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+# CORRUPTED IMAGE MODELING FOR SELF-SUPERVISED VISUAL PRE-TRAINING
+
+Yuxin Fang 1, 2∗ Li Dong 2 Hangbo Bao 2 Xinggang Wang 1† Furu Wei 2 1 School of EIC, Huazhong University of Science & Technology 2 Microsoft Research {yxf,xgwang}@hust.edu.cn
+
+# ABSTRACT
+
+We introduce Corrupted Image Modeling (CIM) for self-supervised visual pretraining. CIM uses an auxiliary generator with a small trainable BEiT (Bao et al., 2021) to corrupt the input image instead of using artificial [MASK] tokens, where some patches are randomly selected and replaced with plausible alternatives sampled from the BEiT output distribution. Given this corrupted image, an enhancer network learns to either recover all the original image pixels, or predict whether each visual token is replaced by a generator sample or not. The generator and the enhancer are simultaneously trained and synergistically updated. After pre-training, the enhancer can be used as a high-capacity visual encoder for downstream tasks. CIM is a general and flexible visual pre-training framework that is suitable for various network architectures. For the first time, CIM demonstrates that both ViT and CNN can learn rich visual representations using a unified, non-Siamese framework. Experimental results show that our approach achieves compelling results in vision benchmarks, such as ImageNet classification and ADE20K semantic segmentation.
+
+# 1 INTRODUCTION
+
+Vision Transformers (ViTs) (Dosovitskiy et al., 2020) are transferring the landscape of computer vision, not only in terms of the network architecture design, but also the self-supervised pre-training recipe. Masked image modeling (MIM) (Bao et al., 2021), which randomly masks out some input tokens and then recovers the masked content by conditioning on the visible context, is able to learn rich visual representations and shows promising performance on various vision benchmarks (Zhou et al., 2021; He et al., 2021; Xie et al., 2021; Dong et al., 2021; Wei et al., 2021).
+
+Originated in masked language modeling (Devlin et al., 2019), MIM (Figure 1a) is tailor-made for specific architectures (Vaswani et al., 2017), which is generally capable of receiving and processing tokenized inputs such as the artificial [MASK] tokens. Meanwhile, the more common and natural input signal in computer vision is the image in RGB domain with 2D regular grid structures. In order to apply MIM pre-training for images, ViT has to “patchify” the input image into a 1D sequence of non-overlapping patch embeddings, and then use [MASK] tokens to perturb them.
+
+MIM is tightly coupled with the Transformer family, and the usage of [MASK] tokens limits its scope of application to some extent. More importantly, MIM is not directly suitable for convolutional neural networks (CNNs) (LeCun et al., 1989), the dominant architecture for computer vision in the last decade. Introducing [MASK] tokens in any intermediate stage of CNN is infeasible, as convolution’s intrinsic dense-sliding-window paradigm causes information leakage between visual features in previous layers and therefore impedes the MIM. Therefore the large CNN family cannot directly benefit from the upsurge of this new pre-training scheme. Moreover, the usage of [MASK] tokens causes a discrepancy between pre-training and fine-tuning (Devlin et al., 2019; Clark et al., 2020), as the artificial [MASK] tokens never appear in the fine-tuning stage.
+
+In this paper, we present a new visual pre-training framework, called Corrupted Image Modeling (CIM, Figure 1b), which avoids directly manipulating [MASK] tokens on pre-trained models and generalizes quite well to both ViT and CNN architectures. Rather than directly using artificial [MASK] tokens to corrupt a portion of non-overlapping patch embeddings as in MIM, CIM uses a small trainable BEiT (Bao et al., 2021) as an auxiliary generator to corrupt the input image. Specifically, the BEiT generator learns to predict visual tokens at the masked positions, where we utilize the predicted distribution to sample visual tokens’ replacements. The replaced visual tokens together with the golden tokens that directly produced by a pre-trained frozen image tokenizer encoder (e.g., the DALL-E (Ramesh et al., 2021) dVAE encoder) given the same input as the small trainable BEiT are then mapped back to the image RGB domain by a pre-trained frozen tokenizer decoder (e.g., the DALL-E dVAE decoder). The resulting corrupted image serves as the input of the enhancer, which is the model to be pre-trained and transferred.
+
+![](images/4dd8395ea4882213cb68da1f6b25faa4ebd6cb6bd3705e0df1e770aeb9b9d374.jpg)  
+Figure 1: Overview of our Corrupted Image Modeling (CIM) and comparisons with Masked Image Modeling (MIM). MIM (Figure 1a) requires the pre-trained architecture to receive and process the artificial [MASK] tokens, while CIM (Figure 1b) relaxes these restrictions by using a trainable generator to sample corrupted images serving as the input for the enhancer. Similar to BEiT, the small generator learns to predict the golden visual token produced by the pre-trained frozen image tokenizer encoder (not shown in the figure) based on partial observations of the input. The enhancer can be various architectures including CNN and learns either a generative or a discriminative visual pre-training objective. After pre-training, we throw out the generator and fine-tune the enhancer on downstream tasks. The dice icon in Figure 1b refers to the visual tokens’ stochastic sampling process, and the lock icon means the pre-trained image tokenizer decoder is frozen.
+
+For the enhancer, the choice of pre-training objectives is quite flexible. We study two representatives: a generative objective that regresses all the original image pixels given the corrupted image (Dosovitskiy et al., 2020; Chen et al., 2020a), dubbed as Pixel Residual learning (RESPIX), and a discriminative objective that predicts whether each visual token is replaced by the small generator or not (Clark et al., 2020), dubbed as Replaced Visual token Detection (REVDET). After pre-training, the enhancer can be used as a strong feature extractor for visual downstream tasks.
+
+Overall, CIM is a general and flexible pre-training framework suited for different kinds of visual encoders. For the first time, we demonstrate that both ViT and CNN can learn rich visual representations using a unified non-Siamese structure. Experimental results show that our approach achieves compelling results in vision benchmarks, such as ImageNet classification and ADE20K semantic segmentation. We hope CIM can serve as a promising starting point for exploring flexible & unified visual representation learning of various architectures.
+
+# 2 CORRUPTED IMAGE MODELING (CIM)
+
+Figure 1b shows the overview of CIM. Our approach simultaneously learns two neural networks: an auxiliary generator and an enhancer. The generator is used to corrupt the input image, while the enhancer receives the corrupted image (Figure 2) and learns either a generative or a discriminative visual pretext task. After pre-training, we throw out the generator and fine-tune the enhancer on downstream tasks.
+
+# 2.1 GENERATOR
+
+Rather than using artificial [MASK] tokens to corrupt the input image, we learn a trainable auxiliary generator to relax the architectural constraints of MIM. Moreover, the generator enriches the diversity of corrupted images via stochastic sampling, which helps the enhancer generalize. The generator consists of a pre-trained frozen image tokenizer, and a small trainable BEiT (Bao et al., 2021).
+
+![](images/5050220e448020d78790b1e83d4696485816144f9fb9557d3b542de7e5a3860c.jpg)  
+(a) Corrupted image samples from ImageNet-1K training set. Although the model is trained using the same dataset, the corrupted image samples still vary to a certain extent. Therefore during pre-training, the generator is able to continuously provide abundant and diverse corrupted samples for the enhancer.
+
+![](images/0c8a620d9099ed9ff0ad3e2aaed16fcd2e9d97c08f253ca8ff92b89ace11e791.jpg)  
+(b) Corrupted image samples from COCO val split (Lin et al., 2014) using ImageNet-1K pre-trained model.   
+Figure 2: Visualizations of some corrupted image samples. For each image set, we show (from left to right) the original image, the masked image, and four different corrupted images sampled from the generator output distribution with the same masked input. Simple stochastic sampling can greatly enrich the corrupted image distribution in terms of both low-level features and high-level semantics, which feeds the enhancer better.
+
+The frozen image tokenizer in CIM is a pre-trained discrete variational autoencoder (dVAE) (Rolfe, 2016; Van Den Oord et al., 2017), consisting of a paired encoder and decoder. The tokenizer encoder maps the input image into a sequence of discrete visual tokens with a fixed vocabulary size. The tokenizer decoder can recover semantically plausible images given a permutation of appropriate and meaningful visual tokens. We directly use the DALL-E (Ramesh et al., 2021) tokenizer, following BEiT.
+
+The small BEiT consists of several Transformer encoder layers and is trained to perform MIM, which uses two views for each input image, i.e., a sequence of non-overlapping patch embeddings, and their corresponding discrete visual tokens. Patch embeddings are linearly embedded from non-overlapping input image patches. Discrete visual tokens are from the DALL-E tokenizer encoder, serving as the prediction target for BEiT.
+
+Given a sequence of patch embeddings, the small BEiT randomly masks out a set of positions. The patch embeddings at the masked positions are replaced with special mask embeddings. The small BEiT takes this corrupted sequence of patch embeddings as the input, and learns to predict the corresponding discrete visual tokens at all masked positions given the visible context only. In CIM pre-training, the size of the small BEiT we use is typically a quarter or a half of the enhancer.
+
+Using discrete visual tokens to represent images enables CIM to perform stochastic sampling during the corrupted image’s generation process, which greatly enriches the output set of the generator. In this paper, we directly sample from softmax with a temperature of 1 at all the masked positions according to the small BEiT output distribution. All the masked tokens are replaced by the sampled visual tokens. The sampled tokens together with the golden tokens that are directly produced by the image tokenizer encoder at all the non-masked positions constitute the input for the image tokenizer decoder. Then the decoder maps those plausible visual tokens to a corrupted image (refer to examples in Figure 2), which serves as the input for the enhancer.
+
+![](images/c649970c6ab9f97e43291e9e16de40c65e8ad4cf1995b66201d058e9c24be0c1.jpg)  
+(a) CIM-RESPIX pre-training objective with sliding window normalized pixels as the enhancer prediction target.
+
+![](images/06a181c2f58d7ee657036e02167e76fee2211bdd65d0593da1ded42af9144f35.jpg)  
+(b) CIM-RESPIX pre-training objective with unnormalized pixels as the enhancer prediction target.   
+Figure 3: Example visualization results on COCO val split images from vanilla ViT-Base/16 model pre-trained with the RESPIX objective using ImageNet-1K training data. For each image quadruplet, we show the original input image (1st column), the masked input image for the generator (2nd column), the corrupted image sampled from the generator output (3rd column), and the enhancer output (4th column). Given the corrupted image, the enhancer is able to perform image denoising, deblurring and completion, etc., and learns to predict plausible output in terms of both low-level features as well as high-level semantics.
+
+# 2.2 ENHANCER
+
+Given the corrupted image sampled from the auxiliary generator, the enhancer learns either a generative or a discriminative visual pretext task. The prediction head is a simple linear layer, and the choice of pre-training objectives is quite flexible. In this paper, we study two representative objectives, coined as Pixel Residual learning (RESPIX) and Replaced Visual token Detection (REVDET).
+
+RESPIX (Figure 3) is a generative visual pretext task that requires the enhancer to predict the uncorrupted pixel value for all positions given the corrupted input. Instead of directly regressing the original pixel, MAE (He et al., 2021) suggests learning the normalized counterpart. Specifically, the image is partitioned into a set of non-overlapping patches, and each pixel is normalized by the mean and standard deviation of all pixels in the patch it lives in, i.e., patches with layer normalization (Ba et al., 2016) are the reconstruction target.
+
+In CIM, we further propose to normalize the prediction target inside a sliding window, i.e., each pixel is normalized by all pixels in a local $8 \times 8$ sized window centered at where the target pixel lives in. We observe improved representation quality using the sliding window normalization paradigm.
+
+![](images/bff27fbe41eea6e635bbeb3ed3ffc0bcf18122b22ff97b3a0c695ab06f6813fe.jpg)  
+Figure 4: Normalizations as learning templates for RESPIX. For each image triplet, we visualize the original image (left), the template of using non-overlapping window normalization (He et al., 2021), and the template of the proposed sliding window normalization paradigm. Our approach can provide more accurate and moderate hints that can boost the enhancer’s pre-training as well as improve its representation quantity.
+
+Naive pixel recovery without normalization tends to waste modeling capability on learning short-range dependencies and high-frequency details (Ramesh et al., 2021; Bao et al., 2021), while the normalized target can mitigate irrelevant information fittings. From another perspective, normalizations are equal to providing learning templates, as shown in Figure 4. With the normalized prediction target, the enhancer only needs to learn the residual pixel value at each position given the normalized pixel value, while the unnormalized target provides no hint therefore the enhancer has to “learn to see in the dark” (i.e., regress from RGB: 0, 0, 0). It is also hard for the enhancer to learn without a template since the corrupted image usually provides bad priors (refer to the corrupted image samples in Figure 2 and Figure 3). Therefore, we believe appropriate and moderate hints will help the enhancer see better.
+
+REVDET is a discriminative visual pretext task that requires the enhancer to determine whether each visual token is replaced by a generator sample or not. To be specific, the visual tokens produced by the pre-trained frozen image tokenizer encoder are considered as golden tokens. If a generated visual token is different from the golden token at the same position, that generated token is considered “replaced”, and vice versa.
+
+REVDET is inspired by ELECTRA (Clark et al., 2020) in language modeling. The main difference is, in the proposed CIM, the determining criterion of replacement is hidden in the corrupted image. Token replacement is a kind of local, high-frequency operation by nature. However, the visual token set after sampling and replacement is further smoothed and processed by the image tokenizer decoder. Therefore the token sampling and replacement operations are finally embodied as non-local, high-level semantics changes in the corrupted image. The enhancer is required to “decrypt” it and identify all the replaced tokens given the corrupted input, which yields a nontrivial and meaningful visual pretext task1. To some extent, REVDET also learns the DALL-E dVAE’s visual codebook similar to BEiT, but in a discriminative manner.
+
+The enhancer is regarded as the visual encoder after pre-training. Moreover, unlike masked image modeling, CIM does not assume too many architectural priors for the pre-trained network. We successfully pre-train a high-capacity vanilla ResNet-50 (He et al., 2016), ResNet-50x2 and ResNet$5 0 { \bf x } 4$ enhancers that achieve compelling transfer learning performance using a similar configuration as pre-training a ViT enhancer. For the first time, we demonstrate that both ViT and CNN can learn strong visual representations using a unified non-Siamese framework.
+
+# 2.3 TRAINING AND OPTIMIZATION
+
+The auxiliary generator and the enhancer are simultaneously trained and synergistically (rather than adversarially as GAN (Goodfellow et al., 2014)) updated. The trainable part of the generator, i.e., the small BEiT, learns a MIM objective in the same vein as in (Bao et al., 2021). The whole pre-trained image tokenizer is frozen.
+
+For the RESPIX visual pretext task, the enhancer is optimized by a combination of $l _ { 1 }$ and $l _ { 2 }$ loss. For the REVDET visual pretext task, the enhancer is learned by binary cross-entropy loss. Notice that the gradients of the enhancer are not back-propagated through the generator. A detailed formulation is presented in Appendix A.3.
+
+# 3 EXPERIMENTS
+
+We study CIM self-supervised pre-trained vanilla ViT-Small/16 (Touvron et al., 2021a), vanilla ViT-Base/16 (Dosovitskiy et al., 2020) and vanilla ResNet-50 (He et al., 2016) models. We use the actual processed images / views to measure the pre-training epochs (PT epochs). ImageNet-1K (Deng et al., 2009) training data is used to pre-train the small BEiT and the enhancer. Our pre-training setting generally follows BEiT (Bao et al., 2021). Unlike BEiT, CIM only uses cropping and flipping for data argumentation, while dropout (Srivastava et al., 2014) and stochastic depth (Huang et al., 2016) are not applied. The detailed pre-training settings are summarized in the Appendix A.4. Notably, the pre-training configurations are almost the same for both ViT and CNN architectures.
+
+In order to evaluate the pre-trained representations from CIM, for both ViT and CNN architectures, we conduct supervised end-to-end fine-tuning (FT) experiments on ImageNet-1K (Deng et al., 2009) image classification in $\ S 3 . 1$ , and ADE20K (Zhou et al., 2019) semantic segmentation in $\ S 3 . 2$ .
+
+Table 1: ImageNet-1K end-to-end fine-tuning top-1 accuracy of vanilla ViT-Small/16 and ViT-Base/16 models. †Doubled attention heads. ‡Our reproduction.   
+
+<table><tr><td>Models PT Epochs Top-1 ViT-Small/16 model results</td></tr><tr><td>Scratch (Touvron et al., 2021a) MoCo-v3† (Chen et al., 2021) 600 DINO (Caron et al., 2021) 1600 81.5 BEiT (Bao et al., 2021) 300</td></tr><tr><td>CIM-RESPIX (Ours) 300 81.5 CIM-REVDET (Ours) 300 81.6</td></tr><tr><td>ViT-Base/l6 model results 81.8</td></tr><tr><td>Scratch (Touvron et al., 2021a)</td></tr><tr><td>Scratch (He et al., 2021) 82.3</td></tr><tr><td>DINO (Caron et al., 2021) 1600 82.8 MoCo-v3 (Chen et al.,2021) 600 83.2</td></tr><tr><td>BEiT (Bao et al.,2021) 300 82.9 BEiT (Bao et al., 2021) 800 83.2</td></tr></table>
+
+Ablation study on ImageNet-1K is presented in $\ S 3 . 3$ . For ImageNet-1K, we observe ${ \sim } 0 . 2$ Top-1 acc. fluctuations. For ADE20K, we observe ${ \sim } 0 . 5$ mIoU fluctuations. We report key results using the median of 3 independent runs.
+
+Table 2: ImageNet-1K end-to-end fine-tuning top-1 accuracy of vanilla ResNet-50 model. RSB (Wightman et al., 2021) is the current vanilla ResNet stateof-the-art training procedure.   
+
+<table><tr><td>Models</td><td>PT Epochs Top-1</td></tr><tr><td>Fine-tuning for l0o epochs RSB A3 (Wightman et al., 2021) CIM-REVDET (Ours) 300</td><td>78.1 78.8</td></tr><tr><td>Fine-tuning for 300 epochs RSB A2 (Wightman et al., 2021) SimSiam (Chen &amp; He,2021) MoCo-v2 (Chen et al., 2020c) SimCLR (Chen et al., 2020b) SimCLR (Chen et al., 2020b) BYOL (Grill et al., 2020) SwAV (Caron et al., 2020) CIM-RESPIX(Ours) CIM-REVDET (Ours)</td><td>79.8 400 79.1 400 79.6 800 79.9 2000 80.0 400 80.0 600 80.1 300 79.9 300</td></tr><tr><td>Fine-tuning for 60o epochs</td><td>80.5</td></tr><tr><td>RSB A1 (Wightman et al., 2021) CIM-REVDET (Ours) 300</td><td>80.4 80.7</td></tr></table>
+
+# 3.1 IMAGE CLASSIFICATION
+
+ViT. The ImageNet-1K end-to-end fine-tuning top-1 accuracy of vanilla ViT-Small/16 and ViTBase/16 models are presented in Table 1. We fine-tune the small-sized model for 200 epochs, and the base-sized model for 100 epochs. Other self-supervised methods in Table 1 use the same or longer fine-tuning schedule. The fine-tuning hyperparameters mostly follow BEiT, while our layerwise lr decay rate is set to 0.8 as suggested by Clark et al. (2020). See Appendix A.4 for detailed configurations.
+
+As shown in Table 1, CIM is able to achieve better accuracy with fewer pre-training epochs compared with other representative self-supervised vanilla ViT models. Moreover, we find both REVDET and RESPIX visual pretext task can help the ViT enhancer learn useful representations.
+
+ResNet-50. We demonstrate that CIM can also pre-train a high-capacity ResNet-50 model with the fewest possible modifications from the ViT pre-training settings that can achieve compelling fine-tuning performances on ImageNet-1K. We use the AdamW optimizer (Loshchilov & Hutter, 2017) for fine-tuning, and other configurations basically follow the advanced training recipe of RSB (Wightman et al., 2021). For other self-supervised baselines, we select the best lr out of $\{ 5 \mathrm { e } \mathrm { - } 3$ , 8e-3, 12e-3} and keep other settings unchanged to ensure a fair and challenging competition. The detailed configurations are given in Appendix A.4.
+
+As shown in Table 2, under such a demanding training procedure, CIM pre-trained ResNet-50 model can still outperform several representative self-supervised methods based on the Siamese framework as well as the modernized state-of-the-art ResNet-50 results. Using the improved fine-tuning recipe, we also observe performance degeneration for some self-supervised baselines compared with the RSB from scratch results. Notably, even with the extreme 600-epoch training schedule, the CIM representation can still improve the state-of-the-art RSB A1 by $0 . 3 \%$ .
+
+# 3.2 SEMANTIC SEGMENTATION
+
+We study the transfer learning performance of CIM pre-trained vanilla ViT-Base/16 and ResNet-50 models on the ADE20K semantic segmentation benchmark. The pre-trained models are used as an encoder, and we purposefully choose simple decoders to better reveal the pre-trained representations. Experiments are based on the code of Bao et al. (2021); MMSegmentation (2020).
+
+Specifically, for ViT-Base/16 we use a simple linear layer as the decoder, and for ResNet-50 we choose the ubiquitous FCN (Long et al., 2015) as the decoder. For ViT, the baseline settings as well as the fine-tuning recipes are from (Bao et al., 2021). We select the best lr out of $\{ 1 \mathrm { e } { - } 4 , 3 \mathrm { e } { - } 4 , 5 \mathrm { e } { - } 4 , 7 \mathrm { e } { - } 4 \}$ for DINO. For BEiT we use the default setting (lr 7e4 with a decay rate of 0.65). For CIM pretrained ViT, we set the fine-tuning lr equal to 3e-4 with a decay rate of 0.8 as suggested by Clark et al. (2020). For ResNet-50, we use the canonical configuration for all methods, i.e., the optimizer is SGD with a momentum of 0.9, lr follows a poly decay schedule, and the batch size is 16. The training crop size is set to 512 for all models, and we use singlescale inference.
+
+As summarized in Table 3, when transferred to semantic segmentation task, CIM pre-trained models can still achieve competitive performances compared with other approaches. Notably, for ResNet-50, as the fine-tuning schedule becomes longer (i.e., 80k iterations 160k iterations), the performance gain from the ImageNet-1K supervised pre-trained representation is small. Moreover, the performance is even worse than training from scratch. Meanwhile, the CIM pre-trained ResNet-50 representation can provide sustaining performance gain for a longer fine-tuning schedule.
+
+Table 3: ADE20K semantic segmentation performances (mIoU) of ViT and ResNet-50 models.   
+
+<table><tr><td>Models PT Epochs Top-1</td></tr><tr><td>Fine-tuning for l60k iterations</td></tr><tr><td>DINO (Caron et al., 2021) 1600 43.0</td></tr><tr><td>BEiT (Bao et al., 2021) 300 43.2</td></tr><tr><td>CIM-RESPIX (Ours) 300 43.5</td></tr><tr><td>CIM-REVDET (Ours) 300 43.6</td></tr></table>
+
+(a) Vanilla ViT-Base/16 as encoder with one linear layer as decoder.
+
+<table><tr><td>Models PT Epochs mloU</td></tr><tr><td>Fine-tuning for 80k iterations Training from Scratch 29.9 IN1K Supervised† (He et al., 2019) 120 35.9 CIM-REVDET (Ours)</td></tr><tr><td>300 36.2 Fine-tuning forl6Ok iterations Training from Scratch 36.7 IN1K Supervised (He et al., 2019) 120 36.1 BYOL (Grill et al., 2020) 400 37.1</td></tr><tr><td>SimCLR (Chen et al.,2020b) 2000 37.7 CIM-RESPIX (Ours) 300 38.7</td></tr><tr><td>SimSiam (Chen &amp; He,2021) 400 37.1 SwAV (Caron et al., 2020) 600 37.2 MoCo-v2 (Chen et al.,2020c) 400 37.5 SimCLR (Chen et al., 2020b) 800 37.6</td></tr></table>
+
+(b) Vanilla ResNet-50 as encoder with a classic FCN as decoder.
+
+Together with the observation from $\ S 3 . 1$ , we demonstrate CIM is a general, non-Siamese framework that is capable of pre-training both strong ViT and CNN visual encoders.
+
+# 3.3 ABLATION STUDIES
+
+Ablation studies are conducted using 300-epoch CIM-RESPIX pre-trained ViT-Base model with 100 epochs fine-tuning on ImageNet-1K unless specified. Some additional analysis is available in Appendix A.1.
+
+Masking Strategy and Masking Ratio. As shown in Table 4, we observe CIM works better with simple random masking (He et al., 2021; Xie et al., 2021) compared with the blockwise masking strategy (Bao et al., 2021).
+
+The optimal random masking ratio is around $50 \%$ , which we find also holds for the REVDET pretext task, in part because it provides almost equal amounts of positive and negative training samples.
+
+The Small BEiT Depth and Weight Sharing. Following Meng et al. (2021); Chi et al. (2021), we adjust the size of the small trainable BEiT by varying its depth (i.e., the number of Transformer encoder layers) instead of its width (i.e., the feature dimension). As summarized in Table 5, the small BEiT with 4 to 6 layers is generally fine.
+
+It is also beneficial to share the patch embedding layer as well as the first two Transformer encoder layers between the small BEiT and enhancer as long as the enhancer is also ViT. We hypothesize that sharing the earlier layers can help calibrate the enhancer since the small BEiT receives the real inputs while the enhancer sees the same sources but with corrupted views.
+
+Table 4: Ablation study: masking strategy and masking ratio.   
+
+<table><tr><td>Masking Strategy</td><td>Masking Ratio</td><td>Top-1 Acc.</td></tr><tr><td>Blockwise</td><td>40%</td><td>82.8</td></tr><tr><td>Blockwise</td><td>50%</td><td>82.9</td></tr><tr><td>Blockwise</td><td>60%</td><td>82.8</td></tr><tr><td>Random</td><td>40%</td><td>83.0</td></tr><tr><td>Random</td><td>50%</td><td>83.3</td></tr><tr><td>Random</td><td>60%</td><td>83.1</td></tr></table>
+
+Table 5: Ablation study: depth of the small BEiT in the generator and weight sharing.   
+
+<table><tr><td># Enc.Layers</td><td>Weight Sharing</td><td>Top-1 Acc.</td></tr><tr><td>4</td><td>X</td><td>83.1</td></tr><tr><td>4</td><td>√</td><td>83.3</td></tr><tr><td>5</td><td>√</td><td>83.2</td></tr><tr><td>6</td><td>√</td><td>83.2</td></tr><tr><td>7</td><td>√</td><td>83.1</td></tr><tr><td>8</td><td>√</td><td>82.9</td></tr></table>
+
+Table 6: Ablation study: pixel reconstruction target for RESPIX pre-training objective.   
+
+<table><tr><td>REsPIX Recon. Target</td><td>Top-1 Acc.</td></tr><tr><td>w/o norm.</td><td>82.8</td></tr><tr><td>norm.w/ non-overlap win.</td><td>83.0</td></tr><tr><td>norm. w/ sliding win.</td><td>83.3</td></tr></table>
+
+Table 7: Ablation study: sampling strategy for visual tokens.   
+
+<table><tr><td>Sampling Strategy</td><td>Top-1 Acc.</td></tr><tr><td>Uniform sampling</td><td>77.2</td></tr><tr><td>argmax sampling</td><td>78.5</td></tr><tr><td>softmax sampling</td><td>83.3</td></tr></table>
+
+Target for RESPIX. We believe an appropriate normalization technique can provide moderate hints that can help improve the enhancer’s representation quality with the RESPIX visual pretext task (see our discussion of Figure 4). As shown in Table 6, the proposed sliding window normalization improves the fine-tuning accuracy by $0 . 5 \%$ vs. the reconstruction target without normalization, and is also $0 . 3 \%$ better than the normalization method proposed in He et al. (2021).
+
+Sampling Strategy for Visual Tokens. Using discrete visual tokens to represent images enables CIM to use stochastic sampling techniques during the corrupted image’s generation process, which can greatly enrich the output set of the generator and help the enhancer generalize well. For masked image modeling, randomly masking out a portion of patch embeddings can help regularize the pre-training, while for our approach, regularization for the enhancer mainly comes from the diversity of the corrupted images, therefore regularizations such as dropout & droppath are not used in CIM.
+
+As presented in Table 7, the visual token representation with simple stochastic sampling from the generator output distribution is crucial for CIM. In contrast, we find that uniform sampling from the codebook of the image tokenizer regardless of the generator distribution or argmax sampling from the distribution cannot provide meaningful or diverse samples and therefore fails to pre-train the enhancer as expected.
+
+Image Corrupting Strategy. We find that it is crucial to use a generator with a small trainable BEiT to corrupt images in order to successfully pre-train CNN with the proposed CIM. We experiment with another generative visual pretext task for ResNet-50 pre-training, i.e., using $50 \%$ random erasing (Zhong et al., 2020) to corrupt the input image, and the model is required to recover the erased pixels based on the visible context. We find this pretext task fails to transfer well. A parallel work Tian et al. (2022) also finds that only using hand-crafted transformations to corrupt images is not quite satisfactory in generative visual pre-training of ViT.
+
+Table 8: Scaling CIM pre-training to larger ResNet.   
+
+<table><tr><td>Methods</td><td>PT Epochs FT Epochs Top-1 Acc.</td><td></td><td></td></tr><tr><td>ResNet-50x2 (#params: 94M)</td><td></td><td></td><td></td></tr><tr><td>From Scratch</td><td>=</td><td>400</td><td>81.1</td></tr><tr><td>SimCLR (Chen et al., 2020b)</td><td>1000</td><td>100 /200</td><td>81.6 /82.1</td></tr><tr><td>CIM-REVDET (Ours)</td><td>300</td><td>100/200</td><td>81.7 /82.2</td></tr><tr><td>ResNet-50x4 (#params:375M)</td><td></td><td></td><td></td></tr><tr><td>From Scratch</td><td></td><td>400</td><td>80.9</td></tr><tr><td>SimCLR (Chen et al., 2020b)</td><td>1000</td><td>100</td><td>82.6</td></tr><tr><td>SimMIM (Xie et al.,2021)</td><td>300</td><td>100</td><td>81.6</td></tr><tr><td>CIM-REVDET (Ours)</td><td>300</td><td>100</td><td>82.6</td></tr></table>
+
+Scaling CIM to Larger CNNs. We study the scaling behavior of our CIM to larger CNNs. We choose two popular architectures in self-supervised learning literature: ResNet- $5 0 \mathrm { x } 2$ and ResNet-50x4 (with width multipliers of $2 \mathbf { x }$ and $4 \mathbf { x }$ of vanilla ResNet50, respectively), and study the endto-end fine-tuning performance on ImageNet-1K in Table 8. We use an improved training recipe following Touvron et al. (2021a); Wightman et al. (2021), therefore our from
+
+scratch and SimCLR baselines are much higher ( ${ \sim } 2$ points higher) than the original results in Chen et al. (2020b). Notice that it is non-trivial to pre-train those large CNNs (e.g., ResNet-50x4 is 14 times bigger than ResNet-50 in #params). Under the end-to-end fine-tuning protocol, CIM is better than the recent MIM-based approach SimMIM and competitive with the representative Siamese model SimCLR.
+
+Scaling CIM to Larger ViT. We study the scaling behavior of our CIM to ViT-Large in Table 9. Indeed, our approach can give ViT-Large a better initialization compared with the random initialization, and can also achieve better performance than MoCov3 that based on the canonical Siamese framework. Meanwhile, CIM still lags behind the MIM-based BEiT. Nevertheless, we believe CIM can serve as a promising starting point for exploring unified visual pre-training of various architectures.
+
+Table 9: Scaling CIM pre-training for ViT-Large.   
+
+<table><tr><td>Methods</td><td>Top-1 Acc.</td></tr><tr><td>ViT-Large (#params: 304M)</td><td></td></tr><tr><td>From Scratch (He et al., 2021)</td><td>82.6</td></tr><tr><td>MoCo-v3 (Chen et al., 2021)</td><td>84.1</td></tr><tr><td>BEiT (Bao et al., 2021)</td><td>85.2</td></tr><tr><td>CIM-RESPIX (Ours)</td><td>84.3</td></tr></table>
+
+Limitation and Discussion. The image corrupting process of CIM still has a large room for improvement, which determines the characteristics and styles of the corrupted image distribution. The tokenizer we currently use is essentially a large CNN and adds nontrivial overhead during pre-training, i.e., the wall-clock time of 1-epoch training is about $2 \times$ of BEiT. Other image tokenizers, such as ViT-VQGAN (Yu et al., 2021), which report much higher throughput and better generation quality, deserve an in-depth study for CIM pre-training in the future.
+
+# 4 RELATED WORK
+
+Siamese Framework is the dominating self-supervised visual pre-training approach over the past few years, which typically relies on strong hand-crafted data augmentations to generate different views of the same image and learns in a contrastive manner. To maintain a large and informative negative sample set, memory banks (He et al., 2020) or large batch size (Chen et al., 2020b) is used. Follow-ups (Grill et al., 2020; Chen & He, 2021) further eliminate the requirement of using negative samples. Recent works (Caron et al., 2021; Chen et al., 2021) study self-supervised visual pre-training of ViT within Siamese frameworks.
+
+Masked Image Modeling (MIM) learns rich visual representations via masked parts prediction by conditioning on visible context only. ViT (Dosovitskiy et al., 2020) and iGPT (Chen et al., 2020a) report the first meaningful MIM visual pre-training results. BEiT (Bao et al., 2021) greatly improves MIM’s performance via masked visual token prediction, and PeCo (Dong et al., 2021) finds injecting perceptual similarity during visual codebook learning benefits MIM pre-trained representation. Recent work (He et al., 2021; Xie et al., 2021; Wei et al., 2021) re-explore pixel / feature regression in MIM, while Li et al. (2021); Zhou et al. (2021); El-Nouby et al. (2021) incorporate MIM within Siamese frameworks. As MIM is originated in masked language modeling (Devlin et al., 2019), CIM is inspired by Clark et al. (2020). In CIM, visual-token-based MIM plays an important role during the corrupted image generation process, as the stochastic sampling ability greatly enriches the corrupted image set.
+
+# 5 CONCLUSION
+
+We introduce a general self-supervised visual pre-training framework with few architectural constraints for the model to be pre-trained and transferred. Unlike the mainstream Siamese pre-training methods based on strong artificial data augmentations as well as MIM pre-training relying on randomly inserting artificial [MASK] tokens to input embeddings, CIM pre-trained encoder learns from the corrupted view generated from a trainable neural network’s output distribution. Given the stochastic sampling ability, CIM defends using discrete visual token representations during pre-training to some extent. Experimental results show that our approach achieves competitive performance on canonical ViT and CNN models. We hope CIM can serve as a promising starting point for exploring flexible & unified visual representation learning of various architectures.
+
+# ACKNOWLEDGMENT
+
+This work is in part supported by the National Key Research and Development Program of China under Grant 2022YFB4500602. We would like to acknowledge Yaru Hao for the helpful discussions.
+
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+
+# A APPENDIX
+
+# A.1 ADDITIONAL ANALYSIS
+
+Relationship between the type of the generator and the performance of the enhancer. What makes a "good" generator for the enhancer? We believe there are three main factors that affect the output quality of the generator: (1) The masking strategy and masking ratio of the generator’s inputs. (2) The size / capacity of the small trainable BEiT. (3) The type of image tokenizers.
+
+While there are many perspectives / ways to evaluate a generator, this study focuses on visual pretraining of the enhancer, so we are particularly interested in how these factors affect the enhancer’s fine-tuning performance on downstream visual recognition tasks.
+
+Factor 1 & 2 has already been well studied in Table 4 & Table 5 respectively: either a too “weak” generator (e.g., too much masking or the size of the trainable BEiT is too small) or a too “strong” generator (e.g., too less masking or the trainable BEiT is too large) is harmful to the fine-tuning performance of the enhancer.
+
+As for Factor 3, the image tokenizer represents a given image in the RGB domain as a permutation of discrete tokens with a fixed vocabulary size. This compact representation along with the stochastic sampling process can generate an abundant & diverse input set to feed the enhancer better. However, if the generator is too strong & robust that can always generate near ground truth output regardless of the stochastic sampling, the enhancer can hardly learn useful representations or even be wrongly penalized.
+
+To show that, in Table 10 we study another well-established and open-sourced image tokenizer, VQGAN (Esser et al., 2021), on the ViT-B enhancer with 300 epochs pre-training & 100 epochs fine-tuning on ImageNet-1k. We also study the effects of directly using a MAE-Base model as the generator.
+
+Table 10: Study of different generator tpye of CIM pre-training for ViT-Base.   
+
+<table><tr><td>Generator Type of CIM</td><td>Top-1 Acc.</td></tr><tr><td>MAE-style generator w/ 50% masking ratio</td><td>82.6 (-0.7)</td></tr><tr><td>BEiT-Style generator w/ VQGAN tokenizer</td><td>82.9 (-0.4)</td></tr><tr><td>BEiT-Style generator w/DALL-E tokenizer (our default seting)</td><td>83.3</td></tr></table>
+
+For the MAE-style generator, we sample RGB color values at all masked positions of the MAE decoder outputs. Since the stochastic sampling is performed on the RGB domain, only some low-level features (mainly color) can be changed and corrupted. Therefore the enhancer only learns to correct low-level attributes.
+
+For the BEiT-style generator w/ VQGAN tokenizer, compared with the DALL-E tokenizer used as default, the VQGAN tokenizer is trained with two additional losses, i.e., the perceptual loss (Zhang et al., 2018) as well as the GAN loss (Isola et al., 2017). These two additional losses are originally intended for high-quality image synthesis, but could make the tokenizer become too strong & robust to generate appropriate corrupted samples for the enhancer. We visualize the corrupted samples from the VQGAN tokenizer, and we find it nearly reconstructs the original input even with stochastic token sampling. Therefore the samples from the VQGAN tokenizer are not diverse enough and cannot provide rich supervision for the enhancer to learn transferable representations.
+
+Overall, it is hard to find a good indicator from the generator that can directly reflect and measure the representation quality of the enhancer. By now, the best way is to honestly fine-tune the pre-trained enhancer on downstream tasks.
+
+Study of training the generator first and keeping it fixed for the enhancer’s pre-training. We tried first train the generator separately for 300 epochs and then pre-train the enhancer for another 300 epochs while keeping the generator’s weights fixed. The performance suffers from a $0 . 4 \%$ degeneration. We hypothesize synergetic & simultaneous training provides a curriculum-like pretraining strategy for the enhancer where the generator starts off weak but gets better throughout training.
+
+Additional training cost of CIM compared to simple mask prediction with the same mask ratio. We study the relationship between the pre-training time and downstream performances of different approaches for both ViTs and ConvNets in Table 11 and Table 12 respectively.
+
+Since CIM is built upon BEiT, we choose BEiT as the masked image modeling baseline approach of ViTs. Here, we first study the ViT-B model’s 100-epoch fine-tuning performance on ImageNet-1k val set with different pre-training schedules in Table 11. The wall-clock time of 1-epoch pre-training of CIM is about $1 . 8 \mathrm { x }$ of BEiT (CIM has an additional tokenizer decoder compared with BEiT) on the same machine.
+
+Table 11: Study of the training cost for ViT-Base pre-training.   
+
+<table><tr><td>Methods</td><td>PT Epochs</td><td>Relative PT Time</td><td>Top-1 Acc.</td></tr><tr><td>BEiT</td><td>300</td><td>1.0x</td><td>82.9</td></tr><tr><td>BEiT</td><td>800</td><td>2.7x</td><td>83.2</td></tr><tr><td>BEiT</td><td>1600</td><td>5.3x</td><td>83.3</td></tr><tr><td>CIM</td><td>800</td><td>1.8x</td><td>83.3</td></tr><tr><td>CIM</td><td>800</td><td>4.8x</td><td>83.4</td></tr></table>
+
+In Table 12, we also study the ResNet-50x4 model’s 100-epoch fine-tuning performance on ImageNet1k val set with different pre-training schedules. We choose SimMIM as the masked image modeling baseline approach of ConvNets, for it reports the ResNet-50x4 model’s result in Appendix E of its paper. The wall-clock time of 1-epoch pre-training of CIM is about $2 . 6 \mathbf { x }$ of SimMIM (CIM has an additional generator, including a small BEiT and a tokenizer encoder & decoder compared with SimMIM) on the same machine.
+
+Table 12: Study of the training cost for ResNet-50x4 pre-training.   
+
+<table><tr><td>Methods</td><td>PT Epochs</td><td>Relative PT Time</td><td> Top-1 Acc.</td></tr><tr><td>SimMIM</td><td>300</td><td>1.0x</td><td>81.6</td></tr><tr><td>CIM</td><td>100</td><td>0.9x</td><td>82.2</td></tr></table>
+
+These results imply that CIM can obtain better fine-tuning performance with less pre-training time compared with baseline approaches for both ViTs and ConvNets.
+
+# A.2 A NOTE ON VISUALIZATIONS IN $\ S 2 . 2$ AND FIGURE 3
+
+Since there exists information loss in any form of normalization, we have to inject the original image’s information in order to visualize the enhancer output (4th column in Figure 3a). In order to comprehensively demonstrate our method’s behavior, we also include the unnormalized counterpart in Figure 3b for reference, where there is no additional information injection during visualization.
+
+# A.3 TRAINING AND OPTIMIZATION DETAILS
+
+The auxiliary generator and the enhancer are simultaneously trained and synergistically (rather than adversarially as GAN (Goodfellow et al., 2014)) updated. The trainable part of the generator, i.e., the small BEiT, learns a MIM objective in the same vein as in BEiT (Bao et al., 2021). Formally, given an input image’s patch embedding sequence $\pmb { x } = ( \pmb { x } _ { 1 } , . . . , \pmb { x } _ { n } )$ , we randomly mask $k$ embeddings at positions $\pmb { m } = ( m _ { 1 } , . . . , m _ { k } )$ using [MASK] token2. The resulting masked input sequence $_ { \textbf { \em x } }$ masked for BEiT is:
+
+$$
+\begin{array} { r } { m _ { i } \sim \mathrm { u n i f o r m } \{ 1 , n \} , \mathrm { f o r } i = 1 , . . . , k , } \\ { \pmb { x } ^ { \mathrm { m a s k e d } } = \mathrm { r e p l a c e } ( \pmb { x } , \pmb { m } , [ \mathrm { M A S K } ] ) , \quad \quad } \end{array}
+$$
+
+where the replace $( x , m$ , [MASK]) operation denotes using the special [MASK] token to replace patch embeddings of $_ { \textbf { \em x } }$ at positions $_ { m }$ . The small BEiT then encodes $x ^ { \mathrm { m a s k e d } }$ and learns to maximize
+
+$\log p _ { \mathrm { B E i T } } ( \pmb { g } \mid \pmb { x } ^ { \mathrm { m a s k e d } } )$ , i.e., the log-likelihood of the golden visual tokens $\pmb { g } = ( g _ { 1 } , . . . , g _ { k } )$ at the masked positions $_ { \mathbf { \nabla } } \mathbf { m } _ { \mathbf { \nabla } }$ conditioned on $x ^ { \mathrm { m a s k e d } }$ . Notice that the golden tokens are obtained by feeding the original image to the image tokenizer encoder.
+
+In order to generate corrupted image samples $\mathcal { T } ^ { \mathrm { c o r r u p t e d } }$ for the enhancer, we sample tokens’ replacements from the BEiT output distribution $p _ { \mathrm { B E i T } }$ at each masked position $j$ of the encoded $\pmb { x } ^ { \mathrm { m a s k } \bar { \mathrm { e } } \mathrm { d } }$ :
+
+$$
+\begin{array} { r l } & { x _ { j } ^ { \mathrm { s a m p l e d } } \sim p _ { \mathrm { B E i T } } ( x _ { j } ^ { \mathrm { s a m p l e d } } \mid x ^ { \mathrm { m a s k e d } } ) , \mathrm { f o r } j \in m , } \\ & { x ^ { \mathrm { c o r r u p t e d } } = \mathrm { r e p l a c e } ( g , m , x ^ { \mathrm { s a m p l e d } } ) , } \end{array}
+$$
+
+where the replace $( \pmb { g } , \pmb { m } , \pmb { x } ^ { \mathrm { s a m p l e d } } )$ operation denotes using the sampled visual token $x ^ { \mathrm { s a m p l e d } }$ to replace golden tokens of $\textbf {  { g } }$ at positions $_ { m }$ . Next, the image tokenizer decoder maps $\pmb { x } ^ { \mathrm { c o r r u p t e d } }$ to a corrupted image $\mathcal { T } ^ { \mathrm { c o r r u p t e d } }$ . The whole image tokenizer is frozen (i.e., not updated throughout the pre-training phase), which directly uses the publicly available3 pre-trained DALL-E dVAE weight (Ramesh et al., 2021) following BEiT.
+
+The enhancer takes the corrupted image $\mathcal { T } ^ { \mathrm { c o r r u p t e d } }$ as input. For the RESPIX visual pretext task, the enhancer is optimized by a combination of $l _ { 1 }$ and $l _ { 2 }$ loss for pixel regression. For the REVDET variant, the enhancer is learned by binary cross-entropy loss for replaced visual token detection. The gradients of the enhancer are not back-propagated through the generator.
+
+In this paper, we study CIM self-supervised pre-trained vanilla ViT (Dosovitskiy et al., 2020) and vanilla ResNet (He et al., 2016) models. The vanilla ViT models refer to the design from (Dosovitskiy et al., 2020; Touvron et al., 2021a) without further architectural change such as using relative position embeddings (Shaw et al., 2018) and LayerScale (Touvron et al., 2021b). The vanilla ResNet-50 model refers to the torchvision ResNet-50 (Paszke et al., 2019) without any architectural change. The larger ResNet-50x2 and ResNet-50x4 models follows the canonical design in SimCLR (Chen et al., 2020b). We conduct experiments on $1 6 \times$ or $3 2 \times$ V100 GPUs with 32GB memory.
+
+A.4 PRE-TRAINING & FINE-TUNING CONFIGURATIONS
+
+A.4.1 THE IMAGENET-1K CIM PRE-TRAINING CONFIGURATIONS FOR VANILLA VIT AND RESNET MODELS   
+Table 13: The ImageNet-1K CIM pre-training settings for vanilla ViT-S/16, ViT-B/16 and ResNet-50 models. Notably, the pre-training configurations are almost the same for different architectures. We implement the pre-training using the codebase of BEiT (Bao et al., 2021). Mixed precision and deepspeed acceleration are used.   
+
+<table><tr><td>Pre-training Config. (ViT &amp; ResNet)</td><td>Value</td></tr><tr><td>Optimizer</td><td>AdamW (Loshchilov &amp; Hutter, 2017)</td></tr><tr><td>Pre-training Epochs</td><td>300</td></tr><tr><td>Peak Learning Rate</td><td>1.5e-3</td></tr><tr><td>Batch Size</td><td>2048</td></tr><tr><td>Weight Decay</td><td>0.05</td></tr><tr><td>Optimizer Momentum (β1,β2)</td><td>(0.9, 0.98) (Vaswani et al., 2017)</td></tr><tr><td>Learning Rate Schedule</td><td>Cosine Decay</td></tr><tr><td>Gradient Clipping</td><td>3.0</td></tr><tr><td>Warmup Epochs</td><td>10</td></tr><tr><td>#Masked Patches for the Generator</td><td>100 to 120, Random Masking</td></tr><tr><td>The Generator&#x27;s Depth</td><td>4 to 6</td></tr><tr><td>The Generator&#x27;s Width</td><td>Same to the Enhancer (ViT), 384 (ResNet)</td></tr><tr><td>The Enhancer&#x27;s Loss Weight</td><td>1 forREVDET,1O forREsPIX</td></tr><tr><td>Data Augmentation</td><td>RandomResizedCrop Only</td></tr><tr><td>Dropout (Srivastava et al., 2014)</td><td>X X</td></tr><tr><td>Stochastic Depth (Huang et al., 2016)</td><td></td></tr><tr><td>LayerScale (Touvron et al., 2021b) Pos.Emb.in TransformerLayers</td><td>X</td></tr><tr><td></td><td>1-D Absolute Pos. Emb. (Dosovitskiy et al., 2020)</td></tr><tr><td>Patch Size</td><td>16 224</td></tr><tr><td>Pre-training Resolution</td><td></td></tr></table>
+
+A.4.2 THE IMAGENET-1K IMAGE CLASSIFICATION FINE-TUNING CONFIGURATIONS FOR VANILLA VIT MODELS   
+Table 14: The ImageNet-1K image classification fine-tuning recipes for vanilla ViT-S/16 and ViT-B/16. We implement the fine-tuning using the codebase of BEiT (Bao et al., 2021). Mixed precision and deepspeed acceleration are used. We select the best learning rate out of $\{ 3 \mathrm { e } { - } 3 , 4 \mathrm { e } { - } 3 , 5 \mathrm { e } { - } 3 \}$ for different sized models and pre-training objectives, and the absolute difference between the worst and the best learning rate is less than 0.3 in terms of the top-1 accuracy.   
+
+<table><tr><td>Fine-tuning Config. (ViT)</td><td>Value</td></tr><tr><td>Optimizer</td><td>AdamW (Loshchilov &amp; Hutter, 2017)</td></tr><tr><td>Fine-tuning Epochs</td><td>200 forViT-S/16,10O forViT-B/16</td></tr><tr><td>Peak Learning Rate</td><td>3e-3 forViT-B/16REsPIX,5e-3 forViT-B/16 REVDET,3e-3 or4e-3 forViT-S/16</td></tr><tr><td>Layer-wise Learning Rate Decay (Bao et al.,</td><td>0.8 (Clark et al., 2020)</td></tr><tr><td>2021) Batch Size</td><td>1024</td></tr><tr><td>Weight Decay</td><td>0.05</td></tr><tr><td>Optimizer Momentum (β1, β2)</td><td>(0.9, 0.999)</td></tr><tr><td>Learning Rate Schedule</td><td>Cosine Decay</td></tr><tr><td>Warmup Epochs</td><td>5</td></tr><tr><td>Gradient Clipping</td><td>X</td></tr><tr><td>Dropout (Srivastava et al., 2014)</td><td>X</td></tr><tr><td>Stochastic Depth (Huang et al., 2016)</td><td>0.1</td></tr><tr><td>Label Smoothing (Szegedy et al., 2016)</td><td>0.1</td></tr><tr><td>Mixup (Zhang et al., 2017)</td><td>0.8</td></tr><tr><td>CutMix (Yun et al., 2019)</td><td>1.0</td></tr><tr><td>Random Augmentation (Cubuk et al., 2020)</td><td>9 /0.5</td></tr><tr><td>Patch Size</td><td>16</td></tr><tr><td>Fine-tuning Resolution</td><td>224</td></tr><tr><td>Test Resolution</td><td>224</td></tr><tr><td>Test Crop Ratio</td><td>0.95</td></tr><tr><td>Loss Function</td><td>Cross Entropy Loss</td></tr></table>
+
+A.4.3 THE IMAGENET-1K IMAGE CLASSIFICATION FINE-TUNING CONFIGURATIONS FOR VANILLA RESNET-50   
+Table 15: The ImageNet-1K image classification fine-tuning recipes for vanilla ResNet-50. We use the AdamW optimizer. The hyperparameter settings basically follows (Wightman et al., 2021). We implement the fine-tuning based on the codebase of BEiT (Bao et al., 2021). Mixed precision and deepspeed acceleration are used. For other self-supervised baseline approaches we compared in Table 2, we select the best learning rate out of $\{ 5 \mathrm { e } { - } 3 , 8 \mathrm { e } { - } 3 , 1 2 \mathrm { e } { - } 3 \}$ and keep other settings unchanged.   
+
+<table><tr><td>Fine-tuning Config. (ResNet-50)</td><td>100 Epoch FT</td><td>300Epoch FT</td><td>600 Epoch FT</td></tr><tr><td>Optimizer</td><td colspan="3">AdamW (Loshchilov &amp; Hutter, 2017)</td></tr><tr><td>Peak Learning Rate</td><td colspan="3">12e-3</td></tr><tr><td>Layer-wise Learning Rate Decay (Bao et al., 2021)</td><td colspan="3">X</td></tr><tr><td>Batch Size</td><td colspan="3">2048</td></tr><tr><td>Learning Rate Schedule</td><td colspan="3">Cosine Decay</td></tr><tr><td>Loss Function</td><td colspan="3">Binary Cross Entropy Loss</td></tr><tr><td>Warmup Epochs</td><td colspan="3">5</td></tr><tr><td>Weight Decay</td><td>0.02</td><td>0.02</td><td>0.01</td></tr><tr><td>Fine-tuning Resolution</td><td>160</td><td>224</td><td>224</td></tr><tr><td>Test Resolution</td><td></td><td>224</td><td></td></tr><tr><td>Test Crop Ratio</td><td></td><td>0.95</td><td></td></tr><tr><td>Repeated Augmentation (Berman et al.,</td><td>X</td><td>√</td><td>1</td></tr><tr><td>2019; Hoffer et al., 2019) Random Augmentation (Cubuk et al.,</td><td>6/0.5</td><td>7 /0.5</td><td>7 /0.5</td></tr><tr><td>2020)</td><td></td><td></td><td></td></tr><tr><td>Mixup (Zhang et al., 2017) CutMix (Yun et al., 2019)</td><td>0.1</td><td>0.1 1.0</td><td>0.2</td></tr><tr><td>Label Smoothing (Szegedy et al., 2016)</td><td>0.1</td><td></td><td>0.1</td></tr><tr><td>Stochastic Depth (Huang et al.,2016)</td><td></td><td>X</td><td></td></tr><tr><td></td><td>X</td><td>X</td><td>0.05</td></tr><tr><td>Dropout (Srivastava et al., 2014)</td><td></td><td>X</td><td></td></tr><tr><td>Layer-wise Learning Rate Decay</td><td></td><td>X</td><td></td></tr></table>

parse/dev/09hVcSDkea/09hVcSDkea_content_list.json

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+    {
+        "type": "text",
+        "text": "CORRUPTED IMAGE MODELING FOR SELF-SUPERVISED VISUAL PRE-TRAINING ",
+        "text_level": 1,
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+        "text": "Yuxin Fang 1, 2∗ Li Dong 2 Hangbo Bao 2 Xinggang Wang 1† Furu Wei 2 1 School of EIC, Huazhong University of Science & Technology 2 Microsoft Research {yxf,xgwang}@hust.edu.cn ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            250,
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+            263
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "We introduce Corrupted Image Modeling (CIM) for self-supervised visual pretraining. CIM uses an auxiliary generator with a small trainable BEiT (Bao et al., 2021) to corrupt the input image instead of using artificial [MASK] tokens, where some patches are randomly selected and replaced with plausible alternatives sampled from the BEiT output distribution. Given this corrupted image, an enhancer network learns to either recover all the original image pixels, or predict whether each visual token is replaced by a generator sample or not. The generator and the enhancer are simultaneously trained and synergistically updated. After pre-training, the enhancer can be used as a high-capacity visual encoder for downstream tasks. CIM is a general and flexible visual pre-training framework that is suitable for various network architectures. For the first time, CIM demonstrates that both ViT and CNN can learn rich visual representations using a unified, non-Siamese framework. Experimental results show that our approach achieves compelling results in vision benchmarks, such as ImageNet classification and ADE20K semantic segmentation. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Vision Transformers (ViTs) (Dosovitskiy et al., 2020) are transferring the landscape of computer vision, not only in terms of the network architecture design, but also the self-supervised pre-training recipe. Masked image modeling (MIM) (Bao et al., 2021), which randomly masks out some input tokens and then recovers the masked content by conditioning on the visible context, is able to learn rich visual representations and shows promising performance on various vision benchmarks (Zhou et al., 2021; He et al., 2021; Xie et al., 2021; Dong et al., 2021; Wei et al., 2021). ",
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+    {
+        "type": "text",
+        "text": "Originated in masked language modeling (Devlin et al., 2019), MIM (Figure 1a) is tailor-made for specific architectures (Vaswani et al., 2017), which is generally capable of receiving and processing tokenized inputs such as the artificial [MASK] tokens. Meanwhile, the more common and natural input signal in computer vision is the image in RGB domain with 2D regular grid structures. In order to apply MIM pre-training for images, ViT has to “patchify” the input image into a 1D sequence of non-overlapping patch embeddings, and then use [MASK] tokens to perturb them. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "MIM is tightly coupled with the Transformer family, and the usage of [MASK] tokens limits its scope of application to some extent. More importantly, MIM is not directly suitable for convolutional neural networks (CNNs) (LeCun et al., 1989), the dominant architecture for computer vision in the last decade. Introducing [MASK] tokens in any intermediate stage of CNN is infeasible, as convolution’s intrinsic dense-sliding-window paradigm causes information leakage between visual features in previous layers and therefore impedes the MIM. Therefore the large CNN family cannot directly benefit from the upsurge of this new pre-training scheme. Moreover, the usage of [MASK] tokens causes a discrepancy between pre-training and fine-tuning (Devlin et al., 2019; Clark et al., 2020), as the artificial [MASK] tokens never appear in the fine-tuning stage. ",
+        "bbox": [
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+        "text": "In this paper, we present a new visual pre-training framework, called Corrupted Image Modeling (CIM, Figure 1b), which avoids directly manipulating [MASK] tokens on pre-trained models and generalizes quite well to both ViT and CNN architectures. Rather than directly using artificial [MASK] tokens to corrupt a portion of non-overlapping patch embeddings as in MIM, CIM uses a small trainable BEiT (Bao et al., 2021) as an auxiliary generator to corrupt the input image. Specifically, the BEiT generator learns to predict visual tokens at the masked positions, where we utilize the predicted distribution to sample visual tokens’ replacements. The replaced visual tokens together with the golden tokens that directly produced by a pre-trained frozen image tokenizer encoder (e.g., the DALL-E (Ramesh et al., 2021) dVAE encoder) given the same input as the small trainable BEiT are then mapped back to the image RGB domain by a pre-trained frozen tokenizer decoder (e.g., the DALL-E dVAE decoder). The resulting corrupted image serves as the input of the enhancer, which is the model to be pre-trained and transferred. ",
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+    {
+        "type": "image",
+        "img_path": "images/4dd8395ea4882213cb68da1f6b25faa4ebd6cb6bd3705e0df1e770aeb9b9d374.jpg",
+        "image_caption": [
+            "Figure 1: Overview of our Corrupted Image Modeling (CIM) and comparisons with Masked Image Modeling (MIM). MIM (Figure 1a) requires the pre-trained architecture to receive and process the artificial [MASK] tokens, while CIM (Figure 1b) relaxes these restrictions by using a trainable generator to sample corrupted images serving as the input for the enhancer. Similar to BEiT, the small generator learns to predict the golden visual token produced by the pre-trained frozen image tokenizer encoder (not shown in the figure) based on partial observations of the input. The enhancer can be various architectures including CNN and learns either a generative or a discriminative visual pre-training objective. After pre-training, we throw out the generator and fine-tune the enhancer on downstream tasks. The dice icon in Figure 1b refers to the visual tokens’ stochastic sampling process, and the lock icon means the pre-trained image tokenizer decoder is frozen. "
+        ],
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+    {
+        "type": "text",
+        "text": "For the enhancer, the choice of pre-training objectives is quite flexible. We study two representatives: a generative objective that regresses all the original image pixels given the corrupted image (Dosovitskiy et al., 2020; Chen et al., 2020a), dubbed as Pixel Residual learning (RESPIX), and a discriminative objective that predicts whether each visual token is replaced by the small generator or not (Clark et al., 2020), dubbed as Replaced Visual token Detection (REVDET). After pre-training, the enhancer can be used as a strong feature extractor for visual downstream tasks. ",
+        "bbox": [
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+    {
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+        "text": "Overall, CIM is a general and flexible pre-training framework suited for different kinds of visual encoders. For the first time, we demonstrate that both ViT and CNN can learn rich visual representations using a unified non-Siamese structure. Experimental results show that our approach achieves compelling results in vision benchmarks, such as ImageNet classification and ADE20K semantic segmentation. We hope CIM can serve as a promising starting point for exploring flexible & unified visual representation learning of various architectures. ",
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+    {
+        "type": "text",
+        "text": "2 CORRUPTED IMAGE MODELING (CIM) ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Figure 1b shows the overview of CIM. Our approach simultaneously learns two neural networks: an auxiliary generator and an enhancer. The generator is used to corrupt the input image, while the enhancer receives the corrupted image (Figure 2) and learns either a generative or a discriminative visual pretext task. After pre-training, we throw out the generator and fine-tune the enhancer on downstream tasks. ",
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+    {
+        "type": "text",
+        "text": "2.1 GENERATOR ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Rather than using artificial [MASK] tokens to corrupt the input image, we learn a trainable auxiliary generator to relax the architectural constraints of MIM. Moreover, the generator enriches the diversity of corrupted images via stochastic sampling, which helps the enhancer generalize. The generator consists of a pre-trained frozen image tokenizer, and a small trainable BEiT (Bao et al., 2021). ",
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+        "img_path": "images/5050220e448020d78790b1e83d4696485816144f9fb9557d3b542de7e5a3860c.jpg",
+        "image_caption": [
+            "(a) Corrupted image samples from ImageNet-1K training set. Although the model is trained using the same dataset, the corrupted image samples still vary to a certain extent. Therefore during pre-training, the generator is able to continuously provide abundant and diverse corrupted samples for the enhancer. "
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+        "image_caption": [
+            "(b) Corrupted image samples from COCO val split (Lin et al., 2014) using ImageNet-1K pre-trained model. ",
+            "Figure 2: Visualizations of some corrupted image samples. For each image set, we show (from left to right) the original image, the masked image, and four different corrupted images sampled from the generator output distribution with the same masked input. Simple stochastic sampling can greatly enrich the corrupted image distribution in terms of both low-level features and high-level semantics, which feeds the enhancer better. "
+        ],
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+        "text": "",
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+    {
+        "type": "text",
+        "text": "The frozen image tokenizer in CIM is a pre-trained discrete variational autoencoder (dVAE) (Rolfe, 2016; Van Den Oord et al., 2017), consisting of a paired encoder and decoder. The tokenizer encoder maps the input image into a sequence of discrete visual tokens with a fixed vocabulary size. The tokenizer decoder can recover semantically plausible images given a permutation of appropriate and meaningful visual tokens. We directly use the DALL-E (Ramesh et al., 2021) tokenizer, following BEiT. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The small BEiT consists of several Transformer encoder layers and is trained to perform MIM, which uses two views for each input image, i.e., a sequence of non-overlapping patch embeddings, and their corresponding discrete visual tokens. Patch embeddings are linearly embedded from non-overlapping input image patches. Discrete visual tokens are from the DALL-E tokenizer encoder, serving as the prediction target for BEiT. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Given a sequence of patch embeddings, the small BEiT randomly masks out a set of positions. The patch embeddings at the masked positions are replaced with special mask embeddings. The small BEiT takes this corrupted sequence of patch embeddings as the input, and learns to predict the corresponding discrete visual tokens at all masked positions given the visible context only. In CIM pre-training, the size of the small BEiT we use is typically a quarter or a half of the enhancer. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Using discrete visual tokens to represent images enables CIM to perform stochastic sampling during the corrupted image’s generation process, which greatly enriches the output set of the generator. In this paper, we directly sample from softmax with a temperature of 1 at all the masked positions according to the small BEiT output distribution. All the masked tokens are replaced by the sampled visual tokens. The sampled tokens together with the golden tokens that are directly produced by the image tokenizer encoder at all the non-masked positions constitute the input for the image tokenizer decoder. Then the decoder maps those plausible visual tokens to a corrupted image (refer to examples in Figure 2), which serves as the input for the enhancer. ",
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+        "page_idx": 2
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+    {
+        "type": "image",
+        "img_path": "images/c649970c6ab9f97e43291e9e16de40c65e8ad4cf1995b66201d058e9c24be0c1.jpg",
+        "image_caption": [
+            "(a) CIM-RESPIX pre-training objective with sliding window normalized pixels as the enhancer prediction target. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 3
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+    {
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+        "img_path": "images/06a181c2f58d7ee657036e02167e76fee2211bdd65d0593da1ded42af9144f35.jpg",
+        "image_caption": [
+            "(b) CIM-RESPIX pre-training objective with unnormalized pixels as the enhancer prediction target. ",
+            "Figure 3: Example visualization results on COCO val split images from vanilla ViT-Base/16 model pre-trained with the RESPIX objective using ImageNet-1K training data. For each image quadruplet, we show the original input image (1st column), the masked input image for the generator (2nd column), the corrupted image sampled from the generator output (3rd column), and the enhancer output (4th column). Given the corrupted image, the enhancer is able to perform image denoising, deblurring and completion, etc., and learns to predict plausible output in terms of both low-level features as well as high-level semantics. "
+        ],
+        "image_footnote": [],
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "2.2 ENHANCER ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "Given the corrupted image sampled from the auxiliary generator, the enhancer learns either a generative or a discriminative visual pretext task. The prediction head is a simple linear layer, and the choice of pre-training objectives is quite flexible. In this paper, we study two representative objectives, coined as Pixel Residual learning (RESPIX) and Replaced Visual token Detection (REVDET). ",
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "RESPIX (Figure 3) is a generative visual pretext task that requires the enhancer to predict the uncorrupted pixel value for all positions given the corrupted input. Instead of directly regressing the original pixel, MAE (He et al., 2021) suggests learning the normalized counterpart. Specifically, the image is partitioned into a set of non-overlapping patches, and each pixel is normalized by the mean and standard deviation of all pixels in the patch it lives in, i.e., patches with layer normalization (Ba et al., 2016) are the reconstruction target. ",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In CIM, we further propose to normalize the prediction target inside a sliding window, i.e., each pixel is normalized by all pixels in a local $8 \\times 8$ sized window centered at where the target pixel lives in. We observe improved representation quality using the sliding window normalization paradigm. ",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/bff27fbe41eea6e635bbeb3ed3ffc0bcf18122b22ff97b3a0c695ab06f6813fe.jpg",
+        "image_caption": [
+            "Figure 4: Normalizations as learning templates for RESPIX. For each image triplet, we visualize the original image (left), the template of using non-overlapping window normalization (He et al., 2021), and the template of the proposed sliding window normalization paradigm. Our approach can provide more accurate and moderate hints that can boost the enhancer’s pre-training as well as improve its representation quantity. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            500,
+            655,
+            821,
+            824
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Naive pixel recovery without normalization tends to waste modeling capability on learning short-range dependencies and high-frequency details (Ramesh et al., 2021; Bao et al., 2021), while the normalized target can mitigate irrelevant information fittings. From another perspective, normalizations are equal to providing learning templates, as shown in Figure 4. With the normalized prediction target, the enhancer only needs to learn the residual pixel value at each position given the normalized pixel value, while the unnormalized target provides no hint therefore the enhancer has to “learn to see in the dark” (i.e., regress from RGB: 0, 0, 0). It is also hard for the enhancer to learn without a template since the corrupted image usually provides bad priors (refer to the corrupted image samples in Figure 2 and Figure 3). Therefore, we believe appropriate and moderate hints will help the enhancer see better. ",
+        "bbox": [
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+            103,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "REVDET is a discriminative visual pretext task that requires the enhancer to determine whether each visual token is replaced by a generator sample or not. To be specific, the visual tokens produced by the pre-trained frozen image tokenizer encoder are considered as golden tokens. If a generated visual token is different from the golden token at the same position, that generated token is considered “replaced”, and vice versa. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "REVDET is inspired by ELECTRA (Clark et al., 2020) in language modeling. The main difference is, in the proposed CIM, the determining criterion of replacement is hidden in the corrupted image. Token replacement is a kind of local, high-frequency operation by nature. However, the visual token set after sampling and replacement is further smoothed and processed by the image tokenizer decoder. Therefore the token sampling and replacement operations are finally embodied as non-local, high-level semantics changes in the corrupted image. The enhancer is required to “decrypt” it and identify all the replaced tokens given the corrupted input, which yields a nontrivial and meaningful visual pretext task1. To some extent, REVDET also learns the DALL-E dVAE’s visual codebook similar to BEiT, but in a discriminative manner. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The enhancer is regarded as the visual encoder after pre-training. Moreover, unlike masked image modeling, CIM does not assume too many architectural priors for the pre-trained network. We successfully pre-train a high-capacity vanilla ResNet-50 (He et al., 2016), ResNet-50x2 and ResNet$5 0 { \\bf x } 4$ enhancers that achieve compelling transfer learning performance using a similar configuration as pre-training a ViT enhancer. For the first time, we demonstrate that both ViT and CNN can learn strong visual representations using a unified non-Siamese framework. ",
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "2.3 TRAINING AND OPTIMIZATION ",
+        "text_level": 1,
+        "bbox": [
+            176,
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The auxiliary generator and the enhancer are simultaneously trained and synergistically (rather than adversarially as GAN (Goodfellow et al., 2014)) updated. The trainable part of the generator, i.e., the small BEiT, learns a MIM objective in the same vein as in (Bao et al., 2021). The whole pre-trained image tokenizer is frozen. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "For the RESPIX visual pretext task, the enhancer is optimized by a combination of $l _ { 1 }$ and $l _ { 2 }$ loss. For the REVDET visual pretext task, the enhancer is learned by binary cross-entropy loss. Notice that the gradients of the enhancer are not back-propagated through the generator. A detailed formulation is presented in Appendix A.3. ",
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+    },
+    {
+        "type": "text",
+        "text": "3 EXPERIMENTS ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We study CIM self-supervised pre-trained vanilla ViT-Small/16 (Touvron et al., 2021a), vanilla ViT-Base/16 (Dosovitskiy et al., 2020) and vanilla ResNet-50 (He et al., 2016) models. We use the actual processed images / views to measure the pre-training epochs (PT epochs). ImageNet-1K (Deng et al., 2009) training data is used to pre-train the small BEiT and the enhancer. Our pre-training setting generally follows BEiT (Bao et al., 2021). Unlike BEiT, CIM only uses cropping and flipping for data argumentation, while dropout (Srivastava et al., 2014) and stochastic depth (Huang et al., 2016) are not applied. The detailed pre-training settings are summarized in the Appendix A.4. Notably, the pre-training configurations are almost the same for both ViT and CNN architectures. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In order to evaluate the pre-trained representations from CIM, for both ViT and CNN architectures, we conduct supervised end-to-end fine-tuning (FT) experiments on ImageNet-1K (Deng et al., 2009) image classification in $\\ S 3 . 1$ , and ADE20K (Zhou et al., 2019) semantic segmentation in $\\ S 3 . 2$ . ",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/459f801e7ff81d17f3cfa23c0fd8ec3c9133f10c7e6196636b03f74ece08238a.jpg",
+        "table_caption": [
+            "Table 1: ImageNet-1K end-to-end fine-tuning top-1 accuracy of vanilla ViT-Small/16 and ViT-Base/16 models. †Doubled attention heads. ‡Our reproduction. "
+        ],
+        "table_footnote": [
+            "Ablation study on ImageNet-1K is presented in $\\ S 3 . 3$ . For ImageNet-1K, we observe ${ \\sim } 0 . 2$ Top-1 acc. fluctuations. For ADE20K, we observe ${ \\sim } 0 . 5$ mIoU fluctuations. We report key results using the median of 3 independent runs. "
+        ],
+        "table_body": "<table><tr><td>Models PT Epochs Top-1 ViT-Small/16 model results</td></tr><tr><td>Scratch (Touvron et al., 2021a) MoCo-v3† (Chen et al., 2021) 600 DINO (Caron et al., 2021) 1600 81.5 BEiT (Bao et al., 2021) 300</td></tr><tr><td>CIM-RESPIX (Ours) 300 81.5 CIM-REVDET (Ours) 300 81.6</td></tr><tr><td>ViT-Base/l6 model results 81.8</td></tr><tr><td>Scratch (Touvron et al., 2021a)</td></tr><tr><td>Scratch (He et al., 2021) 82.3</td></tr><tr><td>DINO (Caron et al., 2021) 1600 82.8 MoCo-v3 (Chen et al.,2021) 600 83.2</td></tr><tr><td>BEiT (Bao et al.,2021) 300 82.9 BEiT (Bao et al., 2021) 800 83.2</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/2f2175fb1329d3136feceda47e76b8d02304ba1093ecd6911c001590c997ed9b.jpg",
+        "table_caption": [
+            "Table 2: ImageNet-1K end-to-end fine-tuning top-1 accuracy of vanilla ResNet-50 model. RSB (Wightman et al., 2021) is the current vanilla ResNet stateof-the-art training procedure. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Models</td><td>PT Epochs Top-1</td></tr><tr><td>Fine-tuning for l0o epochs RSB A3 (Wightman et al., 2021) CIM-REVDET (Ours) 300</td><td>78.1 78.8</td></tr><tr><td>Fine-tuning for 300 epochs RSB A2 (Wightman et al., 2021) SimSiam (Chen &amp; He,2021) MoCo-v2 (Chen et al., 2020c) SimCLR (Chen et al., 2020b) SimCLR (Chen et al., 2020b) BYOL (Grill et al., 2020) SwAV (Caron et al., 2020) CIM-RESPIX(Ours) CIM-REVDET (Ours)</td><td>79.8 400 79.1 400 79.6 800 79.9 2000 80.0 400 80.0 600 80.1 300 79.9 300</td></tr><tr><td>Fine-tuning for 60o epochs</td><td>80.5</td></tr><tr><td>RSB A1 (Wightman et al., 2021) CIM-REVDET (Ours) 300</td><td>80.4 80.7</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "3.1 IMAGE CLASSIFICATION ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "ViT. The ImageNet-1K end-to-end fine-tuning top-1 accuracy of vanilla ViT-Small/16 and ViTBase/16 models are presented in Table 1. We fine-tune the small-sized model for 200 epochs, and the base-sized model for 100 epochs. Other self-supervised methods in Table 1 use the same or longer fine-tuning schedule. The fine-tuning hyperparameters mostly follow BEiT, while our layerwise lr decay rate is set to 0.8 as suggested by Clark et al. (2020). See Appendix A.4 for detailed configurations. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "As shown in Table 1, CIM is able to achieve better accuracy with fewer pre-training epochs compared with other representative self-supervised vanilla ViT models. Moreover, we find both REVDET and RESPIX visual pretext task can help the ViT enhancer learn useful representations. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "ResNet-50. We demonstrate that CIM can also pre-train a high-capacity ResNet-50 model with the fewest possible modifications from the ViT pre-training settings that can achieve compelling fine-tuning performances on ImageNet-1K. We use the AdamW optimizer (Loshchilov & Hutter, 2017) for fine-tuning, and other configurations basically follow the advanced training recipe of RSB (Wightman et al., 2021). For other self-supervised baselines, we select the best lr out of $\\{ 5 \\mathrm { e } \\mathrm { - } 3$ , 8e-3, 12e-3} and keep other settings unchanged to ensure a fair and challenging competition. The detailed configurations are given in Appendix A.4. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "As shown in Table 2, under such a demanding training procedure, CIM pre-trained ResNet-50 model can still outperform several representative self-supervised methods based on the Siamese framework as well as the modernized state-of-the-art ResNet-50 results. Using the improved fine-tuning recipe, we also observe performance degeneration for some self-supervised baselines compared with the RSB from scratch results. Notably, even with the extreme 600-epoch training schedule, the CIM representation can still improve the state-of-the-art RSB A1 by $0 . 3 \\%$ . ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "3.2 SEMANTIC SEGMENTATION ",
+        "text_level": 1,
+        "bbox": [
+            176,
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We study the transfer learning performance of CIM pre-trained vanilla ViT-Base/16 and ResNet-50 models on the ADE20K semantic segmentation benchmark. The pre-trained models are used as an encoder, and we purposefully choose simple decoders to better reveal the pre-trained representations. Experiments are based on the code of Bao et al. (2021); MMSegmentation (2020). ",
+        "bbox": [
+            174,
+            864,
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Specifically, for ViT-Base/16 we use a simple linear layer as the decoder, and for ResNet-50 we choose the ubiquitous FCN (Long et al., 2015) as the decoder. For ViT, the baseline settings as well as the fine-tuning recipes are from (Bao et al., 2021). We select the best lr out of $\\{ 1 \\mathrm { e } { - } 4 , 3 \\mathrm { e } { - } 4 , 5 \\mathrm { e } { - } 4 , 7 \\mathrm { e } { - } 4 \\}$ for DINO. For BEiT we use the default setting (lr 7e4 with a decay rate of 0.65). For CIM pretrained ViT, we set the fine-tuning lr equal to 3e-4 with a decay rate of 0.8 as suggested by Clark et al. (2020). For ResNet-50, we use the canonical configuration for all methods, i.e., the optimizer is SGD with a momentum of 0.9, lr follows a poly decay schedule, and the batch size is 16. The training crop size is set to 512 for all models, and we use singlescale inference. ",
+        "bbox": [
+            174,
+            104,
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+            353
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "As summarized in Table 3, when transferred to semantic segmentation task, CIM pre-trained models can still achieve competitive performances compared with other approaches. Notably, for ResNet-50, as the fine-tuning schedule becomes longer (i.e., 80k iterations 160k iterations), the performance gain from the ImageNet-1K supervised pre-trained representation is small. Moreover, the performance is even worse than training from scratch. Meanwhile, the CIM pre-trained ResNet-50 representation can provide sustaining performance gain for a longer fine-tuning schedule. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/257b2d046b6a80a0c4242edb91b80120eb4cc02c4fc1ff7be23b230fa7763efd.jpg",
+        "table_caption": [
+            "Table 3: ADE20K semantic segmentation performances (mIoU) of ViT and ResNet-50 models. "
+        ],
+        "table_footnote": [
+            "(a) Vanilla ViT-Base/16 as encoder with one linear layer as decoder. "
+        ],
+        "table_body": "<table><tr><td>Models PT Epochs Top-1</td></tr><tr><td>Fine-tuning for l60k iterations</td></tr><tr><td>DINO (Caron et al., 2021) 1600 43.0</td></tr><tr><td>BEiT (Bao et al., 2021) 300 43.2</td></tr><tr><td>CIM-RESPIX (Ours) 300 43.5</td></tr><tr><td>CIM-REVDET (Ours) 300 43.6</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/2f3f4d7c5fe049564a76505d36cdc91369e5917e24856f2a77ca68e436f7de97.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "(b) Vanilla ResNet-50 as encoder with a classic FCN as decoder. "
+        ],
+        "table_body": "<table><tr><td>Models PT Epochs mloU</td></tr><tr><td>Fine-tuning for 80k iterations Training from Scratch 29.9 IN1K Supervised† (He et al., 2019) 120 35.9 CIM-REVDET (Ours)</td></tr><tr><td>300 36.2 Fine-tuning forl6Ok iterations Training from Scratch 36.7 IN1K Supervised (He et al., 2019) 120 36.1 BYOL (Grill et al., 2020) 400 37.1</td></tr><tr><td>SimCLR (Chen et al.,2020b) 2000 37.7 CIM-RESPIX (Ours) 300 38.7</td></tr><tr><td>SimSiam (Chen &amp; He,2021) 400 37.1 SwAV (Caron et al., 2020) 600 37.2 MoCo-v2 (Chen et al.,2020c) 400 37.5 SimCLR (Chen et al., 2020b) 800 37.6</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Together with the observation from $\\ S 3 . 1$ , we demonstrate CIM is a general, non-Siamese framework that is capable of pre-training both strong ViT and CNN visual encoders. ",
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+    {
+        "type": "text",
+        "text": "3.3 ABLATION STUDIES ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Ablation studies are conducted using 300-epoch CIM-RESPIX pre-trained ViT-Base model with 100 epochs fine-tuning on ImageNet-1K unless specified. Some additional analysis is available in Appendix A.1. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Masking Strategy and Masking Ratio. As shown in Table 4, we observe CIM works better with simple random masking (He et al., 2021; Xie et al., 2021) compared with the blockwise masking strategy (Bao et al., 2021). ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The optimal random masking ratio is around $50 \\%$ , which we find also holds for the REVDET pretext task, in part because it provides almost equal amounts of positive and negative training samples. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The Small BEiT Depth and Weight Sharing. Following Meng et al. (2021); Chi et al. (2021), we adjust the size of the small trainable BEiT by varying its depth (i.e., the number of Transformer encoder layers) instead of its width (i.e., the feature dimension). As summarized in Table 5, the small BEiT with 4 to 6 layers is generally fine. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "It is also beneficial to share the patch embedding layer as well as the first two Transformer encoder layers between the small BEiT and enhancer as long as the enhancer is also ViT. We hypothesize that sharing the earlier layers can help calibrate the enhancer since the small BEiT receives the real inputs while the enhancer sees the same sources but with corrupted views. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/ee5dc80eb05b3793abbd4054926c6210fd9d335cfb82360a4506a82308a74359.jpg",
+        "table_caption": [
+            "Table 4: Ablation study: masking strategy and masking ratio. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Masking Strategy</td><td>Masking Ratio</td><td>Top-1 Acc.</td></tr><tr><td>Blockwise</td><td>40%</td><td>82.8</td></tr><tr><td>Blockwise</td><td>50%</td><td>82.9</td></tr><tr><td>Blockwise</td><td>60%</td><td>82.8</td></tr><tr><td>Random</td><td>40%</td><td>83.0</td></tr><tr><td>Random</td><td>50%</td><td>83.3</td></tr><tr><td>Random</td><td>60%</td><td>83.1</td></tr></table>",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/37fd9c891e3f63ff8b76f7ef5135f72ca6de00ce49141b1a69d3e6a1327cb30b.jpg",
+        "table_caption": [
+            "Table 5: Ablation study: depth of the small BEiT in the generator and weight sharing. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td># Enc.Layers</td><td>Weight Sharing</td><td>Top-1 Acc.</td></tr><tr><td>4</td><td>X</td><td>83.1</td></tr><tr><td>4</td><td>√</td><td>83.3</td></tr><tr><td>5</td><td>√</td><td>83.2</td></tr><tr><td>6</td><td>√</td><td>83.2</td></tr><tr><td>7</td><td>√</td><td>83.1</td></tr><tr><td>8</td><td>√</td><td>82.9</td></tr></table>",
+        "bbox": [
+            511,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/78b5233aa69e2b8710b84af8a93310904973cca210d8a5ee594e3a4fbe8b5102.jpg",
+        "table_caption": [
+            "Table 6: Ablation study: pixel reconstruction target for RESPIX pre-training objective. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>REsPIX Recon. Target</td><td>Top-1 Acc.</td></tr><tr><td>w/o norm.</td><td>82.8</td></tr><tr><td>norm.w/ non-overlap win.</td><td>83.0</td></tr><tr><td>norm. w/ sliding win.</td><td>83.3</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/c9f2e2d122de139b2a018c368ebcb283b9709621d2597891c248f8b565ae33bc.jpg",
+        "table_caption": [
+            "Table 7: Ablation study: sampling strategy for visual tokens. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Sampling Strategy</td><td>Top-1 Acc.</td></tr><tr><td>Uniform sampling</td><td>77.2</td></tr><tr><td>argmax sampling</td><td>78.5</td></tr><tr><td>softmax sampling</td><td>83.3</td></tr></table>",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Target for RESPIX. We believe an appropriate normalization technique can provide moderate hints that can help improve the enhancer’s representation quality with the RESPIX visual pretext task (see our discussion of Figure 4). As shown in Table 6, the proposed sliding window normalization improves the fine-tuning accuracy by $0 . 5 \\%$ vs. the reconstruction target without normalization, and is also $0 . 3 \\%$ better than the normalization method proposed in He et al. (2021). ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Sampling Strategy for Visual Tokens. Using discrete visual tokens to represent images enables CIM to use stochastic sampling techniques during the corrupted image’s generation process, which can greatly enrich the output set of the generator and help the enhancer generalize well. For masked image modeling, randomly masking out a portion of patch embeddings can help regularize the pre-training, while for our approach, regularization for the enhancer mainly comes from the diversity of the corrupted images, therefore regularizations such as dropout & droppath are not used in CIM. ",
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+    },
+    {
+        "type": "text",
+        "text": "As presented in Table 7, the visual token representation with simple stochastic sampling from the generator output distribution is crucial for CIM. In contrast, we find that uniform sampling from the codebook of the image tokenizer regardless of the generator distribution or argmax sampling from the distribution cannot provide meaningful or diverse samples and therefore fails to pre-train the enhancer as expected. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Image Corrupting Strategy. We find that it is crucial to use a generator with a small trainable BEiT to corrupt images in order to successfully pre-train CNN with the proposed CIM. We experiment with another generative visual pretext task for ResNet-50 pre-training, i.e., using $50 \\%$ random erasing (Zhong et al., 2020) to corrupt the input image, and the model is required to recover the erased pixels based on the visible context. We find this pretext task fails to transfer well. A parallel work Tian et al. (2022) also finds that only using hand-crafted transformations to corrupt images is not quite satisfactory in generative visual pre-training of ViT. ",
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+    {
+        "type": "table",
+        "img_path": "images/cf62d90ea51b0125ac51771087f802e651e4c0fc7f7efb54455bf3cf8b69c76b.jpg",
+        "table_caption": [
+            "Table 8: Scaling CIM pre-training to larger ResNet. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Methods</td><td>PT Epochs FT Epochs Top-1 Acc.</td><td></td><td></td></tr><tr><td>ResNet-50x2 (#params: 94M)</td><td></td><td></td><td></td></tr><tr><td>From Scratch</td><td>=</td><td>400</td><td>81.1</td></tr><tr><td>SimCLR (Chen et al., 2020b)</td><td>1000</td><td>100 /200</td><td>81.6 /82.1</td></tr><tr><td>CIM-REVDET (Ours)</td><td>300</td><td>100/200</td><td>81.7 /82.2</td></tr><tr><td>ResNet-50x4 (#params:375M)</td><td></td><td></td><td></td></tr><tr><td>From Scratch</td><td></td><td>400</td><td>80.9</td></tr><tr><td>SimCLR (Chen et al., 2020b)</td><td>1000</td><td>100</td><td>82.6</td></tr><tr><td>SimMIM (Xie et al.,2021)</td><td>300</td><td>100</td><td>81.6</td></tr><tr><td>CIM-REVDET (Ours)</td><td>300</td><td>100</td><td>82.6</td></tr></table>",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Scaling CIM to Larger CNNs. We study the scaling behavior of our CIM to larger CNNs. We choose two popular architectures in self-supervised learning literature: ResNet- $5 0 \\mathrm { x } 2$ and ResNet-50x4 (with width multipliers of $2 \\mathbf { x }$ and $4 \\mathbf { x }$ of vanilla ResNet50, respectively), and study the endto-end fine-tuning performance on ImageNet-1K in Table 8. We use an improved training recipe following Touvron et al. (2021a); Wightman et al. (2021), therefore our from ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "scratch and SimCLR baselines are much higher ( ${ \\sim } 2$ points higher) than the original results in Chen et al. (2020b). Notice that it is non-trivial to pre-train those large CNNs (e.g., ResNet-50x4 is 14 times bigger than ResNet-50 in #params). Under the end-to-end fine-tuning protocol, CIM is better than the recent MIM-based approach SimMIM and competitive with the representative Siamese model SimCLR. ",
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+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Scaling CIM to Larger ViT. We study the scaling behavior of our CIM to ViT-Large in Table 9. Indeed, our approach can give ViT-Large a better initialization compared with the random initialization, and can also achieve better performance than MoCov3 that based on the canonical Siamese framework. Meanwhile, CIM still lags behind the MIM-based BEiT. Nevertheless, we believe CIM can serve as a promising starting point for exploring unified visual pre-training of various architectures. ",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/1e98f4f2a2f34a6b30ac5a50bbf903b24ee53ebaff08915364c974e0ceeeea0e.jpg",
+        "table_caption": [
+            "Table 9: Scaling CIM pre-training for ViT-Large. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Methods</td><td>Top-1 Acc.</td></tr><tr><td>ViT-Large (#params: 304M)</td><td></td></tr><tr><td>From Scratch (He et al., 2021)</td><td>82.6</td></tr><tr><td>MoCo-v3 (Chen et al., 2021)</td><td>84.1</td></tr><tr><td>BEiT (Bao et al., 2021)</td><td>85.2</td></tr><tr><td>CIM-RESPIX (Ours)</td><td>84.3</td></tr></table>",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Limitation and Discussion. The image corrupting process of CIM still has a large room for improvement, which determines the characteristics and styles of the corrupted image distribution. The tokenizer we currently use is essentially a large CNN and adds nontrivial overhead during pre-training, i.e., the wall-clock time of 1-epoch training is about $2 \\times$ of BEiT. Other image tokenizers, such as ViT-VQGAN (Yu et al., 2021), which report much higher throughput and better generation quality, deserve an in-depth study for CIM pre-training in the future. ",
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+    {
+        "type": "text",
+        "text": "4 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Siamese Framework is the dominating self-supervised visual pre-training approach over the past few years, which typically relies on strong hand-crafted data augmentations to generate different views of the same image and learns in a contrastive manner. To maintain a large and informative negative sample set, memory banks (He et al., 2020) or large batch size (Chen et al., 2020b) is used. Follow-ups (Grill et al., 2020; Chen & He, 2021) further eliminate the requirement of using negative samples. Recent works (Caron et al., 2021; Chen et al., 2021) study self-supervised visual pre-training of ViT within Siamese frameworks. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Masked Image Modeling (MIM) learns rich visual representations via masked parts prediction by conditioning on visible context only. ViT (Dosovitskiy et al., 2020) and iGPT (Chen et al., 2020a) report the first meaningful MIM visual pre-training results. BEiT (Bao et al., 2021) greatly improves MIM’s performance via masked visual token prediction, and PeCo (Dong et al., 2021) finds injecting perceptual similarity during visual codebook learning benefits MIM pre-trained representation. Recent work (He et al., 2021; Xie et al., 2021; Wei et al., 2021) re-explore pixel / feature regression in MIM, while Li et al. (2021); Zhou et al. (2021); El-Nouby et al. (2021) incorporate MIM within Siamese frameworks. As MIM is originated in masked language modeling (Devlin et al., 2019), CIM is inspired by Clark et al. (2020). In CIM, visual-token-based MIM plays an important role during the corrupted image generation process, as the stochastic sampling ability greatly enriches the corrupted image set. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "5 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We introduce a general self-supervised visual pre-training framework with few architectural constraints for the model to be pre-trained and transferred. Unlike the mainstream Siamese pre-training methods based on strong artificial data augmentations as well as MIM pre-training relying on randomly inserting artificial [MASK] tokens to input embeddings, CIM pre-trained encoder learns from the corrupted view generated from a trainable neural network’s output distribution. Given the stochastic sampling ability, CIM defends using discrete visual token representations during pre-training to some extent. Experimental results show that our approach achieves competitive performance on canonical ViT and CNN models. We hope CIM can serve as a promising starting point for exploring flexible & unified visual representation learning of various architectures. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "ACKNOWLEDGMENT ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "This work is in part supported by the National Key Research and Development Program of China under Grant 2022YFB4500602. We would like to acknowledge Yaru Hao for the helpful discussions. ",
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+        "type": "text",
+        "text": "A APPENDIX ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            102,
+            297,
+            117
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "A.1 ADDITIONAL ANALYSIS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            133,
+            385,
+            147
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Relationship between the type of the generator and the performance of the enhancer. What makes a \"good\" generator for the enhancer? We believe there are three main factors that affect the output quality of the generator: (1) The masking strategy and masking ratio of the generator’s inputs. (2) The size / capacity of the small trainable BEiT. (3) The type of image tokenizers. ",
+        "bbox": [
+            174,
+            160,
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+            215
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "While there are many perspectives / ways to evaluate a generator, this study focuses on visual pretraining of the enhancer, so we are particularly interested in how these factors affect the enhancer’s fine-tuning performance on downstream visual recognition tasks. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Factor 1 & 2 has already been well studied in Table 4 & Table 5 respectively: either a too “weak” generator (e.g., too much masking or the size of the trainable BEiT is too small) or a too “strong” generator (e.g., too less masking or the trainable BEiT is too large) is harmful to the fine-tuning performance of the enhancer. ",
+        "bbox": [
+            174,
+            271,
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+            328
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "As for Factor 3, the image tokenizer represents a given image in the RGB domain as a permutation of discrete tokens with a fixed vocabulary size. This compact representation along with the stochastic sampling process can generate an abundant & diverse input set to feed the enhancer better. However, if the generator is too strong & robust that can always generate near ground truth output regardless of the stochastic sampling, the enhancer can hardly learn useful representations or even be wrongly penalized. ",
+        "bbox": [
+            174,
+            334,
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+            417
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "To show that, in Table 10 we study another well-established and open-sourced image tokenizer, VQGAN (Esser et al., 2021), on the ViT-B enhancer with 300 epochs pre-training & 100 epochs fine-tuning on ImageNet-1k. We also study the effects of directly using a MAE-Base model as the generator. ",
+        "bbox": [
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+            424,
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "table",
+        "img_path": "images/11722fd593ca78fd5d9b310b95d8c94bb026bc8ce78add68a2106de48bc05343.jpg",
+        "table_caption": [
+            "Table 10: Study of different generator tpye of CIM pre-training for ViT-Base. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Generator Type of CIM</td><td>Top-1 Acc.</td></tr><tr><td>MAE-style generator w/ 50% masking ratio</td><td>82.6 (-0.7)</td></tr><tr><td>BEiT-Style generator w/ VQGAN tokenizer</td><td>82.9 (-0.4)</td></tr><tr><td>BEiT-Style generator w/DALL-E tokenizer (our default seting)</td><td>83.3</td></tr></table>",
+        "bbox": [
+            259,
+            511,
+            738,
+            582
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "For the MAE-style generator, we sample RGB color values at all masked positions of the MAE decoder outputs. Since the stochastic sampling is performed on the RGB domain, only some low-level features (mainly color) can be changed and corrupted. Therefore the enhancer only learns to correct low-level attributes. ",
+        "bbox": [
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "For the BEiT-style generator w/ VQGAN tokenizer, compared with the DALL-E tokenizer used as default, the VQGAN tokenizer is trained with two additional losses, i.e., the perceptual loss (Zhang et al., 2018) as well as the GAN loss (Isola et al., 2017). These two additional losses are originally intended for high-quality image synthesis, but could make the tokenizer become too strong & robust to generate appropriate corrupted samples for the enhancer. We visualize the corrupted samples from the VQGAN tokenizer, and we find it nearly reconstructs the original input even with stochastic token sampling. Therefore the samples from the VQGAN tokenizer are not diverse enough and cannot provide rich supervision for the enhancer to learn transferable representations. ",
+        "bbox": [
+            173,
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Overall, it is hard to find a good indicator from the generator that can directly reflect and measure the representation quality of the enhancer. By now, the best way is to honestly fine-tune the pre-trained enhancer on downstream tasks. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Study of training the generator first and keeping it fixed for the enhancer’s pre-training. We tried first train the generator separately for 300 epochs and then pre-train the enhancer for another 300 epochs while keeping the generator’s weights fixed. The performance suffers from a $0 . 4 \\%$ degeneration. We hypothesize synergetic & simultaneous training provides a curriculum-like pretraining strategy for the enhancer where the generator starts off weak but gets better throughout training. ",
+        "bbox": [
+            174,
+            839,
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Additional training cost of CIM compared to simple mask prediction with the same mask ratio. We study the relationship between the pre-training time and downstream performances of different approaches for both ViTs and ConvNets in Table 11 and Table 12 respectively. ",
+        "bbox": [
+            171,
+            103,
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+            146
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "Since CIM is built upon BEiT, we choose BEiT as the masked image modeling baseline approach of ViTs. Here, we first study the ViT-B model’s 100-epoch fine-tuning performance on ImageNet-1k val set with different pre-training schedules in Table 11. The wall-clock time of 1-epoch pre-training of CIM is about $1 . 8 \\mathrm { x }$ of BEiT (CIM has an additional tokenizer decoder compared with BEiT) on the same machine. ",
+        "bbox": [
+            174,
+            151,
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+            222
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "table",
+        "img_path": "images/9f19c80d9892bf0eafbfada72334ba90039256ec6b69592291e8a2703246b3f1.jpg",
+        "table_caption": [
+            "Table 11: Study of the training cost for ViT-Base pre-training. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Methods</td><td>PT Epochs</td><td>Relative PT Time</td><td>Top-1 Acc.</td></tr><tr><td>BEiT</td><td>300</td><td>1.0x</td><td>82.9</td></tr><tr><td>BEiT</td><td>800</td><td>2.7x</td><td>83.2</td></tr><tr><td>BEiT</td><td>1600</td><td>5.3x</td><td>83.3</td></tr><tr><td>CIM</td><td>800</td><td>1.8x</td><td>83.3</td></tr><tr><td>CIM</td><td>800</td><td>4.8x</td><td>83.4</td></tr></table>",
+        "bbox": [
+            313,
+            250,
+            684,
+            353
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "In Table 12, we also study the ResNet-50x4 model’s 100-epoch fine-tuning performance on ImageNet1k val set with different pre-training schedules. We choose SimMIM as the masked image modeling baseline approach of ConvNets, for it reports the ResNet-50x4 model’s result in Appendix E of its paper. The wall-clock time of 1-epoch pre-training of CIM is about $2 . 6 \\mathbf { x }$ of SimMIM (CIM has an additional generator, including a small BEiT and a tokenizer encoder & decoder compared with SimMIM) on the same machine. ",
+        "bbox": [
+            173,
+            376,
+            825,
+            459
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "table",
+        "img_path": "images/2edaafd385f7816c24ee0c69f4e6edba89da99b65dc5010a1a3222e44ff964bb.jpg",
+        "table_caption": [
+            "Table 12: Study of the training cost for ResNet-50x4 pre-training. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Methods</td><td>PT Epochs</td><td>Relative PT Time</td><td> Top-1 Acc.</td></tr><tr><td>SimMIM</td><td>300</td><td>1.0x</td><td>81.6</td></tr><tr><td>CIM</td><td>100</td><td>0.9x</td><td>82.2</td></tr></table>",
+        "bbox": [
+            310,
+            488,
+            684,
+            546
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "These results imply that CIM can obtain better fine-tuning performance with less pre-training time compared with baseline approaches for both ViTs and ConvNets. ",
+        "bbox": [
+            173,
+            566,
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+            594
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "A.2 A NOTE ON VISUALIZATIONS IN $\\ S 2 . 2$ AND FIGURE 3 ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            612,
+            583,
+            627
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "Since there exists information loss in any form of normalization, we have to inject the original image’s information in order to visualize the enhancer output (4th column in Figure 3a). In order to comprehensively demonstrate our method’s behavior, we also include the unnormalized counterpart in Figure 3b for reference, where there is no additional information injection during visualization. ",
+        "bbox": [
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+            694
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "A.3 TRAINING AND OPTIMIZATION DETAILS ",
+        "text_level": 1,
+        "bbox": [
+            178,
+            710,
+            498,
+            726
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "The auxiliary generator and the enhancer are simultaneously trained and synergistically (rather than adversarially as GAN (Goodfellow et al., 2014)) updated. The trainable part of the generator, i.e., the small BEiT, learns a MIM objective in the same vein as in BEiT (Bao et al., 2021). Formally, given an input image’s patch embedding sequence $\\pmb { x } = ( \\pmb { x } _ { 1 } , . . . , \\pmb { x } _ { n } )$ , we randomly mask $k$ embeddings at positions $\\pmb { m } = ( m _ { 1 } , . . . , m _ { k } )$ using [MASK] token2. The resulting masked input sequence $_ { \\textbf { \\em x } }$ masked for BEiT is: ",
+        "bbox": [
+            173,
+            737,
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+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "equation",
+        "img_path": "images/42e8fc53e8f4be30937cdb6ace8fd64d90e6685bfa047e152d28d0e0a10d8902.jpg",
+        "text": "$$\n\\begin{array} { r } { m _ { i } \\sim \\mathrm { u n i f o r m } \\{ 1 , n \\} , \\mathrm { f o r } i = 1 , . . . , k , } \\\\ { \\pmb { x } ^ { \\mathrm { m a s k e d } } = \\mathrm { r e p l a c e } ( \\pmb { x } , \\pmb { m } , [ \\mathrm { M A S K } ] ) , \\quad \\quad } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            356,
+            816,
+            640,
+            856
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "where the replace $( x , m$ , [MASK]) operation denotes using the special [MASK] token to replace patch embeddings of $_ { \\textbf { \\em x } }$ at positions $_ { m }$ . The small BEiT then encodes $x ^ { \\mathrm { m a s k e d } }$ and learns to maximize ",
+        "bbox": [
+            173,
+            858,
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+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "$\\log p _ { \\mathrm { B E i T } } ( \\pmb { g } \\mid \\pmb { x } ^ { \\mathrm { m a s k e d } } )$ , i.e., the log-likelihood of the golden visual tokens $\\pmb { g } = ( g _ { 1 } , . . . , g _ { k } )$ at the masked positions $_ { \\mathbf { \\nabla } } \\mathbf { m } _ { \\mathbf { \\nabla } }$ conditioned on $x ^ { \\mathrm { m a s k e d } }$ . Notice that the golden tokens are obtained by feeding the original image to the image tokenizer encoder. ",
+        "bbox": [
+            174,
+            102,
+            825,
+            146
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "In order to generate corrupted image samples $\\mathcal { T } ^ { \\mathrm { c o r r u p t e d } }$ for the enhancer, we sample tokens’ replacements from the BEiT output distribution $p _ { \\mathrm { B E i T } }$ at each masked position $j$ of the encoded $\\pmb { x } ^ { \\mathrm { m a s k } \\bar { \\mathrm { e } } \\mathrm { d } }$ : ",
+        "bbox": [
+            169,
+            151,
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+            181
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "equation",
+        "img_path": "images/18e6b78eddd4fd2046d76c403975aa716a6ba499d341db868418ae20e32e4835.jpg",
+        "text": "$$\n\\begin{array} { r l } & { x _ { j } ^ { \\mathrm { s a m p l e d } } \\sim p _ { \\mathrm { B E i T } } ( x _ { j } ^ { \\mathrm { s a m p l e d } } \\mid x ^ { \\mathrm { m a s k e d } } ) , \\mathrm { f o r } j \\in m , } \\\\ & { x ^ { \\mathrm { c o r r u p t e d } } = \\mathrm { r e p l a c e } ( g , m , x ^ { \\mathrm { s a m p l e d } } ) , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            336,
+            188,
+            660,
+            231
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "where the replace $( \\pmb { g } , \\pmb { m } , \\pmb { x } ^ { \\mathrm { s a m p l e d } } )$ operation denotes using the sampled visual token $x ^ { \\mathrm { s a m p l e d } }$ to replace golden tokens of $\\textbf {  { g } }$ at positions $_ { m }$ . Next, the image tokenizer decoder maps $\\pmb { x } ^ { \\mathrm { c o r r u p t e d } }$ to a corrupted image $\\mathcal { T } ^ { \\mathrm { c o r r u p t e d } }$ . The whole image tokenizer is frozen (i.e., not updated throughout the pre-training phase), which directly uses the publicly available3 pre-trained DALL-E dVAE weight (Ramesh et al., 2021) following BEiT. ",
+        "bbox": [
+            173,
+            237,
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+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "The enhancer takes the corrupted image $\\mathcal { T } ^ { \\mathrm { c o r r u p t e d } }$ as input. For the RESPIX visual pretext task, the enhancer is optimized by a combination of $l _ { 1 }$ and $l _ { 2 }$ loss for pixel regression. For the REVDET variant, the enhancer is learned by binary cross-entropy loss for replaced visual token detection. The gradients of the enhancer are not back-propagated through the generator. ",
+        "bbox": [
+            173,
+            313,
+            825,
+            371
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we study CIM self-supervised pre-trained vanilla ViT (Dosovitskiy et al., 2020) and vanilla ResNet (He et al., 2016) models. The vanilla ViT models refer to the design from (Dosovitskiy et al., 2020; Touvron et al., 2021a) without further architectural change such as using relative position embeddings (Shaw et al., 2018) and LayerScale (Touvron et al., 2021b). The vanilla ResNet-50 model refers to the torchvision ResNet-50 (Paszke et al., 2019) without any architectural change. The larger ResNet-50x2 and ResNet-50x4 models follows the canonical design in SimCLR (Chen et al., 2020b). We conduct experiments on $1 6 \\times$ or $3 2 \\times$ V100 GPUs with 32GB memory. ",
+        "bbox": [
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+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "A.4 PRE-TRAINING & FINE-TUNING CONFIGURATIONS ",
+        "bbox": [
+            173,
+            103,
+            568,
+            117
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "table",
+        "img_path": "images/4807200fe7e925dbdc60b90edd5d9d60a1d6ba86cf5df067ecbafc9f4a16b409.jpg",
+        "table_caption": [
+            "A.4.1 THE IMAGENET-1K CIM PRE-TRAINING CONFIGURATIONS FOR VANILLA VIT AND RESNET MODELS ",
+            "Table 13: The ImageNet-1K CIM pre-training settings for vanilla ViT-S/16, ViT-B/16 and ResNet-50 models. Notably, the pre-training configurations are almost the same for different architectures. We implement the pre-training using the codebase of BEiT (Bao et al., 2021). Mixed precision and deepspeed acceleration are used. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Pre-training Config. (ViT &amp; ResNet)</td><td>Value</td></tr><tr><td>Optimizer</td><td>AdamW (Loshchilov &amp; Hutter, 2017)</td></tr><tr><td>Pre-training Epochs</td><td>300</td></tr><tr><td>Peak Learning Rate</td><td>1.5e-3</td></tr><tr><td>Batch Size</td><td>2048</td></tr><tr><td>Weight Decay</td><td>0.05</td></tr><tr><td>Optimizer Momentum (β1,β2)</td><td>(0.9, 0.98) (Vaswani et al., 2017)</td></tr><tr><td>Learning Rate Schedule</td><td>Cosine Decay</td></tr><tr><td>Gradient Clipping</td><td>3.0</td></tr><tr><td>Warmup Epochs</td><td>10</td></tr><tr><td>#Masked Patches for the Generator</td><td>100 to 120, Random Masking</td></tr><tr><td>The Generator&#x27;s Depth</td><td>4 to 6</td></tr><tr><td>The Generator&#x27;s Width</td><td>Same to the Enhancer (ViT), 384 (ResNet)</td></tr><tr><td>The Enhancer&#x27;s Loss Weight</td><td>1 forREVDET,1O forREsPIX</td></tr><tr><td>Data Augmentation</td><td>RandomResizedCrop Only</td></tr><tr><td>Dropout (Srivastava et al., 2014)</td><td>X X</td></tr><tr><td>Stochastic Depth (Huang et al., 2016)</td><td></td></tr><tr><td>LayerScale (Touvron et al., 2021b) Pos.Emb.in TransformerLayers</td><td>X</td></tr><tr><td></td><td>1-D Absolute Pos. Emb. (Dosovitskiy et al., 2020)</td></tr><tr><td>Patch Size</td><td>16 224</td></tr><tr><td>Pre-training Resolution</td><td></td></tr></table>",
+        "bbox": [
+            181,
+            170,
+            812,
+            493
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "table",
+        "img_path": "images/83efd4ce5e9f67758c2f3c0126b6bd809a111992d57dd19dce7c41206828fde1.jpg",
+        "table_caption": [
+            "A.4.2 THE IMAGENET-1K IMAGE CLASSIFICATION FINE-TUNING CONFIGURATIONS FOR VANILLA VIT MODELS ",
+            "Table 14: The ImageNet-1K image classification fine-tuning recipes for vanilla ViT-S/16 and ViT-B/16. We implement the fine-tuning using the codebase of BEiT (Bao et al., 2021). Mixed precision and deepspeed acceleration are used. We select the best learning rate out of $\\{ 3 \\mathrm { e } { - } 3 , 4 \\mathrm { e } { - } 3 , 5 \\mathrm { e } { - } 3 \\}$ for different sized models and pre-training objectives, and the absolute difference between the worst and the best learning rate is less than 0.3 in terms of the top-1 accuracy. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Fine-tuning Config. (ViT)</td><td>Value</td></tr><tr><td>Optimizer</td><td>AdamW (Loshchilov &amp; Hutter, 2017)</td></tr><tr><td>Fine-tuning Epochs</td><td>200 forViT-S/16,10O forViT-B/16</td></tr><tr><td>Peak Learning Rate</td><td>3e-3 forViT-B/16REsPIX,5e-3 forViT-B/16 REVDET,3e-3 or4e-3 forViT-S/16</td></tr><tr><td>Layer-wise Learning Rate Decay (Bao et al.,</td><td>0.8 (Clark et al., 2020)</td></tr><tr><td>2021) Batch Size</td><td>1024</td></tr><tr><td>Weight Decay</td><td>0.05</td></tr><tr><td>Optimizer Momentum (β1, β2)</td><td>(0.9, 0.999)</td></tr><tr><td>Learning Rate Schedule</td><td>Cosine Decay</td></tr><tr><td>Warmup Epochs</td><td>5</td></tr><tr><td>Gradient Clipping</td><td>X</td></tr><tr><td>Dropout (Srivastava et al., 2014)</td><td>X</td></tr><tr><td>Stochastic Depth (Huang et al., 2016)</td><td>0.1</td></tr><tr><td>Label Smoothing (Szegedy et al., 2016)</td><td>0.1</td></tr><tr><td>Mixup (Zhang et al., 2017)</td><td>0.8</td></tr><tr><td>CutMix (Yun et al., 2019)</td><td>1.0</td></tr><tr><td>Random Augmentation (Cubuk et al., 2020)</td><td>9 /0.5</td></tr><tr><td>Patch Size</td><td>16</td></tr><tr><td>Fine-tuning Resolution</td><td>224</td></tr><tr><td>Test Resolution</td><td>224</td></tr><tr><td>Test Crop Ratio</td><td>0.95</td></tr><tr><td>Loss Function</td><td>Cross Entropy Loss</td></tr></table>",
+        "bbox": [
+            181,
+            145,
+            810,
+            496
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "table",
+        "img_path": "images/7960520ef2506bb75f22ffff775afd2c62315d6c6cf140e221c32d08d23acb6c.jpg",
+        "table_caption": [
+            "A.4.3 THE IMAGENET-1K IMAGE CLASSIFICATION FINE-TUNING CONFIGURATIONS FOR VANILLA RESNET-50 ",
+            "Table 15: The ImageNet-1K image classification fine-tuning recipes for vanilla ResNet-50. We use the AdamW optimizer. The hyperparameter settings basically follows (Wightman et al., 2021). We implement the fine-tuning based on the codebase of BEiT (Bao et al., 2021). Mixed precision and deepspeed acceleration are used. For other self-supervised baseline approaches we compared in Table 2, we select the best learning rate out of $\\{ 5 \\mathrm { e } { - } 3 , 8 \\mathrm { e } { - } 3 , 1 2 \\mathrm { e } { - } 3 \\}$ and keep other settings unchanged. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Fine-tuning Config. (ResNet-50)</td><td>100 Epoch FT</td><td>300Epoch FT</td><td>600 Epoch FT</td></tr><tr><td>Optimizer</td><td colspan=\"3\">AdamW (Loshchilov &amp; Hutter, 2017)</td></tr><tr><td>Peak Learning Rate</td><td colspan=\"3\">12e-3</td></tr><tr><td>Layer-wise Learning Rate Decay (Bao et al., 2021)</td><td colspan=\"3\">X</td></tr><tr><td>Batch Size</td><td colspan=\"3\">2048</td></tr><tr><td>Learning Rate Schedule</td><td colspan=\"3\">Cosine Decay</td></tr><tr><td>Loss Function</td><td colspan=\"3\">Binary Cross Entropy Loss</td></tr><tr><td>Warmup Epochs</td><td colspan=\"3\">5</td></tr><tr><td>Weight Decay</td><td>0.02</td><td>0.02</td><td>0.01</td></tr><tr><td>Fine-tuning Resolution</td><td>160</td><td>224</td><td>224</td></tr><tr><td>Test Resolution</td><td></td><td>224</td><td></td></tr><tr><td>Test Crop Ratio</td><td></td><td>0.95</td><td></td></tr><tr><td>Repeated Augmentation (Berman et al.,</td><td>X</td><td>√</td><td>1</td></tr><tr><td>2019; Hoffer et al., 2019) Random Augmentation (Cubuk et al.,</td><td>6/0.5</td><td>7 /0.5</td><td>7 /0.5</td></tr><tr><td>2020)</td><td></td><td></td><td></td></tr><tr><td>Mixup (Zhang et al., 2017) CutMix (Yun et al., 2019)</td><td>0.1</td><td>0.1 1.0</td><td>0.2</td></tr><tr><td>Label Smoothing (Szegedy et al., 2016)</td><td>0.1</td><td></td><td>0.1</td></tr><tr><td>Stochastic Depth (Huang et al.,2016)</td><td></td><td>X</td><td></td></tr><tr><td></td><td>X</td><td>X</td><td>0.05</td></tr><tr><td>Dropout (Srivastava et al., 2014)</td><td></td><td>X</td><td></td></tr><tr><td>Layer-wise Learning Rate Decay</td><td></td><td>X</td><td></td></tr></table>",
+        "bbox": [
+            178,
+            145,
+            815,
+            482
+        ],
+        "page_idx": 17
+    }
+]

parse/dev/BIpTWmO_BY/BIpTWmO_BY.md

@@ -0,0 +1,322 @@
+# SLEEPER AGENT: SCALABLE HIDDEN TRIGGER BACKDOORS FOR NEURAL NETWORKS TRAINED FROM SCRATCH
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+As the curation of data for machine learning becomes increasingly automated, dataset tampering is a mounting threat. Backdoor attackers tamper with training data to embed a vulnerability in models that are trained on that data. This vulnerability is then activated at inference time by placing a “trigger” into the model’s input. Typical backdoor attacks insert the trigger directly into the training data, although the presence of such an attack may be visible upon inspection. In contrast, the Hidden Trigger Backdoor Attack achieves poisoning without placing a trigger into the training data at all. However, this hidden trigger attack is ineffective at poisoning neural networks trained from scratch. We develop a new hidden trigger attack, Sleeper Agent, which employs gradient matching, data selection, and target model re-training during the crafting process. Sleeper Agent is the first hidden trigger backdoor attack to be effective against neural networks trained from scratch. We demonstrate its effectiveness on ImageNet and in black-box settings.
+
+# 1 INTRODUCTION
+
+High-performance deep learning systems have grown in scale at a rapid pace. As a result, practitioners seek larger and larger datasets with which to train their data-hungry models. Due to the surging demand for training data along with improved accessibility via the web, the data curation process is increasingly automated. Dataset manipulation attacks exploit vulnerabilities in the curation pipeline to manipulate training data so that downstream machine learning models contain exploitable behaviors. Some attacks degrade inference across samples (Biggio et al., 2012; Fowl et al., 2021), while targeted data poisoning attacks induce a malfunction on a specific target sample (Shafahi et al., 2018; Geiping et al., 2020).
+
+Backdoor attacks are a style of dataset manipulation that induces a model to execute the attacker’s desired behavior when its input contains a backdoor trigger (Gu et al., 2017; Bagdasaryan et al., 2020). To this end, typical backdoor attacks inject the trigger directly into training data so that models trained on this data rely on the trigger to perform inference (Gu et al., 2017; Chen et al., 2017). Such threat models for classification problems typically incorporate label flips as well. However, images poisoned under this style of attack are often easily identifiable since they belong to the incorrect class and contain a visible trigger. One line of work uses only small or realistic-looking triggers, but these may still be visible and are often placed in conspicuous image regions (Chen et al., 2017; Gu et al., 2017; Li et al., 2020). Another recent method, Hidden Trigger Backdoor Attack (HTBD), instead crafts correctly labeled poisons which do not contain the trigger at all, but this feature collision method is not effective on models trained from scratch (Saha et al., 2019; Schwarzschild et al., 2020). The task of crafting backdoor poisons which simultaneously hide the trigger and are also effective at compromising deep models remains an open and challenging problem. This is especially the case in the black-box scenario, where the attacker does not know the victim’s architecture and training routine, and in the clean-label scenario where the attacker cannot flip labels.
+
+In this work, we develop the first hidden trigger attack that can reliably backdoor deep neural networks trained from scratch. Our threat model is illustrated in Figure 1. Our attack, Sleeper Agent, contains the following essential features:
+
+![](images/70312f209f976a747db4540c9abe2d4c162c1d1c40fdd8a411e48bf0f4b08231.jpg)  
+Figure 1: High-level schematic of our attack. A small proportion of slightly perturbed data is added to the training set which “backdoors” the model so that it misclassifies patched images at inference.
+
+• Gradient matching: our attack is based on recent advances which replace direct solvers for bi-level optimization problems with a gradient alignment objective (Geiping et al., 2020). However, we will see that the following technical additions are necessary to successfully backdoor neural networks (see Table 9).   
+• Data selection: we specifically poison images that have a high impact on training in order to maximize the attack’s effect.   
+• Adaptive retraining: while crafting poisons, we periodically retrain the surrogate models to better reflect how models respond to our poisoned data during training.   
+• Ensembles: Sleeper Agent incorporates an ensemble of distinct surrogate architectures in order to achieve transferability across models.   
+• Black-box: our method succeeds in crafting poisons on a surrogate network or ensemble, knowing nothing about the victim’s architecture and training hyperparameters.
+
+We demonstrate empirically that Sleeper Agent is effective against a variety of architectures and in the black-box scenario where the attacker does not know the victim’s architecture. The latter scenario has proved very difficult for existing methods (Schwarzschild et al., 2020), although it is more realistic. An added benefit of the gradient matching strategy is that it scales to large tasks. We demonstrate this property by backdooring models on ImageNet (Russakovsky et al., 2015). Some random clean and poisoned samples from the ImageNet dataset are shown in Figure 2.
+
+# 2 RELATED WORK
+
+Data poisoning attacks come in many shapes and sizes. For a detailed taxonomy of data poisoning attacks, refer to Goldblum et al. (2020). Early data poisoning attacks often focused simply on degrading clean validation performance on simple models like SVMs, logistic regression models, and linear classifiers (Biggio et al., 2012; Munoz-Gonz ˜ alez et al., 2017; Steinhardt et al., 2017). ´ These methods often relied upon the learning problems being convex in order to exactly anticipate the impact of perturbations to training data. Following these early works, attacks quickly became more specialized in their scope and approach. Modern availability attacks on deep networks degrade overall performance via gradient minimization (Shen et al., 2019), easily learnable patterns (Huang et al., 2021), or adversarial noise generated by autoencoders (Feng et al., 2019). However, these works often perturb the entire training set - an unrealistic assumption for many poisoning settings.
+
+Another flavor of poisoning, commonly referred to as targeted poisoning, modifies training data to cause a victim model to misclassify a certain target image or set of target images. Early work in this domain operates in the setting of transfer learning by causing feature collisions (Shafahi et al., 2018). Subsequent work improved results by surrounding a target image in feature space with poisoned features (Zhu et al., 2019). Follow up works further improved targeted poisoning by proposing methods that are effective against from-scratch training regimes (Huang et al., 2020; Geiping et al., 2020). These attacks remain limited in scope, however, and often fail to induce misclassification on more than one target image (Geiping et al., 2020).
+
+![](images/75aec45a53f576b60b6142a15657c76f25add464aa1ddb792aa618ad209a651c.jpg)  
+Figure 2: Sample clean source (first column), patched source (second column), clean target (third column), and poisoned target (fourth column) from the ImageNet dataset. The last column is slightly perturbed, but the perturbed and corresponding clean images are hardly distinguishable by the human eye. More visualizations can be found in the Appendix B.
+
+Adjacent to targeted data poisoning are backdoor attacks. Generally speaking, backdoor attacks, sometimes called Trojan attacks, modify training data in order to embed a trigger vulnerability that can then be activated at test time. Crucially, this attack requires the attacker to modify data at inference time. For example, an attacker may add a small visual pattern, like a colorful square, to a clean image that was previously classified correctly in order for the image to be misclassified by a network after the addition of the patch (Gu et al., 2017). However, these works can require training labels to be flipped, and/or a conspicuous patch to be added to training data.
+
+Of particular relevance to this work is a subset of backdoor attacks that are clean label, meaning that modifications to training data must not change the semantic label of that data. This is especially important because an attacker may not control the labeling method of the victim and therefore cannot rely upon techniques like label flipping in order to induce poisoning. One previous work enforces this criterion by applying patches to adversarial examples, but the patches are clearly visible, even when they are not fully opaque, and the attack fails when patches are transparent enough to be unnoticeable (Turner et al., 2019; Schwarzschild et al., 2020). Another work, “Hidden Trigger Backdoor Attacks” enforces an $\ell _ { \infty }$ constraint on the entire perturbation (as is common in the adversarial attack literature), but this method is only effective on hand selected class pairs and only works in transfer learning scenarios where the pretrained victim model is both fixed and known to the attacker (Saha et al., 2019; Schwarzschild et al., 2020). Another clean label backdoor attack hides the trigger in training data via steganography (Li et al., 2019), however this attack also assumes access to the pretrained model that a victim will use to fine tune on poisoned data. Moreover, the latter attack uses triggers that cover the entire image, and these triggers cannot be chosen by the user.
+
+In contrast to these existing methods, Sleeper Agent does not require knowledge of the victim model, the perturbations are not visible in poisoned training data, and poisons can be adapted to any patch.
+
+# 3 METHOD
+
+# 3.1 THREAT MODEL
+
+We follow commonly used threat models used in the backdoor literature (Gu et al., 2017; Saha et al., 2019). We define two parties, the attacker and the victim. We assume that the attacker perturbs and disseminates data. As in Saha et al. (2019); Geiping et al. (2020), we assume the training data modifications are bounded in $\ell _ { \infty }$ norm. The victim then trains a model on data - a portion of which has been perturbed by the attacker. Once the victim’s model is trained and deployed, we also assume that the attacker can then apply a patch to select images at test time to trigger the backdoor attack.
+
+However, we diverge from Gu et al. (2017); Saha et al. (2019) in our assumptions about the knowledge of the victim. We assume a far more strict threat model wherein the attacker does not have access to the parameters, architecture, or learning procedure of the victim. This represents a realistic scenario wherein a victim trains a randomly initialized deep network from scratch on scraped data.
+
+# 3.2 PROBLEM SETUP
+
+Formally, we aim to craft perturbations $\delta = \{ \delta _ { i } \} _ { i = 1 } ^ { N }$ to training data $\mathcal { T } = \{ ( x _ { i } , y _ { i } ) \} _ { i = 1 } ^ { N }$ for a loss function, $\mathcal { L }$ , and a surrogate network, $F$ , with parameters $\theta$ that solve the following bilevel problem:
+
+$$
+\begin{array} { r } { \underset { \delta \in \mathcal { C } } { \operatorname* { m i n } } \ \mathbb { E } _ { ( x , y ) \sim \mathcal { D } } \bigg [ \mathcal { L } \left( F ( x + p ; \theta ( \delta ) ) , y _ { t } \right) \bigg ] } \\ { \mathrm { s . t . } \ \theta ( \delta ) \in \underset { \theta } { \arg \operatorname* { m i n } } \displaystyle \sum _ { ( x _ { i } , y _ { i } ) \in \mathcal { T } } \mathcal { L } ( F ( x _ { i } + \delta _ { i } ; \theta ) , y _ { i } ) , } \end{array}
+$$
+
+where $p$ denotes the trigger, $y _ { t }$ denotes the intended target label of the attacker, and $\mathcal { C }$ denotes a set of constraints on the perturbations. Naive backdoor attacks often solve this bilevel problem by inserting $p$ directly into training data (belonging to class $y _ { t }$ ) so that the network learns to associate the trigger pattern with the desired class label. However, our threat model is more strict, which is reflected in our constraints on $\delta$ . We require that $\delta$ is bounded in $\ell _ { \infty }$ norm and that $\delta _ { i } = \mathbf { 0 }$ for all but a small fraction of indices, $i$ . WLOG, assume that the first $M \leq N$ perturbations are allowed to be nonzero. In the black-box scenario, the surrogate model, $F$ , may not resemble the victim, in terms of either architecture or training hyperparameters, and yet the attack is effective nonetheless.
+
+We stress that unlike Saha et al. (2019), our primary area of interest is not transfer learning, but rather from-scratch training. This threat model results in a more complex optimization procedure - one where simpler objectives, like feature collision, have failed (Schwarzschild et al., 2020). Due to the inner optimization problem posed in Equation 2, directly computing optimal perturbations is intractable for deep networks as it would require differentiating through the training procedure of $F$ . Thus, heuristics must be used to optimize the poisons.
+
+# 3.3 OUR APPROACH
+
+Recently, several works have proposed solving bilevel problems for deep networks by utilizing gradient alignment. Gradient alignment modifies training data to align the training gradient with the gradient of some desired objective. It has proven useful for dataset condensation (Zhao et al., 2020), as well as integrity and availability poisoning attacks (Geiping et al., 2020; Fowl et al., 2021). Unlike other heuristics like partial unrolling of the computation graph or feature collision, gradient alignment has proven to be a stable way to solve a bilevel problem that involves training a deep network in the inner objective. However, poisoning approaches utilizing gradient alignment have often come with limitations, such as poor performance on multiple target images (Geiping et al., 2020), or strict requirements about poisoning an entire dataset (Fowl et al., 2021).
+
+In contrast, we study the behaviour of a class of attacks capable of causing misclassification of a large proportion of unseen patched images of a selected class, all while modifying only a small fraction of training data. We first define the adversarial objective:
+
+$$
+\mathcal { L } _ { a d v } = \mathbb { E } _ { ( x , y ) \sim \mathcal { D } _ { s } } \bigg [ \mathcal { L } \big ( F ( x + p ; \theta ) , y _ { t } \big ) \bigg ] ,
+$$
+
+where $\mathcal { D } _ { s }$ denotes the source class distribution, $p$ is a patch that the attacker uses to trigger misclassification at test-time, and $y _ { t }$ is the intended target label. This objective is minimized when an image becomes misclassified into a desired class after the attacker’s patch is added to it. For example, an attacker may aim for a network to classify images of dogs correctly but to misclassify the same dog images as cats when a patch is added to the dog images.
+
+To achieve this behavior, we perturb training data by optimizing the following alignment objective:
+
+$$
+\mathcal { A } = 1 - \frac { \nabla _ { \theta } \mathcal { L } _ { t r a i n } \cdot \nabla _ { \theta } \mathcal { L } _ { a d v } } { \left| \left| \nabla _ { \theta } \mathcal { L } _ { t r a i n } \right| \right| \cdot \left| \left| \nabla _ { \theta } \mathcal { L } _ { a d v } \right| \right| } ,
+$$
+
+$$
+\nabla _ { \boldsymbol { \theta } } \mathcal { L } _ { t r a i n } = \frac { 1 } { M } \sum _ { i = 1 } ^ { M } \nabla _ { \boldsymbol { \theta } } \mathcal { L } \big ( F ( x _ { i } + \delta _ { i } ; \boldsymbol { \theta } ) , y _ { i } \big )
+$$
+
+is the training gradient involving the nonzero perturbations. We then estimate the expectation in Equation 3 by calculating the average adversarial loss over $K$ training points from the source class:
+
+$$
+\nabla _ { \theta } \mathcal { L } _ { a d v } = \frac { 1 } { K } \sum _ { ( x , y _ { s } ) \in \mathcal { T } } \nabla _ { \theta } \bigg ( \mathcal { L } \big ( F ( x + p ; \theta ) , y _ { t } \big ) \bigg )
+$$
+
+In our most basic attack, we begin optimizing the objective in Equation 4 by fixing a parameter vector $\theta ^ { * }$ in order to calculate $\mathcal { A }$ . This parameter vector is trained on clean data and is used to calculate the training and adversarial gradients. We then optimize using 250 steps of signed Adam. Note that while this is not a general constraint for our method, we follow the setup in Saha et al. (2019) where all poisons are drawn from a single target class. That is to say, the $M$ poisons the attacker is allowed to perturb have the form $\{ ( x _ { i } , y _ { t } ) \} _ { i = 1 } ^ { \overline { { M } } }$ .
+
+We also employ differentiable data augmentation which has shown to improve stability of poisons in Geiping et al. (2020). While gradient alignment proves more successful than other approaches to the bilevel problem, we additionally introduce two novel techniques that boost success by $> 2 5 0 \%$ :
+
+Poison Selection: Our threat model assumes the attacker disseminates perturbed images online through avenues such as social media. With this in mind, the attacker can choose which images to perturb. For example, the attacker could choose images of dogs in which to “hide” the trigger. While random selection with our objective does successfully poison victims trained from scratch, we experiment with selection by gradient norm. Because we aim to align the training gradient with our adversarial objective, source images which have larger gradients could prove to be more potent poisons. We find that choosing source poison images by taking images with the maximum training gradient norm at the parameter vector $\theta ^ { * }$ noticeably improves poison performance (see Tables 3, 9).
+
+Model Retraining: In the most straightforward version of our attack, the attacker optimizes the perturbations using fixed model parameters for a number of steps (usually 250). However, this may lead to perturbations overfitting to a clean-trained model; during a real attack a model is trained on poisoned data, but we optimize the poisons on a model that trained only with clean data. To close the gap, we introduce model retraining during the poison crafting procedure. After retraining our model on the perturbed data, we again take optimization steps on the perturbations, but this time evaluating the training and adversarial losses at the new parameter vector. We repeat this process of retraining/optimizing several times and find that this noticeably improves the success of the poisons - often boosting success by more than $2 0 \%$ (see Tables 3, 9).
+
+# 4 EXPERIMENTS
+
+In this section, we empirically test the proposed Sleeper Agent backdoor attack on multiple datasets, against black-box settings, using a benchmark, and against popular defenses.
+
+Table 1: Baseline evaluations on CIFAR-10. Perturbations have $\ell _ { \infty }$ -norm bounded above by 16/255, and poison budget is $1 \%$ of training images. Each number denotes an average (and std. error) over 24 crafting and training runs along with randomly sampled source/target class pairs.   
+
+<table><tr><td>Architecture</td><td>ResNet-18</td><td>MobileNetV2</td><td>VGG11</td></tr><tr><td>Clean validation accuracy(%)</td><td>92.31 (±0.08)</td><td>88.19 (±0.05)</td><td>89.00 (±0.03)</td></tr><tr><td>Poison validation accuracy(%)</td><td>92.16 (±0.05)</td><td>88.03 (±0.05)</td><td>88.70 (±0.04)</td></tr><tr><td>Clean source accuracy(%)</td><td>92.36 (±0.93)</td><td>88.55 (±1.64)</td><td>90.62 (±1.23)</td></tr><tr><td>Poison source accuracy(%)</td><td>91.50 (±0.88)</td><td>87.79 (±1.60)</td><td>89.45 (±1.19)</td></tr><tr><td>Triggered source accuracy(%)</td><td>12.96 (±5.40)</td><td>21.09 (±5.41)</td><td>17.97 (±4.00)</td></tr><tr><td>Attack Success Rate(%)</td><td>85.27 (±5.90)</td><td>72.92 (±6.09)</td><td>75.15 (±5.40)</td></tr></table>
+
+Table 2: The effect of poison budget. Experiments on CIFAR-10 with ResNet-18 models (He et al., 2016). Perturbations have $\ell _ { \infty } \mathrm { - n o r m } \le 1 6 / 2 5 5$ . Each number denotes an average (and std. error) over 32 crafting and training runs along with randomly sampled source/target class pairs.   
+
+<table><tr><td>Poison Budget</td><td>50 (0.1%)</td><td>100 (0.2%)</td><td>250 (0.5%)</td><td>400 (0.6%)</td><td>500 (1%)</td></tr><tr><td>Clean validation accuracy(%)</td><td>92.34 (±0.05)</td><td>92.36 (±0.04)</td><td>92.31 (±0.04)</td><td>92.15 (±0.08)</td><td>92.26 (±0.06)</td></tr><tr><td>Poison validation accuracy(%)</td><td>92.33 (±0.04)</td><td>92.34 (±0.05)</td><td>92.25 (±0.04)</td><td>92.12 (±0.06)</td><td>92.17 (±0.04)</td></tr><tr><td>Clean source accuracy(%)</td><td>93.01 (±0.69)</td><td>91.08 (±0.85)</td><td>92.43 (±0.74)</td><td>92.42 (±0.80)</td><td>92.14 (±0.78)</td></tr><tr><td>Poison source accuracy(%)</td><td>93.03 (±0.67)</td><td>90.61 (±0.86)</td><td>91.83 （±0.75)</td><td>91.88 (±0.79)</td><td>91.56 (±0.77)</td></tr><tr><td>Triggered source accuracy(%)</td><td>61.04 (±4.27)</td><td>40.07 (±5.72)</td><td>22.77 （±4.77)</td><td>15.88 (±4.91)</td><td>13.07 (±4.57)</td></tr><tr><td>Attack Success Rate(%)</td><td>24.71 (±4.10)</td><td>49.76 (±6.21)</td><td>72.48 (±5.24)</td><td>81.44 (±5.25)</td><td>85.11 (±5.04)</td></tr></table>
+
+# 4.1 BASELINE EVALUATIONS
+
+Typically, backdoor attacks are considered successful if poisoned models do not suffer from a significant drop in validation accuracy on images without triggers, but they reliably misclassify images from the source class into the target class when a trigger is applied. We begin by testing our method in the gray-box setting. In the gray-box setting, we use the same architecture but different random initialization for crafting poisons and testing. Table 1 depicts the performance of Sleeper Agent on CIFAR-10 when perturbing $1 \%$ of images in the training set with each perturbation constrained in an $\ell _ { \infty }$ -norm ball of radius 16/255. During poison crafting, the surrogate model undergoes four evenly spaced retraining periods $T = 4$ ), and we test the effectiveness of each surrogate model architecture at generating poisons for victim models of the same architecture. In subsequent sections, we will extend these experiments to the black-box setting and to an ensemblized attacker. We observe in these experiments that the poisoned models indeed achieve very similar validation accuracy to their clean counterparts, yet the application of triggers to source class images causes them to be misclassified into the target class as desired. In Table 2, we observe that Sleeper Agent can even be effective when the attacker is only able to poison a very small percentage of the training set. Note that the success of backdoor attacks depends greatly on the choice of source and target classes, especially since some classes contain very large objects which may dominate the image, even when a trigger is inserted. As a result, the variance of attack performance is high since we sample class pairs randomly. The poisoning and victim hyperparameters we use for our experiments can be found in Appendix A.
+
+The benefits of ensembling: One simple way we can improve the transferability of our backdoor attack across initializations of the same architecture is to craft our poisons on an ensemble of multiple copies of the same architecture but trained using different initializations and different batch sampling during their training procedures. In Table 3, we observe that this ensembling strategy indeed can offer major performance boosts, both with and without retraining.
+
+The black-box setting: Now that we have established the transferability of Sleeper Agent across models of the same architecture, we test on the hard black-box scenario where the victim’s architecture is completely unknown to the attacker. This setting has proven extremely challenging for existing methods (Schwarzschild et al., 2020). Table 4 contains four settings. In the first row, we simply craft the poisons on a single ResNet-18 and transfer these to other models. Second, we craft poisons on an ensemble consisting of two MobileNet-V2 and two ResNet-34 architectures and transfer to the remaining models. Third, for each architecture, we craft poisons with an ensemble consisting of the other two architectures and test on the remaining one. The second and third scenarios are ensemblized black-box attacks, and we see that Sleeper Agent is effective. In the last row, we perform the same experiment but with the testing model included in the ensemble, and we observe that a single ensemble can craft poisons that are extremely effective on a range of architectures. We choose ResNet-18, MobileNet-V2, and VGG11 as these are common and contain a wide array of structural diversity (He et al., 2016; Sandler et al., 2018; Simonyan & Zisserman, 2014).
+
+Table 3: Ensembles consisting of copies of the same architecture (ResNet-18). $S$ denotes the size of the ensemble, and $T$ denotes the retraining factor. Experiments are conducted on CIFAR-10, perturbations have $\ell _ { \infty }$ -norm bounded by 16/255, and the attacker can poison $1 \%$ of training images.   
+
+<table><tr><td>Attack</td><td>Clean validation (%)</td><td>Poison validation (%)</td><td>Attack Success Rate (%)</td></tr><tr><td>Sleeper Agent (S = 1,T = 0)</td><td>92.36 (±0.05)</td><td>92.08 （±0.08)</td><td>63.49 (±6.13)</td></tr><tr><td>Sleeper Agent (S= 2,T=0)</td><td>92.10 (±0.04)</td><td>92.12 (±0.06)</td><td>64.70 (±5.65)</td></tr><tr><td>Sleeper Agent (S = 4,T= 0)</td><td>92.14 (±0.03)</td><td>91.98(±0.05)</td><td>74.81 (±4.10)</td></tr><tr><td>Sleeper Agent (S=2,T= 4)</td><td>92.11 (±0.07)</td><td>92.08 (±0.13)</td><td>87.40(±6.23)</td></tr><tr><td>Sleeper Agent (S=4,T=4)</td><td>92.17 (±0.03)</td><td>91.81 (±0.06)</td><td>88.45 (±6.00)</td></tr></table>
+
+Table 4: Black-box attacks: First row: Attacks crafted on a single ResNet-18 and transferred. Second row: attacks crafted on MobileNet-V2 and ResNet-34 and transfered. Third row: attacks crafted on the remaining architectures excluding the victim. The ensemble used in the last row includes the victim architecture. Experiments are conducted on CIFAR-10 and perturbations have $\ell _ { \infty }$ -norm bounded above by 16/255, and the attacker can poison $1 \%$ of training images.   
+
+<table><tr><td>Attack</td><td>ResNet-18</td><td>MobileNet-V2</td><td>VGG11</td><td>Average</td></tr><tr><td>Sleeper Agent (S=1,T=4,ResNet-18)</td><td></td><td>29.10%</td><td>31.96%</td><td>29.86%</td></tr><tr><td>Sleeper Agent (S = 4,T= 0,MobileNet-V2,ResNet-34)</td><td>70.30%</td><td>一</td><td>46.48%</td><td>58.44%</td></tr><tr><td>Sleeper Agent (S= 4,T= 0, victim excluded)</td><td>63.11%</td><td>42.40%</td><td>55.28%</td><td>53.60%</td></tr><tr><td>Sleeper Agent (S= 6,T= O,victim included)</td><td>68.46%</td><td>67.28%</td><td>85.37%</td><td>73.30%</td></tr></table>
+
+ImageNet evaluations: In addition to CIFAR-10, we perform experiments on ImageNet. Table 5 contains the performance of Sleeper Agent on ImageNet where attacks are crafted and tested on randomly initialized ResNet-18 models. Perturbations are constrained in an $\ell _ { \infty }$ -norm ball of radius 16/255 - a bound seen in prior poisoning works on ImageNet (Fowl et al., 2021; Geiping et al., 2020; Saha et al., 2019). We first study the effect of re-training during poison crafting. Even performing only two equally spaced re-training periods improves the success rate significantly. Additionally, we observe that our data selection technique allows Sleeper Agent to maintain a high success rate even with a lower poison budget. Figure 2 contains visualizations of the patched sources and the crafted targets. The poisoning and victim hyperparameters from experiments can be found in Appendix A. Further visualizations and additional experiments are presented in Appendices B and C.
+
+# 4.2 COMPARISON TO OTHER METHODS
+
+There are several existing clean-label hidden-trigger backdoor attacks that claim success in settings different than ours. In order to further demonstrate the success of our method, we compare our poisons to ones generated from these methods in our more strict threat model of from-scratch training. In these experiments, poisons are generated from our attack, clean label backdoor, and hidden trigger backdoor. All poison trials have the same randomly selected source-target class pairs, the same budget, and the same $\varepsilon$ -bound (Note: clean-label backdoor originally did not use $\ell _ { \infty }$ bounds, so we adjust the opacity of their perturbations to ensure the constraint is satisfied). We then train a randomly initialized network from scratch on these poisons and evaluate success over 1000 patched target images. We test three popular network architectures and find that our attack significantly outperforms both methods and is the only backdoor method to exceed single digit success rates, confirming the findings of Schwarzschild et al. (2020) on the fragility of these existing methods. See Table 6 for full results. Note that the difference in results between Table 1 and these results may arise from saving the poisoned images and loading them into this benchmark setup.
+
+Table 5: ImageNet evaluations. Attacks are conducted on ResNet-18 models and perturbations have $\ell _ { \infty }$ -norm bounded above by 16/255. The high standard errors are due to the high variance of the sampling of source/target pairs, and limited number of runs to maintain computational feasibility.   
+
+<table><tr><td>Attack</td><td>Poison budget</td><td>Clean validation (%)</td><td>Poison validation (%)</td><td>Attack Success Rate (%)</td></tr><tr><td>Sleeper Agent (S=1,T=0)</td><td>0.05%</td><td>69.27 (±0.03)</td><td>67.87 (±0.03)</td><td>22.00 (±5.65)</td></tr><tr><td>Sleeper Agent (S=1,T=0)</td><td>0.10%</td><td>69.23 (±0.03)</td><td>67.80 (±0.04)</td><td>23.25 （±5.50)</td></tr><tr><td>Sleeper Agent (S=1,T=2)</td><td>0.05%</td><td>69.21 (±0.04)</td><td>67.84 (±0.10)</td><td>44.00(±6.73)</td></tr><tr><td>Sleeper Agent (S=1,T=2)</td><td>0.10%</td><td>69.14 (±0.03)</td><td>67.75 (±0.08)</td><td>41.00 (±14.45)</td></tr></table>
+
+Table 6: Benchmark results on CIFAR-10. Comparison of our method to popular “clean-label” attacks. Results averaged over the same source/target pairs with $\epsilon = 1 6 / 2 5 5$ and poison budget $1 \%$ .   
+
+<table><tr><td>Attack</td><td>ResNet-18</td><td>MobileNetV2</td><td>VGG11</td><td>Average</td></tr><tr><td>Hidden-Trigger Backdoor (Saha et al.,2019)</td><td>3.50%</td><td>3.76%</td><td>5.02%</td><td>4.09%</td></tr><tr><td>Clean-Label Backdoor (Turner et al., 2019)</td><td>2.78%</td><td>3.50%</td><td>4.70%</td><td>3.66%</td></tr><tr><td>Sleeper Agent (Ours)</td><td>50.72%</td><td>58.21%</td><td>57.86%</td><td>55.59%</td></tr></table>
+
+# 4.3 DEFENSES
+
+A selling point for hidden trigger backdoor attacks is that the trigger that is used to induce misclassification at test-time is not present in any training data, thus making inspection based defenses, or automated pattern matching more difficult. However, there exist numerous defenses, aside from visual inspection, that have been proposed to mitigate the effects of poisoning - both backdoor and other attacks. We test our method against a number of popular defenses.
+
+Spectral Signatures: This defense, proposed in Tran et al. (2018), aims to filter a pre-selected amount of training data based upon correlations with singular vectors of the feature covariance matrix. This defense was originally intended to detect triggers used in backdoor attacks.
+
+Activation Clustering: Chen et al. (2018) cluster activation patterns to detect anomalous inputs.   
+Unlike the spectral signatures defense, this defense does not filter a pre-selected volume of data.
+
+DPSGD: Poison defenses based on differentially private SGD (Abadi et al., 2016) have also been proposed (Hong et al., 2020). Differentially private learning inures models to small changes in training data, which provably imbues robustness to poisoned data.
+
+Data Augmentations: Recent work has suggested that strong data augmentations, such as mixup, break data poisoning (Borgnia et al., 2021). This has been confirmed in recent benchmark tests which demonstrate many poisoning techniques are brittle to slight changes in victim training routine (Schwarzschild et al., 2020). We test against mixup augmentation (Zhang et al., 2017).
+
+STRIP: Gao et al. (2019) propose to add strong perturbations by superimposing input images at test time to detect the backdoored inputs based on the entropy of the predicted class distribution. If the entropy is lower than a predefined threshold, the input is considered backdoored and is rejected.
+
+NeuralCleanse: Wang et al. (2019) propose a defense designed for traditional backdoor attacks by reconstructing the maximally adversarial trigger used to backdoor a model. While this defense was not designed for hidden trigger backdoor attacks, we experiment with this as a detection defense wherein we test whether NeuralCleanse can detect the backdoored class. This modification is denoted by NeuralCleanse\*. In our trials, NeuralCleanse\* does not detect any of the backdoored classes - as determined by taking the maximum mask MAD (see Wang et al. (2019)).
+
+We find that across the board, all of these defenses exhibit a robustness-accuracy trade-off. Many of these defenses do not reliably nullify the attack, and defenses that do degrade attack success also induce such a large drop in validation accuracy that they are unattractive options for practitioners. For example, to lower the attack success to an average of $1 3 . 1 4 \%$ , training with DPSGD degrades natural accuracy on CIFAR-10 to $7 0 \%$ . See Table 7 for the complete results of these experiments.
+
+# 4.4 SLEEPER AGENT CAN POISON IMAGES IN ANY CLASS
+
+Typical backdoor attacks which rely on label flips or feature collisions can only function when poisons come from the source and/or target classes (Saha et al., 2019; Turner et al., 2019). This restriction may be a serious limitation in practice. In contrast, we show that Sleeper Agent can be
+
+Table 7: Defenses. Experiments are conducted on CIFAR-10 with ResNet-18 models, perturbations have $\ell _ { \infty }$ -norm bounded above by 16/255, and poison budget is $1 \%$ of training images.   
+
+<table><tr><td>Defense</td><td>Attack Success Rate (%)</td><td>Clean Validation Accuracy (%)</td></tr><tr><td>Spectral Signatures</td><td>37.17 (±10.10)</td><td>89.94 (±0.19)</td></tr><tr><td>Activation Clustering</td><td>15.17 (±5.38)</td><td>72.38 (±0.48)</td></tr><tr><td>DPSGD</td><td>13.14 (±4.49)</td><td>70.00 (±0.17)</td></tr><tr><td>Data Augmentation</td><td>69.75 (±10.77)</td><td>91.32 (±0.12)</td></tr><tr><td>STRIP</td><td>62.68 (±4.90)</td><td>92.23 (±0.05)</td></tr><tr><td>NeuralCleanse*</td><td>53.20 (±10.49)</td><td>91.92 (±0.12)</td></tr></table>
+
+effective even when we poison images drawn from all classes. To take advantage of our data selection strategy, we select poisons with maximum gradient norm across all classes. Table 8 contains the performance of Sleeper Agent in the aforementioned setting.
+
+Table 8: Random poisons. Experiments are conducted on CIFAR-10 with ResNet-18 models. Perturbations have $\ell _ { \infty }$ -norm bounded above by $1 6 / 2 5 5$ and poisons are drawn from all classes. Each number denotes an average (and standard error) over 16 independent crafting and training runs along with randomly sampled source/target class pairs.   
+
+<table><tr><td>Attack</td><td>Poison budget</td><td>Attack Success Rate (%)</td></tr><tr><td>Sleeper Agent (S = 1,T= 4)</td><td>1%</td><td>41.90 (±7.16)</td></tr><tr><td>Sleeper Agent (S=1,T= 4)</td><td>3%</td><td>66.51 (±6.90)</td></tr></table>
+
+# 4.5 ABLATION STUDIES
+
+Here we analyze the importance of each technique in our algorithm via ablation studies. We focus on three aspects of our method: 1) patch location, 2) retraining during poison crafting, 3) poison selection. Table 9 details several combinations and their effects on poison success. We find that randomizing patch location improves poisoning success, and both retraining and data selection based on maximum gradient significantly improve poison performance. Combining all three boosts poison success more than four-fold. See Section 3.3 for a description of these techniques. Additional experiments and more ablation studies can be found in the Appendix C.
+
+Table 9: Ablation studies. Investigation the effects of random patch-location, retraining, and data selection. Experiments are conducted on CIFAR-10 with ResNet-18 models, perturbations have $\ell _ { \infty }$ -norm bounded above by 16/255, and poison budget is $1 \%$ of training images.   
+
+<table><tr><td>Attack Setup</td><td>Attack Success Rate (%)</td></tr><tr><td>Fix patch-location (bottom-right corner)</td><td>19.25 (±3.01)</td></tr><tr><td>Random patch-location</td><td>33.95 (±4.57)</td></tr><tr><td>Randompatch-location+retraining</td><td>59.42 (±5.78)</td></tr><tr><td>Randompatch-location+ data selection</td><td>63.49 (±6.13)</td></tr><tr><td>Random patch-location + retraining + data selection</td><td>85.27 (±5.90)</td></tr></table>
+
+# 5 CONCLUSION
+
+In this work, we develop the first hidden-trigger backdoor attack that is effective against deep networks trained from scratch. This is a challenging setting for backdoor attacks, and existing attacks typically operate in less strict settings. Nonetheless, we choose the strict setting because practitioners often train networks from scratch in real-world applications, and patched poisons may be easily visible upon human inspection. In order to accomplish the above goal, we use a gradient matching objective as a surrogate for the bilevel optimization problem, and we add features such as re-training and data selection in order to significantly enhance the performance of our method, Sleeper Agent.
+
+# REPRODUCIBILITY STATEMENT
+
+Our full implementation and instructions needed to reproduce the experimental results are included in the supplementary materials, and we explain the training details, models, hyperparameters, and computational resources in Appendix A.
+
+# ETHICS STATEMENT
+
+In this work, we illuminate a new scalable backdoor attack that could be used to stealthily compromise security-critical systems. We hope that by highlighting the potential danger of this nefarious threat model, our work will give rise to stronger defenses and will encourage caution on the part of practitioners.
+
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+
+# APPENDIX
+
+# A IMPLEMENTATION DETAILS
+
+The most challenging setting for evaluating a backdoor attack involves training a model from scratch. It is crucial to compute the average attack success rate on all patched source images in the validation set to evaluate effectiveness reliably. Following the discussion above, for all experiments, we select random source-target pairs. During training, we add our patch to all images from the source class in the training set. To compute the attack success rate, followed by Geiping et al. (2020), we measure the average rate at which patched source images are successfully classified as the target class. To be consistent and to provide a fair comparison to Saha et al. (2019), we use a random patch selected from Saha et al. (2019). Our choice of patch size in the baseline experiments is the same as Saha et al. (2019), which is, $8 \times 8$ for CIFAR-10 $6 . 2 5 \%$ of the pixels) and $3 0 \times 3 0$ for the ImageNet $( 1 . 7 9 \%$ of the pixels). Figure 3 (right) shows the patch we utilize in all of our experiments. Note that the choice of the patch in our implementation is not essential. To show this, we conduct the same baseline evaluation discussed in 4.1 using a random patch generated using a Bernoulli distribution. From table 10, we observe that the choice of the patch does not affect Sleeper Agent’s success rate.
+
+![](images/b538020ce551a981a529acbe4c29ae93e54dcf906579ac2962fb82b513cd6513.jpg)  
+Figure 3: Sample random patch (left) and HTBD patch (right)
+
+Table 10: Baseline evaluations using random patches on CIFAR-10. Perturbations have $\ell _ { \infty }$ -norm bounded above by 16/255, and poison budget is $1 \%$ of training images. Each number denotes an average (and standard error) over 24 independent crafting and training runs along with randomly sampled source/target class pairs. Each run has a unique patch generated randomly. Figure 3 (left) shows a sample random patch we use for the experiments presented in this table.
+
+<table><tr><td>Architecture</td><td>ResNet-18</td></tr><tr><td>Clean validation accuracy(%)</td><td>92.16 (±0.08)</td></tr><tr><td>Poison validation accuracy(%)</td><td>92.00 (±0.07)</td></tr><tr><td>Clean source accuracy(%)</td><td>92.55 (±0.98)</td></tr><tr><td>Poison source accuracy(%)</td><td>91.77 (±1.09)</td></tr><tr><td>Triggered source accuracy(%)</td><td>14.86 (±5.06)</td></tr><tr><td>Attack Success Rate(%)</td><td>82.05 (±5.80)</td></tr></table>
+
+# A.1 MODELS AND HYPERPARAMETERS
+
+For our evaluations we use ResNet-18, ResNet-34, MobileNet-v2, and VGG11 (He et al., 2016; Sandler et al., 2018; Simonyan & Zisserman, 2014). For training ResNet-18 and ResNet-34, we use initial learning rate 0.1, and for MobileNet-v2 and VGG11, we use initial learning rate 0.01. We schedule learning rate drops at epochs 14, 24, and 35 by a factor of 0.1. For all models, we employ SGD with Nesterov momentum, and we set the momentum coefficient to 0.9. We use batches of 128 images and weight decay with a coefficient of $4 \times 1 0 ^ { - 4 }$ . For all CIFAR-10 experiments, we train and retrain for 40 epochs, and for validation, we train the re-initialized model for 80 epochs. For the ImageNet experiments, we employ pre-trained models from torchvision to start crafting, and for retraining and validation, we apply a similar procedure explained: training for 80 epochs for both retraining and validation while we schedule learning rate drops at epochs 30, 50, and 70 by a factor of 0.1. To incorporate data augmentation, for CIFAR-10, we apply horizontal flips with probability 0.5 and random crops of size $3 2 \times 3 2$ with zero-padding of 4. And for the ImageNet, we use the following data augmentations: 1) resize to $2 5 6 \times 2 5 6 , 2$ ) central crop of size $2 2 4 \times 2 2 4$ , 3) horizontal flip with probability 0.5, 4) random crops of size $2 2 4 \times 2 2 4$ with zero-padding of 28. Our complete implementation code is attached.
+
+![](images/cf4abcc4d5fc3d85123c52ff5a9ee9334b047b126a9cddd9a10bf21ae27f6497.jpg)  
+Figure 4: Average poisoning time for various Sleeper Agent setups. All experiments are conducted on CIFAR-10 with ResNet-18 models. Perturbations have $\ell _ { \infty }$ -norm bounded above by 16/255, and the poison budget is $1 \%$ of training images.
+
+# A.2 RUNTIME COST
+
+We use two NVIDIA GEFORCE RTX 2080 Ti GPUs for baseline evaluations on CIFAR-10 and four of the aforementioned GPUs for ImageNet baseline evaluations. Figure 4 shows the time cost of the Sleeper Agent with different settings.
+
+# B VISUALIZATIONS
+
+In this section, we present more triggered source and poisoned targets drawn from the ImageNet dataset. Figures 5 and 6 show patched sources and poisoned targets generated by Sleeper Agent. We observe that the generated perturbed images and their corresponding clean images are hardly distinguishable by the human eye.
+
+# C ADDITIONAL EXPERIMENTS
+
+In this section, we present additional experiments.
+
+# C.1 PATCH SIZE
+
+To further investigate the effect of patch size on the attack success rate, we perform the baseline evaluation discussed in 4.1 using different patch sizes. From Table 11, we observe that by poisoning only $0 . 0 5 \%$ of the training set and using a larger patch, we can effectively poison ImageNet. Furthermore, by using a proper amount of perturbation, Sleeper Agent works well with the smaller patches. Visualizations of patched sources using patch size of $4 5 \times 4 5$ are shown in Figure 6.
+
+# C.2 ARCHITECTURE
+
+Our experiments show that Sleeper Agent works well on other architectures. To explore this, we conduct our ImageNet baseline experiments on MobileNet-v2. Table 12 depicts the performance of Sleeper Agent on MobileNet-v2 when perturbing $0 . 0 5 \%$ of images in the ImageNet training set with each perturbation constrained in an $\ell _ { \infty }$ -norm ball of radius 16/255.
+
+![](images/4607f687feb0e305f7242623c1ee6c998dc3e91cb8939487711c6781585e3464.jpg)  
+Figure 5: Sample clean source (first column), patched source (second column), clean target (third column), and poisoned target (fourth column) from the ImageNet dataset. Perturbations have $\ell _ { \infty }$ - norm bounded above by 16/255, and the patch size is $3 0 \times 3 0$ .
+
+![](images/9ec18b1b2f7ec99bb99cc6c35bccc044ee6422f9528580a4846a808823edf98e.jpg)  
+Figure 6: Sample clean source (first column), patched source (second column), clean target (third column), and poisoned target (fourth column) from the ImageNet dataset. Perturbations have $\ell _ { \infty }$ - norm bounded above by 16/255, and the patch size is $4 5 \times 4 5$ .
+
+Table 11: The effect of patch size. Experiments are conducted on CIFAR-10 and ImageNet datasets with ResNet-18 models.   
+
+<table><tr><td>Attack</td><td>Dataset</td><td>Poison budget</td><td>Patch size</td><td>loo-norm</td><td>Attack Success Rate (%)</td></tr><tr><td>Sleeper Agent (S = 1,T = 4)</td><td>CIFAR-10</td><td>1%</td><td>6×6</td><td>20/255</td><td>64.78</td></tr><tr><td>Sleeper Agent (S = 1, T= 4)</td><td>CIFAR-10</td><td>1%</td><td>8×8</td><td>16/255</td><td>85.27</td></tr><tr><td>Sleeper Agent (S=1,T=2)</td><td>ImageNet</td><td>0.05%</td><td>25×25</td><td>16/255</td><td>38.00</td></tr><tr><td>Sleeper Agent (S=1,T=2)</td><td>ImageNet</td><td>0.05%</td><td>25×25</td><td>24/255</td><td>52.00</td></tr><tr><td>Sleeper Agent (S=1,T=2)</td><td>ImageNet</td><td>0.05%</td><td>30×30</td><td>16/255</td><td>44.00</td></tr><tr><td>Sleeper Agent (S =1,T= 2)</td><td>ImageNet</td><td>0.05%</td><td>45×45</td><td>16/255</td><td>50.50</td></tr></table>
+
+Table 12: ImageNet evaluations on MobileNet-v2. Perturbations have $\ell _ { \infty }$ -norm bounded above by 16/255, and the patch size is $3 0 \times 3 0$ .   
+
+<table><tr><td>Attack</td><td>Poison budget</td><td></td><td>Patch sizeAttack Success Rate (%)</td></tr><tr><td>Sleeper Agent (S=1, T=2)</td><td>0.05%</td><td>30</td><td>41.00</td></tr></table>
+
+# C.3 RETRAINING FACTOR
+
+Table 13 shows the effect of the retraining factor on the attack success rate on the CIFAR-10 dataset. As can be observed from the table, for $T$ larger than 4, we do not see a considerable improvement in the attack success rate. Since increasing $T$ is costly, we choose $T = 4$ as it simultaneously gives us a high success rate and is also significantly faster than $T = 6$ and $T = 8$ . We observe that even with $T = 4$ , the attack success rate is above $9 5 \%$ in most trials.
+
+Table 13: Ablation studies. Investigation of the effects of retraining factor $T$ . Experiments are conducted on CIFAR-10 with ResNet-18 models, perturbations have $\ell _ { \infty }$ -norm bounded above by 16/255, and the poison budget is $1 \%$ of the training images.   
+
+<table><tr><td>Retraining factor</td><td>T= 2</td><td>T=4</td><td>T=6</td><td>T=8</td></tr><tr><td>Attack Success Rate (%)</td><td>70.66 (±6.66)</td><td>84.64 (±6.64)</td><td>84.95 (±6.42)</td><td>86.48 (±6.26)</td></tr></table>

parse/dev/aNWiwR2HiOs/aNWiwR2HiOs.md

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+# MEASURING ASYMMETRIC GRADIENT DISCREPANCY IN PARALLEL CONTINUAL LEARNING
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+In Parallel Continual Learning (PCL), the parallel multiple tasks start and end training unpredictably, thus suffering from training conflict and catastrophic forgetting issues. The two issues are raised because the gradients from parallel tasks differ in directions and magnitudes. Thus, in this paper, we formulate the PCL into a minimum distance optimization problem among gradients and propose an explicit Asymmetric Gradient Distance (AGD) to evaluate the gradient discrepancy in PCL. AGD considers both gradient magnitude ratios and directions, and has a tolerance when updating with a small gradient of inverse direction, which reduces the imbalanced influence of gradients on parallel task training. Moreover, we propose a novel Maximum Discrepancy Optimization (MaxDO) strategy to minimize the maximum discrepancy among multiple gradients. Solving by MaxDO with AGD, parallel training reduces the influence of the training conflict and suppresses the catastrophic forgetting of finished tasks. Extensive experiments validate the effectiveness of our approach on three image recognition datasets.
+
+# 1 INTRODUCTION
+
+Continual Learning (CL) (Kirkpatrick et al., 2017; Li & Hoiem, 2017; Lopez-Paz & Ranzato, 2017), aims to continuously learn new knowledge from a sequence of tasks with non-overlapping data streams over a lifelong time. In the era of Internet of Things (IoT), people are using many smart devices, where data and tasks would be accessed by the learning system at any time. It is necessary for a CL system to respond to parallel data streams from multiple devices. We study Parallel Continual Learning (PCL), as shown in Fig. 1, in which an unfixed number of tasks are trained in a parallel way at any time. Specifically, according to the access time of each task, PCL builds an adaptive number of parallel data pipes, thus enabling instant response to new-coming tasks without pending.
+
+Due to the parallel data streams from different tasks, PCL suffers from not only the catastrophic forgetting but the training conflict among parallel tasks. Most existing methods in CL are proposed to tackle the catastrophic forgetting (French, 1999; Kirkpatrick et al., 2017) of any finished tasks, including regularization-based (Kirkpatrick et al., 2017; Chaudhry et al., 2018; Dhar et al., 2019; Zenke et al., 2017; Aljundi et al., 2018), rehearsal-based (Lopez-Paz & Ranzato, 2017; Chaudhry et al., 2019; Guo et al., 2019; Atkinson et al., 2018; Shah et al., 2018; Pomponi et al., 2020), and architecture-based (Mallya et al., 2018; Yoon et al., 2017; Rusu et al., 2016; Rosenfeld & Tsotsos, 2018) methods. In PCL, the training processes of different tasks are diverse, i.e., each task starts and ends training unpredictably (See Fig. 1). Thereby the gradient from different task differs in direction and magnitude (Yu et al., 2020) and may be neutralized. The gradient discrepancies lead to catastrophic forgetting and training conflict issues, which may fail the learning of some tasks. At any time in PCL, therefore, we present that the problem can be formulated to find an optimal gradient in a minimum distance multi-objective optimization, where each objective is to minimize the distance to a target gradient. In general, the distance metric is proportional to the effect of the optimal gradient on the corresponding task.
+
+In most situations, the mentioned distance metric $D$ between gradients is set to symmetric intuitively, such as the Euclidean distance and cosine distance. In other words, we usually have $D ( \mathbf { x } , \mathbf { y } ) \dot { = }$ $D ( \mathbf { y } , \mathbf { x } )$ for any $\mathbf { x }$ and y. However, the gradient influence is imbalanced among parallel tasks in the gradient descent. For example in Fig. 1, at the marked time, we have three gradients with diverse directions and magnitudes, and updating with any of them provides different influences to the other two. In the minimum distance problem, the optimal solution should have the minimum negative influence on all parallel tasks, but using symmetric metrics means the influences are optimized indistinguishably at the same time. Due to the fact that the gradients are with wide differences, the solution may have large biases, which would get the near-fitting task out of its local minimum but has less impact on a new-coming task.
+
+![](images/dab404c9ad79cca494594c6623c6cf82260916fb7e75be74a652d756a031058f.jpg)  
+Figure 1: Overview of the proposed method in PCL. Left: PCL trains parallel tasks according to their access time without pending. Middle: At any time, gradients from different tasks (corresponding colors) have unpredicted direction and magnitude (the length of vectors). Right: We formulate PCL into a min-distance problem and propose an asymmetric distance for effective optimization.
+
+To measure the gradient discrepancy, we hold the opinion that the distance metric in the min-distance problem should be asymmetric. First, though the metric is bound up with both the gradient magnitude and direction, the influences on model training from gradients should be asymmetric, where the model should have more tolerance to small gradients even if they indicate an inverse direction. Second, because gradients are with different magnitudes, the discrepancy between two large gradients is often set to larger than that between small gradients when using symmetric distance, such as Euclidean distance. Directly optimizing using magnitude-aware distance values may lead to the solution close to large gradients and thus hinder the catastrophic forgetting of old tasks. To mitigate the bias from the magnitude difference, it is better to employ the magnitude ratio instead of magnitude itself.
+
+Motivated by this, in this paper, we propose an explicit measurement for the learning from gradient discrepancy in PCL, named Asymmetric Gradient Distance (AGD), which considers gradient magnitude ratios and directions, and sets a tolerance for smaller gradients. As shown in Fig. 1, the proposed AGD is used in solving the minimum distance problem with multiple gradients from parallel tasks. Then, we propose an effective optimization strategy for minimizing the gradient discrepancy to avoid self-interference. We name the strategy Maximum Discrepancy Optimization (MaxDO), which minimizes the maximum discrepancy from each gradient to the others. Moreover, to address the catastrophic forgetting issue, we follow the rehearsal strategy (Lopez-Paz & Ranzato, 2017) in traditional CL and build an extra memory data stream. The rehearsal data stream is used to provide a gradient of finished tasks in MaxDO. Solving by MaxDO with AGD, parallel training mitigates the impacts of the diverse training process and slows the catastrophic forgetting of finished tasks. Extensive results on three datasets show the superiority and effectiveness of our approach.
+
+Our main contributions are three-fold:
+
+(1) For the first time, we formulate the PCL into a minimum distance problem and compare symmetric and asymmetric distances. Considering the influence of gradient on task training, we show that symmetric metrics are not effective in solving the problem and suggest asymmetric metrics.   
+(2) We propose an asymmetric metric, named AGD, to evaluate the gradient discrepancy, which is proportional to the gradient magnitude ratios and directions. AGD takes the diverse training process into account and measures the imbalance of gradient influence on task training.   
+(3) We propose a MaxDO strategy for minimizing gradient discrepancy of different tasks, which maximumly reduces the asymmetric discrepancy from a gradient to the others. MaxDO avoids the self-interference among gradients and reduces the training conflict and catastrophic forgetting.
+
+# 2 RELATED WORK
+
+Continual Learning (CL) represents receiving data from new domains continually. In traditional CL, the new domains show up one by one, say serial CL. CL methods can be classified into three kinds. (1) Rehearsal (Lopez-Paz & Ranzato, 2017; Chaudhry et al., 2019; Guo et al., 2019; Atkinson et al., 2018; Shah et al., 2018; Pomponi et al., 2020), which saves or generates data of old tasks for retraining together with the current training. (2) Regularization (Kirkpatrick et al., 2017; Chaudhry et al., 2018; Dhar et al., 2019; Zenke et al., 2017; Aljundi et al., 2018; Farajtabar et al., 2020), which leverages extra regularization terms to consolidate previous knowledge when learning new tasks. (3) Dynamic architecture (Mallya et al., 2018; Yoon et al., 2017; Rusu et al., 2016; Rosenfeld & Tsotsos, 2018), which freezes task-specific parameters and grows new branches for new tasks automatically. However, most of the existing CL methods are designed for reducing catastrophic forgetting in the serial scenario. Contrastively, in PCL, we need to tackle not only catastrophic forgetting but training conflict among parallel tasks, which is somehow related to multi-task learning.
+
+Multi-Task Learning (MTL) (Caruana, 1997) is used to address multiple tasks with a single model from one to many domains. Traditional MTL solutions can be mainly grouped into feature-based and parameter-based approaches (Zhang & Yang, 2021). The feature-based approaches focus on learning common feature representations for multiple tasks (Maurer et al., 2013; Wang & Ye, 2015). The parameter-based approaches use model parameters in a task to help learn model parameters in other tasks, such as task clustering (Thrun & O’Sullivan, 1996; Barzilai & Crammer, 2015) and decomposition (Jalali et al., 2010). In recent years, some MTL methods formulate the problem into finding an optimal gradient for updating and can be categorized into three types. (1) Learning-based methods (Chen et al., 2018), which learn a set of weights by backpropagation. (2) Solving-based methods (Sener & Koltun, 2018; Liu et al., 2021), solve the problem by finding an optimal gradient that is not dominated by the gradient from any task. (3) Calculating-based methods (Liu et al., 2019; Javaloy & Valera, 2021; Chen et al., 2020; Wang et al., 2020; Yu et al., 2020; Groenendijk et al., 2021; Lin et al., 2021) compute the gradient weights by combining gradients or losses of all tasks. Inspired by MTL, we also formulate the problem into finding an optimal gradient. Specifically, we consider the optimal gradient should have a small distance to all gradients.
+
+Asymmetric Metric. In most situations, the distance is set to symmetric, e.g., the Euclidean distance. However, the symmetric metric is not always suitable for finding the optimal gradient (see the next section for details). Asymmetric metric (Collins & Zimmer, 2007; Mennucci, 2013), also known as quasi-metric (Collins & Zimmer, 2007) or pseudo metric (Fiol, 2001; Cagliari et al., 2015) is a generalization of a metric but the symmetry axiom is eliminated in the definition of metric spaces. A classical example of using asymmetric metric is the taxicab geometry topology including one-way streets, where a path from point A to B has different streets compared to a path from B to A. In this paper, we propose to measure the gradient discrepancy using an asymmetric metric and raise a novel optimization strategy to minimize the maximum discrepancy.
+
+# 3 OUR APPROACH
+
+# 3.1 PARALLEL CONTINUAL LEARNING
+
+On a timeline, given a sequence of $T$ tasks with parallel data streams $\{ \mathcal { D } _ { 1 } , \cdot \cdot \cdot , \mathcal { D } _ { T } \}$ for continual training, and each data stream can be accessed and suspended at any time. For simplest, we assume each data stream is i.i.d., and tasks are accessed in order from 1 to $T$ and there exists no real gap that no data stream flows on the timeline. Note that traditional CL is an edge situation of PCL that all tasks are nose-to-tail. A PCL model contains a shared backbone with parameter $\pmb \theta$ to learn task-agnostic knowledge and adaptively incremental number of task-specific classifiers with parameters $\theta _ { i }$ . When a new task is accessed, a corresponding task-specific classifier will be constructed.
+
+In PCL, a task will be forgotten by learning any other tasks when its data stream ends. To avoid forgetting, we leverage the popular rehearsal strategy (Lopez-Paz & Ranzato, 2017; Chaudhry et al., 2019; Guo et al., 2019; Atkinson et al., 2018; Shah et al., 2018; Pomponi et al., 2020) in our training. Rehearsal builds an extra data stream sampled from all seen tasks and retrains them to suppress the forgetting of finished tasks. For convenience, we denote the rehearsal data stream as $\mathcal { D } _ { 0 }$ . At time $t$ , we use $\mathcal { T } _ { t }$ to represent the activated data streams (including $\mathcal { D } _ { 0 }$ ). Together with the rehearsal data stream, PCL training yields the following dynamic multi-objective empirical risk minimization:
+
+$$
+\begin{array} { r } { \operatorname* { m i n } _ { \pmb { \theta } , \{ \pmb { \theta } _ { i } | i \in \mathcal { T } _ { t } \} } \qquad \{ \ell _ { i } \left( \mathcal { D } _ { i } \right) | i \in \mathcal { T } _ { t } \} . } \end{array}
+$$
+
+Because the task-specific classifiers are updated by their own gradients $\pmb { \theta } _ { i }  \pmb { \theta } _ { i } - \alpha _ { i } \nabla _ { \pmb { \theta } _ { i } } \ell _ { i }$ $\forall i \in \mathcal { T } _ { t } ,$ ) with step size $\alpha _ { i }$ , we focus on the update of the shared backbone $\pmb { \theta }$ . At any PCL step, the goal of dynamic MOO is to optimize multiple objectives simultaneously while updating only once, and the only update of the shared parameters depends on the gradients of all in-training tasks. In PCL, the update of the shared parameters at any time depends on the gradients of all in-training tasks. It will exit an uncertain number of tasks, and each task will provide a task-specific gradient on the shared parameter $\pmb \theta$ . Let $\mathbf { g } _ { i } = \nabla _ { \pmb { \theta } } \ell _ { i }$ and $\alpha$ be a step size for optimization. The problem of the backbone update can be formulated as follows:
+
+![](images/81e909ddfaad7b96c9f08506433298ba91b10019d253f50fe028c1e454499d3e.jpg)  
+angle (i.e., Figure 2: The measures of two gradient discrepancy from $\angle \mathbf { x } , \mathbf { y } )$ between $\mathbf { x }$ and $\mathbf { y }$ , and the magnitude ratio $\mathbf { x }$ to y. Note that the $\frac { \| \mathbf { x } \| } { \| \mathbf { y } \| }$ , respectively. (a) Cosine distance; $x$ - and -axes are the (b) Euclidean distance where $\| \mathbf { y } \| = 0 . 2$ as an example; (c) Asymmetric gradient distance.
+
+$$
+\mathbf { \theta } \theta \gets \theta - \alpha \mathbf { d } ^ { * } , \quad \mathrm { w h e r e } \ \mathbf { d } ^ { * } = f \big ( \{ \mathbf { g } _ { i } | \forall i \in \mathcal { T } _ { t } \} \big ) .
+$$
+
+The key question is how to compute the optimal gradient $\mathbf { d } ^ { * }$ via the function $f ( \cdot )$ . In this paper, we define the function $f ( \cdot )$ as a min-distance multi-objective problem by minimizing the gradient distance from all in-training tasks:
+
+$$
+\begin{array} { r } { \mathbf { d } ^ { * } = \arg \operatorname* { m i n } _ { \mathbf { d } } \quad \{ D ( \mathbf { d } , \mathbf { g } _ { i } ) \ : | \ : \forall i \in \mathcal { T } \} , } \end{array}
+$$
+
+where we need to identify what distance metric $D$ is used to measure gradient discrepancy. The motivation of Eq. (3) is that for the task $i$ in PCL, its own gradient $\mathrm { g } _ { i }$ is the most qualified update direction for itself. The solution $\mathrm { d } ^ { * }$ should be as close to every gradients as possible.
+
+# 3.2 MEASURING ASYMMETRIC GRADIENT DISCREPANCY
+
+To measure the gradient discrepancy, the Euclidean Distance (EuDist, $D ( \mathbf { x } , \mathbf { y } ) = \| \mathbf { x } - \mathbf { y } \| \in [ 0 , \infty ) \}$ ) and Cosine Distance (CosDist, D(x, y) = 1 − x>ykxkkyk are the two most popular choices. Both of them are symmetric, i.e., $D ( \mathbf { x } , \mathbf { y } ) = D ( \mathbf { y } , \mathbf { x } )$ . A symmetric metric $D ( \mathbf { x } , \mathbf { y } )$ means the forward influence $\mathbf { \bar { x } }$ to y) and backward influence $\left( \mathbf { y } \ \mathrm { t o } \ \mathbf { x } \right)$ are treated as symmetric. For example, given two in-training tasks A and B, the distance $D ( \mathbf { g } _ { \mathbf { A } } , \mathbf { g } _ { \mathbf { B } } )$ represents both the effect of $\mathbf { g } _ { \mathrm { A } }$ on task $\mathbf { B }$ and $\mathbf { g } _ { \mathrm { B } }$ on task A because of $D ( \mathbf { g } _ { \mathrm { A } } , \mathbf { g } _ { \mathrm { B } } ) = D ( \mathbf { g } _ { \mathrm { B } } , \mathbf { g } _ { \mathrm { A } } )$ . Note that large distance from $\mathbf { g } _ { \mathrm { A } }$ to gB means large negative influence on the training of task B with $\mathbf { g } _ { \mathrm { A } }$ .
+
+However, the model update is highly related to gradient magnitude and direction, which are asymmetric to model updating. The influence of the gradient $\mathbf { g } _ { \mathrm { A } }$ on task B may be quite different from that of the gradient $\mathbf { g } _ { \mathrm { B } }$ on task A. In previous studies (Lopez-Paz & Ranzato, 2017; Chaudhry et al., 2019; Yu et al., 2020), the two tasks are treated as conflict when $\langle \mathbf { g } _ { \mathrm { A } } , \mathbf { g } _ { \mathrm { B } } \rangle < 0$ . In PCL, due to the diverse training process, gradients from parallel tasks are diverse in magnitude and direction. When $\| \mathbf { g } _ { \mathrm { A } } \| \ll \| \mathbf { g } _ { \mathrm { B } } \|$ , the gradient $\mathbf { g } _ { \mathrm { A } }$ will have little negative influence on task B even if $\langle \mathbf { g } _ { \mathrm { A } } , \mathbf { g } _ { \mathrm { B } } \rangle < 0$ ; when $\| \mathbf { g } _ { \mathrm { A } } \| \gg \| \mathbf { g } _ { \mathrm { B } } \|$ (e.g., a new task A is accessed when task B has been trained for some time near convergence), the update produces huge impact on task B even if $\langle \mathbf { g } _ { \mathrm { A } } , \mathbf { g } _ { \mathrm { B } } \rangle > 0$ . Using the traditional symmetric distance can hardly represent the asymmetric update influence difference.
+
+To effectively measure gradient discrepancy in PCL, we introduce the asymmetric metric.
+
+Lemma 1 (Asymmetric Metric (Collins & Zimmer, 2007)) $D : \mathcal { X } \times \mathcal { X }  \mathbb { R }$ is an asymmetric metric (also known as quasi-metric (Wilson, 1931)) if $D$ satisfies
+
+The asymmetric metric does not require the symmetric property, i.e., $D ( \mathbf { x } , \mathbf { y } ) = D ( \mathbf { y } , \mathbf { x } ) .$ . Based on the definition, in this paper, we design an asymmetric metric to measure gradient discrepancy named Asymmetric Gradient Distance.
+
+Definition 1 (Asymmetric Gradient Distance (AGD)) Given two gradient $\mathbf { g } _ { A }$ and $\mathbf { g } _ { B }$ , the asymmetric gradient distance is defined as
+
+$$
+\widehat { D } ( \mathbf { g } _ { A } , \mathbf { g } _ { B } ) = \left\{ \begin{array} { c c } { 0 } & { , } & { i f \mathbf { g } _ { A } = \mathbf { g } _ { B } = \mathbf { 0 } , } \\ { \displaystyle \frac { \left. \mathbf { g } _ { A } - \mathbf { g } _ { B } \right. } { \left. \mathbf { g } _ { B } \right. + \left. \mathbf { g } _ { A } - \mathbf { g } _ { B } \right. } , } & { O t h e r w i s e . } \end{array} \right.
+$$
+
+In Definition 1, we consider the edge situation when $\mathbf { g } _ { \mathrm { A } } = \mathbf { g } _ { \mathrm { B } } = \mathbf { 0 }$ to meet the definition of the asymmetric metric in Lemma 1. In AGD, gradient directions and magnitudes are considered. Instead of using gradient magnitude value difference, we use magnitude ratio difference to avoid the diverse training of different tasks in PCL. Therefore, we derive the corollary of the magnitude ratio:
+
+Corollary 1 $\widehat { D } ( \mathbf { g } _ { A } , \mathbf { g } _ { B } ) \in [ 0 , 1 ]$ is an asymmetric metric and holds
+
+$$
+\begin{array} { r } { \operatorname* { l i m } _ { \frac { \| \mathbf { g } _ { A } \| } { \| \mathbf { g } _ { B } \| } \to \infty } \widehat { D } ( \mathbf { g } _ { A } , \mathbf { g } _ { B } ) = 1 , \quad \operatorname* { l i m } _ { \frac { \| \mathbf { g } _ { A } \| } { \| \mathbf { g } _ { B } \| } \to 0 } \widehat { D } ( \mathbf { g } _ { A } , \mathbf { g } _ { B } ) = \frac { 1 } { 2 } . } \end{array}
+$$
+
+We illustrate why AGD is qualified to evaluate the gradient discrepancy according to the definition and corollary. In Definition 1, we use AGD to represent the influence of $\mathbf { g } _ { \mathrm { A } }$ on task $\mathbf { B }$ rather than the inverse. This is the key difference from the symmetric metrics such as Euclidean distance. Specifically, $\mathbf { g } _ { \mathrm { A } }$ may make task B worse if $\widehat { D } ( \mathbf { g } _ { \mathrm { A } } , \mathbf { g } _ { \mathrm { B } } )$ is large (close to 1). If $\widehat { D } ( \mathbf { g } _ { \mathrm { A } } , \mathbf { g } _ { \mathrm { B } } )$ is close to 0, $\mathbf { g } _ { \mathrm { A } }$ and gB has less conflict. Moreover, Corollary 1 involves that when $\| \mathbf { g } _ { \mathrm { A } } \| \ll \| \mathbf { g } _ { \mathrm { B } } \|$ , AGD has a tolerance $\begin{array} { l } { { \frac { 1 } { 2 } } } \end{array}$ even if $\langle \mathbf { g } _ { \mathrm { A } } , \mathbf { g } _ { \mathrm { B } } \rangle < 0$ , which means the impact of $\mathbf { g } _ { \mathrm { A } }$ on task $\mathbf { B }$ is mild. This is because updating with a zero gradient will neither improve nor damage the performance. Even though, we prefer positive influence rather than non-influence. Thus, we define that the distance $\widehat { D } ( \mathbf { g } _ { \mathrm { A } } , \mathbf { g } _ { \mathrm { B } } )$ in this situation is the mid-level in the value range. See different tolerances in Appendix C.
+
+Moreover, we compare AGD (Fig. 2(c)) with Euclidean and cosine distance in Fig. 2. First, the cosine distance (Fig. 2(a)) is magnitude irrelevant, which ignores the magnitude difference in PCL. Second, the Euclidean distance (Fig. 2(b)) depends heavily on the magnitude value difference, but ignores that the gradient influence on the model update is asymmetric. For example, when $\| \mathbf { x } \|  0$ , EuDist will get large if we have large $\| \mathbf { y } \|$ . However, updating with a zero gradient will neither improve nor damage the performance. See the contours of Fig. 2 in Appendix D.
+
+# 3.3 MAXIMUM DISCREPANCY OPTIMIZATION
+
+At time $t$ , let the optimal solution to Problem (3) be $\mathbf { d } ^ { * }$ , where $\mathcal { T } _ { t }$ is the index set of in-training tasks ( $^ { \prime }$ for simplicity). However, directly optimizing the problem is difficult due to the large decision space that has the same dimension as $\pmb { \theta }$ . Following (Lin et al., 2021; Sener & Koltun, 2018), we use linear scalarization to solve the transformed problem that allows only optimizing decision variable w $\in \mathbb { R } ^ { | \mathcal { T } | }$ . That is, let $\begin{array} { r } { \mathbf { d } = \sum _ { i \in \mathcal { T } } \mathbf { w } _ { i } \mathbf { g } _ { i } } \end{array}$ , where $\forall \mathbf { w } _ { i } \geq 0$ and $\textstyle \sum _ { i \in T } \mathbf { w } _ { i } = 1$ , we have
+
+$$
+\begin{array} { r l } { \mathbf { w } ^ { * } = \arg \operatorname* { m i n } _ { \mathbf { w } } } & { { } \left\{ \widehat { D } \left( \sum _ { j } \mathbf { w } _ { j } \mathbf { g } _ { j } , \mathbf { g } _ { i } \right) \Big | \forall i \in \mathcal { T } \right\} . } \end{array}
+$$
+
+Each objective of the dual problem will be highly affected by the minimum discrepancy, i.e., each gradient itself. For example, by minimizing objective $\widehat { D } ( \sum _ { j } \mathbf { w } _ { j } \mathbf { g } _ { j } , \mathbf { g } _ { i } )$ , weight $\mathbf { w } _ { i }$ is more like to be activated than others. Thus, multiple objectives will be compromised by multiple self-interference but fail to reduce the maximum discrepancy in the dual problem optimization.
+
+As shown in Fig. 3., we propose Maximum Discrepancy Optimization (MaxDO) to reduce the maximum gradient discrepancy. Specifically, instead of the weight vector $\mathbf { w } \in \mathbb { R } ^ { | \mathcal { T } | }$ we optimize a weight matrix $\mathbf { W } \in \mathbb { R } ^ { | T | \times | T | }$ , in which $\forall \mathbf { W } _ { i j } \ \geq \ 0$ . W can be combined by a diagonal vector $\dot { \mathbf { w } } = [ \mathbf { W } _ { 1 , 1 } , \cdots , \mathbf { W } _ { | T | , | T | } ]$ and an off-diagonal matrix $\widetilde { \mathbf { W } } = \mathbf { W } - \mathrm { D i a g } ( \dot { \mathbf { w } } )$ , where $\textstyle \sum _ { i \in { \mathcal { T } } } { \dot { \mathbf { w } } } _ { i } = 1$ and Pj∈T $\begin{array} { r } { \sum _ { j \in \mathcal { T } } \widetilde { \mathbf { W } } _ { i j } = 1 , \forall i } \end{array}$ . Thus, $\begin{array} { r } { \sum _ { i , j \in \mathcal { T } } \mathbf { W } _ { i j } = | \mathcal { T } | + 1 } \end{array}$ and the two weights are independent and can be optimized without disturbance: (1) $\widetilde { \mathbf { W } }$ , computed by Stochastic Gradient Descent (SGD), is used to make up the maximum gradient discrepancy for each row. The objectives of any two rows in $\widetilde { \mathbf { W } }$ are different and independent. For row $i$ , to formulate the maximum discrepancy of gradient $\mathrm { g } _ { i }$ , the objective is the combination of non-diagonal entries. The weighted other gradients should be with the smallest asymmetric distance to $\mathbf { g } _ { i }$ . (2) w\` is obtained by the Multiple Gradient Descent Algorithm (MGDA) (Desid ´ eri, 2012) ´ , which is to obtain a weighted gradient that does not damage any tasks with a min-norm optimization. The objective of MGDA is 0 and the resulting point satisfies the Karush–Kuhn–Tucker condition or the solution gives a Pareto descent direction that improves all tasks. See Appendix E for more details of MGDA. For each off-diagonal entry of the $i$ -th column, their sum means the effect of the gradient $\mathbf { g } _ { i }$ reducing the maximum discrepancy from other gradients. MGDA is used to reduce the possible negative effect in MaxDO. On the other hand, MaxDO reduces the training failure of new tasks in MGDA. To sum up, our MaxDO with AGD can be computed by
+
+![](images/48d06abed08fff13a80e6e0a3a63a1a3334f10d4f2eebe97fd3ad7f22ef1f926.jpg)  
+Figure 3: Schematic of Maximum Discrepancy Optimization. Given multiple gradients $\{ \mathbf { g } _ { i } | \forall i \in \mathcal { T } \}$ $( | \bar { \mathcal { T } } | = 4$ for example) (1) A weight matrix W is initialized with $\frac { 1 } { | T | }$ for each entry. (2) For each row, the off-diagonal entries are used to weighted gradients and optimized for minimum AGD to the target gradient. (3) The diagonal entries $( \sqcup )$ are used to optimize with min-norm with MGDA. (4) The final weight matrix is reduced by each column for the final weights $( w ^ { \prime } )$ ). See Sec. 3.3 for details.
+
+$$
+\mathbf { W } ^ { * } = \underset { \mathbf { \widetilde { W } } } { \arg \operatorname* { m i n } } \underset { \mathbf { S } \mathbf { G } } { \underbrace { \{  \sum _ { j \neq i } \widetilde { \mathbf { W } } _ { i , j } \mathbf { g } _ { j } , \mathbf { g } _ { i } ) | \forall i \in \mathcal { T } \} } } + \mathrm { D i a g } \underset { \mathbf { M } \mathbf { G } \mathbf { D } \mathbf { A } ( \mathbf { D } \mathbf { \check { \epsilon } } \mathrm { s i d e t } , 2 0 1 2 ) } { \underbrace { ( \mathrm { a r g } \operatorname* { m i n } \{ | \sum _ { j \neq i } \tilde { \mathbf { W } } _ { i , j } \mathbf { g } _ { j } , \mathbf { g } _ { i } ) | } ) }  .
+$$
+
+In Eq. (7), we can obtain an approximate solution by combining the closed-form solution and the iterative solution. Fig. 3 reveals the diagram of solving MaxDO. We project the solution of SGD onto the feasible set $\begin{array} { r } { ( \sum _ { i \neq j } \mathbf { W } _ { i j } = 1 ) } \end{array}$ via softmax at each step in the multiple steps for fast convergence.. First, we initialize all entries of $\mathbf { W }$ by $\frac { 1 } { | T | }$ . Then, the off-diagonal matrix is used to minimize the maximum gradient discrepancy via SGD and the diagonal vector is optimized by min-norm. Finally, the final weights are reduced to a vector by dividing $| \tau | + 1$ to guarantee that their sum is 1. Note that, MaxDO is implemented only when $| \mathcal { T } | > 1 .$ , i.e., multiple tasks are given at the current time. Otherwise, we have $\mathbf { d } ^ { * } = \mathbf { g } _ { 1 }$ for the only current task 1. Thus, the final gradient $\mathbf { d } ^ { * }$ is computed by
+
+$$
+\mathbf { d } ^ { * } = \left\{ \begin{array} { l l } { \mathbf { g } _ { 1 } , } & { | \mathcal { T } | = 1 , } \\ { \sum _ { i } \left( \displaystyle \frac { 1 } { | \mathcal { T } | + 1 } \sum _ { j } \mathbf { W } _ { j , i } ^ { * } \right) \mathbf { g } _ { i } , } & { | \mathcal { T } | > 1 . } \end{array} \right.
+$$
+
+The detailed algorithm is shown in Algorithm 1. With the rehearsal data stream, our algorithm learns a PCL model through a timeline. At the time $t$ on the timeline, given a mini-batch $\boldsymbol { B }$ from each data stream, we compute the corresponding gradients on shared and task-specific parameters. The task-specific parameters are updated directly and the gradients on the shared backbone are collected for computed the final updated gradient d. By using our MaxDO, we update $\pmb { \theta }$ with the optimal $\mathbf { d } ^ { * }$ and update the shared parameters.
+
+Algorithm 1: MaxDO () in PCL Input: Random-initialized $\overline { { \pmb { \theta } , \pmb { \theta } _ { 1 : T } } }$ ; Step sizes α, $\alpha _ { 1 : T }$ Output: θ, $\pmb { \theta } _ { 1 : T }$ 1 for $t$ in timeline do 2 $\mathcal { T } _ { t } \gets$ in-training task index; 3 for $i \in \mathcal { T } _ { t }$ do 4 $B _ { i } \sim { \mathcal { D } } _ { i }$ ; 5 $\pmb { \theta } _ { i }  \pmb { \theta } _ { i } - \alpha _ { i } \nabla _ { \pmb { \theta } _ { i } } \ell _ { i } ( B _ { i } ) ;$ 6 gi = ∇θ\`i (Bi); 7 end W∗ ← Optimization by Eq. (7); $\mathbf { d } ^ { * } \gets$ Final graident from Eq. (8); 8 9 $\pmb { \theta } \gets \pmb { \theta } - \alpha \mathbf { d } ^ { * }$ ; 10 end
+
+# 4 EXPERIMENT
+
+# 4.1 DATASET
+
+In our experiments, 3 traditional image recognition datasets are transformed into parallel data streams: (1) Parallel Split EMNIST (PS-EMNIST). We split EMNIST (Cohen et al., 2017) (62 classes) into
+
+Table 1: Comparisons (avg ± std) with different buffer sizes on PS-EMNIST (62 classes).   
+
+<table><tr><td rowspan="2">Method (+ Rehearsal)</td><td colspan="2">Buffer size 124(62*2)</td><td colspan="2">Buffer size 186 (62*3)</td><td colspan="2">Buffer size 310 (62*5)</td></tr><tr><td>Ar (%)</td><td>FT(%)</td><td>Ar (%)</td><td>FT(%)</td><td>Ar (%)</td><td>FT(%)</td></tr><tr><td>MGDA(NeurIPS&#x27;18)</td><td>78.975 ± 0.165</td><td>-5.386 ± 1.252</td><td>82.026 ± 0.851</td><td>-7.215 ± 1.637</td><td>84.783±0.190</td><td>-5.780 ± 0.476</td></tr><tr><td>GradNorm(ICML&#x27;18)</td><td>83.985 ± 0.324</td><td>-9.989 ± 0.578</td><td>85.127 ± 0.647</td><td>-8.835 ± 1.215</td><td>86.060±0.094</td><td>-7.896 ±0.208</td></tr><tr><td>DWA(CVPR&#x27;18)</td><td>85.416 ± 0.622</td><td>-8.209 ± 1.279</td><td>85.939 ±0.632</td><td>-7.787 ± 1.255</td><td>86.732 ±0.089</td><td>-6.922 ± 0.175</td></tr><tr><td>GradDrop(NeurIPS&#x27;20)</td><td>87.285 ± 0.527</td><td>-6.983 ± 1.022</td><td>87.699 ±0.870</td><td>-6.580 ± 1.709</td><td>88.460±0.221</td><td>-5.820± 0.469</td></tr><tr><td>PCGrad(NeurIPS&#x27;20)</td><td>86.880 ±0.400</td><td>-7.437±0.800</td><td>87.848 ± 0.317</td><td>-6.464±0.632</td><td>88.524 ± 0.135</td><td>-5.773 ± 0.273</td></tr><tr><td>CVweight(Arxiv&#x27;20)</td><td>85.662 ± 0.396</td><td>-8.581 ±0.809</td><td>86.285 ± 0.740</td><td>-7.971 ± 1.475</td><td>87.174±0.099</td><td>-7.092 ± 0.261</td></tr><tr><td>RLW(Arxiv&#x27;21)</td><td>85.936 ± 0.695</td><td>-8.368 ± 1.380</td><td>87.019 ± 0.440</td><td>-7.284 ± 0.854</td><td>87.397 ± 0.264</td><td>-6.896 ± 0.569</td></tr><tr><td>MaxDO (AGD)</td><td>87.901±0.244</td><td>-6.468±0.270</td><td>88.566±0.585</td><td>-5.776± 0.640</td><td>88.744± 0.361</td><td>-5.573 ±0.382</td></tr></table>
+
+Table 2: Comparisons $( \mathrm { a v g } \pm \mathrm { s t d } )$ with different buffer sizes on PS-CIFAR-100 (100 classes).   
+
+<table><tr><td rowspan="2">Method (+ Rehearsal)</td><td colspan="2">Buffer size 1000</td><td colspan="2">Buffer size 2000</td><td colspan="2">Buffer size 3000</td></tr><tr><td>Ar (%)</td><td>Fr(%)</td><td>Ar (%)</td><td>Fr(%)</td><td>Ar(%)</td><td>Fr(%)</td></tr><tr><td>MGDA(NeurIPS&#x27;18)</td><td>63.578 ± 0.315</td><td>22.866 ±0.639</td><td>67.613 ±0.166</td><td>25.001 ± 0.768</td><td>67.704 ±0.238</td><td>24.725 ± 1.075</td></tr><tr><td>GradNorm(ICML&#x27;18)</td><td>62.498 ± 0.699</td><td>22.506 ± 1.427</td><td>63.932 ± 0.679</td><td>23.845 ± 1.185</td><td>64.538 ±0.627</td><td>24.359 ± 1.450</td></tr><tr><td>DWA(CVPR&#x27;18)</td><td>64.952 ± 0.374</td><td>23.152 ± 0.487</td><td>66.310 ±0.445</td><td>24.697 ± 0.880</td><td>66.947 ± 0.156</td><td>25.384 ± 0.447</td></tr><tr><td>GradDrop(NeurIPS&#x27;20)</td><td>66.371 ± 0.260</td><td>23.054 ± 0.633</td><td>68.483 ±0.499</td><td>24.962 ± 1.007</td><td>69.353 ±0.707</td><td>26.269 ± 1.401</td></tr><tr><td>PCGrad(NeurIPS&#x27;20)</td><td>66.724 ±0.263</td><td>23.601 ± 0.618</td><td>68.652 ± 0.619</td><td>25.183 ±1.081</td><td>68.885 ± 0.134</td><td>25.704 ± 0.849</td></tr><tr><td>CVweight(Arxiv&#x27;20)</td><td>47.521 ± 2.333</td><td>11.868 ± 4.257</td><td>48.155 ± 1.682</td><td>13.202 ± 3.005</td><td>48.424±1.960</td><td>13.138 ± 3.573</td></tr><tr><td>RLW(Arxiv&#x27;21)</td><td>65.974± 0.508</td><td>23.080 ± 1.411</td><td>68.066 ±0.276</td><td>24.915 ± 0.697</td><td>68.162 ± 0.812</td><td>24.765 ± 1.078</td></tr><tr><td>MaxDO (AGD)</td><td>67.415 ± 0.803</td><td>22.359 ± 1.028</td><td>69.372± 0.170</td><td>24.523 ± 0.360</td><td>70.078± 0.134</td><td>24.907 ±0.720</td></tr></table>
+
+5 tasks and the size of the label set for each task, i.e., the number of classes, is larger than 2 while smaller than 15. (2) Parallel Split CIFAR-100 (PS-CIFAR-100). We split CIFAR-100 into 20 tasks and the size of the label set for each task is larger than 2 while smaller than 15. (3) Parallel Split ImageNet-TINY (PS-ImageNet-TINY). We split Tiny ImageNet (Le & Yang, 2015) (200 classes), which has a training set of 100,000 images and a test set of 10,000 images, into 20 tasks, and the size of the label set for each task is larger than 5 while smaller than 20. See more details in Appendix A.
+
+All three datasets have 3 different label sets (3 different class splits), each of which has 3 different timelines (when to access). For each timeline, we have 3 different runs with fixed seeds 1234, 1235, and 1236 for parameter initialization. In other words, we have 27 different settings for each dataset, and we report the average and standard deviation (avg $\pm$ std) for each compared method in our experiments. Note that, we omit all blank time that no data stream flows for simplicity.
+
+# 4.2 EXPERIMENT DETAILS
+
+We implement our experiments using Tensorflow and conduct on a single NVidia RTX 3090Ti GPU card. We take a 2-layer MLP as the backbone network for PS-EMNIST and a Resnet-18 (He et al., 2016) for PS-CIFAR-100 and PS-ImageNet-Tiny. The learning rate is set to 0.003, 0.0004 and 0.0005 for PS-EMNIST, PS-CIFAR-100 and PS-ImageNet-Tiny. The SGD in MaxDO has a learning rate of 5. Each task is trained in a data stream, i.e., each data point passes only once. For each task, we set the batch size to 128 per step. For any new task in PCL, we build a new classifier, which is a fully-connected layer with a softmax function.
+
+To evaluate PCL, we compute the average accuracy and forgetting following previous continual learning studies (Lopez-Paz & Ranzato, 2017; Chaudhry et al., 2019; Aljundi et al., 2019b;a; Risheng et al., 2021). Let $e _ { t }$ be the end time of task $t$ and final time $\bar { e } = \operatorname* { m a x } ( e _ { 1 } , e _ { 2 } , \cdots , e _ { T } )$ , the two metrics are computed as follows:
+
+$$
+A _ { T } = \frac { 1 } { T } et { } { ' } { \sum } _ { t = 1 } ^ { T } a _ { \bar { e } } ^ { t } , \quad F _ { T } = \frac { 1 } { T } et { } { ' } { \sum } _ { t = 1 } ^ { T } a _ { \bar { e } } ^ { t } - a _ { e _ { t } } ^ { t } ,
+$$
+
+where $a _ { k } ^ { j }$ is the mean testing accuracy of task $j$ at time $k$ . The $A _ { T }$ denotes the final average accuracy on all the tasks, and the $F _ { T }$ (also known as backward transfer) means the final performance drop compared to each task that was first trained.
+
+# 4.3 MAIN RESULTS
+
+We compare our method with MTL methods including MGDA (Desid ´ eri, 2012), GradNorm (Chen ´ et al., 2018), DWA (Liu et al., 2019), GradDrop (Chen et al., 2020), PCGrad (Yu et al., 2020), CVWeight (Groenendijk et al., 2021) and RLW (Lin et al., 2021) in the PCL setting. We treat any time on the timeline as an MTL subunit to train PCL. All results of previous MTL methods are produced by ourselves with the claimed design in their papers. We show the main comparisons with the proposed methods in Tables 1, 2 and 3 on the three datasets. We have several major observations. First, the rehearsal strategy is useful for reducing catastrophic forgetting in PCL for all compared methods. On one hand, as an extra data stream aparts from in-training data streams, rehearsal provides data from the finished tasks training together with other tasks to suppress forgetting. On the other hand, the memory buffer size of rehearsal affects the remembering of old knowledge, and larger size means better knowledge keeping, which is similar to traditional CL. For example in PS-CIFAR-100, we have $6 7 . 4 1 5 \%$ , $6 9 . 3 \hat { 7 } 2 \%$ and $\bar { 7 } 0 . 0 7 8 \%$ for buffer size 1,000, 2,000, and 3,000, respectively. Second, due to each task in PCL taking the data stream as input, only one pass of each data point is insufficient to make the model converge. With the rehearsal strategy, the memory may provide continual learning of finished tasks, and even better performance can be obtained, which results in positive forgetting value $F _ { T }$ . Third, the compared methods are designed for balanced training and ignore the diverse training process in PCL. Thus, some gradients may be counteracted because of the large gradient discrepancy when updating the model. In contrast, our MaxDO with AGD obtains the best final accuracy $\bar { A } ^ { T }$ on three datasets and different memory buffer sizes, which shows our superiority in balancing plasticity and stability. For example, we have $5 5 . 1 9 2 \%$ for PS-ImageNet-TINY (buffer size 4,000) while the compared best value is only $5 3 . 8 2 7 \%$ . On one hand, the proposed AGD is used to measure the asymmetric distance between gradients to boost the effective update of each task. On the other hand, the maximum discrepancies between multiple tasks are reduced. Note that, the forgetting measure of the proposed methods may not outperform the compared methods because we got both better new tasks (see the following section) and final accuracy performance, their difference value (forgetting) may be small.
+
+Table 3: Comparisons (avg ± std) with different buffer sizes on PS-ImageNet-TINY (200 classes).   
+
+<table><tr><td rowspan="2">Method (+ Rehearsal)</td><td colspan="2">Buffer size 2000</td><td colspan="2">Buffer size 3000</td><td colspan="2">Buffer size 4000</td></tr><tr><td>Ar (%)</td><td>Fr(%)</td><td>Ar (%)</td><td>Fr(%)</td><td>Ar (%)</td><td>Fr(%)</td></tr><tr><td>MGDA(NeurIPS&#x27;18)</td><td>48.179 ± 0.969</td><td>10.936 ± 1.917</td><td>51.794 ± 0.427</td><td>13.506 ± 0.649</td><td>52.644 ± 1.133</td><td>13.586 ± 2.191</td></tr><tr><td>GradNorm(ICML&#x27;18)</td><td>47.311 ± 1.841</td><td>9.975 ± 3.651</td><td>49.501 ± 1.882</td><td>11.740 ± 3.975</td><td>49.331 ± 1.606</td><td>11.507 ± 3.530</td></tr><tr><td>DWA(CVPR&#x27;18)</td><td>47.429 ± 0.865</td><td>10.640 ± 1.764</td><td>48.387± 0.718</td><td>11.505 ± 1.438</td><td>47.520 ± 2.129</td><td>10.498 ± 4.267</td></tr><tr><td>GradDrop(NeurIPS&#x27;20)</td><td>49.955 ± 1.413</td><td>11.747 ± 2.961</td><td>54.141 ± 0.747</td><td>14.633 ± 1.001</td><td>53.827 ± 1.146</td><td>14.623 ± 1.177</td></tr><tr><td>PCGrad(NeurIPS&#x27;20)</td><td>49.052 ± 0.961</td><td>10.264 ± 1.406</td><td>51.701 ± 0.554</td><td>12.508 ±0.698</td><td>50.837 ± 1.097</td><td>11.605 ± 1.478</td></tr><tr><td>CVweight(Arxiv&#x27;20)</td><td>34.032 ±0.607</td><td>8.221 ± 1.521</td><td>36.992 ± 1.900</td><td>11.055 ± 3.272</td><td>37.007 ± 2.304</td><td>9.954 ± 3.830</td></tr><tr><td>RLW(Arxiv&#x27;21)</td><td>49.355 ± 0.904</td><td>10.857 ± 1.933</td><td>49.629 ± 1.454</td><td>10.973 ± 3.017</td><td>51.947 ± 1.202</td><td>12.907 ± 2.478</td></tr><tr><td>MaxDO (AGD)</td><td>52.165 ± 0.694</td><td>13.287 ± 0.544</td><td>54.485 ± 0.608</td><td>15.192 ± 0.444</td><td>55.192 ± 0.301</td><td>15.571 ± 0.217</td></tr></table>
+
+![](images/162987389dfb24f5f311583f728fa117162b9a574eae3719274255ee745e10d6.jpg)  
+Figure 4: Task accuracy comparisons along parallel continual learning. Each point means a right finished task and its performance. Note that the order is up to its end time rather than the task ids.
+
+# 4.4 ACCURACY TRENDS
+
+As shown in Fig. 4, we show the accuracy trends of the compared methods on the three evaluated datasets with buffer sizes 310, 3,000 and 4,000 for PS-EMNIST, PS-CIFAR-100 and PS-ImageNetTINY, respectively. Each point in the figures means a right finished task and its performance then. Note that the task order is up to the end time of tasks rather than the task ids. We have the following observations. Firstly, in the first several tasks, fewer seen tasks mean that fewer discrepancies need to be considered and the compared methods have similar performance. Secondly, when more new tasks are accessed, MaxDO gains better performance for new tasks on three datasets compared to other methods, especially on PS-CIFAR100 and PS-ImageNet-TINY, which both contain 20 tasks. The observations show the proposed MaxDO is useful in PCL for solving diverse training processes. After learning more tasks, MaxDO balances the asymmetric discrepancies among gradients to improve the new task training and old task keeping at the same time. Because MaxDO gets better first accuracy than other methods, the forgetting value may not achieve the best yet is still comparable to others.
+
+Table 4: Metric comparison (↑) and ablation study (↓).   
+
+<table><tr><td>Method (+ Rehearsal)</td><td>Ar (%)</td><td>FT(%)</td></tr><tr><td>MaxDO (EuDist)</td><td>69.344 ± 0.024</td><td>24.268 ± 0.748</td></tr><tr><td>MaxDO (CosDist)</td><td>69.227 ± 0.370</td><td>24.552 ± 0.837</td></tr><tr><td>MaxDO (Normalized Eudist)</td><td>69.540 ± 0.340</td><td>24.629 ± 0.158</td></tr><tr><td>MGDA (Désidéri,2012)</td><td>67.704± 0.238</td><td>24.725 ± 1.075</td></tr><tr><td>MaxDO (w/o Max-Discrepancy)</td><td>68.866 ±0.443</td><td>24.093 ±0.025</td></tr><tr><td>MaxDO (w/o MGDA)</td><td>69.953 ±0.234</td><td>24.933 ±0.621</td></tr><tr><td>MaxDO (AGD)</td><td>70.078± 0.134</td><td>24.907±0.720</td></tr></table>
+
+Table 5: Training time (second/iter).   
+
+<table><tr><td>Method</td><td>2 tasks</td><td>3 tasks</td><td>4 tasks</td><td>5 tasks</td><td>Total</td></tr><tr><td>MGDA</td><td>5.58</td><td>5.92</td><td>6.06</td><td>6.64</td><td>239</td></tr><tr><td>GradNorm</td><td>5.30</td><td>5.81</td><td>5.87</td><td>6.50</td><td>281</td></tr><tr><td>DWA</td><td>5.56</td><td>5.89</td><td>5.94</td><td>6.56</td><td>245</td></tr><tr><td>GradDrop</td><td>5.33</td><td>6.00</td><td>6.34</td><td>6.38</td><td>275</td></tr><tr><td>PCGrad</td><td>5.71</td><td>5.85</td><td>6.11</td><td>6.46</td><td>229</td></tr><tr><td>CVWeight</td><td>5.56</td><td>5.98</td><td>6.00</td><td>6.56</td><td>227</td></tr><tr><td>RLW</td><td>5.64</td><td>5.89</td><td>5.95</td><td>6.26</td><td>232</td></tr><tr><td>MaxDO</td><td>5.70</td><td>6.12</td><td>6.67</td><td>6.91</td><td>300</td></tr></table>
+
+# 4.5 COMPARISON WITH SYMMETRIC METRICS
+
+As shown in Table 4, we compare AGD with three common symmetric metrics including EuDist, CosDist, and Normalized EuDist. EuDist, CosDist are defined in Sec. 3.2. The vanilla EuDist depends highly on the gradient magnitude difference, thus we also compare with its normalized version $\begin{array} { r } { D ( \mathbf { \bar { x } } , \mathbf { \bar { y } } ) = \frac { \| \mathbf { x } - \mathbf { y } \| } { \| \mathbf { x } \| + \| \mathbf { y } \| } \in [ 0 , 1 ] } \end{array}$ , namely normalized EuDist. The results show that the three metrics can also obtain good performance with MaxDO. However, because of the over-emphasizing of gradient magnitude difference in EuDist, it fails to reduce the catastrophic forgetting effectively. Considering only gradient angle difference, MaxDO with CosDist obtains better performance than EuDist. But CosDist ignores the magnitude difference, which is also important in the min-distance problem, resulting in insufficient performance. Compared to EuDist, normalized EuDist obtains better performance but still set symmetric influence to gradient update. In contrast to the three metrics, MaxDO with AGD considers the asymmetric influence on gradient update, and tolerance is set to reduce the influence from small gradients to new-access tasks, which yields the best performance.
+
+# 4.6 ABLATION STUDY AND PROCEDURE TIME
+
+We evaluate the impact of the two main components of MaxDO in Table 4. First, we block the maximum discrepancy in MaxDO (MaxDO (w/o Max-Discrepancy)), which means that we solve the min-distance problem with Eq. (6) directly. Because of the self-interference, the solution combines the minimum discrepancy but fails to effectively reduce the discrepancy from other gradients $( 6 8 . 8 6 6 \%$ for $A _ { T }$ ). We then block the MGDA that obtains a weighted gradient not damage any tasks. MGDA is quite useful in traditional MTL tasks but is not suitable in PCL $6 7 . 7 0 4 \%$ for $A _ { T }$ ). Because of the diverse training process of parallel tasks, gradients are with large magnitude differences and MGDA prefers to set large factors to small gradients. We solve the problem by both MGDA and the maximum discrepancy, and the whole MaxDO method with AGD outperforms the two ablated methods $7 0 . 0 7 8 \%$ for $A _ { T }$ ), where the characters of the two components are combined.
+
+In Table 5, we show the training time comparison on PS-CIFAR-100. We first compare the training time for 2 to 5 parallel tasks in one iteration. We find that the generation of task numbers will grow the training time, and MaxDO needs more time than other methods because multiple minimum distance optimizations are performed. Thus, in the whole timeline, MaxDO gets slightly longer training time than other methods. It is interesting to explore how to speed up the MaxDO training in the future.
+
+# 5 CONCLUSION
+
+In this paper, we studied to address the training conflict and catastrophic forgetting issues in Parallel Continual Learning (PCL). We presented that the two issues are rooted in the gradient discrepancies and formulated the problem into a minimum distance optimization among gradients. However, the distance metric is often set to be symmetric, which is problematic in gradient descent. To evaluate the gradient discrepancy in PCL, we proposed an explicit Asymmetric Gradient Distance (AGD), which considers both gradient magnitude ratios and directions and has a tolerance when updating with a small gradient of inverse direction. Moreover, we also proposed a novel Maximum Discrepancy Optimization (MaxDO) strategy to minimize the maximum discrepancy among multiple gradients and avoid self-interference. Solving by MaxDO with AGD, the parallel training in PCL reduces the influence of the training conflict and slows the catastrophic forgetting of finished tasks. We verified the proposed benchmark on three image recognition datasets. The experimental results significantly showed the advantage of our MaxDO and the effectiveness of the proposed AGD. We list the latent limitation of our method: (1) The MaxDO cannot guarantee a theoretical Pareto optimum in the training process like MGDA, which means a better trade-off can be obtained in the future. (2) The MaxDO method needs more time for training.
+
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+# MEASURING ASYMMETRIC GRADIENT DISCREPANCY IN PARALLEL CONTINUAL LEARNING (APPENDIX)
+
+# A DATASET CONSTRUCTION
+
+For effective transformation, several requirements are needed: (1) Random label set for each task, in which the data stream length of each task can be different; (2) Random timeline for each label set, in which the debut of each task can be any time between the first access of the former and latter tasks. For simplicity, we omit all blank time that all data streams are unavailable.
+
+• Parallel Split EMNIST (PS-EMNIST): We split EMNIST (62 classes) into 5 tasks and randomly generate 3 label sets for each task and 3 timelines for each label set (say 9 different situations). The size of the label set for each task, i.e., the number of classes, is set to larger than 2 while no more than 15.
+
+• Parallel Split CIFAR-100 (PS-CIFAR-100): We split CIFAR-100 into 20 tasks and randomly generate 3 label sets for each task and 3 timelines for each label set. The size of the label set for each task is set to larger than 2 while no more than 15.
+
+• Parallel Split ImageNet-TINY (PS-ImageNet-TINY): We split it into 20 tasks w.r.t. random 3 label sets, and each label set has 3 randomly generated timelines. The size of the label set for each task is set to larger than 5 while no more than 20.
+
+# B PROOF OF LEMMA 1 ON AGD
+
+As an asymmetric metric, the proposed Asymmetric Gradient Discrepancy (AGD) measure needs to satisfy the two features in Lemma 1.
+
+Proof: Given three arbitrary gradients $\mathbf x , \mathbf y$ and $\mathbf { z }$ , we have
+
+(1) If $\mathbf x = \mathbf y$ , $D ( \mathbf { x } , \mathbf { y } ) = 0$ .
+
+(2) Positivity: If $\mathbf x \neq \mathbf y$ , then $\| \mathbf { x } - \mathbf { y } \| \neq 0$ , and we have $D ( \mathbf { x } , \mathbf { y } ) = { \frac { \| \mathbf { x } - \mathbf { y } \| } { \| \mathbf { y } \| + \| \mathbf { x } - \mathbf { y } \| } } > 0 .$
+
+(3) The triangle inequality:
+
+$$
+\begin{array} { r l } & { \frac { \| \mathbf { x } - \mathbf { z } \| } { \| \mathbf { z } \| + \| \mathbf { x } - \mathbf { z } \| } = \frac { \| \mathbf { x } - \mathbf { y } + \mathbf { y } - \mathbf { z } \| } { \| \mathbf { z } \| + \| \mathbf { x } - \mathbf { y } + \mathbf { y } - \mathbf { z } \| } } \\ { \leq } & { \frac { \| \mathbf { x } - \mathbf { y } \| + \| \mathbf { y } - \mathbf { z } \| } { \| \mathbf { z } \| + \| \mathbf { x } - \mathbf { y } \| + \| \mathbf { y } - \mathbf { z } \| } } \\ { = } & { \frac { \| \mathbf { x } - \mathbf { y } \| } { \| \mathbf { z } \| + \| \mathbf { x } - \mathbf { y } \| + \| \mathbf { y } - \mathbf { z } \| } } \\ { = } & { \frac { \| \mathbf { x } - \mathbf { y } \| } { \| \mathbf { z } \| + \| \mathbf { x } - \mathbf { y } \| + \| \mathbf { y } - \mathbf { z } \| } + \frac { \| \mathbf { y } - \mathbf { z } \| } { \| \mathbf { z } \| + \| \mathbf { x } - \mathbf { y } \| + \| \mathbf { y } - \mathbf { z } \| } } \\ { \leq } & { \frac { \| \mathbf { x } - \mathbf { y } \| } { \| \mathbf { z } \| + \| \mathbf { x } - \mathbf { y } \| + \| \mathbf { y } - \mathbf { z } \| } + \frac { \| \mathbf { y } - \mathbf { z } \| } { \| \mathbf { z } \| + \| \mathbf { y } - \mathbf { z } \| } } \\ { \leq } & { \frac { \| \mathbf { x } - \mathbf { y } \| } { \| \mathbf { y } \| + \| \mathbf { x } - \mathbf { y } \| } + \frac { \| \mathbf { y } - \mathbf { z } \| } { \| \mathbf { z } \| + \| \mathbf { y } - \mathbf { z } \| } . } \end{array}
+$$
+
+(4) Asymmetric: $D ( \mathbf { x } , \mathbf { y } ) = { \frac { \| \mathbf { x } - \mathbf { y } \| } { \| \mathbf { y } \| + \| \mathbf { x } - \mathbf { y } \| } } ,$ , and $D ( \mathbf { y } , \mathbf { x } ) = { \frac { \| \mathbf { x } - \mathbf { y } \| } { \| \mathbf { x } \| + \| \mathbf { x } - \mathbf { y } \| } } ,$ . Thus, it is obvious that $D ( \mathbf { x } , \mathbf { y } ) = D ( \mathbf { y } , \mathbf { x } )$ is not always satisfied when $\mathbf x \neq \mathbf y$ and depends on the magnitude $\| \mathbf { x } \|$ and $\| \mathbf { y } \|$ .
+
+Therefore, the proposed AGD is an asymmetric metric.
+
+C TOLERANCE ANALYSIS AND PROOF OF COROLLARY 1
+
+# C.1 PROOF OF COROLLARY 1
+
+Let us review the definition of AGD:
+
+$$
+{ \widehat { D } } ( \mathbf { x } , \mathbf { y } ) = { \frac { \left\| \mathbf { x } - \mathbf { y } \right\| } { \left\| \mathbf { y } \right\| + \left\| \mathbf { x } - \mathbf { y } \right\| } } .
+$$
+
+$\widehat { D } ( \mathbf { x } , \mathbf { y } )$ represents the gradient influence from $\mathbf { x }$ to $\mathbf { y }$ . The nature of this asymmetric measure is the norm effect should only be from gradient difference $\| \mathbf x - \mathbf y \|$ to $\| \mathbf { y } \|$ rather than to both $\| \mathbf { x } \|$ and $\| \mathbf { y } \|$ . That is, the discrepancy should only depend on the ratio $\frac { \| \mathbf x - \mathbf y \| } { \| \mathbf y \| }$ , which can be further reduced to
+
+$$
+{ \frac { \| \mathbf { x } - \mathbf { y } \| } { \| \mathbf { y } \| } } = { \frac { \sqrt { \| \mathbf { x } \| ^ { 2 } + \| \mathbf { y } \| ^ { 2 } - 2 \| \mathbf { x } \| \| \mathbf { y } \| \cos \angle \mathbf { x } , \mathbf { y } } } { \| \mathbf { y } \| } } = { \sqrt { \left( { \frac { \| \mathbf { x } \| } { \| \mathbf { y } \| } } \right) ^ { 2 } - 2 { \frac { \| \mathbf { x } \| } { \| \mathbf { y } \| } } \cos \angle \mathbf { x } , \mathbf { y } + 1 } } .
+$$
+
+It is easy to know that
+
+$$
+{ \frac { \left\| \mathbf { x } - \mathbf { y } \right\| } { \left\| \mathbf { y } \right\| + \left\| \mathbf { x } - \mathbf { y } \right\| } } = 1 - { \frac { 1 } { 1 + { \frac { \left\| \mathbf { x } - \mathbf { y } \right\| } { \left\| \mathbf { y } \right\| } } } } .
+$$
+
+Because kx−ykkyk ≥ 0, Db(x, y) ∈ [0, 1].
+
+In the paper, we illustrate the proposed AGD is an asymmetric measure of gradient discrepancy because $\bar { \widehat { D } } ( { \bf x } , { \bf y } )$ brings a tolerance when $\| \mathbf { x } \| \ll \| \mathbf { y } \|$ instead of the absolute difference between them. To analyze the values of gradient discrepancy measure $D$ regarding kxkkyk , we consider the following asymmetric limits with $\| y \| \neq 0$ :
+
+$\operatorname* { l i m } _ { \| \mathbf { x } \| } { } _ {  \infty } D$ : When $\| \mathbf { x } \| \gg \| \mathbf { y } \|$ , the conflict should be large from $\mathbf { x }$ to $\mathbf { y }$ ; $\operatorname* { l i m } _ { \frac { \| \mathbf { x } \| } { \| \mathbf { y } \| } \to 0 } D$ : When $\| \mathbf { x } \| \ll \| \mathbf { y } \|$ , the conflict is acceptable to some extend and should approach a tolerance value that less than $\operatorname* { l i m } _ { \| \mathbf { x } \| } { } _ {  \infty } D$ .
+
+We show the two limits for different discrepancy measures including Cosine Similarity, Euclidean Distance, Normalized Euclidean Distance, and AGD.
+
+Cosine Similarity: Using the Cosine Similarity to measure the discrepancy has no relevance to the magnitude difference.
+
+$$
+\operatorname* { l i m } _ { \| \mathbf { x } \|  0 } 1 - { \frac { \mathbf { x } ^ { \mathsf { T } } \mathbf { y } } { \| \mathbf { x } \| \| \mathbf { y } \| } } = \operatorname* { l i m } _ { \| \mathbf { x } \|  \infty } 1 - { \frac { \mathbf { x } ^ { \mathsf { T } } \mathbf { y } } { \| \mathbf { x } \| \| \mathbf { y } \| } } = 1 - \cos \angle \mathbf { x } , \mathbf { y } .
+$$
+
+Euclidean Distance: When $\| \mathbf { y } \| \neq 0$ , we have
+
+$$
+{ \frac { 1 } { 1 + \| \mathbf { x } - \mathbf { y } \| } } = { \frac { 1 } { 1 + \| \mathbf { y } \| \cdot { \frac { \| \mathbf { x } - \mathbf { y } \| } { \| \mathbf { y } \| } } } } .
+$$
+
+Thus, we have
+
+$$
+\operatorname* { l i m } _ { \| \mathbf { x } \| \to 0 } 1 - \frac { 1 } { 1 + \| \mathbf { x } - \mathbf { y } \| } = \frac { \| \mathbf { y } \| } { 1 + \| \mathbf { y } \| } , \quad \operatorname* { l i m } _ { \| \mathbf { x } \| \to \infty } 1 - \frac { 1 } { 1 + \| \mathbf { x } - \mathbf { y } \| } = 1 .
+$$
+
+When $\frac { \| \mathbf { x } \| } { \| \mathbf { y } \| }  0$ , by using the Euclidean Distance highly depends on $\| \mathbf { y } \|$ , which makes it unpredictable.
+
+Normalized Euclidean Distance: When $\| \mathbf { y } \| \neq 0$ , we have
+
+$$
+\operatorname* { l i m } _ { \frac { \| \mathbf { x } \| } { \| \mathbf { y } \| } \to 0 } \frac { \| \mathbf { x } - \mathbf { y } \| } { \| \mathbf { x } \| + \| \mathbf { y } \| } = \operatorname* { l i m } _ { \frac { \| \mathbf { x } \| } { \| \mathbf { y } \| } \to 0 } \frac { \frac { \| \mathbf { x } - \mathbf { y } \| } { \| \mathbf { y } \| } } { \frac { \| \mathbf { x } \| } { \| \mathbf { y } \| } + 1 } = 1 ,
+$$
+
+$$
+\begin{array} { r } { ) \ : z = \frac { \| \mathbf { x } - \mathbf { y } \| } { \| \mathbf { y } \| + \| \mathbf { x } - \mathbf { y } \| } } \end{array}
+$$
+
+![](images/9f4199a70f08998d140b20456d078fc551eadb84925958cf776b7b49c789f7af.jpg)  
+Figure 5: Contours of different measures. Note that the $x$ - and $y \cdot$ -axes are the angle (i.e., $\angle \mathbf { x } , \mathbf { y } )$ between $\mathbf { x }$ and $\mathbf { y }$ , and the magnitude ratio $\frac { \| \mathbf { x } \| } { \| \mathbf { y } \| }$ , respectively. (a) Cosine distance; (b) Euclidean distance where $\| \mathbf { y } \| = 0 . 2$ ; (c) Asymmetric gradient distance.
+
+$$
+\begin{array} { r l } { \underset { \| \mathbf { x } \| } { \operatorname* { l i m } } \underset { \| \mathbf { x } \| } { \operatorname* { l i m } } \left\| \mathbf { x } - \mathbf { y } \right\| } & { = \underset { \| \mathbf { x } \| } { \operatorname* { l i m } } \underset { \| \mathbf { x } \| } { \operatorname* { l i m } } \left\| \left( \frac { \| \mathbf { x } \| } { \| \mathbf { y } \| } \right) ^ { 2 } - 2 \frac { \| \mathbf { x } \| } { \| \mathbf { y } \| } \cos \angle \mathbf { x } , \mathbf { y } + 1 \right. } \\ & { = \underset { \| \mathbf { x } \| } { \operatorname* { l i m } } \underset { \| \mathbf { x } \| } { \operatorname* { l i m } } \left. \frac { 2 \cos \angle \mathbf { x } , \mathbf { y } + 2 } { \| \mathbf { y } \| } - \frac { 2 \cos \angle \mathbf { x } , \mathbf { y } + 2 } { \| \mathbf { y } \| } + 1 \right. } \\ & { = 1 . } \end{array}
+$$
+
+Table 6: Comparisons between different tolerances of AGD on PS-CIFAR-100.   
+
+<table><tr><td>Y</td><td>Tolerance</td><td>Ar (%)</td><td>Fr (%)</td></tr><tr><td>0.2</td><td>5/6</td><td>69.283 ± 0.307</td><td>24.126 ± 0.472</td></tr><tr><td>0.5</td><td>2/3</td><td>69.486 ± 0.204</td><td>24.520 ± 0.570</td></tr><tr><td>1 (ours)</td><td>1/2</td><td>70.078 ± 0.134</td><td>24.907 ± 0.720</td></tr><tr><td>2</td><td>1/ /3</td><td>69.626 ± 0.192</td><td>24.344 ± 0.610</td></tr><tr><td>３４</td><td>1/4</td><td>69.505 ± 0.442</td><td>24.479 ± 0.408</td></tr><tr><td></td><td>1/5</td><td>69.332 ± 0.142</td><td>24.600 ± 0.404</td></tr></table>
+
+The discrepancy using Normalized EuDist has the same value when means no tolerance. $\mathrm { l i m } _ { \frac { \| \mathbf { x } \| } { \| \mathbf { y } \| }  0 }$ and $\operatorname* { l i m } _ { \| \mathbf { x } \| } { } _ { \infty }$ , which
+
+AGD and Proof of Corollary 1: According to Eq. (13), we have
+
+$$
+\operatorname* { l i m } _ { \| \mathbf { x } \| \to 0 } \widehat { D } ( \mathbf { x } , \mathbf { y } ) = \operatorname* { l i m } _ { \frac { \| \mathbf { x } \| } { \| \mathbf { y } \| } \to 0 } 1 - \frac { 1 } { 1 + \frac { \| \mathbf { x } - \mathbf { y } \| } { \| \mathbf { y } \| } } = \frac { 1 } { 2 } ,
+$$
+
+$$
+\operatorname* { l i m } _ { \| \mathbf { x } \|  \infty } \widehat { D } ( \mathbf { x } , \mathbf { y } ) = \operatorname* { l i m } _ { \frac { \| \mathbf { x } \| } { \| \mathbf { y } \| }  \infty } 1 - \frac { 1 } { 1 + \frac { \| \mathbf { x } - \mathbf { y } \| } { \| \mathbf { y } \| } } = 1 .
+$$
+
+The two equations denote that when $\frac { \| \mathbf { x } \| } { \| \mathbf { y } \| }  0$ , AGD has the tolerance value $\begin{array} { r } { { \frac { 1 } { 2 } } < \operatorname* { l i m } _ { \frac { \| \mathbf { x } \| } { \| \mathbf { y } \| }  \infty } = 1 } \end{array}$ , which means that $\| \mathbf { x } \| < < \| \mathbf { y } \|$ is acceptable as the half of perfect equal.
+
+# C.2 DIFFERENT TOLERANCE ANALYSIS
+
+In our paper, we propose an Asymmetric Gradient Distance (AGD) to evaluate the gradient discrepancy. AGD is designed to have a tolerance $\begin{array} { l } { { \frac { 1 } { 2 } } } \end{array}$ in Corollary 1. This is because updating with a zero gradient will neither improve nor damage the performance. Even though, we prefer positive influence rather than non-influence. Thus, we define that the distance $\widehat { D } ( \mathbf { g } _ { \mathrm { A } } , \mathbf { g } _ { \mathrm { B } } )$ in the situation $\| \mathbf { g } _ { \mathrm { A } } \| \ll \| \mathbf { g } _ { \mathrm { B } } \|$ is the mid-level in the value range.
+
+In this subsection, we try to change the tolerance and observe the performance change. The tolerance can be controlled by adding a factor $\gamma > 0$ . Omitting the edge situation, we have
+
+$$
+\widehat { D } ( g _ { \mathrm { A } } , g _ { \mathrm { B } } ) = \frac { \| g _ { \mathrm { A } } - g _ { \mathrm { B } } \| } { \gamma \| g _ { \mathrm { B } } \| + \| g _ { \mathrm { A } } - g _ { \mathrm { B } } \| } .
+$$
+
+The experiments on different tolerances are shown in Table 6. The results show either larger or smaller tolerances compared to $\frac { \mathrm { 1 } } { \mathrm { 2 } }$ will get the performance drop.
+
+# D CONTOUR OF AGD
+
+We show more function contour comparisons with existing measurement methods in Fig. 5, where the axes are the angle $\angle \mathbf { x } , \mathbf { y }$ , the ratio $\frac { \| \mathbf { x } \| } { \| \mathbf { y } \| }$ and the metric contour value $z$ for better visualization. As we can see, the CosDist (Fig. 5(a)) has no relation to the ratio. The tolerance for $\mathrm { l i m } _ { \frac { \| \mathbf { x } \| } { \| \mathbf { y } \| }  0 }$ of EuDist depends on the norm of y (Fig. 5(b)). The proposed AGD has fixed tolerance for $\mathrm { l i m } _ { \frac { \| \mathbf { x } \| } { \| \mathbf { y } \| }  0 }$ as shown in Fig. 5(c).
+
+# E INTRODUCTION OF MGDA
+
+At any time, PCL training yields the following dynamic multi-objective empirical risk minimization formulation:
+
+$$
+\operatorname* { m i n } _ { \theta , \{ \theta _ { i } | i \in { \mathcal { T } } \} } \quad \left\{ { \ell } _ { i } \left( { \mathcal { D } } _ { i } \right) \vert i \in { \mathcal { T } } _ { t } \right\} ,
+$$
+
+where $\tau$ is the task index set with activated data streams at time t.
+
+Table 7: Comparisons between using AGD with and without rehearsal gradient on PS-CIFAR-100.   
+
+<table><tr><td>Method (+ Rehearsal)</td><td>Ar (%)</td><td>FT (%)</td></tr><tr><td>MaxDO (w/o rehearsal gradient)</td><td>68.398 ± 0.776</td><td>23.676 ± 0.583</td></tr><tr><td>MaxDO (w/ rehearsal gradient)</td><td>70.078 ± 0.134</td><td>24.907 ± 0.720</td></tr><tr><td></td><td></td><td></td></tr></table>
+
+An elegant solution to the MOO for Pareto optimality Buchanan (1962) is the Steepest Descent Method (SDM) Fliege & Svaiter (2000), which aims to obtain an optimal descent direction $d ^ { * }$ that satisfies
+
+$$
+d ^ { * } , \alpha ^ { * } = \arg \operatorname* { m i n } \lrcorner d , \alpha \quad \alpha + \frac { 1 } { 2 } \left\| d \right\| ^ { 2 } , \mathrm { s . t . } \quad g . i ^ { \top } d \leq \alpha , \quad \forall i \in \mathcal { T } ,
+$$
+
+where the constraints let each task have non-conflict with gradient $d$ . Considering the Lagrange multipliers and Karush–Kuhn–Tucker (KKT) condition, the dual problem solved by the MultiGradient Descent Algorithm (MGDA) Desid ´ eri (2012) is ´
+
+$$
+w ^ { * } = \arg \operatorname* { m i n } _ { \mathbf { w } } \quad \left\| \sum _ { i } \mathbf { w } _ { i } \mathbf { g } _ { i } \right\| ^ { 2 } , \mathrm { s . t . } \quad \sum _ { i } \mathbf { w } _ { i } = 1 \mathrm { a n d } \mathbf { w } _ { i } \geq 0 , \forall i .
+$$
+
+The objective of MGDA is 0 and the resulting point satisfies the KKT conditions, or the solution gives a Pareto descent direction that improves all tasks.
+
+# F MAXDO EFFECTS ON REHEARSAL
+
+In rehearsal-based PCL, the training conflict may worsen the forgetting of old tasks. That is, the new task produces large gradients and may mislead the replay of old tasks with small gradients. In our method, we consider reducing this gradient conflict and propose to measure the asymmetric gradient distance. Moreover, we propose to minimize the maximum discrepancy among multiple gradients.
+
+To show the MaxDO’s effectiveness of forgetting reduction on rehearsal gradient, we evaluate the result that only leverages MaxDO on new tasks instead memory data stream (i.e., finished tasks). The result is shown in Fig. 7. In this case, the final gradient is calculated by $\begin{array} { r } { \mathbf { d } = \frac { 1 } { 2 } \mathbf { g } _ { \mathrm { r e h e r a s a l } } + \frac { 1 } { 2 } \mathbf { g } _ { \mathrm { n e w } } , } \end{array}$ where $\mathrm { g } _ { \mathrm { n e w } }$ is the solution gradient via MaxDO on only new tasks. The result shows that it is necessary to put the rehearsal gradient to the MaxDO. Otherwise, the model will get worse accuracy and weak forgetting.

parse/dev/o4neHaKMlse/o4neHaKMlse.md

@@ -0,0 +1,287 @@
+# Coarse-to-Fine Vision-Language Pre-training with Fusion in the Backbone
+
+Zi-Yi Dou∗‡, Aishwarya Kamath∗♮, Zhe $\mathbf { G a n ^ { * } } ^ { \star \star }$ , Pengchuan Zhang§, Jianfeng Wang† Linjie $\mathbf { L i } ^ { \dagger }$ , Zicheng $\mathbf { L i u } ^ { \dagger }$ , Ce $\mathbf { L i u } ^ { \dagger }$ , Yann LeCun♮, Nanyun Peng‡, Jianfeng $\mathbf { G a o } ^ { \dagger }$ , Lijuan Wang† †Microsoft ‡University of California, Los Angeles ♮New York University {zdou,violetpeng}@cs.ucla.edu, {aish,yann.lecun}@nyu.edu, pengchuanzhang@fb.com {zhgan,jianfw,linjli,zliu,liuce,jfgao,lijuanw}@microsoft.com
+
+# Abstract
+
+Vision-language (VL) pre-training has recently received considerable attention. However, most existing end-to-end pre-training approaches either only aim to tackle VL tasks such as image-text retrieval, visual question answering (VQA) and image captioning that test high-level understanding of images, or only target region-level understanding for tasks such as phrase grounding and object detection. We present FIBER (Fusion-In-the-Backbone-based transformER), a new VL model architecture that can seamlessly handle both these types of tasks. Instead of having dedicated transformer layers for fusion after the uni-modal backbones, FIBER pushes multimodal fusion deep into the model by inserting cross-attention into the image and text backbones, bringing gains in terms of memory and performance. In addition, unlike previous work that is either only pre-trained on image-text data or on fine-grained data with box-level annotations, we present a two-stage pretraining strategy that uses both these kinds of data efficiently: (i) coarse-grained pre-training based on image-text data; followed by (ii) fine-grained pre-training based on image-text-box data. We conduct comprehensive experiments on a wide range of VL tasks, ranging from VQA, image captioning, and retrieval, to phrase grounding, referring expression comprehension, and object detection. Using deep multimodal fusion coupled with the two-stage pre-training, FIBER provides consistent performance improvements over strong baselines across all tasks, often outperforming methods using magnitudes more data. Code is available at https://github.com/microsoft/FIBER.
+
+# 1 Introduction
+
+Inspired by the success of language model pre-training [11, 51, 42], coupled with the unification of architectures used in the NLP and computer vision communities [12, 4], vision-language pre-training (VLP) [62, 45, 33, 6] has been receiving an increasing amount of attention. It has been proven that VLP can establish state-of-the-art performance on visual question answering [3], visual reasoning [60], image captioning, and image-text retrieval [41]. The pre-training objectives commonly used for these tasks, such as image-text matching, image conditioned masked language modeling and image-text constrastive learning, require multimodal understanding at the image level. Typically, this means the pre-training is done using images at lower resolution (e.g., $3 8 4 \times 3 8 4$ ), making it possible to scale up training by using large batch sizes.
+
+Recently, it has also been shown that tasks such as image classification and object detection (OD), which have been traditionally viewed as vision-only tasks, can benefit from being cast as VL tasks [50, 25, 34, 26]. Inspired by MDETR [26], GLIP [34] reformulates standard classificationbased OD as phrase grounding. This opens up the possibility to leverage VLP for OD, and vice versa, and this unification has led to impressive performance on several established OD as well as phrase grounding benchmarks [49]. Since these tasks involve fine-grained image understanding between regions in the image and phrases in the text, and also require prediction of precise bounding boxes at the output, the pre-training typically involves using high resolution input images (e.g., $8 0 0 \times 1 , 3 3 3 ,$ ).
+
+![](images/8afe3400f4173ca1b0f613fa777f89bb7d2728cb877a2293a26fa7db7f619fb8.jpg)  
+Figure 1: The proposed coarse-to-fine pre-training framework for vision-language tasks. We first perform coarse-grained pre-training with image-text data for VQA, image captioning and retrieval tasks, and then perform fine-grained pre-training with image-text-box data for phrase grounding and object detection tasks. The same FIBER architecture is used for both stages. OD: object detection. MLM: masked language modeling. ITM: image-text matching. ITC: image-text contrastive loss.
+
+Existing multimodal architectures typically do not support both kinds of tasks. Specifically, the fully end-to-end VLP models such as ALBEF [32], METER [13], and SimVLM [67] can achieve the state of the art (SoTA) on image-level understanding tasks, but it is non-trivial to extend them for region-level VL tasks because predicting bounding boxes is typically hard in end-to-end settings. On the other hand, MDETR [26] and GLIP [34] are designed to predict bounding boxes, but have not been shown to support tasks such as image captioning and retrieval. Further, fine-grained pretraining not only requires data with bounding box annotations that are cumbersome to acquire, but the requirement of high input image resolution makes pre-training very costly, especially when using standard Transformer architectures [63] that have quadratic complexity in the size of the image. A natural but challenging question arises: can we have a unified framework for efficient VL pre-training that benefits both image-level and region-level VL tasks (e.g., both VQA and $O D$ )?
+
+We answer this question by proposing two ideas: $( i )$ a novel model architecture that can handle various types of tasks and pre-training strategies (high and low resolution inputs, image and region level outputs) more efficiently than previous work (see Section 3.1 and 4), and $( i i )$ a two-stage pre-training pipeline.
+
+In terms of architecture, we present FIBER, shown in Figure 2, which performs deep multimodal fusion in the backbone. Specifically, instead of having a few dedicated transformer layers on top of the image and text encoders for fusion (e.g., as is commonly done in previous work [36, 6, 13, 26, 34]), we propose to directly insert cross-attention modules into the image and text backbones. Additionally, we support the ability to switch between a dual encoder (for
+
+![](images/59ab2a9918c66b9e49af9c3bd096b5bae7c30e64401511f747661fde80d3d915.jpg)  
+Figure 2: Model architecture for FIBER. Swin transformer is used as the image backbone, simplified here for illustration purposes.
+
+fast image retrieval) and a fusion encoder (for VQA and captioning) readily, by switching on or off the cross-attention modules. With the same model architecture, by simply adding an object detection head (e.g., Dynamic Head [9]) on top, FIBER can be readily extended to visual grounding, referring expression comprehension and (open-vocabulary) OD tasks as well.
+
+![](images/56ac8524c9003e78c420110abadb90484e4955fd886d3631310593a524cc0c16.jpg)  
+Figure 3: FIBER can be readily adapted to various downstream VL tasks, ranging from VQA, image captioning and retrieval, to phrase grounding and object detection (OD).
+
+By considering the nature of different VL tasks, FIBER is pre-trained with a coarse-to-fine two-stage pipeline, as detailed in Figure 1. Specifically,
+
+• During coarse-grained pre-training, FIBER takes low-resolution $( 3 8 4 \times 3 8 4 )$ images as input, and is pre-trained with image-text matching, masked language modeling, and image-text contrastive losses, as used in previous work [13, 66, 64]. The pre-trained model can then be directly finetuned for VQA and image captioning tasks (Figure 3a and 3c). By switching off the cross-attention modules, FIBER also automatically functions as a dual encoder for fast image-text retrieval (Figure 3b). • During fine-grained pre-training, FIBER uses the coarse pre-trained model as initialization, in addition to randomly initialized parameters for the OD head. At this stage, the model takes highresolution $( 8 0 0 \times 1 , 3 3 3 )$ ) images as input, and is pre-trained with bounding box localization loss and word-region alignment loss, as used in GLIP [34]. We use image-text-box data with ground-truth box annotations for pre-training, and the model can be directly fine-tuned for grounding and detection tasks (Figure 3d).
+
+Compared to fine-grained pre-training, coarse-grained pre-training is easier to scale up, as it only requires paired image-text data which can be easily harvested from the web. Crucially, we show that re-using all the parameters from our coarse-grained pre-trained model for fine-grained pre-training alleviates the requirement for large amounts of box-level annotated data. In our experiments, we show that on fine-grained tasks such as Flickr30k Entities, FIBER using coarse-grained pre-training achieves gains even over previous SoTA (GLIP [34]) that uses $2 5 \times$ more box-level annotated images during the fine-grained pre-training stage. We also show that our architecture is much more efficient in terms of training time on OD tasks, as compared to GLIP .
+
+FIBER is the first end-to-end VLP model that can support VL tasks encompassing image-level and region-level outputs. We conduct experiments on VQAv2 [3], $\mathrm { \ N L V R ^ { 2 } }$ [60], COCO captioning [41], NoCaps [1], COCO and Flickr $3 0 \mathrm { k }$ image-text retrieval [49], as well as on phrase grounding [49], referring expression comprehension [75], COCO and LVIS detection [17], and a suite of 13 object detection in the wild datasets [34]. We show that our model can provide consistent performance improvement over strong baselines (e.g., METER [13] and GLIP [34]) across tasks.
+
+# 2 Related Work
+
+VLP for Classical VL Tasks. ViLBERT [45] and LXMERT [62] were the first two methods to introduce using transformers for VLP. Since then, we have witnessed a boom of VLP methods [33, 30, 59, 73, 22, 71, 81, 38, 7, 35]. Early methods mainly focus on the use of pre-trained object detectors to extract image region features offline, such as UNITER [6], OSCAR [36], VILLA [15] and VinVL [79]. More recently, end-to-end VLP methods that use the image directly as input have become popular. In these approaches, convolution networks or vision transformers [12] are used as the image backbone, with additional transformer layers for modeling multimodal fusion [24, 23, 28, 68, 32, 64]. Prominent examples along this line include ViLT [28], ALBEF [32], SimVLM [67], METER [13], X-VLM [77] and BLIP [31]. These models have achieved the current SoTA on major VL benchmarks such as VQA and image captioning. However, they cannot be directly used for tasks such as object detection.
+
+Table 1: Comparison among different VLP models. FIBER is the only VLP model that can support all tasks considered. (†) VQA is used as a representative VL classification task. $( \ddagger )$ $O ( n + m )$ retrieval denotes model backbones process inputs $O ( n + m )$ times given $_ n$ images and $m$ text sentences during image-text retrieval. $( \ast )$ Here, we mainly focus on what tasks CLIP can be directly used for.   
+
+<table><tr><td>Model</td><td>VQA+</td><td>O(n+m) Retrieval* Captioning Grounding</td><td></td><td></td><td>OD</td><td>End2End</td></tr><tr><td>ViLBERT [45],LXMERT [62], UNITER [6]</td><td>√</td><td>xxx&lt;xx&lt;&gt;</td><td>x&lt;x×</td><td></td><td>xxxxxxxx&lt;×</td><td>×</td></tr><tr><td>OSCAR [36],VinVL [79]</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>PixelBERT [24], CLIP-ViL [57],ViLT[28]</td><td>√</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>CLIP [50]*, ALIGN [25]</td><td>×</td><td></td><td></td><td>xxxxxxν</td><td></td><td>x&gt;&gt;&gt;</td></tr><tr><td>VL-T5 [7]</td><td>√</td><td></td><td>&lt;&lt;x&gt;</td><td></td><td></td><td>×√√</td></tr><tr><td>METER[13], SimVLM[67]</td><td>√</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>ALBEF[32],FLAVA [58],VLMo [66]</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>BLIP[31],CoCa [74],Flamingo [2]</td><td></td><td></td><td></td><td></td><td></td><td>√</td></tr><tr><td>MDETR [26], GLIP [34]</td><td>√</td><td>×</td><td>×</td><td></td><td></td><td>√</td></tr><tr><td>UniTAB [70], X-VLM[77],OFA [65]</td><td>√</td><td>×</td><td>√</td><td>√</td><td></td><td>√</td></tr><tr><td>FIBER</td><td>√</td><td>√</td><td>√</td><td>√</td><td>√</td><td>√</td></tr></table>
+
+VLP for Vision Tasks. Recently, it has been shown that image-text data can be used to learn image encoders from scratch [10, 54]. By performing large-scale contrastive pre-training, CLIP [50] and ALIGN [25] display strong zero-shot image classification capabilities. While these models mainly tackle image-level understanding tasks, MDETR [26] extends the end-to-end OD model DETR [4], and uses contrastive learning along with an alignment loss to learn correspondences between image regions and text phrases, opening up the possibility to tackle tasks such as phrase grounding and long-tailed OD using VL models. This has inspired many follow-up works to further enhance the pre-training [37, 72, 46, 69], among which GLIP [34] shows that OD can also be cast as a VL task (i.e., phrase grounding). However, it has not been shown how traditional VL tasks such as VQA, captioning and retrieval can be well supported in GLIP [34] and MDETR [26].
+
+Unified VL Modeling. There have been a few recent attempts that try to develop unified VL models. VL-T5 [7] unifies VL tasks as text generation; however, pre-trained object detectors are used for image feature extraction, so the model cannot be end-to-end pre-trained. UniT [20] proposes a multimodal multi-task framework with a unified transformer; however, it can only support VQA and object detection tasks, but not captioning and grounding. GPV [18] proposes a general-purpose vision system, and FLAVA [58] presents a VL system similar to METER [13]; however, they did not evaluate on grounding and detection tasks, and their performance on other VL tasks is still far from SoTA. UniTAB [70] and OFA [65] reformulate grounding as a sequence generation task, by borrowing ideas from Pix2Seq [5]. However, these approaches have not been demonstrated to work on standard OD benchmarks, and also cannot be used as dual encoders for fast image retrieval. Our model is the first work that can support not only VQA, image captioning and $O ( n + m )$ retrieval, but also visual grounding and object detection, with impressive performance across all tasks. A detailed comparison is provided in Table 1.
+
+# 3 Method
+
+In this section, we first describe the proposed model architecture in Section 3.1. We then illustrate our two-stage pre-training paradigm in Section 3.2, followed by fine-tuning strategies for all the tasks supported by FIBER in Section 3.3.
+
+# 3.1 Fusion in the Backbone
+
+The architecture of FIBER is shown in Figure 2. Different from models that stack a modality fusion module on top of the vision or language backbones [6, 13], we insert multimodal fusion inside the backbones, and include a gating mechanism for the cross-modal layers (shown in Figure 4). Specifically, at each encoding layer, we have:
+
+$$
+\begin{array} { r l } & { \tilde { \pmb { x } } = \mathrm { S E L F - A T T } \big ( \pmb { x } \big ) , } \\ & { \pmb { x } = \pmb { x } + \tilde { \pmb { x } } + \alpha * \mathrm { C R O S S - A T T } \big ( \tilde { \pmb { x } } , \pmb { y } \big ) , } \\ & { \pmb { x } = \pmb { x } + \mathrm { F F N } ( \pmb { x } ) , } \end{array}
+$$
+
+![](images/9f15e12e946c7e98a661c6f229461dc50231eba805caf50b8753e903cd947328.jpg)  
+xFigure 4: Illustration of performing fusion in the backbone. $( { \pmb x } , { \pmb y } )$ are the (image, text) or (text, image) representations, and $\alpha$ is a learnable scalar.
+
+where $\alpha$ is a learnable parameter initialized to 0. For simplicity, we insert the same number of cross-attention layers into the vision and language backbones.
+
+By inserting cross-attention layers with the gating mechanism, we enable cross-modal interactions without affecting the original computational flow of the backbones at the beginning of model training. Also, we can easily switch off the interactions by setting $\alpha$ to 0, and the backbones can be used in the dual-encoder setting. In addition, compared to stacking a large number of transformer layers on top of the backbones, our approach of inserting cross-attention layers is relatively light-weight and thus more memory-efficient. To illustrate, both GLIP [34] and METER [13] use an additional 110M modality fusion parameters for a base-size model, while FIBER only adds about 26M parameters. During training, the fusion module of FIBER only consumes half of the FLOPs needed by METER (12.35 vs. 24.04 GFLOPs for one instance). We experimented with two other model variants for fusion in the backbone, the details of which are provided in Appendix.
+
+# 3.2 Coarse-to-Fine Pre-training
+
+We divide VL tasks into two categories based on whether or not we need to generate region-level outputs on the image side. While these two kinds of tasks are characteristically different, they both require fusion between the vision and language modalities, and we hypothesize that sharing as many parameters as possible between the model used for these two sets of tasks will be beneficial. Based on this motivation, we propose a two-stage pre-training paradigm, where we first pre-train models with image-level objectives on images at low resolution, and then perform further pre-training with region-level objectives where the input images are at a higher resolution. In this way, the coarsegrained supervision from the first stage can provide good initialization for the second stage for all the shared parameters. FIBER with the same architecture (Swin Transformer [43] and RoBERTa [42]) is used as the backbone for both stages of pre-training.
+
+Coarse-grained Pre-training. For tasks like VQA and captioning, it has been demonstrated [32, 13, 66] that masked language modeling (MLM), image-text matching (ITM), and image-text contrastive (ITC) objectives are helpful for ViT-based VLP models. Following previous work, we use all the three objectives during pre-training. Specifically,
+
+• For ITC, the inserted cross-attention modules are switched off, so FIBER functions as a dual encoder. Given a batch of $N$ image-caption pairs, we first compute their representations with our vision and language encoders independently without modality fusion, and then maximize the similarities between $N$ positive image-text pairs while minimizing the similarities between the rest $N ^ { 2 } - N$ negative pairs, via a contrastive loss.   
+• For MLM and ITM, the inserted cross-attention modules are switched on, so FIBER now functions as a fusion encoder. For MLM, we randomly mask $15 \%$ of the input tokens and the model is trained to reconstruct the original tokens. For image-text matching, the model is given an image-text pair and predicts whether they are matched. Following VLMo [66], we sample global hard negatives based on the similarities computed from the above ITC loss.
+
+Fine-grained Pre-training. Most existing VL architectures [6, 62, 26, 31, 65, 7] use vanilla transformers both for encoding the vision as well as language inputs. However, in contrast to tokens in text, the entities of interest in images do not all occur at the same scale. Being able to accurately model the image at different scales is especially important for tasks such as object detection and phrase grounding. To handle this, it is typical in object detection literature to use input images at higher resolutions $( 8 0 0 \times 1 3 3 3 )$ , which becomes problematic when using vanilla transformers that scale quadratically in the length of the input sequence. As mentioned earlier, we use a Swin Transformer [43] as our image encoder, which provides hierarchical representations of the image while having linear complexity in the size of the image. We combine these multi-scale representations using an FPN [39] for object detection training. For fine-grained pre-training, we switch on the cross-attention modules, using FIBER as a fusion encoder. This ensures that the image representations that are passed to the FPN are already text-aware, and is a crucial difference compared to GLIP [34], where the image-text fusion takes place in the object detection head. Once the text-aware image features are extracted by the Swin backbone and image-aware text features are extracted using RoBERTa [42], the image features after the FPN are fed to a DynamicHead [9] which predicts a set of regions. Just as in [34], we compute the dot product between the image region features $R _ { \mathrm { T A } }$ and the contextualized token representations $\mathbf { \delta T _ { \mathrm { I A } } }$ to compute the grounding score:
+
+$$
+\begin{array} { r } { I _ { \mathrm { T A } } , T _ { \mathrm { I A } } = \mathrm { F I B E R } ( I , T ) , R _ { \mathrm { T A } } = \mathrm { O D } { \cdot } \mathrm { H E A D } ( I _ { \mathrm { T A } } ) , S _ { \mathrm { G R O U N D I N G } } = R _ { \mathrm { T A } } T _ { \mathrm { I A } } ^ { \top } , } \end{array}
+$$
+
+where $R _ { \mathrm { T A } }$ represents regions that are text aware, produced using the OD-Head that takes as input $I _ { \mathrm { T A } }$ , which are image representations that are already text-aware and $\mathbf { \delta T _ { \mathrm { I A } } }$ are the text features that have already attended to the image features. The typical object detection model has a classification head that predicts the label of the object, and a localization head that predicts the bounding box. We follow GLIP [34] by substituting the classification head with the grounding score SGROUNDING. The localization loss is composed of two parts: a centerness loss and GIoU loss, which are used to supervise the box prediction. Taken together, FIBER learns the correspondence between regions in the image and phrases in the text, making it possible to tackle tasks such as phrase grounding and object detection using the same framework. We use ATSS framework [80] in our paper, but our method can be combined easily with other object detectors such as Faster-RCNN [52] and RetinaNet [40] as well.
+
+# 3.3 Adaptation to Downstream Tasks
+
+We now describe how we adapt FIBER to different downstream tasks as depicted in Figure 3.
+
+• For VL classification tasks such as VQA, we use FIBER as a fusion encoder. Specifically, the top $M$ layers of the vision and language backbones interact with each other and produce multimodal representations. The final layer representations of the two modalities are concatenated together to generate the final outputs for tasks such as VQA and visual reasoning.
+
+• For retrieval tasks, we switch off the inserted cross-attention modules to use FIBER as a dual encoder for fast image-text retrieval.
+
+• For captioning, we adapt FIBER by only keeping the image-to-text cross-attentions and using causal masks in the decoding side. The representations of the final image encoding layer are fed into the cross-attention modules. In this way, the model is turned into a seq2seq model [61, 8] and performs captioning in an auto-regressive way.
+
+• For phrase grounding, object detection and referring expression comprehension, we use FIBER as a fusion encoder, and the OD-Head introduced during fine-grained pre-training receives image features that are already language aware due to the multimodal representations extracted by FIBER. The pre-trained model is directly used without any modifications for these tasks.
+
+# 4 Experiments
+
+Pre-training Datasets. Following previous work [6, 28, 32, 13, 64, 66], we perform coarsegrained pre-training on COCO [41], Conceptual Captions [56], SBU Captions [47], and Visual Genome [29]. The four datasets consist of about 4M images in total. For fine-grained pretraining, we use two data sources: data curated by MDETR [26] after removing the COCO images, and the Objects365 [55] detection dataset, together consisting of about $0 . 8 { \bf M }$ images. We ensure that we exclude any data that exists in the validation or test splits of downstream tasks.
+
+# Architecture. We adopt Swin-Base [43] and
+
+<table><tr><td>Type of Fusion</td><td>CoCo Val2017</td><td>GPU-hours V100 (32GB)</td><td> Sec/Iter</td></tr><tr><td>No Fuse</td><td>53.9</td><td>511</td><td>1.31</td></tr><tr><td>GLIP-B [34]</td><td>54.6</td><td>840</td><td>2.14</td></tr><tr><td>FIBER-B</td><td>54.5</td><td>540</td><td>1.38</td></tr></table>
+
+Table 2: Object detection on COCO [41], without visionlanguage pre-training. We initialize the text encoder and image backbones using a pre-trained RoBERTa and a Swin transformer pre-trained on ImageNet22k. Our proposed FIBER model achieves the same performance as GLIP [34] while taking much less time to train.
+
+RoBERTa-Base [42] as our vision and text backbones, which are initialized with weights from uni-modal pre-training. We insert cross-attention blocks into the top 6 blocks of the vision and text encoders. The input resolution is $3 8 4 \times 3 8 4$ for coarse-grained pre-training and $8 0 0 \times 1 , 3 3 3$ for fine-grained pre-training. Using a hierarchical vision transformer enables us to efficiently tackle these high resolution tasks, which would be expensive in models such as BLIP [31] that rely on the vanilla transformer architecture. In METER [13], which does explore using a Swin transformer as the image encoder, the multi-modal fusion occurs in layers specifically designed to align the modalities, only after the image and text features are extracted from the uni-modal backbones. This is in contrast to our approach where the hierarchical image features that are used in the FPN for fine-grained training are already language aware, due to the multi-modal fusion being in the backbone. This also lets us avoid adding additional “language-aware deep fusion layers” [34] as part of the OD head as in GLIP, resulting in $1 . 5 \mathrm { x }$ faster training while maintaining performance as shown in Table 2. While in principle it would be possible to use the image features extracted by METER’s backbone for object detection, it would be necessary as in GLIP to add additional layers to make the visual features “language-aware” for good detection performance, especially on datasets with limited training data and with rare and infrequent objects.
+
+Table 3: Results on VL classification and retrieval. We also include models pre-trained on more data and/or with larger size. FIBER and VLMo use dual encoders for retrieval. (†) ALBEF, X-VLM, and BLIP first use its dual encoder to obtain top- $k$ candidates, and then use its fusion encoder to re-rank the candidates. Our retrieval results with re-ranking are provided in Table 4. All the other models use fusion encoders.   
+
+<table><tr><td rowspan="2">Model</td><td rowspan="2">#Pretrain Images</td><td colspan="2">VQAv2</td><td colspan="2">NLVR²</td><td colspan="2">Flickr30k</td><td colspan="2">CoCo</td></tr><tr><td>test-dev test-std</td><td></td><td>dev</td><td></td><td>test-P IR@1 TR@1</td><td></td><td></td><td>IR@1 TR@1</td></tr><tr><td colspan="10">Base-size models pre-trained on COco,VG, SBU, and CC datasets</td></tr><tr><td>UNITER-B [6]</td><td>4M</td><td>72.70</td><td>72.91</td><td>77.18</td><td>77.85</td><td>72.5</td><td>85.9</td><td>50.3</td><td>64.4</td></tr><tr><td>VILLA-B [15]</td><td>4M</td><td>73.59</td><td>73.67</td><td>78.39</td><td>79.30</td><td>74.7</td><td>86.6</td><td>-</td><td>1</td></tr><tr><td>UNIMO-B [35]</td><td>4M</td><td>73.79</td><td>74.02</td><td>1</td><td>-</td><td>1</td><td>1</td><td>-</td><td>-</td></tr><tr><td>ViLT-B [28]</td><td>4M</td><td>71.26</td><td>-</td><td>75.70</td><td>76.13</td><td>64.4</td><td>83.5</td><td>42.7</td><td>61.5</td></tr><tr><td>ALBEF-B [32]</td><td>4M</td><td>74.54</td><td>74.70</td><td>80.24</td><td>80.50</td><td>82.8t</td><td>94.3t</td><td>56.8t</td><td>73.1t</td></tr><tr><td>VLMo-B [66]</td><td>4M</td><td>76.64</td><td>76.89</td><td>82.77</td><td>83.34</td><td>79.3</td><td>92.3</td><td>57.2</td><td>74.8</td></tr><tr><td>METER-Swin-B[13]</td><td>4M</td><td>76.43</td><td>76.42</td><td>82.23</td><td>83.47</td><td>79.02</td><td>92.4</td><td>54.85</td><td>72.96</td></tr><tr><td>X-VLM [77]</td><td>4M</td><td>78.22</td><td>78.37</td><td>84.41</td><td>84.76</td><td>86.9t</td><td>97.0t</td><td>63.4t</td><td>81.2t</td></tr><tr><td colspan="10">Models pre-trained on more data and/or with larger : size</td></tr><tr><td>VLMo-L [66]</td><td>4M</td><td>79.94</td><td>79.98</td><td>85.64</td><td>86.86</td><td>84.5</td><td>95.3</td><td>60.6</td><td>78.2</td></tr><tr><td>BLIPCapFit-L [31]</td><td>129M</td><td>78.25</td><td>78.32</td><td>82.15</td><td>82.24</td><td>87.5†</td><td>97.2t</td><td>64.1†</td><td>81.2t</td></tr><tr><td>SimVLM-B[67]</td><td>1.8B</td><td>77.87</td><td>78.14</td><td>81.72</td><td>81.77</td><td></td><td>-</td><td>-</td><td>1</td></tr><tr><td>SimVLM-H[67]</td><td>1.8B</td><td>80.03</td><td>80.34</td><td>84.53</td><td>85.15</td><td>二</td><td>-</td><td>-</td><td>-</td></tr><tr><td>FIBER-B</td><td>4M</td><td>78.55</td><td>78.46</td><td>84.59</td><td>85.52</td><td>81.44</td><td>92.90</td><td>58.01</td><td>75.38</td></tr></table>
+
+Implementation Details. We perform coarse-grained pre-training for $1 0 0 \mathrm { k }$ steps with 4,096 batch size on 64 A100 GPUs. We use AdamW [44] with the peak learning rates of 1e-4 for the backbones and 5e-4 for the cross-modal parameters. We use linear warmup over the first 1k steps and linear decay. For fine-grained pre-training, we train for $8 0 0 \mathrm { k }$ steps on 64 V100 GPUs, with a batch size of 64. We use a learning rate of 1e-5 for the language backbone, and 1e-4 for the rest of the model with a weight decay of 0.01. We use a linear warmup over the first 2k steps and then a constant learning rate, with two learning rate drops by a factor of 10 at $67 \%$ and $89 \%$ of the total number of steps.
+
+# 4.1 Results on Downstream Tasks
+
+Vision-Language Classification. We first experiment on two representative VL classification tasks, including VQAv2 [3] and $\mathrm { \tt N L V R } ^ { \mathrm { 2 } }$ [60]. As reported in Table 3, we achieve the best performance compared to other models in the same setting. It is worth noting that FIBER pre-trained with 4M images can achieve better performance than BLIP trained with 129M images and SimVLM trained with 1.8B images. The results indicate that introducing fusion modules into the backbone is an effective alternative to appending them on the top of uni-modal backbones.
+
+Image-Text Retrieval. In Table 3 we report image retrieval performance in the dual encoder setting, achieving competitive performance on both Flickr30k [49] and COCO [41] retrieval tasks. However, previous work has shown that fusion encoders obtain superior performance, albeit at the cost of efficiency as it involves feeding every image-text pair into the model. To illustrate, on the COCO test data, ranking the similarities between 5K images and 25K captions requires the model to process each image-caption pair 75M times, whereas the dual encoder model only needs 30K forward passes. As shown in Table 4, the fusion encoder can indeed surpass the dual encoder on retrieval tasks by a large margin. In addition, directly ensembling the two models by summing their similarity scores together for each image-caption pair can bring us huge improvements.
+
+Table 4: Additional results on image-text retrieval, where (i) the fusion encoder is used for retrieval, or (ii) the dual encoder is first used to obtain top- $k$ candidates, and then the fusion encoder is used to re-rank the candidates. We also provide a full set of results on all evaluation metrics.   
+
+<table><tr><td rowspan="2">Model</td><td colspan="6">Flickr30k</td><td colspan="6">CoCo</td></tr><tr><td>IR@1</td><td>IR@5IR@10 TR@1</td><td></td><td></td><td></td><td></td><td></td><td></td><td>TR@5 TR@10 IR@1 IR@5 IR@10 TR@1</td><td></td><td></td><td>TR@5TR@10</td></tr><tr><td>FIBER-ITC</td><td>81.44</td><td>96.72</td><td>98.48</td><td>92.90</td><td>99.50</td><td>99.90</td><td>58.01</td><td>83.45</td><td>90.11</td><td>75.38</td><td>94.04</td><td>97.36</td></tr><tr><td>FIBER-ITM</td><td>84.10</td><td>97.54</td><td>98.88</td><td>95.10</td><td>99.60</td><td>99.90</td><td>59.03</td><td>84.04</td><td>91.03</td><td>75.14</td><td>93.88</td><td>97.36</td></tr><tr><td>FIBER-ITC+ITMEnsemble</td><td>90.96</td><td>98.44</td><td>99.14</td><td>96.00</td><td>99.70</td><td>100.00</td><td>69.73</td><td>90.66</td><td>94.59</td><td>80.10</td><td>95.60</td><td>97.98</td></tr><tr><td>ALBEF [32]</td><td>82.8</td><td>96.7</td><td>98.4</td><td>94.3</td><td>99.4</td><td>99.8</td><td>56.8</td><td>81.5</td><td>89.2</td><td>73.1</td><td>91.4</td><td>96.0</td></tr><tr><td>X-VLM[77]</td><td>86.1</td><td>97.4</td><td>98.7</td><td>96.8</td><td>99.8</td><td>100.0</td><td>63.1</td><td>85.7</td><td>91.6</td><td>80.4</td><td>95.5</td><td>98.2</td></tr><tr><td>FIBER-Rerank-10</td><td>90.94</td><td>98.16</td><td>98.48</td><td>95.80</td><td>99.60</td><td>99.90</td><td>68.71</td><td>87.69</td><td>90.09</td><td>79.66</td><td>95.34</td><td>97.36</td></tr><tr><td>FIBER-Rerank-20</td><td>90.10</td><td>98.38</td><td>99.14</td><td>95.90</td><td>99.80</td><td>100.00</td><td>69.32</td><td>89.52</td><td>93.33</td><td>79.78</td><td>95.20</td><td>97.66</td></tr><tr><td>FIBER-Rerank-50</td><td>91.08</td><td>98.50</td><td>99.37</td><td>96.10</td><td>99.70</td><td>100.00</td><td>69.58</td><td>90.41</td><td>94.35</td><td>79.98</td><td>95.40</td><td>97.76</td></tr><tr><td>FIBER-Rerank-100</td><td>91.02</td><td>98.54</td><td>99.34</td><td>96.00</td><td>99.70</td><td>100.00</td><td>69.63</td><td>90.54</td><td>94.47</td><td>80.06</td><td>95.60</td><td>97.96</td></tr></table>
+
+<table><tr><td rowspan="2">Model</td><td rowspan="2">#Pretrain Images</td><td colspan="4">CoCo</td><td colspan="2">NoCaps Val</td><td colspan="2">NoCaps Test</td></tr><tr><td>B@4</td><td>M</td><td>C</td><td>s</td><td>C</td><td>S</td><td>C</td><td>S</td></tr><tr><td colspan="10">Models trained without CIDEr optimization</td></tr><tr><td>UFO-B [64]</td><td>4M</td><td>36.0</td><td>28.9</td><td>122.8</td><td>22.2</td><td>80.7</td><td>12.5</td><td>78.8</td><td>12.5</td></tr><tr><td>ViTCAP[14]</td><td>4M</td><td>36.3</td><td>29.3</td><td>125.2</td><td>22.6</td><td>1</td><td>1</td><td>1</td><td>1</td></tr><tr><td>METER-CLIP-B[13]</td><td>4M</td><td>38.8</td><td>30.0</td><td>128.2</td><td>23.0</td><td>-</td><td>=</td><td>=</td><td>=</td></tr><tr><td>X-VLM[77]</td><td>4M</td><td>39.8</td><td>-</td><td>133.1</td><td>1</td><td>=</td><td></td><td>=</td><td>=</td></tr><tr><td>VinVL-B [79]</td><td>5.7M</td><td>38.2</td><td>30.3</td><td>129.3</td><td>23.6</td><td>1</td><td>-</td><td></td><td>=</td></tr><tr><td>BLIPCapFilt-L [31]</td><td>129M</td><td>39.7</td><td>−</td><td>133.3</td><td>-</td><td>109.6</td><td>14.7</td><td></td><td>=</td></tr><tr><td>LEMON-B [21]</td><td>200M</td><td>40.3</td><td>30.2</td><td>133.3</td><td>23.3</td><td>106.8</td><td>14.1</td><td></td><td></td></tr><tr><td>SimVLM-B[67]</td><td>1.8B</td><td>39.0</td><td>32.9</td><td>134.8</td><td>24.0</td><td>-</td><td>-</td><td>94.8</td><td>13.1</td></tr><tr><td>FIBER-B</td><td>4M</td><td>39.1</td><td>30.4</td><td>128.4</td><td>23.1</td><td>88.6</td><td>13.0</td><td>86.0</td><td>12.9</td></tr><tr><td>FIBER-GOLD-B</td><td>4M</td><td>40.3</td><td>30.7</td><td>133.6</td><td>23.6</td><td>92.8</td><td>13.4</td><td>90.6</td><td>13.4</td></tr><tr><td colspan="10">Models trained with CIDEr optimization</td></tr><tr><td>ViTCAP [14]</td><td>4M</td><td>41.2</td><td>30.1</td><td>138.1</td><td>24.1</td><td>89.2</td><td>12.7</td><td></td><td>1</td></tr><tr><td>X-VLM[77]</td><td>4M</td><td>41.3</td><td>-</td><td>140.8</td><td>-</td><td>-</td><td>-</td><td>=</td><td>-</td></tr><tr><td>VinVL-B[79]</td><td>5.7M</td><td>40.9</td><td>30.9</td><td>140.4</td><td>25.1</td><td>94.3*</td><td>13.1*</td><td>92.5*</td><td>13.1*</td></tr><tr><td>LEMON-B [21]</td><td>200M</td><td>41.6</td><td>31.0</td><td>142.7</td><td>25.1</td><td>-</td><td>-</td><td>1</td><td>-</td></tr><tr><td>FIBER-B</td><td>4M</td><td>42.8</td><td>31.0</td><td>142.8</td><td>24.3</td><td>96.7</td><td>13.4</td><td>94.1</td><td>13.4</td></tr><tr><td>FIBER-GOLD-B</td><td>4M</td><td>43.4</td><td>31.3</td><td>144.4</td><td>24.6</td><td>99.2</td><td>13.7</td><td>97.1</td><td>13.8</td></tr></table>
+
+Table 5: Results of base-size models on image captioning. We grey models pre-trained on larger magnitudes of data. Numbers with ‘\*’ are obtained with constrained beam search during inference and without VLP. The complete results on all metrics are provided in Appendix. $\mathrm { B } @ 4$ : BLEU $@ 4$ , M: METEOR, C: CIDEr, S: SPICE.
+
+Further, we explore combining the strengths of both strategies by performing re-ranking as in [16, 31, 32]. Specifically, we first retrieve the top- $k$ most similar instances using the dual encoder setup, and then add the similarity scores between the given instance and the top- $k$ candidates provided by the fusion encoder to the original scores to perform retrieval. From Table 4, we can see that this strategy provides a balance between efficiency and performance, and that just re-ranking the top-10 instances can achieve comparable performance with ensembling.
+
+Image Captioning. We also evaluate our models on COCO [41] and NoCaps [1] captioning to test whether FIBER can be adapted to generation tasks. As in Table 5, FIBER can achieve better performance than models trained on the same data with and without CIDEr optimization [53]. We find that integrating GOLD [48] into FIBER can bring significant improvements, outperforming models trained with hundreds of millions of images. Notably, we establish the absolute state-of-the-art CIDEr scores on COCO for base-size models. Considering that FIBER is not pre-trained to perform captioning, the results demonstrate the strong generalization ability of FIBER.
+
+Phrase Grounding. Our fine-grained pre-training stage incorporates Flickr30k entities grounding data, and we achieve 87.4 on the Recall $@ 1$ metric on the test set without any subsequent fine-tuning. This not only surpasses the current SoTA [34] using a smaller sized model (Swin-B compared to their Swin-L), but also uses $2 5 \mathrm { x }$ less fine-grained data. Our FIBER model is able to leverage the image-text coarse-grained pre-training stage better, instead of relying on expensive pseudo-labelling of large web-scale corpus and subsequent high-resolution training on this generated fine-grained data as in [34]. We also compare our approach without using any coarse-grained VL training (image encoder initialized to Swin-B weights from $\mathrm { I N } 2 2 \mathrm { k }$ , and text encoder initialized to pre-trained RoBERTa), and even in this setting, we are able to outperform a similarly sized GLIP model (GLIP-B), proving that our fusion in the backbone is better at capturing fine-grained image-text understanding.
+
+<table><tr><td rowspan="2">Model</td><td rowspan="2">Image Backbone</td><td rowspan="2">#Pretrain Images (fine-grained)</td><td colspan="3">Flickr30k Val</td><td colspan="3">Flickr30k Test</td></tr><tr><td>R@1</td><td>R@5</td><td>R@10</td><td>R@1</td><td>R@5</td><td>R@10</td></tr><tr><td>Visual-BERT[33]</td><td>ResNet-101</td><td>120k</td><td>70.4</td><td>84.5</td><td>86.3</td><td>71.3</td><td>85.0</td><td>86.5</td></tr><tr><td>MDETR [26]</td><td>EN-B5</td><td>200k</td><td>83.6</td><td>93.4</td><td>95.1</td><td>84.3</td><td>93.9</td><td>95.8</td></tr><tr><td>GLIP [34]</td><td>Swin-B</td><td>860k</td><td>85.7</td><td>95.0</td><td>96.2</td><td>86.1</td><td>95.5</td><td>96.4</td></tr><tr><td colspan="9">Models pre-trained on more data and/or with larger size</td></tr><tr><td>GLIP [34]</td><td>Swin-L</td><td>27M</td><td>86.7</td><td>96.4</td><td>97.9</td><td>87.1</td><td>96.9</td><td>98.1</td></tr><tr><td>FIBER-B</td><td>Swin-B</td><td>860k</td><td>87.1</td><td>96.1</td><td>97.4</td><td>87.4</td><td>96.4</td><td>97.6</td></tr><tr><td>w/o C.G. VLP</td><td>Swin-B</td><td>860k</td><td>86.2</td><td>96.0</td><td>97.6</td><td>86.5</td><td>96.4</td><td>97.7</td></tr></table>
+
+Table 6: Phrase grounding performance on Flickr30k entities dataset. We reproduce GLIP-Base sized results, and GLIP-Large sized results are taken from [34]. FIBER with Base size outperforms a GLIP-L which is trained with $2 5 \mathrm { x }$ more fine-grained data on the $\mathbb { R } \ @ 1$ metric. Further, FIBER without coarse-grained VL pretraining outperforms GLIP-B when trained on the same fine-grained data.
+
+Table 7: Results on referring expression comprehension datasets.   
+
+<table><tr><td rowspan="2">Model</td><td colspan="2">Pre-training data</td><td colspan="3">RefCOCO</td><td colspan="3">RefCOCO+</td><td colspan="2">RefCOCOg</td></tr><tr><td>Im-Txt</td><td>Im-Txt-Box</td><td>val</td><td>testA</td><td>testB</td><td>val</td><td>testA</td><td>testB</td><td>val</td><td>test</td></tr><tr><td>MDETR-B [26]</td><td></td><td>√</td><td>87.51</td><td>90.40</td><td>82.67</td><td>81.13</td><td>85.52</td><td>72.96</td><td>83.35</td><td>83.31</td></tr><tr><td>UNICORN-B [70]</td><td></td><td>√</td><td>88.29</td><td>90.42</td><td>83.06</td><td>80.30</td><td>85.05</td><td>71.88</td><td>83.44</td><td>83.93</td></tr><tr><td colspan="9">Models pre-trained on more data and/or with larger size</td><td></td><td></td></tr><tr><td>UNITER-L [6]</td><td>√</td><td></td><td>81.41</td><td>87.04</td><td>74.17</td><td>75.90</td><td>81.45</td><td>66.70</td><td>74.86</td><td>75.77</td></tr><tr><td>VILLA-L [15]</td><td>√</td><td></td><td>82.39</td><td>87.48</td><td>74.84</td><td>76.17</td><td>81.54</td><td>66.84</td><td>76.18</td><td>76.71</td></tr><tr><td>OFA-L [65]</td><td>√</td><td>√</td><td>90.05</td><td>92.93</td><td>85.26</td><td>84.49</td><td>90.10</td><td>77.77</td><td>84.54</td><td>85.20</td></tr><tr><td>FIBER-B</td><td>√</td><td>√</td><td>90.68</td><td>92.59</td><td>87.26</td><td>85.74</td><td>90.13</td><td>79.38</td><td>87.11</td><td>87.32</td></tr></table>
+
+Referring Expression Comprehension (REC). In contrast to many previous works [6, 15, 45] that tackle the REC task by re-ranking object proposals provided by an off-the-shelf detector, we follow [26] to directly predict the bounding box for the given referring expression. Using our proposed two stage pre-training, FIBER achieves better performance than current SoTA [65] that uses a Large sized model. Notably, on RefCOCOg [76], which contains much longer referring expressions than in RefCOCO/RefCOCO $^ +$ [27], we observe more than 2 points boost over OFA-L. On the challenging testB split of both RefCOCO and RefCOCO+, FIBER outperforms current SoTA, OFA-L.
+
+![](images/fa28bd4542719e59db24d0b57b24f7833ac26b73e3cc1c80771962138fa20c51.jpg)  
+Figure 5: Few-shot results on the aggregated 13 ODinW datasets.
+
+Object Detection. We report FIBER results on two standard object detection benchmarks, COCO [41] and LVIS [17], in zero-shot transfer1 as well as fine-tuned settings in Table 8. The LVIS dataset consists of a long-tail of object classes, and is a popular test-bed for evaluating models on their generalization capabilities and robustness to class imbalance. On the APr metric, which is the Average Precision on rare objects, FIBER outperforms GLIP-L which is a bigger model and also trained with $2 5 \times$ more fine-grained data.
+
+<table><tr><td rowspan="2">Model</td><td>COCO Val 2017</td><td colspan="4">LVIS MiniVal</td><td rowspan="2">ODinW</td></tr><tr><td>AP</td><td>APr</td><td>APc</td><td>APf</td><td>AP</td></tr><tr><td></td><td>Zero-shot/Fine-tune</td><td></td><td>Zero-shot/Fine-tune</td><td></td><td></td><td>Zero-shot/Fine-tune</td></tr><tr><td>Mask R-CNN[19]</td><td>-</td><td>- /26.3</td><td>- /34.0</td><td>- /33.9</td><td>- /33.3</td><td></td></tr><tr><td>MDETR [26]</td><td>-</td><td>- /20.9</td><td>- /24.9</td><td>- /24.3</td><td>- /24.2</td><td>-</td></tr><tr><td>GLIP-T [34]</td><td>46.7/55.1</td><td>17.7/-</td><td>19.5/ -</td><td>31.0/-</td><td>24.9/ -</td><td>44.4/63.9</td></tr><tr><td>GLIP-B [34]</td><td>48.1/57.0</td><td>17.0/31.3 23.9/48.3 35.9/56.9</td><td></td><td></td><td>29.1/51.0</td><td>44.8/65.8</td></tr><tr><td colspan="7">Models pre-trained on more data and/or with larger size</td></tr><tr><td>GLIP-L [34]</td><td>49.8/60.8</td><td>28.2/-</td><td>34.3/-</td><td>41.5/-</td><td>37.3/ -</td><td>52.1/68.9</td></tr><tr><td>FIBER-B</td><td>49.3/58.4</td><td>29.5/50.0</td><td>32.2/56.9</td><td>40.1/58.1</td><td>35.8/56.9</td><td>47.0/65.9</td></tr></table>
+
+Table 8: Zero-shot transfer and fine-tuning results for object detection on COCO, LVIS and the average over 13 datasets for object detection in the wild. Detailed scores on the 13 datasets are presented in the Appendix. FIBER achieves better AP across the board compared to similarly sized GLIP-B, trained on the same amount of fine-grained data. On rare objects in LVIS, FIBER outperforms GLIP-L trained on $2 5 \mathrm { x }$ more fine-grained data. Results without coarse-grained pre-training are provided in the Appendix.
+
+We also report zero-shot and fine-tuned results on a suite of 13 ODinW (object detection in the wild) datasets, spanning various domains and show consistent performance improvements over previous SoTA. Additionally, in Figure 5, we report few-shot results aggregated across these 13 datasets and show better data efficiency over GLIP-B trained with the same fine-grained data.
+
+Ablation Study. In Appendix ?? and ??, we have provided detailed ablations that guided our architecture design, including ablations on fusion strategies, pre-training objectives, architecture for captioning, and additional results on open-ended VQA, and detailed few-shot ODinW results. Due to the space limit, these ablations and additional results are only provided in the Appendix. Some important observations are summarized below. (i) Co-attention works similarly to merged attention for fusion in the backbone. (ii) Adding a gating parameter in co-attention allows the addition of fusion in more layers, and also gives better performance than merged attention. (iii) Adding co-attention in the last 6 layers provides a balance between performance and efficiency. (iv) MLM, ITM with hard negative mining, and ITC are all important pre-training objectives for training FIBER-style models.
+
+# 5 Conclusion
+
+We propose (i) FIBER, a novel architecture and (ii) a coarse-to-fine pre-training pipeline. We perform extensive experiments and show consistent improvements over strong baselines across a diverse set of tasks. The results demonstrate the effectiveness of FIBER coupled with our pre-training strategy, by setting new SoTA scores while at the same time reducing the requirement of expensive box-level annotations. Future directions include scaling our models and extending our framework to other modalities.
+
+The approach introduced in our work can potentially inherit undesirable societal biases that exist in our pre-training data. Careful debiasing and filtering of data should be undertaken before real-life deployment of our work. Additionally, pre-training can induce environmental costs, and minimizing these costs is an avenue that we plan to explore further.
+
+# Acknowledgement
+
+We would like to thank Nguyen Bach, Jiayuan Huang, and Luis Vargas for their support. We also thank Wenhui Wang, Li Dong, Furu Wei, Bin Xiao, and Lu Yuan for their helpful discussions. We also thank Liunian Harold Li and Te-Lin Wu for their feedback on the manuscript. Aishwarya is supported in part by the National Science Foundation under NSF Award 1922658. Zi-Yi is supported in part by the DARPA Machine Common Sense (MCS) program under Cooperative Agreement N66001-19-2-4032 and NIH R01HL152270.
+
+# References
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+
+# Checklist
+
+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 Section 5   
+(c) Did you discuss any potential negative societal impacts of your work? [Yes] See Section 5   
+(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? [N/A] (b) Did you include complete proofs of all theoretical results? [N/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]   
+(b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [Yes]   
+(c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? [No]   
+(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)? [Yes]
+
+4. If you are using existing assets (e.g., code, data, models) or curating/releasing new assets...
+
+(a) If your work uses existing assets, did you cite the creators? [Yes]   
+(b) Did you mention the license of the assets? [Yes]   
+(c) Did you include any new assets either in the supplemental material or as a URL? [N/A]   
+(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]   
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parse/dev/o4neHaKMlse/o4neHaKMlse_content_list.json

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+        "text": "Zi-Yi Dou∗‡, Aishwarya Kamath∗♮, Zhe $\\mathbf { G a n ^ { * } } ^ { \\star \\star }$ , Pengchuan Zhang§, Jianfeng Wang† Linjie $\\mathbf { L i } ^ { \\dagger }$ , Zicheng $\\mathbf { L i u } ^ { \\dagger }$ , Ce $\\mathbf { L i u } ^ { \\dagger }$ , Yann LeCun♮, Nanyun Peng‡, Jianfeng $\\mathbf { G a o } ^ { \\dagger }$ , Lijuan Wang† †Microsoft ‡University of California, Los Angeles ♮New York University {zdou,violetpeng}@cs.ucla.edu, {aish,yann.lecun}@nyu.edu, pengchuanzhang@fb.com {zhgan,jianfw,linjli,zliu,liuce,jfgao,lijuanw}@microsoft.com ",
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+        "text": "Vision-language (VL) pre-training has recently received considerable attention. However, most existing end-to-end pre-training approaches either only aim to tackle VL tasks such as image-text retrieval, visual question answering (VQA) and image captioning that test high-level understanding of images, or only target region-level understanding for tasks such as phrase grounding and object detection. We present FIBER (Fusion-In-the-Backbone-based transformER), a new VL model architecture that can seamlessly handle both these types of tasks. Instead of having dedicated transformer layers for fusion after the uni-modal backbones, FIBER pushes multimodal fusion deep into the model by inserting cross-attention into the image and text backbones, bringing gains in terms of memory and performance. In addition, unlike previous work that is either only pre-trained on image-text data or on fine-grained data with box-level annotations, we present a two-stage pretraining strategy that uses both these kinds of data efficiently: (i) coarse-grained pre-training based on image-text data; followed by (ii) fine-grained pre-training based on image-text-box data. We conduct comprehensive experiments on a wide range of VL tasks, ranging from VQA, image captioning, and retrieval, to phrase grounding, referring expression comprehension, and object detection. Using deep multimodal fusion coupled with the two-stage pre-training, FIBER provides consistent performance improvements over strong baselines across all tasks, often outperforming methods using magnitudes more data. Code is available at https://github.com/microsoft/FIBER. ",
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+        "type": "text",
+        "text": "1 Introduction ",
+        "text_level": 1,
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+        "text": "Inspired by the success of language model pre-training [11, 51, 42], coupled with the unification of architectures used in the NLP and computer vision communities [12, 4], vision-language pre-training (VLP) [62, 45, 33, 6] has been receiving an increasing amount of attention. It has been proven that VLP can establish state-of-the-art performance on visual question answering [3], visual reasoning [60], image captioning, and image-text retrieval [41]. The pre-training objectives commonly used for these tasks, such as image-text matching, image conditioned masked language modeling and image-text constrastive learning, require multimodal understanding at the image level. Typically, this means the pre-training is done using images at lower resolution (e.g., $3 8 4 \\times 3 8 4$ ), making it possible to scale up training by using large batch sizes. ",
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+        "text": "Recently, it has also been shown that tasks such as image classification and object detection (OD), which have been traditionally viewed as vision-only tasks, can benefit from being cast as VL tasks [50, 25, 34, 26]. Inspired by MDETR [26], GLIP [34] reformulates standard classificationbased OD as phrase grounding. This opens up the possibility to leverage VLP for OD, and vice versa, and this unification has led to impressive performance on several established OD as well as phrase grounding benchmarks [49]. Since these tasks involve fine-grained image understanding between regions in the image and phrases in the text, and also require prediction of precise bounding boxes at the output, the pre-training typically involves using high resolution input images (e.g., $8 0 0 \\times 1 , 3 3 3 ,$ ). ",
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+        "img_path": "images/8afe3400f4173ca1b0f613fa777f89bb7d2728cb877a2293a26fa7db7f619fb8.jpg",
+        "image_caption": [
+            "Figure 1: The proposed coarse-to-fine pre-training framework for vision-language tasks. We first perform coarse-grained pre-training with image-text data for VQA, image captioning and retrieval tasks, and then perform fine-grained pre-training with image-text-box data for phrase grounding and object detection tasks. The same FIBER architecture is used for both stages. OD: object detection. MLM: masked language modeling. ITM: image-text matching. ITC: image-text contrastive loss. "
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+        "text": "Existing multimodal architectures typically do not support both kinds of tasks. Specifically, the fully end-to-end VLP models such as ALBEF [32], METER [13], and SimVLM [67] can achieve the state of the art (SoTA) on image-level understanding tasks, but it is non-trivial to extend them for region-level VL tasks because predicting bounding boxes is typically hard in end-to-end settings. On the other hand, MDETR [26] and GLIP [34] are designed to predict bounding boxes, but have not been shown to support tasks such as image captioning and retrieval. Further, fine-grained pretraining not only requires data with bounding box annotations that are cumbersome to acquire, but the requirement of high input image resolution makes pre-training very costly, especially when using standard Transformer architectures [63] that have quadratic complexity in the size of the image. A natural but challenging question arises: can we have a unified framework for efficient VL pre-training that benefits both image-level and region-level VL tasks (e.g., both VQA and $O D$ )? ",
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+        "text": "We answer this question by proposing two ideas: $( i )$ a novel model architecture that can handle various types of tasks and pre-training strategies (high and low resolution inputs, image and region level outputs) more efficiently than previous work (see Section 3.1 and 4), and $( i i )$ a two-stage pre-training pipeline. ",
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+        "text": "In terms of architecture, we present FIBER, shown in Figure 2, which performs deep multimodal fusion in the backbone. Specifically, instead of having a few dedicated transformer layers on top of the image and text encoders for fusion (e.g., as is commonly done in previous work [36, 6, 13, 26, 34]), we propose to directly insert cross-attention modules into the image and text backbones. Additionally, we support the ability to switch between a dual encoder (for ",
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+    {
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+        "img_path": "images/59ab2a9918c66b9e49af9c3bd096b5bae7c30e64401511f747661fde80d3d915.jpg",
+        "image_caption": [
+            "Figure 2: Model architecture for FIBER. Swin transformer is used as the image backbone, simplified here for illustration purposes. "
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+        "type": "text",
+        "text": "fast image retrieval) and a fusion encoder (for VQA and captioning) readily, by switching on or off the cross-attention modules. With the same model architecture, by simply adding an object detection head (e.g., Dynamic Head [9]) on top, FIBER can be readily extended to visual grounding, referring expression comprehension and (open-vocabulary) OD tasks as well. ",
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+        "image_caption": [
+            "Figure 3: FIBER can be readily adapted to various downstream VL tasks, ranging from VQA, image captioning and retrieval, to phrase grounding and object detection (OD). "
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+        "text": "By considering the nature of different VL tasks, FIBER is pre-trained with a coarse-to-fine two-stage pipeline, as detailed in Figure 1. Specifically, ",
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+        "text": "• During coarse-grained pre-training, FIBER takes low-resolution $( 3 8 4 \\times 3 8 4 )$ images as input, and is pre-trained with image-text matching, masked language modeling, and image-text contrastive losses, as used in previous work [13, 66, 64]. The pre-trained model can then be directly finetuned for VQA and image captioning tasks (Figure 3a and 3c). By switching off the cross-attention modules, FIBER also automatically functions as a dual encoder for fast image-text retrieval (Figure 3b). • During fine-grained pre-training, FIBER uses the coarse pre-trained model as initialization, in addition to randomly initialized parameters for the OD head. At this stage, the model takes highresolution $( 8 0 0 \\times 1 , 3 3 3 )$ ) images as input, and is pre-trained with bounding box localization loss and word-region alignment loss, as used in GLIP [34]. We use image-text-box data with ground-truth box annotations for pre-training, and the model can be directly fine-tuned for grounding and detection tasks (Figure 3d). ",
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+        "text": "Compared to fine-grained pre-training, coarse-grained pre-training is easier to scale up, as it only requires paired image-text data which can be easily harvested from the web. Crucially, we show that re-using all the parameters from our coarse-grained pre-trained model for fine-grained pre-training alleviates the requirement for large amounts of box-level annotated data. In our experiments, we show that on fine-grained tasks such as Flickr30k Entities, FIBER using coarse-grained pre-training achieves gains even over previous SoTA (GLIP [34]) that uses $2 5 \\times$ more box-level annotated images during the fine-grained pre-training stage. We also show that our architecture is much more efficient in terms of training time on OD tasks, as compared to GLIP . ",
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+        "text": "FIBER is the first end-to-end VLP model that can support VL tasks encompassing image-level and region-level outputs. We conduct experiments on VQAv2 [3], $\\mathrm { \\ N L V R ^ { 2 } }$ [60], COCO captioning [41], NoCaps [1], COCO and Flickr $3 0 \\mathrm { k }$ image-text retrieval [49], as well as on phrase grounding [49], referring expression comprehension [75], COCO and LVIS detection [17], and a suite of 13 object detection in the wild datasets [34]. We show that our model can provide consistent performance improvement over strong baselines (e.g., METER [13] and GLIP [34]) across tasks. ",
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+    {
+        "type": "text",
+        "text": "2 Related Work ",
+        "text_level": 1,
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+        "text": "VLP for Classical VL Tasks. ViLBERT [45] and LXMERT [62] were the first two methods to introduce using transformers for VLP. Since then, we have witnessed a boom of VLP methods [33, 30, 59, 73, 22, 71, 81, 38, 7, 35]. Early methods mainly focus on the use of pre-trained object detectors to extract image region features offline, such as UNITER [6], OSCAR [36], VILLA [15] and VinVL [79]. More recently, end-to-end VLP methods that use the image directly as input have become popular. In these approaches, convolution networks or vision transformers [12] are used as the image backbone, with additional transformer layers for modeling multimodal fusion [24, 23, 28, 68, 32, 64]. Prominent examples along this line include ViLT [28], ALBEF [32], SimVLM [67], METER [13], X-VLM [77] and BLIP [31]. These models have achieved the current SoTA on major VL benchmarks such as VQA and image captioning. However, they cannot be directly used for tasks such as object detection. ",
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+        "table_caption": [
+            "Table 1: Comparison among different VLP models. FIBER is the only VLP model that can support all tasks considered. (†) VQA is used as a representative VL classification task. $( \\ddagger )$ $O ( n + m )$ retrieval denotes model backbones process inputs $O ( n + m )$ times given $_ n$ images and $m$ text sentences during image-text retrieval. $( \\ast )$ Here, we mainly focus on what tasks CLIP can be directly used for. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>VQA+</td><td>O(n+m) Retrieval* Captioning Grounding</td><td></td><td></td><td>OD</td><td>End2End</td></tr><tr><td>ViLBERT [45],LXMERT [62], UNITER [6]</td><td>√</td><td>xxx&lt;xx&lt;&gt;</td><td>x&lt;x×</td><td></td><td>xxxxxxxx&lt;×</td><td>×</td></tr><tr><td>OSCAR [36],VinVL [79]</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>PixelBERT [24], CLIP-ViL [57],ViLT[28]</td><td>√</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>CLIP [50]*, ALIGN [25]</td><td>×</td><td></td><td></td><td>xxxxxxν</td><td></td><td>x&gt;&gt;&gt;</td></tr><tr><td>VL-T5 [7]</td><td>√</td><td></td><td>&lt;&lt;x&gt;</td><td></td><td></td><td>×√√</td></tr><tr><td>METER[13], SimVLM[67]</td><td>√</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>ALBEF[32],FLAVA [58],VLMo [66]</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>BLIP[31],CoCa [74],Flamingo [2]</td><td></td><td></td><td></td><td></td><td></td><td>√</td></tr><tr><td>MDETR [26], GLIP [34]</td><td>√</td><td>×</td><td>×</td><td></td><td></td><td>√</td></tr><tr><td>UniTAB [70], X-VLM[77],OFA [65]</td><td>√</td><td>×</td><td>√</td><td>√</td><td></td><td>√</td></tr><tr><td>FIBER</td><td>√</td><td>√</td><td>√</td><td>√</td><td>√</td><td>√</td></tr></table>",
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+        "type": "text",
+        "text": "VLP for Vision Tasks. Recently, it has been shown that image-text data can be used to learn image encoders from scratch [10, 54]. By performing large-scale contrastive pre-training, CLIP [50] and ALIGN [25] display strong zero-shot image classification capabilities. While these models mainly tackle image-level understanding tasks, MDETR [26] extends the end-to-end OD model DETR [4], and uses contrastive learning along with an alignment loss to learn correspondences between image regions and text phrases, opening up the possibility to tackle tasks such as phrase grounding and long-tailed OD using VL models. This has inspired many follow-up works to further enhance the pre-training [37, 72, 46, 69], among which GLIP [34] shows that OD can also be cast as a VL task (i.e., phrase grounding). However, it has not been shown how traditional VL tasks such as VQA, captioning and retrieval can be well supported in GLIP [34] and MDETR [26]. ",
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+        "type": "text",
+        "text": "Unified VL Modeling. There have been a few recent attempts that try to develop unified VL models. VL-T5 [7] unifies VL tasks as text generation; however, pre-trained object detectors are used for image feature extraction, so the model cannot be end-to-end pre-trained. UniT [20] proposes a multimodal multi-task framework with a unified transformer; however, it can only support VQA and object detection tasks, but not captioning and grounding. GPV [18] proposes a general-purpose vision system, and FLAVA [58] presents a VL system similar to METER [13]; however, they did not evaluate on grounding and detection tasks, and their performance on other VL tasks is still far from SoTA. UniTAB [70] and OFA [65] reformulate grounding as a sequence generation task, by borrowing ideas from Pix2Seq [5]. However, these approaches have not been demonstrated to work on standard OD benchmarks, and also cannot be used as dual encoders for fast image retrieval. Our model is the first work that can support not only VQA, image captioning and $O ( n + m )$ retrieval, but also visual grounding and object detection, with impressive performance across all tasks. A detailed comparison is provided in Table 1. ",
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+        "type": "text",
+        "text": "3 Method ",
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+        "text": "In this section, we first describe the proposed model architecture in Section 3.1. We then illustrate our two-stage pre-training paradigm in Section 3.2, followed by fine-tuning strategies for all the tasks supported by FIBER in Section 3.3. ",
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+        "text": "3.1 Fusion in the Backbone ",
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+        "type": "text",
+        "text": "The architecture of FIBER is shown in Figure 2. Different from models that stack a modality fusion module on top of the vision or language backbones [6, 13], we insert multimodal fusion inside the backbones, and include a gating mechanism for the cross-modal layers (shown in Figure 4). Specifically, at each encoding layer, we have: ",
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+        "img_path": "images/5d2d42f1068123eead76a9dd306fcbce49165a2f6f3af4a899aadd4103b80f2b.jpg",
+        "text": "$$\n\\begin{array} { r l } & { \\tilde { \\pmb { x } } = \\mathrm { S E L F - A T T } \\big ( \\pmb { x } \\big ) , } \\\\ & { \\pmb { x } = \\pmb { x } + \\tilde { \\pmb { x } } + \\alpha * \\mathrm { C R O S S - A T T } \\big ( \\tilde { \\pmb { x } } , \\pmb { y } \\big ) , } \\\\ & { \\pmb { x } = \\pmb { x } + \\mathrm { F F N } ( \\pmb { x } ) , } \\end{array}\n$$",
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+        "image_caption": [
+            "xFigure 4: Illustration of performing fusion in the backbone. $( { \\pmb x } , { \\pmb y } )$ are the (image, text) or (text, image) representations, and $\\alpha$ is a learnable scalar. "
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+        "type": "text",
+        "text": "where $\\alpha$ is a learnable parameter initialized to 0. For simplicity, we insert the same number of cross-attention layers into the vision and language backbones. ",
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+        "type": "text",
+        "text": "By inserting cross-attention layers with the gating mechanism, we enable cross-modal interactions without affecting the original computational flow of the backbones at the beginning of model training. Also, we can easily switch off the interactions by setting $\\alpha$ to 0, and the backbones can be used in the dual-encoder setting. In addition, compared to stacking a large number of transformer layers on top of the backbones, our approach of inserting cross-attention layers is relatively light-weight and thus more memory-efficient. To illustrate, both GLIP [34] and METER [13] use an additional 110M modality fusion parameters for a base-size model, while FIBER only adds about 26M parameters. During training, the fusion module of FIBER only consumes half of the FLOPs needed by METER (12.35 vs. 24.04 GFLOPs for one instance). We experimented with two other model variants for fusion in the backbone, the details of which are provided in Appendix. ",
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+        "text": "3.2 Coarse-to-Fine Pre-training ",
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+        "text": "We divide VL tasks into two categories based on whether or not we need to generate region-level outputs on the image side. While these two kinds of tasks are characteristically different, they both require fusion between the vision and language modalities, and we hypothesize that sharing as many parameters as possible between the model used for these two sets of tasks will be beneficial. Based on this motivation, we propose a two-stage pre-training paradigm, where we first pre-train models with image-level objectives on images at low resolution, and then perform further pre-training with region-level objectives where the input images are at a higher resolution. In this way, the coarsegrained supervision from the first stage can provide good initialization for the second stage for all the shared parameters. FIBER with the same architecture (Swin Transformer [43] and RoBERTa [42]) is used as the backbone for both stages of pre-training. ",
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+        "text": "Coarse-grained Pre-training. For tasks like VQA and captioning, it has been demonstrated [32, 13, 66] that masked language modeling (MLM), image-text matching (ITM), and image-text contrastive (ITC) objectives are helpful for ViT-based VLP models. Following previous work, we use all the three objectives during pre-training. Specifically, ",
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+        "text": "• For ITC, the inserted cross-attention modules are switched off, so FIBER functions as a dual encoder. Given a batch of $N$ image-caption pairs, we first compute their representations with our vision and language encoders independently without modality fusion, and then maximize the similarities between $N$ positive image-text pairs while minimizing the similarities between the rest $N ^ { 2 } - N$ negative pairs, via a contrastive loss.   \n• For MLM and ITM, the inserted cross-attention modules are switched on, so FIBER now functions as a fusion encoder. For MLM, we randomly mask $15 \\%$ of the input tokens and the model is trained to reconstruct the original tokens. For image-text matching, the model is given an image-text pair and predicts whether they are matched. Following VLMo [66], we sample global hard negatives based on the similarities computed from the above ITC loss. ",
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+        "text": "Fine-grained Pre-training. Most existing VL architectures [6, 62, 26, 31, 65, 7] use vanilla transformers both for encoding the vision as well as language inputs. However, in contrast to tokens in text, the entities of interest in images do not all occur at the same scale. Being able to accurately model the image at different scales is especially important for tasks such as object detection and phrase grounding. To handle this, it is typical in object detection literature to use input images at higher resolutions $( 8 0 0 \\times 1 3 3 3 )$ , which becomes problematic when using vanilla transformers that scale quadratically in the length of the input sequence. As mentioned earlier, we use a Swin Transformer [43] as our image encoder, which provides hierarchical representations of the image while having linear complexity in the size of the image. We combine these multi-scale representations using an FPN [39] for object detection training. For fine-grained pre-training, we switch on the cross-attention modules, using FIBER as a fusion encoder. This ensures that the image representations that are passed to the FPN are already text-aware, and is a crucial difference compared to GLIP [34], where the image-text fusion takes place in the object detection head. Once the text-aware image features are extracted by the Swin backbone and image-aware text features are extracted using RoBERTa [42], the image features after the FPN are fed to a DynamicHead [9] which predicts a set of regions. Just as in [34], we compute the dot product between the image region features $R _ { \\mathrm { T A } }$ and the contextualized token representations $\\mathbf { \\delta T _ { \\mathrm { I A } } }$ to compute the grounding score: ",
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+    {
+        "type": "equation",
+        "img_path": "images/218abfcb7bd765b1713f3f79c3bf274aa825cb24799eb579a317663d24e4f436.jpg",
+        "text": "$$\n\\begin{array} { r } { I _ { \\mathrm { T A } } , T _ { \\mathrm { I A } } = \\mathrm { F I B E R } ( I , T ) , R _ { \\mathrm { T A } } = \\mathrm { O D } { \\cdot } \\mathrm { H E A D } ( I _ { \\mathrm { T A } } ) , S _ { \\mathrm { G R O U N D I N G } } = R _ { \\mathrm { T A } } T _ { \\mathrm { I A } } ^ { \\top } , } \\end{array}\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where $R _ { \\mathrm { T A } }$ represents regions that are text aware, produced using the OD-Head that takes as input $I _ { \\mathrm { T A } }$ , which are image representations that are already text-aware and $\\mathbf { \\delta T _ { \\mathrm { I A } } }$ are the text features that have already attended to the image features. The typical object detection model has a classification head that predicts the label of the object, and a localization head that predicts the bounding box. We follow GLIP [34] by substituting the classification head with the grounding score SGROUNDING. The localization loss is composed of two parts: a centerness loss and GIoU loss, which are used to supervise the box prediction. Taken together, FIBER learns the correspondence between regions in the image and phrases in the text, making it possible to tackle tasks such as phrase grounding and object detection using the same framework. We use ATSS framework [80] in our paper, but our method can be combined easily with other object detectors such as Faster-RCNN [52] and RetinaNet [40] as well. ",
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+    {
+        "type": "text",
+        "text": "3.3 Adaptation to Downstream Tasks ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We now describe how we adapt FIBER to different downstream tasks as depicted in Figure 3. ",
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+        "text": "• For VL classification tasks such as VQA, we use FIBER as a fusion encoder. Specifically, the top $M$ layers of the vision and language backbones interact with each other and produce multimodal representations. The final layer representations of the two modalities are concatenated together to generate the final outputs for tasks such as VQA and visual reasoning. ",
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+        "type": "text",
+        "text": "• For retrieval tasks, we switch off the inserted cross-attention modules to use FIBER as a dual encoder for fast image-text retrieval. ",
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+        "type": "text",
+        "text": "• For captioning, we adapt FIBER by only keeping the image-to-text cross-attentions and using causal masks in the decoding side. The representations of the final image encoding layer are fed into the cross-attention modules. In this way, the model is turned into a seq2seq model [61, 8] and performs captioning in an auto-regressive way. ",
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+        "text": "• For phrase grounding, object detection and referring expression comprehension, we use FIBER as a fusion encoder, and the OD-Head introduced during fine-grained pre-training receives image features that are already language aware due to the multimodal representations extracted by FIBER. The pre-trained model is directly used without any modifications for these tasks. ",
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+    {
+        "type": "text",
+        "text": "4 Experiments ",
+        "text_level": 1,
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+        "text": "Pre-training Datasets. Following previous work [6, 28, 32, 13, 64, 66], we perform coarsegrained pre-training on COCO [41], Conceptual Captions [56], SBU Captions [47], and Visual Genome [29]. The four datasets consist of about 4M images in total. For fine-grained pretraining, we use two data sources: data curated by MDETR [26] after removing the COCO images, and the Objects365 [55] detection dataset, together consisting of about $0 . 8 { \\bf M }$ images. We ensure that we exclude any data that exists in the validation or test splits of downstream tasks. ",
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+    {
+        "type": "text",
+        "text": "Architecture. We adopt Swin-Base [43] and ",
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+    {
+        "type": "table",
+        "img_path": "images/8918d3f1c84a88ec6c6ec7ade53beed6ebaa62fc1173069e2e7802e7485a9ccf.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Type of Fusion</td><td>CoCo Val2017</td><td>GPU-hours V100 (32GB)</td><td> Sec/Iter</td></tr><tr><td>No Fuse</td><td>53.9</td><td>511</td><td>1.31</td></tr><tr><td>GLIP-B [34]</td><td>54.6</td><td>840</td><td>2.14</td></tr><tr><td>FIBER-B</td><td>54.5</td><td>540</td><td>1.38</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 2: Object detection on COCO [41], without visionlanguage pre-training. We initialize the text encoder and image backbones using a pre-trained RoBERTa and a Swin transformer pre-trained on ImageNet22k. Our proposed FIBER model achieves the same performance as GLIP [34] while taking much less time to train. ",
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+    {
+        "type": "text",
+        "text": "RoBERTa-Base [42] as our vision and text backbones, which are initialized with weights from uni-modal pre-training. We insert cross-attention blocks into the top 6 blocks of the vision and text encoders. The input resolution is $3 8 4 \\times 3 8 4$ for coarse-grained pre-training and $8 0 0 \\times 1 , 3 3 3$ for fine-grained pre-training. Using a hierarchical vision transformer enables us to efficiently tackle these high resolution tasks, which would be expensive in models such as BLIP [31] that rely on the vanilla transformer architecture. In METER [13], which does explore using a Swin transformer as the image encoder, the multi-modal fusion occurs in layers specifically designed to align the modalities, only after the image and text features are extracted from the uni-modal backbones. This is in contrast to our approach where the hierarchical image features that are used in the FPN for fine-grained training are already language aware, due to the multi-modal fusion being in the backbone. This also lets us avoid adding additional “language-aware deep fusion layers” [34] as part of the OD head as in GLIP, resulting in $1 . 5 \\mathrm { x }$ faster training while maintaining performance as shown in Table 2. While in principle it would be possible to use the image features extracted by METER’s backbone for object detection, it would be necessary as in GLIP to add additional layers to make the visual features “language-aware” for good detection performance, especially on datasets with limited training data and with rare and infrequent objects. ",
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+    {
+        "type": "table",
+        "img_path": "images/13c6fad22e1d7cc8f86ea316c9a86715b07e520fa826ba36909e966fd4dac362.jpg",
+        "table_caption": [
+            "Table 3: Results on VL classification and retrieval. We also include models pre-trained on more data and/or with larger size. FIBER and VLMo use dual encoders for retrieval. (†) ALBEF, X-VLM, and BLIP first use its dual encoder to obtain top- $k$ candidates, and then use its fusion encoder to re-rank the candidates. Our retrieval results with re-ranking are provided in Table 4. All the other models use fusion encoders. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Model</td><td rowspan=\"2\">#Pretrain Images</td><td colspan=\"2\">VQAv2</td><td colspan=\"2\">NLVR²</td><td colspan=\"2\">Flickr30k</td><td colspan=\"2\">CoCo</td></tr><tr><td>test-dev test-std</td><td></td><td>dev</td><td></td><td>test-P IR@1 TR@1</td><td></td><td></td><td>IR@1 TR@1</td></tr><tr><td colspan=\"10\">Base-size models pre-trained on COco,VG, SBU, and CC datasets</td></tr><tr><td>UNITER-B [6]</td><td>4M</td><td>72.70</td><td>72.91</td><td>77.18</td><td>77.85</td><td>72.5</td><td>85.9</td><td>50.3</td><td>64.4</td></tr><tr><td>VILLA-B [15]</td><td>4M</td><td>73.59</td><td>73.67</td><td>78.39</td><td>79.30</td><td>74.7</td><td>86.6</td><td>-</td><td>1</td></tr><tr><td>UNIMO-B [35]</td><td>4M</td><td>73.79</td><td>74.02</td><td>1</td><td>-</td><td>1</td><td>1</td><td>-</td><td>-</td></tr><tr><td>ViLT-B [28]</td><td>4M</td><td>71.26</td><td>-</td><td>75.70</td><td>76.13</td><td>64.4</td><td>83.5</td><td>42.7</td><td>61.5</td></tr><tr><td>ALBEF-B [32]</td><td>4M</td><td>74.54</td><td>74.70</td><td>80.24</td><td>80.50</td><td>82.8t</td><td>94.3t</td><td>56.8t</td><td>73.1t</td></tr><tr><td>VLMo-B [66]</td><td>4M</td><td>76.64</td><td>76.89</td><td>82.77</td><td>83.34</td><td>79.3</td><td>92.3</td><td>57.2</td><td>74.8</td></tr><tr><td>METER-Swin-B[13]</td><td>4M</td><td>76.43</td><td>76.42</td><td>82.23</td><td>83.47</td><td>79.02</td><td>92.4</td><td>54.85</td><td>72.96</td></tr><tr><td>X-VLM [77]</td><td>4M</td><td>78.22</td><td>78.37</td><td>84.41</td><td>84.76</td><td>86.9t</td><td>97.0t</td><td>63.4t</td><td>81.2t</td></tr><tr><td colspan=\"10\">Models pre-trained on more data and/or with larger : size</td></tr><tr><td>VLMo-L [66]</td><td>4M</td><td>79.94</td><td>79.98</td><td>85.64</td><td>86.86</td><td>84.5</td><td>95.3</td><td>60.6</td><td>78.2</td></tr><tr><td>BLIPCapFit-L [31]</td><td>129M</td><td>78.25</td><td>78.32</td><td>82.15</td><td>82.24</td><td>87.5†</td><td>97.2t</td><td>64.1†</td><td>81.2t</td></tr><tr><td>SimVLM-B[67]</td><td>1.8B</td><td>77.87</td><td>78.14</td><td>81.72</td><td>81.77</td><td></td><td>-</td><td>-</td><td>1</td></tr><tr><td>SimVLM-H[67]</td><td>1.8B</td><td>80.03</td><td>80.34</td><td>84.53</td><td>85.15</td><td>二</td><td>-</td><td>-</td><td>-</td></tr><tr><td>FIBER-B</td><td>4M</td><td>78.55</td><td>78.46</td><td>84.59</td><td>85.52</td><td>81.44</td><td>92.90</td><td>58.01</td><td>75.38</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Implementation Details. We perform coarse-grained pre-training for $1 0 0 \\mathrm { k }$ steps with 4,096 batch size on 64 A100 GPUs. We use AdamW [44] with the peak learning rates of 1e-4 for the backbones and 5e-4 for the cross-modal parameters. We use linear warmup over the first 1k steps and linear decay. For fine-grained pre-training, we train for $8 0 0 \\mathrm { k }$ steps on 64 V100 GPUs, with a batch size of 64. We use a learning rate of 1e-5 for the language backbone, and 1e-4 for the rest of the model with a weight decay of 0.01. We use a linear warmup over the first 2k steps and then a constant learning rate, with two learning rate drops by a factor of 10 at $67 \\%$ and $89 \\%$ of the total number of steps. ",
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+    {
+        "type": "text",
+        "text": "4.1 Results on Downstream Tasks ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Vision-Language Classification. We first experiment on two representative VL classification tasks, including VQAv2 [3] and $\\mathrm { \\tt N L V R } ^ { \\mathrm { 2 } }$ [60]. As reported in Table 3, we achieve the best performance compared to other models in the same setting. It is worth noting that FIBER pre-trained with 4M images can achieve better performance than BLIP trained with 129M images and SimVLM trained with 1.8B images. The results indicate that introducing fusion modules into the backbone is an effective alternative to appending them on the top of uni-modal backbones. ",
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+    {
+        "type": "text",
+        "text": "Image-Text Retrieval. In Table 3 we report image retrieval performance in the dual encoder setting, achieving competitive performance on both Flickr30k [49] and COCO [41] retrieval tasks. However, previous work has shown that fusion encoders obtain superior performance, albeit at the cost of efficiency as it involves feeding every image-text pair into the model. To illustrate, on the COCO test data, ranking the similarities between 5K images and 25K captions requires the model to process each image-caption pair 75M times, whereas the dual encoder model only needs 30K forward passes. As shown in Table 4, the fusion encoder can indeed surpass the dual encoder on retrieval tasks by a large margin. In addition, directly ensembling the two models by summing their similarity scores together for each image-caption pair can bring us huge improvements. ",
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+        "type": "table",
+        "img_path": "images/41a8b93dc045d81402659ae1325af9c40db37a5e03fb463aad1332c5cf46aa93.jpg",
+        "table_caption": [
+            "Table 4: Additional results on image-text retrieval, where (i) the fusion encoder is used for retrieval, or (ii) the dual encoder is first used to obtain top- $k$ candidates, and then the fusion encoder is used to re-rank the candidates. We also provide a full set of results on all evaluation metrics. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Model</td><td colspan=\"6\">Flickr30k</td><td colspan=\"6\">CoCo</td></tr><tr><td>IR@1</td><td>IR@5IR@10 TR@1</td><td></td><td></td><td></td><td></td><td></td><td></td><td>TR@5 TR@10 IR@1 IR@5 IR@10 TR@1</td><td></td><td></td><td>TR@5TR@10</td></tr><tr><td>FIBER-ITC</td><td>81.44</td><td>96.72</td><td>98.48</td><td>92.90</td><td>99.50</td><td>99.90</td><td>58.01</td><td>83.45</td><td>90.11</td><td>75.38</td><td>94.04</td><td>97.36</td></tr><tr><td>FIBER-ITM</td><td>84.10</td><td>97.54</td><td>98.88</td><td>95.10</td><td>99.60</td><td>99.90</td><td>59.03</td><td>84.04</td><td>91.03</td><td>75.14</td><td>93.88</td><td>97.36</td></tr><tr><td>FIBER-ITC+ITMEnsemble</td><td>90.96</td><td>98.44</td><td>99.14</td><td>96.00</td><td>99.70</td><td>100.00</td><td>69.73</td><td>90.66</td><td>94.59</td><td>80.10</td><td>95.60</td><td>97.98</td></tr><tr><td>ALBEF [32]</td><td>82.8</td><td>96.7</td><td>98.4</td><td>94.3</td><td>99.4</td><td>99.8</td><td>56.8</td><td>81.5</td><td>89.2</td><td>73.1</td><td>91.4</td><td>96.0</td></tr><tr><td>X-VLM[77]</td><td>86.1</td><td>97.4</td><td>98.7</td><td>96.8</td><td>99.8</td><td>100.0</td><td>63.1</td><td>85.7</td><td>91.6</td><td>80.4</td><td>95.5</td><td>98.2</td></tr><tr><td>FIBER-Rerank-10</td><td>90.94</td><td>98.16</td><td>98.48</td><td>95.80</td><td>99.60</td><td>99.90</td><td>68.71</td><td>87.69</td><td>90.09</td><td>79.66</td><td>95.34</td><td>97.36</td></tr><tr><td>FIBER-Rerank-20</td><td>90.10</td><td>98.38</td><td>99.14</td><td>95.90</td><td>99.80</td><td>100.00</td><td>69.32</td><td>89.52</td><td>93.33</td><td>79.78</td><td>95.20</td><td>97.66</td></tr><tr><td>FIBER-Rerank-50</td><td>91.08</td><td>98.50</td><td>99.37</td><td>96.10</td><td>99.70</td><td>100.00</td><td>69.58</td><td>90.41</td><td>94.35</td><td>79.98</td><td>95.40</td><td>97.76</td></tr><tr><td>FIBER-Rerank-100</td><td>91.02</td><td>98.54</td><td>99.34</td><td>96.00</td><td>99.70</td><td>100.00</td><td>69.63</td><td>90.54</td><td>94.47</td><td>80.06</td><td>95.60</td><td>97.96</td></tr></table>",
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+        "table_caption": [],
+        "table_footnote": [
+            "Table 5: Results of base-size models on image captioning. We grey models pre-trained on larger magnitudes of data. Numbers with ‘\\*’ are obtained with constrained beam search during inference and without VLP. The complete results on all metrics are provided in Appendix. $\\mathrm { B } @ 4$ : BLEU $@ 4$ , M: METEOR, C: CIDEr, S: SPICE. "
+        ],
+        "table_body": "<table><tr><td rowspan=\"2\">Model</td><td rowspan=\"2\">#Pretrain Images</td><td colspan=\"4\">CoCo</td><td colspan=\"2\">NoCaps Val</td><td colspan=\"2\">NoCaps Test</td></tr><tr><td>B@4</td><td>M</td><td>C</td><td>s</td><td>C</td><td>S</td><td>C</td><td>S</td></tr><tr><td colspan=\"10\">Models trained without CIDEr optimization</td></tr><tr><td>UFO-B [64]</td><td>4M</td><td>36.0</td><td>28.9</td><td>122.8</td><td>22.2</td><td>80.7</td><td>12.5</td><td>78.8</td><td>12.5</td></tr><tr><td>ViTCAP[14]</td><td>4M</td><td>36.3</td><td>29.3</td><td>125.2</td><td>22.6</td><td>1</td><td>1</td><td>1</td><td>1</td></tr><tr><td>METER-CLIP-B[13]</td><td>4M</td><td>38.8</td><td>30.0</td><td>128.2</td><td>23.0</td><td>-</td><td>=</td><td>=</td><td>=</td></tr><tr><td>X-VLM[77]</td><td>4M</td><td>39.8</td><td>-</td><td>133.1</td><td>1</td><td>=</td><td></td><td>=</td><td>=</td></tr><tr><td>VinVL-B [79]</td><td>5.7M</td><td>38.2</td><td>30.3</td><td>129.3</td><td>23.6</td><td>1</td><td>-</td><td></td><td>=</td></tr><tr><td>BLIPCapFilt-L [31]</td><td>129M</td><td>39.7</td><td>−</td><td>133.3</td><td>-</td><td>109.6</td><td>14.7</td><td></td><td>=</td></tr><tr><td>LEMON-B [21]</td><td>200M</td><td>40.3</td><td>30.2</td><td>133.3</td><td>23.3</td><td>106.8</td><td>14.1</td><td></td><td></td></tr><tr><td>SimVLM-B[67]</td><td>1.8B</td><td>39.0</td><td>32.9</td><td>134.8</td><td>24.0</td><td>-</td><td>-</td><td>94.8</td><td>13.1</td></tr><tr><td>FIBER-B</td><td>4M</td><td>39.1</td><td>30.4</td><td>128.4</td><td>23.1</td><td>88.6</td><td>13.0</td><td>86.0</td><td>12.9</td></tr><tr><td>FIBER-GOLD-B</td><td>4M</td><td>40.3</td><td>30.7</td><td>133.6</td><td>23.6</td><td>92.8</td><td>13.4</td><td>90.6</td><td>13.4</td></tr><tr><td colspan=\"10\">Models trained with CIDEr optimization</td></tr><tr><td>ViTCAP [14]</td><td>4M</td><td>41.2</td><td>30.1</td><td>138.1</td><td>24.1</td><td>89.2</td><td>12.7</td><td></td><td>1</td></tr><tr><td>X-VLM[77]</td><td>4M</td><td>41.3</td><td>-</td><td>140.8</td><td>-</td><td>-</td><td>-</td><td>=</td><td>-</td></tr><tr><td>VinVL-B[79]</td><td>5.7M</td><td>40.9</td><td>30.9</td><td>140.4</td><td>25.1</td><td>94.3*</td><td>13.1*</td><td>92.5*</td><td>13.1*</td></tr><tr><td>LEMON-B [21]</td><td>200M</td><td>41.6</td><td>31.0</td><td>142.7</td><td>25.1</td><td>-</td><td>-</td><td>1</td><td>-</td></tr><tr><td>FIBER-B</td><td>4M</td><td>42.8</td><td>31.0</td><td>142.8</td><td>24.3</td><td>96.7</td><td>13.4</td><td>94.1</td><td>13.4</td></tr><tr><td>FIBER-GOLD-B</td><td>4M</td><td>43.4</td><td>31.3</td><td>144.4</td><td>24.6</td><td>99.2</td><td>13.7</td><td>97.1</td><td>13.8</td></tr></table>",
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+        "type": "text",
+        "text": "Further, we explore combining the strengths of both strategies by performing re-ranking as in [16, 31, 32]. Specifically, we first retrieve the top- $k$ most similar instances using the dual encoder setup, and then add the similarity scores between the given instance and the top- $k$ candidates provided by the fusion encoder to the original scores to perform retrieval. From Table 4, we can see that this strategy provides a balance between efficiency and performance, and that just re-ranking the top-10 instances can achieve comparable performance with ensembling. ",
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+        "type": "text",
+        "text": "Image Captioning. We also evaluate our models on COCO [41] and NoCaps [1] captioning to test whether FIBER can be adapted to generation tasks. As in Table 5, FIBER can achieve better performance than models trained on the same data with and without CIDEr optimization [53]. We find that integrating GOLD [48] into FIBER can bring significant improvements, outperforming models trained with hundreds of millions of images. Notably, we establish the absolute state-of-the-art CIDEr scores on COCO for base-size models. Considering that FIBER is not pre-trained to perform captioning, the results demonstrate the strong generalization ability of FIBER. ",
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+        "text": "Phrase Grounding. Our fine-grained pre-training stage incorporates Flickr30k entities grounding data, and we achieve 87.4 on the Recall $@ 1$ metric on the test set without any subsequent fine-tuning. This not only surpasses the current SoTA [34] using a smaller sized model (Swin-B compared to their Swin-L), but also uses $2 5 \\mathrm { x }$ less fine-grained data. Our FIBER model is able to leverage the image-text coarse-grained pre-training stage better, instead of relying on expensive pseudo-labelling of large web-scale corpus and subsequent high-resolution training on this generated fine-grained data as in [34]. We also compare our approach without using any coarse-grained VL training (image encoder initialized to Swin-B weights from $\\mathrm { I N } 2 2 \\mathrm { k }$ , and text encoder initialized to pre-trained RoBERTa), and even in this setting, we are able to outperform a similarly sized GLIP model (GLIP-B), proving that our fusion in the backbone is better at capturing fine-grained image-text understanding. ",
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+        "table_footnote": [
+            "Table 6: Phrase grounding performance on Flickr30k entities dataset. We reproduce GLIP-Base sized results, and GLIP-Large sized results are taken from [34]. FIBER with Base size outperforms a GLIP-L which is trained with $2 5 \\mathrm { x }$ more fine-grained data on the $\\mathbb { R } \\ @ 1$ metric. Further, FIBER without coarse-grained VL pretraining outperforms GLIP-B when trained on the same fine-grained data. "
+        ],
+        "table_body": "<table><tr><td rowspan=\"2\">Model</td><td rowspan=\"2\">Image Backbone</td><td rowspan=\"2\">#Pretrain Images (fine-grained)</td><td colspan=\"3\">Flickr30k Val</td><td colspan=\"3\">Flickr30k Test</td></tr><tr><td>R@1</td><td>R@5</td><td>R@10</td><td>R@1</td><td>R@5</td><td>R@10</td></tr><tr><td>Visual-BERT[33]</td><td>ResNet-101</td><td>120k</td><td>70.4</td><td>84.5</td><td>86.3</td><td>71.3</td><td>85.0</td><td>86.5</td></tr><tr><td>MDETR [26]</td><td>EN-B5</td><td>200k</td><td>83.6</td><td>93.4</td><td>95.1</td><td>84.3</td><td>93.9</td><td>95.8</td></tr><tr><td>GLIP [34]</td><td>Swin-B</td><td>860k</td><td>85.7</td><td>95.0</td><td>96.2</td><td>86.1</td><td>95.5</td><td>96.4</td></tr><tr><td colspan=\"9\">Models pre-trained on more data and/or with larger size</td></tr><tr><td>GLIP [34]</td><td>Swin-L</td><td>27M</td><td>86.7</td><td>96.4</td><td>97.9</td><td>87.1</td><td>96.9</td><td>98.1</td></tr><tr><td>FIBER-B</td><td>Swin-B</td><td>860k</td><td>87.1</td><td>96.1</td><td>97.4</td><td>87.4</td><td>96.4</td><td>97.6</td></tr><tr><td>w/o C.G. VLP</td><td>Swin-B</td><td>860k</td><td>86.2</td><td>96.0</td><td>97.6</td><td>86.5</td><td>96.4</td><td>97.7</td></tr></table>",
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+        "table_caption": [
+            "Table 7: Results on referring expression comprehension datasets. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Model</td><td colspan=\"2\">Pre-training data</td><td colspan=\"3\">RefCOCO</td><td colspan=\"3\">RefCOCO+</td><td colspan=\"2\">RefCOCOg</td></tr><tr><td>Im-Txt</td><td>Im-Txt-Box</td><td>val</td><td>testA</td><td>testB</td><td>val</td><td>testA</td><td>testB</td><td>val</td><td>test</td></tr><tr><td>MDETR-B [26]</td><td></td><td>√</td><td>87.51</td><td>90.40</td><td>82.67</td><td>81.13</td><td>85.52</td><td>72.96</td><td>83.35</td><td>83.31</td></tr><tr><td>UNICORN-B [70]</td><td></td><td>√</td><td>88.29</td><td>90.42</td><td>83.06</td><td>80.30</td><td>85.05</td><td>71.88</td><td>83.44</td><td>83.93</td></tr><tr><td colspan=\"9\">Models pre-trained on more data and/or with larger size</td><td></td><td></td></tr><tr><td>UNITER-L [6]</td><td>√</td><td></td><td>81.41</td><td>87.04</td><td>74.17</td><td>75.90</td><td>81.45</td><td>66.70</td><td>74.86</td><td>75.77</td></tr><tr><td>VILLA-L [15]</td><td>√</td><td></td><td>82.39</td><td>87.48</td><td>74.84</td><td>76.17</td><td>81.54</td><td>66.84</td><td>76.18</td><td>76.71</td></tr><tr><td>OFA-L [65]</td><td>√</td><td>√</td><td>90.05</td><td>92.93</td><td>85.26</td><td>84.49</td><td>90.10</td><td>77.77</td><td>84.54</td><td>85.20</td></tr><tr><td>FIBER-B</td><td>√</td><td>√</td><td>90.68</td><td>92.59</td><td>87.26</td><td>85.74</td><td>90.13</td><td>79.38</td><td>87.11</td><td>87.32</td></tr></table>",
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+        "text": "Referring Expression Comprehension (REC). In contrast to many previous works [6, 15, 45] that tackle the REC task by re-ranking object proposals provided by an off-the-shelf detector, we follow [26] to directly predict the bounding box for the given referring expression. Using our proposed two stage pre-training, FIBER achieves better performance than current SoTA [65] that uses a Large sized model. Notably, on RefCOCOg [76], which contains much longer referring expressions than in RefCOCO/RefCOCO $^ +$ [27], we observe more than 2 points boost over OFA-L. On the challenging testB split of both RefCOCO and RefCOCO+, FIBER outperforms current SoTA, OFA-L. ",
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+        "image_caption": [
+            "Figure 5: Few-shot results on the aggregated 13 ODinW datasets. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "Object Detection. We report FIBER results on two standard object detection benchmarks, COCO [41] and LVIS [17], in zero-shot transfer1 as well as fine-tuned settings in Table 8. The LVIS dataset consists of a long-tail of object classes, and is a popular test-bed for evaluating models on their generalization capabilities and robustness to class imbalance. On the APr metric, which is the Average Precision on rare objects, FIBER outperforms GLIP-L which is a bigger model and also trained with $2 5 \\times$ more fine-grained data. ",
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+        "table_caption": [],
+        "table_footnote": [
+            "Table 8: Zero-shot transfer and fine-tuning results for object detection on COCO, LVIS and the average over 13 datasets for object detection in the wild. Detailed scores on the 13 datasets are presented in the Appendix. FIBER achieves better AP across the board compared to similarly sized GLIP-B, trained on the same amount of fine-grained data. On rare objects in LVIS, FIBER outperforms GLIP-L trained on $2 5 \\mathrm { x }$ more fine-grained data. Results without coarse-grained pre-training are provided in the Appendix. "
+        ],
+        "table_body": "<table><tr><td rowspan=\"2\">Model</td><td>COCO Val 2017</td><td colspan=\"4\">LVIS MiniVal</td><td rowspan=\"2\">ODinW</td></tr><tr><td>AP</td><td>APr</td><td>APc</td><td>APf</td><td>AP</td></tr><tr><td></td><td>Zero-shot/Fine-tune</td><td></td><td>Zero-shot/Fine-tune</td><td></td><td></td><td>Zero-shot/Fine-tune</td></tr><tr><td>Mask R-CNN[19]</td><td>-</td><td>- /26.3</td><td>- /34.0</td><td>- /33.9</td><td>- /33.3</td><td></td></tr><tr><td>MDETR [26]</td><td>-</td><td>- /20.9</td><td>- /24.9</td><td>- /24.3</td><td>- /24.2</td><td>-</td></tr><tr><td>GLIP-T [34]</td><td>46.7/55.1</td><td>17.7/-</td><td>19.5/ -</td><td>31.0/-</td><td>24.9/ -</td><td>44.4/63.9</td></tr><tr><td>GLIP-B [34]</td><td>48.1/57.0</td><td>17.0/31.3 23.9/48.3 35.9/56.9</td><td></td><td></td><td>29.1/51.0</td><td>44.8/65.8</td></tr><tr><td colspan=\"7\">Models pre-trained on more data and/or with larger size</td></tr><tr><td>GLIP-L [34]</td><td>49.8/60.8</td><td>28.2/-</td><td>34.3/-</td><td>41.5/-</td><td>37.3/ -</td><td>52.1/68.9</td></tr><tr><td>FIBER-B</td><td>49.3/58.4</td><td>29.5/50.0</td><td>32.2/56.9</td><td>40.1/58.1</td><td>35.8/56.9</td><td>47.0/65.9</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "We also report zero-shot and fine-tuned results on a suite of 13 ODinW (object detection in the wild) datasets, spanning various domains and show consistent performance improvements over previous SoTA. Additionally, in Figure 5, we report few-shot results aggregated across these 13 datasets and show better data efficiency over GLIP-B trained with the same fine-grained data. ",
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+    {
+        "type": "text",
+        "text": "Ablation Study. In Appendix ?? and ??, we have provided detailed ablations that guided our architecture design, including ablations on fusion strategies, pre-training objectives, architecture for captioning, and additional results on open-ended VQA, and detailed few-shot ODinW results. Due to the space limit, these ablations and additional results are only provided in the Appendix. Some important observations are summarized below. (i) Co-attention works similarly to merged attention for fusion in the backbone. (ii) Adding a gating parameter in co-attention allows the addition of fusion in more layers, and also gives better performance than merged attention. (iii) Adding co-attention in the last 6 layers provides a balance between performance and efficiency. (iv) MLM, ITM with hard negative mining, and ITC are all important pre-training objectives for training FIBER-style models. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "5 Conclusion ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We propose (i) FIBER, a novel architecture and (ii) a coarse-to-fine pre-training pipeline. We perform extensive experiments and show consistent improvements over strong baselines across a diverse set of tasks. The results demonstrate the effectiveness of FIBER coupled with our pre-training strategy, by setting new SoTA scores while at the same time reducing the requirement of expensive box-level annotations. Future directions include scaling our models and extending our framework to other modalities. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The approach introduced in our work can potentially inherit undesirable societal biases that exist in our pre-training data. Careful debiasing and filtering of data should be undertaken before real-life deployment of our work. Additionally, pre-training can induce environmental costs, and minimizing these costs is an avenue that we plan to explore further. ",
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+    {
+        "type": "text",
+        "text": "Acknowledgement ",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "We would like to thank Nguyen Bach, Jiayuan Huang, and Luis Vargas for their support. We also thank Wenhui Wang, Li Dong, Furu Wei, Bin Xiao, and Lu Yuan for their helpful discussions. We also thank Liunian Harold Li and Te-Lin Wu for their feedback on the manuscript. Aishwarya is supported in part by the National Science Foundation under NSF Award 1922658. Zi-Yi is supported in part by the DARPA Machine Common Sense (MCS) program under Cooperative Agreement N66001-19-2-4032 and NIH R01HL152270. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "References ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            90,
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+        "page_idx": 10
+    },
+    {
+        "type": "text",
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