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+# A STUDY OF FACE OBFUSCATION IN IMAGENET
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+Face obfuscation (blurring, mosaicing, etc.) has been shown to be effective for privacy protection; nevertheless, object recognition research typically assumes access to complete, unobfuscated images. In this paper, we explore the effects of face obfuscation on the popular ImageNet challenge visual recognition benchmark. Most categories in the ImageNet challenge are not people categories; however, many incidental people appear in the images, and their privacy is a concern. We first annotate faces in the dataset. Then we demonstrate that face blurring and overlaying—two typical obfuscation techniques—have minimal impact on the accuracy of recognition models. Concretely, we benchmark multiple deep neural networks on face-obfuscated images and observe that the overall recognition accuracy drops only slightly $( \leq 1 . 0 \% )$ . Further, we experiment with transfer learning to 4 downstream tasks (object recognition, scene recognition, face attribute classification, and object detection) and show that features learned on face-obfuscated images are equally transferable. Our work demonstrates the feasibility of privacyaware visual recognition, improves the highly-used ImageNet challenge benchmark, and suggests an important path for future visual datasets.
+
+# 1 INTRODUCTION
+
+Visual data is being generated at an unprecedented scale. People share billions of photos daily on social media (Meeker, 2014). There is one security camera for every 4 people in China and the United States (Lin & Purnell, 2019). Even your home can be watched by smart devices taking photos (Butler et al., 2015; Dai et al., 2015). Learning from the visual data has led to computer vision applications that promote the common good, e.g., better traffic management (Malhi et al., 2011) and law enforcement (Sajjad et al., 2020). However, it also raises privacy concerns, as images may capture sensitive information such as faces, addresses, and credit cards (Orekondy et al., 2018).
+
+Extensive prior research has focused on preventing unauthorized access to sensitive information in private datasets (Fredrikson et al., 2015; Shokri et al., 2017). However, are publicly available datasets free of privacy concerns? Taking the popular ImageNet dataset (Deng et al., 2009) as an example, there are only 3 people categories1 in the 1000 categories of the ImageNet Large Scale Visual Recognition Challenge (ILSVRC) (Russakovsky et al., 2015); nevertheless, the dataset exposes many people co-occurring with other objects in images (Prabhu & Birhane, 2021), e.g., people sitting on chairs, walking dogs, or drinking beer (Fig. 1). It is concerning since ILSVRC is freely available for academic use2 and widely used by the research community.
+
+In this paper, we attempt to mitigate ILSVRC’s privacy issues. Specifically, we construct a privacyenhanced version of ILSVRC and gauge its utility as a benchmark for image classification and as a dataset for transfer learning.
+
+Face annotation. As an initial step, we focus on a prominent type of private information—faces. To examine and mitigate their privacy issues, we first annotate faces in ImageNet using face detectors and crowdsourcing. We use Amazon Rekognition to detect faces automatically, and then refine the results through crowdsourcing on Amazon Mechanical Turk to obtain accurate annotations.
+
+We have annotated 1,431,093 images in ILSVRC, resulting in 562,626 faces from 243,198 images ( $17 \%$ of all images have at least one face). Many categories have more than $90 \%$ images with faces, even though they are not people categories, e.g., volleyball and military uniform. Our annotations confirm that faces are ubiquitous in ILSVRC and pose a privacy issue. We release the face annotations to facilitate subsequent research in privacy-aware visual recognition on ILSVRC.
+
+![](images/d819ac9df1e14ca85e27a703221a8817f04c20a4af7752121b67bb812f9e5e04.jpg)  
+Figure 1: Most categories in ImageNet Challenge (Russakovsky et al., 2015) are not people categories. However, the images contain many people co-occurring with the object of interest, posing a potential privacy threat. These are example images (with faces blurred or overlaid) of barber chair, husky, beer bottle, volleyball and military uniform.
+
+Effects of face obfuscation on classification accuracy. Obfuscating sensitive image areas is widely used for preserving privacy (McPherson et al., 2016). We focus on two simple obfuscation methods: blurring and overlaying (Fig. 1), whose privacy effects have been analyzed in prior work (Oh et al., 2016; Li et al., 2017; Hasan et al., 2018). Using our face annotations, we construct face-obfuscated versions of ILSVRC. What are the effects of using them for image classification? At first glance, it seems inconsequential—one should still recognize a car even when the people inside have their faces blurred. Indeed, we verify that validation accuracy drops only slightly $( 0 . \bar { 1 } \% - 0 . 7 \%$ for blurring, $0 . 3 \% { - } 1 . 0 \%$ for overlaying) when using face-obfuscated images to train and evaluate. We analyze this drop in detail (identifying categories which are particularly affected), but this key result demonstrates that we can train privacy-aware visual classifiers on ILSVRC which remain highly competitive, with less than a $1 \%$ accuracy drop.
+
+Effects on feature transferability. Besides a classification benchmark, ILSVRC also serves as pretraining data for transferring to domains where labeled images are scarce (Girshick, 2015; Liu et al., 2015a). So a further question is: Does face obfuscation hurt the transferability of visual features learned from ILSVRC? We investigate by pretraining models on the original/obfuscated images and finetuning on 4 downstream tasks: object recognition on CIFAR-10 (Krizhevsky et al., 2009), scene recognition on SUN (Xiao et al., 2010), object detection on PASCAL VOC (Everingham et al., 2010), and face attribute classification on CelebA (Liu et al., 2015b). They include both classification and spatial localization, as well as both face-centric and face-agnostic recognition. In all of the 4 tasks, models pretrained on face-obfuscated images perform closely with models pretrained on original images. We do not see a statistically significant difference between them, suggesting that visual features learned from face-obfuscated pretraining are equally transferable. Again, this encourages us to adopt face obfuscation as an additional protection on visual recognition datasets without worrying about detrimental effects on the dataset’s utility.
+
+Contributions. Our contributions are twofold. First, we obtain accurate face annotations in ILSVRC, facilitating subsequent research on privacy protection. We will release the code and the annotations. Second, to the best of our knowledge, we are the first to investigate the effects of privacy-aware face obfuscation on large-scale visual recognition. Through extensive experiments, we demonstrate that training on face-obfuscated images does not significantly compromise accuracy on both image classification and downstream tasks, while providing some privacy protection. Therefore, we advocate for face obfuscation to be included in ImageNet and to become a standard step in future dataset creation efforts.
+
+# 2 RELATED WORK
+
+Privacy-preserving machine learning (PPML). Machine learning frequently uses private datasets (Chen et al., 2019b). Research in PPML is concerned with an adversary trying to infer the private data. The privacy breach can happen to the trained model. For example, model inversion attack recovers sensitive attributes (e.g., gender, genotype) of an individual given the model’s output (Fredrikson et al., 2014; 2015; Hamm, 2017; Li et al., 2019; Wu et al., 2019). Membership inference attack infers whether an individual was included in training (Shokri et al., 2017; Nasr et al., 2019; Hisamoto et al., 2020). Training data extraction attack extracts verbatim training data from the model (Carlini et al., 2019; 2020). For defending against these attacks, differential privacy is a general framework (Abadi et al., 2016; Chaudhuri & Monteleoni, 2008; McMahan et al., 2018; Jayaraman & Evans, 2019; Jagielski et al., 2020). It requires the model to behave similarly whether or not an individual is in the training data.
+
+Privacy breaches can also happen in training/inference. To address hardware/software vulnerabilities, researchers have used enclaves—a hardware mechanism for protecting a memory region from unauthorized access—to execute machine learning workloads (Ohrimenko et al., 2016; Tramer & Boneh, 2018). Machine learning service providers can run their models on users’ private data encrypted using homomorphic encryption (Gilad-Bachrach et al., 2016; Brutzkus et al., 2019; Juvekar et al., 2018; Bian et al., 2020; Yonetani et al., 2017). It is also possible for multiple data owners to train a model collectively without sharing their private data using federated learning (McMahan et al., 2017; Bonawitz et al., 2017; Li et al., 2020) or secure multi-party computation (Shokri & Shmatikov, 2015; Melis et al., 2019; Hamm et al., 2016; Pathak et al., 2010; Hamm et al., 2016).
+
+There is a fundamental difference between our work and PPML. PPML focuses on private datasets, whereas we focus on public datasets with private information. ImageNet, like other academic datasets, is publicly available to researchers. There is no point preventing an adversary from inferring the data. However, public datasets can also expose private information about individuals, who may not even be aware of their presence in the data. It is their privacy we are protecting.
+
+Privacy in visual data. To mitigate privacy issues with public visual datasets, researchers have attempted to obfuscate private information before publishing the data. Frome et al. (2009) and Uittenbogaard et al. (2019) use blurring and inpainting to obfuscate faces and license plates in Google Street View. nuScenes (Caesar et al., 2020) is an autonomous driving dataset where faces and license plates are detected and then blurred. Similar method is also used for the action dataset AViD (Piergiovanni & Ryoo, 2020).
+
+We follow this line of work to obfuscate faces in ImageNet but differ in two critical ways. First, to the best of our knowledge, we are the first to thoroughly analyze the effects of face obfuscation on visual recognition. Second, prior works use only automatic methods such as face detectors, whereas we additionally employ crowdsourcing. Human annotations are more accurate and thus more useful for following research on privacy preservation in ImageNet. Most importantly though, automated face recognition methods are known to contain racial and gender biases (Buolamwini & Gebru, 2018); thus using these methods alone is likely to result in more privacy protection to members of majority groups. Including a manual verification step helps partially mitigate these issues.
+
+Finally, we note that face obfuscation alone is not sufficient for privacy protection. Orekondy et al. (2018) constructed Visual Redactions, annotating images with 42 privacy attributes, including faces, names, and addresses. Ideally, we should obfuscate all such information; however, this may not be immediately feasible. Obfuscating faces (omnipresent in visual datasets) is an important first step.
+
+Privacy guarantees of face obfuscation. Unfortunately, face obfuscation does not provide any formal guarantee of privacy. Both humans and machines may be able to infer an individual’s identity from face-obfuscated images, presumably relying on cues outside faces such as height and clothing (Chang et al., 2006; Oh et al., 2016). Researchers have tried to protect sensitive image regions against attacks, e.g., by perturbing the image adversarially to reduce the performance of a recognizer (Oh et al., 2017; Ren et al., 2018; Sun et al., 2018; Wu et al., 2018; Xiao et al., 2020). However, these methods are tuned for a particular model and provide no privacy guarantee either.
+
+Further, guarantees in privacy may reduce dataset utility as shown for example by Cheng et al. (2021). Therefore, we choose two simple local methods—blurring and overlaying—instead of more sophisticated alternatives. Overlaying removes all information in a face bounding box, whereas blurring removes only partial information. Their effectiveness for privacy protection can be ascertained only empirically, which has been the focus of prior work (Oh et al., 2016; Li et al., 2017; Hasan et al., 2018) but is beyond the scope of this paper.
+
+Visual recognition from degraded data. Researchers have studied visual recognition in the presence of various image degradation, including blurring (Vasiljevic et al., 2016), lens distortions (Pei et al., 2018), and low resolution (Ryoo et al., 2016). These undesirable artifacts are due to imperfect sensors rather than privacy concerns. In contrast, we intentionally obfuscate faces for privacy’s sake.
+
+Ethical issues with datasets. Datasets are important in machine learning and computer vision. But recently they have been called out for scrutiny (Paullada et al., 2020), especially regarding the presence of people. A prominent issue is imbalanced representation, e.g., underrepresentation of certain demographic groups in data for face recognition (Buolamwini & Gebru, 2018), activity recognition (Zhao et al., 2017), and image captioning (Hendricks et al., 2018).
+
+For ImageNet, researchers have examined and attempted to mitigate issues such as geographic diversity, the category vocabulary, and imbalanced representation (Shankar et al., 2017; Stock & Cisse, 2018; Dulhanty & Wong, 2019; Yang et al., 2020). We focus on an orthogonal issue: the privacy of people in the images. Prabhu & Birhane (2021) also discussed ImageNet’s privacy issues and suggested face obfuscation as one potential solution. Our face annotations enable face obfuscation to be implemented, and our experiments support its effectiveness. Concurrent work (Asano et al., 2021) addresses the privacy issue by collecting a dataset of unlabeled images without people.
+
+Potential negative impacts. The main concern we see is giving the impression of privacy guarantees when in fact face obfuscation is an imperfect technique for privacy protection. We hope that the above detailed discussion and this clarification will help mitigate this issue. Another important concern is disparate impact on people of different demographics as a result of using automated face detection methods; as mentioned above, we hope that incorporating a manual annotation step will help partially alleviate this issue so that similar privacy preservation is afforded to all.
+
+# 3 ANNOTATING FACES IN ILSVRC
+
+We annotate faces in ILSVRC (Russakovsky et al., 2015). The annotations localize an important type of sensitive information in ImageNet, making it possible to obfuscate the sensitive areas for privacy protection.
+
+It is challenging to annotate faces accurately, at ImageNet’s scale while under a reasonable budget. Automatic face detectors are fast and cheap but not accurate enough, whereas crowdsourcing is accurate but more expensive. Inspired by prior work (Kuznetsova et al., 2018; Yu et al., 2015), we devise a two-stage semi-automatic pipeline that brings the best of both worlds. First, we run the face detector by Amazon Rekognition on all images in ILSVRC. The results contain both false positives and false negatives, so we refine them through crowdsourcing on Amazon Mechanical Turk. Workers are given images with detected bounding boxes, and they adjust existing boxes or create new ones to cover all faces. Please see Appendix A for detail.
+
+Annotation quality. To analyze the quality of the face annotations, we select 20 categories on which the face detector is likely to perform poorly. Then we manually check validation images from these categories; the results characterize an upper bound of the overall annotation accuracy.
+
+Concretely, first, we randomly sample 10 categories under the mammal subtree in the ImageNet hierarchy (the left 10 categories in Table 1). Images in these categories contain many false positives (animal faces detected as humans). Second, we take the 10 categories with the greatest number of detected faces (the right 10 categories in Table 1). Images in those categories contain many people and thus are likely to have more false negatives. Each of the selected categories has 50 validation images, and two graduate students manually inspected all face annotations on them, including the face detection results and the final crowdsourcing results.
+
+Table 1: The number of false positives $( F P s )$ and false negatives (FNs) on validation images from 20 categories challenging for the face detector. Each category has 50 images. The $A$ columns are after automatic face detection, whereas the $H$ columns are human results after crowdsourcing.   
+
+<table><tr><td rowspan="2">Category</td><td colspan="2">#FPs</td><td colspan="2">#FNs</td><td rowspan="2">Category</td><td colspan="2">#FPs</td><td colspan="2">#FNs</td></tr><tr><td>A</td><td>H</td><td>A</td><td>H</td><td></td><td>H</td><td>A</td><td>H</td></tr><tr><td>irish setter</td><td>12</td><td>3</td><td>0</td><td>0</td><td>maypole</td><td>0</td><td>0</td><td>7</td><td>5</td></tr><tr><td>gorilla</td><td>32</td><td>7</td><td>0</td><td>0</td><td>basketball</td><td>0</td><td>0</td><td>7</td><td>2</td></tr><tr><td>cheetah</td><td>3</td><td>1</td><td>0</td><td>0</td><td>volleyball</td><td>0</td><td>0</td><td>10</td><td>5</td></tr><tr><td>basset</td><td>10</td><td>0</td><td>0</td><td>0</td><td>balance beam</td><td>0</td><td>0</td><td>9</td><td>5</td></tr><tr><td>lynx</td><td>9</td><td>1</td><td>0</td><td>0</td><td>unicycle</td><td>0</td><td>1</td><td>6</td><td>1</td></tr><tr><td>rottweiler</td><td>11</td><td>4</td><td>0</td><td>0</td><td>stage</td><td>0</td><td>0</td><td>0</td><td>0</td></tr><tr><td>sorrel</td><td>2</td><td>1</td><td>0</td><td>0</td><td>torch</td><td>2</td><td>1</td><td>1</td><td>1</td></tr><tr><td>impala</td><td>1</td><td>0</td><td>0</td><td>0</td><td>baseball player</td><td>0</td><td>0</td><td>0</td><td>0</td></tr><tr><td>bernese mt. dog</td><td>20</td><td>3</td><td>0</td><td>0</td><td>military uniform</td><td>3</td><td>2</td><td>2</td><td>0</td></tr><tr><td>silky terrier</td><td>4</td><td>0</td><td>0</td><td>0</td><td>steel drum</td><td>1</td><td>1</td><td>1</td><td>0</td></tr><tr><td>Average</td><td>10.4</td><td>2.0</td><td>0.0</td><td>0.0</td><td>Average</td><td>0.6</td><td>0.5</td><td>4.3</td><td>1.9</td></tr></table>
+
+Table 2: Some categories grouped into supercategories in WordNet (Miller, 1998). For each supercategory, we show the fraction of images with faces. These supercategories have fractions significantly deviating from the average of the entire ILSVRC $( 1 7 \% )$ .   
+
+<table><tr><td>Supercategory</td><td>#Categories</td><td>#Images</td><td>With faces (%)</td></tr><tr><td>clothing</td><td>49</td><td>62,471</td><td>58.90</td></tr><tr><td>wheeled 1vehicle</td><td>44</td><td>57,055</td><td>35.30</td></tr><tr><td>musical instrument</td><td>26</td><td>33,779</td><td>47.64</td></tr><tr><td>bird</td><td>59</td><td>76,536</td><td>1.69</td></tr><tr><td>insect</td><td>27</td><td>35,097</td><td>1.81</td></tr></table>
+
+![](images/5f3576705223e01b8d4dff9139dc6cea4b724a74a06e69d5a49c28c45f2b8e8b.jpg)  
+Figure 2: Left: The fraction of images with faces for the 1000 ILSVRC categories. 106 categories have more than half images with faces. 216 categories have more than $2 5 \%$ . Right: A histogram of the number of faces per image, excluding the 1,187,895 images with no face.
+
+The errors are shown in Table 1. As expected, the left 10 categories (mammals) have some false positives but no false negatives. In contrast, the right 10 categories have very few false positives but some false negatives. Crowdsourcing significantly reduces both error types. This demonstrate that we can obtain high-quality face annotations using the two-stage pipeline, but face detection alone is less accurate. Among the 20 categories, we have on average 1.25 false positives and 0.95 false negatives per 50 images. However, our overall accuracy on the entire ILSVRC is much higher as these categories are selected deliberately to be error-prone.
+
+Distribution of faces in ILSVRC. Using our two-stage pipeline, we annotated all 1,431,093 images in ILSVRC. Among them, 243,198 images $( 1 7 \% )$ contain at least one face. And the total number of faces adds up to 562,626.
+
+Fig. 2 Left shows the fraction of images with faces for different categories, ranging from $9 7 . 5 \%$ (bridegroom) to $0 . 1 \%$ (rock beauty, a type of saltwater fish). 106 categories have more than half images with faces. 216 categories have more than $2 5 \%$ . Among the 243K images with faces, Fig. 2 Right shows the number of faces per image. $9 0 . 1 \%$ images contain less than 5. But some of them contain as many as 100 (a cap due to Amazon Rekognition). Most of those images capture sports scenes with a crowd of spectators, e.g., images from baseball player or volleyball.
+
+Since ILSVRC categories are in the WordNet (Miller, 1998) hierarchy, we can group them into supercategories in WordNet. Table 2 lists a few common ones that collectively cover 215 categories. For each supercategory, we calculate the fraction of images with faces. Results suggests that supercategories such as clothing and musical instrument frequently co-occur with people, whereas bird and insect seldom do.
+
+# 4 EFFECTS OF FACE OBFUSCATION ON CLASSIFICATION ACCURACY
+
+Having annotated faces in ILSVRC, we now investigate how face obfuscation—a widely used technique for privacy preservation (Fan, 2019; Frome et al., 2009)—impacts image classification.
+
+Face obfuscation method. We experiment with two simple obfuscation methods—blurring and overlaying. For overlaying, we cover faces with the average color in the ILSVRC training data: a gray shade with RGB value $( 0 . 4 8 5 , 0 . 4 5 6 , 0 . 4 0 6 )$ . For blurring, we use a variant of Gaussian blurring. It achieves better visual quality by removing the sharp boundaries between blurred and unblurred regions (Fig. 1). Let $I$ be an image and $M$ be the mask of face bounding boxes. Applying Gaussian blurring to them gives us $I _ { b l u r r e d } $ and $M _ { b l u r r e d } $ . Then we use $M _ { b l u r r e d } $ as the mask to composite $I$ and $I _ { b l u r r e d }$ : $I _ { n e w } = M _ { b l u r r e d } \cdot I _ { b l u r r e d } + ( 1 - M _ { b l u r r e d } ) \cdot I _ { \ l }$ . Due to the use of $M _ { b l u r r e d } $ instead of $M$ , we avoid sharp boundaries in $I _ { n e w }$ . Please see Appendix $\mathbf { B }$ for detail.
+
+Table 3: Validation accuracies on ILSVRC using original images, face-blurred images, and faceoverlaid images. The accuracy drops slightly but consistently when blurred (the $\Delta _ { \mathrm { b } }$ columns) or overlaid (the $\Delta _ { \mathrm { o } }$ columns), though overlaying leads to larger drop than blurring. Each experiment is repeated 3 times; we report the mean accuracy and its standard error (SEM).   
+
+<table><tr><td rowspan="2">Model</td><td colspan="5">Top-1 accuracy (%)</td><td colspan="5">Top-5 accuracy (%)</td></tr><tr><td>Original</td><td>Blurred</td><td>△b</td><td>overlaid</td><td></td><td>△。 Original</td><td>Blurred</td><td>△b</td><td>overlaid</td><td>△</td></tr><tr><td>AlexNet</td><td>56.0± 0.3</td><td>55.8±0.1</td><td>0.2</td><td>55.5± 0.2</td><td>0.6</td><td>78.8 ± 0.1</td><td>78.6 ± 0.1</td><td>0.3</td><td>78.2 ± 0.2</td><td>0.7</td></tr><tr><td>SqueezeNet</td><td>56.0 ± 0.2</td><td>55.3± 0.0</td><td>0.7</td><td>55.0 ± 0.2</td><td>1.0</td><td>78.6± 0.2</td><td>78.1 ± 0.0</td><td>0.5</td><td>77.6 ± 0.1</td><td>1.0</td></tr><tr><td>ShuffleNet</td><td>64.7 ± 0.2</td><td>64.0 ± 0.1</td><td>0.6</td><td>63.7 ± 0.0</td><td>1.0</td><td>85.9 ± 0.0</td><td>85.5 ± 0.1</td><td>0.5</td><td>85.2 ± 0.2</td><td>0.8</td></tr><tr><td>VGG11</td><td>68.9 ± 0.0</td><td>68.2 ± 0.1</td><td>0.7</td><td>67.8± 0.2</td><td>1.1</td><td>88.7 ± 0.0</td><td>88.3 ± 0.1</td><td>0.4</td><td>87.9 ± 0.0</td><td>0.8</td></tr><tr><td>VGG13</td><td>69.9 ± 0.1</td><td>69.3 ± 0.1</td><td>0.7</td><td>68.8 ± 0.0</td><td>1.2</td><td>89.3 ± 0.1</td><td>88.9± 0.0</td><td>0.4</td><td>88.5 ± 0.1</td><td>0.8</td></tr><tr><td>VGG16</td><td>71.7 ± 0.1</td><td>70.8 ± 0.1</td><td>0.8</td><td>70.6 ± 0.1</td><td>1.1</td><td>90.5 ± 0.1</td><td>89.9 ± 0.1</td><td>0.6</td><td>89.6± 0.0</td><td>0.9</td></tr><tr><td>VGG19</td><td>72.4 ± 0.0</td><td>71.5 ± 0.0</td><td>0.8</td><td>71.2 ± 0.2</td><td>1.2</td><td>90.9 ± 0.1</td><td>90.3±0.0</td><td>0.6</td><td>90.1 ± 0.1</td><td>0.8</td></tr><tr><td>MobileNet</td><td>65.4 ± 0.2</td><td>64.4 ± 0.2</td><td>1.0</td><td>64.3± 0.2</td><td>1.0</td><td>86.7 ± 0.1</td><td>86.0 ± 0.1</td><td>0.7</td><td>85.7 ± 0.1</td><td>0.9</td></tr><tr><td>DenseNet121</td><td>75.0 ± 0.1</td><td>74.2 ± 0.1</td><td>0.8</td><td>74.1 ± 0.1</td><td>1.0</td><td>92.4 ± 0.0</td><td>92.0 ± 0.1</td><td>0.4</td><td>91.7 ± 0.0</td><td>0.7</td></tr><tr><td>DenseNet201</td><td>77.0± 0.0</td><td>76.6 ± 0.0</td><td>0.4</td><td>76.1 ± 0.1</td><td>0.9</td><td>93.5 ± 0.0</td><td>93.2 2±0.1</td><td>0.2</td><td>92.9 ± 0.1</td><td>0.6</td></tr><tr><td>ResNet18</td><td>69.8 ± 0.2</td><td>69.0± 0.2</td><td>0.7</td><td>68.9 ± 0.1</td><td>0.8</td><td>89.2 ± 0.0</td><td>88.7± 0.0</td><td>0.5</td><td>88.7±0.1</td><td>0.6</td></tr><tr><td>ResNet34</td><td>73.1 ± 0.1</td><td>72.3 ± 0.4</td><td>0.8</td><td>72.4 ± 0.1</td><td>0.7</td><td>91.3 ± 0.0</td><td>90.8 ± 0.1</td><td>0.5</td><td>90.7 ± 0.0</td><td>0.6</td></tr><tr><td>ResNet50</td><td>75.5± 0.2</td><td>75.0 ± 0.1</td><td>0.4</td><td>74.9 ± 0.0</td><td>0.6</td><td>92.5 ± 0.0</td><td>92.4± 0.1</td><td>0.1</td><td>92.2 ± 0.0</td><td>0.3</td></tr><tr><td>ResNet101</td><td>77.3 ± 0.1</td><td>76.7 ± 0.1</td><td>0.5</td><td>76.7 ± 0.1</td><td>0.6</td><td>93.6 ± 0.1</td><td>93.3 ± 0.1</td><td>0.3</td><td>93.1 ± 0.1</td><td>0.5</td></tr><tr><td>ResNet152</td><td>77.9 ± 0.1</td><td>77.3 ± 0.1</td><td>0.6</td><td>77.0± 0.3</td><td>0.9</td><td>93.9 ± 0.0</td><td>93.7 ± 0.0</td><td>0.4</td><td>93.3 ±0.3</td><td>0.6</td></tr><tr><td>Average</td><td>70.0</td><td>69.4</td><td>0.7</td><td>69.1</td><td>0.9</td><td>89.1</td><td>88.6</td><td>0.4</td><td>88.4</td><td>0.7</td></tr></table>
+
+![](images/eb3ed92e4683523017bafa1c780af12af11982f6f9960b9c7b7987e6d76f33c2.jpg)  
+Figure 3: The average drop in category-wise accuracies vs. the fraction of blurred area in images. Left: Top-1 accuracies. Right: Top-5 accuracies. The accuracies are averaged across all different model architectures and random seeds.
+
+Experiment setup and training details. To study the effects of face obfuscation on classification, we benchmark various deep neural networks including AlexNet (Krizhevsky et al., 2017), VGG (Simonyan & Zisserman, 2015), SqueezeNet (Iandola et al., 2016), ShuffleNet (Zhang et al., 2018), MobileNet (Howard et al., 2017), ResNet (He et al., 2016), and DenseNet (Huang et al., 2017). Each model is studied in three settings: (1) original images for both training and evaluation; (2) face-blurred images for both; (3) face-overlaid images for both.
+
+Different models share a uniform implementation of the training/evaluation pipeline. During training, we randomly sample a $2 2 4 \times 2 2 4$ image crop and apply random horizontal flipping. During evaluation, we always take the central crop and do not flip. All models are trained with a batch size of 256, a momentum of 0.9, and a weight decay of $1 0 ^ { - 4 }$ . We train with SGD for 90 epochs, dropping the learning rate by a factor of 10 every 30 epochs. The initial learning rate is 0.01 for AlexNet, SqueezeNet, and VGG; 0.1 for other models. Each experiment takes 1–7 days on machines with 2 CPUs, 16GB memory, and 1–6 Nvidia GTX GPUs.
+
+Overall accuracy. Table 3 shows the validation accuracies. Each training instance is replicated 3 times with different random seeds, and we report the mean accuracy and its standard error (SEM). The $\Delta$ columns are the accuracy drop when using face-obfuscated images (original minus blurred). For both blurring and overlaying, we see a small but consistent drop in top-1 and top-5 accuracies. For example, with blurring, top-5 accuracies drop $0 . 1 \% - 0 . 7 \%$ with an average of only $0 . 4 \%$ . Overlaying leads to slightly larger drops averaged at $0 . 7 \%$ since it removes more information.
+
+It is expected to incur a small but consistent drop. On the one hand, face obfuscation removes information that might be useful for classifying the image. On the other hand, it should leave intact most ILSVRC categories since they are non-human. Though not surprising, our results are encouraging. They assure us that we can train privacy-aware visual classifiers on ImageNet with less than $1 \%$ accuracy drop.
+
+![](images/cbeb4d2ec9d285fa87d5c1cf877c0ed3826f9341f4b17dee6a3d90e9aed09201.jpg)  
+Figure 4: The average drop in category-wise accuracies caused by blurring vs. the fraction of object area covered by faces. Left: Top-1 accuracies. Right: Top-5 accuracies. The accuracies are averaged across all different model architectures and random seeds.
+
+Category-wise accuracies and the fraction of blur. To gain insights into the effects on individual categories, we break down the accuracy into the 1000 ILSVRC categories. We hypothesize that if a category has a large fraction of obfuscated area, it will likely incur a large accuracy drop.
+
+To support the hypothesis, we focus on blurring and first average the accuracies for each category across different models. Then, we calculate the correlation between the accuracy drop and the fraction of blurred area: $r = 0 . 2 8$ for top-1 accuracy and $r = 0 . 4 4$ for top-5 accuracy. The correlation is not strong but is statistically significant, with p-values of $6 . 3 1 \times 1 0 ^ { - 2 \dot { 0 } }$ and $2 . 6 9 \times \dot { 1 } 0 ^ { - 4 9 }$ respectively.
+
+The positive correlation is also evident in Fig. 3. On the $\mathbf { X }$ -axis, we divide the blurred fraction into 5 groups from small to large. On the y-axis, we show the average accuracy drop for categories in each group. Using top-5 accuracy (Fig. 3 Right), the drop increases monotonically from $0 . 3 0 \%$ to $4 . 0 4 \%$ when moving from a small blurred fraction $( 0 \% - 1 \% )$ to a larger fraction $( \geq 8 \% )$ ).
+
+The pattern becomes less clear in top-1 accuracy (Fig. 3 Left). The drop stays around $0 . 5 \%$ and begins to increase only when the fraction goes beyond $4 \%$ . However, top-1 accuracy is a worse metric than top-5 accuracy (ILSVRC’s official metric), because top-1 accuracy is ill-defined for images with multiple objects. In contrast, top-5 accuracy allows the model to predict 5 categories for each image and succeed as long as one of them matches the ground truth. In addition, top-1 accuracy suffers from confusion between near-identical categorie (like eskimo dog and siberian husky), an artifact we discuss further below.
+
+In summary, our analysis of category-wise accuracies aligns with a simple intuition—if too much area is obfuscated, models will have difficulty classifying the image.
+
+Most impacted categories. Besides the size of the obfuscated area, another factor is whether it overlaps with the object of interest. Most categories in ILSVRC are non-human and should have very little overlap with faces. However, there are exceptions. Mask, for example, is indeed nonhuman. But masks are worn on the face; therefore, obfuscating faces will make masks harder to recognize. Similar categories include sunglasses, harmonica, etc. Due to their close spatial proximity to faces, the accuracy is likely to drop significantly in the presence of face obfuscation.
+
+To quantify this intuition, we calculate the overlap between objects and faces. Object bounding boxes are available from the localization task of ILSVRC. Given an object bounding box, we calculate the fraction of area covered by face bounding boxes. The fractions are then averaged across different images in a category.
+
+Results in Fig. 4 show that blurring leads to larger accuracy drop for categories with larger fractions covered by faces. Some noteable examples include mask $( 2 4 . 8 4 \%$ covered by faces, $8 . 7 1 \%$ drop in top-5 accuracy), harmonica $( 2 9 . 0 9 \%$ covered by faces, $8 . 9 3 \%$ drop in top-5 accuracy), and snorkel $3 0 . 5 1 \%$ covered, $6 . 0 0 \%$ drop). The correlation between the fraction and the drop is $r = 0 . 3 2$ for top-1 accuracy and $r = 0 . 4 6$ for top-5 accuracy.
+
+Fig. 5a showcases images from harmonica and mask and their blurred versions. We use GradCAM (Selvaraju et al., 2017) to visualize where the model is looking at when classifying the image. For original images, the model can effectively localize and classify the object of interest. For blurred images, however, the model fails to classify the object; neither does it attend to the correct region.
+
+In summary, the categories most impacted by face obfuscation are those overlapping with faces, such as mask and harmonica. These categories have much lower accuracies when using obfuscated images, as obfuscation removes visual cues necessary for recognizing them.
+
+![](images/05590c91b17b6453ba28ade9bd0e343b63a4d65d10ad45f9177eed32198147b5.jpg)  
+(a) Images from mask and harmonica with Grad-CAM (Selvaraju et al., 2017) visualizations of where a ResNet152 (He et al., 2016) model looks at. Original images on the left; face-blurred images on the right.
+
+![](images/c79934a258099f963ae5b007d09a0049ea0c97a17e1d5584c68a8a88067a78c4.jpg)  
+(b) Images from eskimo dog and siberian husky are very similar. However, eskimo dog has a large accuracy drop when using face-blurred images, whereas siberian husky has a large accuracy increase.
+
+Disparate changes for visually similar categories. Our last observation focuses on categories whose top-1 accuracies change drastically. Intriguingly, they come in pairs, consisting of one category with decreasing accuracy and another visually similar category with increasing accuracy. For example, eskimo dog and siberian husky are visually similar (Fig. 5b). When using faceblurred images, eskimo dog’s top-1 accuracy drops by $12 . 8 \%$ , whereas siberian husky’s increases by $1 6 . 9 \%$ . It is strange since most images in these two categories do not even contain human faces. More examples are in Table 4.
+
+Eskimo dog and siberian husky images are so similar that the model faces a seemingly arbitrary choice. We examine the predictions and find that models trained on original images prefer eskimo dog, whereas models trained on blurred images prefer siberian husky. It is the different preferences over these two competing categories that drive the top-1 accuracies to change in different directions. To further investigate, we include two metrics that are less sensitive to competing categories: top-5 accuracy and average precision. In Table 4, the pairwise pattern evaporates when these metrics. A pair of categories no longer have drastic changes, and the changes do not necessarily go in different directions. The results show that models trained on blurred images are still good at recognizing eskimo dog, though siberian husky has an even higher score.
+
+# 5 EFFECTS ON FEATURE TRANSFERABILITY
+
+Visual features learned on ImageNet are effective for a wide range of tasks (Girshick, 2015; Liu et al., 2015a). We now investigate the effects of face obfuscation on feature transferability to downstream tasks. Specifically, we compare models without pretraining and models pretrained on original/blurred/overlaid images by finetuning on 4 tasks: object recognition, scene recognition, object detection, and face attribute classification. They include both classification and spatial localization, as well as both face-centric and face-agnostic recognition. Details are in Appendix E.
+
+Object and scene recognition on CIFAR-10 and SUN. CIFAR-10 (Krizhevsky et al., 2009) contains images from 10 object categories such as horse and truck. SUN (Xiao et al., 2010) contains images from 397 scenes such as bedroom and restaurant. Like ImageNet, they are not peoplecentered but may contain people.
+
+We finetune models to classify images in these two datasets and show the results in Table 5. For both datasets, pretraining helps significantly; models pretrained on blurred or overlaid images perform closely with those pretrained on original images. The results show that visual features learned on face-obfsucated images have no problem transferring to face-agnostic downstream tasks.
+
+Object detection on PASCAL VOC. Next, we finetune models for object detection on PASCAL VOC (Everingham et al., 2010). We choose it instead of COCO (Lin et al., 2014) because it is small enough to benefit from pretraining. We finetune a FasterRCNN (Ren et al., 2015) object detector with a ResNet50 backbone pretrained on original/blurred/overlaid images. The results do not show a significant difference between them ( $7 9 . 4 0 \pm 0 . 3 1$ , $7 9 . 2 9 \pm 0 . 2 2$ , and $7 9 . 3 9 \pm 0 . 0 2$ in mAP).
+
+PASCAL VOC includes person as one of its 20 object categories. And one could hypothesize that the model detects people relying on face cues. However, we do not observe a performance drop in face-obfuscated pretraining, even considering the AP of the person category $( 8 4 . 4 0 \pm 0 . 1 \bar { 4 }$ original, $8 4 . 8 0 \pm 0 . { \bar { 5 } } 0$ blurred, and $8 4 . 4 7 \pm 0 . 0 5$ overlaid).
+
+Table 4: Visually similar categories whose top-1 accuracy varies significantly—but in opposite directions. However, the pattern evaporates when using top-5 accuracy or average precision.   
+
+<table><tr><td rowspan="3">Category</td><td colspan="3">Top-1 accuracy (%)</td><td colspan="3">Top-5 accuracy (%)</td><td colspan="3">Average precision (%)</td></tr><tr><td>Original</td><td>Blurred</td><td>A</td><td>Original</td><td>Blurred</td><td>△</td><td>Original</td><td>Blurred</td><td>A</td></tr><tr><td>eskimo dog</td><td>50.8 ± 1.1</td><td>38.0±0.4</td><td>12.8</td><td>95.5±0.4</td><td>95.1 ±0.2</td><td>0.4</td><td>19.4±0.8</td><td>19.9 ± 0.5</td><td>-0.5</td></tr><tr><td>siberian husky</td><td>46.3 ± 1.8</td><td>63.2 ±0.8</td><td>-16.9</td><td>97.0 ±0.4</td><td>97.2 ± 0.3</td><td>-0.2</td><td>29.2 ± 0.3</td><td>29.6± 0.5</td><td>-0.4</td></tr><tr><td>projectile</td><td>35.6 ± 0.9</td><td>21.7 ± 1.0</td><td>13.9</td><td>86.2± 0.4</td><td>85.5±0.4</td><td>0.7</td><td>23.1 ±0.4</td><td>22.5±0.5</td><td>0.6</td></tr><tr><td>missile</td><td>31.6±0.7</td><td>45.8 ± 0.8</td><td>-14.2</td><td>81.5±0.7</td><td>81.8±0.4</td><td>-0.3</td><td>20.4 ± 0.3</td><td>21.1 ± 0.6</td><td>-0.7</td></tr><tr><td>tub</td><td>35.5 ± 1.5</td><td>27.9 ±0.6</td><td>7.6</td><td>79.4 ± 0.6</td><td>75.6±0.5</td><td>3.8</td><td>19.9 ± 0.4</td><td>18.8±0.2</td><td>1.1</td></tr><tr><td>bathtub</td><td>35.4± 1.0</td><td>42.5± 0.4</td><td>- 7.1</td><td>78.9 ± 0.3</td><td>80.8 ± 1.2</td><td>-1.9</td><td>27.4±0.8</td><td>25.1±0.6</td><td>2.3</td></tr><tr><td>american chameleon</td><td>63.0±0.4</td><td>54.7 ± 1.2</td><td>8.3</td><td>97.0±0.5</td><td>96.6±0.5</td><td>0.4</td><td>40.0±0.2</td><td>39.3±0.5</td><td>0.7</td></tr><tr><td>green lizard</td><td>42.0 ± 0.6</td><td>45.6 ± 1.2</td><td>-3.6</td><td>91.3 ± 0.3</td><td>89.7±0.2</td><td>1.6</td><td>22.6±0.8</td><td>22.4 ± 0.1</td><td>0.2</td></tr></table>
+
+Table 5: Top-1 accuracy on CIFAR-10 (Krizhevsky et al., 2009) and SUN (Xiao et al., 2010) of models without pretraining, pretrained on original images, and pretrained on blurred images.   
+
+<table><tr><td rowspan="2">Model</td><td colspan="4">CIFAR-10</td><td colspan="4">SUN</td></tr><tr><td>No pretrain</td><td>Original</td><td>Blurred</td><td>Overlaid</td><td>No pretrain</td><td>Original</td><td>Blurred</td><td>Overlaid</td></tr><tr><td>AlexNet</td><td>83.3±0.2</td><td>90.6±0.0</td><td>90.9±0.0</td><td>91.1 ± 0.0</td><td>26.2±0.6</td><td>46.3±0.1</td><td>46.5± 0.1</td><td>46.2±0.0</td></tr><tr><td>ShuffleNet</td><td>92.3 ±0.3</td><td>95.7 ± 0.0</td><td>95.4 ± 0.1</td><td>95.2 ± 0.1</td><td>33.8±0.7</td><td>51.2 ± 0.1</td><td>50.4± 0.3</td><td>49.3 ± 0.3</td></tr><tr><td>ResNet18</td><td>92.8± 0.1</td><td>96.1 ± 0.1</td><td>96.1 ± 0.1</td><td>96.1 ± 0.1</td><td>36.9 ± 4.8</td><td>55.0±0.2</td><td>55.0± 0.1</td><td>55.1 ± 0.1</td></tr><tr><td>ResNet34</td><td>90.6 ± 0.9</td><td>96.9 ± 0.1</td><td>97.0± 0.0</td><td>97.1 ± 0.2</td><td>40.3 ± 0.4</td><td>57.8±0.0</td><td>57.9 ± 0.1</td><td>57.8±0.1</td></tr></table>
+
+Face attribute classification on CelebA. But what if the downstream task is entirely about understanding faces? Will face-obfuscated pretraining fail? We explore this question by classifying face attributes on CelebA (Liu et al., 2015b). Given a headshot, the model predicts multiple face attributes such as smiling and eyeglasses.
+
+CelebA is too large to benefit from pretraining, so we finetune on a subset of 5K images. Table 6 shows the results in mAP. There is a discrepancy between different models, so we add a few more models. But overall, blurred/overlaid pretraining performs competitively. This is remarkable given that the task relies heavily on faces. A possible reason is that the model only learns low-level faceagnostic features during pretraining and learns face features in finetuning.
+
+In all of the 4 tasks, pretraining on face-obfuscated images does not hurt the transferability of the learned feature. It suggests that one could use face-obfuscated ILSVRC for pretraining without degrading the downstream task, even when the downstream task requires an understanding of faces.
+
+Table 6: mAP of face attribute classification on CelebA (Liu et al., 2015b), using subset of 5K training images.   
+
+<table><tr><td>Model</td><td>No pretrain</td><td>Original</td><td>Blurred</td><td>Overlaid</td></tr><tr><td>AlexNet</td><td>41.8 ± 0.5</td><td>55.5± 0.7</td><td>50.7 ± 0.8</td><td>52.5 ± 0.4</td></tr><tr><td>ShuffleNet</td><td>36.5 ± 0.7</td><td>55.6 ±1.2</td><td>52.5 ± 1.0</td><td>53.5 ± 1.4</td></tr><tr><td>ResNet18</td><td>45.1 ± 1.0</td><td>51.7 ± 1.9</td><td>51.8 ± 1.0</td><td>52.0 ±0.6</td></tr><tr><td>ResNet34</td><td>49.4 ± 2.4</td><td>55.6 ± 2.4</td><td>56.5 ± 1.9</td><td>56.4 ± 2.3</td></tr><tr><td>ResNet50</td><td>48.7 ± 1.3</td><td>42.8 ± 0.9</td><td>50.9 ± 2.7</td><td>50.4 ± 0.5</td></tr><tr><td>VGG11</td><td>48.7± 0.3</td><td>56.0 ± 0.7</td><td>57.4 ± 0.6</td><td>58.1 ± 0.9</td></tr><tr><td>VGG13</td><td>47.2 ± 0.8</td><td>58.4 ± 0.6</td><td>59.0 ± 0.5</td><td>58.2 ± 0.4</td></tr><tr><td>MobileNet</td><td>43.8 ± 0.2</td><td>49.4 ± 0.8</td><td>49.9 ± 1.3</td><td>49.6 ± 1.3</td></tr></table>
+
+# 6 CONCLUSION
+
+We explored how face obfuscation affects recognition accuracy on ILSVRC. We annotated faces in the dataset and benchmarked deep neural networks on images with faces blurred or overlaid. Experimental results demonstrate face obfuscation enhances privacy with minimal impact on accuracy.
+
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+
+# A SEMI-AUTOMATIC FACE ANNOTATION
+
+We describe our face annotation method in detail. It consists of two stages: face detection followed by crowdsourcing.
+
+![](images/131963d7bea43c4aa9558ef74502f5abae3b5cc4234daa853c2ca94337c8e377.jpg)  
+Figure 6: Face detection results on ILSVRC by Amazon Rekognition. The first row shows correct examples. The second row shows false positives, most of which are animal faces. The third row shows false negatives.
+
+Stage 1: Automatic face detection. First, we run the face detection API provided by Amazon Rekognition3 on all images in ILSVRC, which can be done within one day and $\$ 1500$ . We also explored services from other vendors but found Rekognition to work the best, especially for small faces and multiple faces in one image (Fig. 6 Top).
+
+However, face detectors are not perfect. There are false positives and false negatives. Most false positives, as Fig. 6 Middle shows, are animal faces incorrectly detected as humans. Meanwhile, false negatives are rare; some of them occur under poor lighting or heavy occlusion. For privacy preservation, a small number of false positives are acceptable, but false negatives are undesirable. In that respect, Rekognition hits a suitable trade-off for our purpose.
+
+Stage 2: Refining faces through crowdsourcing. After running the face detector, we refine the results through crowdsourcing on Amazon Mechanical Turk (MTurk). In each task, the worker is given an image with bounding boxes detected by the face detector (Fig. 7 Left). They adjust existing bounding boxes or create new ones to cover all faces and not-safe-for-work (NSFW) areas. NSFW areas may not necessarily contain private information, but just like faces, they are good candidates for image obfuscation (Prabhu & Birhane, 2021).
+
+For faces, we specifically require the worker to cover the mouth, nose, eyes, forehead, and cheeks. For NSFW areas, we define them to include nudity, sexuality, profanity, etc. However, we do not dictate what constitutes, e.g., nudity, which is deemed to be subjective and culture-dependent. Instead, we encourage workers to follow their best judgment.
+
+The worker has to go over 50 images in each HIT (Human Intelligence Task) to get rewarded. However, most images do not require the worker’s action since the face detections are already fairly accurate. The 50 images include 3 gold standard images for quality control. These images have verified ground truth faces, but we intentionally show incorrect annotations for the workers to fix. The entire HIT resembles an action game. Starting with 2 lives, the worker will lose a life when making a mistake on gold standard images. In that case, they will see the ground truth faces (Fig. 7
+
+·human faces ·content thatis NSFW (nudity,sexuality,profanity,violence,etc.)
+
+![](images/11a989115bd2603bd155429a6165a90dbba3e5812f5f533ab2ebfe2457efbb4a.jpg)  
+There are existing rectangles on some images.You have to adjust them if they are not accurate enough,delete them if the areas they cover are not sensitive areas,and draw new rectangles if existing ones fail to cover all sensitive areas.   
+·How much area to cover? For a face,the rectangle you draw should cover at least the mouth, nose,eyes,forehead and cheeks.For NSFW area,use your best judgement.
+
+![](images/2243b98a03d549ccb8af20d87262858e07808fea33dafb404b7ba992e1783ffc.jpg)  
+Figure 7: The UI for face annotation on Amazon Mechanical Turk. Left: The worker is given an image with inaccurate face detections. They correct the results by adjusting existing bounding boxes or creating new ones. Each HIT (Human Intelligence Task) have 50 images, including 3 gold standard images for which we know the ground truth answers. Right: The worker loses a life when making a mistake on gold standard images. They will have to start from scratch after losing both 2 lives.
+
+Right) and the remaining lives. If they lose both 2 lives, the game is over, and they have to start from scratch at the first image. We found this strategy to improve annotation quality. We spent about $\$ 2500$ on worker compensation. At this point, it is impossible to estimate the hourly wage accurately, since we have only the submit time of HITs but not the start time.
+
+We did not distinguish NSFW areas from faces during crowdsourcing. Still, we conduct a study demonstrating that the final data contains only a tiny number of NSFW annotations compared to faces. The number of NSFW areas varies significantly across different ILSVRC categories. Bikini is likely to contain much more NSFW areas than the average. We examined all 1,300 training images and 50 validation images in bikini. We found only 25 images annotated with NSFW areas $( 1 . 8 5 \% )$ . The average number for the entire ILSVRC is expected to be much smaller. For example, we found 0 NSFW images among the validation images from the categories in Table 1.
+
+# B FACE BLURRING METHOD
+
+As illustrated in Fig. 8, we blur human faces using a variant of Gaussian blurring to avoid sharp boundaries between blurred and unblurred regions.
+
+Let $\mathbb { D } = [ 0 , 1 ]$ be the range of pixel values; $I \in \mathbb { D } ^ { h \times w \times 3 }$ is an RGB image with height $h$ and width $w$ (Fig. 8 Middle). We have $m$ face bounding boxes annotated on $I$ :
+
+$$
+\{ ( x _ { 0 } ^ { ( i ) } , y _ { 0 } ^ { ( i ) } , x _ { 1 } ^ { ( i ) } , y _ { 1 } ^ { ( i ) } ) \} _ { i = 1 } ^ { m } . ^ { 4 }
+$$
+
+First, we enlarge each bounding box to be
+
+$$
+\left( x _ { 0 } ^ { ( i ) } - { \frac { d _ { i } } { 1 0 } } , y _ { 0 } ^ { ( i ) } - { \frac { d _ { i } } { 1 0 } } , x _ { 1 } ^ { ( i ) } + { \frac { d _ { i } } { 1 0 } } , y _ { 1 } ^ { ( i ) } + { \frac { d _ { i } } { 1 0 } } \right) ,
+$$
+
+where $d _ { i }$ is the length of the diagonal. Out-of-range coordinates are truncated to $0 , h - 1$ , or $w - 1$
+
+Next, we represent the union of the enlarged bounding boxes as a mask $M \in \mathbb { D } ^ { h \times w \times 1 }$ with value 1 inside bounding boxes and value 0 outside them (Fig. 8 Bottom). We apply Gaussian blurring to
+
+![](images/f9c6428e7ce5f55324287e81be7dcceed8817fcaabaa75e08db5bc77d4f0911a.jpg)  
+Figure 8: The method for face blurring. It avoids sharp boundaries between blurred and unblurred regions. $I$ : the original image; $M$ : the mask of enlarged face bounding boxes; $I _ { n e w }$ : the final face-blurred image.
+
+both $M$ and $I$ :
+
+$$
+\begin{array} { r l r } { { \cal M } _ { b l u r r e d } } & { = } & { G a u s s i a n \left( { \cal M } , \frac { d _ { m a x } } { 1 0 } \right) } \\ & { } & \\ { { \cal I } _ { b l u r r e d } } & { = } & { G a u s s i a n \left( { \cal I } , \frac { d _ { m a x } } { 1 0 } \right) , } \end{array}
+$$
+
+where serves $d _ { m a x }$ is the maximum diagonal length across all boundin radius parameter of Gaussian blurring; it depends on es on image so that the la $I$ . Here est bou $\frac { d _ { m a x } } { 1 0 }$ $d _ { m a x }$   
+box can be sufficiently blurred.
+
+Finally, we use $M _ { b l u r r e d } $ as the mask to composite $I$ and $I _ { b l u r r e d } $
+
+$$
+I _ { n e w } = M _ { b l u r r e d } \cdot I _ { b l u r r e d } + ( 1 - M _ { b l u r r e d } ) \cdot I .
+$$
+
+$I _ { n e w }$ is the final face-blurred image. Due to the use of $M _ { b l u r r e d } $ instead of $M$ , we avoid sharp boundaries in $I _ { n e w }$ .
+
+# C ORIGINAL IMAGES FOR TRAINING AND OBFUSCATED IMAGES FOR EVALUATION
+
+We use obfuscated images to evaluate PyTorch models (Paszke et al., $2 0 1 9 ) ^ { 5 }$ trained on original images. We experiment with 5 different methods for face obfuscation: (1) blurring; (2) overlaying with the average color in the ILSVRC training data: a gray shade with RGB value (0.485, 0.456, 0.406); (3–5) overlaying with red/green/blue patches.
+
+Results in top-5 accuracy are in Table 7. Not surprisingly, face obfuscation lowers the accuracy, which is due to not only the loss of information but also the mismatch between data distributions in training and evaluation. Nevertheless, all obfuscation methods lead to only a small accuracy drop $( 0 . 7 \% - 1 . 5 \%$ on average), and blurring leads to the smallest drop. The reason could be that blurring does not conceal all information in a bounding box compared to overlaying.
+
+Table 7: Top-5 accuracies of models trained on original images but evaluated on images obfuscated using different methods. Original: original images for validation; Mean: validation images overlaid with the average color in the ILSVRC training data; Red/Green/Blue: images overlaid with different colors; Blurred: face-blurred images; $\Delta _ { \mathrm { b } }$ : Original minus blurred.   
+
+<table><tr><td>Model</td><td>Original</td><td>Red</td><td>Green</td><td>Blue</td><td>Mean</td><td>Blurred</td><td>△b</td></tr><tr><td>AlexNet (Krizhevsky et al., 2017)</td><td>79.1</td><td>76.7</td><td>77.1</td><td>76.7</td><td>77.8</td><td>78.2</td><td>0.8</td></tr><tr><td>GoogLeNet (Szegedy et al., 2015)</td><td>89.5</td><td>87.9</td><td>88.2</td><td>87.9</td><td>88.3</td><td>88.7</td><td>0.9</td></tr><tr><td>Inception v3 (Szegedy et al.,2016)</td><td>88.7</td><td>86.7</td><td>87.0</td><td>86.6</td><td>87.2</td><td>87.7</td><td>0.9</td></tr><tr><td>SqueezeNet (Iandola et al., 2016)</td><td>80.6</td><td>78.6</td><td>79.0</td><td>78.5</td><td>79.4</td><td>79.7</td><td>0.9</td></tr><tr><td>ShuffleNet (Zhang et al.,2018)</td><td>88.3</td><td>86.6</td><td>86.8</td><td>86.6</td><td>87.0</td><td>87.4</td><td>1.0</td></tr><tr><td>VGG11 (Simonyan &amp; Zisserman, 2015)</td><td>88.6</td><td>87.1</td><td>87.4</td><td>87.0</td><td>87.6</td><td>87.8</td><td>0.8</td></tr><tr><td>VGG13</td><td>89.3</td><td>87.9</td><td>88.1</td><td>87.9</td><td>88.2</td><td>88.5</td><td>0.8</td></tr><tr><td>VGG16</td><td>90.4</td><td>89.1</td><td>89.1</td><td>88.9</td><td>89.3</td><td>89.7</td><td>0.7</td></tr><tr><td>VGG19</td><td>90.9</td><td>89.4</td><td>89.5</td><td>89.2</td><td>89.7</td><td>90.1</td><td>0.8</td></tr><tr><td>MobileNet (Howard et al.,2017)</td><td>90.3</td><td>88.9</td><td>89.1</td><td>88.9</td><td>89.2</td><td>89.5</td><td>0.8</td></tr><tr><td>MNASNet (Tan et al., 2019)</td><td>91.5</td><td>90.0</td><td>90.2</td><td>90.2</td><td>90.4</td><td>90.8</td><td>0.7</td></tr><tr><td>DenseNet121 (Huang et al., 2017)</td><td>92.0</td><td>90.7</td><td>90.8</td><td>90.7</td><td>91.0</td><td>91.3</td><td>0.7</td></tr><tr><td>DenseNet161</td><td>93.6</td><td>92.5</td><td>92.5</td><td>92.3</td><td>92.8</td><td>93.0</td><td>0.6</td></tr><tr><td>DenseNet169</td><td>92.8</td><td>91.6</td><td>91.7</td><td>91.6</td><td>91.9</td><td>92.2</td><td>0.6</td></tr><tr><td>DenseNet201</td><td>93.4</td><td>92.2</td><td>92.3</td><td>92.0</td><td>92.3</td><td>92.7</td><td>0.7</td></tr><tr><td>ResNet18 (He et al., 2016)</td><td>89.1</td><td>87.5</td><td>87.6</td><td>87.5</td><td>87.8</td><td>88.3</td><td>0.8</td></tr><tr><td>ResNet34</td><td>91.4</td><td>89.8</td><td>90.0</td><td>89.8</td><td>90.2</td><td>90.7</td><td>0.8</td></tr><tr><td>ResNet50</td><td>92.9</td><td>91.7</td><td>91.8</td><td>91.5</td><td>91.8</td><td>92.2</td><td>0.7</td></tr><tr><td>ResNet101</td><td>93.6</td><td>92.3</td><td>92.4</td><td>92.3</td><td>92.5</td><td>92.9</td><td>0.7</td></tr><tr><td>ResNet152</td><td>94.1</td><td>92.9</td><td>93.0</td><td>92.9</td><td>93.1</td><td>93.4</td><td>0.6</td></tr><tr><td>ResNeXt50 (Xie et al., 2017)</td><td>93.7</td><td>92.5</td><td>92.6</td><td>92.4</td><td>92.8</td><td>93.0</td><td>0.7</td></tr><tr><td>ResNeXt101</td><td>94.5</td><td>93.5</td><td>93.5</td><td>93.3</td><td>93.5</td><td>93.9</td><td>0.6</td></tr><tr><td>Wide ResNet50 (Zagoruyko &amp; Komodakis,2016)</td><td>94.1</td><td>92.9</td><td>93.0</td><td>92.9</td><td>93.1</td><td>93.4</td><td>0.7</td></tr><tr><td>WideResNet101</td><td>94.3</td><td>93.2</td><td>93.3</td><td>93.1</td><td>93.4</td><td>93.7</td><td>0.6</td></tr><tr><td>Average</td><td>90.7</td><td>89.3</td><td>89.4</td><td>89.2</td><td>89.6</td><td>89.9</td><td>0.7</td></tr></table>
+
+# D OBFUSCATED IMAGES FOR TRAINING AND ORIGINAL IMAGES FOR EVALUATION
+
+Vice versa, we also experiment with training on blurred images while evaluating on original images. This setting is practically relevant because models used in real-world products may be trained on privacy-preserved data but deployed in the wild without any obfuscation. Results are shown in Table 8. Similarly, training on blurred images lowers the accuracy by only a small amount $( 0 . 2 5 \% -$ $1 . 0 4 \%$ in top-5 accuracy, with an average of $0 . 6 7 \%$ ).
+
+# E DETAILS OF TRANSFER LEARNING EXPERIMENTS
+
+Image classification on CIFAR-10, SUN, and CelebA. Object recognition on CIFAR10 (Krizhevsky et al., 2009), scene recognition on SUN (Xiao et al., 2010), and face attribute classification on CelebA (Liu et al., 2015b) are all image classification tasks. For any model, we simply replace the output layer and finetune for 90 epochs. Hyperparameters are almost identical to those in Sec. 4, except that the learning rate is tuned individually for each model on validation data. Note that face attribute classification on CelebA is a multi-label classification task, so we apply binary cross-entropy loss to each label independently.
+
+Object detection on PASCAL VOC. We adopt a FasterRCNN (Ren et al., 2015) object detector with a ResNet50 backbone pretrained on original or face-obfuscated ILSVRC. The detector is finetuned for 10 epochs on the trainval set of PASCAL VOC 2007 and 2012 (Everingham et al., 2010). It is then evaluated on the test set of 2007.
+
+The system is implemented in MMDetection (Chen et al., 2019a). We finetune using SGD with a momentum of 0.9, a weight decay of $1 0 ^ { - 4 }$ , a batch size of 2, and a learning rate of $\mathrm { { \bar { 1 } } . 2 5 \times 1 0 ^ { - 3 } }$ . The learning rate decreases by a factor of 10 in the last epoch.
+
+Table 8: Validation accuracies on original ILSVRC images of models trained on original/blurred images. Training on blurred images lead to a small but consistent accuracy drop.   
+
+<table><tr><td rowspan="2">Model</td><td colspan="3">Top-1 accuracy (%)</td><td colspan="3">Top-5 accuracy (%)</td></tr><tr><td>Original training</td><td>Blurred training</td><td>△</td><td>Original training</td><td>Blurred training</td><td>△</td></tr><tr><td>AlexNet</td><td>56.0 ± 0.3</td><td>55.3 ± 0.0</td><td>0.7</td><td>78.8 ± 0.1</td><td>78.0 ± 0.1</td><td>0.9</td></tr><tr><td>SqueezeNet</td><td>56.0 ± 0.2</td><td>54.9 ± 0.1</td><td>1.1</td><td>78.6 ± 0.2</td><td>77.6 ± 0.1</td><td>1.0</td></tr><tr><td>ShuffleNet</td><td>64.7 ± 0.2</td><td>63.7 ± 0.0</td><td>1.0</td><td>85.9 ± 0.0</td><td>85.1 ± 0.0</td><td>0.9</td></tr><tr><td>VGG11</td><td>68.9 ± 0.0</td><td>67.9 ± 0.2</td><td>1.0</td><td>88.7 ± 0.0</td><td>87.9 ± 0.1</td><td>0.8</td></tr><tr><td>VGG13</td><td>69.9 ± 0.1</td><td>69.0 ± 0.2</td><td>1.0</td><td>89.3 ± 0.1</td><td>88.6 ± 0.1</td><td>0.7</td></tr><tr><td>VGG16</td><td>71.7 ± 0.1</td><td>70.6 ± 0.1</td><td>1.1</td><td>90.5 ± 0.1</td><td>89.8 ± 0.1</td><td>0.7</td></tr><tr><td>VGG19</td><td>72.4 ± 0.0</td><td>71.2 ± 0.1</td><td>1.2</td><td>90.9 ± 0.1</td><td>90.1 ± 0.0</td><td>0.8</td></tr><tr><td>MobileNet</td><td>65.4 ± 0.2</td><td>64.0 ± 0.2</td><td>1.4</td><td>86.7 ± 0.1</td><td>85.6 ± 0.1</td><td>1.0</td></tr><tr><td>DenseNet121</td><td>75.0 ± 0.1</td><td>74.1 ± 0.0</td><td>0.9</td><td>92.4 ± 0.0</td><td>91.8 ± 0.0</td><td>0.6</td></tr><tr><td>DenseNet201</td><td>77.0 ± 0.0</td><td>76.5 ± 0.1</td><td>0.5</td><td>93.5 ± 0.0</td><td>93.2 ± 0.0</td><td>0.3</td></tr><tr><td>ResNet18</td><td>69.8 ± 0.2</td><td>68.6 ± 0.2</td><td>1.1</td><td>89.2 ± 0.0</td><td>88.5 ± 0.1</td><td>0.7</td></tr><tr><td>ResNet34</td><td>73.1 ± 0.1</td><td>72.0 ± 0.4</td><td>1.1</td><td>91.3 ± 0.0</td><td>90.6 ± 0.2</td><td>0.7</td></tr><tr><td>ResNet50</td><td>75.5 ± 0.2</td><td>74.9 ± 0.1</td><td>0.6</td><td>92.5 ± 0.0</td><td>92.2 ± 0.1</td><td>0.3</td></tr><tr><td>ResNet101</td><td>77.3 ± 0.1</td><td>76.6 ± 0.0</td><td>0.7</td><td>93.6 ± 0.1</td><td>93.2 ± 0.0</td><td>0.4</td></tr><tr><td>ResNet152</td><td>77.9 ± 0.1</td><td>77.2 ± 0.2</td><td>0.7</td><td>93.9 ± 0.0</td><td>93.6 ± 0.0</td><td>0.4</td></tr><tr><td>Average</td><td>70.0</td><td>69.1</td><td>0.9</td><td>89.1</td><td>88.4</td><td>0.7</td></tr></table>

parse/dev/PDYs7Z2XFGv/PDYs7Z2XFGv.md

@@ -0,0 +1,358 @@
+# OMNI-SCALE CNNS: A SIMPLE AND EFFECTIVE KERNEL SIZE CONFIGURATION FOR TIME SERIES CLASSIFICATION
+
+Wensi Tang1, Guodong Long1, Lu Liu1,2,Tianyi Zhou3,4, Michael Blumenstein1, Jing Jiang1 1Australian Artificial Intelligence Institute, University of Technology Sydney,2 Google 3University of Washington, Seattle, 4University of Maryland, College Park {wensi.tang, lu.liu-10}@student.uts.edu.au, {guodong.long, michael.blumenstein, jing.jiang} $@$ uts.edu.au, tianyizh@uw.edu
+
+# ABSTRACT
+
+The Receptive Field (RF) size has been one of the most important factors for One Dimensional Convolutional Neural Networks (1D-CNNs) on time series classification tasks. Large efforts have been taken to choose the appropriate size because it has a huge influence on the performance and differs significantly for each dataset. In this paper, we propose an Omni-Scale block (OS-block) for 1D-CNNs, where the kernel sizes are decided by a simple and universal rule. Particularly, it is a set of kernel sizes that can efficiently cover the best RF size across different datasets via consisting of multiple prime numbers according to the length of the time series. The experiment result shows that models with the OS-block can achieve a similar performance as models with the searched optimal RF size and due to the strong optimal RF size capture ability, simple 1D-CNN models with OS-block achieves the state-of-the-art performance on four time series benchmarks, including both univariate and multivariate data from multiple domains. Comprehensive analysis and discussions shed light on why the OS-block can capture optimal RF sizes across different datasets. Code available here 1
+
+# 1 INTRODUCTION
+
+One of the most challenging problems for Time Series Classification (TSC) tasks is how to tell models in what time scales 2 to extract features. Time series (TS) data is a series of data points ordered by time or other meaningful sequences such as frequency. Due to the variety of information sources (e.g., medical sensors, economic indicators, and logs) and record settings (e.g., sampling rate, record length, and bandwidth), TS data is naturally composed of various types of signals on various time scales (Hills et al., 2014; Schafer, 2015; Dau et al., 2018). Thus, in what time scales ¨ can a model “see” from the TS input data has been a key for the performance of TS classification.
+
+Traditional machine learning methods have taken huge efforts to capture important time scales, and the computational resource consumption increase exponentially with the length of TS increase. For example, for shapelet methods (Hills et al., 2014; Lines et al., 2012), whose discriminatory feature is obtained via finding sub-sequences from TS that can be representative of class membership, the time scale capture work is finding the proper sub-sequences length. To obtain the proper length, even for a dataset with length 512, (Hills et al., 2014) has to try 71 different sub-sequence lengths. For other methods, such as (Berndt & Clifford, 1994; Schafer, 2015; Lucas et al., 2019), despite ¨ the time scale capture might be called by different names such as finding warping size or window length. They all need searching works to identify those important time scales. More recent deep learning based methods also showed that they had to pay a lot of attention to this time scale problem. MCNN (Cui et al., 2016) searches the kernel size to find the best RF of a 1D-CNN for every dataset. Tapnet (Zhang et al., 2020) additionally considers the dilation steps. Chen & Shi (2021) also take the number of layers into considerations. These are all important factors for the RF of CNNs and the performance for TSC.
+
+![](images/0de81077afc0a14742088d5b94bd12b016a9cd78eeb745fcf515465d47d20a88.jpg)  
+Figure 1: Left: A model’s accuracy on the UCR 85 datasets changes by tuning the model’s receptive field sizes from 10 to 200. Right: The average rank results of each receptive field size are pretty similar, which means that no single receptive field size can significantly outperform others on most datasets.
+
+Although a number of researchers have searched for the best RF of 1D-CNNs for TSC, there is still no agreed answer to 1) what size of the RF is the best? And 2) how many different RFs should be used? Models need to be equipped with different sizes and different numbers of RFs for a specific dataset. Using the same setup for every dataset can lead to a significant performance drop for some datasets. For example, as shown by the statistics on the University of California Riverside (UCR) 85 “bake off” datasets in Figure 1a, the accuracy of most datasets can have a variance of more than $5 \%$ just by changing the RF sizes of their model while keeping the rest of the configurations the same. As also shown in Figure 1b, no RF can consistently perform the best over different datasets.
+
+To avoid those complicated and resource-consuming searching work, we propose Omni-Scale block (OS-block), where the kernel choices for 1D-CNNs are automatically set through a simple and universal rule that can cover the RF of all scales. The rule is inspired by Goldbach’s conjecture, where any positive even number can be written as the sum of two prime numbers. Therefore, the OS-block uses a set of prime numbers as the kernel sizes except for the last layer whose kernel sizes are 1 and 2. In this way, a 1D-CNN with these kernel sizes can cover the RF of all scales by transforming TS through different combinations of these prime size kernels. What’s more, the OS-block is easy to implement to various TS datasets via selecting the maximum prime number according to the length of the TS.
+
+In experiments, we show consistent state-of-the-art performance on four TSC benchmarks. These benchmarks contain datasets from different domains, i.e., healthcare, human activity recognition, speech recognition, and spectrum analysis. Despite the dynamic patterns of these datasets, 1DCNNs with our OS-block robustly outperform previous baselines with the unified training hyperparameters for all datasets such as learning rate, batch size, and iteration numbers. We also did a comprehensive study to show our OS-block, the no time scale search solution, always matches the performance with the best RF size for different datasets.
+
+# 2 MOTIVATIONS
+
+Two phenomena of 1D-CNNs inspire the design of the OS-block. In this section, we will introduce the two phenomena with examples in Figure 2 and more discussions can be found in Section 4.6.
+
+Firstly, we found that, although the RF size is important, the 1D-CNNs are not sensitive to the specific kernel size configurations that we take to compose that RF size. An example is given in the right image of the Figure 2
+
+Secondly, the performance of 1D-CNNs is mainly determined by the best RF size it has. To be specific, supposing we have multiple single-RF-size-models which are of similar model size and layer numbers, but each of them has a unique RF size. Let’s denote the set of those RF sizes as $\mathbb { S }$ . When testing those models on a dataset, we will have a set of accuracy results A. Then, supposing we have a multi-kernel model which has multiple RF sizes3 and set of those sizes is also $\mathbb { S }$ . Then, the accuracy of the multiple-RF-sizes-model will be similar to the highest value of A. An example is given in the left image of Figure 2. Specifically, when testing single-RF-size-models on the Google Speechcommands dataset, the model’s performance is positive correlation with the model’s RF size. For example, the light blue line whose set of RF size is $\{ 9 9 \}$ outperforms the light green line $\{ 3 9 \}$ and light red line $\{ \bar { 9 } \}$ . For those multiple-RF-sizes-models which has more than one element in their set of RF sizes, their performance are determined by the best (also the largest because of the positive correlation) RF size it has. Having more worse (smaller) RF sizes will not have much influence on the performance.
+
+![](images/c103d33d684df89b171fd8db12402882c9f99814b52b9590c7e24f74602d1ea5.jpg)  
+Figure 2: Left: The label of each line denotes receptive field size and the kernel configuration of each 1D-CNN. For example, (9):5 5 1 1 1 means the 1D-CNN has five layers and the receptive field size is 9, and from the first layer to the last layer, kernel sizes of each layer are 5, 5, 1, 1, and 1. Lines of similar color are 1D-CNNs with the same receptive field size, and they are also of similar performance. Right: Lines with similar colors are models which have the same best receptive field size. For example, all (red/green/blue) lines have the receptive field size (9/39/99), and their performances are similar to the bright (red/green/blue) line which denotes the model only has the receptive field size (9/39/99).
+
+The second phenomenon means that, instead of searching for the best time scales, if the model covers all RF sizes, its performance will be similar to that of a model with the best RF size. However, there are many designs that can cover all RF sizes. Which one should be preferred? Based on the first phenomenon, from the performance perspective, we could choose any design that we want. However, as we will show in Section 3.3, those candidate designs are not of the same characteristics such as the model size or the expandability for long TS data. Therefore, the design of the OS-block that we propose aims at covering all RF sizes in an efficient manner.
+
+# 3 METHOD
+
+The section is organized as follows: Firstly, we give the problem definition in Section 3.1. Then, we will explain how to construct the Omni-scale block (OS-block) which covers all receptive field sizes in Section 3.2. Section 3.3 will explain the reason why OS-block can cover RF of all sizes in an efficient manner. In Section 3.4, we will introduce how to apply the OS-block on TSC tasks.
+
+# 3.1 PROBLEM DEFINITION
+
+TS data is denoted as $\textbf { \textit { X } } = ~ [ \pmb { x } _ { 1 } , \pmb { x } _ { 2 } , . . . , \pmb { x } _ { m } ]$ , where $m$ is the number of variates. For univariate TS data, $\textit { m } = \textit { 1 }$ and for $m \ > \ 1$ , the TS are multivariate. Each variate is a vector of length $l$ . A TS dataset, which has $n$ data and label pairs, can be denoted as: $\mathbb { D } =$ $\{ ( \boldsymbol { X } ^ { 1 } , \boldsymbol { y } ^ { 1 } ) , \overbar { ( \boldsymbol { X } ^ { 2 } , \boldsymbol { y } ^ { 2 } ) } , . . . , ( \boldsymbol { X } ^ { n } , \boldsymbol { y } ^ { n } ) \}$ , where $( X ^ { * } , y ^ { * } )$ denotes the TS data $x ^ { * }$ belongs to the class $y ^ { * }$ . The task of TSC is to predict the class label $y ^ { * }$ when given a TS $x ^ { * }$ .
+
+# 3.2 ARCHITECTURE OF OS-BLOCK
+
+The architecture of the OS-block is shown in Figure 3. It is a three-layer multi-kernel structure, and each kernel does the same padding convolution with input. For the kernel size configuration, we use $\mathbb { P } ^ { ( i ) }$ to denote the kernel size set of the $i$ -th layer:
+
+$$
+\mathbb { P } ^ { ( i ) } = \left\{ \begin{array} { l l } { \{ 1 , 2 , 3 , 5 , . . . , p _ { k } \} ~ } & { , i \in \{ 1 , 2 \} } \\ { \{ 1 , 2 \} ~ } & { , i = 3 } \end{array} \right.
+$$
+
+![](images/9233984bbc86d0cc295e7b0d82cf4d5c4614b52e390f439f9702504bfb0f06ab.jpg)  
+Figure 3: The left image shows that every even number from 2 to 38 can be composed via two prime numbers from 1 to 19. This phenomenon can be extended to all even numbers. Based on this phenomenon, with the OS-block structure in the middle image, we could cover all receptive field sizes. Specifically, the first two layers have prime-sized kernels from 1 to $p _ { k }$ . Thus, the two layers can cover all even number receptive field sizes. With kernels of sizes 1 and 2 in the third layer, we could cover all integer receptive field sizes in a range via selecting the value $p _ { k }$ . The OS-block is easy to be applied on time series classification tasks. A simple classifier with the OS-block, namely OS-CNN, is given in the right image, which achieves a series of SOTA performances.
+
+Where $\{ 1 , 2 , 3 , 5 , 7 , . . . , p _ { k } \}$ is a set of prime numbers from 1 to $p _ { k }$ . The value of $p _ { k }$ is the smallest prime number that can cover all sizes of RF in a range. Here, the range that we mentioned is all meaningful scales. For example, since the TS length is $l$ , we don’t need to cover RFs that are larger than $l$ or smaller than 1. Therefore, the $p _ { k }$ is the smallest prime number that can cover the RF size from 1 to $l$ . If we have prior knowledge, such as that we know there are cycles in the TS, or we know the length range of the hidden representative pattern. We could change the RF size range of the OS-block by simply changing the prime number list. An example is given in the left image in Figure 3, which uses the prime number list in the blue block to cover the RF size range from 10 to 26.
+
+RF sizes of the OS-block: The RF is defined as the size of the region in the input that produces the feature. Because each layer of the OS-block has more than one convolution kernel, there will be several different paths from the input signal to the final output feature (Araujo et al., 2019; Luo et al., 2016), and each path will have a RF size. For the 3-layer OS-block, which has no pooling layer and the stride size is 1, the set of RF sizes $\mathbb { S }$ is the set of RF size of all paths, and it can be described as:
+
+$$
+\mathbb { S } = \{ p ^ { ( 1 ) } + p ^ { ( 2 ) } + p ^ { ( 3 ) } - 2 \ | \ p ^ { ( i ) } \in \mathbb { P } ^ { ( i ) } , i \in \{ 1 , 2 , 3 \} \} .
+$$
+
+For the reasons that $\mathbb { P } ^ { ( i ) }$ are prime number list when $i \in \{ 1 , 2 \}$ , the set $\{ p ^ { ( 1 ) } + p ^ { ( 2 ) } | p ^ { ( i ) } \in \mathbb { P } ^ { ( i ) } , i \in$ $\{ 1 , 2 \} \}$ is the set of all even numbers $\mathbb { E }$ .4 Thus, we have
+
+$$
+\mathbb { S } = \{ e + p ^ { ( 3 ) } - 2 \mid p ^ { ( 3 ) } \in \mathbb { P } ^ { ( 3 ) } , e \in \mathbb { E } \} .
+$$
+
+With Equation 3 and Equation 1, we have
+
+$$
+\mathbb { S } = \{ e | e \in \mathbb { E } \} \cup \{ e - 1 | e \in \mathbb { E } \} \equiv \mathbb { N } ^ { + } .
+$$
+
+Where $\mathbb { N } ^ { + }$ is the set of all integer numbers in the range. Specifically, the $\mathbb { S } \equiv \mathbb { N } ^ { + }$ is because a real number must be an odd number or an even number, while $\mathbb { E }$ is the even number set, $\{ e - 1 | e \in \mathbb { E } \}$ is
+
+![](images/5c37dd4e643525b376a8b285e8a193ac043160aba88198a014638ff0eeadc244.jpg)  
+Figure 4: Examples of using OS-block with other deep learning structures.
+
+the odd number set. Therefore, with the proper selection of $p _ { k }$ , we could cover any integer RF size in a range. It should be noticed that, there might be many options to cover all RF sizes, we use the Godlach’s conjecture to make sure that we could all scales.
+
+# 3.3 OS-BLOCK COVER ALL SCALES IN AN EFFICIENT MANNER
+
+From the model size perspective, using prime numbers is more efficient than using even numbers or odd numbers. To be specific, to cover receptive fields up to size r, the model size complexity of using prime size kernels is $O ( r ^ { 2 } / l o g ( r ) )$ . On the other hand, no matter we use even number pairs or odd number pairs, the model size complexity is $O ( r ^ { 2 } )$ . We also empirically show the advantage of our model on efficiency in the following table and this table has been added to Appendix A.7:
+
+# 3.4 HOW TO APPLY OS-BLOCK ON TSC TASKS
+
+Firstly, the OS-block could take both univariate and multivariate TS data by adjusting the input channel the same as the variate number of input TS data. A simple example classifier with OSblock, namely OS-CNN, is given in Figure 3. The OS-CNN is composed of an OS-block with one global average pooling layer as the dimensional reduction module and one fully connected layer as the classification module. Other than OS-CNN, the OS-block is flexible and easy to extend. Specifically, convolution layers of OS-block can be calculated parallelly. Thus, each layer can be viewed as one convolutional layer with zero masks. Therefore, both the multi-kernel layers or the OS-block itself are easy to extend with more complicated structures (such as dilation (Oord et al., 2016), attention or transformer (Shen et al., 2018a), and bottleneck) that are normally used in 1DCNN for performance gain. In Figure 4, we give three examples which uses OS-block with other structures.
+
+# 4 EXPERIMENT
+
+# 4.1 BENCHMARKS
+
+We evaluate OS-block on 4 TSC benchmarks which include, in total, 159 datasets. The details of each benchmark is as follows:
+
+• Magnetoencephalography recording for Temporal Lobe Epilepsy diagnosis (MEGTLE) dataset (Gu et al., 2020): The Magnetoencephalography dataset was recorded from epilepsy patients and was introduced to classify two subtypes (simple and complex) of temporal Lobe Epilepsy. The dataset contains 2877 recordings which were obtained at the sampling frequency $1 2 0 0 \mathrm { H z }$ . Each recording is approximately 2 sec. Therefore the length is about 2400. University of East Anglia (UEA) 30 archive (Bagnall et al., 2018): This formulation of the archive was a collaborative effort between researchers at the University of East Anglia and the University of California, Riverside. It is an archive of 30 multivariate TS datasets from various domains such as motion detection, physiological data, audio spectra classification. Besides domains, those datasets also have various characteristics. For instance, among those datasets, the class number various from 2 to 39, the length of each dataset various from 8 to 17,894, and the number of variates various from 2 to 963.
+
+Multivariate dataset archive benchmark   
+
+<table><tr><td colspan="5">Individual dataset benchmark</td></tr><tr><td>Dataset</td><td>Method</td><td>Accuracy(%)</td><td>F1-score</td><td># parameters</td></tr><tr><td rowspan="6">MEG-TLE (Gu et al.,2020)</td><td>CNN(Gu et al.,2020)</td><td>83.2</td><td>82.3</td><td>3.8M</td></tr><tr><td>PF(Gu et al.,2020)</td><td>82.6</td><td>68.2</td><td>1</td></tr><tr><td>SVM (Gu et al.,2020)</td><td>55.2</td><td>85.2</td><td>-</td></tr><tr><td>MSAM (Gu et al.,2020)</td><td>83.6</td><td>83.4</td><td>2.3M</td></tr><tr><td>Rocket (Dempster et al., 2020)</td><td>87.7</td><td>89.9</td><td></td></tr><tr><td>OS-CNN (Ours)</td><td>91.3</td><td>91.6</td><td>235k</td></tr></table>
+
+Univariate dataset archives benchmarks   
+
+<table><tr><td>Archive</td><td>Method</td><td>Baseline wins</td><td>OS-CNN(Ours) wins</td><td>Tie</td><td>Average Rank</td></tr><tr><td rowspan="7">UEA 30 archive (Bagnall et al., 2018)</td><td>DTW-1NND(norm) (Zhang et al.,2020)</td><td>7</td><td>23</td><td>0</td><td>5.68</td></tr><tr><td>DTW-1NN-I(norm) (Zhang et al.,2020)</td><td>5</td><td></td><td>1</td><td>6.70</td></tr><tr><td>ED-1NN(norm) (Zhang et al.,2020)</td><td>5</td><td></td><td>0</td><td>7.45</td></tr><tr><td>DTW-1NND (Zhang et al.,2020)</td><td>7</td><td></td><td>0</td><td>5.28</td></tr><tr><td>DTW-1NN-I (Zhang et al.,2020) ED-1NN (Zhang et al., 2020)</td><td>7 5</td><td>2425232251</td><td>1</td><td>6.07</td></tr><tr><td>WEASEL+MUSE(Schäfer&amp; Leser,2017)</td><td>10</td><td></td><td>0</td><td>7.12</td></tr><tr><td>MLSTM-FCN(Karim et al.,2019)</td><td>7</td><td>23</td><td>1</td><td>4.15</td></tr><tr><td></td><td>9</td><td>20</td><td>0</td><td>5.62</td></tr><tr><td></td><td>TapNet (Zhang et al.,2020) OS-CNN (Ours)</td><td>-</td><td>=</td><td>1 =</td><td>3.80 3.13</td></tr></table>
+
+Table 1: Performance comparison on 4 time series classification benchmarks   
+
+<table><tr><td>Archive</td><td>Method</td><td>Baselinewins</td><td>OS-CNN(Ours) wins</td><td>Tie</td><td>Average rank</td></tr><tr><td rowspan="6">UCR 85 archive (Chen et al.,2015)</td><td>PF (Lucas et al.,2019)</td><td>13</td><td>67</td><td>5</td><td>6.57</td></tr><tr><td>ResNet (Wang et al.,2017)</td><td>19</td><td>61</td><td>5</td><td>5.41</td></tr><tr><td>STC (Hameurlain et al., 2017)</td><td>27</td><td>56</td><td>2</td><td>5.05</td></tr><tr><td>InceptionTime (Ismail Fawaz et al.,2019)</td><td>34</td><td>42</td><td>9</td><td>4.05</td></tr><tr><td>ROCKET (Dempster et al.,2020)</td><td>33</td><td>44</td><td>8</td><td>3.64</td></tr><tr><td>HIVE-COTE(Lines et al., 2016) TS-CHIEF(Shifaz et al.,2020)</td><td>34 42</td><td>43</td><td>8 4</td><td>3.99</td></tr><tr><td>OS-CNN (Ours)</td><td>1</td><td>39 -</td><td></td><td>3.68 3.59</td></tr><tr><td rowspan="4">UCR128 archive (Dau et al., 2018)</td><td>ResNet (Wang et al.,2017)</td><td>19</td><td>83</td><td>- 26</td><td></td></tr><tr><td>InceptionTime (Ismail Fawaz et al.,2019)</td><td>30</td><td>59</td><td>39</td><td>3.21</td></tr><tr><td>ROCKET (Dempster et al.,2020)</td><td>43</td><td>62</td><td>23</td><td>2.41</td></tr><tr><td>OS-CNN (Ours)</td><td>-</td><td>-</td><td>-</td><td>2.36 2.02</td></tr></table>
+
+• University of California, Riverside (UCR) 85 archive (Chen et al., 2015): This is an archive of 85 univariate TS datasets from various domains such as speech reorganizations, health monitoring, and spectrum analysis. What’s more, those datasets also have different characteristics. For instance, among those datasets, the class number varies from 2 to 60, the length of each dataset varies from 24 to 2709. The number of training data varies from 16 to 8,926.
+
+• University of California, Riverside (UCR) 128 archive (Dau et al., 2018): This is an archive of 128 univariate TS datasets. It is the updated version of the UCR 85 archive. However, the new archive cannot be viewed as a replacement for the former because they have different characteristics. For example, for the UCR 85 archive, all TS data within a single dataset are of the same length, but that is not the same for the UCR 128 archive. Besides that, in general, the added data in the UCR 128 archive, their default test set is bigger than the train set to reflect real-world scenarios.
+
+# 4.2 EVALUATION CRITERIA
+
+For all benchmarks, we follow the standard settings from previous literature. Specifically, for the MEG-TLE dataset, following Multi-Head Self-Attention Model (MSAM) (Gu et al., 2020), models are evaluated by test accuracy and f1 score. Besides using recommended metrics of each benchmark, we also compare the model size of OS-block with other deep learning methods. For UEA 30, UCR 85 archives, and UCR 128 archives, following the evaluation advice from the archive (Dau et al., 2018; Bagnall et al., 2018), count of wins, and critical difference diagrams (cd-diagram) (Dau et al., 2018) were selected as the evaluation method. Due to the page limitation, we list the average rank
+
+![](images/1690ddc86abcdb74ef91fcafda3f877cb182a9803b493d66dcbc21aebb97508a.jpg)  
+Figure 5: Classification accuracies for OS-CNN vs. accuracies from 20 1D-CNNs with receptiveCount of datasets by the RF tuning's percentile range that OS result belongs to 50 field size. As we can see, for most of the dataset, the orange points (accuracy of OS-CNN) are near 40 the top of blue points. More analysis for this comparison can be found in Appendix A.1
+
+0  3 (3.53%) 2 (2.35%) 5 (5.88%) 2 (2.35%) 3 (3.53%)  3 (3.53%) 1 (1.18%)  5 (5.88%) 4 (4.71%) in the result table because it is the main criteria of the cd-diagram. The full cd-diagram results are < 0.5 0.55 listed in Appendix A.3.
+
+# 4.3 EXPERIMENT SETUP
+
+For the MEG-TLE dataset, they were normalized by z-normalization (Chen et al., 2015). For the other archives, we take the raw dataset without processing for datasets in those archives already normalized with z-normalization.
+
+Following the setup of (Wang et al., 2017), we use the learning rate of 0.001, batch size of 16, and Adam (Kingma & Ba, 2014) optimizer. The baselines are chosen from the top seven methods from the leaderboard 5 of each benchmark. For UCR archives, we ensemble five OS-CNNs, which stacks two OS-blocks with residential connections followed by the baseline IncpetionTime (Ismail Fawaz et al., 2019). We use PyTorch 6 to implement our method and run our experiments on Nvidia Titan XP.
+
+# 4.4 STATE-OF-THE-ART PERFORMANCE ON BENCHMARKS
+
+We show consistent state-of-the-art performance on four benchmarks as in Table 1. As we can see, for the MIT-TLE dataset, OS-CNN outperforms baselines in a ten times smaller model size. For all dataset archives, the OS-block achieves the best average rank, which means that, in general, the OS-block design can achieve better performance.
+
+# 4.5 OS-BLOCK CAN CAPTURE THE BEST TIME SCALE
+
+To demonstrate that the OS-block can capture the best time scale, we build $2 0 ~ \mathrm { F C N }$ models with different RF sizes (from 10 to 200 with step 10), and compare their performance with OS-CNN on the UCR 85 archive. Specifically, the FCN (Wang et al., 2017) is selected as the backbone model for it has a similar structure as OS-CNN.
+
+To obtain FCN with various RF sizes, we change the kernel size of each layer proportionally. To be specific, the kernel sizes of the original three layer FCN are 8, 5, and 3, and the RF size is 14. To obtain the RF size 30, we will set kernel sizes of each layer as 16,10, and 6. To control variables, when the kernel size increases, we will reduce the channel number to keep the model size constant. This will not influence the conclusion. To check that, in Appendix A.2, we also provide the static result comparison between OS-CNN and FCNs with the fixed channel number.
+
+![](images/a84164c9eb086966cd032e99b14e2ab863246890ce6932e92da955183fe232b0.jpg)  
+Figure 6: The class activation map of OS-CNN is similar to that of the model which has a better performance. For the ScreenType dataset, FCN(10) outperforms FCN(200), and the class activation map of OS-CNN (green) is similar to FCN(10)(blue). For the InsectWingbeatSound dataset, the class activation map is similar to FCN(200) for FCN(200) outperforms FCN(10).
+
+Due to the page limitation, the full result can be found in the supplementary material. And in Figure 5, a simple result comparison is given, and we could see that for most of the datasets, OSCNN can achieve a similar result as models with the best time scale.
+
+# .6 DISCUSSION ABOUT BEST TIME SCALE CAPTURE ABILITY
+
+The result in Figure 5 empirically verifies two phenomena that we mentioned in Section 2 with multiple datasets from multiple domains. Firstly, the OS-block covers all scales. Therefore, besides the important size, it also covers many redundant sizes, but those redundancies will not pull down the performance. Secondly, OS-block composes the RF size via the prime design while the FCN uses a different design. It means that the performances of 1D-CNNs are determined mainly by the RF size instead of the kernel configuration to compose that.
+
+# 4.7 CASE STUDY FOR THE BEST TIME SCALE CAPTURE ABILITY
+
+To further demonstrate the RF size capture ability, we will give a case study that compares the class activation map (Zhou et al., 2016) of OS-CNN with that of models with the best RF size. We select the ScreenType and InsectWingbeatSound datasets for the case study. They were selected because they are of the largest and the smallest accuracy difference calculated by the accuracy of FCN with RF size 10 (FCN(10)) minus accuracy of FCN with RF size 200 (FCN(200)). Specifically, it can be seen as, among UCR 85 datasets, the ScreenType is the dataset which the FCN(10) outperform FCN(200) most, and InsectWingbeatSound is the dataset which the FCN(200) outperforms FCN(10) most. We visualize the class activation map of the first instance in the two datasets, and the results are shown in Figure 6. As we can see in Figure 6, the class activation map of the OS-block is similar to that of the model with the best RF size.
+
+# 5 RELATED WORKS
+
+A TS data is a series of data points. TSC aims at labeling unseen TS data via a model trained by labeled data (Dau et al., 2018; Chen et al., 2015). One well-known challenge for TSC is telling the model in what time scale to extract features (Hills et al., 2014; Schafer, 2015; Berndt & Clifford, ¨ 1994). This is because TS data is naturally composed of multiple signals on different scales (Hills et al., 2014; Schafer, 2015; Dau et al., 2018) but, without prior knowledge, it is hard to find those ¨ scales directly.
+
+The success of deep learning encourages researchers to explore its application on TS data (Langkvist ¨ et al., 2014; Fawaz et al., 2019; Dong et al., 2021). The Recurrent Neural Network (RNN) is designed for temporal sequence. In general, it does not need extra hyper-parameters to identify information extraction scales. However, RNN is rarely applied on TS classification (Fawaz et al., 2019). There are many reasons for this situation. One widely accepted reason is that when faced with long TS data, RNN models suffer from vanishing gradient and exploding gradient (Pascanu et al., 2013; Fawaz et al., 2019; Bengio et al., 1994).
+
+Nowadays, the most popular deep-learning method for TSC is 1D-CNN. However, for 1D-CNNs, the feature extraction scale is still a problem. For example, there is an unresolved challenge with kernel size selection where there exists different approaches but non consensus on which is best. To date, the selection of feature extraction scales for 1D-CNN is regarded as a hyper-parameter selection problem e.g., (Cui et al., 2016) uses a grid search to find kernel sizes, while the following methods tune it empirically (Zheng et al., 2014; Wang et al., 2017; Rajpurkar et al., 2017; Serra\` et al., 2018; Ismail Fawaz et al., 2019; Kashiparekh et al., 2019).
+
+Dilated convolution (Oord et al., 2016) is widely adopted in 1D-CNN to improve generalization ability for TS tasks (Oord et al., 2016; Zhang et al., 2020; Li et al., 2021). It takes a lower sampling frequency than the raw signal input thus can be viewed as a structure-based low bandpass filter. Compared with the OS-block, the dilated convolution also needs prior knowledge or searching work to set the dilation size which will determine the threshold to filter out redundant information from TS data.
+
+Inception structure (Szegedy et al., 2015) is widely used in 1D-CNN for TSC tasks (Ismail Fawaz et al., 2019; Kashiparekh et al., 2019; Chen & Shi, 2021; Dong et al., 2021). The design of the multi-kernel structure of OS-block is inspired from the inception structure (Szegedy et al., 2015). Compared with existing works, the OS-block has two differences. Firstly, the OS-block does not need to assign weight to important scales via complicated methods such as pre-train (Kashiparekh et al., 2019), attention (Chen & Shi, 2021; Shen et al., 2018b), or a series of modifications such as bias removal and bottleneck for convolutions (Ismail Fawaz et al., 2019). Secondly, OS-block does not need to search for candidate scales. Specifically, those methods can only assign weight to a limited number of scales. Thus, they still need searching works to answer a series of questions. For example, Which sequence, such as geometric or arithmetic, should be preferred? What’s the largest length to stop? How do they select the depth of the neural network? And how do they select the common difference or ratio for their sequence?
+
+Adaptive receptive field (Han et al., 2018; Tabernik et al., 2020; Xiong et al., 2020; Pintea et al., 2021; Liu et al., 2021; Tomen et al., 2021; Dong et al., 2021), has been proposed to learn the optimal kernel sizes during the training stage. Generally, it can be viewed as learning a weight mask on kernels to control the receptive field size. The weight of the mask can be learned during the training step. On the other hand, OS-block learns the linkage between kernels and uses kernels of different sizes to compose different receptive field sizes. In principle, the adaptive receptive field can be used on the time series classification tasks. It improves the performance by enabling 1D-CNNs to have the best receptive field size. But the OS-block targets at covering all sizes of receptive filed sizes and assign large weight on important sizes.
+
+Mathematically, OS-block is a very general technique and can be extended to time series vision tasks by using the prime size design on the time dimension. This is because the video classification task and time series classification task share the same challenge (Xie et al., 2018; Bian et al., 2017; Tan et al., 2021; Liu et al., 2020; Li et al., 2020), which is the same region of interest might of different time scales for different data. Thus, using the kernel of various sizes will increase the probability to catch proper scales. However, in this paper, we mainly target the classic 1D time series classification, which is an active research area with many open problems (Fawaz et al., 2019; Zhang et al., 2020; Dempster et al., 2020) unsolven.
+
+# 6 CONCLUSION
+
+The paper presents a simple 1D-CNN block, namely OS-block. It does not need any feature extraction scale tuning and can achieve a similar performance as models with the best feature extraction scales. The key idea is using prime number design to cover all RF sizes in an efficient manner. We conduct experiments to demonstrate that the OS-block can robustly capture the best time scale on datasets from multiple domains. Due to the strong scale capture ability, it achieves a series SOTA performance on multiple TSC benchmarks. Besides that, the OS-CNN results reveal two characteristics of 1D-CNN models, which will benefit the development of the domain. In the future, we could extend our work in the following aspects. Firstly, other than the prime kernel size design, there might be a more efficient design to cover all RF sizes. Secondly, the OS-block can work with existing deep neural structures to achieve better performance, but there might be unique structures or variants of those existing structures that are more suitable for the OS-block. Besides that, characteristics of OS-block are empirically analyzed via the way there must be a theoretical explanation of the characteristics.
+
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+
+# A APPENDIX
+
+# A.1 STATISTIC OF THE COMPARISON (FIX MODEL SIZE)
+
+More statistic results of the result in Figure 5 is shown in Figure 7, Figure 8 and Figure 9Dataset name
+
+![](images/69f81b839642a02bba9f1609e89ee9db150dbce976d7f7517c5810623a16207b.jpg)  
+Figure 7: The histogram statics the count of datasets by which percentile range of the blue line that the orange point belongs to. Specifically, we could see that for more than $56 \%$ datasets $8 { + } 4 0$ out of 85 datasets), the result of OS-block is larger than 0.95 percentile. This means that, for an unknown dataset, using OS-block will have more than $56 \%$ chance to achieve a better result than grid search from 20 candidate scales. When seeing the count of the number larger than 0.5 percentile, we could see that, for an unknown dataset, using OS-block will have more than $96 \%$ chance to achieve a better result than selecting a random scale.
+
+![](images/93dbaa9866ca4dc5fa3eeb1dfc9873aed143ee36d75c38a1149be5c7a5d5278e.jpg)  
+Figure 8: The red line is the accuracy range obtained via subtracting the accuracy of OS-CNN from the accuracy range of FCN with various kernels. We sorted those datasets in ascending order. We could see that for most of the datasets, the highest value of the FCN accuracy range is lower than the accuracy of OS-CNN. Which supports the OS-block has the ability to capture the best scales.
+
+![](images/766fc1ddf377b782abd14e8e304c7c67013e73fdea3c23b85acacba0d73296de.jpg)  
+Figure 9: Sort datasets by dataset type and max accuracy range - accuracy of the OS-CNN. We could see that the best scale capture ability keeps the consistency cross different dataset types.
+
+# A.2 STATISTIC OF THE COMPARISON (FIX CHANNEL NUMBER)
+
+When we keep the number of channels constant in FCN, the statistic result will be as this. The OS-CNN still achieves similar performance as the model with the best scales.
+
+![](images/01ada7cc02e9e0365a0b64db02f2782683baaed600af6d3c8c9f076c73df1e32.jpg)  
+Figure 10: Same static metric as that of Figure 5 and Figure 7Count of datasets by the RF tuning's percentile range that OS result belongs to
+
+![](images/4b73be2d0adc8b99830ce8662f7a48869c0eceffebb4f7f81649a9d9698d68ec.jpg)  
+Figure 11: Same static metric as that of Figure 8
+
+![](images/5c5a1bfa5e6120ac2c175b1b327708ea94c8a648310cb0e395340221a6687184.jpg)  
+Figure 12: Same static metric as that of Figure 9
+
+# A.3 THE CD-DIAGRAM RESULT
+
+The critical difference diagram shows the average rank of each method with Wilcoxon-Holm posthoc analysis between each series.
+
+![](images/2affe89e993b8099057696e41b51467da2278ef633255d4d58e43e8ad5a32dcf.jpg)  
+Figure 13: SOTA for UEA 30 multivariate dataset archive
+
+![](images/4a1ccd48dd3f175c819ca1681f826ffbcbc0f5bf009fc09c04fcba707359534e.jpg)  
+Figure 14: SOTA on the UCR 85 datasets
+
+![](images/b5a684f995315b3a55d6f0e4a49531e74a524c91fd52cb10a5270e3c6e861bea.jpg)  
+Figure 15: SOTA on the UCR 128 datasets
+
+# A.4 EXAMPLES OF THE TWO PHENOMENA
+
+In the Figure 2, the Google speechcommands dataset is selected as the dataset to show the example. This is because, for this dataset, the relationship between performance and receptive field size is proportional (As it is shown in Figure 16). Thus, it is easy to control variables. What’s more, in Figure 18 and Figure 17, we show those two phenomena with more train and test split.
+
+# A.5 EXTEND OS-BLOCK WITH OTHER STRUCTURES
+
+Layers in the OS-block and the OS-block itself are easy to extend with other complicated structures. Figure 19 gives an explanation about the how to view the multi-kernel layers in OS-block as a single layer, and gives an example that how to combine the layer with dilation. The Figure 4 shows that how to view the OS-block as a layer, and gives another two examples rather than OS-CNN.
+
+![](images/949e86a54b6eecb15bbdd283ca376e110ae3ea6497ade9eaf3e9d8512c6fe818.jpg)  
+Figure 16: The relationship between performance and receptive field size are proportional
+
+![](images/b135fba5c81d11ee1b6116d26ae7fa5dc84e7d49fa687c4411e1f56254d368e4.jpg)  
+Figure 17: Lines in the figure are models with different sets of receptive field sizes. Lines with similar colors are models which have the same best receptive field size. We could see that the best receptive field size mainly dominates the performance in the set of receptive fieldsizes.
+
+![](images/d6d0b86b0bf7571ff2267b5610e54825894aa424380e4027b92f9387c71e496f.jpg)  
+Figure 18: The label of each line denotes the kernel configuration of each 1D-CNN. For example, 5 5 1 1 1 means the 1D-CNN has five layers, and from the first layer to the last layer, kernel sizes of each layer are 5, 5, 1, 1, and 1. Lines of similar color are 1D-CNNs with the same receptive field size, and they are also of similar performance.
+
+![](images/718d3534b189c896e844b279b461eda926698493e0d5cea8fef659578e7b0d02.jpg)  
+Figure 19: Purple color in those images are the zero mask and yellow denotes the location where has the ability to hold weight. Left: Convolution layers in of OS-block can be calculated parallelly, thus, each layer can be viewed as one convolutional layer with zero masks.(s) Right: layers in the OS-block can work with the dilation design
+
+# A.6 EXPERIMENT RESULT OF OS-BLOCK WITH OTHER STRUCTURES
+
+The Figure 20 and Figure 21 show that applied OS-block with residual connection, ensemble, and multi-channel architectures (individually or together) could further improve the performance. The evaluation was on both UCR 85 and UEA 30 archives which contain datasets from different domains such as electrical devices analysis, Spectrum analysis, traffic analysis, EEG analysis.
+
+![](images/6d21c94fe3f81ca4e6379dbbfbc9cf3884e458ad896c38e24586427e400e98d5.jpg)  
+Figure 20: Using the OS-block with residual connection and ensemble (individually or together) could increase the performance
+
+![](images/d40bd168df3705d61c3518f7eedc78faa78ebabd1f046b9dde65f12a6a7b044f.jpg)  
+Figure 21: Using the multi-channel architecture with OS-block could improve the performance
+
+A.7 COMPARE THE OS-BLOCK WITH OTHER DESIGNS
+
+Mathematically, finding the optimal kernel configuration is challenging, for it is a constrained combinatorial optimization searching for the best configuration among an exponential number of candidates. Our contribution is a simple and effective model design that does not need to solve the complex optimization problems and achieves state-of-the-art performance on several benchmarks.
+
+From the model size perspective, using prime numbers is more efficient than using even numbers or odd numbers. To be specific, to cover RF of range r, the model size complexity of using prime size kernels is $O ( r ^ { 2 } / l o g ( \dot { r } ) )$ . On the other hand, no matter we use even number pairs or odd number pairs, kernel sizes in each layer, the model size complexity of using the sequence is $O ( r ^ { 2 } )$ . As Table 2 shows, compared with using odd number pairs or even numbers pairs prime numbers can achieve similar performance in a smaller model size.
+
+Accuracy   
+
+<table><tr><td colspan="6">Number of parameters</td></tr><tr><td>Channel number</td><td>RF range</td><td>Prime numbers (Ours)</td><td></td><td>odd numbers</td><td>even numbers</td></tr><tr><td>16</td><td>1 to 45</td><td>304k</td><td></td><td>507k</td><td>491k</td></tr><tr><td>32</td><td>1 to 45</td><td></td><td>1,203 k</td><td>2,009k</td><td>1,948k</td></tr></table>
+
+Table 2: Model size and performance comparison on Google SpeechCommands dataset   
+
+<table><tr><td>Channel number</td><td>RF range</td><td>Prime numbers (Ours)</td><td>odd numbers</td><td>even numbers</td></tr><tr><td>16</td><td>1 to 45</td><td>0.7524</td><td>0.7687</td><td>0.7561</td></tr><tr><td>32</td><td>1 to 45</td><td>0.7845</td><td>0.7783</td><td>0.7725</td></tr></table>

parse/dev/PDYs7Z2XFGv/PDYs7Z2XFGv_content_list.json

@@ -0,0 +1,1950 @@
+[
+    {
+        "type": "text",
+        "text": "OMNI-SCALE CNNS: A SIMPLE AND EFFECTIVE KERNEL SIZE CONFIGURATION FOR TIME SERIES CLASSIFICATION ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Wensi Tang1, Guodong Long1, Lu Liu1,2,Tianyi Zhou3,4, Michael Blumenstein1, Jing Jiang1 1Australian Artificial Intelligence Institute, University of Technology Sydney,2 Google 3University of Washington, Seattle, 4University of Maryland, College Park {wensi.tang, lu.liu-10}@student.uts.edu.au, {guodong.long, michael.blumenstein, jing.jiang} $@$ uts.edu.au, tianyizh@uw.edu ",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            303,
+            544,
+            318
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "The Receptive Field (RF) size has been one of the most important factors for One Dimensional Convolutional Neural Networks (1D-CNNs) on time series classification tasks. Large efforts have been taken to choose the appropriate size because it has a huge influence on the performance and differs significantly for each dataset. In this paper, we propose an Omni-Scale block (OS-block) for 1D-CNNs, where the kernel sizes are decided by a simple and universal rule. Particularly, it is a set of kernel sizes that can efficiently cover the best RF size across different datasets via consisting of multiple prime numbers according to the length of the time series. The experiment result shows that models with the OS-block can achieve a similar performance as models with the searched optimal RF size and due to the strong optimal RF size capture ability, simple 1D-CNN models with OS-block achieves the state-of-the-art performance on four time series benchmarks, including both univariate and multivariate data from multiple domains. Comprehensive analysis and discussions shed light on why the OS-block can capture optimal RF sizes across different datasets. Code available here 1 ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "One of the most challenging problems for Time Series Classification (TSC) tasks is how to tell models in what time scales 2 to extract features. Time series (TS) data is a series of data points ordered by time or other meaningful sequences such as frequency. Due to the variety of information sources (e.g., medical sensors, economic indicators, and logs) and record settings (e.g., sampling rate, record length, and bandwidth), TS data is naturally composed of various types of signals on various time scales (Hills et al., 2014; Schafer, 2015; Dau et al., 2018). Thus, in what time scales ¨ can a model “see” from the TS input data has been a key for the performance of TS classification. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Traditional machine learning methods have taken huge efforts to capture important time scales, and the computational resource consumption increase exponentially with the length of TS increase. For example, for shapelet methods (Hills et al., 2014; Lines et al., 2012), whose discriminatory feature is obtained via finding sub-sequences from TS that can be representative of class membership, the time scale capture work is finding the proper sub-sequences length. To obtain the proper length, even for a dataset with length 512, (Hills et al., 2014) has to try 71 different sub-sequence lengths. For other methods, such as (Berndt & Clifford, 1994; Schafer, 2015; Lucas et al., 2019), despite ¨ the time scale capture might be called by different names such as finding warping size or window length. They all need searching works to identify those important time scales. More recent deep learning based methods also showed that they had to pay a lot of attention to this time scale problem. MCNN (Cui et al., 2016) searches the kernel size to find the best RF of a 1D-CNN for every dataset. Tapnet (Zhang et al., 2020) additionally considers the dilation steps. Chen & Shi (2021) also take the number of layers into considerations. These are all important factors for the RF of CNNs and the performance for TSC. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/0de81077afc0a14742088d5b94bd12b016a9cd78eeb745fcf515465d47d20a88.jpg",
+        "image_caption": [
+            "Figure 1: Left: A model’s accuracy on the UCR 85 datasets changes by tuning the model’s receptive field sizes from 10 to 200. Right: The average rank results of each receptive field size are pretty similar, which means that no single receptive field size can significantly outperform others on most datasets. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Although a number of researchers have searched for the best RF of 1D-CNNs for TSC, there is still no agreed answer to 1) what size of the RF is the best? And 2) how many different RFs should be used? Models need to be equipped with different sizes and different numbers of RFs for a specific dataset. Using the same setup for every dataset can lead to a significant performance drop for some datasets. For example, as shown by the statistics on the University of California Riverside (UCR) 85 “bake off” datasets in Figure 1a, the accuracy of most datasets can have a variance of more than $5 \\%$ just by changing the RF sizes of their model while keeping the rest of the configurations the same. As also shown in Figure 1b, no RF can consistently perform the best over different datasets. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "To avoid those complicated and resource-consuming searching work, we propose Omni-Scale block (OS-block), where the kernel choices for 1D-CNNs are automatically set through a simple and universal rule that can cover the RF of all scales. The rule is inspired by Goldbach’s conjecture, where any positive even number can be written as the sum of two prime numbers. Therefore, the OS-block uses a set of prime numbers as the kernel sizes except for the last layer whose kernel sizes are 1 and 2. In this way, a 1D-CNN with these kernel sizes can cover the RF of all scales by transforming TS through different combinations of these prime size kernels. What’s more, the OS-block is easy to implement to various TS datasets via selecting the maximum prime number according to the length of the TS. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In experiments, we show consistent state-of-the-art performance on four TSC benchmarks. These benchmarks contain datasets from different domains, i.e., healthcare, human activity recognition, speech recognition, and spectrum analysis. Despite the dynamic patterns of these datasets, 1DCNNs with our OS-block robustly outperform previous baselines with the unified training hyperparameters for all datasets such as learning rate, batch size, and iteration numbers. We also did a comprehensive study to show our OS-block, the no time scale search solution, always matches the performance with the best RF size for different datasets. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 MOTIVATIONS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Two phenomena of 1D-CNNs inspire the design of the OS-block. In this section, we will introduce the two phenomena with examples in Figure 2 and more discussions can be found in Section 4.6. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Firstly, we found that, although the RF size is important, the 1D-CNNs are not sensitive to the specific kernel size configurations that we take to compose that RF size. An example is given in the right image of the Figure 2 ",
+        "bbox": [
+            174,
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Secondly, the performance of 1D-CNNs is mainly determined by the best RF size it has. To be specific, supposing we have multiple single-RF-size-models which are of similar model size and layer numbers, but each of them has a unique RF size. Let’s denote the set of those RF sizes as $\\mathbb { S }$ . When testing those models on a dataset, we will have a set of accuracy results A. Then, supposing we have a multi-kernel model which has multiple RF sizes3 and set of those sizes is also $\\mathbb { S }$ . Then, the accuracy of the multiple-RF-sizes-model will be similar to the highest value of A. An example is given in the left image of Figure 2. Specifically, when testing single-RF-size-models on the Google Speechcommands dataset, the model’s performance is positive correlation with the model’s RF size. For example, the light blue line whose set of RF size is $\\{ 9 9 \\}$ outperforms the light green line $\\{ 3 9 \\}$ and light red line $\\{ \\bar { 9 } \\}$ . For those multiple-RF-sizes-models which has more than one element in their set of RF sizes, their performance are determined by the best (also the largest because of the positive correlation) RF size it has. Having more worse (smaller) RF sizes will not have much influence on the performance. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/c103d33d684df89b171fd8db12402882c9f99814b52b9590c7e24f74602d1ea5.jpg",
+        "image_caption": [
+            "Figure 2: Left: The label of each line denotes receptive field size and the kernel configuration of each 1D-CNN. For example, (9):5 5 1 1 1 means the 1D-CNN has five layers and the receptive field size is 9, and from the first layer to the last layer, kernel sizes of each layer are 5, 5, 1, 1, and 1. Lines of similar color are 1D-CNNs with the same receptive field size, and they are also of similar performance. Right: Lines with similar colors are models which have the same best receptive field size. For example, all (red/green/blue) lines have the receptive field size (9/39/99), and their performances are similar to the bright (red/green/blue) line which denotes the model only has the receptive field size (9/39/99). "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The second phenomenon means that, instead of searching for the best time scales, if the model covers all RF sizes, its performance will be similar to that of a model with the best RF size. However, there are many designs that can cover all RF sizes. Which one should be preferred? Based on the first phenomenon, from the performance perspective, we could choose any design that we want. However, as we will show in Section 3.3, those candidate designs are not of the same characteristics such as the model size or the expandability for long TS data. Therefore, the design of the OS-block that we propose aims at covering all RF sizes in an efficient manner. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 METHOD ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The section is organized as follows: Firstly, we give the problem definition in Section 3.1. Then, we will explain how to construct the Omni-scale block (OS-block) which covers all receptive field sizes in Section 3.2. Section 3.3 will explain the reason why OS-block can cover RF of all sizes in an efficient manner. In Section 3.4, we will introduce how to apply the OS-block on TSC tasks. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1 PROBLEM DEFINITION ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "TS data is denoted as $\\textbf { \\textit { X } } = ~ [ \\pmb { x } _ { 1 } , \\pmb { x } _ { 2 } , . . . , \\pmb { x } _ { m } ]$ , where $m$ is the number of variates. For univariate TS data, $\\textit { m } = \\textit { 1 }$ and for $m \\ > \\ 1$ , the TS are multivariate. Each variate is a vector of length $l$ . A TS dataset, which has $n$ data and label pairs, can be denoted as: $\\mathbb { D } =$ $\\{ ( \\boldsymbol { X } ^ { 1 } , \\boldsymbol { y } ^ { 1 } ) , \\overbar { ( \\boldsymbol { X } ^ { 2 } , \\boldsymbol { y } ^ { 2 } ) } , . . . , ( \\boldsymbol { X } ^ { n } , \\boldsymbol { y } ^ { n } ) \\}$ , where $( X ^ { * } , y ^ { * } )$ denotes the TS data $x ^ { * }$ belongs to the class $y ^ { * }$ . The task of TSC is to predict the class label $y ^ { * }$ when given a TS $x ^ { * }$ . ",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2 ARCHITECTURE OF OS-BLOCK ",
+        "text_level": 1,
+        "bbox": [
+            176,
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The architecture of the OS-block is shown in Figure 3. It is a three-layer multi-kernel structure, and each kernel does the same padding convolution with input. For the kernel size configuration, we use $\\mathbb { P } ^ { ( i ) }$ to denote the kernel size set of the $i$ -th layer: ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/235f0eac9ec4db855af6264a0cefa6a125dc9adc30d84563a049b4c6f1c43e45.jpg",
+        "text": "$$\n\\mathbb { P } ^ { ( i ) } = \\left\\{ \\begin{array} { l l } { \\{ 1 , 2 , 3 , 5 , . . . , p _ { k } \\} ~ } & { , i \\in \\{ 1 , 2 \\} } \\\\ { \\{ 1 , 2 \\} ~ } & { , i = 3 } \\end{array} \\right.\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/9233984bbc86d0cc295e7b0d82cf4d5c4614b52e390f439f9702504bfb0f06ab.jpg",
+        "image_caption": [
+            "Figure 3: The left image shows that every even number from 2 to 38 can be composed via two prime numbers from 1 to 19. This phenomenon can be extended to all even numbers. Based on this phenomenon, with the OS-block structure in the middle image, we could cover all receptive field sizes. Specifically, the first two layers have prime-sized kernels from 1 to $p _ { k }$ . Thus, the two layers can cover all even number receptive field sizes. With kernels of sizes 1 and 2 in the third layer, we could cover all integer receptive field sizes in a range via selecting the value $p _ { k }$ . The OS-block is easy to be applied on time series classification tasks. A simple classifier with the OS-block, namely OS-CNN, is given in the right image, which achieves a series of SOTA performances. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Where $\\{ 1 , 2 , 3 , 5 , 7 , . . . , p _ { k } \\}$ is a set of prime numbers from 1 to $p _ { k }$ . The value of $p _ { k }$ is the smallest prime number that can cover all sizes of RF in a range. Here, the range that we mentioned is all meaningful scales. For example, since the TS length is $l$ , we don’t need to cover RFs that are larger than $l$ or smaller than 1. Therefore, the $p _ { k }$ is the smallest prime number that can cover the RF size from 1 to $l$ . If we have prior knowledge, such as that we know there are cycles in the TS, or we know the length range of the hidden representative pattern. We could change the RF size range of the OS-block by simply changing the prime number list. An example is given in the left image in Figure 3, which uses the prime number list in the blue block to cover the RF size range from 10 to 26. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "RF sizes of the OS-block: The RF is defined as the size of the region in the input that produces the feature. Because each layer of the OS-block has more than one convolution kernel, there will be several different paths from the input signal to the final output feature (Araujo et al., 2019; Luo et al., 2016), and each path will have a RF size. For the 3-layer OS-block, which has no pooling layer and the stride size is 1, the set of RF sizes $\\mathbb { S }$ is the set of RF size of all paths, and it can be described as: ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/7fe0eca125404a28165f1c41eea2702cb392f9a726d3671ac7bec9c7facdfb94.jpg",
+        "text": "$$\n\\mathbb { S } = \\{ p ^ { ( 1 ) } + p ^ { ( 2 ) } + p ^ { ( 3 ) } - 2 \\ | \\ p ^ { ( i ) } \\in \\mathbb { P } ^ { ( i ) } , i \\in \\{ 1 , 2 , 3 \\} \\} .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "For the reasons that $\\mathbb { P } ^ { ( i ) }$ are prime number list when $i \\in \\{ 1 , 2 \\}$ , the set $\\{ p ^ { ( 1 ) } + p ^ { ( 2 ) } | p ^ { ( i ) } \\in \\mathbb { P } ^ { ( i ) } , i \\in$ $\\{ 1 , 2 \\} \\}$ is the set of all even numbers $\\mathbb { E }$ .4 Thus, we have ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/779814a2496b431c3b26fdddebd44a0d8bddc1be84c5f79963792e9577de12a7.jpg",
+        "text": "$$\n\\mathbb { S } = \\{ e + p ^ { ( 3 ) } - 2 \\mid p ^ { ( 3 ) } \\in \\mathbb { P } ^ { ( 3 ) } , e \\in \\mathbb { E } \\} .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "With Equation 3 and Equation 1, we have ",
+        "bbox": [
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+            790,
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/62b398a9f23ad63303d85141df9a4486f888ea7d5d40626c9b0420e68adb65a8.jpg",
+        "text": "$$\n\\mathbb { S } = \\{ e | e \\in \\mathbb { E } \\} \\cup \\{ e - 1 | e \\in \\mathbb { E } \\} \\equiv \\mathbb { N } ^ { + } .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Where $\\mathbb { N } ^ { + }$ is the set of all integer numbers in the range. Specifically, the $\\mathbb { S } \\equiv \\mathbb { N } ^ { + }$ is because a real number must be an odd number or an even number, while $\\mathbb { E }$ is the even number set, $\\{ e - 1 | e \\in \\mathbb { E } \\}$ is ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/5c37dd4e643525b376a8b285e8a193ac043160aba88198a014638ff0eeadc244.jpg",
+        "image_caption": [
+            "Figure 4: Examples of using OS-block with other deep learning structures. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            104,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "the odd number set. Therefore, with the proper selection of $p _ { k }$ , we could cover any integer RF size in a range. It should be noticed that, there might be many options to cover all RF sizes, we use the Godlach’s conjecture to make sure that we could all scales. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "3.3 OS-BLOCK COVER ALL SCALES IN AN EFFICIENT MANNER ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "From the model size perspective, using prime numbers is more efficient than using even numbers or odd numbers. To be specific, to cover receptive fields up to size r, the model size complexity of using prime size kernels is $O ( r ^ { 2 } / l o g ( r ) )$ . On the other hand, no matter we use even number pairs or odd number pairs, the model size complexity is $O ( r ^ { 2 } )$ . We also empirically show the advantage of our model on efficiency in the following table and this table has been added to Appendix A.7: ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.4 HOW TO APPLY OS-BLOCK ON TSC TASKS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Firstly, the OS-block could take both univariate and multivariate TS data by adjusting the input channel the same as the variate number of input TS data. A simple example classifier with OSblock, namely OS-CNN, is given in Figure 3. The OS-CNN is composed of an OS-block with one global average pooling layer as the dimensional reduction module and one fully connected layer as the classification module. Other than OS-CNN, the OS-block is flexible and easy to extend. Specifically, convolution layers of OS-block can be calculated parallelly. Thus, each layer can be viewed as one convolutional layer with zero masks. Therefore, both the multi-kernel layers or the OS-block itself are easy to extend with more complicated structures (such as dilation (Oord et al., 2016), attention or transformer (Shen et al., 2018a), and bottleneck) that are normally used in 1DCNN for performance gain. In Figure 4, we give three examples which uses OS-block with other structures. ",
+        "bbox": [
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+        "type": "text",
+        "text": "4 EXPERIMENT ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "4.1 BENCHMARKS ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We evaluate OS-block on 4 TSC benchmarks which include, in total, 159 datasets. The details of each benchmark is as follows: ",
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+    {
+        "type": "text",
+        "text": "• Magnetoencephalography recording for Temporal Lobe Epilepsy diagnosis (MEGTLE) dataset (Gu et al., 2020): The Magnetoencephalography dataset was recorded from epilepsy patients and was introduced to classify two subtypes (simple and complex) of temporal Lobe Epilepsy. The dataset contains 2877 recordings which were obtained at the sampling frequency $1 2 0 0 \\mathrm { H z }$ . Each recording is approximately 2 sec. Therefore the length is about 2400. University of East Anglia (UEA) 30 archive (Bagnall et al., 2018): This formulation of the archive was a collaborative effort between researchers at the University of East Anglia and the University of California, Riverside. It is an archive of 30 multivariate TS datasets from various domains such as motion detection, physiological data, audio spectra classification. Besides domains, those datasets also have various characteristics. For instance, among those datasets, the class number various from 2 to 39, the length of each dataset various from 8 to 17,894, and the number of variates various from 2 to 963. ",
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+    {
+        "type": "table",
+        "img_path": "images/220dd36adc79f6444ea89477c574427825022b5c3b2e5744678d561230ecc1ac.jpg",
+        "table_caption": [
+            "Multivariate dataset archive benchmark "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"5\">Individual dataset benchmark</td></tr><tr><td>Dataset</td><td>Method</td><td>Accuracy(%)</td><td>F1-score</td><td># parameters</td></tr><tr><td rowspan=\"6\">MEG-TLE (Gu et al.,2020)</td><td>CNN(Gu et al.,2020)</td><td>83.2</td><td>82.3</td><td>3.8M</td></tr><tr><td>PF(Gu et al.,2020)</td><td>82.6</td><td>68.2</td><td>1</td></tr><tr><td>SVM (Gu et al.,2020)</td><td>55.2</td><td>85.2</td><td>-</td></tr><tr><td>MSAM (Gu et al.,2020)</td><td>83.6</td><td>83.4</td><td>2.3M</td></tr><tr><td>Rocket (Dempster et al., 2020)</td><td>87.7</td><td>89.9</td><td></td></tr><tr><td>OS-CNN (Ours)</td><td>91.3</td><td>91.6</td><td>235k</td></tr></table>",
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+    {
+        "type": "table",
+        "img_path": "images/21ac56480b50e4b3227e8d086c40b8c17474a91275948d546c4418114ba9d9f5.jpg",
+        "table_caption": [
+            "Univariate dataset archives benchmarks "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Archive</td><td>Method</td><td>Baseline wins</td><td>OS-CNN(Ours) wins</td><td>Tie</td><td>Average Rank</td></tr><tr><td rowspan=\"7\">UEA 30 archive (Bagnall et al., 2018)</td><td>DTW-1NND(norm) (Zhang et al.,2020)</td><td>7</td><td>23</td><td>0</td><td>5.68</td></tr><tr><td>DTW-1NN-I(norm) (Zhang et al.,2020)</td><td>5</td><td></td><td>1</td><td>6.70</td></tr><tr><td>ED-1NN(norm) (Zhang et al.,2020)</td><td>5</td><td></td><td>0</td><td>7.45</td></tr><tr><td>DTW-1NND (Zhang et al.,2020)</td><td>7</td><td></td><td>0</td><td>5.28</td></tr><tr><td>DTW-1NN-I (Zhang et al.,2020) ED-1NN (Zhang et al., 2020)</td><td>7 5</td><td>2425232251</td><td>1</td><td>6.07</td></tr><tr><td>WEASEL+MUSE(Schäfer&amp; Leser,2017)</td><td>10</td><td></td><td>0</td><td>7.12</td></tr><tr><td>MLSTM-FCN(Karim et al.,2019)</td><td>7</td><td>23</td><td>1</td><td>4.15</td></tr><tr><td></td><td>9</td><td>20</td><td>0</td><td>5.62</td></tr><tr><td></td><td>TapNet (Zhang et al.,2020) OS-CNN (Ours)</td><td>-</td><td>=</td><td>1 =</td><td>3.80 3.13</td></tr></table>",
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+    {
+        "type": "table",
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+        "table_caption": [
+            "Table 1: Performance comparison on 4 time series classification benchmarks "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Archive</td><td>Method</td><td>Baselinewins</td><td>OS-CNN(Ours) wins</td><td>Tie</td><td>Average rank</td></tr><tr><td rowspan=\"6\">UCR 85 archive (Chen et al.,2015)</td><td>PF (Lucas et al.,2019)</td><td>13</td><td>67</td><td>5</td><td>6.57</td></tr><tr><td>ResNet (Wang et al.,2017)</td><td>19</td><td>61</td><td>5</td><td>5.41</td></tr><tr><td>STC (Hameurlain et al., 2017)</td><td>27</td><td>56</td><td>2</td><td>5.05</td></tr><tr><td>InceptionTime (Ismail Fawaz et al.,2019)</td><td>34</td><td>42</td><td>9</td><td>4.05</td></tr><tr><td>ROCKET (Dempster et al.,2020)</td><td>33</td><td>44</td><td>8</td><td>3.64</td></tr><tr><td>HIVE-COTE(Lines et al., 2016) TS-CHIEF(Shifaz et al.,2020)</td><td>34 42</td><td>43</td><td>8 4</td><td>3.99</td></tr><tr><td>OS-CNN (Ours)</td><td>1</td><td>39 -</td><td></td><td>3.68 3.59</td></tr><tr><td rowspan=\"4\">UCR128 archive (Dau et al., 2018)</td><td>ResNet (Wang et al.,2017)</td><td>19</td><td>83</td><td>- 26</td><td></td></tr><tr><td>InceptionTime (Ismail Fawaz et al.,2019)</td><td>30</td><td>59</td><td>39</td><td>3.21</td></tr><tr><td>ROCKET (Dempster et al.,2020)</td><td>43</td><td>62</td><td>23</td><td>2.41</td></tr><tr><td>OS-CNN (Ours)</td><td>-</td><td>-</td><td>-</td><td>2.36 2.02</td></tr></table>",
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+        "type": "text",
+        "text": "",
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+        "type": "text",
+        "text": "• University of California, Riverside (UCR) 85 archive (Chen et al., 2015): This is an archive of 85 univariate TS datasets from various domains such as speech reorganizations, health monitoring, and spectrum analysis. What’s more, those datasets also have different characteristics. For instance, among those datasets, the class number varies from 2 to 60, the length of each dataset varies from 24 to 2709. The number of training data varies from 16 to 8,926. ",
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+    {
+        "type": "text",
+        "text": "• University of California, Riverside (UCR) 128 archive (Dau et al., 2018): This is an archive of 128 univariate TS datasets. It is the updated version of the UCR 85 archive. However, the new archive cannot be viewed as a replacement for the former because they have different characteristics. For example, for the UCR 85 archive, all TS data within a single dataset are of the same length, but that is not the same for the UCR 128 archive. Besides that, in general, the added data in the UCR 128 archive, their default test set is bigger than the train set to reflect real-world scenarios. ",
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+    {
+        "type": "text",
+        "text": "4.2 EVALUATION CRITERIA ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "For all benchmarks, we follow the standard settings from previous literature. Specifically, for the MEG-TLE dataset, following Multi-Head Self-Attention Model (MSAM) (Gu et al., 2020), models are evaluated by test accuracy and f1 score. Besides using recommended metrics of each benchmark, we also compare the model size of OS-block with other deep learning methods. For UEA 30, UCR 85 archives, and UCR 128 archives, following the evaluation advice from the archive (Dau et al., 2018; Bagnall et al., 2018), count of wins, and critical difference diagrams (cd-diagram) (Dau et al., 2018) were selected as the evaluation method. Due to the page limitation, we list the average rank ",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/1690ddc86abcdb74ef91fcafda3f877cb182a9803b493d66dcbc21aebb97508a.jpg",
+        "image_caption": [
+            "Figure 5: Classification accuracies for OS-CNN vs. accuracies from 20 1D-CNNs with receptiveCount of datasets by the RF tuning's percentile range that OS result belongs to 50 field size. As we can see, for most of the dataset, the orange points (accuracy of OS-CNN) are near 40 the top of blue points. More analysis for this comparison can be found in Appendix A.1 "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "0  3 (3.53%) 2 (2.35%) 5 (5.88%) 2 (2.35%) 3 (3.53%)  3 (3.53%) 1 (1.18%)  5 (5.88%) 4 (4.71%) in the result table because it is the main criteria of the cd-diagram. The full cd-diagram results are < 0.5 0.55 listed in Appendix A.3. ",
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "4.3 EXPERIMENT SETUP ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "For the MEG-TLE dataset, they were normalized by z-normalization (Chen et al., 2015). For the other archives, we take the raw dataset without processing for datasets in those archives already normalized with z-normalization. ",
+        "bbox": [
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "Following the setup of (Wang et al., 2017), we use the learning rate of 0.001, batch size of 16, and Adam (Kingma & Ba, 2014) optimizer. The baselines are chosen from the top seven methods from the leaderboard 5 of each benchmark. For UCR archives, we ensemble five OS-CNNs, which stacks two OS-blocks with residential connections followed by the baseline IncpetionTime (Ismail Fawaz et al., 2019). We use PyTorch 6 to implement our method and run our experiments on Nvidia Titan XP. ",
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.4 STATE-OF-THE-ART PERFORMANCE ON BENCHMARKS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We show consistent state-of-the-art performance on four benchmarks as in Table 1. As we can see, for the MIT-TLE dataset, OS-CNN outperforms baselines in a ten times smaller model size. For all dataset archives, the OS-block achieves the best average rank, which means that, in general, the OS-block design can achieve better performance. ",
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "4.5 OS-BLOCK CAN CAPTURE THE BEST TIME SCALE ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "To demonstrate that the OS-block can capture the best time scale, we build $2 0 ~ \\mathrm { F C N }$ models with different RF sizes (from 10 to 200 with step 10), and compare their performance with OS-CNN on the UCR 85 archive. Specifically, the FCN (Wang et al., 2017) is selected as the backbone model for it has a similar structure as OS-CNN. ",
+        "bbox": [
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "To obtain FCN with various RF sizes, we change the kernel size of each layer proportionally. To be specific, the kernel sizes of the original three layer FCN are 8, 5, and 3, and the RF size is 14. To obtain the RF size 30, we will set kernel sizes of each layer as 16,10, and 6. To control variables, when the kernel size increases, we will reduce the channel number to keep the model size constant. This will not influence the conclusion. To check that, in Appendix A.2, we also provide the static result comparison between OS-CNN and FCNs with the fixed channel number. ",
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/a84164c9eb086966cd032e99b14e2ab863246890ce6932e92da955183fe232b0.jpg",
+        "image_caption": [
+            "Figure 6: The class activation map of OS-CNN is similar to that of the model which has a better performance. For the ScreenType dataset, FCN(10) outperforms FCN(200), and the class activation map of OS-CNN (green) is similar to FCN(10)(blue). For the InsectWingbeatSound dataset, the class activation map is similar to FCN(200) for FCN(200) outperforms FCN(10). "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Due to the page limitation, the full result can be found in the supplementary material. And in Figure 5, a simple result comparison is given, and we could see that for most of the datasets, OSCNN can achieve a similar result as models with the best time scale. ",
+        "bbox": [
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+        "page_idx": 7
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+    {
+        "type": "text",
+        "text": ".6 DISCUSSION ABOUT BEST TIME SCALE CAPTURE ABILITY ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The result in Figure 5 empirically verifies two phenomena that we mentioned in Section 2 with multiple datasets from multiple domains. Firstly, the OS-block covers all scales. Therefore, besides the important size, it also covers many redundant sizes, but those redundancies will not pull down the performance. Secondly, OS-block composes the RF size via the prime design while the FCN uses a different design. It means that the performances of 1D-CNNs are determined mainly by the RF size instead of the kernel configuration to compose that. ",
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+    {
+        "type": "text",
+        "text": "4.7 CASE STUDY FOR THE BEST TIME SCALE CAPTURE ABILITY ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
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+    {
+        "type": "text",
+        "text": "To further demonstrate the RF size capture ability, we will give a case study that compares the class activation map (Zhou et al., 2016) of OS-CNN with that of models with the best RF size. We select the ScreenType and InsectWingbeatSound datasets for the case study. They were selected because they are of the largest and the smallest accuracy difference calculated by the accuracy of FCN with RF size 10 (FCN(10)) minus accuracy of FCN with RF size 200 (FCN(200)). Specifically, it can be seen as, among UCR 85 datasets, the ScreenType is the dataset which the FCN(10) outperform FCN(200) most, and InsectWingbeatSound is the dataset which the FCN(200) outperforms FCN(10) most. We visualize the class activation map of the first instance in the two datasets, and the results are shown in Figure 6. As we can see in Figure 6, the class activation map of the OS-block is similar to that of the model with the best RF size. ",
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+    {
+        "type": "text",
+        "text": "5 RELATED WORKS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "A TS data is a series of data points. TSC aims at labeling unseen TS data via a model trained by labeled data (Dau et al., 2018; Chen et al., 2015). One well-known challenge for TSC is telling the model in what time scale to extract features (Hills et al., 2014; Schafer, 2015; Berndt & Clifford, ¨ 1994). This is because TS data is naturally composed of multiple signals on different scales (Hills et al., 2014; Schafer, 2015; Dau et al., 2018) but, without prior knowledge, it is hard to find those ¨ scales directly. ",
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "The success of deep learning encourages researchers to explore its application on TS data (Langkvist ¨ et al., 2014; Fawaz et al., 2019; Dong et al., 2021). The Recurrent Neural Network (RNN) is designed for temporal sequence. In general, it does not need extra hyper-parameters to identify information extraction scales. However, RNN is rarely applied on TS classification (Fawaz et al., 2019). There are many reasons for this situation. One widely accepted reason is that when faced with long TS data, RNN models suffer from vanishing gradient and exploding gradient (Pascanu et al., 2013; Fawaz et al., 2019; Bengio et al., 1994). ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Nowadays, the most popular deep-learning method for TSC is 1D-CNN. However, for 1D-CNNs, the feature extraction scale is still a problem. For example, there is an unresolved challenge with kernel size selection where there exists different approaches but non consensus on which is best. To date, the selection of feature extraction scales for 1D-CNN is regarded as a hyper-parameter selection problem e.g., (Cui et al., 2016) uses a grid search to find kernel sizes, while the following methods tune it empirically (Zheng et al., 2014; Wang et al., 2017; Rajpurkar et al., 2017; Serra\\` et al., 2018; Ismail Fawaz et al., 2019; Kashiparekh et al., 2019). ",
+        "bbox": [
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+        "page_idx": 7
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Dilated convolution (Oord et al., 2016) is widely adopted in 1D-CNN to improve generalization ability for TS tasks (Oord et al., 2016; Zhang et al., 2020; Li et al., 2021). It takes a lower sampling frequency than the raw signal input thus can be viewed as a structure-based low bandpass filter. Compared with the OS-block, the dilated convolution also needs prior knowledge or searching work to set the dilation size which will determine the threshold to filter out redundant information from TS data. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Inception structure (Szegedy et al., 2015) is widely used in 1D-CNN for TSC tasks (Ismail Fawaz et al., 2019; Kashiparekh et al., 2019; Chen & Shi, 2021; Dong et al., 2021). The design of the multi-kernel structure of OS-block is inspired from the inception structure (Szegedy et al., 2015). Compared with existing works, the OS-block has two differences. Firstly, the OS-block does not need to assign weight to important scales via complicated methods such as pre-train (Kashiparekh et al., 2019), attention (Chen & Shi, 2021; Shen et al., 2018b), or a series of modifications such as bias removal and bottleneck for convolutions (Ismail Fawaz et al., 2019). Secondly, OS-block does not need to search for candidate scales. Specifically, those methods can only assign weight to a limited number of scales. Thus, they still need searching works to answer a series of questions. For example, Which sequence, such as geometric or arithmetic, should be preferred? What’s the largest length to stop? How do they select the depth of the neural network? And how do they select the common difference or ratio for their sequence? ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Adaptive receptive field (Han et al., 2018; Tabernik et al., 2020; Xiong et al., 2020; Pintea et al., 2021; Liu et al., 2021; Tomen et al., 2021; Dong et al., 2021), has been proposed to learn the optimal kernel sizes during the training stage. Generally, it can be viewed as learning a weight mask on kernels to control the receptive field size. The weight of the mask can be learned during the training step. On the other hand, OS-block learns the linkage between kernels and uses kernels of different sizes to compose different receptive field sizes. In principle, the adaptive receptive field can be used on the time series classification tasks. It improves the performance by enabling 1D-CNNs to have the best receptive field size. But the OS-block targets at covering all sizes of receptive filed sizes and assign large weight on important sizes. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Mathematically, OS-block is a very general technique and can be extended to time series vision tasks by using the prime size design on the time dimension. This is because the video classification task and time series classification task share the same challenge (Xie et al., 2018; Bian et al., 2017; Tan et al., 2021; Liu et al., 2020; Li et al., 2020), which is the same region of interest might of different time scales for different data. Thus, using the kernel of various sizes will increase the probability to catch proper scales. However, in this paper, we mainly target the classic 1D time series classification, which is an active research area with many open problems (Fawaz et al., 2019; Zhang et al., 2020; Dempster et al., 2020) unsolven. ",
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+        "page_idx": 8
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+    {
+        "type": "text",
+        "text": "6 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The paper presents a simple 1D-CNN block, namely OS-block. It does not need any feature extraction scale tuning and can achieve a similar performance as models with the best feature extraction scales. The key idea is using prime number design to cover all RF sizes in an efficient manner. We conduct experiments to demonstrate that the OS-block can robustly capture the best time scale on datasets from multiple domains. Due to the strong scale capture ability, it achieves a series SOTA performance on multiple TSC benchmarks. Besides that, the OS-CNN results reveal two characteristics of 1D-CNN models, which will benefit the development of the domain. In the future, we could extend our work in the following aspects. Firstly, other than the prime kernel size design, there might be a more efficient design to cover all RF sizes. Secondly, the OS-block can work with existing deep neural structures to achieve better performance, but there might be unique structures or variants of those existing structures that are more suitable for the OS-block. Besides that, characteristics of OS-block are empirically analyzed via the way there must be a theoretical explanation of the characteristics. ",
+        "bbox": [
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+        "type": "text",
+        "text": "A APPENDIX ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "A.1 STATISTIC OF THE COMPARISON (FIX MODEL SIZE) ",
+        "text_level": 1,
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "More statistic results of the result in Figure 5 is shown in Figure 7, Figure 8 and Figure 9Dataset name ",
+        "bbox": [
+            174,
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+            756,
+            176
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/69f81b839642a02bba9f1609e89ee9db150dbce976d7f7517c5810623a16207b.jpg",
+        "image_caption": [
+            "Figure 7: The histogram statics the count of datasets by which percentile range of the blue line that the orange point belongs to. Specifically, we could see that for more than $56 \\%$ datasets $8 { + } 4 0$ out of 85 datasets), the result of OS-block is larger than 0.95 percentile. This means that, for an unknown dataset, using OS-block will have more than $56 \\%$ chance to achieve a better result than grid search from 20 candidate scales. When seeing the count of the number larger than 0.5 percentile, we could see that, for an unknown dataset, using OS-block will have more than $96 \\%$ chance to achieve a better result than selecting a random scale. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            178,
+            191,
+            820,
+            286
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/93dbaa9866ca4dc5fa3eeb1dfc9873aed143ee36d75c38a1149be5c7a5d5278e.jpg",
+        "image_caption": [
+            "Figure 8: The red line is the accuracy range obtained via subtracting the accuracy of OS-CNN from the accuracy range of FCN with various kernels. We sorted those datasets in ascending order. We could see that for most of the datasets, the highest value of the FCN accuracy range is lower than the accuracy of OS-CNN. Which supports the OS-block has the ability to capture the best scales. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            174,
+            424,
+            820,
+            594
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/766fc1ddf377b782abd14e8e304c7c67013e73fdea3c23b85acacba0d73296de.jpg",
+        "image_caption": [
+            "Figure 9: Sort datasets by dataset type and max accuracy range - accuracy of the OS-CNN. We could see that the best scale capture ability keeps the consistency cross different dataset types. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            174,
+            693,
+            820,
+            867
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "A.2 STATISTIC OF THE COMPARISON (FIX CHANNEL NUMBER) ",
+        "text_level": 1,
+        "bbox": [
+            179,
+            104,
+            616,
+            117
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "When we keep the number of channels constant in FCN, the statistic result will be as this. The OS-CNN still achieves similar performance as the model with the best scales. ",
+        "bbox": [
+            173,
+            142,
+            825,
+            171
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "image",
+        "img_path": "images/01ada7cc02e9e0365a0b64db02f2782683baaed600af6d3c8c9f076c73df1e32.jpg",
+        "image_caption": [
+            "Figure 10: Same static metric as that of Figure 5 and Figure 7Count of datasets by the RF tuning's percentile range that OS result belongs to "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            176,
+            212,
+            820,
+            385
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "image",
+        "img_path": "images/4b73be2d0adc8b99830ce8662f7a48869c0eceffebb4f7f81649a9d9698d68ec.jpg",
+        "image_caption": [
+            "Figure 11: Same static metric as that of Figure 8 "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            174,
+            464,
+            820,
+            640
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "image",
+        "img_path": "images/5c5a1bfa5e6120ac2c175b1b327708ea94c8a648310cb0e395340221a6687184.jpg",
+        "image_caption": [
+            "Figure 12: Same static metric as that of Figure 9 "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            173,
+            715,
+            820,
+            890
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "A.3 THE CD-DIAGRAM RESULT ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            103,
+            403,
+            117
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "The critical difference diagram shows the average rank of each method with Wilcoxon-Holm posthoc analysis between each series. ",
+        "bbox": [
+            171,
+            130,
+            823,
+            159
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "image",
+        "img_path": "images/2affe89e993b8099057696e41b51467da2278ef633255d4d58e43e8ad5a32dcf.jpg",
+        "image_caption": [
+            "Figure 13: SOTA for UEA 30 multivariate dataset archive "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            178,
+            186,
+            820,
+            280
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "image",
+        "img_path": "images/4a1ccd48dd3f175c819ca1681f826ffbcbc0f5bf009fc09c04fcba707359534e.jpg",
+        "image_caption": [
+            "Figure 14: SOTA on the UCR 85 datasets "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            179,
+            359,
+            813,
+            449
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "image",
+        "img_path": "images/b5a684f995315b3a55d6f0e4a49531e74a524c91fd52cb10a5270e3c6e861bea.jpg",
+        "image_caption": [
+            "Figure 15: SOTA on the UCR 128 datasets "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            181,
+            526,
+            794,
+            590
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "A.4 EXAMPLES OF THE TWO PHENOMENA ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            655,
+            478,
+            669
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "In the Figure 2, the Google speechcommands dataset is selected as the dataset to show the example. This is because, for this dataset, the relationship between performance and receptive field size is proportional (As it is shown in Figure 16). Thus, it is easy to control variables. What’s more, in Figure 18 and Figure 17, we show those two phenomena with more train and test split. ",
+        "bbox": [
+            174,
+            681,
+            825,
+            737
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "A.5 EXTEND OS-BLOCK WITH OTHER STRUCTURES ",
+        "text_level": 1,
+        "bbox": [
+            178,
+            753,
+            544,
+            768
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Layers in the OS-block and the OS-block itself are easy to extend with other complicated structures. Figure 19 gives an explanation about the how to view the multi-kernel layers in OS-block as a single layer, and gives an example that how to combine the layer with dilation. The Figure 4 shows that how to view the OS-block as a layer, and gives another two examples rather than OS-CNN. ",
+        "bbox": [
+            174,
+            780,
+            825,
+            835
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "image",
+        "img_path": "images/949e86a54b6eecb15bbdd283ca376e110ae3ea6497ade9eaf3e9d8512c6fe818.jpg",
+        "image_caption": [
+            "Figure 16: The relationship between performance and receptive field size are proportional "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            305,
+            104,
+            689,
+            309
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "image",
+        "img_path": "images/b135fba5c81d11ee1b6116d26ae7fa5dc84e7d49fa687c4411e1f56254d368e4.jpg",
+        "image_caption": [
+            "Figure 17: Lines in the figure are models with different sets of receptive field sizes. Lines with similar colors are models which have the same best receptive field size. We could see that the best receptive field size mainly dominates the performance in the set of receptive fieldsizes. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            178,
+            353,
+            818,
+            469
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "image",
+        "img_path": "images/d6d0b86b0bf7571ff2267b5610e54825894aa424380e4027b92f9387c71e496f.jpg",
+        "image_caption": [
+            "Figure 18: The label of each line denotes the kernel configuration of each 1D-CNN. For example, 5 5 1 1 1 means the 1D-CNN has five layers, and from the first layer to the last layer, kernel sizes of each layer are 5, 5, 1, 1, and 1. Lines of similar color are 1D-CNNs with the same receptive field size, and they are also of similar performance. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            176,
+            542,
+            821,
+            660
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "image",
+        "img_path": "images/718d3534b189c896e844b279b461eda926698493e0d5cea8fef659578e7b0d02.jpg",
+        "image_caption": [
+            "Figure 19: Purple color in those images are the zero mask and yellow denotes the location where has the ability to hold weight. Left: Convolution layers in of OS-block can be calculated parallelly, thus, each layer can be viewed as one convolutional layer with zero masks.(s) Right: layers in the OS-block can work with the dilation design "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            173,
+            746,
+            821,
+            847
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "A.6 EXPERIMENT RESULT OF OS-BLOCK WITH OTHER STRUCTURES ",
+        "text_level": 1,
+        "bbox": [
+            184,
+            104,
+            655,
+            117
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "The Figure 20 and Figure 21 show that applied OS-block with residual connection, ensemble, and multi-channel architectures (individually or together) could further improve the performance. The evaluation was on both UCR 85 and UEA 30 archives which contain datasets from different domains such as electrical devices analysis, Spectrum analysis, traffic analysis, EEG analysis. ",
+        "bbox": [
+            174,
+            128,
+            825,
+            185
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "image",
+        "img_path": "images/6d21c94fe3f81ca4e6379dbbfbc9cf3884e458ad896c38e24586427e400e98d5.jpg",
+        "image_caption": [
+            "Figure 20: Using the OS-block with residual connection and ensemble (individually or together) could increase the performance "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            176,
+            209,
+            823,
+            281
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "image",
+        "img_path": "images/d40bd168df3705d61c3518f7eedc78faa78ebabd1f046b9dde65f12a6a7b044f.jpg",
+        "image_caption": [
+            "Figure 21: Using the multi-channel architecture with OS-block could improve the performance "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            179,
+            362,
+            821,
+            459
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "A.7 COMPARE THE OS-BLOCK WITH OTHER DESIGNS ",
+        "bbox": [
+            174,
+            515,
+            558,
+            530
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "Mathematically, finding the optimal kernel configuration is challenging, for it is a constrained combinatorial optimization searching for the best configuration among an exponential number of candidates. Our contribution is a simple and effective model design that does not need to solve the complex optimization problems and achieves state-of-the-art performance on several benchmarks. ",
+        "bbox": [
+            174,
+            563,
+            825,
+            619
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "From the model size perspective, using prime numbers is more efficient than using even numbers or odd numbers. To be specific, to cover RF of range r, the model size complexity of using prime size kernels is $O ( r ^ { 2 } / l o g ( \\dot { r } ) )$ . On the other hand, no matter we use even number pairs or odd number pairs, kernel sizes in each layer, the model size complexity of using the sequence is $O ( r ^ { 2 } )$ . As Table 2 shows, compared with using odd number pairs or even numbers pairs prime numbers can achieve similar performance in a smaller model size. ",
+        "bbox": [
+            173,
+            626,
+            825,
+            710
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "table",
+        "img_path": "images/2bbb811f2ddaa465105e99b2ff54ea5b868e8a1508e28f2fdc45956bb6b240c0.jpg",
+        "table_caption": [
+            "Accuracy "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"6\">Number of parameters</td></tr><tr><td>Channel number</td><td>RF range</td><td>Prime numbers (Ours)</td><td></td><td>odd numbers</td><td>even numbers</td></tr><tr><td>16</td><td>1 to 45</td><td>304k</td><td></td><td>507k</td><td>491k</td></tr><tr><td>32</td><td>1 to 45</td><td></td><td>1,203 k</td><td>2,009k</td><td>1,948k</td></tr></table>",
+        "bbox": [
+            178,
+            723,
+            823,
+            808
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "table",
+        "img_path": "images/8d3db78ba688dfee543138d8553d8eab0c1518c4aa6ea5a5d5db107d0e3eacee.jpg",
+        "table_caption": [
+            "Table 2: Model size and performance comparison on Google SpeechCommands dataset "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Channel number</td><td>RF range</td><td>Prime numbers (Ours)</td><td>odd numbers</td><td>even numbers</td></tr><tr><td>16</td><td>1 to 45</td><td>0.7524</td><td>0.7687</td><td>0.7561</td></tr><tr><td>32</td><td>1 to 45</td><td>0.7845</td><td>0.7783</td><td>0.7725</td></tr></table>",
+        "bbox": [
+            178,
+            835,
+            820,
+            886
+        ],
+        "page_idx": 16
+    }
+]

parse/dev/QNBzcgY0f4e/QNBzcgY0f4e.md

@@ -0,0 +1,526 @@
+# Easy incremental learning methods to consider for commercial fine-tuning applications
+
+Anonymous Author(s)   
+Affiliation   
+Address   
+email
+
+# Abstract
+
+Fine-tuning deep learning models for commercial use cases is growing exponentially as more and more companies are adopting AI to enhance their core products and services, as well as automate their diurnal processes and activities. However, not many countries like the U.S. and those in Europe follow quality data collection methods for AI vision or NLP related automation applications. Thus, on many of these kinds of data, existing state-of-the-art pre-trained deep learning models fail to perform accurately, and when fine-tuning is done on these models, issues like catastrophic forgetting or being less specific in predictions as expected occur. Hence, in this paper, simplified incremental learning methods are introduced to be considered in existing fine-tuning infrastructures of pre-trained models (such as those available in huggingface.com) to help mitigate the aforementioned issues for commercial applications. The methods introduced are: 1) Fisher Shut-off, 2) Fractional Data Retention and 3) Border Control. Results show that when applying these methods on vanilla pre-trained models, the models are in fact able to add more to their knowledge without hurting much on what they had learned previously.
+
+# 16 1 Introduction
+
+17 Many companies and organizations today are adopting AI in automation, automating their daily   
+18 processes and activities, as well as offering them in their core products and services. Automation   
+19 has traditionally been in the industry for many years, as a means for which economics of scale could   
+20 be acheived so as to remain competitive in the market. Now with AI, more and more intelligence is   
+21 being brought into automation, and in countries like India, organizations are beginning to adopt AI   
+22 for this particular purpose.   
+23 With recent advancements in AI vision and NLP models such as the GPT-3, Jurassic-1, and so on,   
+24 organizations today are using AI for 1) Document Reading and Understanding, 2) Online Proctoring,   
+25 3) Chatbots, 4) Intelligent Information Parsing and other application related process automations.   
+26 Given these use cases, AI solutions need to be specific to their processes, but yet be an addition to   
+27 their generally known formats. This in a sense, is more like making use of a human employee who   
+28 has some kind of general education on various tasks or processes but still is required to learn the   
+29 companies counterparts well and in detail before he/she is allowed to execute them. These processes   
+30 can include between, reading customer emails for entering relevant information about their product   
+31 requirements onto a structured database, to understanding various types of printed documents for   
+32 information parsing, and to identifying newer objects for either document filtering or malicious   
+33 activity detection.   
+34 For natural language related tasks, powerful models like the GPT-3 are now being widely used, but   
+35 they require good prompt engineering skills to get the best out of them. Also, given that they are   
+36 probabilistic models, the generated outputs can sometimes falter away from what is expected, and   
+37 this can become a problem when selling it to customers, because even the slightest faltering may not   
+38 be acceptable to them at all. Hence, to reduce this, more and more examples have to be provided in   
+39 the prompt, and this can come at a high cost not suitable for low cost of living countries like India.   
+40 The other workaround is to fine-tune the model on the new datasets, but this has epoch limitations   
+41 on how deeply it can fit on the new dataset without hurting the body of general knowledge it gained   
+42 earlier. Also, fine-tuning models like the GPT-3 comes at a very high cost now-a-days, and is no   
+43 more an option. This leaves the automation builders to use huggingface.com transformers instead.   
+44 In vision, although state-of-the-art pre-trained deep learning models are able to achieve human level   
+45 performance on a variety of inputs, they can only perform so in upto close to high quality inputs. If   
+46 the quality goes lower, they fail terribly. Not all organizations have a good quality data collection   
+47 process involved for applying automation, and this is ubiquitously the case in many parts of the world.   
+48 So it becomes quite difficult to sell AI as a human-level performer, and at this point AI becomes of   
+49 lesser use than it could potentially be.   
+50 Another approach typically used to resolve such problems is to employ transfer learning, which   
+51 typically involves replacing the last layers of the model with a new model to get the specific outputs   
+52 required. Some examples done in research are Too, et al. (2019), Dif & Elberrichi (2020), Alshalali   
+53 & Joysula (2018), Jung, et al. (2015), Qian, et al. (2021) and Vrbanciˇ c & Podgorelec (2020). While ˇ   
+54 this may not seem to be a problem with vision based tasks, it is definitely a problem with natural   
+55 language based tasks. This is because the final layers of the natural language models have all the vital   
+56 information of language structure that help with the language generative process. When this is to   
+57 be changed, catastrophic forgetting can happen. Catastrophic forgetting is a phenomenon in which   
+58 previously learned knowledge is lost partly by the application of new data for training. Also, with   
+59 vision based tasks, when the requirement is to just improve the performance on lower quality data,   
+60 transfer learning may not be the appropriate approach. Fine-tuning for these must involve the final   
+61 layers of the model which could inevitably lead to catastrophic forgetting on the higher quality inputs.   
+62 This brings the only solution towards incremental learning. This type of learning is all about   
+63 learning on newer datasets without having the side-effects catastrophic forgetting, and there has been   
+64 substantial amount of research done in this area. Luo, et al. (2020) summarizes all the work that has   
+65 happened in this area so far. There are several approaches to implementing incremental learning on   
+66 pre-trained models, some of which will be discussed in the forthcoming sections. In this paper, a   
+67 few of these approaches will be simplified for commercial applications along with novel intuitive   
+68 additions to further help the learning process. The paper introduces: 1) Fisher Shut-off which is a   
+69 simplification of the work done by Kirkpatrick, et al. (2017), 2) Fractional Data Retention which   
+70 adopts ideas from Castro, et al. (2018), and 3) Border Control which is an extension to the idea   
+71 outlined by Ren, et al. (2018) on reweighting examples by employing a method similar to Adaboost.   
+72 The last one is the novel addition as it formulates a different approach to retaining salient examples   
+73 for incremental learning. It is based on the work by Ruping (2001) on incremental learning with   
+74 SVMs. But since SVMs are too complex in the context on neural networks, a similar but simplified   
+75 approach is proposed.   
+76 The purpose of this work is to initiate the development of a new infrastructure for commercial   
+77 fine-tuning of pre-trained models with simplified incremental learning methods.   
+78 The rest of this paper proceeds as follows: Section 2 will provide a brief discussion on incremental   
+79 learning methods developed so far, followed by the proposal of simplified incremental learning   
+80 methods in Section 3. Section 4 will show sample results of the proposed methods on a vanilla   
+81 pre-trained model using a toy dataset. A toy dataset is used for the only purpose of providing   
+82 visualizations on the performance of the proposed methods. Nevertheless, these methods can be   
+83 extended on to real world datasets. The paper then concludes in Section 5 discussing steps forward   
+84 for implementation.
+
+# 85 2 Incremental Learning
+
+86 This section is a summary of the review published by Luo, et al. (2020). In this review, four different   
+87 types of strategies for incremental learning are highlighted, and every work published in this area   
+88 uses either one or more such strategies. Some examples are Castro, et al. (2018) and He, et al. (2020).   
+89 The four strategies are:
+
+• Architectural • Regularization • Rehearsal • Pseudo-Rehearsal
+
+94 The following subsections will disccuss these briefly.
+
+# 2.1 Architectural Strategy
+
+96 This strategy is similar to boosting techniques where multiple models are trained. But when used in the context of incremental learning, each model is trained on a different task separately. Then another 98 meta-model that effectively selects which model to use for inference is trained. The work done by 99 Poliker, et al. (2001) resembles this in many ways. In this work, multiple classifiers are trained with 0 different training sets, and then a Adaboost style of ensemble learning is employed to combine the model outputs.
+
+102 Another interesting work is by Rusu, et al. (2016) on Progressive Neural Networks (PNN). In this   
+103 work, a neural network is trained sequentially on different tasks or training sets. However, each time,   
+104 new neurons are added in each layer with new weights, and the weights of the previously learned   
+105 neural network are frozen. Then, to prevent catastrophic forgetting, the outputs of each layer of the   
+106 previous neural network on the earlier training set are used in addition to the new task or training   
+107 set, when training the new layer neurons. The results on this type of incremental learning were quite   
+108 encouraging that it set a new direction in the research of dynamically expanding networks that could   
+109 make better use the neural networks capacity than the PNN. In fact, it will be seen later that the Fisher   
+110 Shut-off method proposed in this paper inherently employs the idea of PNNs.
+
+# 2.2 Regularization Strategy
+
+112 In this strategy, as the name suggest, a regularization term is added in the loss function that measures   
+113 the importance of old knowledge when learning on a new training set. The representive work done in   
+114 this is Kirkpatrick, et al. (2017), whereby they introduce the concept of Elastic Weight Consolidation   
+115 (EWC) by means of a Fisher Information Matrix. The EWC brings about the regularization term in   
+116 the loss function as
+
+$$
+R ( w ) = \sum _ { i } \frac { \lambda } { 2 } F _ { i } ( w _ { i } - w _ { i , o l d } ) ^ { 2 }
+$$
+
+117 where $F _ { i }$ is the Fisher Information Matrix which suggests the importance of the $i$ -th weight trained   
+118 on the old (or previous) training set. Here, as one could speculate, the term Fisher Shut-off proposed   
+119 in this paper actually derives itself from the Fisher Information Matrix, meaning that this matrix is   
+120 used as the basis for shutting off the training of certain weights when training on a new set.   
+121 Another popular type of regularization strategy is Knowledge Distillation introduced by Hinton, et al.   
+122 (2015). In this method, knowledge from an ensemble of models trained on different tasks (or training   
+123 sets) separately are distilled into a smaller model that can be deployed much easily for inference.   
+124 There are many huggingface.com transformers that are a product of such knowledge distillation.   
+125 The distillation ensures that the smaller model holds all the knowledge of the ensemble, and that it   
+126 can infer as good as it. Distillation is done by setting soft-targets on the smaller network from all the   
+127 earlier training sets of the ensemble. The soft-targets are the output logits from the ensemble models   
+128 on their respective trained datasets.
+
+# 129 2.3 Rehearsal and Pseudo-Rehearsal Strategies
+
+130 Rehearsal strategies in incremental learning make use of the earlier training sets when training a   
+131 model on new tasks or training sets. This by far is the simplest of all incremental learning strategies   
+132 that ensures catastrophic forgetting is prevented. The only issue is that when this strategy is used for   
+133 deep learning models trained on large datasets, the training on new datasets could become extremely   
+134 slow and even time consuming before any fruitful results are achieved. Hence, newer research work in   
+135 this area formulate methods for retaining only the most important data points to prevent catastrophic   
+136 forgetting. The work done by Castro, et al. (2018) is an example of this. In this work, selection and   
+137 removal mechanisms on data are introduced for assimilation into a memory network.   
+138 Talking about memory networks, the Pseudo-Rehearsal strategy involves training an additional data   
+139 generator to generate the samples, the neural network was trained on earlier. Hence, newer research   
+140 in this area involve GANs for data generation. Examples are Odena, et al. (2017) and Wu, et al.   
+141 (2018).
+
+# 142 3 Proposed Incremental Learning Methods
+
+143 Commercial applications always require simplistic implementations of advanced methods no matter   
+144 how complex they may be. Therefore, it is for this purpose alone this paper proposes some simplified   
+145 methods for implementing incremental learning. As metioned earlier in Section 1, these methods are:   
+146 1) Fisher Shut-off, 2) Fractional Data Retention, and 3) Border Control. This section covers them in   
+147 detail.
+
+# 148 3.1 Fisher Shut-off
+
+149 As mentioned in the previous section, the term Fisher Shut-off derives itself from the Fisher Infor  
+150 mation Matrix which weighs the importance of weights trained on previous datasets. Hence, in this   
+151 sub-section, a brief overview of the details behind this matrix is covered with the help of Aich (2021).   
+152 Let $\mathcal { D }$ represent a dataset coming from a stream of data for incremental learning. Then $p ( w | \mathcal { D } )$   
+153 represents the model trained on data $\mathcal { D }$ . This means that to train a model on a new dataset, the   
+154 following posterior must satisfy:
+
+$$
+p ( w | \mathcal D _ { n e w } ) = \frac { p ( \mathcal D _ { n e w } | w ) p ( w | \mathcal D _ { o l d } ) } { p ( \mathcal D _ { n e w } ) }
+$$
+
+155 Note here that $p ( w | \mathcal { D } _ { o l d } )$ is written in place of $p ( w )$ because when $\mathcal { D } _ { n e w }$ is applied to the model, the   
+156 weights $w$ have already been trained with $\mathcal { D } _ { o l d }$ . Hence, given the model, $p ( w | \mathcal { D } _ { o l d } )$ , the log-likelihood   
+157 loss on $\mathcal { D } _ { n e w }$ becomes,
+
+$$
+\begin{array} { r l } & { \mathcal { L } _ { \mathcal { D } _ { n e w } } ( w ) = l o g ( p ( w | \mathcal { D } _ { n e w } ) ) } \\ & { \qquad = l o g ( p ( \mathcal { D } _ { n e w } | w ) ) + l o g ( p ( w | \mathcal { D } _ { o l d } ) ) - l o g ( p ( \mathcal { D } _ { n e w } ) ) } \\ & { \qquad \approx l o g ( p ( \mathcal { D } _ { n e w } | w ) ) + l o g ( p ( w | \mathcal { D } _ { o l d } ) ) } \end{array}
+$$
+
+158 Here, the $l o g ( p ( \mathcal { D } _ { n e w } | w ) )$ equals the cross-entropy loss of the model on $\mathcal { D } _ { n e w }$ while $l o g ( p ( w | \mathcal { D } _ { o l d } ) )$   
+159 is loss of the model on $\mathcal { D } _ { o l d }$ . To ensure that catastrophic forgetting does not occur on $\mathcal { D } _ { o l d }$ in its   
+160 absence while training on $\mathcal { D } _ { n e w }$ , the loss on $\mathcal { D } _ { o l d }$ will have to be approximated using $w$ alone. To do   
+161 this, the Taylor’s expansion on $l o g ( p ( w | \mathcal { D } _ { o l d } ) )$ is taken as,
+
+$$
+\begin{array} { r l } & { \mathcal { L } _ { \mathcal { D } _ { o l d } } ( w ) \approx \mathcal { L } ( w ) \big | _ { \mathcal { D } _ { o l d } } + \left( \frac { \partial \mathcal { L } ( w ) } { \partial w } \Big | _ { \mathcal { D } _ { o l d } } \right) + \frac { 1 } { 2 } ( w - w \big | _ { \mathcal { D } _ { o l d } } ) ^ { T } \left( \frac { \partial ^ { 2 } \mathcal { L } ( w ) } { \partial ^ { 2 } w } \Big | _ { \mathcal { D } _ { o l d } } \right) ( w - w \big | _ { \mathcal { D } _ { o l d } } ) } \\ & { \qquad \approx \mathcal { L } ( w ) \big | _ { \mathcal { D } _ { o l d } } + \frac { 1 } { 2 } ( w - w \big | _ { \mathcal { D } _ { o l d } } ) ^ { T } \left( \frac { \partial ^ { 2 } \mathcal { L } ( w ) } { \partial ^ { 2 } w } \Big | _ { \mathcal { D } _ { o l d } } \right) ( w - w \big | _ { \mathcal { D } _ { o l d } } ) } \end{array}
+$$
+
+since technically 162 $\begin{array} { r } { \frac { \partial \mathcal { L } ( w ) } { \partial w } \bigg | _ { \mathcal { D } _ { o l d } } = 0 } \end{array}$ , if the model is trained well on $\mathcal { D } _ { o l d }$ . Then, noting that the last term 163 in (4) is equivalent to a regularization term, this term alone could be considered as the loss on $\mathcal { D } _ { o l d }$
+
+164 for preventing catastrophic forgetting. In doing so, the Fisher Information Matrix will equal to the   
+165 Hessian, $\frac { \partial ^ { 2 } \mathcal { L } ( w ) } { \partial ^ { 2 } w } \bigg | _ { \mathscr { D } _ { o l d } } .$ This Hessian, $\mathcal { H }$ , can be simply computed by the model gradients $\frac { \bar { \partial \mathcal { L } } ( w ) } { \partial w } \bigg | _ { \mathscr { D } _ { o l d } }$   
+166 assuming that not all gradients are zero, as,
+
+$$
+\mathcal { H } = \frac { \partial \mathcal { L } ( w ) } { \partial w } \bigg | _ { \mathcal { D } _ { o l d } } \cdot \frac { \partial \mathcal { L } ( w ) } { \partial w } \bigg | _ { \mathcal { D } _ { o l d } } ^ { T }
+$$
+
+167 Doing so, and keeping only the diagonal terms, would imply that the model gradients are more   
+168 than enough to weigh the important weights of the model trained on $\mathcal { D } _ { o l d }$ . Replacing (5) in (4) and   
+169 substituting in (3) would give the loss on $\mathcal { D } _ { n e w }$ as,
+
+$$
+\mathcal { L } _ { \mathcal { D } _ { n e w } } ( w ) \approx l o g ( p ( \mathcal { D } _ { n e w } | w ) ) + \frac { 1 } { 2 } ( w - w \big | _ { \mathcal { D } _ { o l d } } ) ^ { T } \left( \frac { \partial \mathcal { L } ( w ) } { \partial w } \bigg | _ { \mathcal { D } _ { o l d } } \cdot \frac { \partial \mathcal { L } ( w ) } { \partial w } \bigg | _ { \mathcal { D } _ { o l d } } ^ { T } \right) ( w - w \big | _ { \mathcal { D } _ { o l d } } )
+$$
+
+170 which to an extent implies that if the model gradients on $\mathcal { D } _ { o l d }$ are absolutely zero, they get trained on   
+171 $\mathcal { D } _ { n e w }$ without regularization, while those that are not, get regularized towards $w \big | _ { \mathscr { D } _ { o l d } }$ .   
+172 This is what the proposed Fisher Shut-off exploits. In Fisher Shut-off, all weights of the model   
+173 trained on $\mathcal { D } _ { o l d }$ that do not have absolute zero gradients get shut-off for training on $\mathcal { D } _ { n e w }$ , while the   
+174 remaining that do take part. Also, since in practice $R e L U$ functions are commonly used in deep   
+175 learning models as the activation functions of the neurons, shutting off these weights becomes as   
+176 simple as setting a condition. Figure 1 shows a sample performance of Fisher Shut-off on a regression   
+177 model trained sequentially on mutually exclusive batches of data. These batches could represent the   
+178 different tasks or training sets.   
+179 However, when it comes to classification, simple shut-off does not work completely. This is because,   
+180 while in regression problems datasets could inherently employ some kind of piece-wise nonlinear fit   
+181 in their distributions, the same cannot always be guaranteed in classification. Thus, in classification,   
+182 the shut-off weights must also take part in training. And, as per (1), there is a learning constant   
+183 required in the regularization to ensure that the right balances between $\mathcal { D } _ { n e w }$ and $\mathcal { D } _ { o l d }$ are met on   
+184 these weights. This paper provides a novel learning constant determination for this regularization.   
+185 This is detailed in Appendix A.   
+86 Also in regression problems, if datasets have batch distributions that are quite far apart from each   
+87 previous batch, then Fisher-Shutoff may not fully work too. Appendix B shows some of these   
+188 examples
+
+![](images/ec3ca6e1de828ff9f19c334a4f580525e37d7f6bbb827e170bad1c560561bda1.jpg)  
+Figure 1: Fisher Shut-off on a regression model on six mutually exclusive batches of data. Blue dots represent the overall dataset, while green square dots are the batch or task data. The red line is the model’s output after each batch is fed to it. Fisher Shut-off is used from Batch $\# 2$ onwards.
+
+# 3.2 Fractional Data Retention
+
+This is a very simply proposal. The idea is to retain only a fraction of the data trained on the neural network on the earlier tasks or training sets. There is nothing more to this. However, banking on the ideas of selection highlighted in Castro, et al. (2018), whereby data is selected based on their proximity to cluster centers, to be more representative of the classes, this paper uses this as the baseline idea behind its proposal on Fractional Data Retention. Thus in Fractional Data Retention, a fraction of the data within the data cluster is retained and appended in every stage of incremental learning.
+
+# 197 3.3 Border Control
+
+The most important requirement when incrementally learning classes is to ensure that the decision boundaries of the earlier training tasks are protected as much as possible when training on new sets. If data points are used for this purpose, it would seem that, those that lie closest to the decision boundaries after training would be the most important ones to retain, for any succeeding incremental learning tasks. Thus, the Border Control method proposed in this paper exploits this. Ruping (2001) used SVMs to identify these data points as the support vectors that helped define the overall decision boundaries. But with deep learning models or vanilla neural networks, SVM is quite complex and therefore in order to be able retain data points closest to the decision boundaries, a different selection mechanism is required. This selection mechanism could instead be based on selecting data points on how large the absolute errors in sigmoidal outputs are for the applied dataset, as the data points closest to the decision boundaries have this inherent property.
+
+209 Furthermore, since real world data can be quite complex, it would be necessary to not only select data   
+210 points based on how large their errors in sigmoidal outputs are, but also those points that are far away   
+211 from them. This is because, given the context of incremental learning where there is a high chance   
+212 that newer training sets may have data points that could potentially set newer decision boundaries in   
+213 those fartherest regions, these data points would help protect those.   
+214 Hence in Border Control, the top- $\mathtt { k }$ data points that have the largest absolute errors in the sigmoidal   
+215 outputs and their respective top- $\mathtt { k }$ fartherest data points are retained in every task or training set   
+216 for further incremental learning. These points are appended to the newer training sets before further   
+217 training is applied.
+
+# 218 4 Sample Results
+
+219 The proposed methods are tested on a toy dataset, as mentioned in Section 1, only to provide some   
+220 visuals on how the incremental learning progresses using the proposed methods. Figure 2 shows this   
+221 dataset. A vanilla deep neural network of size, 1000-1000-1000-1000-3, is used for incrementally   
+222 learning batches of data from this toy dataset. The activation functions for all layers are $R e L U$ except   
+223 for the output which is a sof tmax. All weights are uniformly but randomly initialized with a single   
+224 random seed to make the results comparable. The weights are also scaled by a $\frac { 2 } { \sqrt { n } }$ factor to ensure   
+225 that minimal overfitting occurs during training. Here $n$ is the layer fan-in.   
+226 To visualize incremental learning on the proposed methods, the dataset is divided into 6 batches   
+227 with mututally exclusive data points. This gives roughly between 100 to 200 data points in each   
+228 batch, a size that is commonly used when training neural networks of this size. Figure 3 shows this.   
+229 In this figure, it can be clearly seen that the batch distributions on the class data for incremental   
+230 learning do not always form a piece-wise nonlinear fit, and therefore, plain shut-off of weights cannot   
+231 fully retain knowledge learned earlier. Also, among these distributions, some allowed incremental   
+232 learning to happen easily, while others did not, and the distribution shown in Figure 3 is one such.   
+233 Table 1 summarizes the results of the proposed methods on this particular distribution. For other batch   
+234 distributions, similar results could be achieved. Note here that quite some ML-Ops were required to   
+235 achieve the results in Table 1. This was especially the case for those that employed Fisher Shut-off,   
+236 since this method has a regularization constant that requires adapting on each batch. Furthermore,   
+237 training on each batch was stopped once $1 0 0 . 0 \%$ accuracy was obtained on the batch. This left quite   
+238 some data points to lie very close to the boundary lines or in some cases just right on them. Thus,   
+239 the neural network was very vulnerable to catastrophic forgetting when succeeding batch trainings   
+240 occurred as part of incremental learning.   
+241 However, taking a look at Table 1, it can be seen that when Fisher Shut-off is applied, additional   
+242 leverage against catastrophic forgetting occurs on each incremental batch, than when it is not used.   
+243 And, among the three methods proposed in this paper, the Border Control method shows much   
+244 stronger performance. In Figure 4, sample decision boundaries learned when each incremental batch   
+245 is applied to the neural network using Fisher Shut-off and Border Control together is shown. A topk   
+246 value of 5 is used for the Border Control. Also, note in Figure 4 that the red circles mark the border   
+247 points accumulated on each batch. It can be seen that they clearly assume the data points closest   
+248 to the decision boundaries, as well as those far away from it. All with respect to their batches. For   
+249 the far away data points, their purpose can be clearly seen between batches #1 and $\# 2$ , where the   
+250 fartherest points of class 2 in Batch #1 helped protect the decision boundaries from the data points   
+251 of class 0 in Batch $\# 2$ . This means that more complex datasets can be accommodated by simply   
+252 applying Border Control. More examples are shown in Appendix C.
+
+![](images/ed5b8993eaca01d170d93842c74b1f8afc29195bd92a7249a0f7e6d54ce3a8c4.jpg)  
+Figure 2: The toy dataset having three nonlinearly arranged classes.
+
+![](images/b02e14d6cf3d7912dafbbcf85b828e0529858490504fb69b8d48e1be08459fa6.jpg)  
+Figure 3: Batches on the toy dataset.
+
+Table 1: Performance of proposed methods on the dataset of Figure 2   
+
+<table><tr><td rowspan="2">Method</td><td colspan="6"> Sample accuracy on accumulated dataset after Batch1</td></tr><tr><td>#1</td><td>#2</td><td>#3</td><td>#4</td><td>#5</td><td>#6</td></tr><tr><td>No Incremental Learning</td><td>100.0%</td><td>90.98%2</td><td>92.76%</td><td>94.89%</td><td>98.32%</td><td>96.11%</td></tr><tr><td>Fisher Shut-off (FS)</td><td>100.0%</td><td>99.74%</td><td>98.19%</td><td>98.88%</td><td>98.96%</td><td>96.89%</td></tr><tr><td>Frac. Data Ret. (FDR)[10%]</td><td>100.0%</td><td>97.94%</td><td>98.39%</td><td>98.89%</td><td>98.71%</td><td>98.67%</td></tr><tr><td>FDR[20%]</td><td>100.0%</td><td>98.71%</td><td>98.59%</td><td>99.36%</td><td>98.97%</td><td>98.78%</td></tr><tr><td>Border Ctrl. (BC)[t opk = 5]</td><td>100.0%</td><td>100.0%</td><td>100.0%</td><td>99.84%</td><td>100.0%</td><td>100.0%</td></tr><tr><td>BC[topk = 10]</td><td>100.0%</td><td>100.0%</td><td>100.0%</td><td>99.84%</td><td>100.0%</td><td>100.0%</td></tr><tr><td>FS + FDR[10%]</td><td>100.0%</td><td>99.74%</td><td>98.79%</td><td>99.52%</td><td>99.23%</td><td>98.78%</td></tr><tr><td>FS + FDR[20%]</td><td>100.0%</td><td>100.0%</td><td>99.19%</td><td>99.52%</td><td>99.48%</td><td>99.11%</td></tr><tr><td>FS +BC[topk = 5]</td><td>100.0%</td><td>100.0%</td><td>100.0%</td><td>99.84%</td><td>100.0%</td><td>100.0%</td></tr><tr><td>FS + BC[topk = 10]</td><td>100.0%</td><td>100.0%</td><td>100.0%</td><td>100.0%</td><td>100.0%</td><td>100.0%</td></tr></table>
+
+![](images/5bccdefef0dd25c13f1ecc98bcf95de7a924e776d8da83295052a7d16b995c74.jpg)  
+Figure 4: Incremental learning using Fisher Shut-off and Border Control together $[ t o p k = 5 ]$ ]. Black circles mark the batch data, while the red circles mark the accumulated border points.
+
+Also, to add on further to this, for the most difficult incremental learning applications such as learning new classes as highlighted in Castro, et al. (2018) and He, et al. (2020), Border Control can help leverage the many issues associated with it like class imbalance, concept drift and so on.
+
+# 5 Conclusion
+
+257 To summarize the work in this paper, three simplified methods for implementing incremental learning   
+258 for commercial fine-tuning of pre-trained models was proposed. Results showed that while Border   
+259 Control performed the best, Fisher Shut-off was able to leverage the performances. However, dataset   
+260 used in this paper was a toy dataset and not one of the benchmark datasets typically used for   
+261 incremental learning. Hence, testing these methods on the benchmark datasets is a potential next step   
+262 forward. Then, preparing the prerequisites for each model available, like say in huggingface.com,   
+263 for incremental learning must be done so that automation companies or any other AI organization   
+264 can make use of them. From the methods proposed in this paper, the prerequisites would be: 1)   
+265 the Shut-off matrix for the neural network weights, and 2) the border points for each of the learned   
+266 classes. Additionally, an ML-Ops infrastructure can be provided to optimize the performances of   
+267 the models that employ the Fisher Shut-off method. Metrics like the Backward Transfer (BWT) and   
+268 Forward Transfer (FWT) proposed in Lopez-Paz & Ranzato (2017) can be used for this purpose.
+
+# 269 References
+
+270 [1] Aich, A. (2021) Elastic weight consolidation (EWC): Nuts and bolts. arXiv preprint arXiv:2105.04093.   
+271 [2] Alshalali, T. & Joysula, D. (2018) Fine-Tuning of Pre-Trained Deep Learning Models with Extreme Learning   
+272 Machine. IEEE International Conference on Computational Science and Computational Intelligence (CSCI), pp.   
+273 469-473.   
+274 [3] Castro, F., Marín-Jiménez, M.J., Guil, N., Schmid, C. & Alahari, K. (2018) End-to-end incremental learning.   
+275 Proceedings of the European Conference on Computer Vision (ECCV), pp. 233-248.   
+276 [4] Dif, N. & Elberrichi, Z. (2020) A New Intra Fine-Tuning Method. International Journal of Service Science,   
+277 Management, Engineering, and Technology, 11(2), pp. 16-40.   
+278 [5] He, J., Mao, R., Shao, Z. & Zhu, F. (2020) Incremental learning in online scenario. IEEE/CVF Conference   
+279 on Computer Vision and Pattern Recognition, pp. 13926-13935.   
+280 [6] Hinton, G., Vinyals, O. & Dean, J. (2015) Distilling the Knowledge in a Neural Network. arXiv preprint   
+281 arXiv:1503.02531, 2(7).   
+282 [7] Jung, H., Lee, S., Yim, J., Park, S. & Kim, J. (2015) Joint fine-tuning in deep neural networks for facial   
+283 expression recognition. Proceedings of the IEEE International Conference on Computer Vision, pp. 2983-2991.   
+284 [8] Kirkpatrick, J., Pascanu, R., Rabinowitz, N., Veness, J., Desjardins, G., Rusu, A.A., Milan, K., Quan, J.,   
+285 Ramalho, T., Grabska-Barwinska, A. & Hassabis, D. (2017) Overcoming catastrophic forgetting in neural   
+286 networks. Proceedings of the National Academy of Sciences, 114(13), pp. 3521-3526.   
+287 [9] Lopez-Paz, D. & Ranzato, M.A. (2017) Gradient episodic memory for continual learning. Proceedings of   
+288 Neural Information Processing Systems (NIPS), pp. 6467-6476.   
+289 [10] Luo, Y., Yin, L., Bai, W. & Mao, K. (2020) An Appraisal of Incremental Learning Methods. Entropy,   
+290 22(11), pp. 1190-1216.   
+291 [11] Odena, A., Olah, C. & Shlens, J. (2017) Conditional image synthesis with auxiliary classifier GANs.   
+292 International Conference on Machine Learning (ICML), pp. 2642–2651.   
+293 [12] Polikar, R., Udpa, L., Udpa, S. & Honavar, V. (2001) Learn++: An Incremental Learning Algorithm for   
+294 Supervised Neural Networks. IEEE Transactions on Systems, Man, and Cybernetics, part C (applications and   
+295 reviews), 31(4), pp. 497-508.   
+296 [13] Qian, X., Zhang, C., Yella, J., Huang, Y., Huang, M.C. & Bom, S. (2021) Soft sensing model visualization:   
+297 Fine-tuning neural network from what model learned. IEEE International Conference on Big Data (Big Data),   
+298 pp. 1900-1908.   
+299 [14] Ren, M., Zeng, W., Yang, B. & Urtasun, R. (2018) Learning to reweight examples for robust deep learning.   
+300 International Conference on Machine Learning (ICML), pp. 4334-4343.   
+301 [15] Ruping, S. (2001) Incremental learning with support vector machines. IEEE International Conference on   
+302 Data Mining, pp. 641-642.   
+303 [16] Rusu, A.A., Rabinowitz, N.C., Desjardins, G., Soyer, H., Kirkpatrick, J., Kavukcuoglu, K., Pascanu, R. &   
+304 Hadsell, R. (2016) Progressive neural networks. arXiv preprint arXiv:1606.04671.   
+305 [17] Too, E., Yujian, L., Njuki, S. & Yingchun, L. (2019) A comparative study of fine-tuning deep learning   
+306 models for plant disease. Computers and Electronics in Agriculture, 161, pp. 272-279.   
+307 [18] Vrbanciˇ c, G. & Podgorelec, V. (2020) ˇ Transfer learning with adaptive fine-tuning. IEEE Access, Volume 8,   
+308 pp. 196197-196211.   
+309 [19] Wu, Y., Chen, Y.P., Wang, L.J., Ye, Y.C., Liu, Z.C., Guo, Y.D., Zhang, Z.Y. & Fu, Y. (2018) Incremental   
+310 Classifier Learning with Generative Adversarial Networks. arXiv preprint arXiv:1802.00853.
+
+The checklist follows the references. Please read the checklist guidelines carefully for information on how to answer these questions. For each question, change the default [TODO] to [Yes] , [No] , or [N/A] . You are strongly encouraged to include a justification to your answer, either by referencing the appropriate section of your paper or providing a brief inline description. For example:
+
+• Did you include the license to the code and datasets? [Yes] See Section ??.   
+• Did you include the license to the code and datasets? [No] The code and the data are proprietary.   
+• Did you include the license to the code and datasets? [N/A]
+
+Please do not modify the questions and only use the provided macros for your answers. Note that the Checklist section does not count towards the page limit. In your paper, please delete this instructions block and only keep the Checklist section heading above along with the questions/answers below.
+
+1. For all authors...
+
+(a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? [Yes]   
+(b) Did you describe the limitations of your work? [Yes] See Sections 4 and 5   
+(c) Did you discuss any potential negative societal impacts of your work? [N/A]   
+(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes]
+
+2. If you are including theoretical results...
+
+(a) Did you state the full set of assumptions of all theoretical results? [Yes] See Section 3 and Appendix A   
+(b) Did you include complete proofs of all theoretical results? [Yes] See Section 3 and Appendix A
+
+3. If you ran experiments...
+
+(a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [Yes] As a supplemental material   
+(b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [No] But it’s in the supplemental material   
+(c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? [No] But additional examples are shown in Appendix C   
+(d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)? [N/A]
+
+4. If you are using existing assets (e.g., code, data, models) or curating/releasing new assets...
+
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+(b) Did you mention the license of the assets? [N/A]   
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+(d) Did you discuss whether and how consent was obtained from people whose data you’re using/curating? [N/A]   
+(e) Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content? [N/A]
+
+5. If you used crowdsourcing or conducted research with human subjects...
+
+(a) Did you include the full text of instructions given to participants and screenshots, if applicable? [N/A]   
+(b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable? [N/A]   
+(c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? [N/A]
+
+362 Here, the derivation of regularization constant for Fisher Shut-off method is detailed. To start with,   
+363 let the neural network be defined as,
+
+$$
+y = w ^ { T } \phi ( x , \omega )
+$$
+
+364 Here, $w$ is the weights of the output layer, $\phi ( \cdot )$ is the output of the preceding layer, $x$ is the input and   
+365 $\omega$ represents the rest of the weights of the neural network. Throughout the derivation, we will be   
+366 dealing with only the output layer, and so the $\phi ( x , \omega )$ will be written in short form as $\Phi$ from here on.   
+367 Let $e _ { k }$ denoted the error of fitting in the $k$ -th iteration, and $g _ { k }$ denote the error gradient. This would   
+368 mean that $g _ { k } = \Phi _ { k } e _ { k }$ .   
+369 Then, given the regularization term in (6), let $\tilde { w }$ denote difference in weights, between the new   
+370 training and the previous training. This would give the weight updation policy as,
+
+$$
+w _ { k + 1 } = w _ { k } - \eta g _ { k } - \beta \tilde { w } _ { k }
+$$
+
+If 371 $e _ { k } = w _ { k } ^ { T } \Phi _ { k } - Y$ , then the error $e _ { k + 1 }$ after the weight updation would equal,
+
+$$
+\begin{array} { r l } & { e _ { k + 1 } = w _ { k + 1 } ^ { T } \Phi _ { k + 1 } - Y } \\ & { \qquad = ( w _ { k } - \eta g _ { k } - \beta \tilde { w } _ { k } ) ^ { T } \Phi _ { k + 1 } - Y } \\ & { \qquad = w _ { k } ^ { T } \Phi _ { k + 1 } - \eta g _ { k } ^ { T } \Phi _ { k + 1 } - \beta \tilde { w } _ { k } ^ { T } \Phi _ { k + 1 } - Y } \end{array}
+$$
+
+372 Asumming for simplicity sake that $\Phi _ { k + 1 } \approx \Phi _ { k } + \delta$ , then (9) can continue as,
+
+$$
+\begin{array} { c } { { e _ { k + 1 } \approx w _ { k } ^ { T } \Phi _ { k } - \eta g _ { k } ^ { T } \Phi _ { k } - \beta \tilde { w } _ { k } ^ { T } \Phi _ { k } - Y + \Delta } } \\ { { { } } } \\ { { \approx e _ { k } - \eta g _ { k } ^ { T } \Phi _ { k } - \beta \tilde { w } _ { k } ^ { T } \Phi _ { k } } } \end{array}
+$$
+
+373 Taking the square norm of $e _ { k + 1 }$ in (10), would equate this to,
+
+$$
+\begin{array} { r l } & { | | e _ { k + 1 } | | ^ { 2 } = | | e _ { k } | | ^ { 2 } + \eta ^ { 2 } | | g _ { k } ^ { T } \Phi _ { k } | | ^ { 2 } + \beta ^ { 2 } | | \tilde { w } _ { k } ^ { T } \Phi _ { k } | | ^ { 2 } } \\ & { ~ - ~ 2 \eta e _ { k } ^ { T } \Phi _ { k } ^ { T } g _ { k } - 2 \beta e _ { k } ^ { T } \Phi _ { k } ^ { T } \tilde { w } _ { k } + 2 \eta \beta \tilde { w } _ { k } ^ { T } \Phi _ { k } \Phi _ { k } ^ { T } g _ { k } } \end{array}
+$$
+
+374 We require that $| | e _ { k + 1 } | | ^ { 2 } < | | e _ { k } | | ^ { 2 }$ at all times, so that regularization does not affect the fit at any   
+375 point during the training. Applying this condition in (11) would give,
+
+$$
+\eta ^ { 2 } | | g _ { k } ^ { T } \Phi _ { k } | | ^ { 2 } + \beta ^ { 2 } | | \tilde { w } _ { k } ^ { T } \Phi _ { k } | | ^ { 2 } - 2 \eta e _ { k } ^ { T } \Phi _ { k } ^ { T } g _ { k } - 2 \beta e _ { k } ^ { T } \Phi _ { k } ^ { T } \tilde { w } _ { k } + 2 \eta \beta \tilde { w } _ { k } ^ { T } \Phi _ { k } \Phi _ { k } ^ { T } g _ { k } < 0
+$$
+
+376 Then, taking the partial derivatives of (12) w.r.t $\eta$ and $\beta$ would give the following equations to be   
+377 satisfied:
+
+$$
+\eta | | g _ { k } ^ { T } \Phi _ { k } | | ^ { 2 } - e _ { k } ^ { T } \Phi _ { k } ^ { T } g _ { k } + \beta \tilde { w } _ { k } ^ { T } \Phi _ { k } \Phi _ { k } ^ { T } g _ { k } = 0
+$$
+
+$$
+\beta | | \tilde { w } _ { k } ^ { T } \Phi _ { k } | | ^ { 2 } - e _ { k } ^ { T } \Phi _ { k } ^ { T } \tilde { w } _ { k } + \eta \tilde { w } _ { k } ^ { T } \Phi _ { k } \Phi _ { k } ^ { T } g _ { k } = 0
+$$
+
+378 Solving, (13) and (14) can result in negative $\eta$ and $\beta$ , which is not acceptable, and so to simplify the   
+379 solution, we neglect the $\beta$ -term in (13). Doing so we get,
+
+$$
+\begin{array} { r l } & { \eta = \frac { e _ { k } ^ { T } \Phi _ { k } ^ { T } g _ { k } } { \vert \vert g _ { k } ^ { T } \Phi _ { k } \vert \vert ^ { 2 } } , } \\ & { } \\ & { \beta = \frac { e _ { k } ^ { T } \Phi _ { k } ^ { T } \tilde { w } _ { k } - \eta \tilde { w } _ { k } ^ { T } \Phi _ { k } \Phi _ { k } ^ { T } g _ { k } } { \vert \vert \tilde { w } _ { k } ^ { T } \Phi _ { k } \vert \vert ^ { 2 } } } \end{array}
+$$
+
+380 Then, substituting for $g _ { k }$ and openning up the norms, we get,
+
+$$
+\eta = \frac { e _ { k } ^ { T } \Phi _ { k } ^ { T } \Phi _ { k } e _ { k } } { e _ { k } ^ { T } ( \Phi _ { k } ^ { T } \Phi _ { k } ) ( \Phi _ { k } ^ { T } \Phi _ { k } ) e _ { k } } ,
+$$
+
+$$
+\beta = \frac { e _ { k } ^ { T } \Phi _ { k } ^ { T } \tilde { w } _ { k } - \eta \tilde { w } _ { k } ^ { T } ( \Phi _ { k } \Phi _ { k } ^ { T } ) \Phi _ { k } e _ { k } } { \tilde { w } _ { k } ^ { T } ( \Phi _ { k } \Phi _ { k } ^ { T } ) \tilde { w } _ { k } }
+$$
+
+381 Simplifying (16) gives,
+
+$$
+\eta = \frac { e _ { k } ^ { T } e _ { k } } { e _ { k } ^ { T } \Phi _ { k } ^ { T } \Phi _ { k } e _ { k } } ,
+$$
+
+$$
+\beta = ( 1 - \eta ) \frac { \tilde { w } _ { k } ^ { T } \Phi _ { k } e _ { k } } { \tilde { w } _ { k } ^ { T } \tilde { w } _ { k } }
+$$
+
+382 Equation (17) gives the raw form for both $\eta$ and $\beta$ to be regulated. However, this will be further   
+383 simplified for computating purposes, but will be used as a basis.   
+384 Since the errors $e _ { k }$ get smaller as the neural network fits the data, using them in learning constants   
+385 will only slow down the fits. A common way to overcome this is by replacing $e _ { k }$ with all ones.   
+386 Similarly, for the $\tilde { w } _ { k }$ , all weights that are to be regularized are replaced with ones. If we denote   
+387 the weights to be regularized as $w _ { r }$ , and there are $m$ patterns in the dataset with $n$ weights to be   
+388 regularized, the $\eta$ and $\beta$ computations become,
+
+$$
+\eta = \frac { 1 } { | | \Phi _ { k } | | ^ { 2 } } ,
+$$
+
+$$
+\beta = \frac { \alpha } { m n } \sum _ { i : w \in w _ { r } } \Phi _ { i , k }
+$$
+
+389 Here, $\alpha$ represents the $( 1 - \eta )$ -term in (17). This constant will not neccessarily take the computed $\eta$   
+390 when being regulated. Instead, this constant will have to be adapted each time for every incremental   
+391 batch applied to the neural network.   
+392 The reason why the computed $\eta$ is not used for the $\alpha$ adaptation is because this $\eta$ can sometimes   
+393 become too small in the adaptation, that the $1 - \eta$ would always tend towards 1. When this was   
+394 empirically tested on the toy dataset, the regularization was found at times to have gone too strong   
+395 that the fit never happened. ML-Ops on the $\alpha$ found that this constant is not always 1, and can be   
+396 anywhere between 0 and 1, or higher in some cases.
+
+398 Additional examples on the regression problem with Fisher Shut-off. Fisher Shut-off could not be used completely, and regularization had to take over for some batches. Figures 5 and 6 show this.
+
+![](images/72e9762490cf8ee10f248a8d3a0d85b6b28ea32a596f13c1b194dc4898ba90c7.jpg)  
+Figure 5: Complete Fisher Shut-off is used in Batches #2 and #6. Batches #3, #4 and #5 are regularized.
+
+![](images/b70e35df8ae79c3da760bbd94c1191f3f81fda2aacf6961298510e013e24a3ed.jpg)  
+Figure 6: Complete Fisher Shut-off is used in Batches $\# 2$ and $\# 6$ . Batches $\# 3$ and $\# 4$ are regularized. Batch #5 is fine-tuned
+
+401 In this appendix, additional examples on the toy dataset classification is shown. Figures 7 and 8 show 402 the batch distributions considered. Among these, Figure 8 has more cases in which the farthest points 403 in Border Control can play a vital role in retaining previously learned knowledge. Tables 2 and 3 summarize their performances.
+
+![](images/df00e79da7646169cbe201b37f70a3bcbb78337b977ceaff9e318f5cd16ecc4a.jpg)  
+Figure 7: Another batch distribution on the toy dataset.
+
+Table 2: Performance of proposed methods on the dataset of Figure 7   
+
+<table><tr><td rowspan="2">Method</td><td colspan="6">Sample accuracy on accumulated dataset after Batch</td></tr><tr><td>#1</td><td>#2</td><td>#3</td><td>#4</td><td>#5</td><td>#6</td></tr><tr><td>No Incremental Learning</td><td>100.0%</td><td>73.14%</td><td>92.07%</td><td>97.56%</td><td>88.33%</td><td>91.67%</td></tr><tr><td>Fisher Shut-off (FS)</td><td>100.0%</td><td>99.43%</td><td>98.26%</td><td>99.54%</td><td>92.85%</td><td>97.78%</td></tr><tr><td>Frac. Data Ret. (FDR)[10%]</td><td>100.0%</td><td>97.43%</td><td>96.13%</td><td>98.93%</td><td>98.75%</td><td>96.78%</td></tr><tr><td>FDR[20%]</td><td>100.0%</td><td>98.86%</td><td>98.84%</td><td>99.69%</td><td>99.75%</td><td>98.89%</td></tr><tr><td>Border Ctrl. (BC)[topk = 5]</td><td>100.0%</td><td>100.0%</td><td>100.0%</td><td>100.0%</td><td>100.0%</td><td>99.78%</td></tr><tr><td>BC[topk = 10]</td><td>100.0%</td><td>100.0%</td><td>100.0%</td><td>100.0%</td><td>100.0%</td><td>100.0%</td></tr><tr><td>FS + FDR[10%]</td><td>100.0%</td><td>99.71%</td><td>98.84%</td><td>99.54%</td><td>98.75%</td><td>98.33%</td></tr><tr><td>FS + FDR[20%]</td><td>100.0%</td><td>100.0%</td><td>99.23%</td><td>99.85%</td><td>99.87%</td><td>98.89%</td></tr><tr><td>FS +BC[topk = 5]</td><td>100.0%</td><td>100.0%</td><td>100.0%</td><td>100.0%</td><td>100.0%</td><td>100.0%</td></tr><tr><td>FS + BC[topk = 10]</td><td>100.0%</td><td>100.0%</td><td>100.0%</td><td>100.0%</td><td>100.0%</td><td>100.0%</td></tr></table>
+
+![](images/198dee612d5cdc63ee02fcb729ec0a2fd31f55ddf925d97353d37ff12ee507bd.jpg)  
+Figure 8: Yet another batch distribution on the toy dataset.
+
+Table 3: Performance of proposed methods on the dataset of Figure 8   
+
+<table><tr><td rowspan="2">Method</td><td colspan="6">Sample accuracy on accumulated dataset after Batch</td></tr><tr><td>#1</td><td>#2</td><td>#3</td><td>#4</td><td>#5</td><td>#6</td></tr><tr><td>No Incremental Learning</td><td>100.0%</td><td>89.34%</td><td>93.80%</td><td>95.60%</td><td>97.81%</td><td>84.78%</td></tr><tr><td>Fisher Shut-off (FS)</td><td>100.0%</td><td>95.36%</td><td>99.59%</td><td>99.55%</td><td>99.36%</td><td>94.56%</td></tr><tr><td>Frac. Data Ret. (FDR)[10%]</td><td>100.0%</td><td>95.08%</td><td>96.07%</td><td>97.42%</td><td>99.61%</td><td>98.67%</td></tr><tr><td>FDR[20%]</td><td>100.0%</td><td>98.36%</td><td>98.97%</td><td>99.85%</td><td>100.0%</td><td>99.67%</td></tr><tr><td>Border Ctrl. (BC)[top k = 5]</td><td>100.0%</td><td>100.0%</td><td>99.79%</td><td>99.85%</td><td>100.0%</td><td>100.0%</td></tr><tr><td>BC[topk = 10]</td><td>100.0%</td><td>100.0%</td><td>100.0%</td><td>100.0%</td><td>99.74%</td><td>100.0%</td></tr><tr><td>FS + FDR[10%]</td><td>100.0%</td><td>95.36%</td><td>99.79%</td><td>98.48%</td><td>99.61%</td><td>98.89%</td></tr><tr><td>FS + FDR[20%]</td><td>100.0%</td><td>98.36%</td><td>99.79%</td><td>99.69%</td><td>100.0%</td><td>99.67%</td></tr><tr><td>FS+BC[topk = 5]</td><td>100.0%</td><td>100.0%</td><td>100.0%</td><td>100.0%</td><td>99.74%</td><td>100.0%</td></tr><tr><td>FS + BC[topk = 10]</td><td>100.0%</td><td>100.0%</td><td>100.0%</td><td>100.0%</td><td>100.0%</td><td>100.0%</td></tr></table>

parse/dev/VB75Pi89p7/VB75Pi89p7.md

@@ -0,0 +1,276 @@
+# BEIT V2: MASKED IMAGE MODELING WITH VECTOR-QUANTIZED VISUAL TOKENIZERS
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+Masked image modeling (MIM) has demonstrated impressive results in selfsupervised representation learning by recovering corrupted image patches. However, most existing studies operate on low-level image pixels, which hinders the exploitation of high-level semantics for representation models. In this work, we propose to use a semantic-rich visual tokenizer as the reconstruction target for masked prediction, providing a systematic way to promote MIM from pixel-level to semantic-level. Specifically, we propose vector-quantized knowledge distillation to train the tokenizer, which discretizes a continuous semantic space to compact codes. We then pretrain vision Transformers by predicting the original visual tokens for the masked image patches. Furthermore, we introduce a patch aggregation strategy which associates discrete image patches to enhance global semantic representation. Experiments on image classification and semantic segmentation show that BEIT V2 outperforms all compared MIM methods. On ImageNet-1K (224 size), the base-size BEIT V2 achieves $8 5 . 5 \%$ top-1 accuracy for fine-tuning and $8 0 . 1 \%$ top-1 accuracy for linear probing. The large-size BEIT V2 obtains $8 7 . 3 \%$ top-1 accuracy for ImageNet-1K (224 size) fine-tuning, and $5 6 . 7 \%$ mIoU on ADE20K for semantic segmentation. The code can be found in the supplementary materials.
+
+# 1 INTRODUCTION
+
+Masked image modeling (MIM), which greatly relieves the annotation-hungry issue of vision Transformers, has demonstrated great potential in learning visual representations (Bao et al., 2022; He et al., 2022). Given an image, the pretraining objective of MIM is to recover the masked patches so that rich context information is captured by the representation model. Taking BEiT (Bao et al., 2022) as an example, each image has two views during pretraining, i.e., image patches, and visual tokens. The original image is first tokenized to discrete tokens. Randomly sampled image patches are then masked before being fed to vision Transformers. The pretraining objective is to recover the original visual tokens based on the corrupted image patches. The pretrained vision encoder can be deployed and finetuned on various downstream tasks by appending lightweight task layers.
+
+Existing MIM approaches can be coarsely categorized to three according to the reconstruction targets: low-level image elements (e.g., raw pixels; He et al. 2022; Fang et al. 2022; Liu et al. 2022), handcrafted features (e.g., HOG features; Wei et al. 2021), and visual tokens; Bao et al. 2022; Wang et al. 2022; Dong et al. 2021; El-Nouby et al. 2021; Chen et al. 2022. However, all the reconstruction targets are about, explicitly or implicitly, low-level image elements while underestimating high-level semantics. In comparison, the masked words in language modeling (Devlin et al., 2019) are all about high-level semantics, which motivates us to tap the potential of MIM by exploiting semantic-aware supervision during pretraining.
+
+In this work, we propose a self-supervised representation learning approach, termed BEIT V2, with the aim to improve MIM pretraining by constructing a semantic-aware visual tokenizer. Our approach is developed on the BEIT method which is simple yet effective. The novelty lies in introducing the Vector-Quantized Knowledge Distillation (VQ-KD) algorithm to discretize a semantic space. The VQ-KD encoder first converts the input image to discrete tokens according to a learnable codebook. The decoder then learns to reconstruct the semantic features encoded by a teacher model, conditioning on the discrete tokens. After training VQ-KD, its encoder is used as a semantic visual tokenizer for BEIT pretraining, where the discrete codes serve as supervision signals.
+
+![](images/6c7aa3ed835bae886efd50e91041fc62684c089925486c85c6784f9c4d8b7124.jpg)  
+Figure 1: Top-1 fine-tuning accuracy on ImageNet (224 size). Left: ViT-B/16. right: ViT-L/16.
+
+Considering the discreteness of tokens, we further introduce a patch aggregation strategy which explicitly encourages the [CLS] token to associate all patches (Gao & Callan, 2021). Such a strategy resolves the issue that MIM put patch reconstruction the first place which diminishes learning global image representations. As a result, BEIT V2 improves the capacity of learned image representation, as supported by the linear probing experiments. Moreover, the enhanced representations also boosts the performance of other tasks.
+
+We conduct self-supervised learning on ImageNet-1k for both base- and large-size vision Transformers, which are evaluated on downstream tasks, e.g., image classification, linear probing, and semantic segmentation. As shown in Figure 1, BEIT V2 outperforms previous self-supervised learning algorithms by a large margin on ImageNet fine-tuning, e.g., improving over BEIT (Bao et al., 2022) by about two points for both ViT-B/16 and ViT-L/16. BEIT V2 outperforms all compared MIM methods on ImageNet linear probing while achieving large performance gains on ADE20k for semantic segmentation.
+
+The contributions of this work are summarized as follows:
+
+• We propose vector-quantized knowledge distillation, promoting masked image modeling from pixel-level to semantic-level for self-supervised representation learning. • We introduce a patch aggregation strategy, which enforces global structure given discrete semantic tokens, and improves the performance of learned representations. • We conduct extensive experiments on downstream tasks including ImageNet fine-tuning, linear probing, and semantic segmentation. Experimental results show that the proposed approach significantly improves performance across model sizes, training steps, and downstream tasks.
+
+# 2 METHODOLOGY
+
+BEIT V2 inherits the masked image modeling framework defined by BEIT (Bao et al., 2022), which uses a visual tokenizer to convert each image to a set of discrete visual tokens. The training target is to recover the masked visual tokens, each of which corresponds to an image patch. In Section 2.2, we introduce a vector-quantized knowledge distillation algorithm, which is used to train a visual tokenizer. In Section 2.3, we employ the visual tokenizer for BEIT pretraining with the help of the patch aggregation strategy.
+
+# 2.1 IMAGE REPRESENTATION
+
+The vision Transformers (ViTs; Dosovitskiy et al. 2020) are employed as the backbone networks to obtain image representations. The input image $\pmb { x } \in \mathbb { R } ^ { H \times W \times C }$ is reshaped to $N = H W / P ^ { 2 }$ patches
+
+![](images/ae30dd1c1a463c2012c94bad578272a2db69efa4bb9976341ca57efcaf14137a.jpg)  
+Figure 2: Pipeline for visual tokenizer training. After training, each image is converted to discrete visual tokens.
+
+$\{ \boldsymbol { x } _ { i } ^ { p } \} _ { i = 1 } ^ { N }$ , w a $\pmb { x } ^ { p } \in \mathbb { R } ^ { N \times ( P ^ { 2 } C ) }$ and  patc $( P , P )$ is the patch size.here each patch is ments, each . The image $2 2 4 \times 2 2 4$ $1 4 \times 1 4$ $1 6 \times 1 6$ $\{ \pmb { x } _ { i } ^ { p } \} _ { i = 1 } ^ { N }$ are denoted as $\{ h _ { i } \} _ { i = 1 } ^ { N }$ , which corresponds to $N$ image patches.
+
+# 2.2 TRAINING VISUAL TOKENIZER
+
+We propose vector-quantized knowledge distillation (VQ-KD) to train the visual tokenizer, Figure 2, where the visual tokenizer and the decoder are two vital modules.
+
+The visual tokenizer maps an image to a sequence of visual tokens, a.k.a., discrete codes. To be specific, an image $_ { \textbf { \em x } }$ is tokenized to $\underline { { z } } = [ z _ { 1 } , z _ { 2 } , \cdot \cdot \cdot , z _ { N } ] \in \mathcal { V } ^ { ( H / P ) \times ( W / P ) }$ , where the visual vocabulary (a.k.a., codebook) $\boldsymbol { \mathcal { V } } \in \mathbb { R } ^ { K \times D }$ contains $K$ discrete codebook embeddings.
+
+The tokenizer is consist of a vision Transformer encoder, and a quantizer. The tokenizer first encodes the input image to vectors. Then, the vector quantizer looks up the nearest neighbor in the codebook for each patch representation $\boldsymbol { h } _ { i }$ . Let $\{ \pmb { v } _ { 1 } , \pmb { v } _ { 2 } , \pmb { \cdot } \cdot \pmb { \cdot } , \pmb { v } _ { K } \}$ denote the codebook embeddings. For the $i$ -th image patch, its quantized code is calculated as
+
+$$
+z _ { i } = \underset { j } { \arg \operatorname* { m i n } } \ \lvert \lvert \ell _ { 2 } ( \pmb { h } _ { i } ) - \ell _ { 2 } ( \pmb { v } _ { j } ) \rvert \rvert _ { 2 } ,
+$$
+
+where $j \in \{ 1 , 2 , \cdots , K \}$ and $\ell _ { 2 }$ normalization is used for codebook lookup (Yu et al., 2021). The above distance is equivalent to finding codes according to cosine similarity.
+
+After quantizing the image to visual tokens, we feed the $\ell _ { 2 }$ -normalized codebook embeddings $\{ \ell _ { 2 } ( \pmb { v } _ { z _ { i } } ) \} _ { i = 1 } ^ { N }$ to the decoder. The decoder is also a multi-layer Transformer. The output vectors $\{ o _ { i } \} _ { i = 1 } ^ { N }$ aim at reconstructing the semantic features of a teacher model, e.g., DINO (Caron et al., 2021), and CLIP (Radford et al., 2021). Let $\mathbf { \Delta } _ { t _ { i } }$ denote the teacher model’s feature vector of the $i$ -th image patch. During training, we maximize the cosine similarity between the decoder output $\mathbf { o } _ { i }$ and the teacher guidance $\mathbf { \Delta } _ { t _ { i } }$ .
+
+Because the quantization process (Equation 1) is non-differentiable, the gradients are directly copied from the decoder input to the encoder output (van den Oord et al., 2017), Figure 2, to back-propagate gradients to the encoder. Intuitively, the quantizer looks up the nearest code for each encoder output, while the gradients of codebook embeddings indicate useful optimization directions for the encoder.
+
+The training objective of VQ-KD is defined as
+
+$$
+\operatorname* { m a x } \sum _ { x \in \mathcal { D } } \sum _ { i = 1 } ^ { N } \cos \left( \boldsymbol { o } _ { i } , t _ { i } \right) - | | \mathrm { s g } [ \ell _ { 2 } ( h _ { i } ) ] - \ell _ { 2 } ( \boldsymbol { v } _ { z _ { i } } ) | | _ { 2 } ^ { 2 } - | | \ell _ { 2 } ( h _ { i } ) - \mathrm { s g } [ \ell _ { 2 } ( \boldsymbol { v } _ { z _ { i } } ) ] | | _ { 2 } ^ { 2 } ,
+$$
+
+where $\mathrm { s g } [ \cdot ]$ stands for the stop-gradient operator which is an identity at the forward pass while having zero gradients during the backward pass. $\mathcal { D }$ represents the image data used for tokenizer training.
+
+![](images/2dadcf052d163431cd7abc25e7ef7bd1d8452054728c322f986f21031108fabc.jpg)  
+Figure 3: The MIM framework equipped with patch aggregation. The pretraining loss is the summation of ${ \mathcal { L } } _ { \mathrm { M I M } }$ and $\mathcal { L } _ { \mathrm { M I M } } ^ { c }$ . The loss term $\mathcal { L } _ { \mathrm { M I M } } ^ { c }$ explicitly encourages the [CLS] token to aggregate patch information to global representations.
+
+Improving codebook utilization. A common issue of vector quantization training is codebook collapse. In other words, only a small proportion of codes are used. Empirical strategies (van den Oord et al., 2017; Yu et al., 2021) can be used to alleviate this issue. Equation 1 shows that we compute the $\ell _ { 2 }$ -normalized distance to find the nearest code while reducing the dimension of codebook embedding space to 32-d. The low-dimensional codebook embeddings are mapped back to higher-dimensional space before being fed to the decoder. Exponential moving average (van den Oord et al., 2017) is employed to update the codebook embeddings. Exponential moving average tends to be more stable for VQ-KD training.
+
+# 2.3 PRETRAINING BEIT V2
+
+We follow the MIM setup in BEIT (Bao et al., 2022) to pretrain vision Transformers for image representations. Given an input image $x$ , around $40 \%$ image patches are block-wisely chosen and masked. The masked position is termed as $\mathcal { M }$ . Then, a shared learnable embedding $e _ { [ \mathbf { M } ] }$ is used to replace the original image patch embeddings $e _ { i } ^ { p }$ if $i \in \mathcal { M }$ $\begin{array} { r } { \boldsymbol { \mathcal { A } } \colon \mathbf { x } _ { i } ^ { \mathcal { M } } = \delta ( i \in \mathcal { M } ) \odot \boldsymbol { e } _ { [ \mathrm { M } ] } + ( 1 - \delta ( i \in } \end{array}$ $\mathcal { M } ) ) \odot \pmb { x } _ { i } ^ { p }$ , where $\delta ( \cdot )$ is the indicator function. Subsequently, we prepend a learnable [CLS] token ito the input, i.e., $[ e _ { \mathrm { C L S } } , \{ \pmb { x } _ { i } ^ { \mathcal { M } } \} _ { i = 1 } ^ { N } ]$ , and feed them to the vision Transformer. The final encoding vectors are denoted as $\{ h _ { i } \} _ { i = 0 } ^ { N }$ , where $h _ { 0 }$ is for the [CLS] token.
+
+Next, we instantiate the MIM head as a simple fully-connection layer, and then use it to predict the visual tokens of the masked positions based on the corrupted image $\pmb { x } ^ { \mathcal { M } }$ . For each masked position $\{ h _ { i } : i \in \mathcal { M } \} _ { i = 1 } ^ { N }$ , a softmax classifier predicts the visual tokens pectively mean weights and biases of the MIM $p ( \bar { z } _ { i } | \pmb { h } _ { i } ) = \mathrm { s o f t m a x } _ { z _ { i } } ( \pmb { W } _ { c } \hat { \pmb { h } } _ { i } + \pmb { b } _ { c } )$ $W _ { c } , b _ { c }$   
+by the tokenizer trained in Section 2.2, which provides supervisions for the MIM self-supervised learning procedure. The training loss of MIM is defined as
+
+$$
+\mathcal { L } _ { \mathrm { M I M } } = - \sum _ { \mathbf { x } \in \mathcal { D } } \sum _ { i \in \mathcal { M } } \log p ( z _ { i } | \mathbf { x } _ { i } ^ { \mathcal { M } } ) ,
+$$
+
+where $z _ { i }$ denotes the visual tokens of the original image, and $\mathcal { D }$ the pretraining images. Notice that the number of visual tokens is the same as the number of image patches in this work.
+
+Pretraining global representation. Inspired by (Gao & Callan, 2021), we pretrain the [CLS] token for global image representation. The goal is to mitigate the discrepancy between patch-level pretraining and image-level representation aggregation. As illustrated in Figure 3, a representation bottleneck is constructed to encourage the [CLS] token to gather information as much as possible. For a $L$ -layer Transformer, let $\{ h _ { i } ^ { l } \} _ { i = 1 } ^ { N }$ denote the $l$ -th layer’s output vectors, where $l \in \{ 1 , 2 , \cdots , L \}$ To pretrain the last layer’s [CLS] token $h _ { \mathrm { C L S } } ^ { L }$ , we concatenate it with the intermediate $l$ -th layer’s patch vectors $\{ h _ { i } ^ { l } \} _ { i = 1 } ^ { N }$ , i.e., ${ \pmb S } = [ { \pmb h } _ { \mathrm { C L S } } ^ { L } , { \pmb h } _ { 1 } ^ { l } , \cdots , { \pmb h } _ { N } ^ { l } ]$ . We then feed $_ { s }$ to a shallow (e.g., two layers)
+
+Transformer decoder and conduct masked prediction again, i.e., $p ( z | S ) = \mathrm { s o f t m a x } _ { z } ( W _ { c } S + b _ { c } )$ Notice that the parameters are shared for both MIM heads and the MIM loss is also computed at mask positions as in Equation 3. Accordingly, the final training loss is defined as the summation of two terms, i.e., the original loss at the $L$ -th layer, and the shallow Transformer decoder’s MIM loss. Overall framework refers to Appendix C.
+
+Intuitively, the model favors pushing the global information to $h _ { \mathrm { C L S } } ^ { L }$ , because the model tends to fully utilize the parameters from $( l + 1 )$ -th layer to $L$ -th layer, to decrease the additional MIM loss. The information-flow bottleneck encourages the [CLS] token towards more reliable global representations than its untrained counterparts. Moreover, the enhanced representations also facilitate various downstream tasks. Notice that the newly added shallow decoder is only used to pretrain the [CLS] token, which is discarded after pretraining.
+
+# 3 EXPERIMENTS
+
+The pretrained models are evaluated on image classification and semantic segmentation tasks. For image classification, the models are trained on ImageNet-1K (Russakovsky et al., 2015) and evaluated by (1) top-1 accuracy about fine-tuning and (2) top-1 accuracy about linear probing (only fine-tuning the classification head). For semantic segmentation, experiments are conducted on the ADE20K dataset (Zhou et al., 2019) and the performance is evaluated using the mIoU protocol.
+
+# 3.1 PRETRAINING SETUP
+
+Visual tokenizer training. We instantiate the visual tokenizer of VQ-KD as ViT-B/16 for both base- and large-size BEIT V2 pretraining. The decoder network is a three-layer standard Transformer, which has the same dimension and number of attention heads as the tokenizer encoder. The OpenAI CLIP-B/16 (Radford et al., 2021) is employed as the teacher model and train VQ-KD on ImageNet-1k with $2 2 4 \times 2 2 4$ resolution. Notice that we use the same base-size teacher to train the visual tokenizer for both base- and large-size pretraining. The code size $K$ is set as 8192 and code dimension $D$ as 32 by default. Refer to Appendix D for more training details.
+
+Masked image modeling. We follow the settings used in BEiT (Bao et al., 2022) pretraining and use ImageNet-1K without labels as the pretraining data for self-supervised learning. The input image resolution is set as $2 2 4 \mathbf { x } 2 2 4$ during pretraining. The pretrained base- and large-size vision Transformers (Dosovitskiy et al., 2020) with $1 6 \times 1 6$ patch size are denoted as ViT-B/16 and ViT-L/16, respectively. For the patch aggregation strategy, we set $l = 9$ for ViT-B/16, $l = 2 1$ for ViT-L/16, and the depth as 2 by default. A block-wise masking mechanism is adopted under the mask ratio of $40 \%$ (i.e., about 75 image patches). More pretraining details can be found in Appendix E.
+
+# 3.2 IMAGE CLASSIFICATION
+
+Both the fine-tuning accuracy and linear probing accuracy are evaluated on ImageNet-1k by default. The models are also evaluated on several ImageNet variants to demonstrate their favorable generalization ability.
+
+Fine-tuning setup. We follow the protocol proposed in BEiT (Bao et al., 2022) to fine-tune the pretrained BEIT V2 model (see Appendix F for more details). In Table 1, we report the top-1 fine-tuning accuracy results and compare BEIT V2 with recent MIM methods.
+
+From Table 1, base-size BEIT V2 with a 300-epoch pretraining schedule reaches $8 5 . 0 \%$ top-1 accuracy, which outperforms BEIT, CAE, SplitMask and $\mathrm { P e C o }$ by $2 . 1 \%$ , $1 . 4 \%$ , $1 . 4 \%$ and $0 . 9 \%$ respectively. Compared with masked distillation methods, like MVP, BEIT V2 also shows superiority. Furthermore, with a longer pretraining schedule, BEIT V2 achieves $8 5 . 5 \%$ top-1 accuracy, developing a new state of the art on ImageNet-1K among self-supervised methods. Meanwhile, BEIT V2 using ViT-L/16 with 300 epochs reaches $8 6 . 6 \%$ top-1 accuracy, which is comparable to data2vec with 1600 epochs. A longer pretraining schedule further boosts the performance to $8 7 . 3 \%$ .
+
+Following BEIT, we add an intermediate fine-tuning phase between the pretraining stage and the fine-tuning stage. Only the intermediate fine-tuning phase uses the ImageNet-21k dataset. As shown in Table 1, we find that intermediate fine-tuning achieves about $1 \%$ performance gain on image classification for both base- and large-size models. Refer to Appendix B for more results of intermediate fine-tuning.
+
+Table 1: Fine-tuning results of image classification and semantic segmentation on ImageNet-1K and ADE20k. UperNet (Xiao et al., 2018) is used as the task layer for semantic segmentation with single-scale (512 size) input.   
+
+<table><tr><td>Methods</td><td>Pretraining Epochs</td><td>ImageNet Top-1 Accuracy(%)</td><td>ADE20k mIoU(%)</td></tr><tr><td>Base-size models (ViT-B/16)</td><td></td><td></td><td></td></tr><tr><td>BEIT (Bao et al., 2022)</td><td>300</td><td>82.9</td><td>44.7</td></tr><tr><td>CAE (Chen et al., 2022)</td><td>300</td><td>83.6</td><td>48.3</td></tr><tr><td>SplitMask (El-Nouby et al., 2021)</td><td>300</td><td>83.6</td><td>45.7</td></tr><tr><td>MaskFeat (Wei et al., 2021)</td><td>300</td><td>83.6</td><td>N/A</td></tr><tr><td>PeCo (Dong et al., 2021)</td><td>300</td><td>84.1</td><td>46.7</td></tr><tr><td>MVP(Wei et al., 2022)</td><td>300</td><td>84.4</td><td>52.4</td></tr><tr><td>iBoT (Zhou et al., 2022)</td><td>400</td><td>83.8</td><td>50.0</td></tr><tr><td>BEIT v2 (ours)</td><td>300</td><td>85.0</td><td>52.7</td></tr><tr><td>Base-size models (ViT-B/16) + pretrain longer</td><td></td><td></td><td></td></tr><tr><td>BEIT (Bao et al., 2022)</td><td>800</td><td>83.2</td><td>45.6</td></tr><tr><td>PeCo (Dong et al., 2021)</td><td>800</td><td>84.5</td><td>48.5</td></tr><tr><td>data2vec (Baevski et al., 2022)</td><td>800</td><td>84.2</td><td>N/A</td></tr><tr><td>MAE (He et al., 2022)</td><td>1600</td><td>83.6</td><td>48.1</td></tr><tr><td>CAE (Chen et al.,2022)</td><td>1600</td><td>83.9</td><td>50.2</td></tr><tr><td>BEIT v2 (ours)</td><td>1600</td><td>85.5</td><td>53.1</td></tr><tr><td>+ Intermediate fine-tuning with ImageNet-21k</td><td></td><td>86.5</td><td>53.5</td></tr><tr><td>Large-size models (ViT-L/16)</td><td></td><td></td><td></td></tr><tr><td>iBoT (Zhou et al.,2022)</td><td>250</td><td>84.8</td><td>N/A</td></tr><tr><td>MaskFeat (Wei et al., 2021)</td><td>300</td><td>84.4</td><td>N/A</td></tr><tr><td>MVP (Wei et al., 2022)</td><td>300</td><td>86.3</td><td>54.3</td></tr><tr><td>BEIT V2 (ours)</td><td>300</td><td>86.6</td><td>55.0</td></tr><tr><td> Large-size models (ViT-L/16) + pretrain longer</td><td></td><td></td><td></td></tr><tr><td>BEIT (Bao et al., 2022)</td><td>800</td><td>85.2</td><td>53.3</td></tr><tr><td>MaskFeat (Wei et al., 2021)</td><td>1600</td><td>85.7</td><td>N/A</td></tr><tr><td>MAE (He et al., 2022)</td><td>1600</td><td>85.9</td><td>53.6</td></tr><tr><td>CAE (Chen et al., 2022)</td><td>1600</td><td>86.3</td><td>54.7</td></tr><tr><td>data2vec (Baevski et al.,2022)</td><td>1600</td><td>86.6</td><td>N/A</td></tr><tr><td>BEIT V2 (ours)</td><td>1600</td><td>87.3</td><td>56.7</td></tr><tr><td>+ Intermediate fine-tuning with ImageNet-21k</td><td></td><td>88.4</td><td>57.5</td></tr><tr><td colspan="2"></td><td></td><td></td></tr></table>
+
+Table 2: Top-1 accuracy of linear probing on ImageNet-1k. All methods are based on ViTB/16 pretrained for 300 epochs except MAE for 1600 epochs.   
+
+<table><tr><td>Methods</td><td>Linear Probe</td></tr><tr><td>BEIT (Bao et al., 2022)</td><td>56.7</td></tr><tr><td>CAE (Chen et al., 2022)</td><td>64.1</td></tr><tr><td>MAE (He et al., 2022)</td><td>67.8</td></tr><tr><td>MVP(Wei et al., 2022)</td><td>75.4</td></tr><tr><td>MoCo v3 (Chen et al., 2021)</td><td>76.7</td></tr><tr><td>BEIT v2 (ours)</td><td>80.1</td></tr></table>
+
+Table 3: Robustness evaluation on three ImageNet variants (Hendrycks et al., 2021b;a; Wang et al., 2019).   
+
+<table><tr><td>Methods</td><td>ImageNet Adversarial</td><td>ImageNet Rendition</td><td>ImageNet Sketch</td></tr><tr><td>ViT-B/16</td><td></td><td></td><td></td></tr><tr><td>MAE</td><td>35.9</td><td>48.3</td><td>34.5</td></tr><tr><td>BEIT V2</td><td>54.4</td><td>61.0</td><td>45.6</td></tr><tr><td>ViT-L/16</td><td></td><td></td><td></td></tr><tr><td>MAE</td><td>57.1</td><td>59.9</td><td>45.3</td></tr><tr><td>BEIT V2</td><td>69.0</td><td>69.9</td><td>53.5</td></tr></table>
+
+Linear probing. Keeping the backbone model frozen and training a linear classification head atop the image-level representations, linear probing has been a widely considered measure for selfsupervised learning. We average the patch tokens as the global representation for the models without patch aggregation. Otherwise, we consider the [CLS] token as the global representation. Table 2 presents the top-1 accuracy for linear probing and compares BEIT V2 with recent methods including BEIT, CAE, MAE, MVP and MoCo v3. All the compared methods are based on ViT-B/16 and pretrained for 300 epochs except MAE for 1600 epochs. BEIT V2 respectively outperforms BEIT, CAE and MVP by $2 3 . 4 \%$ , $1 6 . 0 \%$ and $4 . 7 \%$ . BEIT V2 also outperforms MoCo v3, which learns a global representation through a contrastive learning fashion. The comparisons indicate that the representation models learned by BEIT V2 enjoy higher adaptation capability.
+
+Table 4: Ablation studies under VQ-KD settings. “Base&1x768x12” denotes that the encoder network is ViT-Base while the decoder is a Transformer with depth 1, dimensions 768, and head 12. “Reconst. Loss” is the reconstruction loss of VQ-KD. Reconstruction loss and codebook usage are measured on the validation set. After 300 epochs of pretraining, our method reports the top-1 fine-tuning accuracy and linear probing accuracy on ImageNet-1k, and mIoU on ADE20k. The default setting is highlighted in gray .   
+
+<table><tr><td>VQ-KD Architecture</td><td>Codebook</td><td>Reconst. Loss</td><td>Codebook Usage</td><td>ImageNet Fine-tuning</td><td>ImageNet Linear Probe</td><td>ADE20k</td></tr><tr><td>Small &amp; 1x384x6</td><td rowspan="4">8192×32</td><td>0.183</td><td>100%</td><td>84.3</td><td>76.0</td><td>51.0</td></tr><tr><td>Base&amp;1x768x12</td><td>0.164</td><td>100%</td><td>84.7</td><td>78.5</td><td>51.8</td></tr><tr><td>Base&amp;3x768x12</td><td>0.145</td><td>95%</td><td>84.7</td><td>77.9</td><td>51.9</td></tr><tr><td>Base&amp; 6x768x12</td><td>0.136</td><td>77%</td><td>84.6</td><td>63.0</td><td>50.1</td></tr><tr><td rowspan="2">Base &amp;3x768x12</td><td>8192×16</td><td>0.145</td><td>100%</td><td>84.7</td><td>76.7</td><td>51.7</td></tr><tr><td>8192×64</td><td>0.148</td><td>67%</td><td>84.7</td><td>77.6</td><td>51.6</td></tr></table>
+
+Robustness evaluation. We evaluate the robustness of BEIT V2 on various ImageNet validation sets, i.e., ImageNet-Adversarial (Hendrycks et al., 2021b), ImageNet-Rendition (Hendrycks et al., 2021a) and ImageNet-Sketch (Wang et al., 2019). As shown in Table 3, compared with MAE (He et al., 2022), BEIT V2 achieves dramatic gains across datasets, demonstrating the superiority of the proposed method in terms of model generalization.
+
+# 3.3 SEMANTIC SEGMENTATION
+
+Semantic segmentation is a dense prediction task, which generates class label for each pixel of the input image. Following the setting proposed in BEIT (Bao et al., 2022), we conduct experiments on ADE20K benchmark (Zhou et al., 2019), which includes 25K mages and 150 semantic categories. We use UperNet (Xiao et al., 2018) task layer and fine-tune the model for 160K iterations with the input resolution $5 1 2 \times 5 1 2$ . Refer to Appendix G for details. Table 1 shows that BEIT V2 significantly outperforms previous self-supervised methods. Moreover, using the ViT-L/16 model, the performance can reach 56.7, which builds a new state-of-the-art for masked image modeling on ADE20k.
+
+# 3.4 ANALYSIS
+
+Visual tokenizer training. We investigate the impact of VQ-KD on BEIT V2 in terms of the model architecture and codebook size and report the results in Table 4. ViT-B/16 without the patch aggregation strategy is used as the baseline model, which is pretrained for 300 epochs. As shown in Table 4, we find that a deeper decoder of VQ-KD obtains better reconstruction, but lower codebook usage and downstream task performance. Reducing dimension for codebook lookup improves codebook utilization (Yu et al., 2021).
+
+Patch aggregation strategy. Table 5 presents the ablation studies of the patch aggregation strategy. The shallower head (i.e., 1/2-layer) performs better than the deeper head (i.e., 3-layer), suggesting the shallower head pays more attention to the input [CLS] token than the deeper head. Moreover, the proposed method outperforms the baseline variant without patch aggregation strategy. The improvement of linear probe indicates better image-level representations. In addition, the results indicate that sharing the MIM head improves downstream performance.
+
+Table 5: Ablation studies for patch aggregation strategy. $l$ -th Layer denotes patch tokens from the $l$ -th layer of the backbone. Head Depth means the patch aggregation head depth. Shared MIM Head means whether we share the MIM head parameters or not. Default settings are in gray .   
+
+<table><tr><td>l-th Layer</td><td>Head Depth</td><td>Shared MIM Head</td><td>ImageNet Fine-tuning</td><td>ImageNet Linear Probe</td><td>ADE20k</td></tr><tr><td>1</td><td>=</td><td>Without patch aggregation =</td><td>84.7</td><td>77.9</td><td>51.9</td></tr><tr><td>With patch aggregation</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>9</td><td>2</td><td>√</td><td>85.0</td><td>80.1</td><td>52.7</td></tr><tr><td>9</td><td>2</td><td>X</td><td>84.8</td><td>79.5</td><td>51.9</td></tr><tr><td>9</td><td>1</td><td>√</td><td>84.8</td><td>78.9</td><td>51.7</td></tr><tr><td>9</td><td>3</td><td></td><td>84.7</td><td>78.1</td><td>52.0</td></tr><tr><td>6</td><td>2</td><td></td><td>84.9</td><td>77.5</td><td>53.1</td></tr><tr><td>11</td><td>2</td><td></td><td>84.5</td><td>69.4</td><td>51.8</td></tr></table>
+
+Table 6: Comparisons between different VQ-KD targets. We also report the fine-tuning results of VQ-KD target models.   
+
+<table><tr><td>VQ-KD Targets</td><td>ImageNet</td><td>ADE20k</td></tr><tr><td>Pretrain 300 epochs</td><td></td><td></td></tr><tr><td>DINO</td><td>84.4</td><td>49.2</td></tr><tr><td>CLIP</td><td>85.0</td><td>52.7</td></tr><tr><td>Pretrain 1600 epochs</td><td></td><td></td></tr><tr><td>CLIP</td><td>85.5</td><td>53.1</td></tr><tr><td>Performance of VQ-KD target models</td><td></td><td></td></tr><tr><td>DINO</td><td>83.6</td><td>46.8</td></tr><tr><td>CLIP</td><td>84.9</td><td></td></tr><tr><td>Performance of VQ-KD encoder model</td><td></td><td></td></tr><tr><td>VQ-KD encoder (CLIP as target)</td><td>83.6</td><td></td></tr></table>
+
+VQ-KD targets. In Table 6, we report the results about VQ-KDs are trained under the supervision of DINO (Caron et al., 2021) and CLIP (Radford et al., 2021). DINO is pretrained solely on ImageNet1k while CLIP is pretrained on 400M image-text pairs datasets in house. We also directly fine-tune the official base-size checkpoints and report the results in Table 6. One can see that when using DINO as the teacher model, BEIT V2 respectively reaches $8 4 . 4 \%$ and $4 9 . 2 \%$ on ImageNet and ADE20k, outperforming DINO itself by a large margin. When using CLIP as the teacher model, BEIT V2 can get consistent improvements, demonstrating the scalability of the proposed VQ-KD. In addition, we directly fine-tune the VQ-KD encoder on ImageNet. The results show that transfer performance of the VQ-KD encoder is lower than the teacher model. After performing masked image modeling, the pretrained model outperforms both the teacher model and the visual tokenizer encoder. It demonstrates the superiority of the proposed method for self-supervised learning.
+
+Visualization of codebook. We utilize the proposed VQ-KD to calculate discrete codes about the ImageNet-1k validation set. Image patches are grouped according to their corresponding codes. Figure 4 shows that the grouped image patches represent explicit semantics. For instance, the image patches corresponding to code 7856 are about “eyes” of human, cat, dog, fish and snake. Refer to Appendix A) for more examples. The introduction of codebook and feature quantization reduces the sensitiveness to the change of image details while facilitates exploitation of high-level semantics for representation models. VQ-KD compresses and quantizes the continuous feature values to a codebook, which constructs a discrete semantic space. The dimensionality of such a semantic space is significantly lower than that of the original continuous feature space. This reduces difficulty of masked patch reconstruction and alleviates the curse of dimensionality in the pretraining phase.
+
+![](images/c9e69eb7bba48bcd175a31fbbb91b7a5f363e4b62b5885355c27126c5c52d8ef.jpg)  
+Figure 4: Visualization of semantic concepts corresponding to the learned codebook.
+
+# 4 RELATED WORK
+
+Visual tokenizer. VQ-VAE (van den Oord et al., 2017) converts an image into a sequence of discrete codes and then reconstructs the input image based on discrete codes. DALL-E (Ramesh et al., 2021) uses the Gumbel-softmax relaxation for quantization instead of the nearest neighbor lookup in VQ-VAE. VQGAN (Esser et al., 2021) and ViT-VQGAN (Yu et al., 2021) introduce Transformer block to train a better autoencoder to maintain fine details with adversarial and perceptual loss. Moreover, ViT-VQGAN proposes factorized and $\ell _ { 2 }$ -normalized code for codebook learning. In comparison, the proposed VQ-KD aims at reconstructing semantic knowledge from the teacher rather than original pixels. So we can construct a highly compact semantic codebook for MIM.
+
+Masked image modeling. The MIM method has achieved great success in language task (Devlin et al., 2019). Motivated by it, BEIT (Bao et al., 2022) mitigated the MIM method to computer vision tasks by recovering discrete visual tokens (Ramesh et al., 2021). The prediction targets for MIM habe been explored by many recent works. MAE (He et al., 2022) treated MIM as a denoising pixel-level reconstruction task. Knowledge distillation (Wei et al., 2021; 2022) and self-distillation (Zhou et al., 2022; Baevski et al., 2022) proposed to mimic the features provided by the teacher at the masked positions. PeCo (Dong et al., 2021) regarded MoCo v3 (Chen et al., 2021) as the perceptual model in VQGAN training (Esser et al., 2021), to pursue a better tokenizer for BEIT pretraining. Despite of the progress, most existing studies remain operating on low-level image pixels, this work explores how to promote masked image modeling from pixel-level to semantic-level.
+
+# 5 CONCLUSION
+
+We proposed vector-quantized knowledge distillation (VQ-KD) to train a visual tokenizer for vision Transformer pretraining. VQ-KD discretized a continuous semantic space that provides supervision for masked image modeling rather than relying on image pixels. The semantic visual tokenizer greatly improved the BEIT pretraining and significantly boosted the transfer performance upon downstream tasks, such as image classification, and semantic segmentation. Moreover, a patch aggregation mechanism was introduced to explicitly encourage the model to produce global image representations, narrowing the gap between the patch-level pretraining and image-level representation aggregation. In the future, we would like to learn a universal tokenizer that projects words and images into the same vocabulary, so that we can conduct masked prediction for vision-language pretraining.
+
+# REPRODUCIBILITY
+
+Details of VQ-KD training, BEIT V2 pretraining, fine-tuning recipes are given in Appendix D, E, F and G. The models used for VQ-KD training are from the official repositories https:// github.com/facebookresearch/dino and https://github.com/openai/CLIP. The datasets (e.g., ImageNet, and ADE20k) are derived from publicly available data buckets. The code can be found in the supplementary materials. We will also provide pretrained checkpoints to reproduce the numbers.
+
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+Chen Wei, Haoqi Fan, Saining Xie, Chao-Yuan Wu, Alan Yuille, and Christoph Feichtenhofer. Masked feature prediction for self-supervised visual pre-training. arXiv preprint arXiv:2112.09133, 2021.
+
+Longhui Wei, Lingxi Xie, Wengang Zhou, Houqiang Li, and Qi Tian. MVP: Multimodality-guided visual pre-training. arXiv preprint arXiv:2203.05175, 2022.
+
+Tete Xiao, Yingcheng Liu, Bolei Zhou, Yuning Jiang, and Jian Sun. Unified perceptual parsing for scene understanding. In ECCV, 2018.
+
+Jiahui Yu, Xin Li, Jing Yu Koh, Han Zhang, Ruoming Pang, James Qin, Alexander Ku, Yuanzhong Xu, Jason Baldridge, and Yonghui Wu. Vector-quantized image modeling with improved vqgan. arXiv preprint arXiv:2110.04627, 2021.
+
+Xiaohua Zhai, Alexander Kolesnikov, Neil Houlsby, and Lucas Beyer. Scaling vision Transformers. arXiv preprint arXiv:2106.04560, 2021.
+
+Bolei Zhou, Hang Zhao, Xavier Puig, Tete Xiao, Sanja Fidler, Adela Barriuso, and Antonio Torralba. Semantic understanding of scenes through the ADE20K dataset. Int. J. Comput. Vis., 127(3): 302–321, 2019.
+
+Jinghao Zhou, Chen Wei, Huiyu Wang, Wei Shen, Cihang Xie, Alan Yuille, and Tao Kong. Image BERT pre-training with online tokenizer. In International Conference on Learning Representations, 2022.
+
+# A VISUALIZATION OF CODEBOOK
+
+It is observed that a discrete code tends to represent explicit semantics (Section 3.4). In Figure 5(upper), we show image examples corresponding to a given discrete code. One can see that discrete codes ignore image details, such as color, illumination, rotation and scale.
+
+In the lower part of Figure 5, we also show some patches that mismatch the semantic concepts. Taking the fish (the first image at the last row) as instance, VQ-KD misclassifies the spot on the fish body as the eye concept due to the local structure similarity.
+
+![](images/9349f26f06a59d420a53dbecc8d394059a22dcdd7b7065b9af2ea7af701f7791.jpg)  
+Figure 5: Visualization of image patches corresponding to discrete codes. Upper: examples matching the learned semantic concepts; Lower: patches mis-matching the semantic concepts. Corresponding patches are marked in red rectangle
+
+# B COMPARISON WITH LARGE-SCALE SUPERVISED PRETRAINING
+
+We report the performance by using the ImageNet-1k for pretraining in Table 1. To show the data scalability of BEIT V2, we conduct intermediate fine-tuning experiments on ImagNet-21k and final fine-tuning on ImageNet-1k, by using the 1600 epoch pretraining models in Table 1. From Table 7, BEIT V2 using ViT-L/16 with $3 8 4 \times 3 8 4$ input resolution, achieves $8 9 . 0 \%$ top-1 accuracy, which even outperforms ViT-H/14 using Google JFT-3B labeled dataset by $0 . 5 \%$ . This significant performance gain indicates the data efficiency and superiority of the proposed BEIT V2.
+
+Table 7: Top-1 accuracy on ImageNet-1K fine-tuning. $2 2 4 ^ { 2 }$ and $3 8 4 ^ { 2 }$ denote model resolutions.   
+
+<table><tr><td>Models</td><td>Model Size</td><td>Labeled Data Size</td><td>ImageNet-1k 224²</td><td>384²</td></tr><tr><td>Supervised Pretraining on ImageNet-21K</td><td></td><td></td><td></td><td></td></tr><tr><td>ViT-B/16 (Dosovitskiy et al.,2020)</td><td>86M</td><td>14M</td><td></td><td>84.0</td></tr><tr><td>ViT-L/16 (Dosovitskiy et al., 2020)</td><td>307M</td><td>14M</td><td></td><td>85.2</td></tr><tr><td>ViT-H/14 (Dosovitskiy et al., 2020)</td><td>632M</td><td>14M</td><td></td><td>85.1</td></tr><tr><td>Supervised Pretraining on Google JFT-3OOM (using labeled data)</td><td></td><td></td><td></td><td></td></tr><tr><td>ViT-B/16 (Dosovitskiy et al., 2020)</td><td>86M</td><td>300M</td><td></td><td>84.2</td></tr><tr><td>ViT-L/16 (Dosovitskiy et al., 2020)</td><td>307M</td><td>300M</td><td></td><td>87.1</td></tr><tr><td>ViT-H/14 (Dosovitskiy et al., 2020)</td><td>632M</td><td>300M</td><td></td><td>88.0</td></tr><tr><td>Supervised Pretraining on Google JFT-3B</td><td></td><td></td><td></td><td></td></tr><tr><td>ViT-B/16 (Zhai et al., 2021)</td><td>86M</td><td>3000M</td><td></td><td>86.6</td></tr><tr><td>ViT-L/16 (Zhai et al., 2021)</td><td>307M</td><td>3000M</td><td></td><td>88.5</td></tr><tr><td colspan="5">BEIT Pretraining on ImageNet-21K, and Intermediate Fine-Tuning on ImageNet-21K</td></tr><tr><td>BEIT ViT-B/16 (Bao et al., 2022)</td><td>86M</td><td>14M</td><td>85.2</td><td>86.8</td></tr><tr><td>BEIT ViT-L/16 (Bao et al.,2022)</td><td>307M</td><td>14M</td><td>87.4</td><td>88.4</td></tr><tr><td>BEIT v2 Pretraining on ImageNet-1K, and Intermediate Fine-Tuning on ImageNet-21K</td><td></td><td></td><td></td><td></td></tr><tr><td>BEIT V2 ViT-B/16 (ours)</td><td>86M</td><td>14M</td><td>86.5</td><td>87.5</td></tr><tr><td>BEIT V2 ViT-L/16 (ours)</td><td>307M</td><td>14M</td><td>88.4</td><td>89.0</td></tr></table>
+
+# C OVERALL FRAMEWORK FOR BEIT V2
+
+We show the tokenizer training part and BEIT V2 pretraining part in Figure 2 and Figure 3, respectively. In addition, we present the whole pretraining process in Figure 6.
+
+![](images/f6cbe28a663368e427f2f3fe98bfefab5ceff46263372f3b12685cfa812fb8e2.jpg)  
+Figure 6: Overall framework for BEIT V2 pretraining.
+
+# D HYPERPARAMETERS FOR VQ-KD TRAINING
+
+Table 8: Hyperparameters for training VQ-KD on ImageNet-1K.   
+
+<table><tr><td rowspan=1 colspan=1>Hyperparameters</td><td rowspan=1 colspan=1>Values</td></tr><tr><td rowspan=1 colspan=1>Encoder layersDecoder layersHidden sizeFFN inner hidden sizeAttention headsAttention head sizePatch sizeCodebook size</td><td rowspan=1 colspan=1>12{1,3}7683072126416 ×168192 × 32</td></tr><tr><td rowspan=1 colspan=1>Training epochsBatch sizeAdam βPeak learning rateMinimal learning rateLearning rate scheduleWarmup epochs</td><td rowspan=1 colspan=1>100512(0.9, 0.99)2e-41e-5Cosine5</td></tr><tr><td rowspan=1 colspan=1>Gradient clippingDropoutStoch.depthWeight decay</td><td rowspan=1 colspan=1>×XX1e-4</td></tr><tr><td rowspan=1 colspan=1>Data AugmentInput resolution</td><td rowspan=1 colspan=1>RandomResizeAndCrop224× 224</td></tr></table>
+
+# E HYPERPARAMETERS FOR BEIT V2 PRETRAINING
+
+Table 9: Hyperparameters for BEIT V2 pretraining on ImageNet-1K. ∗ denotes that the hyperparame ters are adopted when the pretraining schedule is 300 epochs.   
+
+<table><tr><td>Hyperparameters</td><td>Base Size</td><td>Large Size</td></tr><tr><td>Layers Hidden size</td><td>12 768</td><td>24</td></tr><tr><td>FFN inner hidden size</td><td>3072</td><td>1024 4096</td></tr><tr><td>Attention heads</td><td></td><td></td></tr><tr><td></td><td>12</td><td>16</td></tr><tr><td>Layer scale Patch size</td><td>0.1</td><td>1e-5</td></tr><tr><td>Relative positional embeddings</td><td colspan="2">16 ×16</td></tr><tr><td>Shared relative positional embeddings</td><td colspan="2">√ √</td></tr><tr><td>Training epochs Batch size</td><td colspan="2">300*/1600 2048</td></tr><tr><td>Adam β</td><td colspan="2">(0.9, 0.98*/0.999)</td></tr><tr><td>Peak learning rate</td><td colspan="2"></td></tr><tr><td></td><td colspan="2">1.5e-3</td></tr><tr><td>Minimal learning rate</td><td colspan="2">1e-5</td></tr><tr><td>Learning rate schedule</td><td colspan="2">Cosine</td></tr><tr><td>Warmup epochs</td><td colspan="2">10</td></tr><tr><td>Gradient clipping</td><td colspan="2">3.0</td></tr><tr><td>Dropout</td><td colspan="2">X</td></tr><tr><td>Drop path</td><td colspan="2">0*/0.1</td></tr><tr><td>Weight decay</td><td colspan="2">0.05</td></tr><tr><td>Data Augment</td><td colspan="2">RandomResizeAndCrop</td></tr><tr><td>Input resolution Color jitter</td><td colspan="2">224× 224</td></tr></table>
+
+# F HYPERPARAMETERS FOR IMAGE CLASSIFICATION FINE-TUNING
+
+Table 10: Hyperparameters for fine-tuning BEIT V2 on ImageNet-1K.   
+
+<table><tr><td>Hyperparameters</td><td>ViT-B/16</td><td>ViT-L/16</td></tr><tr><td rowspan="2">Peak learning rate Fine-tuning epochs Warmup epochs</td><td>5e-4 100</td><td>5e-4</td></tr><tr><td>20 0.65</td><td>50 5</td></tr><tr><td>Layer-wise learning rate decay Batch size Adam e Adam β</td><td colspan="2">0.8 1024 1e-8 (0.9, 0.999)</td></tr><tr><td>Minimal learning rate Learning rate schedule Repeated Aug Weight decay Label smoothing ε</td><td colspan="2">1e-6 Cosine X 0.05 0.1</td></tr><tr><td>Stoch. depth Dropout Gradient clipping Erasing prob.</td><td>0.1 X X 0.25</td><td>0.2</td></tr><tr><td>Input resolution Rand Augment Mixup prob. Cutmix prob. Relative positional embeddings Shared relative positional embeddings</td><td>224 × 224 9/0.5 0.8 1.0 √ X</td><td></td></tr></table>
+
+# G HYPERPARAMETERS FOR ADE20K SEMANTIC SEGMENTATIONFINE-TUNING
+
+Table 11: Hyperparameters for fine-tuning BEIT V2 on ADE20K.   
+
+<table><tr><td rowspan=1 colspan=1>Hyperparameters</td><td rowspan=1 colspan=1>ViT-B/16  ViT-L/16</td></tr><tr><td rowspan=1 colspan=1>Input resolution</td><td rowspan=1 colspan=1>512 × 512</td></tr><tr><td rowspan=1 colspan=1>Peak learning rateFine-tuning stepsBatch sizeAdam eAdam βLayer-wise learning rate decayMinimal learning rateLearning rate scheduleWarmup steps</td><td rowspan=1 colspan=1>{0.5, 0.8, 1.0}e-4160K161e-8(0.9, 0.999){0.75, 0.8, 0.85}0Linear1500</td></tr><tr><td rowspan=1 colspan=1>DropoutStoch. depthWeight decay</td><td rowspan=1 colspan=1>X0.1         0.20.05</td></tr><tr><td rowspan=1 colspan=1>Relative positional embeddingsShared relative positional embeddings</td><td rowspan=1 colspan=1>√X</td></tr></table>

parse/dev/cwjh8lqmOL/cwjh8lqmOL.md

@@ -0,0 +1,272 @@
+# GPT4Tools: Teaching Large Language Model to Use Tools via Self-instruction
+
+Rui Yang1∗‡, Lin Song2∗†, Yanwei $\mathbf { L i ^ { 3 } }$ , Sijie Zhao2, Yixiao $\mathbf { G e ^ { 2 } }$ , Xiu Li1, Ying Shan2 1Tsinghua Shenzhen International Graduate School, Tsinghua University 2Tencent AI Lab 3Chinese University of Hong Kong rayyang0116@gmail.com ronnysong@tencent.com
+
+The essential difference between humans and animals is that humans are capable of making and using tools.
+
+—Friedrich Engels
+
+# Abstract
+
+This paper aims to efficiently enable Large Language Models (LLMs) to use multimodal tools. Advanced proprietary LLMs, such as ChatGPT and GPT-4, have shown great potential for tool usage through sophisticated prompt engineering. Nevertheless, these models typically rely on prohibitive computational costs and publicly inaccessible data. To address these challenges, we propose the GPT4Tools based on self-instruct to enable open-source LLMs, such as LLaMA and OPT, to use tools. We generate an instruction-following dataset by prompting an advanced teacher with various multi-modal contexts. By using the Low-Rank Adaptation (LoRA) optimization, our approach facilitates the open-source LLMs to solve a range of visual problems, including visual comprehension and image generation. Moreover, we provide a benchmark to evaluate the ability of LLMs to use tools, which is performed in both zero-shot and fine-tuning ways. Extensive experiments demonstrate the effectiveness of our method on various language models, which not only significantly improves the accuracy of invoking seen tools but also enables the zero-shot capacity for unseen tools. The code and demo have been available at https://github.com/AILab-CVC/GPT4Tools.
+
+# 1 Introduction
+
+Recent advances in large language models (LLMs), such as GPT-3 [1], InstructGPT [2], and GPT3.5 [3], have demonstrated substantial potential in the area of zero-shot learning and logical reasoning. These models are typically trained on a large volume of text-only data, primarily sourced from the internet. However, as promising as they may seem, these advanced proprietary LLMs [3, 4] have significant limitations. One of the major hindrances is the high computational cost associated with these models, which may not be affordable or accessible to many scenarios. Additionally, these models typically depend on specialized data, such as source code and conversation history, which are not easily available to the public.
+
+Instead of solely focusing on language processing, many recent researches [5, 6] attempt to bridge the gap between language models and multi-modal models. Intelligent agents like Visual ChatGPT [5] and MMREACT [6] have made efforts to meet this goal by sophisticated prompt engineering. These agents utilize a pre-defined template to create instructions that vision-language foundation models can execute. Although these approaches have led to impressive results, the primary process of instruction decomposition is heavily based on GPT-3.5 [3], which is expensive and not publicly available, thus limiting further advancements. In addition, equipping these agents with the capability to use tools requires a large amount of data [3]. This brings up an open question: how to efficiently enable a primitive language model to use multi-modal tools?
+
+Table 1: Comparison of related works. ‘LM’ is the language model. ’Mechanism’ denotes how the language model learns to invoke tools. ‘Unseen’ indicates the zero-shot capability on unseen tools.   
+
+<table><tr><td>Method</td><td>LM</td><td>Mechanism</td><td>Teacher</td><td>Multi-Modal</td><td>Unseen</td></tr><tr><td>Lazaridou et al. [10]</td><td>Gopher-280B[15]</td><td> prompt</td><td>X</td><td>X</td><td>X</td></tr><tr><td>ToolFormer [11]</td><td>GPT-J (6B)[16]</td><td> self-instruct</td><td>×</td><td>X</td><td>X</td></tr><tr><td>Visual ChatGPT[5]</td><td>GPT-3.5 (175B) [3]</td><td>prompt</td><td>X</td><td></td><td></td></tr><tr><td>MMREACT [6]</td><td>GPT-3.5 (175B) [3]</td><td> prompt</td><td>X</td><td></td><td></td></tr><tr><td>GPT4Tools (ours)</td><td>Vicuna-13B [12]</td><td> self-instruct</td><td>←</td><td></td><td></td></tr></table>
+
+To achieve it, different from previous studies [7–11], we explore a new perceptive as illustrated in Table 1. We propose a simple yet effective method, called GPT4Tools, designed to empower open-source LLMs with the ability to use tools via self-instruct from advanced LLMs. To be specific, we construct an instruction dataset by prompting advanced teachers, such as GPT-3.5 [3], conditional on visual contents and tool descriptions, which results in a great deal of tool-related instructions. Unlike Toolformer [11], our method can utilize visual content description to improve data diversity significantly. Furthermore, with the generated instruction-following dataset, we employ Low-Rank Adaptation (LoRA) to fine-tune the primitive language models including Vicuna [12], LLaMa [13], and OPT [14]. Besides intrinsic language abilities, GPT4Tools-based language models are also able to solve a variety of visual problems by using tools. The tasks involve visual comprehension and image generation, such as object grounding and segmentation, generating and instructing images, and visual question answering (VQA). The proposed GPT4Tools not only significantly improve the accuracy of LLMs to invoke seen tools but also enable the zero-shot capacity for unseen tools in a zero-shot manner.
+
+Furthermore, we propose an evaluation metric to assess the effectiveness of LLMs in utilizing tools across diverse tasks. With this metric, two human-curated validation sets are constructed to evaluate the LLMs in zero-shot and fine-tuning ways, offering a comprehensive measure of the ability to use tools. To demonstrate the effectiveness of GPT4Tools, we conduct extensive experiments on various language models. The results show the efficacy of teaching LLMs when and how to use tools. Specifically, the Vicuna-13B fine-tuned on our GPT4Tools achieves $9 . 3 \%$ absolute gains in successful rate over GPT-3.5 [3] that acquires tool priors in context. In addition, the fine-tuned Vicuna-13B shows a solid capacity to invoke unseen tools, wihich can be comparable to GPT-3.5’s success rate.
+
+Our GPT4Tools stands distinct from previous and concurrent studies [5–11] in three ways. First, our method enables primitive open-source language models to use tools, eliminating the dependence on advanced proprietary LLMs like ChatGPT. Second, we design a new approach based on multi-modal contexts for self-instruction and augmentation, which significantly promote multi-modal tool usage and can be deployed in different directions. Third, we propose a new benchmark to assess the effectiveness of using tools, and our method shows remarkable improvements.
+
+# 2 Related Work
+
+Vision and Language Model. In the quest to achieve multi-modal models capable of addressing both language and vision tasks, several studies [17–22] have explored methods to enable language models to comprehend visual input. These include techniques such as transforming images into discrete textual representations [17, 18] or projecting continuous image features into the textual feature space [23–26]. Concurrently, other research has been dedicated to the development of generalist models [19, 20, 22, 21], which permit a model to simultaneously input images and text, eliminating the necessity for a projection process. For instance, OFA [27] devised a unified sequence-to-sequence decoding architecture applicable to language and object detection tasks. Similarly, Pixel2Pixel [21] converted the outcome of visual comprehension tasks into a series of discrete tokens akin to language tasks. Gato [22] brought together a range of vision and control tasks into a sequential prediction issue,
+
+# Image Content
+
+# Tool Pocket
+
+![](images/c183aeadddf0d709c5ac740836224402e0a4f5af78ea500ce27cf8fd830e33bd.jpg)
+
+<tool name>: <usage scenario>, <arguments>
+
+A person is leaning low on their motorcycle on the tracks.   
+A person leaning down on a motorcycle as they ride on a track.   
+A man is nearly sideways while racing a   
+motorcycle around a track.   
+A man with a helmet is riding a motorcycle on it's side.   
+motorcycle: [179.44, 105.55, 411.64, 220.7] person: [136.26, 77.72, 356.95, 124.75]
+
+![](images/9708f6f6d2085b89d3142fb022fa7908e30277608dd1713f3a2bfb4403e22da7.jpg)
+
+# ChatGPT
+
+![](images/e104d59c1b20c2474a30f790b00d842bcfcabb09e669a40a40d069e4be487825.jpg)  
+Figure 1: Diagram of the GPT4Tools. We prompt the ChatGPT with image content and definition of tools in order to obtain a tool-related instruction dataset. Subsequently, we employ LoRA [38] to train an open-source LLM on the collected instruction dataset, thus adapting the LLM to use tools.
+
+while UViM [28] and Unified-IO [20] advocated for the learned discrete codes as a means to unify an array of vision tasks. By contrast, we equip the language model with diverse specialized multi-modal tools to process distinct vision tasks. This approach not only promotes the scalability of the model for various tasks but also avoids the issue of forgetfulness stemming from repeated fine-tuning.
+
+Instruction Tuning. Recent studies [29, 2, 30–33] have turned out that pre-trained language models could follow natural language instructions and complete various real-world tasks if they are tuned on specific instruction-following data. Notably, InstructGPT [2], FLAN-T5 [31], OPT-IML [33] demonstrated remarkable performance on specific tasks after being fine-tuned with instruction data. In order to release the cost of human-written instructions, Self-Instruction [34] found that the instructionfollowing capabilities of language models can be enhanced by turning on their own generated instruction data. More importantly, this approach inspired a feasible means to improve the zero- and few-shot abilities of language models, i.e., distilling off-the-shelf language models using instructional data from strong GPT-3.5 [3] or GPT-4 [4]. As a result, many recent works [12, 35–37] tried to construct excellent language models for various applications based on the LLaMA [13]. For instance, Stanford-Alpaca has employed 52K instructions generated by GPT-3.5 [3] to construct an exceptional dialogue model. LLaVa [37] has adopted GPT-3.5 [3] and GPT-4 [4] to incorporate instructionfollowing data related to visual content. In this paper, we use GPT-3.5 [3] to construct tool-related instruction datasets, thereby allowing other language models to acquire tool usage capabilities.
+
+Tool Usage. In the Natural Language Processing (NLP) community, several arts [7–11] sought to endow language models with the ability to use tools. For instance, Komeili et al. [7] proposed to generate conversation responses conditioned on the results of the search engine. LaMDA [9] created a set of tools (comprising an information retrieval system, a calculator, and a translator) to avoid plausible outputs. Lazaridou et al. [10] utilized few-shot prompting on Gopher-280B [15] to enable the search engine to ground its output in factual and current information. Similarly, Visual ChatGPT [5] and MMREACT [6] prompted ChatGPT to invoke visual foundation models. In addition,
+
+ToolFormer [11] used self-instruction and bootstrapping to teach GPT-J (6B) [16] using five tools, which include a question and answer system, a calculator, a search engine, a machine translation system, and a calendar. On the contrary, we focus on using the GPT-3.5 model as a powerful teacher to distill off-the-shelf language models and enable them to access many visual models.
+
+# 3 Method
+
+Large language models (LLMs) [1, 14, 15] have shown remarkable in-context learning abilities. Among them, GPT-3.5 [3] and GPT-4 [4] are proven to effectively perform text-annotation tasks [39] or instruct other models to follow instructions of specific domains [40, 35, 12, 37]. Inspired by these findings, we propose to enable off-the-shelf language models to acquire tool usage capabilities by taking GPT-3.5 as a powerful teacher. Specifically, we utilize GPT-3.5 to generate tools-related instruction-following data, which is then used to tune the language model. This process offers language models the ability to access multi-modal information by invoking visual models. Furthermore, we propose an evaluation metric to assess the tool-use ability of the given language model. In the following, we elaborate on the data generation, instruction tuning, and evaluation metric in turn.
+
+# 3.1 Dataset Construction
+
+Data Generation. Figure 1 illustrates the process of generating tool-related instruction dataset. Given an image, we construct the image content $X _ { C }$ according to the captions and bounding boxes, which is a straightforward means of establishing connections between an image and a language model [17, 18]. Conditioned upon the $X _ { C }$ , we provide the GPT-3.5 [3] $( \mathrm { M _ { T } } )$ with a tool-related prompt $P _ { t }$ whereby attaining a large number of instruction-following data:
+
+$$
+Y \sim \operatorname { M } _ { \mathrm { T } } ( P _ { t } | X _ { C } ) .
+$$
+
+The $P _ { t }$ comprises the system message, the definition of tools (<tool name> : <usage scenario>, <arguments>), and the suffix prompt which encourages $M _ { T }$ to generate visual instructions and desired outputs. $Y$ , the outcome of $\mathrm { M _ { T } }$ , consists of $N$ instruction-output pairs $\{ y ^ { 1 } , y ^ { 2 } , . . . , y ^ { N } \}$ , where $y _ { i }$ has the format of "<instruction>, <tool name>, <arguments>", and $N$ is the number of defined tools. As each input of $\mathrm { M _ { T } }$ is grounded to the image content $X _ { C }$ , the generated instructions are inherently connected to the image, thus avoiding arbitrary generation. In detail, the $X _ { C }$ consists of ground-truth captions and bounding boxes with tags corresponding to the images. The rich variability of the image brings up a higher diversity of instructions when compared to imagined ones. To provide contrast, we also collect instruction follow-up data without image content $X _ { C }$ , which is similar to ToolFormer [11]. As depicted in Figure 2, without image context priors, GPT-3.5 tends to generate objects of visual instructions towards a small subset, which is reflected in t-SNE as sparser clusters. On the contrary, instructions generated with image-conditioned prompts are notably informative and diverse due to changes in the image content, reflected in the visualization as denser and more widely distributed results. The language model tuned by image-conditioned data is more robust than models without the image content (Table 3).
+
+Data Formation. Upon the collected raw dataset ( $7 0 K$ items), we apply a filtering process to remove duplicate instructions, incorrectly formatted instructions, calls with incorrect tool names, and calls with incorrect tool-arguments formats. This step results in $4 1 K$ retained items. Subsequently, we transform the retained data into an instruction-response format utilizing a standardized template as shown in the bottom-left corner of Figure 1. This procedure produces a new dataset, denoted as $Y _ { S } ^ { \mp }$ . The instruction component of $Y _ { S } ^ { + }$
+
+![](images/e7c531eb0db6a033da2be444a918f10dc75c11ce3b2e4d6b0b71c16f6732b87b.jpg)  
+Figure 2: t-SNE1visualization for instruction data with and without image content.
+
+incorporates a prefix prompt that encompasses system messages and tool definitions, <image content> that denotes the image content, <user input $>$ that is replaced with the generated visual instruction, and a suffix prompt designed to prompt the language model to reply the user input using given tools. The response in $\bar { Y } _ { S } ^ { + }$ comprises 4 elements: (1) Thought, meaning the model’s cognition when to use tools; (2) Action, signifying which tools the model will use or action the model will take; (3) Action Input, representing arguments of the selected tool; and (4) Observation, reflecting outcomes of the used tool. A sample from $Y _ { S } ^ { + }$ is presented in the Figure 3 (a).
+
+![](images/575be921710ea40eb291c86878ff801b6be89a21cbc5fd05414ff28ae00996d1.jpg)  
+Figure 3: Samples of the single-turn instruction, negative instruction, and contextual instruction.
+
+Data Augmentation. Although we have successfully acquired instruction-following data related to the tool usage, this simplistic format lacks complexity and depth in both instructions and responses. To tackle this challenge, we augment the generated data from two perspectives:
+
+• Negative samples. The generated instructions primarily focus on tool usage, i.e., the decision after the Thought is always "Yes". Consequently, there is a potential risk that the fine-tuned model overfits such a decision. When the user instruction is not associated with the tool usage, the fine-tuned model may erroneously execute irrelevant actions by invoking unnecessary tools. To mitigate this issue, we synthesize negative samples $Y _ { S } ^ { - }$ by selecting conversation data from the existing dataset [40] and converting them into the required template, as illustrated in Figure 3 (b). By tuning with $Y _ { S } ^ { + } \cup Y _ { S } ^ { - }$ , the model can accurately decide when to use tools. • Context samples. The generated instructions adopt a standard and fixed single-tune format, which lacks a contextual structure. Thus, as shown in Figure 3 (c), we augment the dataset by cutting off the chain of action. We also randomly select multiple instructions from $Y _ { S } ^ { + } \cup Y _ { S } ^ { - }$ and reformat them into multi-turn conversation data. In this way, we synthesize the contextual instruction-following data $Y _ { S } ^ { c }$ , enabling the tuned model to call tools within the given context.
+
+So far, we have constructed the tool-related instructional dataset, including positive samples, negative samples, and context samples: $Y _ { S } = Y _ { S } ^ { + } \cup Y _ { S } ^ { - } \cup Y _ { S } ^ { c }$ .
+
+# 3.2 Instruction Tuning
+
+Based on the dataset $Y _ { S }$ , we tune the off-the-self language model using its original auto-regressive training objective. To make the tuning feasible, we leverage LoRA [38] optimization, which freezes the language model and only optimizes rank decomposition components of the Transformer layers.
+
+For a sequence with $L$ tokens, we compute the probability of the target response $X _ { r }$ by:
+
+$$
+p ( X _ { r } | X _ { C } , X _ { i n s t } ) = \prod _ { i = 1 } ^ { L } p _ { \theta } ( x _ { i } | X _ { C } , X _ { i n s t } , x _ { 1 : i - 1 } ) ,
+$$
+
+where $X _ { i n s t }$ denotes the instruction tokens; and $\theta$ is the trainable parameters. In practice, prefix prompt and suffix prompt are also involved but we here skip them for better readability.
+
+# 3.3 Evaluation Approach
+
+Numerous benchmarks [42, 43, 8, 44] typically utilize human-annotated datasets to evaluate the performance of a model. For the purpose of measuring the tool-usage capacity of the language model, we construct an evaluation dataset following the same procedures detailed in $\ S \ 3 . 1$ and manually verify the accuracy of each item. This evaluation dataset is partitioned into two components: the first part (validation set) has the same ingredients as the training set, encompassing 23 tools; the second part (test set) comprises 8 novel tools absent from the training set. We will use the validation set to validate whether the model can adhere to user commands correctly after tuning with the training set. The test set will verify whether the model can generalize to new tools after tuning. Based on the human-annotated evaluation dataset with $N$ instructions, we design a successful rate to measure the model’s performance from three aspects:
+
+• Successful Rate of Thought $\mathrm { ( S R } _ { t } ^ { } \mathrm { ) }$ ) measures whether the predicted decision matches the groundtruth decision. It is calculated as $\begin{array} { r } { \mathrm { S R } _ { t } = \frac { 1 } { N } \sum _ { i = 1 } ^ { N } \mathbb { I } ( \tau _ { i } ) } \end{array}$ , where $\tau _ { i }$ signifies a singular process. If the thought is correct, $\mathbb { I } ( \tau _ { i } )$ is equal to 1, and 0 otherwise.
+
+• Successful Rate of Action $\mathrm { ( S R } _ { a c t }$ ) measures whether the predicted tool name is in agreement with the name of the ground truth tool. It is calculated as $\begin{array} { r } { \mathrm { S R } _ { a c t } ^ { \mathrm { - } } = \frac { 1 } { N } \sum _ { i = 1 } ^ { N } \mathbb { I } ( \alpha _ { i } ) } \end{array}$ , where $\alpha _ { i }$ denotes the matching process for the tool names. In cases where the predicted tool name matches the pre-defined name, $\mathbb { I } ( \alpha _ { i } )$ equals 1, and 0 otherwise.
+
+• Successful Rate of Arguments $\mathrm { ( S R } _ { a r g s } )$ evaluates whether the predicted arguments match the ground-truth arguments. It can be calculated using the following equation:
+
+$$
+\mathrm { S R } _ { a r g s } = \frac { 1 } { N } \sum _ { i = 1 } ^ { N } \eta _ { i } , \mathrm { w h e r e } \eta _ { i } = \frac { 1 } { K } \sum _ { j } ^ { K } \eta _ { i , j } .
+$$
+
+Here, $\eta _ { i }$ denotes a sequence of arguments encompassing both the image path and the input text. For instance, ControlNet [45] needs the image path saved conditions (e.g., the pose map, depth map, or segment map) and the input text described user commands. $K$ represents the quantity of arguments in $\eta _ { i }$ . When the argument belongs to the image path, $\eta _ { i , j }$ equals 1 if the predicted and ground-truth image paths share the same suffix, and 0 otherwise. When the argument is the input text, $\eta _ { i , j }$ is equal to the BLEU score between the predicted and the ground truth text.
+
+• Successful Rate (SR) measures whether a chain of actions are executed successfully, which requires the correctness of thought, tool name, and tool arguments at the same time:
+
+$$
+{ \mathrm { S R } } = { \frac { 1 } { N } } \sum _ { i = 1 } ^ { N } \mathbb { I } ( \tau _ { i } ) \cdot \mathbb { I } ( \alpha _ { i } ) \cdot \mathbb { I } ( \eta _ { i } > 0 . 5 )
+$$
+
+Additionally, when a procedure comprises two consecutive actions, the SR equals $1 0 0 \%$ only if both actions are executed correctly.
+
+# 4 Experiments
+
+# 4.1 Implementation Details
+
+We employ the ChatGPT (gpt-3.5-turbo) [3] as the teacher model to generate the raw instructionfollowing data. Since this study focused on teaching the off-the-self language models to use tools instead of prompt engineering, we adopted a methodology outlined in the Visual ChatGPT [5] to construct tool-related prompts. Our tool pocket consists of 31 tools, including the 23 tools defined in Visual ChatGPT [5] and 8 extra tools (please refer to Appendix for detailed tool names). During generation, all image information utilized in GPT4Tools is sourced from the training set of COCO [43]. After generation, the training set comprises $7 1 K$ instruction-response pairs, wherein all instructional data is related to the 23 tools. We divided the human-annotated evaluation dataset into two parts: the validation set and the test set. The validation set contains the same tools as the training set, with approximately 50 items associated with each tool. The test set includes tools that are not present in the training set (further details provided in Appendix).
+
+Table 2: Comparison of different language models. The zero-shot prediction is adopted for unseen tools and the models without GPT4Tools.   
+
+<table><tr><td rowspan="2">Model</td><td rowspan="2">GPT4Tools</td><td colspan="4">Validation (seen tools)</td><td colspan="4">Test (unseen tools)</td></tr><tr><td>SRt</td><td>SRact</td><td>SRargs</td><td>SR</td><td>SRt</td><td>SRact</td><td>SRargs</td><td>SR</td></tr><tr><td>GPT-3.5 [3] (text-davinci-003)</td><td>×</td><td>93.5</td><td>96.1</td><td>78.0</td><td>84.8</td><td>99.5</td><td>99.5</td><td>91.5</td><td>91.5</td></tr><tr><td rowspan="2">OPT-13B [14]</td><td>X</td><td>1.1</td><td>1.2</td><td>0.0</td><td>0.0</td><td>0.0</td><td>0.0</td><td>0.0</td><td>0.0</td></tr><tr><td></td><td>99.4</td><td>98.3</td><td>89.2</td><td>93.2</td><td>97.8</td><td>89.6</td><td>84.0</td><td>78.6</td></tr><tr><td rowspan="2">LLaMa-13B [13]</td><td>X</td><td>20.4</td><td>15.7</td><td>16.5</td><td>3.2</td><td>16.1</td><td>17.6</td><td>21.7</td><td>2.0</td></tr><tr><td></td><td>77.3</td><td>74.9</td><td>71.4</td><td>66.4</td><td>74.2</td><td>72.2</td><td>70.9</td><td>69.9</td></tr><tr><td rowspan="2">Vicuna-13B [12]</td><td>X</td><td>69.2</td><td>25.1</td><td>25.2</td><td>12.4</td><td>84.4</td><td>43.7</td><td>46.7</td><td>26.2</td></tr><tr><td></td><td>98.7</td><td>97.6</td><td>91.4</td><td>94.1</td><td>98.2</td><td>97.0</td><td>92.2</td><td>90.6</td></tr></table>
+
+Based on the collected data, we tuned language models (LLaMA [13], Vicuna [12], and OPT [14]) with LoRA [38] technology. Specifically, we equipped the projection layers of query, key, value, and output with LoRA layers. The LoRA attention dimension and scaling alpha were set to 16. While the language model was kept frozen, the LoRA layers were optimized using the AdamW [46]. All models were fine-tuned over 3 epochs, with a batch size 512. The learning rate was set to $3 \times 1 0 ^ { - 4 }$ , and the maximum length of new tokens was restricted to 2048. Unless otherwise specified, we used Vicuna-13B for the ablation experiments.
+
+# 4.2 Main Result
+
+Can instruction datasets teach language model using tools? The outcomes of GPT-3.5 [3], OPT13B [14], LLaMA-13B [13], and Vicuna-13B [12] are presented in Table 2. GPT-3.5 is considered analogous to Visual ChatGPT [5]. Upon prompting GPT-3.5 with tool-associated instructions, it can attain a SR of $8 4 . 8 \%$ on the validation set, thereby underscoring its zero-shot ability to follow a standardized format and utilize tools effectively. Notably, OPT-13B fails to invoke tools with the prompts alone. In contrast, LLaMA-13B and Vicuna-13B exhibit a certain level of comprehension of tool usage, while they still face challenges in executing a chain of actions. Specifically, LLaMA-13B achieves $3 . 2 \%$ SR, which is absolutely lower than $\mathrm { S R } _ { t }$ , $\mathrm { S R } _ { a c t }$ , and $\mathrm { S R } _ { a r g s }$ . In the case of Vicuna13B, its SR is $5 6 . 8 \%$ less than $\mathrm { S R } _ { t }$ , implying that under a zero-shot setup, Vicuna-13B displays commendable discernment in determining when to use tools within a given context. After fine-tuned with GPT4Tools, there are substantial alterations in the tool invocation competencies of each model. Specifically, the SR of OPT-13B witnessed a sharp increase from 0 to $9 3 . 2 \%$ . Similarly, the SR for LLaMA-13B escalates from $3 . 2 \%$ to $6 6 . 4 \%$ , and Vicuna-13B’s SR rises from $1 2 . 4 \%$ to ${ \dot { 9 } } 4 . 1 \%$ . These outcomes unequivocally validate that the GPT4Tools developed in this study are indeed effective in instructing language models to use tools.
+
+Can the model be generalized to unseen tools after fine-tuning? The right side of Table 2 shows the results when prompting a novel tool and corresponding utilization. On the test set, GPT-3.5 attaines $9 1 . 5 \%$ SR in a zero-shot manner. The outcomes for other models, which are not fine-tuned on the GPT4Tools and directly invoke tools utilizing prompts, are analogous to those on the validation set. In contrast, models that are fine-tuned on the GPT4Tools dataset exhibit a degree of competence in invoking tools that have not been previously encountered (did not appear in the training set). More specifically, the fine-tuned LLaMA-13B model achieves a superior SR on new tools by a margin of $6 7 . 9 \%$ when compared to the original model. The fine-tuned Vicuna-13B model demonstrates $9 0 . 6 \%$ SR on new tools, which is comparable to GPT-3.5. This observation indicates that the language model can invoke unseen tools after fine-tuned with GPT4Tools.
+
+Table 3: Ablation study for data augmentations on the validation set. ’IC’, ’CS’, ’NS’ denotes image content, context samples, and negative samples, respectively.   
+
+<table><tr><td></td><td>CS</td><td>NS</td><td>SRt</td><td>SRact</td><td>SRargs</td><td>SR</td></tr><tr><td></td><td></td><td></td><td>70.0</td><td>55.7</td><td>51.7</td><td>36.9</td></tr><tr><td>v</td><td></td><td></td><td>89.6</td><td>89.9</td><td>84.5</td><td>81.6</td></tr><tr><td>v</td><td>v</td><td></td><td>97.4</td><td>95.7</td><td>88.5</td><td>91.6</td></tr><tr><td>&lt;</td><td>v</td><td>v</td><td>98.7</td><td>97.6</td><td>91.4</td><td>94.1</td></tr></table>
+
+Table 4: Ablation study for different model scales on the validation set. 7B and 13B refer to Vicuna7B [12] and Vicuna-13B [12] models, respectively.   
+
+<table><tr><td>Model</td><td>GPT4Tools</td><td>SRt</td><td>SRact</td><td>SRargs</td><td>SR</td></tr><tr><td>7B</td><td>× v</td><td>27.7 96.2</td><td>15.8 94.5</td><td>11.5</td><td>4.5</td></tr><tr><td rowspan="2">13B</td><td></td><td>69.2</td><td>25.1</td><td>89.8</td><td>92.9</td></tr><tr><td>X</td><td>98.7</td><td>97.6</td><td>25.2 91.4</td><td>12.4 94.1</td></tr></table>
+
+# 4.3 Ablation Study
+
+Data Augmentation. As depicted in Table 3, we execute a series of ablation studies on various tricks implemented during the creation of the dataset. When instructions are not conditioned upon the image content, the SR of the fine-tuned model on the validation set is a mere $3 6 . 9 \%$ . In contrast, when instructions are generated with conditioning on the image content, the SR on the validation set is enhanced substantially to $8 1 . 6 \%$ . This uptick can be primarily attributed to the elevated diversity and intricacy of the generated instructions. Moreover, an augmentation of the SR to $9 1 . 6 \%$ is observed upon introducing context samples into the instructions. This finding underscores the fact that partitioning the chain of actions and allocating them to the in
+
+![](images/58985c6ee658faac5ee7721fa7e9611e13d7059f9d4fffc187922dec798155e0.jpg)  
+Figure 4: Performance variation curve with the fine-tuning iteration.
+
+struction and response can strengthen the model’s comprehension of the tool. It is noteworthy to mention that with the incorporation of negative samples into the generated instructions, the SR increases to $9 4 . 1 \%$ . This outcome can be traced back to the propensity of the model, when trained exclusively with positive samples, to bias toward tool invocation. This tendency consequently diminishes the capacity to discern the appropriate cases for tool usage. Adding negative samples equips the model with the ability to determine when to use tools.
+
+Model Scales. We attempt experiments with models at different scales. The results in Table 4 demonstrate that after fine-tuned on the generated dataset, Vicuna-7B [12] is also capable of invoking tools in a fixed format. Specifically, under a zero-shot setting, Vicuna-7B achieves only a $4 . 5 \%$ SR. By contrast, after fine-tuning, it can achieve an SR of $9 2 . 9 \%$ .
+
+Tuning Iteration. We increase the number of iterations for fine-tuning and present the results in Figure 4. Notably, during the range of iterations from 400 to 800, the model’s performance demonstrates substantial fluctuations in tool invocation. However, subsequent to this range, there is a steady improvement in $\mathrm { S R } t$ , SRact, $\mathrm { S R } _ { a r g s }$ , and SR. This indicates that the model progressively adapts to the dataset, enhancing its capability to invoke tools.
+
+# 4.4 Case Study
+
+Figure 5 presents a comparative analysis of our model with Visual ChatGPT [5] and LLaVa [37]. When an image is submitted by the user alongside the instruction "Generate a picture of real people based on the edge", Visual ChatGPT delivers an image that exhibits a weak correlation with the given instruction. Owing to its inability to generate images, LLaVa only returns a caption. In contrast, our model produces an accurate result, thereby evidencing that the tool-related instruction tuning method proposed in this paper can effectively instruct language models in the correct usage of tools. In Figure 6, we further demonstrate that the Vicuna-13B fine-tuned on GPT4Tools is capable of finishing some visual commands by invoking visual tools. This finding indicates that imparting knowledge to language models regarding the tool invocation could potentially be a way toward the development of a generalist model. More case studies are presented in the Appendix.
+
+![](images/0647e7eb50fc800b9a45d9f2dbc9bc549d9f6dadaf129d365e619f3048b5458e.jpg)  
+Figure 5: Comparison with other models. Our GPT4Tools responds correctly, while Visual ChatGPT [5] replies with the wrong image, and LLaVa [37] can not generate the image.
+
+![](images/dea45d1bc86efc49d4055fa47f2baaaba6cff90cc950c1f4c116c42b2243f85f.jpg)  
+Figure 6: Cases of invoking tools from Vicuna-13B [12] fine-tuned on our GPT4Tools.
+
+Table 5: Results of GPT4Tools using Top-K related tools. The total number of tools equals 23.   
+
+<table><tr><td>Model</td><td>Retrieval Top-K</td><td>SRt</td><td>SRact</td><td>SRargs</td><td>SR</td></tr><tr><td>Vicuna-13B[12]</td><td>1</td><td>69.2</td><td>25.1</td><td>25.2</td><td>12.4</td></tr><tr><td>w/ GPT4Tools</td><td>1</td><td>87.0</td><td>55.8</td><td>57.5</td><td>54.0</td></tr><tr><td>w/ GPT4Tools</td><td>2</td><td>93.1</td><td>70</td><td>69.5</td><td>67.8</td></tr><tr><td>w/ GPT4Tools</td><td>3</td><td>95.8</td><td>74.4</td><td>72.9</td><td>73.1</td></tr><tr><td>w/ GPT4Tools</td><td>23</td><td>98.7</td><td>97.6</td><td>91.4</td><td>94.1</td></tr></table>
+
+# 5 Discussion
+
+Although the proposed GPT4Tools can teach plug-and-play language models to use tools effectively, it still has some limitations. As shown in Figure 2 the success rate of all models is not $1 0 0 \%$ . Thus, further improvements are still necessary for practical applications. Additionally, GPT4Tools teaches the model to explicitly invoke tools using a verbose and fixed prompt. This approach decreases the computational efficiency since attention-based architectures compute the relationships between all tokens. Besides, with the increased number of tools, the prompt length might surpass the limited context length of LLMs. In this case, we can alternatively utilize a tool retrieval technique to filter out a small set of tools and then apply GPT4Tools-based LLMs for tool selection and invocation. We employ BM25, based on the user input, to retrieve the top-K tools from the defined 23 tools. As shown in Table 5, SR is only $5 4 \%$ while retrieving the top-1 tool. When the number of retrieved tools increases to 3, SR is boosted to $7 3 . 1 \%$ . Although the retrieval strategy can mitigate the reliance on long context models for a large number of tools to some extent, its SR can not match the original model. This result can be attributed to the inabilities of the retriever. Therefore, in the future, it is imperative to build a specialized retriever for the tool name retrieval. Moreover, it should be explored how to enable the model to implicitly invoke various tools instead of using the complex prompt. Nevertheless, our GPT4Tools method provides a viable approach for equipping language models with the ability to use multi-modal tools.
+
+# 6 Conclusion
+
+In this paper, we introduce GPT4Tools, a novel method that enables open-source language models to utilize multi-modal tools efficiently. Specifically, We construct a tool-related instructional dataset by prompting advanced GPT-3.5 conditional on image context. Then, we augment the generated data by introducing negative and context samples. Based on the built dataset, we employ LoRA fine-tuning technology to enhance the tool-usage capability of language models, thus allowing them to handle various visual tasks, e.g., visual comprehension and image generation. Moreover, we propose a benchmark to assess tool usage accuracy from the decision when to use tools, which tools to use, and arguments of invoked tools. In this benchmark, language models tuned with our GPT4Tools perform comparably to GPT-3.5 on unseen tools. We desire the GPT4Tools to pave the way for equipping open-source language models with the ability to use multi-modal tools.
+
+# Acknowledgments
+
+This research is partly supported by the National Key R&D Program of China (Grants No.   
+2020AAA0108302 & 2020AAA0108303), and Shenzhen Science and Technology Project (Grant No.   
+JCYJ20200109143041798) & Shenzhen Stable Supporting Program (WDZC20200820200655001) & Shenzhen Key Laboratory of next-generation interactive media innovative technology (Grant No.   
+ZDSYS20210623092001004).
+
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parse/dev/cwjh8lqmOL/cwjh8lqmOL_content_list.json

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+    {
+        "type": "text",
+        "text": "GPT4Tools: Teaching Large Language Model to Use Tools via Self-instruction ",
+        "text_level": 1,
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+        "text": "Rui Yang1∗‡, Lin Song2∗†, Yanwei $\\mathbf { L i ^ { 3 } }$ , Sijie Zhao2, Yixiao $\\mathbf { G e ^ { 2 } }$ , Xiu Li1, Ying Shan2 1Tsinghua Shenzhen International Graduate School, Tsinghua University 2Tencent AI Lab 3Chinese University of Hong Kong rayyang0116@gmail.com ronnysong@tencent.com ",
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+    {
+        "type": "text",
+        "text": "The essential difference between humans and animals is that humans are capable of making and using tools. ",
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+    {
+        "type": "text",
+        "text": "—Friedrich Engels ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Abstract ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "This paper aims to efficiently enable Large Language Models (LLMs) to use multimodal tools. Advanced proprietary LLMs, such as ChatGPT and GPT-4, have shown great potential for tool usage through sophisticated prompt engineering. Nevertheless, these models typically rely on prohibitive computational costs and publicly inaccessible data. To address these challenges, we propose the GPT4Tools based on self-instruct to enable open-source LLMs, such as LLaMA and OPT, to use tools. We generate an instruction-following dataset by prompting an advanced teacher with various multi-modal contexts. By using the Low-Rank Adaptation (LoRA) optimization, our approach facilitates the open-source LLMs to solve a range of visual problems, including visual comprehension and image generation. Moreover, we provide a benchmark to evaluate the ability of LLMs to use tools, which is performed in both zero-shot and fine-tuning ways. Extensive experiments demonstrate the effectiveness of our method on various language models, which not only significantly improves the accuracy of invoking seen tools but also enables the zero-shot capacity for unseen tools. The code and demo have been available at https://github.com/AILab-CVC/GPT4Tools. ",
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+        "type": "text",
+        "text": "1 Introduction ",
+        "text_level": 1,
+        "bbox": [
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+    },
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+        "type": "text",
+        "text": "Recent advances in large language models (LLMs), such as GPT-3 [1], InstructGPT [2], and GPT3.5 [3], have demonstrated substantial potential in the area of zero-shot learning and logical reasoning. These models are typically trained on a large volume of text-only data, primarily sourced from the internet. However, as promising as they may seem, these advanced proprietary LLMs [3, 4] have significant limitations. One of the major hindrances is the high computational cost associated with these models, which may not be affordable or accessible to many scenarios. Additionally, these models typically depend on specialized data, such as source code and conversation history, which are not easily available to the public. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Instead of solely focusing on language processing, many recent researches [5, 6] attempt to bridge the gap between language models and multi-modal models. Intelligent agents like Visual ChatGPT [5] and MMREACT [6] have made efforts to meet this goal by sophisticated prompt engineering. These agents utilize a pre-defined template to create instructions that vision-language foundation models can execute. Although these approaches have led to impressive results, the primary process of instruction decomposition is heavily based on GPT-3.5 [3], which is expensive and not publicly available, thus limiting further advancements. In addition, equipping these agents with the capability to use tools requires a large amount of data [3]. This brings up an open question: how to efficiently enable a primitive language model to use multi-modal tools? ",
+        "bbox": [
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+    {
+        "type": "table",
+        "img_path": "images/1887c3219a4d342e3c7880de123b5978dc3984bd23f66b07320699e00cc6baea.jpg",
+        "table_caption": [
+            "Table 1: Comparison of related works. ‘LM’ is the language model. ’Mechanism’ denotes how the language model learns to invoke tools. ‘Unseen’ indicates the zero-shot capability on unseen tools. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>LM</td><td>Mechanism</td><td>Teacher</td><td>Multi-Modal</td><td>Unseen</td></tr><tr><td>Lazaridou et al. [10]</td><td>Gopher-280B[15]</td><td> prompt</td><td>X</td><td>X</td><td>X</td></tr><tr><td>ToolFormer [11]</td><td>GPT-J (6B)[16]</td><td> self-instruct</td><td>×</td><td>X</td><td>X</td></tr><tr><td>Visual ChatGPT[5]</td><td>GPT-3.5 (175B) [3]</td><td>prompt</td><td>X</td><td></td><td></td></tr><tr><td>MMREACT [6]</td><td>GPT-3.5 (175B) [3]</td><td> prompt</td><td>X</td><td></td><td></td></tr><tr><td>GPT4Tools (ours)</td><td>Vicuna-13B [12]</td><td> self-instruct</td><td>←</td><td></td><td></td></tr></table>",
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+        "type": "text",
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+    {
+        "type": "text",
+        "text": "To achieve it, different from previous studies [7–11], we explore a new perceptive as illustrated in Table 1. We propose a simple yet effective method, called GPT4Tools, designed to empower open-source LLMs with the ability to use tools via self-instruct from advanced LLMs. To be specific, we construct an instruction dataset by prompting advanced teachers, such as GPT-3.5 [3], conditional on visual contents and tool descriptions, which results in a great deal of tool-related instructions. Unlike Toolformer [11], our method can utilize visual content description to improve data diversity significantly. Furthermore, with the generated instruction-following dataset, we employ Low-Rank Adaptation (LoRA) to fine-tune the primitive language models including Vicuna [12], LLaMa [13], and OPT [14]. Besides intrinsic language abilities, GPT4Tools-based language models are also able to solve a variety of visual problems by using tools. The tasks involve visual comprehension and image generation, such as object grounding and segmentation, generating and instructing images, and visual question answering (VQA). The proposed GPT4Tools not only significantly improve the accuracy of LLMs to invoke seen tools but also enable the zero-shot capacity for unseen tools in a zero-shot manner. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Furthermore, we propose an evaluation metric to assess the effectiveness of LLMs in utilizing tools across diverse tasks. With this metric, two human-curated validation sets are constructed to evaluate the LLMs in zero-shot and fine-tuning ways, offering a comprehensive measure of the ability to use tools. To demonstrate the effectiveness of GPT4Tools, we conduct extensive experiments on various language models. The results show the efficacy of teaching LLMs when and how to use tools. Specifically, the Vicuna-13B fine-tuned on our GPT4Tools achieves $9 . 3 \\%$ absolute gains in successful rate over GPT-3.5 [3] that acquires tool priors in context. In addition, the fine-tuned Vicuna-13B shows a solid capacity to invoke unseen tools, wihich can be comparable to GPT-3.5’s success rate. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Our GPT4Tools stands distinct from previous and concurrent studies [5–11] in three ways. First, our method enables primitive open-source language models to use tools, eliminating the dependence on advanced proprietary LLMs like ChatGPT. Second, we design a new approach based on multi-modal contexts for self-instruction and augmentation, which significantly promote multi-modal tool usage and can be deployed in different directions. Third, we propose a new benchmark to assess the effectiveness of using tools, and our method shows remarkable improvements. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "2 Related Work ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Vision and Language Model. In the quest to achieve multi-modal models capable of addressing both language and vision tasks, several studies [17–22] have explored methods to enable language models to comprehend visual input. These include techniques such as transforming images into discrete textual representations [17, 18] or projecting continuous image features into the textual feature space [23–26]. Concurrently, other research has been dedicated to the development of generalist models [19, 20, 22, 21], which permit a model to simultaneously input images and text, eliminating the necessity for a projection process. For instance, OFA [27] devised a unified sequence-to-sequence decoding architecture applicable to language and object detection tasks. Similarly, Pixel2Pixel [21] converted the outcome of visual comprehension tasks into a series of discrete tokens akin to language tasks. Gato [22] brought together a range of vision and control tasks into a sequential prediction issue, ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Image Content ",
+        "text_level": 1,
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Tool Pocket ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/c183aeadddf0d709c5ac740836224402e0a4f5af78ea500ce27cf8fd830e33bd.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "<tool name>: <usage scenario>, <arguments> ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "A person is leaning low on their motorcycle on the tracks.   \nA person leaning down on a motorcycle as they ride on a track.   \nA man is nearly sideways while racing a   \nmotorcycle around a track.   \nA man with a helmet is riding a motorcycle on it's side.   \nmotorcycle: [179.44, 105.55, 411.64, 220.7] person: [136.26, 77.72, 356.95, 124.75] ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/9708f6f6d2085b89d3142fb022fa7908e30277608dd1713f3a2bfb4403e22da7.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "ChatGPT ",
+        "text_level": 1,
+        "bbox": [
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+            280
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/e104d59c1b20c2474a30f790b00d842bcfcabb09e669a40a40d069e4be487825.jpg",
+        "image_caption": [
+            "Figure 1: Diagram of the GPT4Tools. We prompt the ChatGPT with image content and definition of tools in order to obtain a tool-related instruction dataset. Subsequently, we employ LoRA [38] to train an open-source LLM on the collected instruction dataset, thus adapting the LLM to use tools. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            183,
+            287,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "while UViM [28] and Unified-IO [20] advocated for the learned discrete codes as a means to unify an array of vision tasks. By contrast, we equip the language model with diverse specialized multi-modal tools to process distinct vision tasks. This approach not only promotes the scalability of the model for various tasks but also avoids the issue of forgetfulness stemming from repeated fine-tuning. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Instruction Tuning. Recent studies [29, 2, 30–33] have turned out that pre-trained language models could follow natural language instructions and complete various real-world tasks if they are tuned on specific instruction-following data. Notably, InstructGPT [2], FLAN-T5 [31], OPT-IML [33] demonstrated remarkable performance on specific tasks after being fine-tuned with instruction data. In order to release the cost of human-written instructions, Self-Instruction [34] found that the instructionfollowing capabilities of language models can be enhanced by turning on their own generated instruction data. More importantly, this approach inspired a feasible means to improve the zero- and few-shot abilities of language models, i.e., distilling off-the-shelf language models using instructional data from strong GPT-3.5 [3] or GPT-4 [4]. As a result, many recent works [12, 35–37] tried to construct excellent language models for various applications based on the LLaMA [13]. For instance, Stanford-Alpaca has employed 52K instructions generated by GPT-3.5 [3] to construct an exceptional dialogue model. LLaVa [37] has adopted GPT-3.5 [3] and GPT-4 [4] to incorporate instructionfollowing data related to visual content. In this paper, we use GPT-3.5 [3] to construct tool-related instruction datasets, thereby allowing other language models to acquire tool usage capabilities. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Tool Usage. In the Natural Language Processing (NLP) community, several arts [7–11] sought to endow language models with the ability to use tools. For instance, Komeili et al. [7] proposed to generate conversation responses conditioned on the results of the search engine. LaMDA [9] created a set of tools (comprising an information retrieval system, a calculator, and a translator) to avoid plausible outputs. Lazaridou et al. [10] utilized few-shot prompting on Gopher-280B [15] to enable the search engine to ground its output in factual and current information. Similarly, Visual ChatGPT [5] and MMREACT [6] prompted ChatGPT to invoke visual foundation models. In addition, ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "ToolFormer [11] used self-instruction and bootstrapping to teach GPT-J (6B) [16] using five tools, which include a question and answer system, a calculator, a search engine, a machine translation system, and a calendar. On the contrary, we focus on using the GPT-3.5 model as a powerful teacher to distill off-the-shelf language models and enable them to access many visual models. ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3 Method ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            166,
+            269,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Large language models (LLMs) [1, 14, 15] have shown remarkable in-context learning abilities. Among them, GPT-3.5 [3] and GPT-4 [4] are proven to effectively perform text-annotation tasks [39] or instruct other models to follow instructions of specific domains [40, 35, 12, 37]. Inspired by these findings, we propose to enable off-the-shelf language models to acquire tool usage capabilities by taking GPT-3.5 as a powerful teacher. Specifically, we utilize GPT-3.5 to generate tools-related instruction-following data, which is then used to tune the language model. This process offers language models the ability to access multi-modal information by invoking visual models. Furthermore, we propose an evaluation metric to assess the tool-use ability of the given language model. In the following, we elaborate on the data generation, instruction tuning, and evaluation metric in turn. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.1 Dataset Construction ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Data Generation. Figure 1 illustrates the process of generating tool-related instruction dataset. Given an image, we construct the image content $X _ { C }$ according to the captions and bounding boxes, which is a straightforward means of establishing connections between an image and a language model [17, 18]. Conditioned upon the $X _ { C }$ , we provide the GPT-3.5 [3] $( \\mathrm { M _ { T } } )$ with a tool-related prompt $P _ { t }$ whereby attaining a large number of instruction-following data: ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/29f06a28a32b8f69956e93666177ea685500ca30508f5fab3472fba321d37c8e.jpg",
+        "text": "$$\nY \\sim \\operatorname { M } _ { \\mathrm { T } } ( P _ { t } | X _ { C } ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            436,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The $P _ { t }$ comprises the system message, the definition of tools (<tool name> : <usage scenario>, <arguments>), and the suffix prompt which encourages $M _ { T }$ to generate visual instructions and desired outputs. $Y$ , the outcome of $\\mathrm { M _ { T } }$ , consists of $N$ instruction-output pairs $\\{ y ^ { 1 } , y ^ { 2 } , . . . , y ^ { N } \\}$ , where $y _ { i }$ has the format of \"<instruction>, <tool name>, <arguments>\", and $N$ is the number of defined tools. As each input of $\\mathrm { M _ { T } }$ is grounded to the image content $X _ { C }$ , the generated instructions are inherently connected to the image, thus avoiding arbitrary generation. In detail, the $X _ { C }$ consists of ground-truth captions and bounding boxes with tags corresponding to the images. The rich variability of the image brings up a higher diversity of instructions when compared to imagined ones. To provide contrast, we also collect instruction follow-up data without image content $X _ { C }$ , which is similar to ToolFormer [11]. As depicted in Figure 2, without image context priors, GPT-3.5 tends to generate objects of visual instructions towards a small subset, which is reflected in t-SNE as sparser clusters. On the contrary, instructions generated with image-conditioned prompts are notably informative and diverse due to changes in the image content, reflected in the visualization as denser and more widely distributed results. The language model tuned by image-conditioned data is more robust than models without the image content (Table 3). ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Data Formation. Upon the collected raw dataset ( $7 0 K$ items), we apply a filtering process to remove duplicate instructions, incorrectly formatted instructions, calls with incorrect tool names, and calls with incorrect tool-arguments formats. This step results in $4 1 K$ retained items. Subsequently, we transform the retained data into an instruction-response format utilizing a standardized template as shown in the bottom-left corner of Figure 1. This procedure produces a new dataset, denoted as $Y _ { S } ^ { \\mp }$ . The instruction component of $Y _ { S } ^ { + }$ ",
+        "bbox": [
+            174,
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/e7c531eb0db6a033da2be444a918f10dc75c11ce3b2e4d6b0b71c16f6732b87b.jpg",
+        "image_caption": [
+            "Figure 2: t-SNE1visualization for instruction data with and without image content. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "incorporates a prefix prompt that encompasses system messages and tool definitions, <image content> that denotes the image content, <user input $>$ that is replaced with the generated visual instruction, and a suffix prompt designed to prompt the language model to reply the user input using given tools. The response in $\\bar { Y } _ { S } ^ { + }$ comprises 4 elements: (1) Thought, meaning the model’s cognition when to use tools; (2) Action, signifying which tools the model will use or action the model will take; (3) Action Input, representing arguments of the selected tool; and (4) Observation, reflecting outcomes of the used tool. A sample from $Y _ { S } ^ { + }$ is presented in the Figure 3 (a). ",
+        "bbox": [
+            173,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/575be921710ea40eb291c86878ff801b6be89a21cbc5fd05414ff28ae00996d1.jpg",
+        "image_caption": [
+            "Figure 3: Samples of the single-turn instruction, negative instruction, and contextual instruction. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            181,
+            88,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Data Augmentation. Although we have successfully acquired instruction-following data related to the tool usage, this simplistic format lacks complexity and depth in both instructions and responses. To tackle this challenge, we augment the generated data from two perspectives: ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "• Negative samples. The generated instructions primarily focus on tool usage, i.e., the decision after the Thought is always \"Yes\". Consequently, there is a potential risk that the fine-tuned model overfits such a decision. When the user instruction is not associated with the tool usage, the fine-tuned model may erroneously execute irrelevant actions by invoking unnecessary tools. To mitigate this issue, we synthesize negative samples $Y _ { S } ^ { - }$ by selecting conversation data from the existing dataset [40] and converting them into the required template, as illustrated in Figure 3 (b). By tuning with $Y _ { S } ^ { + } \\cup Y _ { S } ^ { - }$ , the model can accurately decide when to use tools. • Context samples. The generated instructions adopt a standard and fixed single-tune format, which lacks a contextual structure. Thus, as shown in Figure 3 (c), we augment the dataset by cutting off the chain of action. We also randomly select multiple instructions from $Y _ { S } ^ { + } \\cup Y _ { S } ^ { - }$ and reformat them into multi-turn conversation data. In this way, we synthesize the contextual instruction-following data $Y _ { S } ^ { c }$ , enabling the tuned model to call tools within the given context. ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "So far, we have constructed the tool-related instructional dataset, including positive samples, negative samples, and context samples: $Y _ { S } = Y _ { S } ^ { + } \\cup Y _ { S } ^ { - } \\cup Y _ { S } ^ { c }$ . ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.2 Instruction Tuning ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            843,
+            344,
+            858
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Based on the dataset $Y _ { S }$ , we tune the off-the-self language model using its original auto-regressive training objective. To make the tuning feasible, we leverage LoRA [38] optimization, which freezes the language model and only optimizes rank decomposition components of the Transformer layers. ",
+        "bbox": [
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+            869,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "For a sequence with $L$ tokens, we compute the probability of the target response $X _ { r }$ by: ",
+        "bbox": [
+            173,
+            90,
+            748,
+            107
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/d722307c52a5d596130366994ed5292dc9ff6f8bd9b90b082bcaef1bd96c7d09.jpg",
+        "text": "$$\np ( X _ { r } | X _ { C } , X _ { i n s t } ) = \\prod _ { i = 1 } ^ { L } p _ { \\theta } ( x _ { i } | X _ { C } , X _ { i n s t } , x _ { 1 : i - 1 } ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            330,
+            112,
+            666,
+            156
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where $X _ { i n s t }$ denotes the instruction tokens; and $\\theta$ is the trainable parameters. In practice, prefix prompt and suffix prompt are also involved but we here skip them for better readability. ",
+        "bbox": [
+            173,
+            161,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "3.3 Evaluation Approach ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            205,
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+            220
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Numerous benchmarks [42, 43, 8, 44] typically utilize human-annotated datasets to evaluate the performance of a model. For the purpose of measuring the tool-usage capacity of the language model, we construct an evaluation dataset following the same procedures detailed in $\\ S \\ 3 . 1$ and manually verify the accuracy of each item. This evaluation dataset is partitioned into two components: the first part (validation set) has the same ingredients as the training set, encompassing 23 tools; the second part (test set) comprises 8 novel tools absent from the training set. We will use the validation set to validate whether the model can adhere to user commands correctly after tuning with the training set. The test set will verify whether the model can generalize to new tools after tuning. Based on the human-annotated evaluation dataset with $N$ instructions, we design a successful rate to measure the model’s performance from three aspects: ",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "• Successful Rate of Thought $\\mathrm { ( S R } _ { t } ^ { } \\mathrm { ) }$ ) measures whether the predicted decision matches the groundtruth decision. It is calculated as $\\begin{array} { r } { \\mathrm { S R } _ { t } = \\frac { 1 } { N } \\sum _ { i = 1 } ^ { N } \\mathbb { I } ( \\tau _ { i } ) } \\end{array}$ , where $\\tau _ { i }$ signifies a singular process. If the thought is correct, $\\mathbb { I } ( \\tau _ { i } )$ is equal to 1, and 0 otherwise. ",
+        "bbox": [
+            174,
+            382,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "• Successful Rate of Action $\\mathrm { ( S R } _ { a c t }$ ) measures whether the predicted tool name is in agreement with the name of the ground truth tool. It is calculated as $\\begin{array} { r } { \\mathrm { S R } _ { a c t } ^ { \\mathrm { - } } = \\frac { 1 } { N } \\sum _ { i = 1 } ^ { N } \\mathbb { I } ( \\alpha _ { i } ) } \\end{array}$ , where $\\alpha _ { i }$ denotes the matching process for the tool names. In cases where the predicted tool name matches the pre-defined name, $\\mathbb { I } ( \\alpha _ { i } )$ equals 1, and 0 otherwise. ",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "• Successful Rate of Arguments $\\mathrm { ( S R } _ { a r g s } )$ evaluates whether the predicted arguments match the ground-truth arguments. It can be calculated using the following equation: ",
+        "bbox": [
+            174,
+            493,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/91cc906a01b83a3b0058478399798181c0e00c28f2abab37ba80a06f3eedaffb.jpg",
+        "text": "$$\n\\mathrm { S R } _ { a r g s } = \\frac { 1 } { N } \\sum _ { i = 1 } ^ { N } \\eta _ { i } , \\mathrm { w h e r e } \\eta _ { i } = \\frac { 1 } { K } \\sum _ { j } ^ { K } \\eta _ { i , j } .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+            529,
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+            573
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Here, $\\eta _ { i }$ denotes a sequence of arguments encompassing both the image path and the input text. For instance, ControlNet [45] needs the image path saved conditions (e.g., the pose map, depth map, or segment map) and the input text described user commands. $K$ represents the quantity of arguments in $\\eta _ { i }$ . When the argument belongs to the image path, $\\eta _ { i , j }$ equals 1 if the predicted and ground-truth image paths share the same suffix, and 0 otherwise. When the argument is the input text, $\\eta _ { i , j }$ is equal to the BLEU score between the predicted and the ground truth text. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "• Successful Rate (SR) measures whether a chain of actions are executed successfully, which requires the correctness of thought, tool name, and tool arguments at the same time: ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/68842e3eb184afebd535ed9225716b58296d5fd978413d5640e6bc1a02c6691e.jpg",
+        "text": "$$\n{ \\mathrm { S R } } = { \\frac { 1 } { N } } \\sum _ { i = 1 } ^ { N } \\mathbb { I } ( \\tau _ { i } ) \\cdot \\mathbb { I } ( \\alpha _ { i } ) \\cdot \\mathbb { I } ( \\eta _ { i } > 0 . 5 )\n$$",
+        "text_format": "latex",
+        "bbox": [
+            375,
+            702,
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+            744
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Additionally, when a procedure comprises two consecutive actions, the SR equals $1 0 0 \\%$ only if both actions are executed correctly. ",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4 Experiments ",
+        "text_level": 1,
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1 Implementation Details ",
+        "text_level": 1,
+        "bbox": [
+            174,
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+    },
+    {
+        "type": "text",
+        "text": "We employ the ChatGPT (gpt-3.5-turbo) [3] as the teacher model to generate the raw instructionfollowing data. Since this study focused on teaching the off-the-self language models to use tools instead of prompt engineering, we adopted a methodology outlined in the Visual ChatGPT [5] to construct tool-related prompts. Our tool pocket consists of 31 tools, including the 23 tools defined in Visual ChatGPT [5] and 8 extra tools (please refer to Appendix for detailed tool names). During generation, all image information utilized in GPT4Tools is sourced from the training set of COCO [43]. After generation, the training set comprises $7 1 K$ instruction-response pairs, wherein all instructional data is related to the 23 tools. We divided the human-annotated evaluation dataset into two parts: the validation set and the test set. The validation set contains the same tools as the training set, with approximately 50 items associated with each tool. The test set includes tools that are not present in the training set (further details provided in Appendix). ",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/1af2dff374b73e2c2431a8c4e0ccee8ec668280a60166932bd7aa49cb194b1d9.jpg",
+        "table_caption": [
+            "Table 2: Comparison of different language models. The zero-shot prediction is adopted for unseen tools and the models without GPT4Tools. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Model</td><td rowspan=\"2\">GPT4Tools</td><td colspan=\"4\">Validation (seen tools)</td><td colspan=\"4\">Test (unseen tools)</td></tr><tr><td>SRt</td><td>SRact</td><td>SRargs</td><td>SR</td><td>SRt</td><td>SRact</td><td>SRargs</td><td>SR</td></tr><tr><td>GPT-3.5 [3] (text-davinci-003)</td><td>×</td><td>93.5</td><td>96.1</td><td>78.0</td><td>84.8</td><td>99.5</td><td>99.5</td><td>91.5</td><td>91.5</td></tr><tr><td rowspan=\"2\">OPT-13B [14]</td><td>X</td><td>1.1</td><td>1.2</td><td>0.0</td><td>0.0</td><td>0.0</td><td>0.0</td><td>0.0</td><td>0.0</td></tr><tr><td></td><td>99.4</td><td>98.3</td><td>89.2</td><td>93.2</td><td>97.8</td><td>89.6</td><td>84.0</td><td>78.6</td></tr><tr><td rowspan=\"2\">LLaMa-13B [13]</td><td>X</td><td>20.4</td><td>15.7</td><td>16.5</td><td>3.2</td><td>16.1</td><td>17.6</td><td>21.7</td><td>2.0</td></tr><tr><td></td><td>77.3</td><td>74.9</td><td>71.4</td><td>66.4</td><td>74.2</td><td>72.2</td><td>70.9</td><td>69.9</td></tr><tr><td rowspan=\"2\">Vicuna-13B [12]</td><td>X</td><td>69.2</td><td>25.1</td><td>25.2</td><td>12.4</td><td>84.4</td><td>43.7</td><td>46.7</td><td>26.2</td></tr><tr><td></td><td>98.7</td><td>97.6</td><td>91.4</td><td>94.1</td><td>98.2</td><td>97.0</td><td>92.2</td><td>90.6</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Based on the collected data, we tuned language models (LLaMA [13], Vicuna [12], and OPT [14]) with LoRA [38] technology. Specifically, we equipped the projection layers of query, key, value, and output with LoRA layers. The LoRA attention dimension and scaling alpha were set to 16. While the language model was kept frozen, the LoRA layers were optimized using the AdamW [46]. All models were fine-tuned over 3 epochs, with a batch size 512. The learning rate was set to $3 \\times 1 0 ^ { - 4 }$ , and the maximum length of new tokens was restricted to 2048. Unless otherwise specified, we used Vicuna-13B for the ablation experiments. ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.2 Main Result ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            531,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Can instruction datasets teach language model using tools? The outcomes of GPT-3.5 [3], OPT13B [14], LLaMA-13B [13], and Vicuna-13B [12] are presented in Table 2. GPT-3.5 is considered analogous to Visual ChatGPT [5]. Upon prompting GPT-3.5 with tool-associated instructions, it can attain a SR of $8 4 . 8 \\%$ on the validation set, thereby underscoring its zero-shot ability to follow a standardized format and utilize tools effectively. Notably, OPT-13B fails to invoke tools with the prompts alone. In contrast, LLaMA-13B and Vicuna-13B exhibit a certain level of comprehension of tool usage, while they still face challenges in executing a chain of actions. Specifically, LLaMA-13B achieves $3 . 2 \\%$ SR, which is absolutely lower than $\\mathrm { S R } _ { t }$ , $\\mathrm { S R } _ { a c t }$ , and $\\mathrm { S R } _ { a r g s }$ . In the case of Vicuna13B, its SR is $5 6 . 8 \\%$ less than $\\mathrm { S R } _ { t }$ , implying that under a zero-shot setup, Vicuna-13B displays commendable discernment in determining when to use tools within a given context. After fine-tuned with GPT4Tools, there are substantial alterations in the tool invocation competencies of each model. Specifically, the SR of OPT-13B witnessed a sharp increase from 0 to $9 3 . 2 \\%$ . Similarly, the SR for LLaMA-13B escalates from $3 . 2 \\%$ to $6 6 . 4 \\%$ , and Vicuna-13B’s SR rises from $1 2 . 4 \\%$ to ${ \\dot { 9 } } 4 . 1 \\%$ . These outcomes unequivocally validate that the GPT4Tools developed in this study are indeed effective in instructing language models to use tools. ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Can the model be generalized to unseen tools after fine-tuning? The right side of Table 2 shows the results when prompting a novel tool and corresponding utilization. On the test set, GPT-3.5 attaines $9 1 . 5 \\%$ SR in a zero-shot manner. The outcomes for other models, which are not fine-tuned on the GPT4Tools and directly invoke tools utilizing prompts, are analogous to those on the validation set. In contrast, models that are fine-tuned on the GPT4Tools dataset exhibit a degree of competence in invoking tools that have not been previously encountered (did not appear in the training set). More specifically, the fine-tuned LLaMA-13B model achieves a superior SR on new tools by a margin of $6 7 . 9 \\%$ when compared to the original model. The fine-tuned Vicuna-13B model demonstrates $9 0 . 6 \\%$ SR on new tools, which is comparable to GPT-3.5. This observation indicates that the language model can invoke unseen tools after fine-tuned with GPT4Tools. ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/3b90c22445f4a71f7a6db82156f3426f8152220954c5707c6330c75cc608b65f.jpg",
+        "table_caption": [
+            "Table 3: Ablation study for data augmentations on the validation set. ’IC’, ’CS’, ’NS’ denotes image content, context samples, and negative samples, respectively. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>CS</td><td>NS</td><td>SRt</td><td>SRact</td><td>SRargs</td><td>SR</td></tr><tr><td></td><td></td><td></td><td>70.0</td><td>55.7</td><td>51.7</td><td>36.9</td></tr><tr><td>v</td><td></td><td></td><td>89.6</td><td>89.9</td><td>84.5</td><td>81.6</td></tr><tr><td>v</td><td>v</td><td></td><td>97.4</td><td>95.7</td><td>88.5</td><td>91.6</td></tr><tr><td>&lt;</td><td>v</td><td>v</td><td>98.7</td><td>97.6</td><td>91.4</td><td>94.1</td></tr></table>",
+        "bbox": [
+            176,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/2e51a00e415f26ac72fa75c2d4c19de063beba1039276e6b7a3638cdd08357a6.jpg",
+        "table_caption": [
+            "Table 4: Ablation study for different model scales on the validation set. 7B and 13B refer to Vicuna7B [12] and Vicuna-13B [12] models, respectively. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>GPT4Tools</td><td>SRt</td><td>SRact</td><td>SRargs</td><td>SR</td></tr><tr><td>7B</td><td>× v</td><td>27.7 96.2</td><td>15.8 94.5</td><td>11.5</td><td>4.5</td></tr><tr><td rowspan=\"2\">13B</td><td></td><td>69.2</td><td>25.1</td><td>89.8</td><td>92.9</td></tr><tr><td>X</td><td>98.7</td><td>97.6</td><td>25.2 91.4</td><td>12.4 94.1</td></tr></table>",
+        "bbox": [
+            506,
+            154,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.3 Ablation Study ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            275,
+            318,
+            290
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Data Augmentation. As depicted in Table 3, we execute a series of ablation studies on various tricks implemented during the creation of the dataset. When instructions are not conditioned upon the image content, the SR of the fine-tuned model on the validation set is a mere $3 6 . 9 \\%$ . In contrast, when instructions are generated with conditioning on the image content, the SR on the validation set is enhanced substantially to $8 1 . 6 \\%$ . This uptick can be primarily attributed to the elevated diversity and intricacy of the generated instructions. Moreover, an augmentation of the SR to $9 1 . 6 \\%$ is observed upon introducing context samples into the instructions. This finding underscores the fact that partitioning the chain of actions and allocating them to the in",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/58985c6ee658faac5ee7721fa7e9611e13d7059f9d4fffc187922dec798155e0.jpg",
+        "image_caption": [
+            "Figure 4: Performance variation curve with the fine-tuning iteration. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            508,
+            309,
+            812,
+            482
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "struction and response can strengthen the model’s comprehension of the tool. It is noteworthy to mention that with the incorporation of negative samples into the generated instructions, the SR increases to $9 4 . 1 \\%$ . This outcome can be traced back to the propensity of the model, when trained exclusively with positive samples, to bias toward tool invocation. This tendency consequently diminishes the capacity to discern the appropriate cases for tool usage. Adding negative samples equips the model with the ability to determine when to use tools. ",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Model Scales. We attempt experiments with models at different scales. The results in Table 4 demonstrate that after fine-tuned on the generated dataset, Vicuna-7B [12] is also capable of invoking tools in a fixed format. Specifically, under a zero-shot setting, Vicuna-7B achieves only a $4 . 5 \\%$ SR. By contrast, after fine-tuning, it can achieve an SR of $9 2 . 9 \\%$ . ",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Tuning Iteration. We increase the number of iterations for fine-tuning and present the results in Figure 4. Notably, during the range of iterations from 400 to 800, the model’s performance demonstrates substantial fluctuations in tool invocation. However, subsequent to this range, there is a steady improvement in $\\mathrm { S R } t$ , SRact, $\\mathrm { S R } _ { a r g s }$ , and SR. This indicates that the model progressively adapts to the dataset, enhancing its capability to invoke tools. ",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.4 Case Study ",
+        "text_level": 1,
+        "bbox": [
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+        "type": "text",
+        "text": "Figure 5 presents a comparative analysis of our model with Visual ChatGPT [5] and LLaVa [37]. When an image is submitted by the user alongside the instruction \"Generate a picture of real people based on the edge\", Visual ChatGPT delivers an image that exhibits a weak correlation with the given instruction. Owing to its inability to generate images, LLaVa only returns a caption. In contrast, our model produces an accurate result, thereby evidencing that the tool-related instruction tuning method proposed in this paper can effectively instruct language models in the correct usage of tools. In Figure 6, we further demonstrate that the Vicuna-13B fine-tuned on GPT4Tools is capable of finishing some visual commands by invoking visual tools. This finding indicates that imparting knowledge to language models regarding the tool invocation could potentially be a way toward the development of a generalist model. More case studies are presented in the Appendix. ",
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+        "type": "image",
+        "img_path": "images/0647e7eb50fc800b9a45d9f2dbc9bc549d9f6dadaf129d365e619f3048b5458e.jpg",
+        "image_caption": [
+            "Figure 5: Comparison with other models. Our GPT4Tools responds correctly, while Visual ChatGPT [5] replies with the wrong image, and LLaVa [37] can not generate the image. "
+        ],
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+        "image_caption": [
+            "Figure 6: Cases of invoking tools from Vicuna-13B [12] fine-tuned on our GPT4Tools. "
+        ],
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+    {
+        "type": "table",
+        "img_path": "images/b806b45a8cda0ae482a9895dbe0e1b6970a84f28e31cccb9363ba742bb3524ac.jpg",
+        "table_caption": [
+            "Table 5: Results of GPT4Tools using Top-K related tools. The total number of tools equals 23. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Retrieval Top-K</td><td>SRt</td><td>SRact</td><td>SRargs</td><td>SR</td></tr><tr><td>Vicuna-13B[12]</td><td>1</td><td>69.2</td><td>25.1</td><td>25.2</td><td>12.4</td></tr><tr><td>w/ GPT4Tools</td><td>1</td><td>87.0</td><td>55.8</td><td>57.5</td><td>54.0</td></tr><tr><td>w/ GPT4Tools</td><td>2</td><td>93.1</td><td>70</td><td>69.5</td><td>67.8</td></tr><tr><td>w/ GPT4Tools</td><td>3</td><td>95.8</td><td>74.4</td><td>72.9</td><td>73.1</td></tr><tr><td>w/ GPT4Tools</td><td>23</td><td>98.7</td><td>97.6</td><td>91.4</td><td>94.1</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "5 Discussion ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Although the proposed GPT4Tools can teach plug-and-play language models to use tools effectively, it still has some limitations. As shown in Figure 2 the success rate of all models is not $1 0 0 \\%$ . Thus, further improvements are still necessary for practical applications. Additionally, GPT4Tools teaches the model to explicitly invoke tools using a verbose and fixed prompt. This approach decreases the computational efficiency since attention-based architectures compute the relationships between all tokens. Besides, with the increased number of tools, the prompt length might surpass the limited context length of LLMs. In this case, we can alternatively utilize a tool retrieval technique to filter out a small set of tools and then apply GPT4Tools-based LLMs for tool selection and invocation. We employ BM25, based on the user input, to retrieve the top-K tools from the defined 23 tools. As shown in Table 5, SR is only $5 4 \\%$ while retrieving the top-1 tool. When the number of retrieved tools increases to 3, SR is boosted to $7 3 . 1 \\%$ . Although the retrieval strategy can mitigate the reliance on long context models for a large number of tools to some extent, its SR can not match the original model. This result can be attributed to the inabilities of the retriever. Therefore, in the future, it is imperative to build a specialized retriever for the tool name retrieval. Moreover, it should be explored how to enable the model to implicitly invoke various tools instead of using the complex prompt. Nevertheless, our GPT4Tools method provides a viable approach for equipping language models with the ability to use multi-modal tools. ",
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+    {
+        "type": "text",
+        "text": "6 Conclusion ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In this paper, we introduce GPT4Tools, a novel method that enables open-source language models to utilize multi-modal tools efficiently. Specifically, We construct a tool-related instructional dataset by prompting advanced GPT-3.5 conditional on image context. Then, we augment the generated data by introducing negative and context samples. Based on the built dataset, we employ LoRA fine-tuning technology to enhance the tool-usage capability of language models, thus allowing them to handle various visual tasks, e.g., visual comprehension and image generation. Moreover, we propose a benchmark to assess tool usage accuracy from the decision when to use tools, which tools to use, and arguments of invoked tools. In this benchmark, language models tuned with our GPT4Tools perform comparably to GPT-3.5 on unseen tools. We desire the GPT4Tools to pave the way for equipping open-source language models with the ability to use multi-modal tools. ",
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+    {
+        "type": "text",
+        "text": "Acknowledgments ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "This research is partly supported by the National Key R&D Program of China (Grants No.   \n2020AAA0108302 & 2020AAA0108303), and Shenzhen Science and Technology Project (Grant No.   \nJCYJ20200109143041798) & Shenzhen Stable Supporting Program (WDZC20200820200655001) & Shenzhen Key Laboratory of next-generation interactive media innovative technology (Grant No.   \nZDSYS20210623092001004). ",
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+]

parse/dev/dEelotBE6e2/dEelotBE6e2.md

@@ -0,0 +1,570 @@
+# DEFENDING AGAINST BACKDOOR ATTACKS USING ENSEMBLES OF WEAK LEARNERS
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+A recent line of work has shown that deep networks are susceptible to backdoor data poisoning attacks. Specifically, by injecting a small amount of malicious data into the training distribution, an adversary gains the ability to control the behavior of the model during inference. We propose an iterative training procedure for removing poisoned data from the training set. Our approach consists of two steps. We first train an ensemble of weak learners to automatically discover distinct subpopulations in the training set. We then leverage a boosting framework to exclude the poisoned data and recover the clean data. Our algorithm is based on a novel bootstrapped measure of generalization, which provably separates the clean from the dirty data under mild assumptions. Empirically, our method successfully defends against a state-of-the-art dirty label backdoor attack. We find that our approach significantly outperforms previous defenses.
+
+# 1 OVERVIEW
+
+The past few years has seen the rapid adoption of deep learning in real world applications, from digital personal assistants to autonomous vehicles. This trend shows no sign of abating, given the remarkable (super)human performance of deep neural networks on tasks such as computer vision (He et al., 2016a), speed recognition (Graves et al., 2013), and game playing (Silver et al., 2016).
+
+However, this widespread integration of deep networks presents a potential security risk, particularly in performance- and safety-critical applications. In this work, we focus on defending against backdoor attacks (Chen et al., 2017; Adi et al., 2018). Specifically, it has been demonstrated that deep networks can be attacked by injecting small amounts of poisoned (i.e., maliciously perturbed) data during training to create a backdoor in the model; once installed, an adversary can exploit the backdoor to change the network’s predictions at inference time. For instance, Gu et al. (2019) demonstrate a backdoor that causes a model to misclassify stop signs as speed signs by applying a (physical) sticker. These attacks are particularly pernicious in that the accuracy of the model on unperturbed data is generally not affected by the backdoor, thus making it difficult to identify compromised models during standard operation.
+
+Techniques We first introduce the notion of self-expanding sets, which based on a bootstrapped measure of how well a set generalizes to itself. Under certain compatibility properties, we show that the process of identifying self-expanding sets naturally separates a dataset into a collection of homogeneous components (i.e., completely clean or completely poisoned subsets of the training data). Given such a collection, we then provide a method to identify the clean distribution by boosting an ensemble of weak learners over the components.
+
+To separate the training set into homogeneous components, we present the Inverse Self-Paced Learning algorithm. This algorithm uses quantile statistics to repeatedly identify and exclude samples with high loss. Recursively applying the technique to sets of excluded samples produces the collection of homogeneous components. We prove sufficient conditions for the convergence of the algorithm.
+
+Experimental Evaluation We implement the proposed Inverse Self-Paced Learning algorithm within our boosting framework and evaluate its performance on two different backdoor attacks on CIFAR-10 (?). Our method completely defends against the attacks in almost every setting and substantially reduces the success rate of the attack in the remaining cases, while reducing the accuracy on clean data by only $2 \mathrm { - } 3 \%$ . Our results also show that previous approaches (Tran et al., 2018; Chen et al., 2018; Shen and Sanghavi, 2019) are substantial weaker at identifying poisoned samples. These previous approaches also either require an explicit upper bound on expected amount of poison or suffer from high levels of false positives. Our approach thus presents a novel, empirically verified method for defending against backdoor attacks.
+
+# 2 RELATED WORK
+
+Our separation results can be viewed as solutions to a clustering problem, where we exploit weak supervision in the form of class labels, related via our notions of self-expansion and compatibility. Many previous works analyze similar properties for weak or semi-supervised learning based on clustering (Seeger, 2000; Rigollet, 2007; Singh et al., 2008) or expansion (Wei et al., 2020). In general, these works define expansion as an intrinsic property of the input data, rather than with respect to a (weak) learner as we do. Balcan et al. (2005) show that under a similar expansion property, learners fit independently to two different “views” of the data can supervise each other to improve their joint performance. However, a major departure from these prior works is that we do not use an expansion property to leverage a small set of trusted or confident labels for minimizing a global classification error, but rather use self-expansion to identify homogeneous components by fitting weak learners to certain local minima.
+
+We also introduce the Inverse Self Paced Learning algorithm for efficiently finding self-expanding sets. Self paced learning (SPL) was introduced by Kumar et al. (2010) as an type of curriculum learning (Bengio et al., 2009). SPL is a heuristic that dynamically creates a curriculum based on the losses of the model after each epoch, so as to incorporate the easier samples first. SPL and its variants have been observed to be resilient to noise both in theory (Meng et al., 2016) and practice (Jiang et al., 2018; Zhang et al., 2020), though prior works focus mostly on clean accuracy under unrealizeable label noise. In contrast, we measure targeted misclassification accuracy under more challenging noise distributions that are adversarially selected to be realizeable.
+
+Finally, several prior works propose methods for defending against backdoor attacks on neural networks. In general, it has been observed that standard techniques from robust statistics applied directly to the data do not successfully identify the poisoned data (Tran et al., 2018). The standard approach is therefore to first fit a deep network to the poisoned distribution, then apply techniques to the learned representations in the network layers. The Activation Clustering defense (Chen et al., 2018) uses dimensionality reduction followed by $\mathbf { k }$ -means clustering $( \mathrm { k } \mathrm { = } 2 )$ ) on the activation patterns, and discards the smallest cluster. Tran et al. (2018) propose a Spectral Signature defense that removes the data with the top $\epsilon$ eigenvalues, where $\epsilon$ is set to 1.5 times the amount of expected poison. TRIM (Jagielski et al., 2021) (for linear regression) and Iterative Trimmed Loss Minimization (Shen and Sanghavi, 2019) (for generalized linear models and deep neural networks) iteratively train on a subset of the data after removing a constant fraction of the samples with the highest loss. However, the majority of works do not evaluate their defenses on CIFAR-10, opting instead for simpler datasets, such as traffic signs or MNIST. Furthermore the triggers skew large and obvious (such as $3 \mathrm { x } 3$ patches (Qiao et al., 2019) or legible text overlays (Gao et al., 2019a)), and are often constrained to lie in the center of the image; our evaluation shows that existing defenses fail when evaluated on the more subtle triggers we use.
+
+# 3 BACKGROUND AND SETTING
+
+We first establish some basic notation and the scope of our classification setting. Let $X$ be the input space, $Y$ be the label space, and $L ( \cdot , \cdot )$ be a loss function over $Y \times Y$ . We assume a bounded loss function, which includes many commonly used loss functions such as the zero-one or cross entropy loss. Given a target distribution $\mathcal { D }$ supported on $X \times Y$ and a parametric family of functions $f _ { \theta }$ , the goal is to find the parameters $\theta$ that minimize the population risk $\begin{array} { r } { R ( \theta ) : = \int _ { X \times Y } L ( f _ { \theta } ( x ) , y ) d P _ { \mathcal { D } } ( x , y ) } \end{array}$ .
+
+The learning problem $( f _ { \boldsymbol { \theta } } , \mathcal { D } )$ is realizable if (1) for every label $y$ , the marginals $\mathcal { D } ( \cdot | y )$ have disjoint support; and (2) there exist ground truth parameters $\theta ^ { * }$ with $R ( \theta ^ { * } ) = 0$ . For simplicity, we assume a (possibly stochastic) learning algorithm $\boldsymbol { A }$ that performs empirical risk minimization, i.e., given a set of samples $T$ , $\mathcal { A }$ tries to return $\theta$ minimizing $\begin{array} { r } { \mathbf { \bar { \rho } } _ { R _ { e m p } } ( \theta ; T ) \mathrel { \mathop : } = \sum _ { i \in T } L ( f _ { \theta } ( x _ { i } ) , y _ { i } ) } \end{array}$ . Clearly, given enough training samples $S = \{ ( x _ { 1 } , y _ { 1 } ) . . . , ( x _ { n } , y _ { n } ) \}$ iid from $\mathcal { D }$ , the empirical risk gets arbitrarily close to the population risk. We will identify the training set $S$ with its indices $[ n ]$ .
+
+# 3.1 DATA AND THREAT MODEL
+
+We consider a mixture of $n$ distributions $\{ ( \alpha _ { i } , \mathcal { D } _ { i } ) \} _ { i = 1 } ^ { n }$ such that ${ \mathcal { D } } = \cup _ { i } \{ { \mathcal { D } } _ { i } \}$ and $\textstyle \sum _ { i } \alpha _ { i } = 1$ . We observe $N$ inputs according to the following two-step procedure:
+
+$$
+\begin{array} { r } { d \sim \mathrm { C a t } ( \alpha _ { 1 } , . . . , \alpha _ { n } ) } \\ { x , y \sim \mathcal { D } _ { d } } \end{array}
+$$
+
+where $\mathrm { { C a t } ( \cdot ) }$ is a categorical random variable that returns $i$ with probability $\alpha _ { i }$ . If $S$ is a set of samples produced by this process, for any subset $S ^ { \prime } \subseteq S$ , we will denote the samples drawn from the $i ^ { t h }$ distribution as $S _ { i } ^ { \prime }$ , so that $S ^ { \prime } = \cup _ { i } S _ { i } ^ { \prime }$ .
+
+Our evaluation focuses on the backdoor data poisoning model. It has been observed empirically that injecting a small amount of malicious data into the training distribution effectively installs a backdoor in the model, whereby the behavior on clean data is otherwise unaffected, but an attacker can cause targeted misclassification during inference by overlaying a small trigger. In this case sampling from the training distribution is modeled as follows:
+
+$$
+\begin{array} { r } { d \sim  { \mathbf { C a t } } ( \alpha _ { 1 } , . . . , \alpha _ { n } ) } \\ { x , y \sim  { \mathcal { D } } _ { d } } \\ { p \sim  { \mathbf { B e r n } } ( \rho ) } \\ { x  \tau ( x ) , y  \pi ( y ) , \mathrm { i f } p } \end{array}
+$$
+
+where $\tau ( \cdot )$ is the function which applies a small trigger, $\pi ( \cdot )$ is a permutation on classes, and $\rho$ controls the probability of observing a poisoned sample. Note that this procedure can easily be replicated within the original data model. We will also assume the attack is non-trivial in the sense that the perturbed source distributions $\tau ( \mathcal { D } _ { i } )$ and target distributions $\mathcal { D } _ { \pi ( i ) }$ are disjoint for all $i$ .
+
+Given a model $f _ { \theta } ( \cdot )$ , we measure the success of the attack using the targeted misclassification rate:
+
+$$
+A _ { e m p } ( \theta ; T ) : = \sum _ { i \in T } [ f _ { \theta } ( x _ { i } ) = y _ { i } \land f _ { \theta } ( \tau ( x _ { i } ) ) = \pi ( y _ { i } ) ]
+$$
+
+In other words, the attack succeeds if, during inference, it can flip the label of a correctly-classified instance by applying the trigger $\tau ( \cdot )$ .
+
+# 3.2 LEARNING OBJECTIVE
+
+We formulate our learning objective in the general data model of Equations 1-2. Without loss of generality, we assume the first $p$ distributions are primary distributions, and the remaining $n - p$ are noise distributions. Given a training set $S$ , we write $S _ { P } = S _ { 1 } \cup \ldots \cup S _ { p }$ for the samples from the primary distributions, and $S _ { N } = S _ { p + 1 } \cup \ldots \cup S _ { n }$ for the samples from the noise distributions.
+
+Our goal is to learn parameters $\tilde { \theta }$ which correspond to training only on the primary distributions: $ { \tilde { \theta } } : =  { \mathcal { A } } ( S _ { P } )$ . Note this objective differs significantly from simply minimizing the risk over the primary distributions when the mixed distribution $\mathcal { D }$ is realizable, i.e., we are also interested in avoiding effects that occur on portions of the input space that have low density in the primary distributions. More explicitly, in terms of the data poisoning threat model (Equation 7), we note that training on $S _ { P } \cup S _ { N }$ would yield low risk over the unperturbed distributions, but also high targeted misclassification risk. Conversely, for sufficiently separated distributions $\tau ( \mathcal { D } _ { i } )$ and $\mathcal { D } _ { \pi ( i ) }$ , we expect that the hypothesis class $f _ { \theta }$ enjoys low targeted misclassification risk when trained only on clean data.
+
+# 4 SEPARATION OF MIXED DISTRIBUTIONS
+
+We next introduce the main theoretical properties that allow us to separate the primary and noise distributions. Our main tool is a property of “self-expanding” sets; intuitively, given a set, we resample at a given rate and measure how well the learning algorithm generalizes to the rest of the set. Given primary and noise components satisfying certain compatibility properties, we show that the set with the optimal expansion must be homogeneous, i.e., drawn entirely from either the primary or noise components. Finally, we fit weak learners to the recovered (homogeneous) sets in a simplified boosting framework to identify the primary component.
+
+# 4.1 SELF-EXPANSION AND COMPATIBILITY
+
+We begin by stating a formal characterization of the self-expanding property of sets:
+
+Definition 4.1 (Self-expansion of sets.). Let $S$ and $T$ be sets. We define the $\alpha$ -expansion error of $S$ given $T$ for all $0 \leq \alpha \leq 1$ such that $\alpha | S |$ is integral as
+
+$$
+\epsilon ( S | T ; \alpha ) : = | S | ^ { - 1 } \mathbb { E } [ R _ { e m p } ( A ( S ^ { \prime } \cup T ) ; S ) ]
+$$
+
+where the expectation is over both the randomness in $\mathcal { A }$ and $S ^ { \prime }$ , a random variable of $\alpha | S |$ samples drawn from $S$ with replacement.
+
+This self-expansion property measures the ability of the learning algorithm $\mathcal { A }$ to generalize to the empirical distribution of a set $S$ with the help of additional training samples $T$ ; intuitively, a smaller expansion error means that the set $S$ is both “easier” and “more homogeneous” with respect to the learning algorithm and $T$ . When $T = \emptyset$ we will also write $\epsilon ( S ; \alpha )$ instead of $\epsilon ( S | \emptyset ; \alpha )$ . $\alpha$ is also referred to as the subsampling rate. Finally, we will extend $\epsilon ( S | T ; \alpha )$ to all $0 \leq \alpha \leq 1$ by linearly interpolating between the value at integral sample sizes.
+
+We now use self-expansion to define a notion of compatibility between sets:
+
+Definition 4.2 (Compatibility of sets.). $A$ (nonempty) set $T$ is $\alpha$ -compatible with set $S$ with margin $\delta \geq 0$ if
+
+$$
+\epsilon ( S | T ; \alpha ) + \delta \leq \epsilon ( S ; \alpha )
+$$
+
+where the expectation is over the same random variables as in the definition of self-expansion. Furthermore, $T$ is completely $\alpha$ -compatible with $S$ if all (nonempty) subsets $T ^ { \prime } \subseteq T$ are $\alpha$ -compatible with $S$ . Conversely, $T$ is $\alpha$ -incompatible with $S$ if the opposite holds, i.e.,
+
+$$
+\epsilon ( S ; \alpha ) + \delta \leq \epsilon ( S | T ; \alpha )
+$$
+
+(and similarly for complete incompatibility). We also say that strict compatibility (incompatibility) holds when $\delta > 0$ .
+
+In other words, $T$ is compatible with $S$ if the self-expansion error of $S$ given $T$ is not worse than the self-expansion error of $S$ by itself.
+
+In what follows, we make use of the following assumptions about expansion:
+
+Assumption 4.3 (Properties of expansion). The learning procedure satisfies the following:
+
+(1) $\epsilon ( S | T ; \alpha )$ is a convex function of $\alpha \in [ 0 , 1 ]$ such that $\epsilon ( S | T ; 1 ) = 0$ for all $S , T$ (2) if $T$ is $\alpha$ -incompatible with $S$ , then $T$ is $\beta$ -incompatible with $S$ for all $\beta \geq \alpha$ .
+
+The first assumption rules out the existence of pathological sets where increasing the number of samples degrades performance and also says that memorization of the training set always occurs. Convexity holds when the expected marginal information gained from additional samples decreases as the number of samples increases. The second assumption says that increase the amount of data from $S$ in the training set (which always improves performance, regardless of the compatibility of $T$ ) should not flip an incompatible $T$ into a compatible set.
+
+The following key property enables us to separate the primary and noise distributions. Intuitively, we want the primary and noise mixture components to be negatively correlated (or at least independent) in the sense that training on a noise distribution should not improve performance on a primary distribution, and vice versa:
+
+Property 4.4 (Incompatibility of primary and noise distributions). Let α be given. Then any pair of (nonempty) sets $S _ { P }$ and $S _ { N }$ drawn from $\mathcal { D } _ { 1 } \cup \ldots \cup \mathcal { D } _ { p }$ and $\mathcal { D } _ { p + 1 } \cup \ldots \cup \mathcal { D } _ { n }$ , respectively, are strictly and completely $\alpha$ -incompatible.
+
+Our technique is designed for separating primary and noise distributions that satisfy this property.
+
+We are now ready to state the main result of this section. Given Property 4.4, we show that any subset of $S$ which achieves the minimum expansion error consists entirely of data drawn from either the primary or noise distributions:
+
+Theorem 4.5 (Sets minimizing expansion error are homogeneous.). Let $S = S _ { 1 } \cup \ldots \cup S _ { n }$ be a set of samples drawn from a mixture of distributions $\{ ( \alpha _ { i } , { \mathcal { D } } _ { i } \} _ { i = 1 } ^ { n }$ . Define
+
+$$
+S ^ { * } : = \arg \operatorname* { m i n } _ { S ^ { \prime } \subseteq S } \epsilon ( S ^ { \prime } ; \alpha )
+$$
+
+for some expansion factor $\alpha$ . Then if Property 4.4 holds for $\alpha$ , we have either that $S ^ { * } \subseteq S _ { P }$ or $S ^ { * } \subseteq S _ { N }$ , where $S _ { P } = S _ { 1 } \cup \ldots \cup S _ { p }$ and $S _ { N } = S _ { p + 1 } \cup \ldots \cup S _ { n }$ .
+
+We defer the proof to Appendix A. Intuitively, if two distributions are incompatible, then adding data from one distribution to a homogeneous set of the other should only increase the self-expansion error.
+
+Remark 1 Theorem 4.5 relies crucially on the incompatibility between the samples from the primary distribution $S _ { 1 } \cup \ldots \cup S _ { p }$ and the noise distribution $S _ { p + 1 } \cup \ldots \cup S _ { n }$ derive the homogeneity of $S ^ { * }$ , a condition which depends on the interaction between the data $S$ and the learning algorithm $\mathcal { A }$ . We note that the requirement is empirically satisfied in many data poisoning settings. For example, a common adversary for backdoor attacks against deep neural networks inserts a small synthetic patch in the corner of the image, which, by design, is a location on which the classification does not depend. In this case, the labels for the primary and noise distributions depend on disjoint dimensions of the input, which gives a very clean example of incompatible distributions; given the number of shared (spurious) features, empirical results suggest that the two distributions are, in fact, strictly incompatible for moderately large sets as well.
+
+Remark 2 In general, the larger $\alpha$ is in Property 4.4, the easier it is to estimate the value of $\epsilon ( S ; \alpha )$ ; the most convenient case would be for incompatibility to hold even when $\alpha = 1$ , in which case $\epsilon ( S ; \alpha )$ can be evaluated exactly with one call to $\mathcal { A }$ . Unfortunately, for overparameterized models trained using empirical risk minimization, we have that $\epsilon ( S ; 1 ) = \mathrm { { 0 } }$ for all $S$ (since we assume the problem is realizable in the limit). One method to circumvent this problem is to prevent $\mathcal { A }$ from converging, e.g., by using early stopping. In fact, it is well known that regularizing deep neural networks trained with Stochastic Gradient Descent using early stopping is resilient to noise (Li et al., 2020). In our experiments, we find that combining early stopping with our self-expansion property leads to further improvements in performance.
+
+# 4.2 IDENTIFICATION USING WEAK LEARNERS
+
+The development of the previous section suggests an iterative approach to separating the primary and noise distributions. In particular, if we fix the expansion factor $\alpha$ , at each step, we can identify the set $S ^ { * }$ which achieves the lowest expansion error and remove it from the training set. Repeating this procedure partitions the training set into groups of compatible sets. While this suffices to separate the primary and noise distributions, it remains to identify which components belong to the primary distribution.
+
+We next propose a simplified boosting framework for identification of the primary distribution. We assume the setting of binary classification and use the 0-1 loss, so that the empirical risk simply counts the number of elements which are misclassified. Our approach is to fit a weak learner to each component, then use each learner to vote on the other components.
+
+Algorithm 1 presents our approach for boosting from homogeneous sets. The subroutine $\mathrm { L o s s _ { 0 , 1 } }$ takes a set of parameters and a set of samples, and returns the empirical zero-one loss over the entire set. Note that votes are weighted by size.
+
+The correctness of Algorithm 1 follows from an analogous compatibility property (cf. Property 4.4):
+
+Property 4.6 (Compatibility of primary distribution). Let α be given. Then any pair of (nonempty) sets $S _ { i }$ and $S _ { j }$ drawn from $\mathcal { D } _ { i }$ and $\mathcal { D } _ { j }$ , respectively, such that $i , j \le n$ , are strictly and completely $\alpha$ -compatible.
+
+Finally, we also require unbiased priors for weak learners:
+
+# Algorithm 1 Boosting Homogeneous Sets
+
+Input: Homogeneous sets $S _ { 1 } , . . . , S _ { N }$ , total number of samples $n$ , number of estimates $B$ , weak   
+learner $\mathcal { A }$   
+Output: Votes $V _ { 1 } , . . . , V _ { N }$   
+1: $C _ { 1 } , . . . , C _ { N } \gets 0$   
+2: for $i = 1$ to $N$ do   
+3: $V _ { i 1 } , . . . , V _ { i N } \gets 0$   
+4: for $j = 1$ to $B$ do   
+5: $\theta _ { i j }  A ( S _ { i } )$   
+6: for $k = 1$ to $N$ do   
+7: $V _ { i k } \gets V _ { i k } + \mathrm { L o s s } _ { 0 , 1 } ( \theta _ { i j } ; S _ { k } ) / B$   
+8: end for   
+9: end for   
+10: for $k = 1$ to $N$ do   
+11: if $V _ { i k } > | S _ { k } | / 2$ then   
+12: $C _ { k } \gets \mathsf { \tilde { C } } _ { k } + | S _ { i } |$   
+13: end if   
+14: end for   
+15: end for   
+16: for $i = 1$ to $N$ do   
+17: $V _ { i } \gets C _ { i } > n / 2$   
+18: end for
+
+Property 4.7 (Weak learners are unbiased.). Let $S _ { i }$ be any sets. Then for any untrained weak learner, we have also that $\mathbb { E } [ R _ { e m p } ( A ( \emptyset ) ; S _ { i } ) ] = | S _ { i } | / 2$ .
+
+This condition is necessary in that the weak learners should not be biased toward learning the noise distributions. Finally, we state the main result of this section, whose proof is deferred to Appendix A.
+
+Theorem 4.8 (Identification of primary samples). Let $s$ be a set of samples drawn from a mixture of distributions $\{ ( \alpha _ { i } , \mathcal { D } _ { i } \} _ { i = 1 } ^ { n }$ such that Properties 4.4, 4.6, and 4.7 hold, and assume that the ratio of primary samples $p = | S _ { P } | / | S | > 1 / 2$ . Let $S _ { 1 } , . . . , S _ { N }$ be a partition of $S$ produced by iteratively applying Theorem 4.5. Then if $\mathcal { A }$ is deterministic, Algorithm $I$ returns 1 with $B = 1$ for all components containing samples from the primary distribution, and 0 otherwise.
+
+$\mathcal { A }$ is stochastic, the same result holds with probability
+
+$$
+[ 1 - 2 \exp ( - 2 \delta ^ { 2 } B ) ] ^ { M N }
+$$
+
+where $M$ is the number of primary components, and $B$ is the number of independent weak learners used to fit each primary component.
+
+Remark 3 At a high level, the approach to identifying the primary distribution presented in Theorems 4.5 and 4.8 follows a simplified boosting framework: at each step, we fit a weak learner to a subset of the distribution, then reweight the remaining training samples by removing the identified component; the ensemble of weak learners is then aggregated using a majority vote. However, our setting is somewhat unique so for clarity we mention several key differences. First, in general the objective of standard boosting is to achieve low population risk, thus the reweighting is performed via more sophisticated methods such as using the empirical loss of the ensemble thus far, e.g., AdaBoost (Freund et al., 1996); in contrast, in our setting there are subpopulations over which we would actually like to maximize the risk. Another difference is that in standard boosting, the ensemble is used during inference to vote on new observations to perform classification, whereas in our algorithm, we use each learner to vote over components of the training set to filter out the noise distributions. Finally, note that we can succeed with arbitrary probability by taking the number of samples $B$ to infinity.
+
+# 5 INVERSE SELF-PACED LEARNING
+
+A major question raised by Theorem 4.5 is how to identify the set $S ^ { * }$ in its statement. In this section, we propose an algorithm called Inverse Self-Paced Learning (ISPL) to solve this problem. Rather
+
+# Algorithm 2 Inverse Self-Paced Learning
+
+Input: training set $S$ , total iterations $N$ , annealing schedule $1 \ge \beta _ { 0 } \ge . . . \ge \beta _ { N } = \beta _ { \mathrm { m i n } } > 0$ expansion $\alpha \leq 1$ , momentum $\eta$ , incremental learning procedure $\mathcal { A }$ , initial parameters $\theta _ { 0 }$
+
+Output: $S _ { N } \subseteq S$ such that $| S _ { N } | = \beta _ { N } | S |$   
+1: $S _ { 0 }  S$   
+2: $L \gets \mathbf { 0 }$   
+3: for $t = 1$ to $N$ do   
+4: $S ^ { \prime } \gets \mathrm { S a m p l e } ( S _ { t - 1 } , \alpha )$   
+5: $\theta _ { t }  { \mathcal { A } } ( S ^ { \prime } , \theta _ { t - 1 } )$   
+6: $L \gets \eta L + ( 1 - \eta ) R _ { e m p } ( \theta _ { t } ; S )$   
+7: $S _ { t } \gets \operatorname { T r i m } ( L , \beta _ { t } )$   
+8: end for
+
+than optimizing over all possible subsets of the training data, our objective will instead be to minimize the expansion error over subsets of fixed size $\beta | S |$ . The optimization objective is defined as:
+
+$$
+S _ { \beta } ^ { * } : = \arg \operatorname* { m i n } _ { S ^ { \prime } \subseteq S : | S ^ { \prime } | = \beta | S | } \epsilon ( S ^ { \prime } ; \alpha )
+$$
+
+We attempt to solve for $S _ { \beta } ^ { * }$ by alternating between optimizing parameters $\theta _ { t }$ and the training subset $S _ { t }$ . More explicitly, given $S ^ { \prime }$ we update $\theta$ using a single subset from $S ^ { \prime }$ of size $\alpha ^ { - 1 } | S ^ { \prime } |$ . Then we use $\theta$ to compute the loss for each element in $S$ , and set $S ^ { \prime }$ to be the $\beta$ fraction of the samples with the lowest losses. To encourage stability of the learning algorithm, the losses are smoothed with an optional momentum term $\eta$ . We also anneal the parameter $\beta$ from an initial value $\beta _ { 0 }$ down to the target value $\beta _ { \mathrm { m i n } }$ in order encourage more global exploration in the initial stages.
+
+Algorithm 2 presents the full algorithm. In addition to the incremental learning procedure $\mathcal { A }$ (e.g., standard SGD), the subroutine Sample takes a training set $S$ and returns $\alpha | S |$ elements uniformly at random; while Trim takes losses $L$ and returns the $\beta | L |$ samples with the lowest loss.
+
+Finally, we show for certain parameters that Algorithm 2 converges on the following objective over the training set $S$ :
+
+$$
+F ( \theta _ { t } , v _ { t } ; \beta _ { t } ) : = \sum _ { i \in S } v _ { t } [ i ] L ( f _ { \theta _ { t } } ( x _ { i } ) , y _ { i } ) + c \operatorname* { m a x } ( 0 , \beta _ { t } | S | - | v _ { t } | )
+$$
+
+where $v _ { t }$ is a 0-1 vector, $\beta _ { t }$ is decreasing, and $L ( \cdot , \cdot ) \leq c$
+
+Proposition 5.1. Let $\alpha = 1$ and $\eta = 0$ in the setting of Algorithm 2, and assume that $\mathcal { A }$ returns the empirical risk minimizer. Then we have that for each round of the algorithm, $F ( \theta _ { t } , v _ { t } ; \beta _ { t } )$ is decreasing in t and furthermore, $| F ( \theta _ { t } , v _ { t } ; \beta _ { t } ) - F ( \theta _ { t + 1 } , v _ { t + 1 } ; \beta _ { t + 1 } ) | \xrightarrow { t  \infty } 0 .$ .
+
+We defer the proof of Proposition 5.1 to Appendix A.
+
+Remark 4 When $\alpha = 1$ and $\eta = 0$ , we recover vanilla self-paced learning (SPL) with two major differences. First, we start on the full set of samples and train on incrementally smaller sets, while SPL starts with a small set of samples and trains on larger sets. This discrepancy is due to the differing objectives; whereas SPL is a heuristic for converging faster to a global minimizer of the population loss by training first on easy samples, ISPL attempts to converge to a local minimum over a subpopulation. Second, our annealing schedule is defined using the quantile statistics, while SPL uses an absolute loss threshold that generally scales by a multiplicative factor in each iteration. We chose this to counteract the propensity of deep neural networks to suddenly and rapidly interpolate the training data; in our experiments, we found this behavior made the performance of ISPL very sensitive to the specific annealing schedule when using absolute losses. Conversely, in SPL the final threshold is generally set high enough that most (or all) the samples are incorporated by the end, and so the specific schedule may have a smaller impact on the final performance.
+
+# 6 EXPERIMENTAL EVALUATION
+
+We evaluate our defense against the standard patch-based backdoor attack with dirty labels, where the adversary inserts a small patch into a training image from the source class, then changes the label
+
+![](images/e1cd6fabec31c0c55afa82eb91618216ed9980d17f21c5a8cb103cb7e6b5ef3e.jpg)  
+Figure 1: CIFAR-10 images with triggers applied (top), selected to maximize trigger visibility.
+
+Table 1: Results against dirty label backdoor adversary for select pairs of CIFAR-10 classes using a single pixel trigger. The numbers in column 1 refer to the standard CIFAR-10 labels (e.g., $0 =$ airplane, $1 =$ automobile, etc.). Column 2 gives the $( \mathbf { x } , \mathbf { y } )$ coordinates of the trigger. ${ \boldsymbol { \mathrm { S } } } =$ source class, $\mathrm { { T } = }$ target class, $\mathbf { C } =$ clean accuracy (higher is better), $\mathbf { A } =$ targeted misclassification rate (lower is better). Results for our method are in the last two columns under TW (this work).
+
+<table><tr><td rowspan="2">S/T</td><td rowspan="2">pos</td><td rowspan="2">E</td><td colspan="2">No defense</td><td colspan="2">SS</td><td colspan="2">AC</td><td colspan="2">ITLM</td><td colspan="2">TW</td></tr><tr><td>C</td><td>A</td><td>C</td><td>A</td><td>C</td><td>A</td><td>C</td><td>A</td><td>C</td><td>A</td></tr><tr><td rowspan="3">2/5</td><td rowspan="3">(27,9)</td><td>5</td><td>94.5</td><td>75.6</td><td>94.3</td><td>74.7</td><td>92.4</td><td>53.9</td><td>94.7</td><td>79.4</td><td>92.5</td><td>0.1</td></tr><tr><td>10</td><td>94.6</td><td>95.2</td><td>94.4</td><td>0.0</td><td>92.9</td><td>81.8</td><td>94.7</td><td>92.4</td><td>93.0</td><td>0.0</td></tr><tr><td>20</td><td>94.7</td><td>98.1</td><td>94.2</td><td>0.0</td><td>92.6</td><td>89.4</td><td>94.6</td><td>96.3</td><td>92.8</td><td>0.0</td></tr><tr><td rowspan="3">1/3</td><td rowspan="3">(15,4)</td><td>5</td><td>94.8</td><td>99.3</td><td>94.6</td><td>50.0</td><td>92.2</td><td>39.2</td><td>94.6</td><td>57.2</td><td>92.0</td><td>0.1</td></tr><tr><td>10</td><td>94.5</td><td>99.2</td><td>94.2</td><td>10.4</td><td>92.0</td><td>47.9</td><td>94.5</td><td>75.0</td><td>92.9</td><td>0.3</td></tr><tr><td>20</td><td>94.5</td><td>98.8</td><td>94.3</td><td>1.5</td><td>91.9</td><td>60.5</td><td>94.2</td><td>92.3</td><td>92.3</td><td>1.3</td></tr><tr><td rowspan="3">8/6</td><td rowspan="3">(4,1)</td><td>5</td><td>94.7</td><td>84.1</td><td>94.8</td><td>80.5</td><td>92.8</td><td>73.3</td><td>94.4</td><td>76.3</td><td>93.1</td><td>0.0</td></tr><tr><td>10</td><td>94.6</td><td>96.4</td><td>94.2</td><td>96.0</td><td>92.2</td><td>97.0</td><td>94.5</td><td>94.2</td><td>93.0</td><td>0.0</td></tr><tr><td>20</td><td>94.1</td><td>98.1</td><td>94.3</td><td>0.0</td><td>92.5</td><td>96.4</td><td>94.1</td><td>96.4</td><td>92.9</td><td>0.0</td></tr><tr><td rowspan="3">9/2</td><td rowspan="3">(4,27)</td><td>5</td><td>94.9</td><td>98.0</td><td>94.4</td><td>65.7</td><td>92.8</td><td>79.7</td><td>94.7</td><td>97.6</td><td>93.0</td><td>0.0</td></tr><tr><td>10</td><td>94.9</td><td>99.1</td><td>94.6</td><td>0.0</td><td>92.6</td><td>80.8</td><td>94.4</td><td>99.3</td><td>92.9</td><td>0.0</td></tr><tr><td>20</td><td>94.7</td><td>99.1</td><td>94.3</td><td>0.0</td><td>93.1</td><td>98.9</td><td>94.1</td><td>99.1</td><td>93.1</td><td>0.0</td></tr></table>
+
+of the image to the target class. The goal is to induce the learner to misclassify images from the source class as the target class upon application of the patch. Results in this section use a standard PreActResNet18 architecture (He et al., 2016b) that achieves $94 \%$ accuracy on CIFAR-10 when trained on a clean dataset. The appendix provides full experimental details and additional results.
+
+# 6.1 RESULTS
+
+Our implementation of the dirty label backdoor adversary follows the threat model described in Gu et al. (2017). The perturbation function $\tau$ simply overlays a small pattern on the image. For evaluation, we use the same dataset (CIFAR-10 (?)) and setup for our experiments as Tran et al. (2018). Example pairs of clean and poisoned data are shown in Figure 1.
+
+Table 1 presents results for the single-pixel backdoor attack, in which the adversary randomly selects a position and color for the backdoor and applies the trigger by replacing the pixel at that position with the selected color. The first column, $S / \mathrm { T } ,$ , presents numbers in the form $S / \mathrm { T } ,$ where S is the source class and T is the target class in CIFAR-10. The goal of the attacker is to induce the network to misclassify poisoned images from the S class to the T class. The second column, pos, presents numbers in the form (X,Y) where X,Y is the position of the single pixel trigger. The third column, $\epsilon$ presents the percentage of the source class in the training set that is poisoned by the adversary.
+
+We report results for our defense, This Work (TW), in the last column, in addition to four baseline defenses: 1) No defense, 2) Spectral Signatures (SS) (Tran et al., 2018), 3) Activation Clustering (AC) (Chen et al., 2018), and 4) Iterative Trimmed Loss Minimization (ITLM) (Shen and Sanghavi, 2019). For each defense we report the percent accuracy over the clean images in the test set (column C, higher is better, maximum is $100 \%$ when all clean images are classified correctly) and the targeted misclassification rate (Equation 7) over patched images of the target class in the test set (column A, lower is better, minimum is $0 \%$ when none of the poisoned images are misclassified). The results show that the technique we present in this paper 1) almost completely defends against this attack (column A ranges from $0 . 0 \%$ to $1 . 3 \%$ ) at the cost of 2) a small (roughly $2 \%$ ) decrease in the clean accuracy (column C, clean accuracies around $9 2 \div 9 3 \%$ ). All other defenses exhibit significant vulnerability to this attack (column A, No defense, SS, AC, and ITLM).
+
+# 6.2 DISCUSSION
+
+Many data poisoning defenses in the literature are evaluated on simpler datasets than those considered in this paper, such as traffic signs (GTSRB (Houben et al., 2013) or LISA (Mogelmose et al., 2012)) and MNIST (?). Furthermore, these datasets are tested in conjunction with larger or otherwise more obvious triggers. For instance, the Neural Cleanse (Wang et al., 2019) defense uses a 4x4 white box as the trigger on the MNIST and GTSRB datasets; MESA (Qiao et al., 2019) uses a 3x3 image as the trigger on CIFAR-10 and test only at $\epsilon = 1 \%$ ; TABOR (Guo et al., 2019) uses a 6x6 square as the trigger for GTSRB for images that are $3 2 \mathrm { x } 3 2$ (they additionally test on ImageNet but do not report good results until the trigger is over $2 5 \%$ of each dimension); and STRIP (Gao et al., 2019b) uses an 8x8 box on CIFAR-10. Our hypothesis is that the combination of a smaller trigger and more complex classes breaks defenses that demonstrate good performance in simpler contexts. Table 1 reports results using a single pixel trigger, which is often placed at the border of the image, within the region cropped by the standard random cropping data augmentation during training.
+
+For comparison, we implemented the AC defense, which is included in the Adversarial Robustness Toolbox (Nicolae et al., 2019), an open-source collection of tools for security in machine learning. The authors report that AC achieves nearly perfect performance on two popular settings, namely, MNIST and traffic signs. We also implemented ITLM, which was tested on CIFAR-10 at $\epsilon = 5 \%$ using larger L- and $\mathrm { X }$ -shaped triggers. Our results in Table 1 indicate that both AC and ITLM fail to completely defend against the poison in every setting, with the best targeted misclassification rate achieved by AC at $3 9 . 2 \%$ (compared to nearly $0 \%$ in every case with our defense).
+
+To the best of our knowledge, SS is the only other defense in the literature which is evaluated using the same dataset (CIFAR-10) and class of triggers. The defense uses the eigenvectors of the feature matrix to separate clean and poisoned data. However, the authors do not appear to use triggers that can be cropped out during training by data augmentation. They also limit evaluation to “successfully” attacked networks, which they define as over $90 \%$ targeted misclassification rate of the undefended network (Column A, No defense). While our experiments suggest that SS is the strongest baseline after ours, successfully defending against the poison in 6 of the 12 scenarios considered in Table 1, its performance is poor particularly at lower $\epsilon$ . Our results suggest that SS may fail to defend against harder to learn triggers requiring more complex feature representations.
+
+# 7 CONCLUSION
+
+Backdoor data poisoning attacks on deep neural networks are an emerging class of threats in the growing landscape of deployed machine learning applications. Though defenses exist, our experiments suggest that they only work against narrowly defined adversaries and fail dramatically when evaluated using more subtle threat models.
+
+We introduce a new approach to defending against backdoor attacks based on an analysis of a novel self-expansion property in the training data. For a poisoned dataset satisfying mild compatibility properties, we show that an ensemble of weak learners fit to self-expanding sets successfully removes the poisoned data. Empirically, our method is resilient to a strong version of the dirty label backdoor attack introduced by Gu et al. (2017), which successfully evades all the baseline defenses. We believe our analysis and techniques present a valuable addition to the toolbox for secure deep learning.
+
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+
+# A DEFERRED PROOFS
+
+Lemma A.1. Let $S _ { N }$ and $S _ { P }$ be two sets satisfying Property 4.4, and let $S$ and $T$ be drawn from $S _ { N }$ and $S _ { P }$ , respectively. Then for all $0 < \gamma \leq \alpha$ , $S$ and $T$ are mutually strictly $\gamma$ -incompatible.
+
+Proof. We will show that $T$ is $\gamma$ -incompatible with $S$ for all $\gamma \leq \alpha$ ; mutual incompatibility follows by a symmetric argument. First, $T$ is $\alpha$ -incompatible with $S$ by consequence of Property 4.4. Fix $\gamma < \alpha$ . Our main approach will be to subsample $S$ twice: first, we sample $S$ at a rate of $\gamma / \alpha$ to create $S ^ { \prime }$ such that $| S ^ { \prime } | \approx \gamma / \alpha | S |$ . Then $S ^ { \prime }$ is $\alpha$ -incompatible with $T$ , so $\epsilon ( S ^ { \prime } | T , \alpha ) \geq \epsilon ( S ^ { \prime } , \alpha )$ . However we need take some care to ensure $\gamma / \alpha | S |$ is an integer.
+
+Define
+
+$$
+\alpha ^ { \prime } : = \frac { \gamma | S | } { \lfloor \gamma | S | / \alpha \rfloor }
+$$
+
+Then $\alpha ^ { \prime } \geq \alpha$ and $\gamma / \alpha ^ { \prime } | S | = \lfloor \gamma | S | / \alpha \rfloor$ . Thus, we will subsample $S$ at a rate of $\gamma / \alpha ^ { \prime }$ to create $S ^ { \prime }$ ; by Assumption 4.3, $T$ is $\alpha ^ { \prime }$ -incompatible with $S ^ { \prime }$ . Note that the resulting training sets produced by this double subsampling procedure have size $\gamma | S |$ as desired.
+
+Next, we will show that there exists some constant $c$ such that
+
+$$
+\begin{array} { c } { { \epsilon ( S | T , \gamma ) = c ( \gamma / \alpha ^ { \prime } | S | ) ^ { - 1 } \mathbb { E } [ \epsilon ( S ^ { \prime } | T , \alpha ^ { \prime } ) ] } } \\ { { \epsilon ( S , \gamma ) = c ( \gamma / \alpha ^ { \prime } | S | ) ^ { - 1 } \mathbb { E } [ \epsilon ( S ^ { \prime } , \alpha ^ { \prime } ) ] } } \end{array}
+$$
+
+where the expectations are taken over the subset $S ^ { \prime } \subset S$ , $| S ^ { \prime } | = \gamma / \alpha ^ { \prime } | S |$ . Then since $T$ is strictly $\alpha ^ { \prime }$ -incompatible with all such $S ^ { \prime }$ by Property 4.4,
+
+$$
+\begin{array} { r l } & { \epsilon ( S | T , \gamma ) = c | S ^ { \prime } | ^ { - 1 } \mathbb { E } [ \epsilon ( S ^ { \prime } | T , \alpha ^ { \prime } ) ] } \\ & { ~ > c | S ^ { \prime } | ^ { - 1 } \mathbb { E } [ \epsilon ( S ^ { \prime } , \alpha ^ { \prime } ) ] } \\ & { ~ = \epsilon ( S , \gamma ) } \end{array}
+$$
+
+which is what we wanted to prove.
+
+Fix a training set $S ^ { \prime \prime }$ , $| S ^ { \prime \prime } | = \gamma | S |$ , and let $T$ be arbitrary. By Assumption 4.3 we have that $R _ { e m p } ( A ( S ^ { \prime \prime } \cup T ) ; S ^ { \prime \prime } ) = 0$ for all $T ^ { \prime }$ . Then conditioning on the training set $S ^ { \prime \prime }$ , we have that
+
+$$
+\begin{array} { r l } & { \mathbb { E } [ \epsilon ( S ^ { \prime } | T , \alpha ^ { \prime } ) | S ^ { \prime \prime } ] = \mathbb { E } [ R _ { e m p } ( A ( S ^ { \prime \prime } \cup T ) ; S ^ { \prime } ) | S ^ { \prime \prime } ] } \\ & { \qquad = \mathbb { E } [ R _ { e m p } ( A ( S ^ { \prime \prime } \cup T ) ; S ^ { \prime } - S ^ { \prime \prime } ) | S ^ { \prime \prime } ] } \end{array}
+$$
+
+where the expectation is over $S ^ { \prime }$ such that $S ^ { \prime \prime } \subset S ^ { \prime }$ . Now $S ^ { \prime } - S ^ { \prime \prime }$ is a random variable consisting of $\left| S ^ { \prime } \right| - \left| S ^ { \prime \prime } \right|$ independent draws from $S$ with replacement; thus Equation 22 is just equal to $\left| S ^ { \prime } \right| - \left| S ^ { \prime \prime } \right|$ times the empirical risk of a random element in $S$ . On the other hand, $R _ { e m p } ( A ( S ^ { \prime \prime } \cup T ) ; S )$ is the empirical risk over all elements in $S$ , or equivalently, $| S |$ times the empirical risk of a random element.
+
+Since $T$ was arbitrary, summing over all possible training sets $S ^ { \prime \prime }$ yields the desired identities with
+
+$$
+c = { \frac { \left| S \right| } { \left| S ^ { \prime } \right| - \left| S ^ { \prime \prime } \right| } } .
+$$
+
+Proof of Theorem 4.5. We first prove a slightly more general result. Assume by way of contradiction that there exists a partition of $S ^ { * }$ into two nonempty sets $P$ and $Q$ that are mutually strictly incompatible.
+
+Let $\epsilon ^ { * }$ be the expansion error of $S ^ { * }$ . Recall that this means
+
+$$
+| S ^ { * } | \epsilon ^ { * } = | S ^ { * } | \epsilon ( S ^ { * } ; \alpha ) = \mathbb { E } [ R _ { e m p } ( A ( S ^ { \prime } ) ; S ^ { * } ) ]
+$$
+
+where the expectation is taken over samples $S ^ { \prime }$ of size $\alpha ^ { - 1 } | S ^ { * } |$ drawn from $S ^ { * }$ with replacement. Since the empirical risk is a linear function of $S ^ { * }$ , we can decompose this last term as
+
+$$
+{  { \mathbb E } } [ R _ { e m p } ( A ( S ^ { \prime } ) ; S ^ { * } ) ] = {  { \mathbb E } } [ R _ { e m p } ( A ( S ^ { \prime } ) ; P ) ] + {  { \mathbb E } } [ R _ { e m p } ( A ( S ^ { \prime } ) ; Q ) ]
+$$
+
+Given a set of training samples $S ^ { \prime }$ , we will denote the elements drawn from $P$ and $Q$ as $P ^ { \prime } = S ^ { \prime } \cap P$ and $Q ^ { \prime } = S ^ { \prime } \cap Q$ , respectively. Now consider the term
+
+$$
+\mathbb { E } [ R _ { e m p } ( A ( S ^ { \prime } ) ; P ) ] = \mathbb { E } [ R _ { e m p } ( A ( P ^ { \prime } \cup Q ^ { \prime } ) ; P ) ]
+$$
+
+If we fix $Q ^ { \prime }$ , then $P ^ { \prime }$ is drawn uniformly at random from $P$ with replacement, where $| P ^ { \prime } | =$ $\alpha | S ^ { * } | - | Q ^ { \prime } |$ . Define
+
+$$
+\alpha _ { Q ^ { \prime } } : = \frac { \alpha | S ^ { * } | - | Q ^ { \prime } | } { | P | }
+$$
+
+which is the subsampling rate of $P ^ { \prime }$ given $Q ^ { \prime }$ . Note that if $\alpha ^ { \prime } \geq \alpha$ , then $Q ^ { \prime }$ is $\alpha ^ { \prime }$ -incompatible with $P ^ { \prime }$ by Assumption 4.3, and otherwise $\alpha ^ { \prime } < \alpha$ and $Q ^ { \prime }$ is strictly $\alpha ^ { \prime }$ -incompatible with $P ^ { \prime }$ by Lemma A.1. Thus,
+
+$$
+\begin{array} { r l r } {  { \mathbb { E } [ R _ { e m p } ( \boldsymbol { A } ( P ^ { \prime } \cup Q ^ { \prime } ) ; P ) ] = \sum _ { Q ^ { \prime } } \operatorname* { P r } [ Q ^ { \prime } ] \mathbb { E } [ R _ { e m p } ( \boldsymbol { A } ( P ^ { \prime } \cup Q ^ { \prime } ) ; P ) | Q ^ { \prime } ] } } \\ & { } & { = | P | \sum _ { Q ^ { \prime } } \operatorname* { P r } [ Q ^ { \prime } ] \epsilon ( P | Q ^ { \prime } ; \alpha _ { Q ^ { \prime } } ) } \\ & { } & { > | P | \sum _ { Q ^ { \prime } } \operatorname* { P r } [ Q ^ { \prime } ] \epsilon ( P ; \alpha _ { Q ^ { \prime } } ) } \end{array}
+$$
+
+On the other hand, $\mathbb { E } [ \alpha _ { Q ^ { \prime } } ] = \alpha$ , and since $\epsilon ( P ; \alpha )$ is convex in $\alpha$ by Assumption 4.3, we can apply Jensen’s inequality to conclude
+
+$$
+\sum _ { Q ^ { \prime } } P r [ Q ^ { \prime } ] \epsilon ( P ; \alpha _ { Q ^ { \prime } } ) \geq \epsilon ( P ; \alpha ) ,
+$$
+
+i.e.,
+
+$$
+\mathbb { E } [ R _ { e m p } ( A ( P ^ { \prime } \cup Q ^ { \prime } ) ; P ) ] > | P | \epsilon ( P ; \alpha ) .
+$$
+
+Similarly,
+
+$$
+\mathbb { E } [ R _ { e m p } ( A ( P ^ { \prime } \cup Q ^ { \prime } ) ; Q ) ] > | Q | \epsilon ( Q ; \alpha ) .
+$$
+
+Combining these two results yields
+
+$$
+| S ^ { * } | \epsilon ^ { * } > | P | \epsilon ( P ; \alpha ) + | Q | \epsilon ( Q ; \alpha ) .
+$$
+
+Since $| P | + | Q | = | S ^ { * } |$ , we have that at least one of $\epsilon ( P ; \alpha )$ or $\epsilon ( Q ; \alpha )$ must be less than $\epsilon ^ { * }$ , which contradicts the optimality of $S ^ { * }$ . Thus one of $P$ or $Q$ must be empty.
+
+Finally, we note that by Property 4.4, the partition $P = S ^ { * } \cap S _ { P }$ and $Q = S ^ { * } \cap S _ { N }$ gives an incompatible partition, which yields the result.
+
+Proof of Theorem 4.8. We begin with the simple observation that if Properties 4.4 and 4.6 hold for $S$ , they also hold for $S \setminus S ^ { \prime }$ for any set $S ^ { \prime }$ . Thus we are able to apply Theorem 4.5 at each step and so in fact $S _ { 1 } , . . . , S _ { N }$ are all homogeneous. Additionally, since $p > 1 / 2$ and a component’s vote is weighted by its size, a sufficient condition for success is when all the primary components vote correctly.
+
+We start with the case when $\mathcal { A }$ is deterministic. Let $S _ { i }$ and $S _ { j }$ be a primary component and noise component, respectively. By strict incompatibility, we have that $R _ { e m p } ( { \cal { A } } ( { \bf { \bar { S } } } _ { i } ) ; S _ { j } ) ~ >$ $R _ { e m p } ( A ( \emptyset ) ; S _ { j } ) = | \bar { S _ { j } } | / 2$ . Thus $S _ { i }$ votes 0 on $S _ { j }$ . Conversely, if $S _ { j }$ is a primary component, then $R _ { e m p } ( A ( { \cal S } _ { i } ) ; { \cal S } _ { j } ) \ < R _ { e m p } ( A ( \emptyset ) ; { \cal S } _ { j } ) = | { \cal S } _ { j } | / 2$ , so $S _ { i }$ votes 1 on $S _ { j }$ . Putting these together and using the fact that $p > 1 / 2$ , we find that the noise components have weighted vote strictly less than $| S | / \bar { 2 }$ , while the primary components have weighted vote strictly greater than $| S | / 2$ , as required.
+
+For the case when $\mathcal { A }$ is stochastic, we apply standard concentration bounds to our estimates of the empirical risk of each component (over the randomness in $\mathcal { A }$ ). Let $S _ { i }$ and $S _ { j }$ be a primary and noise component, respectively. Again, strict incompatibility gives $R _ { e m p } ( { \cal A } ( S _ { i } ) ; \tilde { S _ { j } } ) \geq R _ { e m p } ( { \cal A } ( \emptyset ) ; S _ { j } ) +$ $\delta | S _ { j } | = ( 1 / 2 + \bar { \delta } ) | S _ { j } |$ . Define the sample average empirical risk
+
+$$
+V _ { B } : = \frac { 1 } { B | S _ { j } | } \sum _ { b = 1 } ^ { B } R _ { e m p } ( A _ { b } ( S _ { i } ) ; S _ { j } )
+$$
+
+computed from $B$ samples over the randomness in $\mathcal { A }$ . Then $\mathbb { E } [ V _ { B } ] \ge ( 1 / 2 + \delta )$ and so by Hoeffding’s inequality
+
+$$
+\begin{array} { r } { \mathrm { P r } [ | V _ { B } < 1 / 2 ] \le \mathrm { P r } [ | V _ { B } - ( 1 / 2 + \delta ) | > \delta ] } \\ { < 2 \exp ( - 2 \delta ^ { 2 } B ) \qquad } \end{array}
+$$
+
+Thus with probability at least $1 - 2 \exp ( - 2 \delta ^ { 2 } B )$ , primary component $S _ { i }$ votes 0 when $S _ { j }$ is a noise component. By the same argument and using strict compatibility, the bound also holds for $S _ { i }$ voting 1 when $S _ { i }$ and $S _ { j }$ are both from primary components. Putting this together, we recall that a sufficient condition for success of the algorithm occurs when all the primary components vote correctly on all components (both primary and noise), which happens with probability at least
+
+$$
+[ 1 - 2 \exp ( - 2 \delta ^ { 2 } B ) ] ^ { M N }
+$$
+
+as claimed.
+
+Proof of Proposition 5.1. The statement is more or less a direct consequence of the alternating convex minimization strategy. Recall first that since $\alpha = 1$ and $\eta = 0$ , Lines 4 and 6 in Algorithm 2 have no effect.
+
+We prove the statement in two steps. First we claim that
+
+$$
+F ( \theta _ { t + 1 } , v _ { t } ; \beta _ { t } ) \leq F ( \theta _ { t } , v _ { t } ; \beta _ { t } )
+$$
+
+Note that $v _ { t }$ in the optimization objective $F$ plays the role of $S _ { t }$ in Algorithm 2. The inequality follows from the optimization on Line 5 in Algorithm 2, which sets $\theta _ { t + 1 }$ to the empirical risk minimizer of the set $v _ { t }$ .
+
+Next, we claim that
+
+$$
+F ( \theta _ { t + 1 } , v _ { t + 1 } ; \beta _ { t + 1 } ) \leq F ( \theta _ { t + 1 } , v _ { t } ; \beta _ { t } )
+$$
+
+Since $0 \leq L ( \cdot , \cdot ) < c$ , the optimal size of the set $S _ { t }$ is $| v _ { t } | = \beta _ { t } | S |$ . Since $\beta _ { t }$ is decreasing, we have that $| v _ { t + 1 } | \leq | v _ { t } |$ . Thus the number of elements in the trimmed empirical loss is non-increasing (Line 7).
+
+Combining the two inequalities shows that the objective function is decreasing in $t$ . Since $F ( \theta _ { t } , v _ { t } ; \beta _ { t } )$ is a decreasing sequence bounded from below by zero, the monotone convergence theorem gives the second result.
+
+# B EXPERIMENTAL DETAILS
+
+# B.1 DEFENSE SET UP AND HYPERPARAMETERS
+
+ISPL $^ +$ Boosting (this work). For our defense, we use the same set of hyperparameters across all experiments. We run 8 rounds of ISPL, each of which returns a component consisting of roughly $12 \%$ of the total samples. Let $p$ be the target percentage of samples over the remaining samples (i.e., $p \approx 1 / ( 8 - i + 1 )$ in the $i ^ { t h }$ iteration). Then the number of iterations $N$ is set to $2 + \operatorname* { m i n } ( 3 , 1 / p )$ . $\beta$ starts at $3 * p$ in the first iteration, then drops linearly to its final value of $p$ over the next 2 iterations. When trimming the training set, we also additionally include the top $p / 8$ samples per class to prevent the network from collapsing to a trivial solution. For the learning procedure $\mathcal { A }$ , we use standard SGD, trained for 4 epochs per iteration, with a warm-up in the first iteration of 8 epochs. The expansion factor $\alpha$ is set to $1 / 4$ , and the momentum factor $\eta$ is set to 0.9.
+
+We run ISPL 3 times to generate 24 weak learners. Each weak learner is trained for 40 epochs on its respective subset. For the boosting framework, each component votes on a per-sample basis. The sample is preserved if the modal vote equals the given label, with ties broken randomly.
+
+We also include a final self-training step by training a fresh model for 100 epochs on the recovered samples. The main idea is that a model fit to the full “clean” training data can be used to test the excluded training data, thereby recovering additional consistent data which may have been originally excluded because the weak learners were fit to a small subset of data for fewer epochs. However, it may take several repetitions of training a model from scratch before this self-training process no longer identifies new samples to recover. Therefore, we use a simple self-paced learning algorithm to dynamically adjust the samples during training to limit the self-training to a single iteration. More explicitly, we start with the “clean” samples as returned by the boosting framework. Every 5 epochs, we update the training set to be the samples whose labels agree with the model’s current predictions. Due to the relative frequency with which we resample the training set, we smooth the predictions by a momentum factor of 0.8 so that the training process is less noisy. The samples used for training in the last epoch are returned as the defended dataset. In our experiments, this process decreases the false positive rate (and thus increases the clean accuracy) but does not materially affect the false negative rate (nor the targeted misclassification rate).
+
+Spectral Signatures. We use the official implementation of the Spectral Signatures defense (Tran et al., 2018) by the authors, available on Github, except that we replace the training procedure with PyTorch (instead of Tensorflow $1 . \mathbf { x }$ as in the authors’ original implementation). The authors suggest removing 1.5 times the maximum expected amount of poison from each class for the defense. We remove $20 \%$ of each class for $\epsilon = 5$ , $\bar { 1 0 \% }$ and $30 \%$ of each class for $\epsilon = 2 0 \%$ . In selecting the layer for the activations, for the ResNet32 architecture, we use the input to the third block of the third layer (which matches the authors’ implementation), and for the PreActResNet18 architecture, we use the input to the first block of the four layer (which was found empirically to remove the most poison on the first set of scenarios). We note that the authors indicate the defense should be fairly successful at any of the later layers of the network.
+
+Iterative Trimmed Loss Minimization. The Iterative Trimmed Loss Minimization defense (Shen and Sanghavi, 2019) consists of an iterative procedure. Given a setting $0 < \alpha \leq 1$ , one first trains a model for a number of epochs. Then the $\alpha$ fraction of samples with the lowest loss are retained for the next iteration. This process is repeated several times, with a fresh model beginning each iteration. The defended dataset is the $\alpha$ fraction of samples with the lowest loss after the last iteration. For the backdoor data poisoning experiments on CIFAR-10, the authors use 80 epochs for the first round of training, then 40 epochs thereafter; they also set $\alpha = 9 8 \%$ for $\epsilon = 5 \%$ , and do not test at other values of $\epsilon$ . We use the same settings, and scale $\alpha$ linearly with $\epsilon$ , i.e., $\alpha = 9 6 \%$ for $\epsilon = 1 0 \%$ and $\alpha = 9 2 \%$ for $\epsilon = 2 0 \%$ .
+
+Activation Clustering. The Activation Clustering defense (Chen et al., 2018) has an actively maintained official implementation in the Adversarial Robustness Toolbox (ART) (Nicolae et al., 2019), an open-source collection of tools for security in machine learning. We use the official implementation with the default parameters values in ART v1.6.2, the most current version at the time of writing. In selecting the layer for the activations, we used the same layer as for Spectral Signatures.
+
+Models. The PreActResNet18 He et al. (2016b) model is optimized using vanilla SGD with learning rate 0.02, momentum 0.9, and weight decay 5e-4. For the final dataset, we train for 200 epochs and drop the learning rate by 10 at epochs 100, 150, and 180. Using these parameters, we achieve $9 4 . 7 \%$ accuracy on CIFAR-10 when trained and tested with clean data.
+
+The ResNet32 He et al. (2016a) model is optimized using vanilla SGD with learning rate 0.1, momentum 0.9, and weight decay 1e-4. For the final dataset, we train for 200 epochs and drop the learning rate by 10 at epochs 100 and 150. Using these parameters, we achieve $9 1 . 8 \%$ accuracy on CIFAR-10 when trained and tested with clean data.
+
+# B.2 BACKDOOR POISON DATASET CONSTRUCTION
+
+Each scenario has a single source and target class. We use the same (source, target) pairs as in Tran et al. (2018): (airplane, bird), (automobile, cat), (bird, dog), (cat, dog), (cat, horse), (horse, deer), (ship, frog), (truck, bird).
+
+To generate a perturbation, we choose a shape (L-shape, X-shape, or pixel) uniformly at random. The (X,Y) coordinates of the perturbation are randomly selected to guarantee that the entire shape is visible before data augmentation (e.g., the pixel-based perturbation can be placed anywhere within the $3 2 \mathrm { x } 3 2 $ image, but the X-shape is larger and so must be centered in a $3 0 \mathbf { x } 3 0$ region, one pixel away from the border). The color of the perturbation is also selected uniformly at random, with each of the (R,G,B) coordinates ranging from 0 to 255. Finally, we randomly select an $\epsilon = 5$ , 10, $2 0 \%$ percentage of the source class, apply the perturbation by replacing the pixels in the corresponding locations with the selected shape and color, then relabel the poisoned images as the target class.
+
+Table 2 displays the generated triggers used in our experiments with examples of poisoned images. Within the row for each (source, target) pair, the first subrow gives the parameters for poison 1, the second subrow gives the parameters for poison 2, and the third subrow gives the parameters for poison 3. We also provide an example of the corresponding clean image for poison 1 in column clean 1. Note that the results presented in Table 1 of the main paper use the first scenario of each (source, target) pair (poison 1).
+
+Table 2: CIFAR-10 dirty label backdoor scenarios.   
+
+<table><tr><td>source</td><td>target</td><td>color</td><td>position</td><td>method</td><td>clean 1</td><td>poison 1</td><td>poison 2</td><td>poison 3</td></tr><tr><td rowspan="3">0 /Plane</td><td rowspan="3">2/Bird</td><td>(103,87,79)</td><td>(24,3)</td><td>pixel</td><td rowspan="3"></td><td rowspan="3"></td><td rowspan="3"></td><td rowspan="3"></td></tr><tr><td>(92, 1,189)</td><td>(27,30)</td><td>pixel</td></tr><tr><td>(47,2,21)</td><td>(21,8)</td><td>pixel</td></tr><tr><td rowspan="3">1/Car</td><td rowspan="3">3/Cat</td><td>(180,98,53)</td><td>(10,30)</td><td>pixel</td><td rowspan="3"></td><td rowspan="3"></td><td rowspan="3"></td><td rowspan="3"></td></tr><tr><td>(40,105,92)</td><td>(25,13)</td><td>pixel</td></tr><tr><td>(145,70,200)</td><td>(9,29)</td><td>pixel</td></tr><tr><td rowspan="3">2 /Bird</td><td rowspan="3">5/Dog</td><td>(93,86,130)</td><td>(27,9)</td><td>pixel</td><td rowspan="3"></td><td rowspan="3"></td><td rowspan="3"></td><td rowspan="3"></td></tr><tr><td>(156,158,244)</td><td>(18,30)</td><td>pixel</td></tr><tr><td>(74,162,26)</td><td>(11,9)</td><td>pixel</td></tr><tr><td rowspan="3">3/Cat</td><td rowspan="3">5/Dog</td><td>(34, 241, 240)</td><td>(2,14)</td><td>L</td><td rowspan="3"></td><td rowspan="3"></td><td rowspan="3"></td><td rowspan="3"></td></tr><tr><td>(239,42, 58)</td><td>(28,13)</td><td>pixel</td></tr><tr><td>(39,221, 162)</td><td>(7,23)</td><td>X</td></tr><tr><td rowspan="3">3 /Cat</td><td rowspan="3">7 /Horse</td><td>(61,14,183)</td><td>(16,2)</td><td>X</td><td rowspan="3"></td><td rowspan="3"></td><td rowspan="3"></td><td rowspan="3"></td></tr><tr><td>(180,50,21)</td><td>(11,0)</td><td>pixel</td></tr><tr><td>(4,221, 78)</td><td>(24,22)</td><td>L</td></tr><tr><td rowspan="3">7 /Horse</td><td rowspan="3">4/Deer</td><td>(107,60,58)</td><td>(15,4)</td><td>pixel</td><td rowspan="3"></td><td rowspan="3"></td><td rowspan="3"></td><td rowspan="3"></td></tr><tr><td>(242, 30,233)</td><td>(4,21)</td><td>X</td></tr><tr><td>(76,14,15)</td><td>(11, 19)</td><td>L</td></tr><tr><td rowspan="3">8 / Ship</td><td rowspan="3">6/Frog</td><td>(141,245,211)</td><td>(4,1)</td><td>pixel</td><td rowspan="3"></td><td rowspan="3"></td><td rowspan="3"></td><td rowspan="3"></td></tr><tr><td>(213,221,138)</td><td>(19,29)</td><td>X</td></tr><tr><td>(121,158,6)</td><td>(3,13)</td><td>pixel</td></tr><tr><td rowspan="3">9 /Truck</td><td rowspan="3">2/Bird</td><td>(187, 67, 135)</td><td>(4,27)</td><td>pixel</td><td rowspan="3"></td><td rowspan="3"></td><td rowspan="3"></td><td rowspan="3"></td></tr><tr><td>(69,204,11)</td><td>(14,29)</td><td>L</td></tr><tr><td>(239,186,219)</td><td>(1,29)</td><td>X</td></tr></table>
+
+Table 3: Performance on CIFAR-10, dirty label backdoor scenario, using the PreActResNet18 architecture. The S / T column lists the CIFAR-10 source and target classes.  refers to the percentage of the source class which is poisoned. For the remainder of the columns, the top level column headers give the defense type: L (clean), ND (no defense), SS (spectral signatures), AC (activation clustering), ITLM (iterative trimmed loss minimization, and TW (this work); the second level column headers give the metric type: M (misclassification rate), C (clean accuracy, higher is better), A (targeted misclassification rate, lower is better), FP (false positives, lower is better), FN (false negatives, lower is better). Please refer to the text for a more detailed explanation of the table.   
+
+<table><tr><td>S/T</td><td>E</td><td>L</td><td>ND</td><td></td><td></td><td>ss</td><td></td><td></td><td></td><td>AC</td><td></td><td></td><td></td><td>ITLM</td><td></td><td></td><td></td><td>TW</td><td></td><td></td></tr><tr><td></td><td>5</td><td>M 1.3</td><td>C 94.5</td><td>A 91.3</td><td>C 94.5</td><td>A 79.9</td><td>FP 7381</td><td>FN 130</td><td>C</td><td>A</td><td>FP</td><td>FN</td><td>C</td><td>A</td><td>FP</td><td>FN</td><td>C</td><td>A</td><td>FP</td><td>FN</td></tr><tr><td>0/2</td><td>10 20</td><td>1.3 1.1</td><td>94.1</td><td>90.6 94.6 80.2</td><td>94.5 94.2</td><td>66.0 64.2</td><td>7383 14335</td><td>383 335</td><td>91.9 92.3 92.4</td><td>58.3 85.9 73.9</td><td>18926 19790 19127</td><td>155 320 601</td><td>94.2 93.8</td><td>94.6 84.9 92.8 93.8</td><td>994 1961 3897</td><td>244 461 897</td><td>92.8 92.8 91.6</td><td>0.0 0.0 22.9</td><td>3640 3479 3711</td><td>23 25 237</td></tr><tr><td>1/310</td><td>5 20</td><td>0.0 0.0 0.0</td><td>94.4</td><td>92.9 94.698.4 94.4 99.6</td><td>94.7 94.5 94.6</td><td>5.5 0.0 0.0</td><td>7319 7035 14007</td><td>68 35 7</td><td>90.9 92.568.7 92.2</td><td>19.5 91.8</td><td>19791 19033 18317</td><td>155 333 622</td><td>94.8 94.6 98.0 94.4</td><td>96.5 99.4</td><td>986 1981 3914</td><td>236 481 914</td><td>92.8 93.0 93.0</td><td>0.0 0.0 0.0</td><td>3434 3348 3253</td><td>2 3 2</td></tr><tr><td>2/510</td><td>5 20</td><td>1.1 0.9 1.2</td><td>94.4</td><td>80.4 94.497.2 94.494.0</td><td>94.6 94.4 94.5</td><td>76.4 0.1 87.7</td><td>7494 7053 14263</td><td>243 53 263</td><td>92.4 92.9 92.6</td><td>53.9 81.8 89.4</td><td>19937 18657 20531</td><td>172 313 406</td><td>94.7 94.7 94.6</td><td>79.4 92.4 95.4</td><td>985 990 966</td><td>235 490 966</td><td>92.6 92.9 92.8</td><td>0.2 0.2 0.3</td><td>3704 3200 3540</td><td>5 16 38</td></tr><tr><td>3/5</td><td>5 10 20</td><td>7.6 5.9 7.6</td><td>94.7</td><td>91.0 94.8 94.0</td><td>94.7 94.4</td><td>88.5 8.6</td><td>7281 7014</td><td>30 14</td><td>92.6</td><td>90.8 92.391.620293</td><td>19172</td><td>172 296</td><td>94.5 94.6 92.3</td><td>91.4</td><td>993 988</td><td>243 488</td><td>92.8</td><td>81.1 92.6 90.2</td><td>3693 3355</td><td>167 496</td></tr><tr><td>3/710</td><td>5</td><td>0.6 0.7</td><td></td><td>94.7 90.8 94.333.8 94.4 98.5</td><td>94.3 94.6 94.6</td><td>90.6 98.3 96.6</td><td>14092 7500 7135</td><td>92 249 135</td><td>92.6 92.6 91.9 92.2 98.2</td><td>97.2</td><td>18236 21289 20630</td><td>652 246 484</td><td>94.7 94.7 94.5</td><td>91.7 98.4 98.6</td><td>974 995 1979</td><td>974 245 479</td><td>92.6 92.7 92.7</td><td>87.4 0.0 2.4</td><td>3210 3692 3427</td><td>995 5 22</td></tr><tr><td>7/410</td><td>20 5</td><td>0.7 1.5 1.5</td><td>94.7 94.6 94.7</td><td>94.4 98.5 92.0</td><td>94.6 94.4</td><td>93.778.5 0.6 0.0</td><td>14675 7280 7023</td><td>675 29 23</td><td>92.3 98.2 92.3 39.2 92.0 47.9</td><td></td><td>20470 19353 19631</td><td>987 150 285</td><td>94.4 94.8 91.6 94.4</td><td>98.9 94.5</td><td>980 992 1979</td><td>980 242 479</td><td>92.9 92.8 93.0</td><td>10.5 0.5 0.3</td><td>3259 3258 3627</td><td>43 30 293</td></tr><tr><td></td><td>20 5</td><td>1.5 0.2</td><td>94.6 94.7</td><td>96.5 97.0</td><td>94.3 94.8</td><td>0.1 80.5</td><td>14000 7470</td><td>0 219</td><td>92.1 92.8</td><td>78.6 73.3</td><td>21292 19293</td><td>22 152</td><td>94.4 94.5</td><td>96.5 98.3</td><td>3910 993</td><td>910 243</td><td>92.8 92.8</td><td>84.5 0.0</td><td>3203 3494</td><td>867 2</td></tr><tr><td>8/610</td><td>20</td><td>0.2 0.2</td><td>94.4 94.7</td><td>99.5 99.5</td><td>94.7 94.4</td><td>0.0 0.0</td><td>7008 14000</td><td>8 0</td><td>92.6 92.5 96.4</td><td>97.6</td><td>19544 18946</td><td>288 597</td><td>94.4 94.2</td><td>99.4 99.5</td><td>1981 3908</td><td>481 908</td><td>92.9 92.6</td><td>0.0 0.2</td><td>3571 3492</td><td>1 8</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td>5</td><td>0.1</td><td></td><td>95.0 92.0</td><td></td><td>94.4 93.3</td><td>7501</td><td>250</td><td></td><td>91.7 85.0 23573</td><td></td><td>151</td><td>94.6 97.3</td><td></td><td>988</td><td>238</td><td>93.0</td><td>0.0</td><td></td><td></td></tr><tr><td>9/210</td><td></td><td></td><td></td><td></td><td></td><td>94.393.1</td><td>7500</td><td>500</td><td>92.1</td><td>95.1</td><td>22896</td><td>251</td><td></td><td></td><td>1970 471</td><td></td><td></td><td></td><td>3291</td><td>2</td></tr><tr><td></td><td></td><td>0.1</td><td></td><td>94.593.9</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>94.498.6</td><td></td><td></td><td></td><td>93.1</td><td>0.0</td><td>3133</td><td>1</td></tr><tr><td></td><td>20</td><td></td><td></td><td>94.496.1</td><td>94.7</td><td>0.0</td><td>14010</td><td>10</td><td>93.1</td><td>98.9</td><td>18651</td><td>575</td><td>94.1</td><td>99.0</td><td>3906906</td><td></td><td>93.1</td><td>0.0</td><td>3223</td><td>2</td></tr><tr><td></td><td></td><td>0.1</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></table>
+
+# C ADDITIONAL EXPERIMENTAL RESULTS
+
+Tables 3 and 4 summarizes our main results for all the (source, target) pairs using two standard architectures for image classification: a PreActResNet18 He et al. (2016b) network and a ResNet32 He et al. (2016a) network, respectively.
+
+For each (source, target) pair, we generated three scenarios. For each (source, target) pair and setting of epsilon, we report results for the scenario in which the defense’s targeted misclassification rate (column A) was the median of all three scenarios. For the clean and no defense columns, we report results for the same scenario as TW (This Work).
+
+The set of defenses consists of
+
+1. (L) Clean, training on the entire clean training set. We report only the misclassification rate (M), which is the number of poisoned samples from the test set of the source class that are misclassified as the target class.   
+2. (ND) No Defense, training on entire poisoned training set. We report only the clean accuracy (C) and targeted misclassification rate (A) in this case.   
+3. (SS) Spectral Signatures (Tran et al., 2018)   
+4. (AC) Activation Clustering (Chen et al., 2018)
+
+Table 4: Performance on CIFAR-10, dirty label backdoor scenario, using the ResNet32 architecture. The S / T column lists the CIFAR-10 source and target classes.  refers to the percentage of the source class which is poisoned. For the remainder of the columns, the top level column headers give the defense type: L (clean), ND (no defense), SS (spectral signatures), AC (activation clustering), ITLM (iterative trimmed loss minimization, and TW (this work); the second level column headers give the metric type: M (misclassification accuracy), C (clean accuracy, higher is better), A (targeted misclassification rate, lower is better), FP (false positives, lower is better), FN (false negatives, lower is better). Please refer to the text for a more detailed explanation of the table.   
+
+<table><tr><td>S/T</td><td>E</td><td>L</td><td>ND</td><td></td><td></td><td>ss</td><td></td><td></td><td></td><td>AC</td><td></td><td></td><td></td><td>ITLM</td><td></td><td></td><td></td><td>TW</td><td></td><td></td></tr><tr><td></td><td></td><td>M 1.1</td><td>C</td><td>A</td><td>C</td><td>A</td><td>FP</td><td>FN</td><td>C</td><td>A</td><td>FP</td><td>FN</td><td>C</td><td>A</td><td>FP</td><td>FN</td><td>C</td><td>A</td><td>FP</td><td>FN</td></tr><tr><td>0/2</td><td>5 10 20</td><td>1.1 1.5</td><td>92.4</td><td>92.685.0 92.6 92.594.9</td><td>91.7 90.4</td><td>91.8 57.3 91.5 64.2</td><td>7499 7422 14590</td><td>248 422 590</td><td>88.8 88.8 88.6</td><td>0.6 78.6 62.7</td><td>24211 24031 23686</td><td>133 250 455</td><td>91.7 91.9</td><td>91.8 83.3 92.3 94.2</td><td>988 1969 3890</td><td>238 469 890</td><td>89.8 89.5 88.0</td><td>0.0 0.0 0.0</td><td>5752 5445 6992</td><td>31 33 86</td></tr><tr><td>1/310</td><td>5 20</td><td>|0.1 0.1 0.0</td><td>92.7 92.1</td><td>98.5 91.635.0 98.1</td><td>91.7 91.1 91.5</td><td>5.7 3.3 0.0</td><td>7479 7436 14004</td><td>227 436</td><td>88.8 88.3</td><td>2.4 24.9</td><td>23903 23891</td><td>125 254</td><td>91.9 92.0 69.2</td><td>12.7</td><td>988 988</td><td>238 488</td><td>89.8 89.8</td><td>0.0 0.0</td><td>5776 5736</td><td>1 3</td></tr><tr><td></td><td>5 2/510</td><td>1.7 1.6</td><td>92.2</td><td>62.7 92.592.4</td><td>91.2 91.9</td><td>43.2 89.8</td><td>7493 7476</td><td>4 242 476</td><td>89.1 88.0 89.3</td><td>0.4 1.4 81.5</td><td>21145 24001 23827</td><td>70 128 275</td><td>91.9 92.2 91.6 93.2</td><td>97.3 75.7</td><td>3900 994 1975</td><td>900 244 475</td><td>89.4 88.8 89.2</td><td>0.0 0.1 0.0</td><td>5833 6358 5985</td><td>1 6 26</td></tr><tr><td></td><td>20 5</td><td>1.6 6.3</td><td>91.7 91.3</td><td>95.8 88.9</td><td>89.9 91.7</td><td>3.5 87.9</td><td>14349 7466</td><td>349 215</td><td>88.5 88.9</td><td>87.2 80.0</td><td>21086 23817</td><td>711</td><td>91.9</td><td>95.1</td><td>3905</td><td>905</td><td>89.8</td><td>0.2</td><td>5684</td><td>40</td></tr><tr><td>3/5</td><td>10 20</td><td>6.2 6.3</td><td>92.3 90.8</td><td>91.8 90.8</td><td>91.6 90.5</td><td>86.4 71.9</td><td>7348 14090</td><td>348 90</td><td>88.7 89.3</td><td>73.1 78.5</td><td>21299 20694</td><td>131 136 156</td><td>92.2 92.2 89.5 90.9</td><td>90.8 88.8</td><td>996 990 3918</td><td>246 490 918</td><td>89.2 89.1 89.8</td><td>27.5 82.1 86.7</td><td>5974 5681 5093</td><td>59 344 994</td></tr><tr><td>3/710</td><td>5</td><td>1.1</td><td>92.6</td><td>98.4</td><td>91.0</td><td>97.1</td><td>7452</td><td>201</td><td>86.2</td><td>72.8</td><td>23823</td><td>189</td><td>92.1</td><td>97.1</td><td>994</td><td>244</td><td>89.4</td><td>0.2</td><td>5498</td><td>13</td></tr><tr><td></td><td>20</td><td>1.1 1.1</td><td>92.4 92.9</td><td>98.6 98.6</td><td>91.8 90.9</td><td>96.7 97.0</td><td>7315 14167</td><td>315 167</td><td>88.6 89.1</td><td>96.2 95.4</td><td>23648 20600</td><td>482 551</td><td>92.3 92.4</td><td>98.0 98.1</td><td>1981 3924</td><td>481 924</td><td>89.8 88.6</td><td>0.0 0.2</td><td>5126 6642</td><td>16 26</td></tr><tr><td>7/410</td><td>5</td><td>1.7 1.7</td><td>92.1 92.7</td><td>88.5 93.9</td><td>91.6 87.5 91.9</td><td>94.2</td><td>7486 7371</td><td>235 371</td><td>89.3 88.3 59.2</td><td>72.2</td><td>23928 23753</td><td>149 193</td><td>92.4 92.1</td><td>92.2 96.2</td><td>992 1973</td><td>242 473</td><td>88.8</td><td>0.4</td><td>6643</td><td>27 32</td></tr><tr><td></td><td>20</td><td>1.7</td><td>92.6</td><td>96.9</td><td>91.1</td><td>94.1</td><td>14397</td><td>397</td><td>88.2</td><td>47.6</td><td>23737</td><td>423</td><td>91.7</td><td>95.8</td><td>3904</td><td>904</td><td>88.9 88.6</td><td>0.8 46.9</td><td>6478 6322</td><td>209</td></tr><tr><td></td><td></td><td></td><td>92.7</td><td>98.0</td><td>91.3</td><td>97.8</td><td>7441</td><td>190</td><td>89.1</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>8/610</td><td>5</td><td>0.2</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>88.7</td><td>23658</td><td>164</td><td>92.5</td><td>96.9</td><td>988</td><td>238</td><td>89.6</td><td>0.0</td><td>5991</td><td>0</td></tr><tr><td></td><td></td><td>0.2</td><td>92.1</td><td>97.7</td><td>91.8</td><td>97.2</td><td>7089</td><td>89</td><td>90.2</td><td>95.1</td><td>19585</td><td>280</td><td>92.3</td><td>98.7</td><td>973</td><td>473</td><td>89.3</td><td>0.0</td><td>6007</td><td>2</td></tr><tr><td></td><td>20</td><td>0.2</td><td>92.8 98.8</td><td></td><td></td><td>91.396.0</td><td>14297</td><td>297</td><td>87.2 64.2</td><td></td><td>23347</td><td>646</td><td>92.398.6</td><td></td><td>975</td><td>975</td><td>89.4</td><td>0.0</td><td></td><td>3</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>5691</td><td></td></tr><tr><td></td><td>5</td><td>|0.1</td><td>92.9</td><td>93.2</td><td>91.2</td><td>93.2</td><td>7478</td><td>225</td><td>88.7</td><td>1.2</td><td>23518</td><td>136</td><td>92.1</td><td>94.0</td><td>991</td><td>241</td><td>90.3</td><td>0.0</td><td></td><td></td></tr><tr><td>9/210</td><td></td><td></td><td>92.698.6</td><td></td><td></td><td>91.494.7</td><td>7497</td><td>497</td><td>88.5 91.5</td><td></td><td>24034</td><td>242</td><td></td><td></td><td></td><td></td><td></td><td></td><td>5444</td><td>2</td></tr><tr><td></td><td></td><td>0.1</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>92.5 97.8</td><td></td><td>986</td><td>486</td><td>88.1</td><td>0.0</td><td>7220</td><td>2</td></tr><tr><td></td><td>20</td><td>0.1</td><td></td><td>92.6 97.4</td><td>90.5</td><td>0.0</td><td>14011</td><td>11</td><td>90.6 97.7</td><td></td><td>18658</td><td>578</td><td>91.9</td><td>99.2</td><td>3881</td><td>811</td><td>89.6</td><td>0.0</td><td>5742</td><td>1</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></table>
+
+5. (ITLM) Iterative Trimmed Loss Minimization (Shen and Sanghavi, 2019)
+
+6. (TW) This Work
+
+For each defense, we report
+
+1. (C) clean accuracy, which is the accuracy of the defended network on the entire clean test set (higher is better).   
+2. (A) targeted misclassification rate as defined in Equation 7, which is measured over the entire source class of the test set (lower is better).   
+3. (FP) false positives, which counts the number of clean samples excluded from the defended training set (lower is better).   
+4. (FN) false negatives, which counts the number of poisoned samples included in the defended training set (lower is better).
+
+# C.1 DISCUSSION
+
+Our approach consistently outperforms all other defenses by targeted misclassification rate (column A) across both architectures. If we define a “successful” run as achieving less than $1 \%$ targeted misclassification rate, then for the PreActResNet18 architecture, our defense succeeds in 17/24 scenarios, SS succeeds 9/24 scenarios, and both AC and ITLM do not succeed a single time; for the ResNet32 architecture, our defense succeeds in 20/24 scenarios, SS succeeds in 2/24 scenarios, AC succeeds in 1/24 scenarios, and ITLM again fails all 24 scenarios.
+
+In general, our defense results in a $2 \mathrm { - } 3 \%$ drop in clean accuracy for both architectures, when compared to a model trained and tested using clean data. AC achieves a clean accuracy which is on par with (or slightly below) ours. Surprisingly, this clean accuracy is despite AC having false positives (FP) of approximate 6x and $4 \mathbf { x }$ ours for the PreActResNet18 and ResNet32 models, respectively. Similarly, compared to our defense, SS has a slightly higher FP rate (which is roughly constant, as the defense always removes a fixed amount of data), but suffers a negligible drop in clean accuracy. We attribute this behavior to the existence of small, difficult to learn subpopulations (that may be removed by the weak learners as incompatible after training for only 40 epochs) but are responsible for the last $2 - 3 \%$ of performance. However, we note that our defense is designed to remove incompatible data, rather than poisoned data specifically, and therefore some such behavior is expected. Conversely, we hypothesize that SS and AC are removing “easy” data according to statistical properties of the activation patterns of a trained network, which may constitute redundant data in terms of the training distribution. ITLM achieves good clean accuracy and the lowest number of false positives (though its performance is negligible in terms of defending against poison).
+
+The only scenario which consistently evades our defense is the (3 / Cat, 5 / Dog) scenario. This scenario is also the only one for which the poison misclassification rate of a clean network is noticeable large at around $6 \%$ (primary column L, secondary column M), which is consistent with the results in Tran et al. (2018). These results suggest that the scenario violates Property 4.4, i.e., the poison and clean distributions are not incompatible—training on a clean dataset yields non-negligible performance on poisoned cats when mislabeled as dogs. Because the poisoned data is compatible with the clean data, our theoretical analysis suggests that our defense will struggle to separate the clean and poisoned data, as is reflected in our results. Despite this, we note that the performance of our defense still exceeds that of the SS, AC, and ITLM defenses in several cases for this scenario.
+
+Finally, to reconcile our results with the results presented in the Spectral Signatures paper, we note that the training code in official implementation of the SS defenses uses some non-standard methodologies, including a random crop with only $2 \mathbf { x } 2$ padding (instead of the $4 \mathbf { x } 4$ commonly used for CIFAR-10); no normalization of the input data according to the mean and standard deviation; and custom initialization of all the layers (such as using a normal distribution to initialize the convolutional layers, rather than the default Kaiming initialization (He et al., 2015) in PyTorch). The authors also only report results for cases where the network was “successfully poisoned”, which they defined as “approximately $90 \%$ or higher accuracy on the poisoned set” (corresponding to primary column ND, secondary column A, in Tables 3 and 4). To verify our results, we ran the first scenario of the first (source, target) pair (i.e., the first row of Table 2) through the authors’ own implementation and found that at $\epsilon = 5 \%$
+
+– an undefended network had a $7 1 . 9 \%$ poison misclassification rate; – the defense left 205 false negatives (out of 250 poisoned images); – trained on the defended dataset, the network had a $5 2 . 9 \%$ poison misclassification rate,
+
+and at $\epsilon = 1 0 \%$
+
+– an undefended network had a $7 4 . 1 \%$ poison misclassification rate;   
+– the defense left 193 false negatives (out of 500 poisoned images);   
+– trained on the defended dataset, the network had a $2 3 . 3 \%$ poison misclassification rate.
+
+These results are not within the scope of the results considered in the original paper (due to not being over $90 \%$ poisoned pre-defense). In contrast, in our experiments, the pre-defense poison misclassification rate is much higher, which we attribute to more modern training methodologies.
+
+Table 5: Ablation studies on CIFAR-10, dirty label backdoor scenario, using the PreActResNet18 architecture, with various settings of $\alpha$ and $\beta$ . The $\textnormal { S } / \textnormal { T }$ column lists the CIFAR-10 source and target classes.  refers to the percentage of the source class which is poisoned. The second level headings are C (clean accuracy, higher is better), A (targeted misclassification rate, lower is better). Please refer to the text for a more detailed explanation of the table.   
+
+<table><tr><td colspan="2">S/T</td><td>E</td><td>C</td><td>β=1/16 A</td><td>β=1/8 C</td><td>A</td><td>β=1/4 C</td><td>A</td><td>β=1 C</td><td>A</td></tr><tr><td rowspan="5">α=1/4</td><td>3/5</td><td>5 10 20 5</td><td>92.7 92.6 92.3 92.9</td><td>79.8 87.3 76.1 2.4</td><td>92.8 92.6 92.6 92.8</td><td>81.1 90.2 87.4 0.5</td><td>92.9 93.1 92.8 93.3</td><td>71.8 89.9 88.4 0.2</td><td>93.0 93.5 93.3 93.3</td><td>55.7 91.9 92.3</td></tr><tr><td>7/4</td><td>10 20 5</td><td>92.6 92.7 92.8</td><td>9.3 83.5 0.0</td><td>92.9 92.8 93.1</td><td>0.3 84.5 0.0</td><td>93.2 92.8 93.3</td><td>27.6 84.7</td><td>93.2 93.2</td><td>48.2 76.7 43.0</td></tr><tr><td>8/6</td><td>10 20 5</td><td>92.7 92.8 92.9</td><td>0.0 0.1 0.0</td><td>93.0 92.6</td><td>0.0 0.2</td><td>93.3 93.1</td><td>0.0 0.0 0.0</td><td>93.4 93.5 93.1</td><td>0.0 0.1 95.5</td></tr><tr><td>9/2</td><td>10 20 5</td><td>92.8 92.7 92.8</td><td>0.0 0.0 80.6</td><td>93.0 92.9 93.1</td><td>0.0 0.0 0.0</td><td>93.3 92.9 93.0</td><td>0.0 0.0 0.0</td><td>93.2 92.8 93.3</td><td>0.0 0.0 0.0</td></tr><tr><td colspan="2"></td><td>3/5 10 20 5</td><td>92.4 91.5 92.6</td><td>86.8 79.8 0.9</td><td>92.8 92.3 92.6 93.4</td><td>74.7 86.1 85.3 0.9</td><td>93.0 92.8 93.0 92.9</td><td>73.6 91.4 87.6 5.7</td><td>92.7 93.0 93.1 93.5</td><td>87.1 90.1 90.4</td></tr><tr><td rowspan="2">a=1</td><td>7/4</td><td>10 20 5</td><td>92.9 92.7 92.8</td><td>2.3 91.7 0.0</td><td>92.8 92.6 92.2</td><td>72.1 83.4 0.0</td><td>93.1 92.9 92.8</td><td>0.5 88.4 0.0</td><td>93.5 93.0 93.3</td><td>0.2 72.1 86.6</td></tr><tr><td>8/6 9/2</td><td>10 20 5 10</td><td>92.8 92.3 92.6 92.8</td><td>0.1 0.0 0.0 0.0</td><td>93.1 92.7 92.9 93.0</td><td>0.0 0.0 0.0 0.0</td><td>93.2 93.5 93.1 93.1</td><td>0.0 0.0 0.0 0.0</td><td>93.5 93.2 93.1 93.0</td><td>0.0 0.0 0.0 0.0 0.0</td></tr></table>
+
+# C.2 ABLATION STUDIES
+
+We conduct some additional ablation studies to better understand the effects of the two main hyperparameters in Algorithm 2: the expansion factor $\alpha$ and the subset size $\beta$ . Computationally, larger $\beta$ means fewer components and fewer outer iterations of ISPL (and is thus more efficient); in our main experiments, we use $\beta = 1 / 8$ and run ISPL 8 times in sequence to generate 8 components. Additionally, as discussed in Remark 2, smaller $\alpha$ is a more stringer requirement, since mixing distributions increases the expansion factor. Therefore we would expect that increasing $\alpha$ leads to worse identification of homogeneous components on average.
+
+Tables 5 presents the full results of the ablation studies. Our main finding is that our method is quite robust to both the expansion factor $\alpha$ and subset size $\beta$ . There is also a slight trend that smaller $\alpha$ and $\beta$ are better at identifying poison, with a small drop in clean accuracy.