Title: NOVELTY DETECTION VIA BLURRING

Abstract: Conventional out-of-distribution (OOD) detection schemes based on variational autoencoder or Random Network Distillation (RND) have been observed to assign lower uncertainty to the OOD than the target distribution. In this work, we discover that such conventional novelty detection schemes are also vulnerable to the blurred images. Based on the observation, we construct a novel RND-based OOD detector, SVD-RND, that utilizes blurred images during training. Our detector is simple, efficient at test time, and outperforms baseline OOD detectors in various domains. Further results show that SVD-RND learns better target distribution representation than the baseline RND algorithm. Finally, SVD-RND combined with geometric transform achieves near-perfect detection accuracy on the CelebA dataset.

1. INTRODUCTION:

Out-of distribution (OOD) or novelty detection aims to distinguish samples in unseen distribution from the training distribution. A majority of novelty detection methods focus on noise filtering or representation learning. For example, we train an autoencoder to learn a mapping from the data to the bottleneck layer and use the bottleneck representation or reconstruction error to detect the OOD (Sakruada et al., 2014; Pidhorskyi et al., 2018) . Recently, deep generative models (Kingma et al., 2014; Dinh et al., 2017; Goodfellow et al., 2014; Kingma et al., 2018; Schlegl et al., 2017) are widely used for novelty detection due to their ability to model high dimensional data. However, OOD detection performance of deep generative models has been called into question since they have been observed to assign a higher likelihood to the OOD data than the training data (Nalisnick et al., 2019; Choi et al., 2018) .

On the other hand, adversarial examples are widely employed to fool the classifier, and training classifiers against adversarial attacks has shown effectiveness in detecting unknown adversarial attacks (Tramer et al., 2018) . In this work, we propose blurred data as adversarial examples. When we test novelty detection schemes on the blurred data generated by Singular Value Decomposition (SVD), we found that the novelty detection schemes assign higher confidence to the blurred data than the original data.

Motivated by this observation, we employ blurring to prevent the OOD detector from overfitting to low resolution. We propose a new OOD detection model, SVD-RND, which is trained using the idea of Random Network Distillation (RND) (Burda et al., 2019) to discriminate the training data from their blurred versions. SVD-RND is evaluated in some challenging scenarios where vanilla generative models show nearly 50% detection accuracy, such as CIFAR-10 vs. SVHN and ImageNet vs. CIFAR-10 (Nalisnick et al., 2019) . Compared to conventional baselines, SVD-RND shows a significant performance gain from 50% to over 90% in these domains. Moreover, SVD-RND shows improvements over baselines on domains where conventional OOD detection schemes show moderate results, such as CIFAR-10 vs. LSUN.

2. PROBLEM FORMULATION AND RELATED WORK:

The goal of OOD detection is to determine whether the data is sampled from the target distribution D. Therefore, based on the training data D train Ă D, we train a scalar function that expresses the confidence, or uncertainty of the data. The performance of the OOD detector is tested on the D test Ă D against the OOD dataset D OOD . We denote an in-distribution data and OOD pair as In : Out in this paper, e.g., CIFAR-10 : SVHN.

In this section, we mention only closely related work to our research. For a broader survey on deep OOD detection, we recommend the paper from Chalapathy et al. (2019) .

OOD Detection: Majority of OOD detection methods rely on a reconstruction error and representation learning. (Ruff et al., 2018) trained a deep neural network to map data into a minimum volume hypersphere. Generative probabilistic novelty detection (GPND) (Pidhorskyi et al., 2018) employed the distance to the latent data manifold as the confidence measure and trained the adversarial autoencoder (AAE) to model the manifold. Deep generative models are widely employed for latent space modeling in OOD detection (Zenati et al., 2018; Sabokrou et al., 2018) . However, a recent paper by Nalisnick et al. (2019) discovered that popular deep generative models, such as variational autoencoder (VAE) (Kingma et al., 2014) or GLOW (Kingma et al., 2018) , fail to detect simple OOD. While adversarially trained generative models, such as generative adversarial networks (GAN) (Goodfellow et al., 2014) or AAE, are not discussed in Nalisnick et al. (2019) , our experiments with GPND show that such models can also struggle to detect such simple OODs.

OOD Detection with Additional Data: Some methods try to solve OOD detection by appending additional data or labels for training. Hendrycks et al. (2019) trained the detector with additional outlier data independent of the test OOD data. Ruff et al. (2019) employed semi-supervised learning for anomaly detection in the scenario where we have ground truth information on few training data. Golan et al. (2018) designed geometrically transformed data and trained the classifier to distinguish geometric transforms, such as translation, flipping, and rotation. Shalev et al. (2018) fine-tuned the image classifier to predict word embedding. However, the intuition behind these methods is to benefit from potential side information, while our self-generated blurred image focuses on compensating for the deep model's vulnerability to OOD data with a lower effective rank.

Adversarial Examples and Labeled Data: Some methods combine OOD detection with classification, resulting in OOD detection utilizing labeled data. Adversarial examples can be viewed as generated OOD data that attacks the confidence of a pretrained classifier. Therefore, they share some similarities. For example, Hendrycks et al. (2017) set the confidence as the maximum value of the probability output, which is vulnerable against the adversarial examples generated by the Fast Sign Gradient Method (FSGM) (Goodfellow et al., 2014) . On the other hand, Liang et al. (2018) employed FSGM counterintuitively to shift the OOD data from the target further, therefore improving OOD detection. Lee et al. (2018) employed Mahalanobis distance to measure uncertainty in the hidden features of the network, which also proved efficient in adversarial defense.

Bayesian Uncertainty Calibration: Bayesian formulation is widely applied for better calibration of the model uncertainty. Recent works employed Bayesian neural networks (Sun et al., 2017) or interpreted a neural network's architecture in the Bayesian formulation, such as dropout (Gal et al., 2016) , and Adam optimizer (Khan et al., 2018) . Our baseline, RND (Burda et al., 2019) , can be viewed as the Bayesian uncertainty of the model weight under randomly initialized prior (Osband et al., 2018) .

3. METHODOLOGY:

In this section, we motivate our use of blurred data as adversarial examples to conventional deep OOD detection methods. Motivatied by the observation, we present our proposed algorithm, SVD-RND, and provide intuitions why SVD-RND help OOD detection.

3.1. GENERATING BLURRED DATA:

In this work, blurred images function as adversarial examples. We directly employ the SVD on the data matrix of each image in the training data and force the bottom non-zero singular values to zero to construct a blurred image. Suppose that data image d P D consists of multiple channels, where the j-th channel has N j nonzero singular values σ j1 ě σ j2 ě . . . σ jNj ą 0. Then, the j-th channel can be represented as the weighted sum of orthonormal vectors. 

d j " Σ Nj t"1 σ jt u jt v T jt (1)

We discard the bottom K non-zero singular values of each channel to construct the blurred image. We test conventional novelty detection methods on blurred images. We first train the VQ-VAE (Oord et al., 2017) in the CIFAR-10 ( Krizhevsky et al., 2009) dataset. Figure 1 shows the loss of VQ-VAE on the test data and blurred test data (K " 28). We follow the settings of the original paper. VQ-VAE assigns higher likelihood to the blurred data than the original data.

We note that this phenomenon is not constrained to the generative models. We trained the RND on the CIFAR-10 dataset and plot the L 2 loss in the test data and blurred test data in Figure 1 . We refer to Appendix B for detailed explanation and employed architecture for the RND in the experiment. Furthermore, we plot the average loss on the blurred test data and original test data during the training procedure. Throughout the training phase, the model assigns lower uncertainty to the blurred data. This trend is similar to the CIFAR-10 : SVHN case observed by Nalisnick et al. (2019) , where the generative model assigns more confidence to the OOD data throughout the training process.

While we employ SVD for our main blurring technique, conventional techniques in image processing can be applied for blurring, such as Discrete Cosine Transform (DCT) or Gaussian Blurring. However, DCT is quadratic in the size of the hyperparameter search space, therefore much harder to optimize than SVD. We further compare the performance between SVD and other blurring techniques in Section 4.

3.2. OOD DETECTION VIA SVD-RND:

We now present our proposed algorithm, SVD-RND. SVD-RND trains the predictor network f to discriminate between the original and blurred datasets. We first generate blurred datasets D i from D train by zeroing the bottom K i non-zero singular values of each data channel (i " 1, . . . , b train , where b train is the number of generated blurred datasets used for training). We then construct b train `1 target networks, i.e., g 0 , g 1 , . . . , g btrain . The target networks are independently randomly initialized and their parameters are unchanged during training. Predictor network f is trained to minimize the l 2 loss against the corresponding target network on each dataset.

f ˚" arg min f " Σ xPDtrain }f pxq ´g0 pxq} 2 2 `Σbtrain i"1 Σ xPDi }f pxq ´gi pxq} 2 2 ı (2)

SVD-RND optimizes the predictor network f as shown in p2q. When a new test sample x is given, SVD-RND outputs }f pxq ´g0 pxq} 2 2 as the uncertainty of the sample. Figure 2 shows the training process of SVD-RND. While the original RND paper employs a single target network to train the predictor network, SVD-RND employs multiple target networks to discriminate the original data from the blurred images.

While SVD-RND directly regularizes only on the blurred images, OODs can be generated in alternative directions. For completeness, we investigate the performance of conventional models in OODs generated in orthogonal direction to blurring. We refer to Appendix D for the detailed experiment.

4. EXPERIMENTAL RESULTS:

4.1 EXPERIMENT SETTING SVD-RND is examined in the cases in Table 1 . CIFAR-10 : SVHN, CelebA (Liu et al., 2015) : SVHN (Netzer et al., 2011) , and TinyImageNet (Deng et al., 2009) : (SVHN, CIFAR-10, CIFAR-100) are the cases studied by Nalisnick et al. (2019) . We also studied CIFAR-10 : (LSUN (Yu et al., 2015) , TinyImageNet), LSUN : (SVHN, CIFAR-10, CIFAR-100) and CelebA: (CIFAR-10, CIFAR-100) pairs. We implement the baselines and SVD-RND in the PyTorch framework.1 For a unified treatment, we resized all images in all datasets to 32ˆ32. We refer to Appendix C for the detailed setting.

For SVD-RND, we optimize the number of discarded singular values over different datasets. We choose the detector with the best performance across the validation data. We refer to Appendix C for the parameter setting. We also examine the case where each image is blurred by DCT and Gaussian blurring. For DCT, we apply the DCT to the image, discard low magnitude signals, and generate the blurred image by inverse DCT. In DCT-RND, we optimize the number of discarded components in the frequency domain. For Gaussian blurring, we optimize the shape of the Gaussian kernel. We denote this method as GB-RND.

We compare the performance of SVD-RND, DCT-RND, and GB-RND to the following baselines.

Generative Probabilistic Novelty Detector: GPND (Pidhorskyi et al., 2018) is the conventional generative-model-based novelty detection method that models uncertainty as a deviation from the latent representation, which is modeled by the adversarial autoencoder. We trained GPND with further parameter optimization.

Geometric Transforms: Golan et al. (2018) trained a classifier to discriminate in-distribution data against geometrically transformed data to achieve better OOD detection performance. The authors used four types of geometric transforms: flip, rotation, vertical translation, and horizontal translation. We test each transformation by setting them as OOD proxies in the RND framework. Moreover, we also investigate the effect of pixel inversion, contrast reduction, and shearing. We refer to Cubuk et al. ( 2019) for detailed explanation of the augmentation strategies.

RND::

We test the original RND (Burda et al., 2019) baseline. All criteria are bounded between 0 and 1, and the results close to 1 imply better OOD detection.

4.2. OOD DETECTION RESULTS:

We summarize our results on the TNR at 95% TPR in Table 2 . For example, TNR of 96.9% is achieved by SVD-RND for CIFAR-10 : SVHN pair. We refer to Appendix A for the full results. In all In : Out domains except the CelebA : (CIFAR-10, CIFAR-100) domain, SVD-RND outperforms all other baselines in every metric. Furthermore, all the proposed techniques outperform GPND and RND on all In : Out domains. We further visualize the CIFAR-10 data before and after blurring in Appendix E. We plot the performance of SVD-RND over different K 1 in Figure 3 . In Figure 3 , we experimented with 4 seeds. In the best performing parameter for each OOD data, SVD-RND shows stable performance. See Appendix F for results under small K 1 .

Furthermore, we plot the output of SVD-RND on target CIFAR-10 data and OOD SVHN data when K 1 " 28 in Figure 3 . Compared to the results in Figure 1 , SVD-RND better discriminates SVHN data from the in-distribution data. GPND and RND fail to discriminate OOD from the targets in CIFAR-10 : SVHN, LSUN : (SVHN, CIFAR-10, CIFAR-100), TinyImageNet : (SVHN, CIFAR-10, CIFAR-100), and CelebA : SVHN domains. Moreover, GPND performs the SVD of the Jacobian matrix in test time, which makes GPND slower than SVD-RND. Furthermore, we visualize the uncertainty prediction of RND and SVD-RND in Figure 4 , which shows the top-9 examples on CIFAR-10 test data, where SVD-RND and RND assign the highest uncertainty. We observe that SVD-RND tends to assign higher uncertainty to blurry or hardly recognizable images compared to RND.

On the other hand, OOD detection schemes based on geometric transformations (Golan et al., 2018) show generally improved results against GPND and RND on detecting OOD data compared to RND and GPND. Especially in CelebA : (SVHN, CIFAR-10, CIFAR-100) domains, rotation-based methods and translation-based methods show excellent performance. However, in the CIFAR-10 target domain, OOD detection schemes based on geometric transformations show degraded performance against RND or GPND on LSUN and TinyImageNet OOD data.

Furthermore, typicality test shows mixed results compared to the baseline algorithms.

Finally, we also investigate the case where limited training data is available. We examined the performance of SVD-RND and RND in CIFAR-10 : (LSUN, TinyImageNet) domains. Figure 4 shows the TNR at 95% TPR metric of each method when the number of training examples is reduced.

For each OOD data, we denote the result on SVD-RND as OOD SVD, and denote the result on RND as OOD RND.

5. FURTHER ANALYSIS:

In this section, we examine some other aspects of SVD-RND. In Section 5.1, we examine whether SVD-RND learns better representation compared to the baseline. Furthermore, we propose a novel heuristic for training SVD-RND in Section 5.2, where no validation OOD data is available. Finally, we show that we can further improve the performance of SVD-RND by incorporating geometric transformations in Section 5.3. While SVD-RND outperforms RND on every In : Out domains in Section 4, we provide further evidence that SVD-RND learns superior target distribution representation compared to RND. For the evidence, we fine-tune a classifier over the fixed activation map of SVD-RND and RND. We set the activation map as the output of the first 15 or 27 layers of RND and SVD-RND predictor network trained in CIFAR-10 datasets. For the fine-tuning, we either appended three residual blocks and a linear output layer with softmax activation (denoted as 7-layer in Table 3 ) or a linear layer (denoted as linear in Table 3 ). Then, we fine-tune the appended network for the CIFAR-10 classification task.

The SGD optimizer with learning rate 0.1 is used for fine-tuning, and the learning rate is annealed from 0.1 to 0.01 and 0.001 after 30 and 60 epochs over 100 epochs of training, respectively. We average the result across three fixed random seeds.

We show our results in Table 3 . SVD-RND consistently outperforms RND on the fine-tuning task. Therefore, the result supports that SVD-RND learns better target distribution-specific knowledge.

5.2. SVD-RND WITHOUT OOD VALIDATION DATA:

In our main experiments in Section 4, we used the OOD validation data for optimizing each K i . However, in realistic scenarios, OOD data are generally unknown to the detector. We propose an effective rank (Roy et al., 2007) based design of SVD-RND that does not use the OOD validation dataset and compare its performance against the results in Section 4. Log effective rank of the single image matrix D is defined as the entropy of the normalized singular values pσ 1 , . . . , σ N q of the image matrix.

LER D " H ˜σ1 Σ N j"1 σ j , . . . , σ N Σ N j"1 σ j ¸(3)

In p3q, H is the entropy function. Then, the effective rank is defined as the two to the power of the log effective rank. We set the effective rank of image data as the averaged effective rank of each channel.

Based on p3q, we propose selecting each K i such that average of log effective rank on each blurred dataset is equally spaced. Specifically, suppose the log effective rank of the data averaged in training dataset D train is LER Dtrain . Then, we set the target log effective rank LER 1 , LER 2 , . . . , LER btrain as follows.

LER i " ˆ0.5 `0.5 ˆi ´1 b train ˙LER Dtrain (4) Then, we select K i such that the average of the log effective rank in the blurred dataset with K i discarded singular values is closest to LER i . We test our criterion in CIFAR-10 and TinyImageNet data with different b train . We train SVD-RND for 25 epochs for b train " 3, and 20 epochs for b train " 4. We show the performance of SVD-RND based on p4q in Table 4 , which is denoted as SVD-RND (uniform). We also show results of SVD-RND optimized with the validation OOD data from Table 2 and denote them as SVD-RND (optimized) in Table 4 . Uniform SVD-RND already outperforms the second-best methods in Table 2 . Furthermore, as b train increases, uniform SVD-RND approaches the performance of the optimized SVD-RND. While SVD-RND achieves reasonable OOD detection performance, combining SVD-RND with other baseline algorithms may further enhance the performance. For example, as shown in Table 2 , training against rotated data benefits OOD detection in CelebA dataset. Therefore, we combine SVD-RND and geometric transform-based methods to further improve SVD-RND. We treat both blurred data and geometrically transformed data as OOD and train the predictor network to discriminate the original data from the OOD. We combine rotation and vertical translation with SVD-RND and denote them as SVD-ROT-RND and SVD-VER-RND, respectively.

We compare the performance of SVD-ROT-RND and SVD-VER-RND against rotation and vertical translation in CelebA : (SVHN, CIFAR-10, CIFAR-100) domains. We refer readers to the results in Table 5 . We observe that SVD-ROT-RND and SVD-VER-RND outperform their counterparts and SVD-RND. Especially, SVD-ROT-RND and SVD-VER-RND show significant performance gains in CelebA : (CIFAR-10, CIFAR-100) domains.

6. CONCLUSION:

In this work, blurred images are introduced as adversarial examples in deep OOD detection. SVD-RND is employed for adversarial defense against blurred images. SVD-RND achieves significant performance gain in all In : Out domains. Even without the validation OOD data, we can design SVD-RND to outperform conventional OOD detection models.

7. ACKNOWLEDGEMENT B RANDOM NETWORK DISTILLATION:

We use RND (Burda et al., 2019) as the base model of our OOD detector. RND consists of a trainable predictor network f , and a randomly initialized target network g. The predictor network is trained to minimize the l 2 distance against the target network on training data. The target network g remains fixed throughout the training phase.

f ˚" arg min f Σ xPDtrain }f pxq ´gpxq} 2 2

(5)

Then, for unseen test data x, RND outputs }f pxq ´gpxq} 2 2 as an uncertainty measure. The main intuition of the RND is to reduce the distance between f and g only on the in-distribution, hence naturally distinguish between the in-distribution and the OOD.

We employ RND for our base OOD detector due to its simplicity over generative models. Also, RND has already shown to be effective in novelty detection on MNIST dataset (Burda et al., 2019) .

In RND (Burda et al., 2019) , the predictor network f has two more layers than the target network g, where g consists of 3 convolution layers and a fully connected layer. In our experiments, we set g as the first 33 layers of ResNet34 without ReLU activation in the end. f is constructed by appending two sequential residual blocks. The output size of each residual block is 1024 and 512. We also discard ReLU activation in the second residual block to match the output layer of g. In SVD-RND, DCT-RND, and GB-RND, we used b train " 1 for CIFAR-10 and CelebA dataset, and b train " 2 for TinyImageNet and LSUN dataset. For SVD-RND, We optimize across K 1 P t18, 20, 22, 24, 25, 26, 27, 28u in the CIFAR-10 and CelebA datasets. For TinyImageNet and LSUN datasets, we optimize over K 1 P t8, 10, 12, 14u and K 2 P t22, 24, 26, 28u. In DCT-RND, we define K i as the number of unpruned signals in the frequency domain. For CIFAR-10 and CelebA datasets, we optimize K 1 across t4, 8, 12, 14, 16, 20, 24, 28u. For TinyImageNet and LSUN datasets, we optimize over K 1 P t20, 24, 28, 32u and K 2 P t40, 44, 48, 52u. For Gaussian blurring, we optimize over the shape px i , y i q of the Gaussian kernel. We optimized the parameter over x i P t1, 3, 5u , y i P t1, 3, 5u for each blurred data. To fix the number of updates, we train SVD-RND, DCT-RND, and GB-RND for 50 epochs in the CIFAR-10 and CelebA datasets, and for 34 epochs for the rest.

For GPND, the settings for the original paper are followed. Furthermore, we optimize the reconstruction loss λ 1 and adversarial loss λ 2 for discriminator D z across λ 1 P t8, 9, 10, 11, 12u and λ 2 P t1, 2, 3u. We choose the parameters with the best validation performance at 100 epochs, For RND, we trained over 100 epochs.

For geometric transforms, we optimize the magnitude of the shift of shear, horizontal translation and vertical translation methods. We optimize the magnitude of translation across t4, 8, 12, 16u and choose the parameter with the best validation performance. Detector is trained for r 100

|T |`1 s epochs, where |T | is the number of transformations. The number of transformations is 1 in flipping and invert, 2 for horizontal translation, vertical translation, and shear, and 3 for rotation and contrast. Finally, for typicality test, we estimated the average test loss of the RND for 50000 training examples.

For each test sample, we use the distance between the test loss of the sample and the estimated average loss as the OOD metric.

D GENERATING OOD BY ADDING ORTHOGONAL VECTORS:

We present the performance of RND on OODs generated by adding vectors orthogonal to the data.

To genetrate such OODs, we sample a Gaussian vector z and compute the component of the random vector z orth,x that is orthogonal to the data x.

z orth,x " z ´zT x x T x x (6)

We scaled the l 2 norm of the orthogonal vector z orth,x on each data to be α% of the l 2 norm of the signal. We plot the average uncertainty of RND on the original data, blurred data, and the perturbed data in Table 7 . From the 20 independent runs on the perturbed data, we report the case with smallest test uncertainty in Table 7 . We varied α from 5 to 20. While blurring reduces the average test uncertainty of RND, adding orthogonal vector to the data incerases the test uncertainty of RND. 

:

Our code is based on https://github.com/kuangliu/pytorch-cifar

This work was supported by Samsung Electronics and the ICT R&D program of MSIP/IITP. [2016-0-00563, Research on Adaptive Machine Learning Technology Development for Intelligent Autonomous Digital Companion]

Figures and Tables:

Figure 1: Test loss of VQ-VAE (left) and RND (middle) on original image and blurred image (K " 28) of CIFAR-10 data. RND assigns higher confidence to blurred image and OOD data throughout the training process (right).

Figure 2: Training of SVD-RND (b train " 1)

Figure 3: Left: Performance of SVD-RND (proposed) for different K 1 in CIFAR-10 : (SVHN, LSUN, TinyImageNet) domains. Each filled region is the 95% confidence interval of the detector. SVD-RND shows a small confidence interval in the best performing parameters. Right: Histogram of SVD-RND's test loss for CIFAR-10 and SVHN datasets.

Figure 4: Left: Novelty detection performance (TNR at 95% TPR) of SVD-RND and RND on reduced CIFAR-10 training data. SVD-RND is robust to reduced training data while RND's detection performance decreases. Middle: Top-9 anomalous CIFAR-10 test samples detected by SVD-RND. Right: Top-9 anomalous CIFAR-10 test samples detected by RND.

DATA PREPROCESSING, NETWORK SETTINGS, PARAMETER SETTINGS FOR MAIN EXPERIMENT To make the OOD detection task harder, we reduce each of the training dataset of CelebA, Tiny-ImageNet, and LSUN to 50000 examples and test dataset of CelebA to 26032 examples. For TinyImageNet data, we discard half of the images in each class, resulting in 250 training examples for each of the 200 classes. Reduction in LSUN dataset results in 5000 examples for each of the 10 classes. Also, the first 1000 images of the test OOD data are used for validation. For SVD-RND and all other RND-based detectors, we use the same structure for f and g defined in Appendix B. The number of parameter updates is fixed across the experiments. The Adam optimizer, with a learning rate of 10 ´4, is used for RND-based OOD detection methods. The learning rate is annealed from 10 ´4 to 10 ´5 in half of the training process. For our main experiment, we average the result across two fixed random seeds.

Figure 5: Sample visualization on the best performing parameters of SVD-RND, DCT-RND, and GB-RND. (a): original CIFAR-10 sample. (b), (c): sample after SVD-RND. (d), (e): sample after DCT-RND. (f), (g): sample after GB-RND.

Experiment In : Out domains

Table content: <table><tr><td>Target</td><td>OOD</td><td/></tr><tr><td>CIFAR-10</td><td>SVHN LSUN</td><td>TinyImageNet</td></tr><tr><td colspan="3">TinyImageNet SVHN CIFAR-10 CIFAR-100</td></tr><tr><td>LSUN</td><td colspan="2">SVHN CIFAR-10 CIFAR-100</td></tr><tr><td>CelebA</td><td colspan="2">SVHN CIFAR-10 CIFAR-100</td></tr></table>

OOD detection results (TNR at 95% TPR) on CIFAR-10, TinyImageNet, LSUN, and CelebA datasets. See Table1for OODs used in each case.

Table content: <table><tr><td/><td/><td>TNR(95% TPR)</td><td/><td/></tr><tr><td>Method</td><td>CIFAR-10</td><td>TinyImageNet</td><td>LSUN</td><td>CelebA</td></tr><tr><td>SVD-RND (proposed)</td><td>0.969/0.956/0.952</td><td>0.991/0.926/0.911</td><td>0.995/0.621/0.614</td><td>0.999/0.897/0.897</td></tr><tr><td>DCT-RND (proposed)</td><td>0.899/0.797/0.748</td><td>0.929/0.104/0.169</td><td>0.971/0.117/0.213</td><td>0.989/0.491/0.587</td></tr><tr><td>GB-RND (proposed)</td><td>0.474/0.803/0.738</td><td>0.982/0.264/0.321</td><td>0.986/0.176/0.266</td><td>0.994/0.455/0.526</td></tr><tr><td>RND</td><td>0.008/0.762/0.736</td><td>0.001/0.001/0.003</td><td>0.012/0.034/0.075</td><td>0.067/0.231/0.253</td></tr><tr><td>GPND</td><td>0.050/0.767/0.665</td><td>0.077/0.085/0.118</td><td>0.051/0.059/0.102</td><td>0.084/0.230/0.250</td></tr><tr><td>Flip</td><td>0.057/0.091/0.081</td><td>0.160/0.212/0.231</td><td>0.060/0.055/0.083</td><td>0.055/0.728/0.750</td></tr><tr><td>Rotate</td><td>0.235/0.246/0.308</td><td>0.711/0.669/0.688</td><td>0.341/0.278/0.334</td><td>0.950/0.937/0.945</td></tr><tr><td>Vertical Translation</td><td>0.105/0.649/0.648</td><td>0.050/0.012/0.012</td><td>0.117/0.044/0.076</td><td>0.930/0.887/0.897</td></tr><tr><td>Horizontal Translation</td><td>0.070/0.675/0.630</td><td>0.109/0.005/0.011</td><td>0.140/0.043/0.101</td><td>0.894/0.874/0.889</td></tr><tr><td>Vertical Shear</td><td>0.077/0.744/0.684</td><td>0.094/0.058/0.094</td><td>0.143/0.079/0.134</td><td>0.940/0.883/0.897</td></tr><tr><td>Horizontal Shear</td><td>0.227/0.720/0.672</td><td>0.072/0.072/0.098</td><td>0.148/0.084/0.132</td><td>0.897/0.885/0.888</td></tr><tr><td>Contrast</td><td>0.468/0.000/0.002</td><td>0.670/0.143/0.142</td><td>0.616/0.123/0.146</td><td>0.701/0.295/0.329</td></tr><tr><td>Invert</td><td>0.473/0.614/0.622</td><td>0.455/0.057/0.061</td><td>0.508/0.142/0.172</td><td>0.766/0.740/0.721</td></tr><tr><td>Typicality Test</td><td>0.008/0.734/0.691</td><td>0.004/0.003/0.008</td><td>0.004/0.024/0.057</td><td>0.064//0.245/0.274</td></tr><tr><td>0.95</td><td/><td/><td/><td/></tr><tr><td colspan="2">Discarded Nonzero Singular Values 20 21 22 23 24 25 26 27 28 0.65 0.70 0.75 0.80 0.85 0.90 TNR_TPR_0.95 SVHN LSUN TinyImageNet</td><td/><td/><td/></tr></table>



Table content: <table><tr><td/><td colspan="2">Target: CIFAR-10</td></tr><tr><td colspan="3">Activation map SVD-RND (K=28) RND</td><td>Random</td></tr><tr><td>15th (linear)</td><td>55.62 (1.10)</td><td colspan="2">42.09 (0.66) 36.55 (0.56)</td></tr><tr><td>15th (7-layer)</td><td>86.29 (0.09)</td><td colspan="2">83.78 (0.29) 86,56 (0.36)</td></tr><tr><td>27th (linear)</td><td>52.69 (0.24)</td><td colspan="2">38.21 (2.00) 24.46 (0.42)</td></tr><tr><td>27th (7-layer)</td><td>70.31 (0.24)</td><td colspan="2">57.18 (0.49) 66.40 (0.31)</td></tr></table>

Performance of uniform SVD-RND and optimized SVD-RND

Table content: <table><tr><td colspan="6">Target: CIFAR-10, OOD: SVHN/LSUN/TinyImageNet. Target: TinyImageNet (TIMG), OOD: SVHN/CIFAR-10/CIFAR-100</td></tr><tr><td>Dataset/btrain</td><td>AUROC</td><td>TNR(95% TPR)</td><td>Detection accuracy</td><td>AUPR in</td><td>AUPR out</td></tr><tr><td>CIFAR-10/3 (uniform)</td><td>0.967/0.961/0.961</td><td>0.944/0.827/0.836</td><td>0.962/0.904/0.904</td><td>0.843/0.966/0.962</td><td>0.989/0.949/0.953</td></tr><tr><td>CIFAR-10/4 (uniform)</td><td>0.964/0.987/0.988</td><td>0.941/0.954/0.959</td><td>0.958/0.957/0.961</td><td>0.848/0.989/0.989</td><td>0.987/0.983/0.985</td></tr><tr><td>CIFAR-10/1 (optimized)</td><td>0.981/0.985/0.982</td><td>0.969/0.956/0.952</td><td>0.980/0.955/0.953</td><td>0.903/0.987/0.983</td><td>0.993/0.975/0.976</td></tr><tr><td>TIMG/3 (uniform)</td><td>0.993/0.831/0.814</td><td>0.999/0.745/0.701</td><td>0.989/0.855/0.832</td><td>0.991/0.741/0.725</td><td>0.995/0.878/0.864</td></tr><tr><td>TIMG/4 (uniform)</td><td>0.984/0.939/0.923</td><td>0.954/0.880/0.842</td><td>0.976/0.927/0.908</td><td>0.982/0.915/0.894</td><td>0.989/0.938/0.928</td></tr><tr><td>TIMG/2 (optimized)</td><td>0.983/0.969/0.960</td><td>0.991/0.926/0.911</td><td>0.980/0.963/0.953</td><td>0.978/0.965/0.951</td><td>0.989/0.958/0.953</td></tr><tr><td colspan="3">5.1 REPRESENTATION LEARNING IN SVD-RND</td><td/><td/><td/></tr></table>

OOD detection performance of SVD-ROT-RND and SVD-VER-RND

Table content: <table><tr><td/><td colspan="4">Target: CelebA, OOD: SVHN/CIFAR-10/CIFAR-100</td><td/></tr><tr><td>Method</td><td>AUROC</td><td>TNR(95 % TPR)</td><td>Detection accuracy</td><td>AUPR in</td><td>AUPR out</td></tr><tr><td>SVD-ROT-RND</td><td>0.997/0.996/0.996</td><td>0.999/0.993/0.994</td><td>0.996/0.991/0.991</td><td>0.998/0.998/0.998</td><td>0.993/0.986/0.988</td></tr><tr><td>SVD-VER-RND</td><td>0.999/0.993/0.994</td><td>0.999/0.982/0.982</td><td>0.998/0.982/0.981</td><td>0.999/0.997/0.997</td><td>0.998/0.984/0.986</td></tr><tr><td>SVD-RND</td><td>0.999/0.963/0.964</td><td>0.999/0.897/0.897</td><td>0.998/0.928/0.928</td><td>0.999/0.981/0.981</td><td>0.998/0.941/0.943</td></tr><tr><td>ROT-RND</td><td>0.974/0.979/0.982</td><td>0.950/0.937/0.945</td><td>0.964/0.952/0.956</td><td>0.950/0.989/0.991</td><td>0.981/0.964/0.969</td></tr><tr><td>VER-RND</td><td>0.964/0.961/0.964</td><td>0.930/0.887/0.897</td><td>0.952/0.923/0.926</td><td>0.934/0.979/0.980</td><td>0.975/0.941/0.946</td></tr><tr><td colspan="3">5.3 FURTHER IMPROVEMENT OF SVD-RND</td><td/><td/><td/></tr></table>

Test uncertainty of RND on OOD CIFAR-10 data generated by adding orthogonal noise to the CIFAR-10 dataDataOriginal Blurred α " 5 α " 10 α " 15 α " 20

Table content: <table><tr><td>Average Uncertainty(ˆ10 ´5) 5.631</td><td>5.190</td><td>5.648</td><td>5.795</td><td>6.051</td><td>6.437</td></tr></table>

Peer review (iclr2020):
This paper proposed a method called SVD-RND to solve the out-of-distribution (OOD) detection problem. The proposed SVD-RND is under the Random Network Distillation (RND) framework, but make use of blurred images as adversarial samples. SVD-RND outperforms state-of-the-art methods in several OOD tasks. In general, this paper is well-structured. It is not difficult to understand the problem this paper focuses on and the proposed method. I believe the proposed method is interesting, and I have not seen a similar approach before. It is a simple method, but it achieves excellent performance in multiple OOD tasks. Although the authors try to explain why SVD-RND performs well, I am not entirely convinced and believe that more investigations might be necessary. Are the images from different datasets of similar average effective rank? I am also wondering how the proposed model will perform if we use other images as the adversarial examples. For example, we can use random low-rank images, which can be generated via Equation (3) by first randomly sampling , , and , and then let a certain number of singular values be zero. In summary, I am inclined to accept this paper because it proposes a simple method that gives high performance. However, I would suggest the authors include more ablation studies to help the readers understand why the proposed method works. Minor: I suggest the authors explicitly state that we do not update the network in Equation (1) and (4), such that the readers are less likely to be confused. The authors might also need to briefly explain why RND works. Is a specific strategy applied to initialize the network randomly? Are weights in initialized using Gaussian distribution, uniform distribution, or via other initialization strategies? In Table 1, all the datasets in columns 2, 3, and 4 are OOD samples, correct? To ensure that the TPR is as described in Table 2, we need to tune the threshold for , right? If a sample gives a that is higher than the threshold, it is considered as an OOD sample, correct?