+2.5%** on the COCO-AD dataset. These significant improvements across datasets with different distributions and scenarios validate the effectiveness and robustness of our method.\n| Extra Datasets | RD4AD | UniAD | SimpleNet | DeSTSeg | DiAD | MambaAD |\n| --------------- | ----- | ----- | --------- | ------- | ---- | ------- |\n|Uni-Medical| 70.2  | 69.9  | 69.1| 60.9| 70.5 | **74.7**|\n|MVTec-3D| 74.3  | 71.1  | 66.9| 69.1| 73.8 | **78.0**|\n|COCO-AD| 45.0  | 42.3  | 40.7| 40.0| 44.1 | **47.5**|\n\n**Q3: Robustness Under Different Environmental Conditions**\n\n**Currently, the anomaly detection field lacks specialized datasets that account for varying lighting conditions and occlusions.** However, the **COCO-AD[3] dataset** we use is a general-purpose anomaly detection dataset derived **from real-world detection and segmentation scenarios**. It includes a wide variety of objects and categories from real-world settings. As illustrated in Fig. 1(a) of the [3] paper, the dataset encompasses diverse scenes with significant variations between them. These scenes exhibit different data distributions and **include various environmental conditions such as sunny and cloudy days**. Additionally, the dataset features **occlusions both within the same object and between different objects**. In the table above, our method achieves SoTA on the COCO-AD, with an improvement of over **+2.5%** in the mAD metric. This further validates the robustness of our method in complex and general anomaly detection scenarios.\n\n[1] Exploring plain vit reconstruction for multi-class unsupervised anomaly detection. Zhang *et al.*. arXiv'23.\n\n[2] The mvtec 3d-ad dataset for unsupervised 3d anomaly detection and localization. Bergmann *et al.*. arXiv'21.\n\n[3] Learning Feature Inversion for Multi-class Anomaly Detection under General-purpose COCO-AD Benchmark. Zhang et al.. arXiv'24.\n\n**Q4: Limitations and Future Work**\n\nThe primary limitations lie in **high-resolution application scenarios** and the **Mamba-based encoder**. These areas will be the focus of future research. For a more detailed explanation, please refer to **Q1** addressed to Reviewer **FXx2**.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "qwXAAkDlVE", "reviewer": "Reviewer_gwhg", "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.", "questions": "1. Why the params and FLOPs are higher than the transformer-based model?\n2. 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.", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. As far as I am concerned, MambaAD is the first attempt to use Mamba in the anomaly detection domain.\n2. The experimental results are SOTA.\n3. 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.\n2. 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.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Q1: Compared with Transformer-based Method**\n\n*(1)* As shown in Fig. 1 of the main text, although UniAD is a Transformer-based method, it employs a **single-scale approach**, whereas our MambaAD, based on Mamba, utilizes a **multi-scale approach**. Specifically, **single-scale methods model and reconstruct only the smallest scale feature map during the decoder stage**. In contrast, multi-scale methods progressively increase the resolution from the smallest scale feature map during the decoder stage, modeling and reconstructing feature maps at multiple scales. **Due to the quadratic computational complexity of Transformers, UniAD opts for a single-scale framework as its primary architecture.** Consequently, UniAD, which reconstructs only the smallest scale feature map, naturally has the least parameter count and FLOPs. On the other hand, MambaAD, which models feature maps at three different scale resolutions, has slightly higher parameter counts and FLOPs compared to UniAD.\n\n*(2)* To ensure a fair comparison, **we used the same encoder, ResNet-34**, as the feature extraction network. **Within the current multi-scale framework** of MambaAD, we employed both a pure Transformer-based decoder and a pure Mamba-based decoder to validate the efficiency of the method. The results are shown in the table below. It can be observed that, **under the same framework**, the pure Mamba-based decoder has significantly fewer parameters **-4.6M** and FLOPs **-0.9G** compared to the pure Transformer-based decoder, demonstrating a clear efficiency advantage. Additionally, in terms of performance, the Mamba-based method shows a notable improvement in the mAD metric (**+1.9%**), achieving a significant advantage in effectiveness as well.\n|Decoder| Params(M)|FLOPs(G)|mAD|\n|---|---|---|---|\n|Transformer-based|27.1|8.4|80.2|\n|Mamba-based|22.5|7.5|**82.1**|\n\n**Q2: Different Backbone**\n\n*(1)* The backbone feature extraction network used in MambaAD is **ResNet-34**. Although WideResNet-50 can achieve slightly better performance (+0.6%), it has **ten times the number of parameters and more than eight times the computational complexity**. Therefore, we opted for the more **lightweight ResNet-34 as the backbone**.\n\n*(2)* To ensure a fairer comparison with UniAD and eliminate the influence of different backbone networks, we replaced the backbone networks in UniAD with three different options: **EfficientNet-b4, ResNet-34, and WideResNet-50**. Similarly, we replaced the backbone networks in MambaAD with these three options. Originally, UniAD with an EfficientNet-b4 has 3.6G FLOPs and an accuracy of 81.7. When we replaced the MambaAD backbone with EfficientNet-b4, it achieved only **2.7G** FLOPs and an accuracy of 84.1, which is **+2.4%** higher than UniAD. **With the same backbone network, MambaAD has fewer parameters and FLOPs and better performance compared to UniAD**. Subsequently, replacing the UniAD backbone with ResNet-34 resulted in a performance decline, while further replacing it with WideResNet-50 led to a +0.7% improvement in performance, albeit with doubled parameters and FLOPs. \n\nIn conclusion, **under the same backbone network, MambaAD consistently outperforms the Transformer-based single-scale UniAD method**, demonstrating significant improvements in performance.\n|UniAD | Params(M) | FLOPs(G) | mAD |\n|---|---|---|---|\n|EfficientNet-b4|24.5|3.6|81.7|\n|ResNet-34|16.1|6.1|78.2|\n|WideResNet-50|33.5|14.4|78.9|\n\n|MambaAD|Params(M)|FLOPs(G)|mAD|\n|---|---|---|---|\n|EfficientNet-b4|23.6|2.7| 84.1 |\n|ResNet-34|25.7|8.3|86.0|\n|WideResNet-50|268|68.1| 86.6 |\n\n**Q3: Evaluation Metrics**\n\n*(1)* From the perspective of method categorization, our method and the compared SoTA methods can be distinguished as follows: RD4AD, UniAD, DiAD, and MambaAD are **rec.-based** anomaly detection methods. DeSTSeg, on the other hand, is a **hybrid method that combines data augmentation and reconstruction**. During training, **DeSTSeg artificially introduces random anomalous regions to construct anomalous data, enabling the segmentation network to learn the precise locations of these regions**, thereby reducing the probability of missed and false detections. In contrast, other **rec.-based methods only learn the feature distribution of normal samples and perform comparisons at the feature level during testing**. Consequently, the hybrid DeSTSeg method may outperform other rec.-based methods in certain anomaly localization metrics. However, MambaAD, with its simpler approach, **achieves the majority of SoTA metrics and a few near-optimal results overall**.\n\n*(2)* When comparing rec.-based methods, MambaAD demonstrates its effectiveness and robustness across four anomaly localization evaluation metrics on **six different datasets**. Recent work [1] has suggested that existing anomaly localization evaluation standards are **not specifically designed for segmentation-based anomaly detection tasks**. We selected the most commonly used **IoU metric to demonstrate the accuracy of anomaly localization which intuitively reflects the accuracy and overlap**. We tested the **mIoU** of rec.-based SoTA methods on six different types of six datasets. The results, as shown in **Tab. 6** in Rebuttal PDF, indicate that MambaAD significantly outperforms existing SoTA methods in terms of mIoU values across all six datasets, thereby proving the accuracy and robustness of our method in anomaly localization.\n\nFinally, we conduct a **qualitative analysis** of the MambaAD method in comparison to RD4AD within the same framework. As visualized in **Fig. 1** in Rebuttal PDF, MambaAD demonstrates higher localization accuracy on anomaly images compared to RD4AD. This further validates the accuracy of the method in anomaly localization.\n\n[1] Learning Feature Inversion for Multi-class Anomaly Detection under General-purpose COCO-AD Benchmark. Zhang *et al.*. arXiv'24.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "UfWhJet8DP", "reviewer": "Reviewer_wfnx", "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.", "questions": "See the weakness.", "limitations": "See the weakness.", "rating": 8, "confidence": 5, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "This 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.", "weaknesses": "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?\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?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Q1: Motivation**\n\n*(1)* Since the model needs to learn the **data distribution among samples with significant differences in a multi-class anomaly detection task, it requires a global modeling capability**, such as that provided by Transformers. UniAD, as the first model to propose a multi-class anomaly detection task, uses a Transformer decoder to model global features. However, **due to the quadratic computational complexity of Transformers, UniAD only uses Transformers on the smallest scale feature maps, which limits its performance in detecting small defects**. \n\n*(2)* Mamba, a model with **linear computational complexity**, is appropriately applied to multi-class anomaly detection. Its global modeling capability allows it to **better learn the data distribution of different category samples, and its linear computational complexity enables modeling at multiple scales, improving the detection performance for small defects**.\n\nIn summary, Mamba's linear computational complexity and global modeling capability make it well-suited for addressing multi-class anomaly detection problems. As illustrated in Fig. 1 in the main text, MambaAD enhances its performance in multi-class anomaly detection by integrating CNNs with local modeling capabilities into the Mamba structure of the decoder, thereby improving its ability to learn the distribution of each feature.\n\n**Q2: Local/Global Branches**\n\nWe conducted three ablation experiments to verify the impact of branches in the LSS module. 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. \nThe 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.\n| Method       | Params(M) | FLOPs(G) | mAD  |\n| ------------ | --------- | -------- | ---- |\n| Local        | 13.0      | 5.0      | 81.7 |\n| Global       | 22.5      | 7.5      | 82.1 |\n| Global+Local | 25.7      | 8.3      | **86.0**|\n\n**Q3: Evaluation Metrics**\n\nPlease refer to **Q3** to **Reviewer gwhg** for more quantitative analysis in **Tab. 6** of the Rebuttal PDF and qualitative analysis in **Fig. 1** of the Rebuttal PDF.\n\n**Q4: Mamba Encoder**\n\n*(1)* Existing anomaly detection methods primarily use pre-trained encoders based on CNN backbone networks. For instance, [1,3] utilize WideResNet-50, while [2] employs EfficientNet-b4. Additionally, [4] uses the Transformer-based ViT as the feature extraction backbone. **Currently, no pre-trained encoder based on Mamba has been applied to the anomaly detection domain**. Therefore, MambaAD also uses widely adopted CNNs as the pre-trained backbone network. \n\n*(2)* In the main text, Tab. 2 presents ablation experiments on different CNN networks. The results show that ResNet-34 achieves a good balance between efficiency and performance. Although WideResNet-50 can achieve better results, its computational complexity and parameter count are eight to ten times higher than those of ResNet-34. Hence, MambaAD selects ResNet-34 as the backbone network.\n\n*(3)* To explore the impact of pre-trained Mamba encoders on anomaly detection tasks, we selected two recently popular vision Mamba models as backbone feature extraction networks: **VMamba [5] and EfficientVMamba [6]**. We replaced the original ResNet-34 backbone with these models, and the results are shown in the table below. The parameter count and FLOPs represent the values for the backbone network only, not the entire model, to facilitate the comparison of different backbone network performances. **EfficientVMamba-T has the fewest parameters and FLOPs but performs poorly on the MVTec-AD dataset in terms of the mAD metric. VMamba-T has a parameter count nearly four times that of ResNet-34, but its FLOPs are only 1.5 times higher. However, its mAD results are still inferior to those of ResNet-34.**\n\nCurrently, existing pre-trained Mamba-based backbone networks are neither lightweight nor effective for feature extraction in anomaly detection. Therefore, **we will continue to research lightweight, efficient, and high-accuracy Mamba-based backbone networks and apply them as feature extractors in the anomaly detection domain.**\n| Backbone          | Params | FLOPs | mAD  |\n| ----------------- | ------ | ----- | ---- |\n| EfficientVMamba-T | 6.3M   | 1.0G  | 72.7 |\n| VMamba-T          | 30.2M  | 6.0G  | 82.9 |\n| ResNet34          | 8.2M   | 4.0G  | **86.0** |\n\n[1] Anomaly detection via reverse distillation from one-class embedding. Deng *et al.*. CVPR'22.\n\n[2] A unified model for multi-class anomaly detection. You *et al.*. NeurIPS'22.\n\n[3] Hierarchical vector quantized transformer for multi-class unsupervised anomaly detection. Lu *et al.*. NeurIPS'23.\n\n[4] Exploring plain vit reconstruction for multi-class unsupervised anomaly detection. Zhang *et al.*. arXiv'23.\n\n[5] Vmamba: Visual state space model. Liu *et al.*. arXiv'24.\n\n[6] Efficientvmamba: Atrous selective scan for light weight visual mamba. Pei *et al.*. arXiv'24.\n\n**Q5: Scanning Methods**\n\nPlease refer to **Q1** to **Reviewer aMDx** and additional ablation experiments in **Tab. 5** of the Rebuttal PDF.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:
**We would like to express our sincere gratitude for the constructive comments and suggestions from the reviewers. We appreciate the efforts of all reviewers in evaluating and helping to improve the quality of our manuscript.**

***The primary contributions of this paper are as follows:***

This paper is the **first to explore the application of Mamba in multi-class unsupervised anomaly detection**, proposing MambaAD. Existing CNN-based methods are limited by their long-distance modeling capabilities, while Transformer-based methods are constrained by their quadratic computational complexity. Therefore, this paper introduces the Locality-Enhanced State Space (**LSS**) module, which includes parallel cascaded Hybrid State Space (**HSS**) blocks and multi-kernel convolution operations. This module **integrates Mamba's linear computational complexity for global modeling with CNN's locally enhanced modeling capabilities at multiple scales in the decoder**. The HSS block employs Hybrid Scanning (**HS**) to map features into **five different scanning patterns and eight different scanning directions**, enhancing the global modeling capability of the State Space Model (SSM).

The effectiveness and robustness of MambaAD are validated across **six different datasets**: MVTec-AD, VisA, Real-IAD (**industrial**), Uni-Medical (**medical**), MVTec-3D (**3D**), and COCO-AD (**general scenarios**). The evaluation is conducted using **seven metrics at the image level (AUROC, AP, F1-Max) and pixel level (AUROC, AP, F1-Max, AUPRO)**. Additionally, during the Rebuttal phase, the **mIoU metric** for anomaly localization was included, making a total of **eight evaluation metrics**. The results demonstrate that MambaAD achieves **SoTA performance**. The **efficiency** of the method is also validated in both the main text and the Rebuttal. This work provides a foundation for further research on the application of Mamba in anomaly detection.

***Below is a brief summary of our responses to all reviewers' questions, along with their corresponding relationships to the tables and figure in the PDF.***

### Reviewer FXx2
- **Q1:** We discuss the **methodology** of MambaAD and its relationship with the RD4AD method.
- **Q2:**
  - We conducted additional ablation experiments on the **decoder**, corresponding to Tab. 1 in the PDF, demonstrating the efficiency and effectiveness of the Mamba decoder.
  - We performed **incremental ablation** experiments on each proposed module, corresponding to Tab. 3, showcasing the effectiveness of the proposed method.
- **Q3:** We elaborated on the **limitations of the method**, noting that it is not lightweight enough for high-resolution anomaly detection tasks. Additionally, the current Mamba-based encoder has certain gaps when directly applied to the anomaly detection domain, as shown in the ablation experiments in Tab. 10. We will continue to investigate these issues in future research.

### Reviewer aMDx
- **Q1:** We further explored:
  - The **scanning directions**, corresponding to Tab. 2.
  - The **scanning methods**, corresponding to Tab. 5, and their sensitivity to the method.
- **Q2:** We added three **additional datasets** from different categories to demonstrate the method's effectiveness, including medical, 3D, and general scene anomaly detection datasets, with ablation experiments corresponding to Tab. 4.
- **Q3:** We discussed the **robustness of the method** under different environmental conditions.
- **Q4:** We addressed the same issue as in Reviewer FXx2's Q3 and further discussed the method's **limitations and future work**.

### Reviewer gwhg
- **Q1:** We explored **comparisons with Transformer-based methods**, with ablation experiments in Tab. 1.
- **Q2:** We conducted fair comparisons by replacing the **backbone networks** of UniAD and MambaAD with three different networks, with ablation results shown in Tabs. 7 and 8.
- **Q3:** We discussed the reasons for poor anomaly localization performance and validated the method's effectiveness in pixel-level anomaly localization using the additional **mIoU anomaly localization evaluation metric** on six datasets, as shown in Tab. 6. We also provided more qualitative analysis with the RD4AD framework in Fig. 1.

### Reviewer wfnx
- **Q1:** We delved deeper into the **motivation** of this study.
- **Q2:** We conducted ablation experiments on the **local and global branches of LSS**, as shown in Tab. 9.
- **Q3:** We addressed the same issue as in Reviewer gwhg's Q3, discussing the reasons for poor anomaly localization performance and validating the method's effectiveness in pixel-level anomaly localization using the additional **mIoU anomaly localization evaluation metric** on six datasets, as shown in Tab. 6. We also provided more qualitative analysis with the RD4AD framework in Fig. 1.
- **Q4:** We conducted additional ablation experiments on the **Mamba-based encoder**, as shown in Tab. 10.
- **Q5:** We addressed the same issue as in Reviewer aMDx's Q1, with in-depth exploration and ablation experiments on the **scanning method**, as shown in Tab. 5.

Meta-review: 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.
Decision: Accept (poster)