Going beyond familiar features for deep anomaly detection

Thank you for the constructive feedback and comments. We have answered the questions and edited the draft to incorporate the clarifications in the writing.

W1. We recognize the importance of formalizing the definition of these concepts. This can not only help AD but also tasks like Open set recognition, anomaly detection and novel class detection. We revised Section 3 to highlight the definitions from other discussions. Our primary aim is to define the idea of familiar and novel features in a test input in the context of anomaly detection and illustrate the practical implications. Taking forward the hypothesis in [2], a future work that approaches the theoretical foundation can help the field.

W2. This design choice is taken from prior art for a fair comparison. We keep design choices of familiar feature branch same as the prior art [1]. Furthermore, the familiarity branch is shown to be robust to change of the nearest neighbor to a large extent. Below are the results of [1] to value of k. We add this to the appendix.

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      Dataset                   KNN
                k=1     k=2     k=5     k=10     k=50

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     CIFAR-10   99.0    99.1    98.9    98.9     98.7
     C10v100    89.8    90.0    90.0    90.0     89.7

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W3. Thank you for the suggestion, have added that to the section. The anomaly score computed as, novelty and familiarity score combined is highlighted.

W4. Figure 6 is an ablation of the familiarity and novelty branch. Also the comparison of [1] to our method also shows the effectiveness of incorporating novelty. Except for the choice of encoder. As mentioned in section 4 “In order to detect an anomaly by the lack of familiar features in a test sample, we use a mechanism similar to prior art.” The improvement in performance of the evaluated framework from [1] can be attributed to accounting for novelty.

W5. Thank you for the reference. We have added it to the related work as other notions of hybrid anomaly detection. [b] proposes a method to unify the approaches of generative modelling for regular training data and discriminating with respect to negative training data for anomaly detection. This is an interesting idea yet different from the notion of familiarity hypothesis explored in our work.

[1] Fake it until you make it : towards accurate near-distribution novelty detection [2] The Familiarity Hypothesis: Explaining the Behavior of Deep Open Set Methods

Thank you for recognizing the novelty and contributions in the paper and the constructive feedback. We have edited the draft to incorporate the clarifications in the writing.

Question 1 Thanks for seeking clarification on the experimental details. We have added the details in the appendix. This evaluation strategy and choice of classes is the same as the prior art [12]. As mentioned in the 3rd para of section 5.2, for the near ND benchmark, we choose CIFAR-10 vs CIFAR-100, where the closest classes of CIFAR-100 is the anomaly corresponding to each class of CIFAR-10. To evaluate a model on this benchmark, first, the model is trained on each of the classes of Cifar10 as a normal class. The model trained on a class, say class 'cat' from Cifar-10, uses all samples from the train split of class 'cat' as normal for training. The model is then evaluated on all classes of Cifar-100 one after the other, each as an anomaly with the test samples of class 'cat' as test normal samples. Then, the most challenging class (least AUROC) from Cifar-100 is selected as the test anomaly. This is repeated for all 10 classes of Cifar-10. Correspondingly, we get a near anomaly from cifar100. Below are the normal class near anomaly pairs following the format cifar10_normal_class:{c100_anomaly}:

   C10_100 = {'airplane': 'rocket', 'automobile': 'pickup_truck', 'bird': 'kangaroo', 'cat': 'rabbit', 'deer': 'kangaroo', 'dog': 'wolf', 'frog': 'lizard', 'horse': 'camel', 'ship': 'bridge', 'truck': 'pickup_truck'}

The intuition here is that any other class in the Cifar-100 as anomaly would yield a better AUROC score, making this the most challenging benchmark. For instance, [12] reports a 20% drop in performance of previous SOTA, PANDAS[11] on this benchmark compared to global Cifar-10-100 evaluation.

Question 2 The key motivation here is to compare the method's performance between the SOTA background class (diffusion model to approximate normal semantic distribution) and simpler approximation (the distribution statistics are the same as the normal class with no guarantees on the semantics). There is a correlation between AD performance and the FID distance between the normal and the background used to train the model. The two are negatively correlated until the FID is too low (normal~background). The intuition here is that the closer the background is to the normal (or more challenging the discriminative task for the encoder ), the better suited the learned feature is for AD. In the paper, we say that we hypothesize that reduced reliance on encoder derived features in our method can be the cause of this reduced reliance on the choice of background class.

CIFAR10 - 100 (Near ND trained with SDE)

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FID          400             300               200            100              50   
AUC         82.3             83.4              86.0           88.5            89.2

Using a normal approximation as background is a simpler, and comes at much lesser computation (~zero training) giving an FID of : 523.7 across classes. For familiarity methods, using high quality approximations gives an improvement of more than 7% on the near-ND benchmark[12]. Proposed method shows the performance is consistent across the 2 evaluations showing the reduced reliance on background for AD by incorporating novelty.

The table below shows the AD performance with other standard generators for generating background for FFS. We picked the best method from this for our experiment.

                      Baseline-VAE    Baseline-Gan       BigGAN    StyleGAN-ADA  StyleGAN-XL  DenseFlow     SDE    
CIFAR10                 93.8             94.5             96.9         97.8         96.5        96.4       99.1    
MyTecAD                 68.8            71.8              76.4         80.5         73.2        78.93      86.4

[11] PANDA: Adapting Pretrained Features for Anomaly Detection and Segmentation [12] Fake it until you make it : towards accurate near-distribution novelty detection [13] Opengan: open-set recognition via open data generation

Question 3 Explanation of B-cos gives a faithful summary of the encoder computation. Lack of this explanation implies the feature has not been used in the encoding (represented in the feature space). Absence of explanation is captured as the cosine distance between input features and the B-cos encoder explanation. Please note that computing novelty scores does not involve the use of train normal features or train normal explanations. It is computed between the input sample and the corresponding explanation as the distance of the test sample from the explanation of the encoder. This is enabled by the explanation faithful to the computation of the encoder (Bcos) and has a one-to-one correspondence with input features (enabling inspection for absence of features). In this framework lack of explanation means that the encoder has not captured that feature well.

Thank you for the feedback. We address a few points raised in the weakness and answer questions on details of the method. Updated draft to reflect clarifications.

Weaknesses

1: We would like to clarify that novelty branch does not rely on the explanation of normal samples, and the proposed method does not involve computing explanations for normal samples. Novel features are defined as the input features the encoder does not meaningfully represent in the feature space, captured with the distance of the test encoder explanation to the test sample. Contrasting Equations (4) and (5) show that familiarity uses normal features while novelty computation at inference does not rely on normal samples, its features, or its explanations. (Section 3: novel features, Section 4 ENS computation). Just transfer from the feature space to the B-cos network’s explanations is a mischaracterization of the method.

2: Thank you for highlighting the potential confusion in the definition. We have included clarification in the definition to avoid confusing background samples with background pixels within images. What we call background is different from what previous methods have called ‘training outliers’ [2], ‘outliers’ [5] [1], irregular samples[4], or just anomalies[1]. In prior art, background has been used to denote novel distributions/classes [2][3]. We use background for denoting complimentary set not in the normal distribution, including novel semantic classes, abnormal images, and random pixel configurations. Furthermore, Appendix 1 shows how training on a subset of background actually can reduce test AD performance in some cases (even on SOTA-generated background), motivating not just calling them anomalies.

3: Explainability is a desirable property in AD[6], and having a method that reliably explains anomalies can be a helpful addition. ML explainability has focused on reliability of the explanation methods[11], and the need to going beyond saliency explanation[12]. A limitation of feature-KNN methods is the lack of explanation [7]. Explanation research has application beyond localizing anomalies as well. Our evaluation of sensory anomaly is the same as the benchmarks used in [1] the SOTA familiar feature-based AD method. The paper states that we do not match the sensory anomaly SOTA with dense feature matching and shows a comparison with the familiar feature KNN methods. MVTec is one of the most popular and widely used industrial anomaly datasets suited for sensory anomaly detection [8][9]. Localization papers have also used it as the only sensory AD benchmark [8].

Answers

1. The paper does not assume that ‘untrained anomalies’ will be false negatives. [10] Present Familiarity Hypothesis: Existing AD methods succeed by detecting the presence and absence of familiar features (features the encoder has learned to represent) rather than the presence of novelty. The paper shows how this is an essential shortcoming of feature based anomaly detection. Anomalies represented differently from normal samples in the feature space can be captured using the familiarity branch. The novelty branch helps capture the features the encoder is not trained to represent meaningfully in the feature space. Our experiment shows how incorporating novel features into computing anomaly scores improves AD performance, especially reducing false negatives.

2. Evaluation on different types of benchmarks show the AD performance improvement on different 'kind of anomalies'. We compare AD performance using the familiarity branch alone and after incorporating novelty across 3 AD types to show the effect of incorporating novel features into AD computation. 'Likely unfair': We have now clarified the description in section 5.2. Please note that, the figure shows how incorporating novelty to the familiarity branch reduces FNR. We use a mechanism similar to SOTA to detect the lack of familiar features[1].

3. The figure shows two dominant axes of the PCA plot. It is shown to visualize the inner workings of incorporating novelty. The improvement in performance and the reduction in FN is the quantitative proof that incorporating novelty is effective in improving the anomaly score shown as distance in the plot.

[1] Fake it until you make it : towards accurate near-distribution novelty detection [2] Opengan: open-set recognition via open data generation [3] The pascal visual object classes challenge: a retrospective [4] G2d: generate to detect anomaly [5] Deep anomaly detection with outlier exposure [6] A survey on explainable anomaly detection [7] Sub-Image Anomaly Detection with Deep Pyramid Correspondences [8] Towards Total Recall in Industrial Anomaly Detection [9] PaDiM: a Patch Distribution Modeling Framework for Anomaly Detection and Localization [10] The Familiarity Hypothesis: Explaining the Behavior of Deep Open Set Methods [11] Towards A Rigorous Science Interpretable Machine Learning [12] The (Un)reliability of saliency methods