Add files using upload-large-folder tool

parse/train/2vubO341F_E/2vubO341F_E.md

@@ -0,0 +1,255 @@
+# All Tokens Matter: Token Labeling for Training Better Vision Transformers
+
+Zihang Jiang1∗ Qibin Hou2,1† Li Yuan3 Daquan Zhou1 Yujun Shi1
+
+Xiaojie Jin4 Anran Wang4 Jiashi Feng4
+
+1National University of Singapore 2Nankai University
+
+# 3 Peking University 4ByteDance
+
+{jzh0103,andrewhoux,ylustcnus,zhoudaquan21,shiyujun1016}@gmail.com xjjin0731@gmail.com, anran.wang@bytedance.com, jshfeng@gmail.com
+
+# Abstract
+
+In this paper, we present token labeling—a new training objective for training high-performance vision transformers (ViTs). Different from the standard training objective of ViTs that computes the classification loss on an additional trainable class token, our proposed one takes advantage of all the image patch tokens to compute the training loss in a dense manner. Specifically, token labeling reformulates the image classification problem into multiple token-level recognition problems and assigns each patch token with an individual location-specific supervision generated by a machine annotator. Experiments show that token labeling can clearly and consistently improve the performance of various ViT models across a wide spectrum. For a vision transformer with 26M learnable parameters serving as an example, with token labeling, the model can achieve $8 4 . 4 \%$ Top-1 accuracy on ImageNet. The result can be further increased to $8 6 . 4 \%$ by slightly scaling the model size up to 150M, delivering the minimal-sized model among previous models $( 2 5 0 \mathbf { M } + )$ reaching $86 \%$ . We also show that token labeling can clearly improve the generalization capability of the pretrained models on downstream tasks with dense prediction, such as semantic segmentation. Our code and model are publicly available at https://github.com/zihangJiang/TokenLabeling.
+
+# 1 Introduction
+
+Transformers [39] have achieved great performance for almost all the natural language processing (NLP) tasks over the past years [4, 14, 24]. Motivated by such success, recently, many researchers attempt to build transformer models for vision tasks, and their encouraging results have shown the great potential of transformer based models for image classification [6, 15, 25, 36, 40, 46], especially the strong benefits of the self-attention mechanism in building long-range dependencies between pairs of input tokens.
+
+Despite the importance of gathering long-range dependencies, recent work on local data augmentation [57] has demonstrated that well modeling and leveraging local information for image classification would avoid biasing the model towards skewed and non-generalizable patterns and substantially improve the model performance. However, recent vision transformers normally utilize class tokens that aggregate global information to predict the output class while neglecting the role of other patch tokens that encode rich information on their respective local image patches.
+
+![](images/9c7bb663ccabca3baefdad385c72c84db533d97dbd497ac18638700c9e1d548b.jpg)  
+Figure 1: Comparison between the proposed LV-ViT and other recent works based on vision transformers, including T2T-ViT [46], ConViT [12], BoTNet [31], DeepViT [59], DeiT [36], ViT [15], Swin Transformer [25], LambdaNet [1], CvT [43], CrossViT [6], PVT [40], CaiT [37]. Note that we only show models whose model sizes are under 100M. As can be seen, our LV-ViT achieves the best results using the least amount of learnable parameters. The default test resolution is $2 2 4 \times 2 2 4$ unless specified after $@$ .
+
+In this paper, we present a new training objective for vision transformers, termed token labeling, that takes advantage of both the patch tokens and the class tokens. Our method takes a $K$ -dimensional score map generated by a machine annotator as supervision to supervise all the tokens in a dense manner, where $K$ is the number of categories for the target dataset. In this way, each patch token is explicitly associated with an individual location-specific supervision indicating the existence of the target objects inside the corresponding image patch, so as to improve the object grounding and recognition capabilities of vision transformers with negligible computation overhead. To the best of our knowledge, this is the first work demonstrating that dense supervision is beneficial to vision transformers in image classification.
+
+According to our experiments, utilizing the proposed token labeling objective can clearly boost the performance of vision transformers. As shown in Figure 1, our model, named LV-ViT, with 56M parameters, yields $8 5 . 4 \%$ top-1 accuracy on ImageNet [13], behaving better than all the other transformer-based models having no more than 100M parameters. When the model size is scaled up to 150M, the result can be further improved to $8 6 . 4 \%$ . In addition, we have empirically found that the pretrained models with token labeling are also beneficial to downstream tasks with dense prediction, such as semantic segmentation.
+
+# 2 Related Work
+
+Transformers [39] refer to the models that entirely rely on the self-attention mechanism to build global dependencies, which are originally designed for natural language processing tasks. Due to their strong capability of capturing spatial information, transformers have also been successfully applied to a variety of vision problems, including low-level vision tasks like image enhancement [7, 45], as well as more challenging tasks such as image classification [9, 15], object detection [5, 11, 55, 61], segmentation [7, 33, 41] and image generation [28]. Some works also extend transformers for video and 3D point cloud processing [50, 53, 60].
+
+Vision Transformer (ViT) is one of the earlier attempts that achieved state-of-the-art performance on ImageNet classification, using pure transformers as basic building blocks. However, ViTs need pretraining on very large datasets, such as ImageNet-22k and JFT-300M, and huge computation resources to achieve comparable performance to ResNet [18] with a similar model size trained on ImageNet. Later, DeiT [36] manages to tackle the data-inefficiency problem by simply adjusting the network architecture and adding an additional token along with the class token for Knowledge Distillation [21, 47] to improve model performance.
+
+![](images/77890e011e8cc08c2d9f50310be754cb08f7894ee6cb766ac590a7580f42e616.jpg)  
+Figure 2: Pipeline of training vision transformers with token labeling. Other than utilizing the class token (pink rectangle), we also take advantage of all the output patch tokens (orange rounded rectangle) by assigning each patch token an individual location-specific prediction generated by a machine annotator [3] as supervision (see the part in the red dash rectangle). Our proposed token labeling method can be treated as an auxiliary objective to provide each patch token the local details that aid vision transformers to more accurately locate and recognize the target objects. Note that the traditional vision transformer training does not include the red dash rectangle part.
+
+Some recent works [6, 16, 43, 46] also attempt to introduce the local dependency into vision transformers by modifying the patch embedding block or the transformer block or both, leading to significant performance gains. Moreover, there are also some works [20, 25, 40] adopting a pyramid structure to reduce the overall computation while maintaining the model’s ability to capture low-level features.
+
+Unlike most aforementioned works that design new transformer blocks or transformer architectures, we attempt to improve vision transformers by studying the role of patch tokens that embed rich local information inside image patches. We show that by slightly tuning the structure of vision transformers and employing the proposed token labeling objective, we can achieve strong baselines for transformer models at different model size levels.
+
+# 3 Token Labeling Method
+
+In this section, we first briefly review the structure of the vision transformer [15] and then describe the proposed training objective—token labeling.
+
+# 3.1 Revisiting Vision Transformer
+
+A typical vision transformer [15] first decomposes a fixed-size input image into a sequence of small patches. Each small patch is mapped to a feature vector, or called a token, by projection with a linear layer. Then, all the tokens combined with an additional learnable class token for classification score prediction are sent into a stack of transformer blocks for feature encoding.
+
+In loss computing, the class token from the output tokens of the last transformer block is usually selected and sent into a linear layer for the classification score prediction. Mathematically, given an image $I$ , denote the output of the last transformer block as $[ \bar { X } ^ { c l s } , X ^ { 1 } , . . . , X ^ { N } ]$ , where $N$ is the total number of patch tokens, and $X ^ { c l s }$ and $X ^ { 1 } , . . . , X ^ { N }$ correspond to the class token and the patch tokens, respectively. The classification loss for image $I$ can be written as
+
+$$
+L _ { c l s } = H ( { X } ^ { c l s } , { y } ^ { c l s } ) ,
+$$
+
+where $H ( \cdot , \cdot )$ is the softmax cross-entropy loss and $y ^ { c l s }$ is the class label.
+
+![](images/c741b481df54f67e411d3cc1b30dc7deb904c80d9d11e57036dbf5b27cdbfb8f.jpg)  
+Figure 3: Comparison between CutMix [48] (Left) and our proposed MixToken (Right). CutMix is operated on the input images. This results in patches containing mixed regions from the two images (see the patches enclosed by red bounding boxes). Differently, MixToken targets at mixing tokens after patch embedding. This enables each token after patch embedding to have clean content as shown in the right part of this figure. The detailed advantage of MixToken can be found in Sec. 4.2.
+
+# 3.2 Token Labeling
+
+The above classification problem only adopts an image-level label as supervision whereas it neglects the rich information embedded in each image patch. In this subsection, we present a new training objective—token labeling—that takes advantage of the complementary information between the patch tokens and the class tokens.
+
+Token Labeling: Different from the classification loss as formulated in Eqn. (1) that measures the distance between the single class token (representing the whole input image) and the corresponding image-level label, token labeling emphasizes the importance of all output tokens and advocates that each output token should be associated with an individual location-specific label. Therefore, in our method, the ground truth for an input image involves not only a single $K$ -dimensional vector $y ^ { c l s }$ but also a $K \times N$ matrix or called a $K$ -dimensional score map as represented by $[ y ^ { 1 } , . . . , y ^ { N } ]$ , where $N$ is the number of the output patch tokens.
+
+Specifically, we leverage a dense score map for each training image and use the cross-entropy loss between each output patch token and the corresponding aligned label in the dense score map as an auxiliary loss at the training phase. Figure 2 provides an intuitive interpretation. Given the output patch tokens $X ^ { 1 } , . . . , X ^ { N }$ and the corresponding labels $[ y ^ { 1 } , . . . , y ^ { N } ]$ , the token labeling objective can be defined as
+
+$$
+L _ { t l } = \frac { 1 } { N } \sum _ { i = 1 } ^ { N } H ( X ^ { i } , y ^ { i } ) .
+$$
+
+Recall that $H$ is the cross-entropy loss. Therefore, the total loss function can be written as
+
+$$
+\begin{array} { l } { { { \cal L } _ { t o t a l } = H ( X ^ { c l s } , y ^ { c l s } ) + \beta \cdot L _ { t l } , } } \\ { { { } } } \\ { { = H ( X ^ { c l s } , y ^ { c l s } ) + \beta \cdot \displaystyle \frac { 1 } { N } \sum _ { i = 1 } ^ { N } H ( X ^ { i } , y ^ { i } ) , } } \end{array}
+$$
+
+where $\beta$ is a hyper-parameter to balance the two terms. In our experiment, we empirically set it to 0.5.
+
+Advantages: Our token labeling offers the following advantages. First of all, unlike knowledge distillation methods that require a teacher model to generate supervision labels online, token labeling is a cheap operation. The dense score map can be generated by a pretrained model in advance (e.g., EfficientNet [34] or NFNet [3]). During training, we only need to crop the score map and perform interpolation to make it aligned with the cropped image in the spatial coordinate. Thus, the additional computations are negligible. Second, rather than utilizing a single label vector as supervision as done in most classification models and the ReLabel strategy [49], we also harness score maps to supervise the models in a dense manner and thereby the label for each patch token provides location-specific information, which can aid the training models to easily discover the target objects and improve the recognition accuracy. Last but not the least, as dense supervision is adopted in training, we found that the pretrained models with token labeling benefit downstream tasks with dense prediction, like semantic segmentation.
+
+# 3.3 Token Labeling with MixToken
+
+While training vision transformer, previous studies [36, 46] have shown that augmentation methods, like MixUp [52] and CutMix [48], can effectively boost the performance and robustness of the models. However, vision transformers rely on patch-based tokenization to map each input image to a sequence of tokens and our token labeling strategy also operates on patch-based token labels. If we apply CutMix directly on the raw image, some of the resulting patches may contain content from two images, leading to mixed regions within a small patch as shown in Figure 3. When performing token labeling, it is difficult to assign each output token a clean and correct label. Taking this situation into account, we rethink the CutMix augmentation method and present MixToken, which can be viewed as a modified version of CutMix operating on the tokens after patch embedding as illustrated in the right part of Figure 3.
+
+To be specific, for two images denoted as $I _ { 1 } , I _ { 2 }$ and their corresponding token labels $Y _ { 1 } = [ y _ { 1 } ^ { 1 } , . . . , y _ { 1 } ^ { N } ]$ as well as $Y _ { 2 } = [ y _ { 2 } ^ { 1 } , . . . , y _ { 2 } ^ { N } ]$ , we first feed the two images into the patch embedding module to tokenize each as a sequence of tokens, resulting in $T _ { 1 } = [ t _ { 1 } ^ { 1 } , . . . , t _ { 1 } ^ { N } ]$ and $\bar { T _ { 2 } } = [ t _ { 2 } ^ { 1 } , . . . , t _ { 2 } ^ { N } ]$ . Then, we produce a new sequence of tokens by applying MixToken using a binary mask $M$ as follows:
+
+$$
+\hat { T } = T _ { 1 } \odot M + T _ { 2 } \odot ( 1 - M ) ,
+$$
+
+where $\odot$ is element-wise multiplication. We use the same way to generate the mask $M$ as in [48]. For the corresponding token labels, we also mix them using the same mask $M$ :
+
+$$
+\hat { Y } = Y _ { 1 } \odot M + Y _ { 2 } \odot ( 1 - M ) .
+$$
+
+The label for the class token can be written as
+
+$$
+y ^ { \hat { c } l s } = \bar { M } y _ { 1 } ^ { c l s } + ( 1 - \bar { M } ) y _ { 2 } ^ { c l s } ,
+$$
+
+where $\bar { M }$ is the average of all element values of $M$ .
+
+# 4 Experiments
+
+# 4.1 Experiment Setup
+
+We evaluate our method on the ImageNet [13] dataset. All experiments are built and conducted upon PyTorch [29] and the timm [42] library. We follow the standard training schedule and train our models on the ImageNet dataset for 300 epochs. Besides normal augmentations like CutOut [57] and RandAug [10], we also explore the effect of applying MixUp [52] and CutMix [48] together with our proposed token labeling. Empirically, we have found that using MixUp together with token labeling brings no benefit to the performance, and thus we do not apply it in our experiments.
+
+For optimization, by default, we use the AdamW optimizer [27] with a linear learning rate scaling strategy $\begin{array} { r } { l r = 1 0 ^ { - 3 } \times \frac { b a t c h \_ s i z e } { 6 4 0 } } \end{array}$ and $5 \times 1 0 ^ { - 2 }$ weight decay rate. For Dropout regularization, we observe that for small models, using Dropout hurts the performance. This has also been observed in a few other works related to training vision transformers [36, 37, 46]. As a result, we do not apply Dropout [32] and use Stochastic Depth [23] instead. More details on hyper-parameters and finetuning can be found in our supplementary materials.
+
+We use the NFNet-F6 [3] trained on ImageNet with an $8 6 . 3 \%$ Top-1 accuracy as the machine annotator to generate dense score maps for the ImageNet dataset, yielding a 1000-dimensional score map for each image for training. The score map generation procedure is similar to [49], but we limit our experiment setting by training all models from scratch on ImageNet without extra data support, such as JFT-300M and ImageNet-22K. This is different from the original ReLabel paper [49], in which the EfficientNet-L2 model pretrained on JFT-300M is used. The input resolution for NFNet-F6 is $5 7 6 \times 5 7 6$ , and the dimension of the corresponding output score map for each image is $L \in \mathbb { R } ^ { 1 8 \times 1 8 \times 1 0 0 0 }$ . During training, the target labels for the tokens are generated by applying RoIAlign [17] on the corresponding score map. In practice, we only store the top-5 score maps for each position in half-precision to save space as storing the entire score maps for all the images results in 2TB storage. In our experiment, we only need 10GB of storage to store all the score maps.
+
+Table 1: Performance of the proposed LV-ViT with different model sizes. Here, ‘depth’ denotes the number of transformer blocks used in different models. By default, the test resolution is set to $2 2 4 \times 2 2 4$ except the last one which is $2 8 8 \times 2 8 8$ .   
+
+<table><tr><td>Name</td><td>Depth</td><td>Embed dim.</td><td>MLP Ratio</td><td>#Heads</td><td>#Params</td><td>Throughput (im/s)</td><td>Test size</td><td>Top-1 Acc. (%)</td></tr><tr><td>LV-ViT-T</td><td>12</td><td>240</td><td>3.0</td><td>4</td><td>8.5M</td><td>2032.6</td><td>224</td><td>79.1</td></tr><tr><td>LV-ViT-S</td><td>16</td><td>384</td><td>3.0</td><td>6</td><td>26M</td><td>1018.2</td><td>224</td><td>83.3</td></tr><tr><td>LV-ViT-M</td><td>20</td><td>512</td><td>3.0</td><td>8</td><td>56M</td><td>668.9</td><td>224</td><td>84.1</td></tr><tr><td>LV-ViT-L</td><td>24</td><td>768</td><td>3.0</td><td>12</td><td>150M</td><td>204.8</td><td>288</td><td>85.3</td></tr></table>
+
+# 4.2 Ablation Analysis
+
+Model Settings: The default settings of the proposed LV-ViT are given in Table 1, where both token labeling and MixToken are used. A slight architecture modification to ViT [15] is that we replace the patch embedding module with a 4-layer convolution to better tokenize the input image and integrate local information. Detailed ablation about patch embedding can be found in our supplementary materials. As can be seen, our LV-ViT-T with only $8 . 5 { \bf M }$ parameters can already achieve a top-1 accuracy of $7 9 . 1 \%$ on ImageNet. Increasing the embedding dimension and network depth can further boost the performance. More experiments compared to other methods can be found in Sec. 4.3. In the following ablation experiments, we will set our LV-ViT-S as baseline and show the advantages of the proposed token labeling and MixToken methods.
+
+MixToken: We use MixToken as a substitution for CutMix while applying token labeling. Our experiments show that MixToken performs better than CutMix for token-based transformer models. As shown in Table 2, when training with the original ImageNet labels, using MixToken is $0 . 1 \%$ higher than using CutMix. When using the ReLabel supervision, we can also see an advantage of $0 . { \bar { 2 } } \%$ over the CutMix baseline. Combining with our token labeling, the performance can be further raised to $8 3 . 3 \%$ .
+
+Table 2: Ablation on the proposed MixToken and token labeling augmentations. We also show results with either the ImageNet hard label and the ReLabel [49] as supervision.   
+
+<table><tr><td>Aug. Method</td><td>Supervision</td><td>Top-1 Acc.</td></tr><tr><td>MixToken</td><td>Token labeling</td><td>83.3</td></tr><tr><td>MixToken</td><td>ReLabel</td><td>83.0</td></tr><tr><td>CutMix</td><td>ReLabel</td><td>82.8</td></tr><tr><td>Mixtoken</td><td>ImageNet Label</td><td>82.5</td></tr><tr><td>CutMix</td><td>ImageNet Label</td><td>82.4</td></tr></table>
+
+Table 3: Ablation on different widely-used data augmentations. We have empirically found our proposed MixToken performs even better than the combination of MixUp and CutMix in vision transformers.   
+
+<table><tr><td>MixToken</td><td>MixUp</td><td>CutOut</td><td>RandAug</td><td>Top-1 Acc.</td></tr><tr><td></td><td></td><td></td><td></td><td>83.3</td></tr><tr><td></td><td></td><td></td><td></td><td>81.3</td></tr><tr><td>&gt;x&gt;</td><td>xx&gt;</td><td>&gt;&gt;&gt;</td><td>&gt;&gt;&gt;</td><td>83.1</td></tr><tr><td></td><td>X</td><td></td><td>√</td><td>83.0</td></tr><tr><td>广</td><td>X</td><td>X</td><td>X</td><td>82.8</td></tr></table>
+
+Data Augmentation: Here, we study the compatibility of MixToken with other augmentation techniques, such as MixUp [52], CutOut [57] and RandAug [10]. The ablation results are shown in Table 3. We can see when all the four augmentation methods are used, a top-1 accuracy of $8 3 . 1 \%$ is achieved. Interestingly, when the MixUp augmentation is removed, the performance can be improved to $8 3 . 3 \%$ . This may be explained as, using MixToken and MixUp at the same time would bring too much noise in the label, and consequently cause confusion of the model. Moreover, the CutOut augmentation, which randomly erases some parts of the image, is also effective and removing it brings a performance drop of $\dot { 0 } . 3 \%$ . Similarly, the RandAug augmentation also contributes to the performance and using it brings an improvement of $0 . 5 \%$ .
+
+All Tokens Matter: To show the importance of involving all tokens in our token labeling method, we attempt to randomly drop some tokens and use the remaining ones for computing the token labeling loss. The percentage of the remaining tokens is denoted as Token Participation Rate. As shown in Figure 4 (Left), we conduct experiments on two models: LV-ViT-S and LV-ViT-M. As can be seen, using only $2 0 \%$ of the tokens to compute the token labeling loss decreases the performance $( - 0 . 5 \%$ for LV-ViT-S and $- 0 . 4 \%$ for LV-ViT-M). Involving more tokens for loss computation consistently leads to better performance. Since involving all tokens brings negligible computation cost and gives the best performance, we always set the token participation rate as $\mathrm { \bar { 1 0 0 \% } }$ in the following experiments.
+
+![](images/810578c2e36580b46aa98e4ec01030b20f6e00994c33dafcaa4cde435beb4d46.jpg)  
+Figure 4: Left: LV-ViT ImageNet Top-1 Accuracy w.r.t. the token participation rate while applying token labeling. Token participation rate indicates the percentage of patch tokens involved in computing the token labeling loss. This experiment reflects that all tokens matter for vision transformers. Right: LV-ViT-S ImageNet Top-1 Accuracy w.r.t. different annotator models. The point size indicates the parameter number of the annotator model. Clearly, our token labeling objective is robust to different annotator models.
+
+Table 4: Comparison of token labeling (TL), knowledge distillation (KD) based method and ReLabel method based on utilized tokens, DeiT-S/LV-ViT-S Top-1 accuracy on ImageNet validation set and training time on a single V100 GPU node.   
+
+<table><tr><td>Method</td><td>Online KD</td><td>Online TL</td><td>TL</td><td>ReLabel</td><td>Vanilla</td></tr><tr><td>Tokens Utilized</td><td>2</td><td>All</td><td>All</td><td>1</td><td>1</td></tr><tr><td>DeiT-S Acc. (%)</td><td>81.2</td><td>81.8</td><td>81.0</td><td>80.4</td><td>79.9</td></tr><tr><td>LV-ViT-S Acc. (%)</td><td>83.0</td><td>83.5</td><td>83.3</td><td>82.8</td><td>82.4</td></tr><tr><td>Training Time (8× V100)</td><td>63 hrs</td><td>63 hrs</td><td>45 hrs</td><td>45 hrs</td><td>41 hrs</td></tr></table>
+
+Online Token Labeling: Unlike the online knowledge distillation method which generates labels by a teacher model online, our token labeling approach utilizes the dense label map generated in advance and directly applies the corresponding augmentation methods, such as random crop, on the label map to obtain token-level labels. To directly compare with the online knowledge distillation based method and validate the effectiveness of token-level supervision, we further conduct experiments on the online version of our token labeling method, which generates token-level labels online during training. Following DeiT [36], we use RegNetY-16GF [30] as the online teacher model. Results in terms of DeiT-S/LV-ViT-S Top-1 accuracy and training time for our token labeling, online knowledge distillation, and ReLabel [49] are listed in Table 4, with number of utilized tokens also included for clear comparison. As can be seen, for both online and offline cases, using token-level supervision can improve the overall performance with only negligible additional training cost. Meanwhile, compared to the vanilla training baseline, our proposed offline token labeling brings almost no additional training cost, and boosts the overall performance of LV-ViT-S by $0 . 9 \%$ , which well demonstrates its efficiency and effectiveness.
+
+Robustness to Different Annotators: To evaluate the robustness of our token labeling method, we use different pretrained CNNs, including EfficientNet-B3,B4,B5,B6,B7,B8 [34], NFNet-F6 [3] and ResNest269E [51], as annotator models to provide dense supervision. Results are shown in the right part of Figure 4. We can see that, even if we use an annotator with relatively lower performance, such as EfficientNet-B3 whose Top-1 accuracy is $8 1 . 6 \%$ , it can still provide multi-label location-specific supervision and help improve the performance of our LV-ViT-S model. Meanwhile, annotator models with better performance can provide more accurate supervision, bringing even better performance, as stronger annotator models can generate better token-level labels. The largest annotator NFNet-F6 [3], which has the best performance of $8 6 . 3 \%$ , allows us to achieve the best result for LV-ViT-S, which is $8 3 . 3 \%$ . In addition, we also attempt to use a better model, EfficientNet-L2 pretrained on JFT-300M as described in [49] which has $8 8 . 2 \%$ Top-1 ImageNet accuracy, as our annotator. The performance of LV-ViT-S can be further improved to $8 \mathrm { { 3 . 5 \% } }$ . However, to fairly compare with the models without extra training data, we only report results based on dense supervision produced by NFNet-F6 [3] that uses only ImageNet training data.
+
+![](images/a3d559defddf629a8a69e1ea7f71228daa68e20f028756c9b3671f019cf5ad40.jpg)  
+Figure 5: Performance of the proposed token labeling objective on three different vision transformers: DeiT [36] (Left), T2T-ViT [46] (Middle), and LV-ViT (Right). Our method has a consistent improvement on all 7 different ViT models.
+
+Robustness to Different ViT Variants: To further evaluate the robustness of our token labeling, we train different transformer-based networks, including DeiT [36], T2T-ViT [3] and our model LV-ViT, with the proposed training objective. Results are shown in Figure 5. It can be found that, all the models trained with token labeling consistently outperform their vanilla counterparts, demonstrating the robustness of token labeling with respect to different variants of patch-based vision transformers. Meanwhile, for different scales of the models, the improvement is also consistent. Interestingly, we observe larger improvements for larger models. These indicate that our proposed token labeling method is widely applicable to a large range of patch-based vision transformer variants.
+
+Beyond Vision Transformers: We further explore the performance of token labeling on other CNN-based and MLP-based models. Results are shown in Table 5. Besides our re-implementation with more data augmentation and regularization techniques, we also provide the results from the original papers. It can be found that for both MLP-based and CNN-based models, our token labeling objective can also improve the performance over strong baselines by providing location-specific dense supervision.
+
+Table 5: Performance of the proposed token labeling objective on representative CNN-based (ResNeSt) and MLP-based (Mixer-MLP) models. Our method has a consistent improvement on all different models. Here † indicates results reported in original papers.   
+
+<table><tr><td>Model</td><td colspan="3">Mixer-S/16 [35]</td><td colspan="3">Mixer-B/16 [35]</td><td colspan="3">Mixer-L/16 [35]</td><td colspan="3">ResNeSt-50 [51]</td></tr><tr><td>Token Labeling</td><td>X</td><td>X</td><td>√</td><td>×</td><td>X</td><td>√</td><td>×</td><td>×</td><td>√</td><td>×</td><td>×</td><td>√</td></tr><tr><td>Parameters</td><td>18M</td><td>18M18M</td><td></td><td>59M</td><td>59M 59M</td><td></td><td>207M</td><td></td><td>207M207M</td><td>27M</td><td></td><td>27M 27M</td></tr><tr><td>Top-1 Acc. (%)</td><td>73.8t</td><td>75.6</td><td>76.1</td><td>76.4</td><td>78.3</td><td>79.5</td><td>71.6t</td><td>77.7</td><td>80.1</td><td>81.1t</td><td>80.9</td><td>81.5</td></tr></table>
+
+# 4.3 Comparison to Other Methods
+
+We compare our proposed model LV-ViT with other state-of-the-art methods in Table 6. For smallsized models, when the test resolution is set to $2 2 4 \times 2 2 4$ , we achieve an $8 3 . 3 \%$ accuracy on ImageNet with only 26M parameters, which is $3 . 4 \%$ higher than the strong baseline DeiT-S [36]. For mediumsized models, when the test resolution is set to $3 8 4 \times 3 8 4$ we achieve the performance of $8 5 . 4 \%$ , the same as CaiT-S36 [37], but with much less computational cost and parameters. Note that both DeiT and CaiT use knowledge distillation to improve their models, which introduce much more computations in training. However, we do not require any extra computations in training and only have to compute and store the dense score maps in advance. For large-sized models, our LV-ViT-L with a test resolution of $4 4 8 \times 4 4 8$ achieves an $8 6 . 2 \%$ top-1 accuracy, which is comparable to CaiT-M36 [37] but with far fewer FLOPs and parameters.
+
+Table 6: Top-1 accuracy comparison with other methods on ImageNet [13] and ImageNet Real [2]. All models are trained without external data. With the same computation and parameter constraint, our model consistently outperforms other CNN-based and transformer-based counterparts. The results of CNNs and ViT are referenced from [37].   
+
+<table><tr><td>Network</td><td>Params</td><td>FLOPs</td><td>Train size</td><td>Test size</td><td>Top-1(%)</td><td>Real Top-1 (%)</td></tr><tr><td>EfficientNet-B5 [34] SNNO</td><td>30M</td><td>9.9B</td><td>456</td><td>456</td><td>83.6</td><td>88.3</td></tr><tr><td>EfficientNet-B7 [34]</td><td>66M</td><td>37.0B</td><td>600</td><td>600</td><td>84.3</td><td></td></tr><tr><td>Fix-EfficientNet-B8 [34,38]</td><td>87M</td><td>89.5B</td><td>672</td><td>800</td><td>85.7</td><td>90.0</td></tr><tr><td>NFNet-F3 [3]</td><td>255M</td><td>114.8B</td><td>320</td><td>416</td><td>85.7</td><td>89.4</td></tr><tr><td>NFNet-F4 [3]</td><td>316M</td><td>215.3B</td><td>384</td><td>512</td><td>85.9</td><td>89.4</td></tr><tr><td>NFNet-F5[3]</td><td>377M</td><td>289.8B</td><td>416</td><td>544</td><td>86.0</td><td>89.2</td></tr><tr><td>ViT-B/16 [15]</td><td>86M</td><td>55.4B</td><td>224</td><td>384</td><td>77.9</td><td>83.6</td></tr><tr><td>ViT-L/16[15]</td><td>307M</td><td>190.7B</td><td>224</td><td>384</td><td>76.5</td><td>82.2</td></tr><tr><td>T2T-ViT-14 [46]</td><td>22M</td><td>5.2B</td><td>224</td><td>224</td><td>81.5</td><td></td></tr><tr><td>T2T-ViT-14↑384 [46]</td><td>22M</td><td>17.1B</td><td>224</td><td>384</td><td>83.3</td><td>1</td></tr><tr><td>Cross ViT [6]</td><td>45M</td><td>56.6B</td><td>224</td><td>480</td><td>84.1</td><td>一</td></tr><tr><td>Swin-B[25]</td><td>88M</td><td>47.0B</td><td>224</td><td>384</td><td>84.2</td><td></td></tr><tr><td>TNT-B[16]</td><td>66M</td><td>14.1B</td><td>224</td><td>224</td><td>82.8</td><td></td></tr><tr><td>iriirrrrrs DeepViT-S [59]</td><td>27M</td><td>6.2B</td><td>224</td><td>224</td><td>82.3</td><td></td></tr><tr><td>DeepViT-L [59]</td><td>55M</td><td>12.5B</td><td>224</td><td>224</td><td>83.1</td><td></td></tr><tr><td>DeiT-S[36]</td><td>22M</td><td>4.6B</td><td>224</td><td>224</td><td>79.9</td><td>85.7</td></tr><tr><td>Distilled DeiT-S [36]</td><td>22M</td><td>4.6B</td><td>224</td><td>224</td><td>81.2</td><td>86.8</td></tr><tr><td>DeiT-B [36]</td><td>86M</td><td>17.5B</td><td>224</td><td>224</td><td>81.8</td><td>86.7</td></tr><tr><td>DeiT-B↑384 [36]</td><td>86M</td><td>55.4B</td><td>224</td><td>384</td><td>83.1</td><td>87.7</td></tr><tr><td>Distilled DeiT-B [36]</td><td>87M</td><td>17.5B</td><td>224</td><td>224</td><td>83.4</td><td>88.3</td></tr><tr><td>BoTNet-S1-128 [31]</td><td>79.1M</td><td>19.3B</td><td>256</td><td>256</td><td>84.2</td><td></td></tr><tr><td>BoTNet-S1-128↑384 [31]</td><td>79.1M</td><td>45.8B</td><td>256</td><td>384</td><td>84.7</td><td>-</td></tr><tr><td>CaiT-S36↑384 [37]</td><td>68M</td><td>48.0B</td><td>224</td><td>384</td><td>85.4</td><td>- 89.8</td></tr><tr><td>CaiT-M36[37]</td><td>271M</td><td>53.7B</td><td>224</td><td>224</td><td>85.1</td><td>89.3</td></tr><tr><td>CaiT-M36↑448 [37]</td><td>271M</td><td>247.8B</td><td>224</td><td>448</td><td>86.3</td><td>90.2</td></tr><tr><td>LV-ViT-S</td><td>26M</td><td>6.6B</td><td>224</td><td>224</td><td>83.3</td><td></td></tr><tr><td>江 LV-ViT-S↑384</td><td>26M</td><td>22.2B</td><td>224</td><td>384</td><td>84.4</td><td>88.1 88.9</td></tr><tr><td>LV-ViT-M</td><td>56M</td><td>16.0B</td><td>224</td><td>224</td><td>84.1</td><td>88.4</td></tr><tr><td>W LV-ViT-M↑384</td><td>56M</td><td>42.2B</td><td>224</td><td>384</td><td>85.4</td><td>89.5</td></tr><tr><td>LV-ViT-L</td><td>150M</td><td>59.0B</td><td>288</td><td>288</td><td>85.3</td><td>89.3</td></tr><tr><td>0 LV-ViT-L↑448</td><td>150M</td><td>157.2B</td><td>288</td><td>448</td><td>85.9</td><td>89.7</td></tr><tr><td>LV-ViT-L↑448</td><td>150M</td><td>157.2B</td><td>448</td><td>448</td><td>86.2</td><td>89.9</td></tr><tr><td>LV-ViT-L↑512</td><td>151M</td><td>214.8B</td><td>448</td><td>512</td><td>86.4</td><td>90.1</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></table>
+
+# 4.4 Semantic Segmentation on ADE20K
+
+It has been shown in [19] that different training techniques for pretrained models have different impacts on downstream tasks with dense prediction, like semantic segmentation. To demonstrate the advantage of the proposed token labeling objective on tasks with dense prediction, we apply our pretrained LV-ViT with token labeling to the semantic segmentation task.
+
+Similar to previous work [25], we run experiments on the widely-used ADE20K [58] dataset. ADE20K contains 25K images in total, including 20K images for training, 2K images for validation and 3K images for test, and covering 150 different foreground categories. We take both FCN [26] and UperNet [44] as our segmentation frameworks and use the mmseg toolbox to implement. During training, following [25], we use the AdamW optimizer with an initial learning rate of 6e-5 and a weight decay of 0.01. We also use a linear learning schedule with a minimum learning rate of 5e-6. All models are trained on 8 GPUs and with a batch size of 16 (i.e., 2 images on each GPU). The input resolution is set to $5 1 2 \times 5 1 2$ . In inference, a multi-scale test with interpolation rates of [0.75, 1.0, 1.25, 1.5, 1.75] is used. As suggested by [58], we report results in terms of both mean intersection-over-union (mIoU) and the average pixel accuracy (Pixel Acc.).
+
+In Table 7, we test the performance of token labeling on both FCN and UperNet frameworks. The FCN framework has a light convolutional head and can directly reflect the performance of the pretrained models in terms of transferable capability. As can be seen, pretrained models with token labeling perform better than those without token labeling. This indicates token labeling is indeed beneficial to semantic segmentation.
+
+Table 7: Transfer performance of the proposed LV-ViT in semantic segmentation. We take two classic methods, FCN and UperNet, as segmentation architectures and show both single-scale (SS) and multi-scale (MS) results on the validation set.   
+
+<table><tr><td>Method</td><td>Token Labeling</td><td>Model Size</td><td>mIoU (SS)</td><td>P. Acc. (SS)</td><td>mIoU (MS)</td><td>P. Acc. (MS)</td></tr><tr><td>LV-ViT-S + FCN</td><td>×</td><td>30M</td><td>46.1</td><td>81.9</td><td>47.3</td><td>82.6</td></tr><tr><td>LV-ViT-S + FCN</td><td></td><td>30M</td><td>47.2</td><td>82.4</td><td>48.4</td><td>83.0</td></tr><tr><td>LV-ViT-S + UperNet</td><td></td><td>44M</td><td>46.5</td><td>82.1</td><td>47.6</td><td>82.7</td></tr><tr><td>LV-ViT-S + UperNet</td><td>X</td><td>44M</td><td>47.9</td><td>82.6</td><td>48.6</td><td>83.1</td></tr></table>
+
+We also compare our segmentation results with previous state-of-the-art segmentation methods in Table 8. Without pretraining on large-scale datasets such as ImageNet-22K, our LV-ViT-M with the UperNet segmentation architecture achieves an mIoU score of 50.6 with only 77M parameters. This result is much better than the previous CNN-based and transformer-based models. Furthermore, using our LV-ViT-L as the pretrained model yields a better result of 51.8 in terms of mIoU. As far as we know, this is the best result reported on ADE20K with no pretraining on ImageNet-22K or other large-scale datasets.
+
+Table 8: Comparison with previous work on ADE20K validation set. As far as we know, our LVViT-L $^ +$ UperNet achieves the best result on ADE20K with only ImageNet-1K as training data in pretraining. †Pretrained on ImageNet-22K.   
+
+<table><tr><td></td><td>Backbone</td><td>Segmentation Architecture</td><td>Model Size</td><td>mIoU (MS)</td><td>Pixel Acc. (MS)</td></tr><tr><td rowspan="5">SNNO</td><td>ResNet-269</td><td>PSPNet [54]</td><td></td><td>44.9</td><td>81.7</td></tr><tr><td>ResNet-101</td><td>UperNet [44]</td><td>86M</td><td>44.9</td><td>-</td></tr><tr><td>ResNet-101</td><td>Strip Pooling [22]</td><td></td><td>45.6</td><td>82.1</td></tr><tr><td>ResNeSt200</td><td>DeepLabV3+ [8]</td><td>88M</td><td>48.4</td><td>1</td></tr><tr><td>DeiT-S</td><td>UperNet</td><td>52M</td><td>44.0</td><td>-</td></tr><tr><td rowspan="5">Tirriiirrss</td><td>ViT-Larget</td><td>SETR [56]</td><td>308M</td><td>50.3</td><td>83.5</td></tr><tr><td>Swin-T[25]</td><td>UperNet</td><td>60M</td><td>46.1</td><td>1</td></tr><tr><td>Swin-S [25]</td><td>UperNet</td><td>81M</td><td>49.3</td><td>=</td></tr><tr><td>Swin-B [25]</td><td>UperNet</td><td>121M</td><td>49.7</td><td></td></tr><tr><td>Swin-B† [25]</td><td>UperNet</td><td>121M</td><td>51.6</td><td>-</td></tr><tr><td rowspan="4">LIA-AT</td><td>LV-ViT-S</td><td>FCN</td><td>30M</td><td>48.4</td><td>83.0</td></tr><tr><td>LV-ViT-S</td><td>UperNet</td><td>44M</td><td>48.6</td><td>83.1</td></tr><tr><td>LV-ViT-M</td><td>UperNet</td><td>77M</td><td>50.6</td><td>83.5</td></tr><tr><td>LV-ViT-L</td><td>UperNet</td><td>209M</td><td>51.8</td><td>84.1</td></tr></table>
+
+# 5 Conclusions and Discussion
+
+In this paper, we introduce a new token labeling method to help improve the performance of vision transformers. We also analyze the effectiveness and robustness of our token labeling with respect to different annotators and different variants of patch-based vision transformers. By applying token labeling, our proposed LV-ViT achieves $8 4 . 4 \%$ Top-1 accuracy with only 26M parameters and $8 6 . 4 \%$ Top-1 accuracy with 150M parameters on ImageNet-1K benchmark.
+
+Despite the effectiveness, token labeling has a limitation of requiring a pretrained model as the machine annotator. Fortunately, the machine annotating procedure can be done in advance to avoid introducing extra computational cost in training. This makes our method quite different from knowledge distillation methods that rely on online teaching. For users with limited machine resources on hand, our token labeling provides a promising training technique to improve the performance of vision transformers.
+
+References   
+[1] Irwan Bello. Lambdanetworks: Modeling long-range interactions without attention. arXiv preprint arXiv:2102.08602, 2021.   
+[2] Lucas Beyer, Olivier J Hénaff, Alexander Kolesnikov, Xiaohua Zhai, and Aäron van den Oord. Are we done with imagenet? arXiv preprint arXiv:2006.07159, 2020.   
+[3] Andrew Brock, Soham De, Samuel L Smith, and Karen Simonyan. High-performance large-scale image recognition without normalization. arXiv preprint arXiv:2102.06171, 2021.   
+[4] Tom B Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, et al. Language models are few-shot learners. arXiv preprint arXiv:2005.14165, 2020.   
+[5] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. End-to-end object detection with transformers. arXiv preprint arXiv:2005.12872, 2020.   
+[6] Chun-Fu Chen, Quanfu Fan, and Rameswar Panda. Crossvit: Cross-attention multi-scale vision transformer for image classification. arXiv preprint arXiv:2103.14899, 2021.   
+[7] Hanting Chen, Yunhe Wang, Tianyu Guo, Chang Xu, Yiping Deng, Zhenhua Liu, Siwei Ma, Chunjing Xu, Chao Xu, and Wen Gao. Pre-trained image processing transformer. arXiv preprint arXiv:2012.00364, 2020.   
+[8] Liang-Chieh Chen, Yukun Zhu, George Papandreou, Florian Schroff, and Hartwig Adam. Encoder-decoder with atrous separable convolution for semantic image segmentation. In Proceedings of the European conference on computer vision (ECCV), pages 801–818, 2018.   
+[9] Mark Chen, Alec Radford, Rewon Child, Jeffrey Wu, Heewoo Jun, David Luan, and Ilya Sutskever. Generative pretraining from pixels. In International Conference on Machine Learning, pages 1691–1703. PMLR, 2020.   
+[10] Ekin D Cubuk, Barret Zoph, Jonathon Shlens, and Quoc V Le. Randaugment: Practical automated data augmentation with a reduced search space. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, pages 702–703, 2020.   
+[11] Zhigang Dai, Bolun Cai, Yugeng Lin, and Junying Chen. Up-detr: Unsupervised pre-training for object detection with transformers. arXiv preprint arXiv:2011.09094, 2020.   
+[12] Stéphane d’Ascoli, Hugo Touvron, Matthew Leavitt, Ari Morcos, Giulio Biroli, and Levent Sagun. Convit: Improving vision transformers with soft convolutional inductive biases. arXiv preprint arXiv:2103.10697, 2021.   
+[13] Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scale hierarchical image database. In 2009 IEEE conference on computer vision and pattern recognition, pages 248–255. Ieee, 2009.   
+[14] Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. Bert: Pre-training of deep bidirectional transformers for language understanding. arXiv preprint arXiv:1810.04805, 2018.   
+[15] Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, et al. An image is worth 16x16 words: Transformers for image recognition at scale. arXiv preprint arXiv:2010.11929, 2020.   
+[16] Kai Han, An Xiao, Enhua Wu, Jianyuan Guo, Chunjing Xu, and Yunhe Wang. Transformer in transformer. arXiv preprint arXiv:2103.00112, 2021.   
+[17] Kaiming He, Georgia Gkioxari, Piotr Dollár, and Ross Girshick. Mask r-cnn. In Proceedings of the IEEE international conference on computer vision, pages 2961–2969, 2017.   
+[18] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 770–778, 2016.   
+[19] Tong He, Zhi Zhang, Hang Zhang, Zhongyue Zhang, Junyuan Xie, and Mu Li. Bag of tricks for image classification with convolutional neural networks. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 558–567, 2019.   
+[20] Byeongho Heo, Sangdoo Yun, Dongyoon Han, Sanghyuk Chun, Junsuk Choe, and Seong Joon Oh. Rethinking spatial dimensions of vision transformers. arXiv preprint arXiv:2103.16302, 2021.   
+[21] Geoffrey Hinton, Oriol Vinyals, and Jeff Dean. Distilling the knowledge in a neural network. arXiv preprint arXiv:1503.02531, 2015.   
+[22] Qibin Hou, Li Zhang, Ming-Ming Cheng, and Jiashi Feng. Strip pooling: Rethinking spatial pooling for scene parsing. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4003–4012, 2020.   
+[23] Gao Huang, Yu Sun, Zhuang Liu, Daniel Sedra, and Kilian Q Weinberger. Deep networks with stochastic depth. In European conference on computer vision, pages 646–661. Springer, 2016.   
+[24] Yinhan Liu, Myle Ott, Naman Goyal, Jingfei Du, Mandar Joshi, Danqi Chen, Omer Levy, Mike Lewis, Luke Zettlemoyer, and Veselin Stoyanov. Roberta: A robustly optimized bert pretraining approach. arXiv preprint arXiv:1907.11692, 2019.   
+[25] Ze Liu, Yutong Lin, Yue Cao, Han Hu, Yixuan Wei, Zheng Zhang, Stephen Lin, and Baining Guo. Swin transformer: Hierarchical vision transformer using shifted windows. arXiv preprint arXiv:2103.14030, 2021.   
+[26] Jonathan Long, Evan Shelhamer, and Trevor Darrell. Fully convolutional networks for semantic segmentation. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 3431–3440, 2015.   
+[27] Ilya Loshchilov and Frank Hutter. Decoupled weight decay regularization. arXiv preprint arXiv:1711.05101, 2017.   
+[28] Niki Parmar, Ashish Vaswani, Jakob Uszkoreit, Łukasz Kaiser, Noam Shazeer, Alexander Ku, and Dustin Tran. Image transformer. arXiv preprint arXiv:1802.05751, 2018.   
+[29] Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, et al. Pytorch: An imperative style, high-performance deep learning library. In Advances in neural information processing systems, pages 8026–8037, 2019.   
+[30] Ilija Radosavovic, Raj Prateek Kosaraju, Ross Girshick, Kaiming He, and Piotr Dollár. Designing network design spaces. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 10428–10436, 2020.   
+[31] Aravind Srinivas, Tsung-Yi Lin, Niki Parmar, Jonathon Shlens, Pieter Abbeel, and Ashish Vaswani. Bottleneck transformers for visual recognition. arXiv preprint arXiv:2101.11605, 2021.   
+[32] Nitish Srivastava, Geoffrey Hinton, Alex Krizhevsky, Ilya Sutskever, and Ruslan Salakhutdinov. Dropout: a simple way to prevent neural networks from overfitting. The journal of machine learning research, 15(1):1929–1958, 2014.   
+[33] Zhiqing Sun, Shengcao Cao, Yiming Yang, and Kris Kitani. Rethinking transformer-based set prediction for object detection. arXiv preprint arXiv:2011.10881, 2020.   
+[34] Mingxing Tan and Quoc V Le. Efficientnet: Rethinking model scaling for convolutional neural networks. arXiv preprint arXiv:1905.11946, 2019.   
+[35] Ilya Tolstikhin, Neil Houlsby, Alexander Kolesnikov, Lucas Beyer, Xiaohua Zhai, Thomas Unterthiner, Jessica Yung, Daniel Keysers, Jakob Uszkoreit, Mario Lucic, et al. Mlp-mixer: An all-mlp architecture for vision. arXiv preprint arXiv:2105.01601, 2021.   
+[36] Hugo Touvron, Matthieu Cord, Matthijs Douze, Francisco Massa, Alexandre Sablayrolles, and Hervé Jégou. Training data-efficient image transformers & distillation through attention. arXiv preprint arXiv:2012.12877, 2020.   
+[37] Hugo Touvron, Matthieu Cord, Alexandre Sablayrolles, Gabriel Synnaeve, and Hervé Jégou. Going deeper with image transformers. arXiv preprint arXiv:2103.17239, 2021.   
+[38] Hugo Touvron, Andrea Vedaldi, Matthijs Douze, and Hervé Jégou. Fixing the train-test resolution discrepancy. arXiv preprint arXiv:1906.06423, 2019.   
+[39] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin. Attention is all you need. Advances in neural information processing systems, 30:5998–6008, 2017.   
+[40] Wenhai Wang, Enze Xie, Xiang Li, Deng-Ping Fan, Kaitao Song, Ding Liang, Tong Lu, Ping Luo, and Ling Shao. Pyramid vision transformer: A versatile backbone for dense prediction without convolutions. arXiv preprint arXiv:2102.12122, 2021.   
+[41] Yuqing Wang, Zhaoliang Xu, Xinlong Wang, Chunhua Shen, Baoshan Cheng, Hao Shen, and Huaxia Xia. End-to-end video instance segmentation with transformers. arXiv preprint arXiv:2011.14503, 2020.   
+[42] Ross Wightman. Pytorch image models. https://github.com/rwightman/ pytorch-image-models, 2019.   
+[43] Haiping Wu, Bin Xiao, Noel Codella, Mengchen Liu, Xiyang Dai, Lu Yuan, and Lei Zhang. Cvt: Introducing convolutions to vision transformers. arXiv preprint arXiv:2103.15808, 2021.   
+[44] Tete Xiao, Yingcheng Liu, Bolei Zhou, Yuning Jiang, and Jian Sun. Unified perceptual parsing for scene understanding. In Proceedings of the European Conference on Computer Vision (ECCV), pages 418–434, 2018.   
+[45] Fuzhi Yang, Huan Yang, Jianlong Fu, Hongtao Lu, and Baining Guo. Learning texture transformer network for image super-resolution. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5791–5800, 2020.   
+[46] Li Yuan, Yunpeng Chen, Tao Wang, Weihao Yu, Yujun Shi, Francis EH Tay, Jiashi Feng, and Shuicheng Yan. Tokens-to-token vit: Training vision transformers from scratch on imagenet. arXiv preprint arXiv:2101.11986, 2021.   
+[47] Li Yuan, Francis EH Tay, Guilin Li, Tao Wang, and Jiashi Feng. Revisiting knowledge distillation via label smoothing regularization. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 3903–3911, 2020.   
+[48] Sangdoo Yun, Dongyoon Han, Seong Joon Oh, Sanghyuk Chun, Junsuk Choe, and Youngjoon Yoo. Cutmix: Regularization strategy to train strong classifiers with localizable features. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 6023–6032, 2019.   
+[49] Sangdoo Yun, Seong Joon Oh, Byeongho Heo, Dongyoon Han, Junsuk Choe, and Sanghyuk Chun. Re-labeling imagenet: from single to multi-labels, from global to localized labels. arXiv preprint arXiv:2101.05022, 2021.   
+[50] Yanhong Zeng, Jianlong Fu, and Hongyang Chao. Learning joint spatial-temporal transformations for video inpainting. In European Conference on Computer Vision, pages 528–543. Springer, 2020.   
+[51] Hang Zhang, Chongruo Wu, Zhongyue Zhang, Yi Zhu, Zhi Zhang, Haibin Lin, Yue Sun, Tong He, Jonas Muller, R. Manmatha, Mu Li, and Alexander Smola. Resnest: Split-attention networks. arXiv preprint arXiv:2004.08955, 2020.   
+[52] Hongyi Zhang, Moustapha Cisse, Yann N Dauphin, and David Lopez-Paz. mixup: Beyond empirical risk minimization. arXiv preprint arXiv:1710.09412, 2017.   
+[53] Hengshuang Zhao, Li Jiang, Jiaya Jia, Philip Torr, and Vladlen Koltun. Point transformer. arXiv preprint arXiv:2012.09164, 2020.   
+[54] Hengshuang Zhao, Jianping Shi, Xiaojuan Qi, Xiaogang Wang, and Jiaya Jia. Pyramid scene parsing network. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 2881–2890, 2017.   
+[55] Minghang Zheng, Peng Gao, Xiaogang Wang, Hongsheng Li, and Hao Dong. End-to-end object detection with adaptive clustering transformer. arXiv preprint arXiv:2011.09315, 2020.   
+[56] Sixiao Zheng, Jiachen Lu, Hengshuang Zhao, Xiatian Zhu, Zekun Luo, Yabiao Wang, Yanwei Fu, Jianfeng Feng, Tao Xiang, Philip HS Torr, et al. Rethinking semantic segmentation from a sequence-to-sequence perspective with transformers. arXiv preprint arXiv:2012.15840, 2020.   
+[57] Zhun Zhong, Liang Zheng, Guoliang Kang, Shaozi Li, and Yi Yang. Random erasing data augmentation. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 34, pages 13001–13008, 2020.   
+[58] Bolei Zhou, Hang Zhao, Xavier Puig, Tete Xiao, Sanja Fidler, Adela Barriuso, and Antonio Torralba. Semantic understanding of scenes through the ade20k dataset. International Journal of Computer Vision, 127(3):302–321, 2019.   
+[59] Daquan Zhou, Bingyi Kang, Xiaojie Jin, Linjie Yang, Xiaochen Lian, Qibin Hou, and Jiashi Feng. Deepvit: Towards deeper vision transformer. arXiv preprint arXiv:2103.11886, 2021.   
+[60] Luowei Zhou, Yingbo Zhou, Jason J Corso, Richard Socher, and Caiming Xiong. End-to-end dense video captioning with masked transformer. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 8739–8748, 2018.   
+[61] Xizhou Zhu, Weijie Su, Lewei Lu, Bin Li, Xiaogang Wang, and Jifeng Dai. Deformable detr: Deformable transformers for end-to-end object detection. arXiv preprint arXiv:2010.04159, 2020.

parse/train/2vubO341F_E/2vubO341F_E_content_list.json

@@ -0,0 +1,1035 @@
+[
+    {
+        "type": "text",
+        "text": "All Tokens Matter: Token Labeling for Training Better Vision Transformers ",
+        "text_level": 1,
+        "bbox": [
+            209,
+            122,
+            790,
+            172
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Zihang Jiang1∗ Qibin Hou2,1† Li Yuan3 Daquan Zhou1 Yujun Shi1 ",
+        "bbox": [
+            199,
+            219,
+            794,
+            237
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Xiaojie Jin4 Anran Wang4 Jiashi Feng4 ",
+        "bbox": [
+            264,
+            256,
+            733,
+            272
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1National University of Singapore 2Nankai University ",
+        "bbox": [
+            302,
+            292,
+            694,
+            308
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "3 Peking University 4ByteDance ",
+        "text_level": 1,
+        "bbox": [
+            379,
+            328,
+            619,
+            343
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "{jzh0103,andrewhoux,ylustcnus,zhoudaquan21,shiyujun1016}@gmail.com xjjin0731@gmail.com, anran.wang@bytedance.com, jshfeng@gmail.com ",
+        "bbox": [
+            209,
+            344,
+            789,
+            371
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract ",
+        "text_level": 1,
+        "bbox": [
+            462,
+            406,
+            535,
+            422
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we present token labeling—a new training objective for training high-performance vision transformers (ViTs). Different from the standard training objective of ViTs that computes the classification loss on an additional trainable class token, our proposed one takes advantage of all the image patch tokens to compute the training loss in a dense manner. Specifically, token labeling reformulates the image classification problem into multiple token-level recognition problems and assigns each patch token with an individual location-specific supervision generated by a machine annotator. Experiments show that token labeling can clearly and consistently improve the performance of various ViT models across a wide spectrum. For a vision transformer with 26M learnable parameters serving as an example, with token labeling, the model can achieve $8 4 . 4 \\%$ Top-1 accuracy on ImageNet. The result can be further increased to $8 6 . 4 \\%$ by slightly scaling the model size up to 150M, delivering the minimal-sized model among previous models $( 2 5 0 \\mathbf { M } + )$ reaching $86 \\%$ . We also show that token labeling can clearly improve the generalization capability of the pretrained models on downstream tasks with dense prediction, such as semantic segmentation. Our code and model are publicly available at https://github.com/zihangJiang/TokenLabeling. ",
+        "bbox": [
+            232,
+            438,
+            766,
+            674
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 Introduction ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            699,
+            310,
+            717
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Transformers [39] have achieved great performance for almost all the natural language processing (NLP) tasks over the past years [4, 14, 24]. Motivated by such success, recently, many researchers attempt to build transformer models for vision tasks, and their encouraging results have shown the great potential of transformer based models for image classification [6, 15, 25, 36, 40, 46], especially the strong benefits of the self-attention mechanism in building long-range dependencies between pairs of input tokens. ",
+        "bbox": [
+            174,
+            731,
+            825,
+            814
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Despite the importance of gathering long-range dependencies, recent work on local data augmentation [57] has demonstrated that well modeling and leveraging local information for image classification would avoid biasing the model towards skewed and non-generalizable patterns and substantially improve the model performance. However, recent vision transformers normally utilize class tokens that aggregate global information to predict the output class while neglecting the role of other patch tokens that encode rich information on their respective local image patches. ",
+        "bbox": [
+            176,
+            820,
+            825,
+            863
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/9c7bb663ccabca3baefdad385c72c84db533d97dbd497ac18638700c9e1d548b.jpg",
+        "image_caption": [
+            "Figure 1: Comparison between the proposed LV-ViT and other recent works based on vision transformers, including T2T-ViT [46], ConViT [12], BoTNet [31], DeepViT [59], DeiT [36], ViT [15], Swin Transformer [25], LambdaNet [1], CvT [43], CrossViT [6], PVT [40], CaiT [37]. Note that we only show models whose model sizes are under 100M. As can be seen, our LV-ViT achieves the best results using the least amount of learnable parameters. The default test resolution is $2 2 4 \\times 2 2 4$ unless specified after $@$ . "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            174,
+            87,
+            825,
+            265
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            174,
+            382,
+            825,
+            425
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we present a new training objective for vision transformers, termed token labeling, that takes advantage of both the patch tokens and the class tokens. Our method takes a $K$ -dimensional score map generated by a machine annotator as supervision to supervise all the tokens in a dense manner, where $K$ is the number of categories for the target dataset. In this way, each patch token is explicitly associated with an individual location-specific supervision indicating the existence of the target objects inside the corresponding image patch, so as to improve the object grounding and recognition capabilities of vision transformers with negligible computation overhead. To the best of our knowledge, this is the first work demonstrating that dense supervision is beneficial to vision transformers in image classification. ",
+        "bbox": [
+            174,
+            431,
+            825,
+            556
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "According to our experiments, utilizing the proposed token labeling objective can clearly boost the performance of vision transformers. As shown in Figure 1, our model, named LV-ViT, with 56M parameters, yields $8 5 . 4 \\%$ top-1 accuracy on ImageNet [13], behaving better than all the other transformer-based models having no more than 100M parameters. When the model size is scaled up to 150M, the result can be further improved to $8 6 . 4 \\%$ . In addition, we have empirically found that the pretrained models with token labeling are also beneficial to downstream tasks with dense prediction, such as semantic segmentation. ",
+        "bbox": [
+            174,
+            563,
+            825,
+            660
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 Related Work ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            679,
+            321,
+            696
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Transformers [39] refer to the models that entirely rely on the self-attention mechanism to build global dependencies, which are originally designed for natural language processing tasks. Due to their strong capability of capturing spatial information, transformers have also been successfully applied to a variety of vision problems, including low-level vision tasks like image enhancement [7, 45], as well as more challenging tasks such as image classification [9, 15], object detection [5, 11, 55, 61], segmentation [7, 33, 41] and image generation [28]. Some works also extend transformers for video and 3D point cloud processing [50, 53, 60]. ",
+        "bbox": [
+            174,
+            710,
+            825,
+            809
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Vision Transformer (ViT) is one of the earlier attempts that achieved state-of-the-art performance on ImageNet classification, using pure transformers as basic building blocks. However, ViTs need pretraining on very large datasets, such as ImageNet-22k and JFT-300M, and huge computation resources to achieve comparable performance to ResNet [18] with a similar model size trained on ImageNet. Later, DeiT [36] manages to tackle the data-inefficiency problem by simply adjusting the network architecture and adding an additional token along with the class token for Knowledge Distillation [21, 47] to improve model performance. ",
+        "bbox": [
+            174,
+            814,
+            825,
+            911
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/77890e011e8cc08c2d9f50310be754cb08f7894ee6cb766ac590a7580f42e616.jpg",
+        "image_caption": [
+            "Figure 2: Pipeline of training vision transformers with token labeling. Other than utilizing the class token (pink rectangle), we also take advantage of all the output patch tokens (orange rounded rectangle) by assigning each patch token an individual location-specific prediction generated by a machine annotator [3] as supervision (see the part in the red dash rectangle). Our proposed token labeling method can be treated as an auxiliary objective to provide each patch token the local details that aid vision transformers to more accurately locate and recognize the target objects. Note that the traditional vision transformer training does not include the red dash rectangle part. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            209,
+            89,
+            794,
+            318
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Some recent works [6, 16, 43, 46] also attempt to introduce the local dependency into vision transformers by modifying the patch embedding block or the transformer block or both, leading to significant performance gains. Moreover, there are also some works [20, 25, 40] adopting a pyramid structure to reduce the overall computation while maintaining the model’s ability to capture low-level features. ",
+        "bbox": [
+            174,
+            452,
+            825,
+            522
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Unlike most aforementioned works that design new transformer blocks or transformer architectures, we attempt to improve vision transformers by studying the role of patch tokens that embed rich local information inside image patches. We show that by slightly tuning the structure of vision transformers and employing the proposed token labeling objective, we can achieve strong baselines for transformer models at different model size levels. ",
+        "bbox": [
+            174,
+            529,
+            825,
+            598
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 Token Labeling Method ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            619,
+            406,
+            637
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this section, we first briefly review the structure of the vision transformer [15] and then describe the proposed training objective—token labeling. ",
+        "bbox": [
+            174,
+            652,
+            823,
+            681
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1 Revisiting Vision Transformer ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            699,
+            421,
+            714
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "A typical vision transformer [15] first decomposes a fixed-size input image into a sequence of small patches. Each small patch is mapped to a feature vector, or called a token, by projection with a linear layer. Then, all the tokens combined with an additional learnable class token for classification score prediction are sent into a stack of transformer blocks for feature encoding. ",
+        "bbox": [
+            173,
+            726,
+            825,
+            781
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In loss computing, the class token from the output tokens of the last transformer block is usually selected and sent into a linear layer for the classification score prediction. Mathematically, given an image $I$ , denote the output of the last transformer block as $[ \\bar { X } ^ { c l s } , X ^ { 1 } , . . . , X ^ { N } ]$ , where $N$ is the total number of patch tokens, and $X ^ { c l s }$ and $X ^ { 1 } , . . . , X ^ { N }$ correspond to the class token and the patch tokens, respectively. The classification loss for image $I$ can be written as ",
+        "bbox": [
+            174,
+            787,
+            823,
+            859
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/592dd559a9882895a0bc985fe4c80cb9b1f3f3afab9946d0fd9a87b3424793a9.jpg",
+        "text": "$$\nL _ { c l s } = H ( { X } ^ { c l s } , { y } ^ { c l s } ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            424,
+            868,
+            573,
+            887
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where $H ( \\cdot , \\cdot )$ is the softmax cross-entropy loss and $y ^ { c l s }$ is the class label. ",
+        "bbox": [
+            173,
+            896,
+            651,
+            912
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/c741b481df54f67e411d3cc1b30dc7deb904c80d9d11e57036dbf5b27cdbfb8f.jpg",
+        "image_caption": [
+            "Figure 3: Comparison between CutMix [48] (Left) and our proposed MixToken (Right). CutMix is operated on the input images. This results in patches containing mixed regions from the two images (see the patches enclosed by red bounding boxes). Differently, MixToken targets at mixing tokens after patch embedding. This enables each token after patch embedding to have clean content as shown in the right part of this figure. The detailed advantage of MixToken can be found in Sec. 4.2. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            197,
+            90,
+            490,
+            242
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2 Token Labeling ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            275,
+            321,
+            291
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The above classification problem only adopts an image-level label as supervision whereas it neglects the rich information embedded in each image patch. In this subsection, we present a new training objective—token labeling—that takes advantage of the complementary information between the patch tokens and the class tokens. ",
+        "bbox": [
+            174,
+            304,
+            825,
+            359
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Token Labeling: Different from the classification loss as formulated in Eqn. (1) that measures the distance between the single class token (representing the whole input image) and the corresponding image-level label, token labeling emphasizes the importance of all output tokens and advocates that each output token should be associated with an individual location-specific label. Therefore, in our method, the ground truth for an input image involves not only a single $K$ -dimensional vector $y ^ { c l s }$ but also a $K \\times N$ matrix or called a $K$ -dimensional score map as represented by $[ y ^ { 1 } , . . . , y ^ { N } ]$ , where $N$ is the number of the output patch tokens. ",
+        "bbox": [
+            173,
+            366,
+            825,
+            464
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Specifically, we leverage a dense score map for each training image and use the cross-entropy loss between each output patch token and the corresponding aligned label in the dense score map as an auxiliary loss at the training phase. Figure 2 provides an intuitive interpretation. Given the output patch tokens $X ^ { 1 } , . . . , X ^ { N }$ and the corresponding labels $[ y ^ { 1 } , . . . , y ^ { N } ]$ , the token labeling objective can be defined as ",
+        "bbox": [
+            174,
+            469,
+            825,
+            540
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/a9d480948e81c19661ff7ef1b5daada45648302552f0f35ccc9e1a4855e07862.jpg",
+        "text": "$$\nL _ { t l } = \\frac { 1 } { N } \\sum _ { i = 1 } ^ { N } H ( X ^ { i } , y ^ { i } ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            415,
+            546,
+            583,
+            590
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Recall that $H$ is the cross-entropy loss. Therefore, the total loss function can be written as ",
+        "bbox": [
+            171,
+            603,
+            764,
+            619
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/c5da8361fd2faf0126b83503cc2cc4f9798363630c4f410a80eef81deafa2915.jpg",
+        "text": "$$\n\\begin{array} { l } { { { \\cal L } _ { t o t a l } = H ( X ^ { c l s } , y ^ { c l s } ) + \\beta \\cdot L _ { t l } , } } \\\\ { { { } } } \\\\ { { = H ( X ^ { c l s } , y ^ { c l s } ) + \\beta \\cdot \\displaystyle \\frac { 1 } { N } \\sum _ { i = 1 } ^ { N } H ( X ^ { i } , y ^ { i } ) , } } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            338,
+            632,
+            658,
+            698
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $\\beta$ is a hyper-parameter to balance the two terms. In our experiment, we empirically set it to 0.5. ",
+        "bbox": [
+            174,
+            710,
+            825,
+            738
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Advantages: Our token labeling offers the following advantages. First of all, unlike knowledge distillation methods that require a teacher model to generate supervision labels online, token labeling is a cheap operation. The dense score map can be generated by a pretrained model in advance (e.g., EfficientNet [34] or NFNet [3]). During training, we only need to crop the score map and perform interpolation to make it aligned with the cropped image in the spatial coordinate. Thus, the additional computations are negligible. Second, rather than utilizing a single label vector as supervision as done in most classification models and the ReLabel strategy [49], we also harness score maps to supervise the models in a dense manner and thereby the label for each patch token provides location-specific information, which can aid the training models to easily discover the target objects and improve the recognition accuracy. Last but not the least, as dense supervision is adopted in training, we found that the pretrained models with token labeling benefit downstream tasks with dense prediction, like semantic segmentation. ",
+        "bbox": [
+            173,
+            744,
+            825,
+            911
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3 Token Labeling with MixToken ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            90,
+            431,
+            106
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "While training vision transformer, previous studies [36, 46] have shown that augmentation methods, like MixUp [52] and CutMix [48], can effectively boost the performance and robustness of the models. However, vision transformers rely on patch-based tokenization to map each input image to a sequence of tokens and our token labeling strategy also operates on patch-based token labels. If we apply CutMix directly on the raw image, some of the resulting patches may contain content from two images, leading to mixed regions within a small patch as shown in Figure 3. When performing token labeling, it is difficult to assign each output token a clean and correct label. Taking this situation into account, we rethink the CutMix augmentation method and present MixToken, which can be viewed as a modified version of CutMix operating on the tokens after patch embedding as illustrated in the right part of Figure 3. ",
+        "bbox": [
+            173,
+            117,
+            825,
+            257
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To be specific, for two images denoted as $I _ { 1 } , I _ { 2 }$ and their corresponding token labels $Y _ { 1 } = [ y _ { 1 } ^ { 1 } , . . . , y _ { 1 } ^ { N } ]$ as well as $Y _ { 2 } = [ y _ { 2 } ^ { 1 } , . . . , y _ { 2 } ^ { N } ]$ , we first feed the two images into the patch embedding module to tokenize each as a sequence of tokens, resulting in $T _ { 1 } = [ t _ { 1 } ^ { 1 } , . . . , t _ { 1 } ^ { N } ]$ and $\\bar { T _ { 2 } } = [ t _ { 2 } ^ { 1 } , . . . , t _ { 2 } ^ { N } ]$ . Then, we produce a new sequence of tokens by applying MixToken using a binary mask $M$ as follows: ",
+        "bbox": [
+            174,
+            262,
+            825,
+            319
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/cdf5e3aab4339f76c0c2c44221d0f16054703d72f085272d761449ddf6e388dc.jpg",
+        "text": "$$\n\\hat { T } = T _ { 1 } \\odot M + T _ { 2 } \\odot ( 1 - M ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            392,
+            329,
+            604,
+            349
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $\\odot$ is element-wise multiplication. We use the same way to generate the mask $M$ as in [48]. For the corresponding token labels, we also mix them using the same mask $M$ : ",
+        "bbox": [
+            173,
+            358,
+            823,
+            387
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/fa81133b791d6c30dfc1c80f85c7a073a5241a9fada2c61ef2a3b397042bb25e.jpg",
+        "text": "$$\n\\hat { Y } = Y _ { 1 } \\odot M + Y _ { 2 } \\odot ( 1 - M ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            392,
+            397,
+            606,
+            417
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The label for the class token can be written as ",
+        "bbox": [
+            176,
+            428,
+            473,
+            441
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/1bb8081440df26328f22eeb83ce87e3030fb4e4f726532138a58c694ac3a6d6a.jpg",
+        "text": "$$\ny ^ { \\hat { c } l s } = \\bar { M } y _ { 1 } ^ { c l s } + ( 1 - \\bar { M } ) y _ { 2 } ^ { c l s } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            397,
+            449,
+            599,
+            469
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $\\bar { M }$ is the average of all element values of $M$ . ",
+        "bbox": [
+            173,
+            479,
+            513,
+            494
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4 Experiments ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            517,
+            312,
+            535
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1 Experiment Setup ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            551,
+            339,
+            566
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We evaluate our method on the ImageNet [13] dataset. All experiments are built and conducted upon PyTorch [29] and the timm [42] library. We follow the standard training schedule and train our models on the ImageNet dataset for 300 epochs. Besides normal augmentations like CutOut [57] and RandAug [10], we also explore the effect of applying MixUp [52] and CutMix [48] together with our proposed token labeling. Empirically, we have found that using MixUp together with token labeling brings no benefit to the performance, and thus we do not apply it in our experiments. ",
+        "bbox": [
+            173,
+            578,
+            825,
+            662
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "For optimization, by default, we use the AdamW optimizer [27] with a linear learning rate scaling strategy $\\begin{array} { r } { l r = 1 0 ^ { - 3 } \\times \\frac { b a t c h \\_ s i z e } { 6 4 0 } } \\end{array}$ and $5 \\times 1 0 ^ { - 2 }$ weight decay rate. For Dropout regularization, we observe that for small models, using Dropout hurts the performance. This has also been observed in a few other works related to training vision transformers [36, 37, 46]. As a result, we do not apply Dropout [32] and use Stochastic Depth [23] instead. More details on hyper-parameters and finetuning can be found in our supplementary materials. ",
+        "bbox": [
+            174,
+            667,
+            825,
+            752
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We use the NFNet-F6 [3] trained on ImageNet with an $8 6 . 3 \\%$ Top-1 accuracy as the machine annotator to generate dense score maps for the ImageNet dataset, yielding a 1000-dimensional score map for each image for training. The score map generation procedure is similar to [49], but we limit our experiment setting by training all models from scratch on ImageNet without extra data support, such as JFT-300M and ImageNet-22K. This is different from the original ReLabel paper [49], in which the EfficientNet-L2 model pretrained on JFT-300M is used. The input resolution for NFNet-F6 is $5 7 6 \\times 5 7 6$ , and the dimension of the corresponding output score map for each image is $L \\in \\mathbb { R } ^ { 1 8 \\times 1 8 \\times 1 0 0 0 }$ . During training, the target labels for the tokens are generated by applying RoIAlign [17] on the corresponding score map. In practice, we only store the top-5 score maps for each position in half-precision to save space as storing the entire score maps for all the images results in 2TB storage. In our experiment, we only need 10GB of storage to store all the score maps. ",
+        "bbox": [
+            173,
+            758,
+            825,
+            911
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/8ab634b915f17e8f746292568270ed165dd5bacd94d1fed7927449e1328c4232.jpg",
+        "table_caption": [
+            "Table 1: Performance of the proposed LV-ViT with different model sizes. Here, ‘depth’ denotes the number of transformer blocks used in different models. By default, the test resolution is set to $2 2 4 \\times 2 2 4$ except the last one which is $2 8 8 \\times 2 8 8$ . "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Name</td><td>Depth</td><td>Embed dim.</td><td>MLP Ratio</td><td>#Heads</td><td>#Params</td><td>Throughput (im/s)</td><td>Test size</td><td>Top-1 Acc. (%)</td></tr><tr><td>LV-ViT-T</td><td>12</td><td>240</td><td>3.0</td><td>4</td><td>8.5M</td><td>2032.6</td><td>224</td><td>79.1</td></tr><tr><td>LV-ViT-S</td><td>16</td><td>384</td><td>3.0</td><td>6</td><td>26M</td><td>1018.2</td><td>224</td><td>83.3</td></tr><tr><td>LV-ViT-M</td><td>20</td><td>512</td><td>3.0</td><td>8</td><td>56M</td><td>668.9</td><td>224</td><td>84.1</td></tr><tr><td>LV-ViT-L</td><td>24</td><td>768</td><td>3.0</td><td>12</td><td>150M</td><td>204.8</td><td>288</td><td>85.3</td></tr></table>",
+        "bbox": [
+            173,
+            138,
+            825,
+            220
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2 Ablation Analysis ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            244,
+            336,
+            260
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Model Settings: The default settings of the proposed LV-ViT are given in Table 1, where both token labeling and MixToken are used. A slight architecture modification to ViT [15] is that we replace the patch embedding module with a 4-layer convolution to better tokenize the input image and integrate local information. Detailed ablation about patch embedding can be found in our supplementary materials. As can be seen, our LV-ViT-T with only $8 . 5 { \\bf M }$ parameters can already achieve a top-1 accuracy of $7 9 . 1 \\%$ on ImageNet. Increasing the embedding dimension and network depth can further boost the performance. More experiments compared to other methods can be found in Sec. 4.3. In the following ablation experiments, we will set our LV-ViT-S as baseline and show the advantages of the proposed token labeling and MixToken methods. ",
+        "bbox": [
+            173,
+            270,
+            825,
+            395
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "MixToken: We use MixToken as a substitution for CutMix while applying token labeling. Our experiments show that MixToken performs better than CutMix for token-based transformer models. As shown in Table 2, when training with the original ImageNet labels, using MixToken is $0 . 1 \\%$ higher than using CutMix. When using the ReLabel supervision, we can also see an advantage of $0 . { \\bar { 2 } } \\%$ over the CutMix baseline. Combining with our token labeling, the performance can be further raised to $8 3 . 3 \\%$ . ",
+        "bbox": [
+            173,
+            401,
+            825,
+            484
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/ecc151313b3142fbf655b4065fd6e4b0c147ea2803b47139c3e90b472d0b2137.jpg",
+        "table_caption": [
+            "Table 2: Ablation on the proposed MixToken and token labeling augmentations. We also show results with either the ImageNet hard label and the ReLabel [49] as supervision. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Aug. Method</td><td>Supervision</td><td>Top-1 Acc.</td></tr><tr><td>MixToken</td><td>Token labeling</td><td>83.3</td></tr><tr><td>MixToken</td><td>ReLabel</td><td>83.0</td></tr><tr><td>CutMix</td><td>ReLabel</td><td>82.8</td></tr><tr><td>Mixtoken</td><td>ImageNet Label</td><td>82.5</td></tr><tr><td>CutMix</td><td>ImageNet Label</td><td>82.4</td></tr></table>",
+        "bbox": [
+            173,
+            560,
+            472,
+            654
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/51895f2ce4fa7182e488e57176934e6ab370cc3160e81c0730e961fdd370158d.jpg",
+        "table_caption": [
+            "Table 3: Ablation on different widely-used data augmentations. We have empirically found our proposed MixToken performs even better than the combination of MixUp and CutMix in vision transformers. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>MixToken</td><td>MixUp</td><td>CutOut</td><td>RandAug</td><td>Top-1 Acc.</td></tr><tr><td></td><td></td><td></td><td></td><td>83.3</td></tr><tr><td></td><td></td><td></td><td></td><td>81.3</td></tr><tr><td>&gt;x&gt;</td><td>xx&gt;</td><td>&gt;&gt;&gt;</td><td>&gt;&gt;&gt;</td><td>83.1</td></tr><tr><td></td><td>X</td><td></td><td>√</td><td>83.0</td></tr><tr><td>广</td><td>X</td><td>X</td><td>X</td><td>82.8</td></tr></table>",
+        "bbox": [
+            483,
+            559,
+            825,
+            654
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Data Augmentation: Here, we study the compatibility of MixToken with other augmentation techniques, such as MixUp [52], CutOut [57] and RandAug [10]. The ablation results are shown in Table 3. We can see when all the four augmentation methods are used, a top-1 accuracy of $8 3 . 1 \\%$ is achieved. Interestingly, when the MixUp augmentation is removed, the performance can be improved to $8 3 . 3 \\%$ . This may be explained as, using MixToken and MixUp at the same time would bring too much noise in the label, and consequently cause confusion of the model. Moreover, the CutOut augmentation, which randomly erases some parts of the image, is also effective and removing it brings a performance drop of $\\dot { 0 } . 3 \\%$ . Similarly, the RandAug augmentation also contributes to the performance and using it brings an improvement of $0 . 5 \\%$ . ",
+        "bbox": [
+            173,
+            669,
+            825,
+            795
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "All Tokens Matter: To show the importance of involving all tokens in our token labeling method, we attempt to randomly drop some tokens and use the remaining ones for computing the token labeling loss. The percentage of the remaining tokens is denoted as Token Participation Rate. As shown in Figure 4 (Left), we conduct experiments on two models: LV-ViT-S and LV-ViT-M. As can be seen, using only $2 0 \\%$ of the tokens to compute the token labeling loss decreases the performance $( - 0 . 5 \\%$ for LV-ViT-S and $- 0 . 4 \\%$ for LV-ViT-M). Involving more tokens for loss computation consistently leads to better performance. Since involving all tokens brings negligible computation cost and gives the best performance, we always set the token participation rate as $\\mathrm { \\bar { 1 0 0 \\% } }$ in the following experiments. ",
+        "bbox": [
+            173,
+            800,
+            825,
+            911
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/810578c2e36580b46aa98e4ec01030b20f6e00994c33dafcaa4cde435beb4d46.jpg",
+        "image_caption": [
+            "Figure 4: Left: LV-ViT ImageNet Top-1 Accuracy w.r.t. the token participation rate while applying token labeling. Token participation rate indicates the percentage of patch tokens involved in computing the token labeling loss. This experiment reflects that all tokens matter for vision transformers. Right: LV-ViT-S ImageNet Top-1 Accuracy w.r.t. different annotator models. The point size indicates the parameter number of the annotator model. Clearly, our token labeling objective is robust to different annotator models. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            178,
+            103,
+            790,
+            275
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/ae9fdf37e5d602133531450f1b69751afa30b0104c5bff5b6433f7a76be69066.jpg",
+        "table_caption": [
+            "Table 4: Comparison of token labeling (TL), knowledge distillation (KD) based method and ReLabel method based on utilized tokens, DeiT-S/LV-ViT-S Top-1 accuracy on ImageNet validation set and training time on a single V100 GPU node. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Online KD</td><td>Online TL</td><td>TL</td><td>ReLabel</td><td>Vanilla</td></tr><tr><td>Tokens Utilized</td><td>2</td><td>All</td><td>All</td><td>1</td><td>1</td></tr><tr><td>DeiT-S Acc. (%)</td><td>81.2</td><td>81.8</td><td>81.0</td><td>80.4</td><td>79.9</td></tr><tr><td>LV-ViT-S Acc. (%)</td><td>83.0</td><td>83.5</td><td>83.3</td><td>82.8</td><td>82.4</td></tr><tr><td>Training Time (8× V100)</td><td>63 hrs</td><td>63 hrs</td><td>45 hrs</td><td>45 hrs</td><td>41 hrs</td></tr></table>",
+        "bbox": [
+            209,
+            431,
+            789,
+            518
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Online Token Labeling: Unlike the online knowledge distillation method which generates labels by a teacher model online, our token labeling approach utilizes the dense label map generated in advance and directly applies the corresponding augmentation methods, such as random crop, on the label map to obtain token-level labels. To directly compare with the online knowledge distillation based method and validate the effectiveness of token-level supervision, we further conduct experiments on the online version of our token labeling method, which generates token-level labels online during training. Following DeiT [36], we use RegNetY-16GF [30] as the online teacher model. Results in terms of DeiT-S/LV-ViT-S Top-1 accuracy and training time for our token labeling, online knowledge distillation, and ReLabel [49] are listed in Table 4, with number of utilized tokens also included for clear comparison. As can be seen, for both online and offline cases, using token-level supervision can improve the overall performance with only negligible additional training cost. Meanwhile, compared to the vanilla training baseline, our proposed offline token labeling brings almost no additional training cost, and boosts the overall performance of LV-ViT-S by $0 . 9 \\%$ , which well demonstrates its efficiency and effectiveness. ",
+        "bbox": [
+            173,
+            545,
+            825,
+            738
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Robustness to Different Annotators: To evaluate the robustness of our token labeling method, we use different pretrained CNNs, including EfficientNet-B3,B4,B5,B6,B7,B8 [34], NFNet-F6 [3] and ResNest269E [51], as annotator models to provide dense supervision. Results are shown in the right part of Figure 4. We can see that, even if we use an annotator with relatively lower performance, such as EfficientNet-B3 whose Top-1 accuracy is $8 1 . 6 \\%$ , it can still provide multi-label location-specific supervision and help improve the performance of our LV-ViT-S model. Meanwhile, annotator models with better performance can provide more accurate supervision, bringing even better performance, as stronger annotator models can generate better token-level labels. The largest annotator NFNet-F6 [3], which has the best performance of $8 6 . 3 \\%$ , allows us to achieve the best result for LV-ViT-S, which is $8 3 . 3 \\%$ . In addition, we also attempt to use a better model, EfficientNet-L2 pretrained on JFT-300M as described in [49] which has $8 8 . 2 \\%$ Top-1 ImageNet accuracy, as our annotator. The performance of LV-ViT-S can be further improved to $8 \\mathrm { { 3 . 5 \\% } }$ . However, to fairly compare with the models without extra training data, we only report results based on dense supervision produced by NFNet-F6 [3] that uses only ImageNet training data. ",
+        "bbox": [
+            174,
+            746,
+            825,
+            911
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            174,
+            92,
+            825,
+            119
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/a3d559defddf629a8a69e1ea7f71228daa68e20f028756c9b3671f019cf5ad40.jpg",
+        "image_caption": [
+            "Figure 5: Performance of the proposed token labeling objective on three different vision transformers: DeiT [36] (Left), T2T-ViT [46] (Middle), and LV-ViT (Right). Our method has a consistent improvement on all 7 different ViT models. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            179,
+            143,
+            825,
+            260
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Robustness to Different ViT Variants: To further evaluate the robustness of our token labeling, we train different transformer-based networks, including DeiT [36], T2T-ViT [3] and our model LV-ViT, with the proposed training objective. Results are shown in Figure 5. It can be found that, all the models trained with token labeling consistently outperform their vanilla counterparts, demonstrating the robustness of token labeling with respect to different variants of patch-based vision transformers. Meanwhile, for different scales of the models, the improvement is also consistent. Interestingly, we observe larger improvements for larger models. These indicate that our proposed token labeling method is widely applicable to a large range of patch-based vision transformer variants. ",
+        "bbox": [
+            173,
+            337,
+            825,
+            449
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Beyond Vision Transformers: We further explore the performance of token labeling on other CNN-based and MLP-based models. Results are shown in Table 5. Besides our re-implementation with more data augmentation and regularization techniques, we also provide the results from the original papers. It can be found that for both MLP-based and CNN-based models, our token labeling objective can also improve the performance over strong baselines by providing location-specific dense supervision. ",
+        "bbox": [
+            173,
+            454,
+            825,
+            537
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/163ebee6ecc8c4b165c6f3e5a941947668dd1d76a42075b0fcd4b5d7c14a71c5.jpg",
+        "table_caption": [
+            "Table 5: Performance of the proposed token labeling objective on representative CNN-based (ResNeSt) and MLP-based (Mixer-MLP) models. Our method has a consistent improvement on all different models. Here † indicates results reported in original papers. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td colspan=\"3\">Mixer-S/16 [35]</td><td colspan=\"3\">Mixer-B/16 [35]</td><td colspan=\"3\">Mixer-L/16 [35]</td><td colspan=\"3\">ResNeSt-50 [51]</td></tr><tr><td>Token Labeling</td><td>X</td><td>X</td><td>√</td><td>×</td><td>X</td><td>√</td><td>×</td><td>×</td><td>√</td><td>×</td><td>×</td><td>√</td></tr><tr><td>Parameters</td><td>18M</td><td>18M18M</td><td></td><td>59M</td><td>59M 59M</td><td></td><td>207M</td><td></td><td>207M207M</td><td>27M</td><td></td><td>27M 27M</td></tr><tr><td>Top-1 Acc. (%)</td><td>73.8t</td><td>75.6</td><td>76.1</td><td>76.4</td><td>78.3</td><td>79.5</td><td>71.6t</td><td>77.7</td><td>80.1</td><td>81.1t</td><td>80.9</td><td>81.5</td></tr></table>",
+        "bbox": [
+            181,
+            613,
+            815,
+            688
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.3 Comparison to Other Methods ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            742,
+            426,
+            757
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We compare our proposed model LV-ViT with other state-of-the-art methods in Table 6. For smallsized models, when the test resolution is set to $2 2 4 \\times 2 2 4$ , we achieve an $8 3 . 3 \\%$ accuracy on ImageNet with only 26M parameters, which is $3 . 4 \\%$ higher than the strong baseline DeiT-S [36]. For mediumsized models, when the test resolution is set to $3 8 4 \\times 3 8 4$ we achieve the performance of $8 5 . 4 \\%$ , the same as CaiT-S36 [37], but with much less computational cost and parameters. Note that both DeiT and CaiT use knowledge distillation to improve their models, which introduce much more computations in training. However, we do not require any extra computations in training and only have to compute and store the dense score maps in advance. For large-sized models, our LV-ViT-L with a test resolution of $4 4 8 \\times 4 4 8$ achieves an $8 6 . 2 \\%$ top-1 accuracy, which is comparable to CaiT-M36 [37] but with far fewer FLOPs and parameters. ",
+        "bbox": [
+            173,
+            772,
+            826,
+            911
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/1ffe2c2d40127fa5107472db1c5e025901208024a3c26b0c26ca4a1ac6751875.jpg",
+        "table_caption": [
+            "Table 6: Top-1 accuracy comparison with other methods on ImageNet [13] and ImageNet Real [2]. All models are trained without external data. With the same computation and parameter constraint, our model consistently outperforms other CNN-based and transformer-based counterparts. The results of CNNs and ViT are referenced from [37]. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Network</td><td>Params</td><td>FLOPs</td><td>Train size</td><td>Test size</td><td>Top-1(%)</td><td>Real Top-1 (%)</td></tr><tr><td>EfficientNet-B5 [34] SNNO</td><td>30M</td><td>9.9B</td><td>456</td><td>456</td><td>83.6</td><td>88.3</td></tr><tr><td>EfficientNet-B7 [34]</td><td>66M</td><td>37.0B</td><td>600</td><td>600</td><td>84.3</td><td></td></tr><tr><td>Fix-EfficientNet-B8 [34,38]</td><td>87M</td><td>89.5B</td><td>672</td><td>800</td><td>85.7</td><td>90.0</td></tr><tr><td>NFNet-F3 [3]</td><td>255M</td><td>114.8B</td><td>320</td><td>416</td><td>85.7</td><td>89.4</td></tr><tr><td>NFNet-F4 [3]</td><td>316M</td><td>215.3B</td><td>384</td><td>512</td><td>85.9</td><td>89.4</td></tr><tr><td>NFNet-F5[3]</td><td>377M</td><td>289.8B</td><td>416</td><td>544</td><td>86.0</td><td>89.2</td></tr><tr><td>ViT-B/16 [15]</td><td>86M</td><td>55.4B</td><td>224</td><td>384</td><td>77.9</td><td>83.6</td></tr><tr><td>ViT-L/16[15]</td><td>307M</td><td>190.7B</td><td>224</td><td>384</td><td>76.5</td><td>82.2</td></tr><tr><td>T2T-ViT-14 [46]</td><td>22M</td><td>5.2B</td><td>224</td><td>224</td><td>81.5</td><td></td></tr><tr><td>T2T-ViT-14↑384 [46]</td><td>22M</td><td>17.1B</td><td>224</td><td>384</td><td>83.3</td><td>1</td></tr><tr><td>Cross ViT [6]</td><td>45M</td><td>56.6B</td><td>224</td><td>480</td><td>84.1</td><td>一</td></tr><tr><td>Swin-B[25]</td><td>88M</td><td>47.0B</td><td>224</td><td>384</td><td>84.2</td><td></td></tr><tr><td>TNT-B[16]</td><td>66M</td><td>14.1B</td><td>224</td><td>224</td><td>82.8</td><td></td></tr><tr><td>iriirrrrrs DeepViT-S [59]</td><td>27M</td><td>6.2B</td><td>224</td><td>224</td><td>82.3</td><td></td></tr><tr><td>DeepViT-L [59]</td><td>55M</td><td>12.5B</td><td>224</td><td>224</td><td>83.1</td><td></td></tr><tr><td>DeiT-S[36]</td><td>22M</td><td>4.6B</td><td>224</td><td>224</td><td>79.9</td><td>85.7</td></tr><tr><td>Distilled DeiT-S [36]</td><td>22M</td><td>4.6B</td><td>224</td><td>224</td><td>81.2</td><td>86.8</td></tr><tr><td>DeiT-B [36]</td><td>86M</td><td>17.5B</td><td>224</td><td>224</td><td>81.8</td><td>86.7</td></tr><tr><td>DeiT-B↑384 [36]</td><td>86M</td><td>55.4B</td><td>224</td><td>384</td><td>83.1</td><td>87.7</td></tr><tr><td>Distilled DeiT-B [36]</td><td>87M</td><td>17.5B</td><td>224</td><td>224</td><td>83.4</td><td>88.3</td></tr><tr><td>BoTNet-S1-128 [31]</td><td>79.1M</td><td>19.3B</td><td>256</td><td>256</td><td>84.2</td><td></td></tr><tr><td>BoTNet-S1-128↑384 [31]</td><td>79.1M</td><td>45.8B</td><td>256</td><td>384</td><td>84.7</td><td>-</td></tr><tr><td>CaiT-S36↑384 [37]</td><td>68M</td><td>48.0B</td><td>224</td><td>384</td><td>85.4</td><td>- 89.8</td></tr><tr><td>CaiT-M36[37]</td><td>271M</td><td>53.7B</td><td>224</td><td>224</td><td>85.1</td><td>89.3</td></tr><tr><td>CaiT-M36↑448 [37]</td><td>271M</td><td>247.8B</td><td>224</td><td>448</td><td>86.3</td><td>90.2</td></tr><tr><td>LV-ViT-S</td><td>26M</td><td>6.6B</td><td>224</td><td>224</td><td>83.3</td><td></td></tr><tr><td>江 LV-ViT-S↑384</td><td>26M</td><td>22.2B</td><td>224</td><td>384</td><td>84.4</td><td>88.1 88.9</td></tr><tr><td>LV-ViT-M</td><td>56M</td><td>16.0B</td><td>224</td><td>224</td><td>84.1</td><td>88.4</td></tr><tr><td>W LV-ViT-M↑384</td><td>56M</td><td>42.2B</td><td>224</td><td>384</td><td>85.4</td><td>89.5</td></tr><tr><td>LV-ViT-L</td><td>150M</td><td>59.0B</td><td>288</td><td>288</td><td>85.3</td><td>89.3</td></tr><tr><td>0 LV-ViT-L↑448</td><td>150M</td><td>157.2B</td><td>288</td><td>448</td><td>85.9</td><td>89.7</td></tr><tr><td>LV-ViT-L↑448</td><td>150M</td><td>157.2B</td><td>448</td><td>448</td><td>86.2</td><td>89.9</td></tr><tr><td>LV-ViT-L↑512</td><td>151M</td><td>214.8B</td><td>448</td><td>512</td><td>86.4</td><td>90.1</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></table>",
+        "bbox": [
+            174,
+            150,
+            825,
+            604
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "4.4 Semantic Segmentation on ADE20K ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            635,
+            464,
+            650
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "It has been shown in [19] that different training techniques for pretrained models have different impacts on downstream tasks with dense prediction, like semantic segmentation. To demonstrate the advantage of the proposed token labeling objective on tasks with dense prediction, we apply our pretrained LV-ViT with token labeling to the semantic segmentation task. ",
+        "bbox": [
+            174,
+            662,
+            825,
+            718
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Similar to previous work [25], we run experiments on the widely-used ADE20K [58] dataset. ADE20K contains 25K images in total, including 20K images for training, 2K images for validation and 3K images for test, and covering 150 different foreground categories. We take both FCN [26] and UperNet [44] as our segmentation frameworks and use the mmseg toolbox to implement. During training, following [25], we use the AdamW optimizer with an initial learning rate of 6e-5 and a weight decay of 0.01. We also use a linear learning schedule with a minimum learning rate of 5e-6. All models are trained on 8 GPUs and with a batch size of 16 (i.e., 2 images on each GPU). The input resolution is set to $5 1 2 \\times 5 1 2$ . In inference, a multi-scale test with interpolation rates of [0.75, 1.0, 1.25, 1.5, 1.75] is used. As suggested by [58], we report results in terms of both mean intersection-over-union (mIoU) and the average pixel accuracy (Pixel Acc.). ",
+        "bbox": [
+            174,
+            724,
+            825,
+            863
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In Table 7, we test the performance of token labeling on both FCN and UperNet frameworks. The FCN framework has a light convolutional head and can directly reflect the performance of the pretrained models in terms of transferable capability. As can be seen, pretrained models with token labeling perform better than those without token labeling. This indicates token labeling is indeed beneficial to semantic segmentation. ",
+        "bbox": [
+            176,
+            869,
+            825,
+            911
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/70c1d4e41ceddea09bd2be3af5115392c9cbb1586a4c7cf96581f2f713f425f0.jpg",
+        "table_caption": [
+            "Table 7: Transfer performance of the proposed LV-ViT in semantic segmentation. We take two classic methods, FCN and UperNet, as segmentation architectures and show both single-scale (SS) and multi-scale (MS) results on the validation set. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Token Labeling</td><td>Model Size</td><td>mIoU (SS)</td><td>P. Acc. (SS)</td><td>mIoU (MS)</td><td>P. Acc. (MS)</td></tr><tr><td>LV-ViT-S + FCN</td><td>×</td><td>30M</td><td>46.1</td><td>81.9</td><td>47.3</td><td>82.6</td></tr><tr><td>LV-ViT-S + FCN</td><td></td><td>30M</td><td>47.2</td><td>82.4</td><td>48.4</td><td>83.0</td></tr><tr><td>LV-ViT-S + UperNet</td><td></td><td>44M</td><td>46.5</td><td>82.1</td><td>47.6</td><td>82.7</td></tr><tr><td>LV-ViT-S + UperNet</td><td>X</td><td>44M</td><td>47.9</td><td>82.6</td><td>48.6</td><td>83.1</td></tr></table>",
+        "bbox": [
+            178,
+            138,
+            820,
+            228
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            174,
+            256,
+            821,
+            284
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "We also compare our segmentation results with previous state-of-the-art segmentation methods in Table 8. Without pretraining on large-scale datasets such as ImageNet-22K, our LV-ViT-M with the UperNet segmentation architecture achieves an mIoU score of 50.6 with only 77M parameters. This result is much better than the previous CNN-based and transformer-based models. Furthermore, using our LV-ViT-L as the pretrained model yields a better result of 51.8 in terms of mIoU. As far as we know, this is the best result reported on ADE20K with no pretraining on ImageNet-22K or other large-scale datasets. ",
+        "bbox": [
+            173,
+            290,
+            825,
+            387
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "table",
+        "img_path": "images/7675f5b12a93d9e094cea27ffe903eaa1865bea2f706e0842c5d4c04af07ac46.jpg",
+        "table_caption": [
+            "Table 8: Comparison with previous work on ADE20K validation set. As far as we know, our LVViT-L $^ +$ UperNet achieves the best result on ADE20K with only ImageNet-1K as training data in pretraining. †Pretrained on ImageNet-22K. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Backbone</td><td>Segmentation Architecture</td><td>Model Size</td><td>mIoU (MS)</td><td>Pixel Acc. (MS)</td></tr><tr><td rowspan=\"5\">SNNO</td><td>ResNet-269</td><td>PSPNet [54]</td><td></td><td>44.9</td><td>81.7</td></tr><tr><td>ResNet-101</td><td>UperNet [44]</td><td>86M</td><td>44.9</td><td>-</td></tr><tr><td>ResNet-101</td><td>Strip Pooling [22]</td><td></td><td>45.6</td><td>82.1</td></tr><tr><td>ResNeSt200</td><td>DeepLabV3+ [8]</td><td>88M</td><td>48.4</td><td>1</td></tr><tr><td>DeiT-S</td><td>UperNet</td><td>52M</td><td>44.0</td><td>-</td></tr><tr><td rowspan=\"5\">Tirriiirrss</td><td>ViT-Larget</td><td>SETR [56]</td><td>308M</td><td>50.3</td><td>83.5</td></tr><tr><td>Swin-T[25]</td><td>UperNet</td><td>60M</td><td>46.1</td><td>1</td></tr><tr><td>Swin-S [25]</td><td>UperNet</td><td>81M</td><td>49.3</td><td>=</td></tr><tr><td>Swin-B [25]</td><td>UperNet</td><td>121M</td><td>49.7</td><td></td></tr><tr><td>Swin-B† [25]</td><td>UperNet</td><td>121M</td><td>51.6</td><td>-</td></tr><tr><td rowspan=\"4\">LIA-AT</td><td>LV-ViT-S</td><td>FCN</td><td>30M</td><td>48.4</td><td>83.0</td></tr><tr><td>LV-ViT-S</td><td>UperNet</td><td>44M</td><td>48.6</td><td>83.1</td></tr><tr><td>LV-ViT-M</td><td>UperNet</td><td>77M</td><td>50.6</td><td>83.5</td></tr><tr><td>LV-ViT-L</td><td>UperNet</td><td>209M</td><td>51.8</td><td>84.1</td></tr></table>",
+        "bbox": [
+            173,
+            454,
+            825,
+            676
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "5 Conclusions and Discussion ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            708,
+            436,
+            727
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we introduce a new token labeling method to help improve the performance of vision transformers. We also analyze the effectiveness and robustness of our token labeling with respect to different annotators and different variants of patch-based vision transformers. By applying token labeling, our proposed LV-ViT achieves $8 4 . 4 \\%$ Top-1 accuracy with only 26M parameters and $8 6 . 4 \\%$ Top-1 accuracy with 150M parameters on ImageNet-1K benchmark. ",
+        "bbox": [
+            174,
+            741,
+            825,
+            811
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Despite the effectiveness, token labeling has a limitation of requiring a pretrained model as the machine annotator. Fortunately, the machine annotating procedure can be done in advance to avoid introducing extra computational cost in training. This makes our method quite different from knowledge distillation methods that rely on online teaching. For users with limited machine resources on hand, our token labeling provides a promising training technique to improve the performance of vision transformers. ",
+        "bbox": [
+            174,
+            818,
+            825,
+            901
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "References   \n[1] Irwan Bello. Lambdanetworks: Modeling long-range interactions without attention. arXiv preprint arXiv:2102.08602, 2021.   \n[2] Lucas Beyer, Olivier J Hénaff, Alexander Kolesnikov, Xiaohua Zhai, and Aäron van den Oord. Are we done with imagenet? arXiv preprint arXiv:2006.07159, 2020.   \n[3] Andrew Brock, Soham De, Samuel L Smith, and Karen Simonyan. High-performance large-scale image recognition without normalization. arXiv preprint arXiv:2102.06171, 2021.   \n[4] Tom B Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, et al. Language models are few-shot learners. arXiv preprint arXiv:2005.14165, 2020.   \n[5] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. End-to-end object detection with transformers. arXiv preprint arXiv:2005.12872, 2020.   \n[6] Chun-Fu Chen, Quanfu Fan, and Rameswar Panda. Crossvit: Cross-attention multi-scale vision transformer for image classification. arXiv preprint arXiv:2103.14899, 2021.   \n[7] Hanting Chen, Yunhe Wang, Tianyu Guo, Chang Xu, Yiping Deng, Zhenhua Liu, Siwei Ma, Chunjing Xu, Chao Xu, and Wen Gao. Pre-trained image processing transformer. arXiv preprint arXiv:2012.00364, 2020.   \n[8] Liang-Chieh Chen, Yukun Zhu, George Papandreou, Florian Schroff, and Hartwig Adam. Encoder-decoder with atrous separable convolution for semantic image segmentation. In Proceedings of the European conference on computer vision (ECCV), pages 801–818, 2018.   \n[9] Mark Chen, Alec Radford, Rewon Child, Jeffrey Wu, Heewoo Jun, David Luan, and Ilya Sutskever. Generative pretraining from pixels. In International Conference on Machine Learning, pages 1691–1703. PMLR, 2020.   \n[10] Ekin D Cubuk, Barret Zoph, Jonathon Shlens, and Quoc V Le. Randaugment: Practical automated data augmentation with a reduced search space. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, pages 702–703, 2020.   \n[11] Zhigang Dai, Bolun Cai, Yugeng Lin, and Junying Chen. Up-detr: Unsupervised pre-training for object detection with transformers. arXiv preprint arXiv:2011.09094, 2020.   \n[12] Stéphane d’Ascoli, Hugo Touvron, Matthew Leavitt, Ari Morcos, Giulio Biroli, and Levent Sagun. Convit: Improving vision transformers with soft convolutional inductive biases. arXiv preprint arXiv:2103.10697, 2021.   \n[13] Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scale hierarchical image database. In 2009 IEEE conference on computer vision and pattern recognition, pages 248–255. Ieee, 2009.   \n[14] Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. Bert: Pre-training of deep bidirectional transformers for language understanding. arXiv preprint arXiv:1810.04805, 2018.   \n[15] Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, et al. An image is worth 16x16 words: Transformers for image recognition at scale. arXiv preprint arXiv:2010.11929, 2020.   \n[16] Kai Han, An Xiao, Enhua Wu, Jianyuan Guo, Chunjing Xu, and Yunhe Wang. Transformer in transformer. arXiv preprint arXiv:2103.00112, 2021.   \n[17] Kaiming He, Georgia Gkioxari, Piotr Dollár, and Ross Girshick. Mask r-cnn. In Proceedings of the IEEE international conference on computer vision, pages 2961–2969, 2017.   \n[18] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 770–778, 2016.   \n[19] Tong He, Zhi Zhang, Hang Zhang, Zhongyue Zhang, Junyuan Xie, and Mu Li. Bag of tricks for image classification with convolutional neural networks. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 558–567, 2019.   \n[20] Byeongho Heo, Sangdoo Yun, Dongyoon Han, Sanghyuk Chun, Junsuk Choe, and Seong Joon Oh. Rethinking spatial dimensions of vision transformers. arXiv preprint arXiv:2103.16302, 2021.   \n[21] Geoffrey Hinton, Oriol Vinyals, and Jeff Dean. Distilling the knowledge in a neural network. arXiv preprint arXiv:1503.02531, 2015.   \n[22] Qibin Hou, Li Zhang, Ming-Ming Cheng, and Jiashi Feng. Strip pooling: Rethinking spatial pooling for scene parsing. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4003–4012, 2020.   \n[23] Gao Huang, Yu Sun, Zhuang Liu, Daniel Sedra, and Kilian Q Weinberger. Deep networks with stochastic depth. In European conference on computer vision, pages 646–661. Springer, 2016.   \n[24] Yinhan Liu, Myle Ott, Naman Goyal, Jingfei Du, Mandar Joshi, Danqi Chen, Omer Levy, Mike Lewis, Luke Zettlemoyer, and Veselin Stoyanov. Roberta: A robustly optimized bert pretraining approach. arXiv preprint arXiv:1907.11692, 2019.   \n[25] Ze Liu, Yutong Lin, Yue Cao, Han Hu, Yixuan Wei, Zheng Zhang, Stephen Lin, and Baining Guo. Swin transformer: Hierarchical vision transformer using shifted windows. arXiv preprint arXiv:2103.14030, 2021.   \n[26] Jonathan Long, Evan Shelhamer, and Trevor Darrell. Fully convolutional networks for semantic segmentation. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 3431–3440, 2015.   \n[27] Ilya Loshchilov and Frank Hutter. Decoupled weight decay regularization. arXiv preprint arXiv:1711.05101, 2017.   \n[28] Niki Parmar, Ashish Vaswani, Jakob Uszkoreit, Łukasz Kaiser, Noam Shazeer, Alexander Ku, and Dustin Tran. Image transformer. arXiv preprint arXiv:1802.05751, 2018.   \n[29] Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, et al. Pytorch: An imperative style, high-performance deep learning library. In Advances in neural information processing systems, pages 8026–8037, 2019.   \n[30] Ilija Radosavovic, Raj Prateek Kosaraju, Ross Girshick, Kaiming He, and Piotr Dollár. Designing network design spaces. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 10428–10436, 2020.   \n[31] Aravind Srinivas, Tsung-Yi Lin, Niki Parmar, Jonathon Shlens, Pieter Abbeel, and Ashish Vaswani. Bottleneck transformers for visual recognition. arXiv preprint arXiv:2101.11605, 2021.   \n[32] Nitish Srivastava, Geoffrey Hinton, Alex Krizhevsky, Ilya Sutskever, and Ruslan Salakhutdinov. Dropout: a simple way to prevent neural networks from overfitting. The journal of machine learning research, 15(1):1929–1958, 2014.   \n[33] Zhiqing Sun, Shengcao Cao, Yiming Yang, and Kris Kitani. Rethinking transformer-based set prediction for object detection. arXiv preprint arXiv:2011.10881, 2020.   \n[34] Mingxing Tan and Quoc V Le. Efficientnet: Rethinking model scaling for convolutional neural networks. arXiv preprint arXiv:1905.11946, 2019.   \n[35] Ilya Tolstikhin, Neil Houlsby, Alexander Kolesnikov, Lucas Beyer, Xiaohua Zhai, Thomas Unterthiner, Jessica Yung, Daniel Keysers, Jakob Uszkoreit, Mario Lucic, et al. Mlp-mixer: An all-mlp architecture for vision. arXiv preprint arXiv:2105.01601, 2021.   \n[36] Hugo Touvron, Matthieu Cord, Matthijs Douze, Francisco Massa, Alexandre Sablayrolles, and Hervé Jégou. Training data-efficient image transformers & distillation through attention. arXiv preprint arXiv:2012.12877, 2020.   \n[37] Hugo Touvron, Matthieu Cord, Alexandre Sablayrolles, Gabriel Synnaeve, and Hervé Jégou. Going deeper with image transformers. arXiv preprint arXiv:2103.17239, 2021.   \n[38] Hugo Touvron, Andrea Vedaldi, Matthijs Douze, and Hervé Jégou. Fixing the train-test resolution discrepancy. arXiv preprint arXiv:1906.06423, 2019.   \n[39] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin. Attention is all you need. Advances in neural information processing systems, 30:5998–6008, 2017.   \n[40] Wenhai Wang, Enze Xie, Xiang Li, Deng-Ping Fan, Kaitao Song, Ding Liang, Tong Lu, Ping Luo, and Ling Shao. Pyramid vision transformer: A versatile backbone for dense prediction without convolutions. arXiv preprint arXiv:2102.12122, 2021.   \n[41] Yuqing Wang, Zhaoliang Xu, Xinlong Wang, Chunhua Shen, Baoshan Cheng, Hao Shen, and Huaxia Xia. End-to-end video instance segmentation with transformers. arXiv preprint arXiv:2011.14503, 2020.   \n[42] Ross Wightman. Pytorch image models. https://github.com/rwightman/ pytorch-image-models, 2019.   \n[43] Haiping Wu, Bin Xiao, Noel Codella, Mengchen Liu, Xiyang Dai, Lu Yuan, and Lei Zhang. Cvt: Introducing convolutions to vision transformers. arXiv preprint arXiv:2103.15808, 2021.   \n[44] Tete Xiao, Yingcheng Liu, Bolei Zhou, Yuning Jiang, and Jian Sun. Unified perceptual parsing for scene understanding. In Proceedings of the European Conference on Computer Vision (ECCV), pages 418–434, 2018.   \n[45] Fuzhi Yang, Huan Yang, Jianlong Fu, Hongtao Lu, and Baining Guo. Learning texture transformer network for image super-resolution. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5791–5800, 2020.   \n[46] Li Yuan, Yunpeng Chen, Tao Wang, Weihao Yu, Yujun Shi, Francis EH Tay, Jiashi Feng, and Shuicheng Yan. Tokens-to-token vit: Training vision transformers from scratch on imagenet. arXiv preprint arXiv:2101.11986, 2021.   \n[47] Li Yuan, Francis EH Tay, Guilin Li, Tao Wang, and Jiashi Feng. Revisiting knowledge distillation via label smoothing regularization. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 3903–3911, 2020.   \n[48] Sangdoo Yun, Dongyoon Han, Seong Joon Oh, Sanghyuk Chun, Junsuk Choe, and Youngjoon Yoo. Cutmix: Regularization strategy to train strong classifiers with localizable features. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 6023–6032, 2019.   \n[49] Sangdoo Yun, Seong Joon Oh, Byeongho Heo, Dongyoon Han, Junsuk Choe, and Sanghyuk Chun. Re-labeling imagenet: from single to multi-labels, from global to localized labels. arXiv preprint arXiv:2101.05022, 2021.   \n[50] Yanhong Zeng, Jianlong Fu, and Hongyang Chao. Learning joint spatial-temporal transformations for video inpainting. In European Conference on Computer Vision, pages 528–543. Springer, 2020.   \n[51] Hang Zhang, Chongruo Wu, Zhongyue Zhang, Yi Zhu, Zhi Zhang, Haibin Lin, Yue Sun, Tong He, Jonas Muller, R. Manmatha, Mu Li, and Alexander Smola. Resnest: Split-attention networks. arXiv preprint arXiv:2004.08955, 2020.   \n[52] Hongyi Zhang, Moustapha Cisse, Yann N Dauphin, and David Lopez-Paz. mixup: Beyond empirical risk minimization. arXiv preprint arXiv:1710.09412, 2017.   \n[53] Hengshuang Zhao, Li Jiang, Jiaya Jia, Philip Torr, and Vladlen Koltun. Point transformer. arXiv preprint arXiv:2012.09164, 2020.   \n[54] Hengshuang Zhao, Jianping Shi, Xiaojuan Qi, Xiaogang Wang, and Jiaya Jia. Pyramid scene parsing network. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 2881–2890, 2017.   \n[55] Minghang Zheng, Peng Gao, Xiaogang Wang, Hongsheng Li, and Hao Dong. End-to-end object detection with adaptive clustering transformer. arXiv preprint arXiv:2011.09315, 2020.   \n[56] Sixiao Zheng, Jiachen Lu, Hengshuang Zhao, Xiatian Zhu, Zekun Luo, Yabiao Wang, Yanwei Fu, Jianfeng Feng, Tao Xiang, Philip HS Torr, et al. Rethinking semantic segmentation from a sequence-to-sequence perspective with transformers. arXiv preprint arXiv:2012.15840, 2020.   \n[57] Zhun Zhong, Liang Zheng, Guoliang Kang, Shaozi Li, and Yi Yang. Random erasing data augmentation. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 34, pages 13001–13008, 2020.   \n[58] Bolei Zhou, Hang Zhao, Xavier Puig, Tete Xiao, Sanja Fidler, Adela Barriuso, and Antonio Torralba. Semantic understanding of scenes through the ade20k dataset. International Journal of Computer Vision, 127(3):302–321, 2019.   \n[59] Daquan Zhou, Bingyi Kang, Xiaojie Jin, Linjie Yang, Xiaochen Lian, Qibin Hou, and Jiashi Feng. Deepvit: Towards deeper vision transformer. arXiv preprint arXiv:2103.11886, 2021.   \n[60] Luowei Zhou, Yingbo Zhou, Jason J Corso, Richard Socher, and Caiming Xiong. End-to-end dense video captioning with masked transformer. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 8739–8748, 2018.   \n[61] Xizhou Zhu, Weijie Su, Lewei Lu, Bin Li, Xiaogang Wang, and Jifeng Dai. Deformable detr: Deformable transformers for end-to-end object detection. arXiv preprint arXiv:2010.04159, 2020. ",
+        "bbox": [
+            171,
+            87,
+            828,
+            919
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            171,
+            73,
+            828,
+            919
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            171,
+            65,
+            828,
+            921
+        ],
+        "page_idx": 12
+    }
+]

parse/train/H1cKvl-Rb/H1cKvl-Rb_content_list.json

@@ -0,0 +1,1744 @@
+[
+    {
+        "type": "text",
+        "text": "UCB EXPLORATION VIA $Q$ -ENSEMBLES ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            98,
+            658,
+            122
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Anonymous authors Paper under double-blind review ",
+        "bbox": [
+            183,
+            150,
+            398,
+            178
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            213,
+            544,
+            229
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "We show how an ensemble of $Q ^ { * }$ -functions can be leveraged for more effective exploration in deep reinforcement learning. We build on well established algorithms from the bandit setting, and adapt them to the $Q$ -learning setting. We propose an exploration strategy based on upper-confidence bounds (UCB). Our experiments show significant gains on the Atari benchmark. ",
+        "bbox": [
+            232,
+            244,
+            764,
+            315
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            342,
+            336,
+            357
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Deep reinforcement learning seeks to learn mappings from high-dimensional observations to actions. Deep $Q$ -learning (Mnih et al. (2015)) is a leading technique that has been used successfully, especially for video game benchmarks. However, fundamental challenges remain, for example, improving sample efficiency and ensuring convergence to high quality solutions. Provably optimal solutions exist in the bandit setting and for small MDPs, and at the core of these solutions are exploration schemes. However these provably optimal exploration techniques do not extend to deep RL in a straightforward way. ",
+        "bbox": [
+            174,
+            372,
+            825,
+            469
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Bootstrapped DQN (Osband et al. (2016)) is a previous attempt at adapting a theoretically verified approach to deep RL. In particular, it draws inspiration from posterior sampling for reinforcement learning (PSRL, Osband et al. (2013); Osband and Van Roy (2016)), which has near-optimal regret bounds. PSRL samples an MDP from its posterior each episode and exactly solves $Q ^ { * }$ , its optimal $Q$ -function. However, in high-dimensional settings, both approximating the posterior over MDPs and solving the sampled MDP are intractable. Bootstrapped DQN avoids having to establish and sample from the posterior over MDPs by instead approximating the posterior over $Q ^ { * }$ . In addition, bootstrapped DQN uses a multi-headed neural network to represent the $Q$ -ensemble. While the authors proposed bootstrapping to estimate the posterior distribution, their empirical findings show best performance is attained by simply relying on different initializations for the different heads, not requiring the sampling-with-replacement process that is prescribed by bootstrapping. ",
+        "bbox": [
+            174,
+            478,
+            825,
+            631
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we design new algorithms that build on the $Q$ -ensemble approach from Osband et al. (2016). However, instead of using posterior sampling for exploration, we construct uncertainty estimates from the $Q$ -ensemble. Specifically, we first propose the Ensemble Voting algorithm where the agent takes action by a majority vote from the $Q$ -ensemble. Next, we propose the UCB exploration strategy. This strategy is inspired by established UCB algorithms in the bandit setting and constructs uncertainty estimates of the $Q$ -values. In this strategy, agents are optimistic and take actions with the highest UCB. We demonstrate that our algorithms significantly improve performance on the Atari benchmark. ",
+        "bbox": [
+            173,
+            637,
+            825,
+            748
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "2 BACKGROUND ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            768,
+            326,
+            785
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "2.1 NOTATION ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            799,
+            287,
+            814
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "We model reinforcement learning as a Markov decision process (MDP). We define an MDP as $( S , A , T , R , p _ { 0 } , \\gamma )$ , in which both the state space $s$ and action space $\\mathcal { A }$ are discrete, $T : S \\times \\mathcal { A } \\times \\mathcal { S } \\mapsto$ $\\mathbb { R } _ { + }$ is the transition distribution, $R : S \\times \\mathcal { A } \\mapsto \\mathbb { R }$ is the reward function, assumed deterministic given the state and action, and $\\gamma \\in ( 0 , 1 ]$ is a discount factor, and $p _ { 0 }$ is the initial state distribution. We denote a transition experience as $\\tau = ( s , a , r , s ^ { \\prime } )$ where $s ^ { \\prime } \\sim T ( s ^ { \\prime } | s , a )$ and $r = R ( s , a )$ . A policy $\\pi : { \\mathcal { S } } \\mapsto A$ specifies the action taken after observing a state. We denote the $Q$ -function for policy $\\pi$ as $\\begin{array} { r } { Q ^ { \\pi } ( s , a ) : = \\mathbb E _ { \\pi } \\big [ \\sum _ { t = 0 } ^ { \\infty } \\gamma ^ { t } r _ { t } | s _ { 0 } = s , a _ { 0 } = a \\big ] } \\end{array}$ where $r _ { t } = R ( s _ { t } , a _ { t } )$ . The optimal $Q ^ { * }$ -function ",
+        "bbox": [
+            173,
+            825,
+            825,
+            926
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "corresponds to taking the optimal policy ",
+        "bbox": [
+            174,
+            103,
+            439,
+            118
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "img_path": "images/585c41a817ea806365929ea09dd3db34a8a3fee59a73dc7c9db4daae6e8aa0b6.jpg",
+        "text": "$$\nQ ^ { \\ast } ( s , a ) : = \\operatorname* { s u p } _ { \\pi } Q ^ { \\pi } ( s , a )\n$$",
+        "text_format": "latex",
+        "bbox": [
+            413,
+            121,
+            584,
+            145
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "and satisfies the Bellman equation ",
+        "bbox": [
+            174,
+            147,
+            400,
+            161
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "img_path": "images/9029853fe46dcb5f0d5c68c08fc9599dc35a0b40542bbf04df25b8852d736340.jpg",
+        "text": "$$\nQ ^ { * } ( s , a ) = \\mathbb { E } _ { s ^ { \\prime } \\sim T ( \\cdot \\mid s , a ) } \\big [ r + \\gamma \\cdot \\operatorname* { m a x } _ { a ^ { \\prime } } Q ^ { * } ( s ^ { \\prime } , a ^ { \\prime } ) \\big ] .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            336,
+            162,
+            660,
+            186
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.2 EXPLORATION IN REINFORCEMENT LEARNING ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            202,
+            537,
+            215
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "A notable early optimality result in reinforcement learning was the proof by Watkins and Dayan Watkins (1989); Watkins and Dayan (1992) that an online $Q$ -learning algorithm is guaranteed to converge to the optimal policy, provided that every state is visited an infinite number of times. However, the convergence of Watkins’ Q-learning can be prohibitively slow in MDPs where $\\epsilon$ - greedy action selection explores state space randomly. Later work developed reinforcement learning algorithms with provably fast (polynomial-time) convergence (Kearns and Singh (2002); Brafman and Tennenholtz (2002); Strehl et al. (2006)). At the core of these provably-optimal learning methods is some exploration strategy, which actively encourages the agent to visit novel state-action pairs. For example, R-MAX optimistically assumes that infrequently-visited states provide maximal reward, and delayed $Q$ -learning initializes the $Q$ -function with high values to ensure that each state-action is chosen enough times to drive the value down. ",
+        "bbox": [
+            174,
+            227,
+            826,
+            380
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Since the theoretically sound RL algorithms are not computationally practical in the deep RL setting, deep RL implementations often use simple exploration methods such as $\\epsilon$ -greedy and Boltzmann exploration, which are often sample-inefficient and fail to find good policies. One common approach of exploration in deep RL is to construct an exploration bonus, which adds a reward for visiting state-action pairs that are deemed to be novel or informative. In particular, several prior methods define an exploration bonus based on a density model or dynamics model. Examples include VIME by Houthooft et al. (2016), which uses variational inference on the forward-dynamics model, and Tang et al. (2016), Bellemare et al. (2016), Ostrovski et al. (2017), Fu et al. (2017). While these methods yield successful exploration in some problems, a major drawback is that this exploration bonus does not depend on the rewards, so the exploration may focus on irrelevant aspects of the environment, which are unrelated to reward. ",
+        "bbox": [
+            174,
+            387,
+            825,
+            539
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.3 BAYESIAN REINFORCEMENT LEARNING ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            556,
+            488,
+            570
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Earlier works on Bayesian reinforcement learning include Dearden et al. (1998; 1999). Dearden et al. (1998) studied Bayesian $Q$ -learning in the model-free setting and learned the distribution of $Q ^ { * }$ - values through Bayesian updates. The prior and posterior specification relied on several simplifying assumptions, some of which are not compatible with the MDP setting. Dearden et al. (1999) took a model-based approach that updates the posterior distribution of the MDP. The algorithm samples from the MDP posterior multiple times and solving the $Q ^ { * }$ values at every step. This approach is only feasible for RL problems with very small state space and action space. Strens (2000) proposed posterior sampling for reinforcement learning (PSRL). PSRL instead takes a single sample of the MDP from the posterior in each episode and solves the $Q ^ { * }$ values. Recent works including Osband et al. (2013) and Osband and Van Roy (2016) established near-optimal Bayesian regret bounds for episodic RL. Sorg et al. (2012) models the environment and constructs exploration bonus from variance of model parameters. These methods are experimented on low dimensional problems only, because the computational cost of these methods is intractable for high dimensional RL. ",
+        "bbox": [
+            174,
+            582,
+            825,
+            762
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.4 BOOTSTRAPPED DQN ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            779,
+            369,
+            794
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Inspired by PSRL, but wanting to reduce computational cost, prior work developed approximate methods. Osband et al. (2014) proposed randomized least-square value iteration for linearly-parameterized value functions. Bootstrapped DQN Osband et al. (2016) applies to $Q$ -functions parameterized by deep neural networks. Bootstrapped DQN (Osband et al. (2016)) maintains a $Q$ -ensemble, represented by a multi-head neural net structure to parameterize $K \\in \\mathbb { N } _ { + }$ $Q$ -functions. This multi-head structure shares the convolution layers but includes multiple “heads”, each of which defines a $Q$ -function $Q _ { k }$ . ",
+        "bbox": [
+            174,
+            804,
+            825,
+            888
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Bootstrapped DQN diversifies the $Q$ -ensemble through two mechanisms. The first mechanism is independent initialization. The second mechanism applies different samples to train each $Q$ -function. ",
+        "bbox": [
+            174,
+            895,
+            823,
+            924
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "These $Q$ -functions can be trained simultaneously by combining their loss functions with the help of a random mask $m _ { \\tau } \\in \\mathbb { R } _ { + } ^ { K }$ C ",
+        "bbox": [
+            169,
+            103,
+            825,
+            133
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/554949743a237969dd6d0aa476836d424be4c434fb5a0dcdc1f97be541606197.jpg",
+        "text": "$$\nL = \\sum _ { \\tau \\in { \\cal B } _ { \\mathrm { m i n i } } } \\sum _ { k = 1 } ^ { K } m _ { \\tau } ^ { k } \\cdot ( Q ^ { k } ( s , a ; \\theta ) - y _ { \\tau } ^ { Q _ { k } } ) ^ { 2 } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            326,
+            150,
+            668,
+            180
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where $y _ { \\tau } ^ { Q _ { k } }$ is the target of the $k$ th $Q$ -function. Thus, the transition $\\tau$ updates $Q _ { k }$ only if $m _ { \\tau } ^ { k }$ is nonzero. To avoid the overestimation issue in DQN, bootstrapped DQN calculates the target value $y _ { \\tau } ^ { Q _ { k } }$ using the approach of Double DQN (Van Hasselt et al. (2016)), such that the current $Q _ { k } ( \\cdot ; \\theta _ { t } )$ network determines the optimal action and the target network $Q _ { k } \\big ( \\cdot ; \\theta ^ { - } \\big )$ estimates the value ",
+        "bbox": [
+            173,
+            196,
+            826,
+            253
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/ccd49d06bffb4624bb90294bf014c922f655ebda5448b2ab077deed9d20903b2.jpg",
+        "text": "$$\ny _ { \\tau } ^ { Q _ { k } } = r + \\gamma \\operatorname* { m a x } _ { a } Q ^ { k } ( s ^ { \\prime } , \\operatorname * { a r g m a x } _ { a } Q _ { k } ( s ^ { \\prime } , a ; \\theta _ { t } ) ; \\theta ^ { - } ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            325,
+            270,
+            671,
+            296
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In their experiments on Atari games, Osband et al. (2016) set the mask $m _ { \\tau } = ( 1 , \\ldots , 1 )$ such that all $\\left\\{ Q _ { k } \\right\\}$ are trained with the same samples and their only difference is initialization. Bootstrapped DQN picks one $Q _ { k }$ uniformly at random at the start of an episode and follows the greedy action $a _ { t } = \\operatorname { a r g m a x } _ { a } Q _ { k } ( s _ { t } , a )$ for the whole episode. ",
+        "bbox": [
+            173,
+            313,
+            825,
+            369
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 ENSEMBLE VOTING ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            400,
+            370,
+            416
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Ignoring computational costs, the ideal Bayesian approach to reinforcement learning is to maintain a posterior over the MDP. However, with limited computation and model capacity, it is more tractable to maintain a posterior of the $Q ^ { * }$ -function. This motivates using a $Q$ -ensemble as a particle filter-based approach to approximate the posterior over $Q ^ { * }$ -function and we display our first proposed method, Ensemble Voting, in Algorithm 1. ",
+        "bbox": [
+            173,
+            439,
+            825,
+            510
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Each $Q _ { k }$ in the $Q$ -ensemble $\\{ Q _ { k } \\} _ { k = 1 } ^ { K }$ is parametrized with a deep neural network whose parameters are initialized independently at the start of training. Each $Q _ { k }$ proposes an action that maximizes the $Q$ -value according to $Q _ { k }$ at every time step and the agent chooses the action by a majority vote ",
+        "bbox": [
+            174,
+            515,
+            825,
+            559
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/be15c40e9293b32696349156add62173ac8516b290f0b01bdbc992e20510a470.jpg",
+        "text": "$$\na _ { t } = \\mathop { \\mathrm { M a j o r i t y } } \\mathrm { V o t e } ( \\{ \\operatorname { a r g m a x } Q _ { k } ( s _ { t } , a ) \\} _ { k = 1 } ^ { K } ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            346,
+            574,
+            650,
+            601
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "At each learning interval, a minibatch of transitions is sampled from the replay buffer and each $Q _ { k }$ takes a Bellman update based on this minibatch. For stability, Algorithm 1 also uses a target network for each $Q _ { k }$ as in Double DQN in the batched update. ",
+        "bbox": [
+            174,
+            616,
+            825,
+            660
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We point out that the difference among the parameters of the $Q$ -ensemble $\\left\\{ Q _ { k } \\right\\}$ comes only from the independent random initialization. The deep neural network parametrization of the $Q$ -ensemble introduces nonconvexity into the objective function of Bellman update, so the $Q$ -ensemble $\\left\\{ Q _ { k } \\right\\}$ do not converge to the same $Q$ -function during training even though they are trained with the same minibatches at every update. We also experimented with bagging by updating each $Q _ { k }$ using an independently drawn minibatch. However, bagging led to inferior learning performance. This phenomenon that that bagging deteriorates the performance of deep ensembles is also observed in supervised learning settings. Lee et al. (2015) observed that supervised learning trained with deep ensembles with random initializations perform better than bagging for deep ensembles. Lakshminarayanan et al. (2016) used deep ensembles for uncertainty estimates and also observed that bagging deteriorated performance in their experiments. ",
+        "bbox": [
+            173,
+            665,
+            825,
+            819
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Lu and Van Roy (2017) develop ensemble sampling for bandit problems with deep neural network parametrized policies and the theoretical justification. We derive a posterior update rule for the $Q ^ { * }$ function and approximations to the posterior update using ensembles in Appendix C. We note that in bootstrapped DQN, ensemble voting is applied for evaluation while Algorithm 1 uses ensemble voting during learning. In the experiments (Sec. 5), we demonstrate that Algorithm 1 is superior to bootstrapped DQN. The action choice of Algorithm 1 is exploitation only. In the next section, we propose our UCB exploration strategy. ",
+        "bbox": [
+            173,
+            825,
+            825,
+            924
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Algorithm 1 Ensemble Voting ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            103,
+            377,
+            118
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "1: Input: $K \\in \\mathbb { N } _ { + }$ copies of independently initialized $Q ^ { * }$ -functions $\\{ Q _ { k } \\} _ { k = 1 } ^ { K }$ .   \n2: Let $B$ be a replay buffer storing transitions for training   \n3: for each episode do do   \n4: Obtain initial state from environment $s _ { 0 }$   \n5: for step $t = 1 , \\dots$ until end of episode do   \n6: Pick an action according to $\\hat { a } _ { t } = \\mathrm { M a j o r i t y V o t e } ( \\{ \\operatorname { a r g m a x } _ { a } Q _ { k } ( s _ { t } , a ) \\} _ { k = 1 } ^ { K } )$   \n7: Execute $a _ { t }$ . Receive state $s _ { t + 1 }$ and reward $r _ { t }$ from the environment   \n8: Add $\\left( { { s _ { t } } , { a _ { t } } , { r _ { t } } , { s _ { t + 1 } } } \\right)$ to replay buffer $B$   \n9: At learning interval, sample random minibatch and update $\\left\\{ Q _ { k } \\right\\}$   \n10: end for   \n11: end for ",
+        "bbox": [
+            179,
+            121,
+            750,
+            279
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4 UCB EXPLORATION STRATEGY USING $Q$ -ENSEMBLES ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            303,
+            661,
+            320
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In this section, we propose optimism-based exploration by adapting the UCB algorithms (Auer et al. (2002); Audibert et al. (2009)) from the bandit setting. The UCB algorithms maintain an upper-confidence bound for each arm, such that the expected reward from pulling each arm is smaller than this bound with high probability. At every time step, the agent optimistically chooses the arm with the highest UCB. Auer et al. (2002) constructed the UCB based on empirical reward and the number of times each arm is chosen. Audibert et al. (2009) incorporated the empirical variance of each arm’s reward into the UCB, such that at time step $t$ , an arm $A _ { t }$ is pulled according to ",
+        "bbox": [
+            173,
+            334,
+            826,
+            433
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/954f078fad211df1f6f64f010ac189beb0de98bb47a9bc8efbf18c0cbdf9c80b.jpg",
+        "text": "$$\nA _ { t } = \\underset { i } { \\operatorname { a r g m a x } } \\left\\{ \\hat { r } _ { i , t } + c _ { 1 } \\cdot \\sqrt { \\frac { \\hat { V } _ { i , t } \\log ( t ) } { n _ { i , t } } } + c _ { 2 } \\cdot \\frac { \\log ( t ) } { n _ { i , t } } \\right\\}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            316,
+            436,
+            679,
+            479
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $\\hat { r } _ { i , t }$ and $\\hat { V } _ { i , t }$ are the empirical reward and variance of arm $i$ at time $t$ , $n _ { i , t }$ is the number of times arm $i$ has been pulled up to time $t$ , and $c _ { 1 } , c _ { 2 }$ are positive constants. ",
+        "bbox": [
+            173,
+            484,
+            823,
+            515
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We extend the intuition of UCB algorithms to the RL setting. Using the outputs of the $\\left\\{ Q _ { k } \\right\\}$ functions, we construct a UCB by adding the empirical standard deviation $\\tilde { \\sigma } ( s _ { t } , a )$ of $\\{ Q _ { k } ( s _ { t } , a ) \\} _ { k = 1 } ^ { K }$ to the empirical mean $\\tilde { \\mu } ( s _ { t } , a )$ of $\\{ Q _ { k } ( s _ { t } , a ) \\} _ { k = 1 } ^ { K }$ . The agent chooses the action that maximizes this UCB ",
+        "bbox": [
+            173,
+            520,
+            826,
+            565
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/b6510d2fb041bf9b71551eb8c5e65fc457aeece694383a9f447bd4f716941e3d.jpg",
+        "text": "$$\na _ { t } \\in \\mathop { \\operatorname { a r g m a x } } _ { a } \\left\\{ \\tilde { \\mu } ( s _ { t } , a ) + \\lambda \\cdot \\tilde { \\sigma } ( s _ { t } , a ) \\right\\} ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            367,
+            569,
+            627,
+            595
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $\\lambda \\in \\mathbb { R } _ { + }$ is a hyperparameter. ",
+        "bbox": [
+            174,
+            599,
+            406,
+            614
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We present Algorithm 2, which incorporates the UCB exploration. The hyperparemeter $\\lambda$ controls the degrees of exploration. In Section 5, we compare the performance of our algorithms on Atari games using a consistent set of parameters. ",
+        "bbox": [
+            174,
+            619,
+            825,
+            662
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Algorithm 2 UCB Exploration with $Q$ -Ensembles ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            676,
+            506,
+            693
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "1: Input: Value function networks $Q$ with $K$ outputs $\\{ Q _ { k } \\} _ { k = 1 } ^ { K }$ . Hyperparameter $\\lambda$ .   \n2: Let $B$ be a replay buffer storing experience for training.   \n3: for each episode do   \n4: Obtain initial state from environment $s _ { 0 }$   \n5: for step $t = 1 , \\dots$ until end of episode do   \n6: Pick an action according to $\\begin{array} { r } { \\grave { a _ { t } } \\in \\mathrm { a r g m a x } _ { a } \\left\\{ \\tilde { \\mu } ( s _ { t } , a ) + \\lambda \\cdot \\tilde { \\sigma } ( s _ { t } , a ) \\right\\} } \\end{array}$   \n7: Receive state $s _ { t + 1 }$ and reward $r _ { t }$ from environment, having taken action $a _ { t }$   \n8: Add $\\left( { { s _ { t } } , { a _ { t } } , { r _ { t } } , { s _ { t + 1 } } } \\right)$ to replay buffer $B$   \n9: At learning interval, sample random minibatch and update $\\left\\{ Q _ { k } \\right\\}$   \n10: end for   \n11: end for ",
+        "bbox": [
+            179,
+            695,
+            741,
+            852
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "5 EXPERIMENT ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            878,
+            316,
+            895
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In this section, we conduct experiments to answer the following questions: ",
+        "bbox": [
+            173,
+            909,
+            661,
+            924
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "1. does Ensemble Voting, Algorithm 1, improve upon existing algorithms including Double DQN and bootstrapped DQN?   \n2. is the proposed UCB exploration strategy of Algorithm 2 effective in improving learning compared to Algorithm 1, Double DQN and bootstrapped DQN?   \n3. how does UCB exploration compare with prior exploration methods such as the count-based exploration method of Bellemare et al. (2016)? ",
+        "bbox": [
+            212,
+            103,
+            825,
+            204
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We evaluate the algorithms on each Atari game of the Arcade Learning Environment (Bellemare et al. (2013)). We use the multi-head neural net architecture of Osband et al. (2016). We fix the common hyperparameters of all algorithms based on a well-tuned double DQN implementation, which uses the Adam optimizer (Kingma and Ba (2014)), different learning rate and exploration schedules compared to Mnih et al. (2015). Appendix A tabulates the hyperparameters. The number of $\\left\\{ Q _ { k } \\right\\}$ functions is $K = 1 0$ . Experiments are conducted on the OpenAI Gym platform (Brockman et al. (2016)) and trained with 40 million frames and 2 trials on each game. ",
+        "bbox": [
+            174,
+            217,
+            825,
+            315
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We take the following directions to evaluate the performance of our algorithms: ",
+        "bbox": [
+            173,
+            321,
+            692,
+            337
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "1. we compare Algorithm 1 against Double DQN and bootstrapped DQN,   \n2. we isolate the impact of UCB exploration by comparing Algorithm 2 with $\\lambda = 0 . 1$ , denoted as ucb exploration, against Algorithm 1, Double DQN, and bootstrapped DQN.   \n3. we compare Algorithm 1 and Algorithm 2 with the count-based exploration method of Bellemare et al. (2016).   \n4. we aggregate the comparison according to different categories of games, to understand when our methods are suprior. ",
+        "bbox": [
+            210,
+            348,
+            825,
+            472
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Figure 1 compares the normalized learning curves of all algorithms across Atari games. Overall, Ensemble Voting, Algorithm 1, outperforms both Double DQN and bootstrapped DQN. With exploration, ucb exploration improves further by outperforming Ensemble Voting. ",
+        "bbox": [
+            174,
+            486,
+            825,
+            527
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In Appendix B, we tabulate detailed results that compare our algorithms, Ensemble Voting and ucb exploration, against prior methods. In Table 2, we tabulate the maximal mean reward in 100 consecutive episodes for Ensemble Voting, ucb exploration, bootstrapped DQN and Double DQN. Without exploration, Ensemble Voting already achieves higher maximal mean reward than both Double DQN and bootstrapped DQN in a majority of Atari games. Ensemble Voting performs better than Double DQN in 37 games out of the total 49 games evaluated, better than bootstrapped DQN in 41 games. ucb exploration achieves the highest maximal mean reward among these four algorithms in 30 games out of the total 49 games evaluated. Specifically, ucb exploration performs better than Double DQN in 38 out of 49 games evaluated, better than bootstrapped DQN in 45 games, and better than Ensemble Voting in 35 games. Figure 2 displays the learning curves of these five algorithms on a set of six Atari games. Ensemble Voting outperforms Double DQN and bootstrapped DQN. ucb exploration outperforms Ensemble Voting. ",
+        "bbox": [
+            174,
+            535,
+            825,
+            702
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In Table 3, we compare our proposed methods with the count-based exploration method ${ \\bf A } 3 { \\bf C } +$ of Bellemare et al. (2016) based on their published results of ${ \\bf A } 3 { \\bf C } +$ trained with 200 million frames. We point out that even though our methods were trained with only 40 million frames, much less than ${ \\bf A } 3 { \\bf C } +$ ’s 200 million frames, UCB exploration achieves the highest average reward in 28 games, Ensemble Voting in 10 games, and ${ \\bf A } 3 { \\bf C } +$ in 10 games. Our approach outperforms ${ \\bf A } 3 { \\bf C } +$ . ",
+        "bbox": [
+            174,
+            708,
+            825,
+            777
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Finally to understand why and when the proposed methods are superior, we aggregate the comparison results according to four categories: Human Optimal, Score Explicit, Dense Reward, and Sparse Reward. These categories follow the taxonomy in Table 1 of Ostrovski et al. (2017). Out of all games evaluated, 23 games are Human Optimal, 8 are Score Explicit, 8 are Dense Reward, and 5 are Sparse Reward. The comparison results are tabulated in Table 4, where we see ucb exploration achieves top performance in more games than Ensemble Voting, Double DQN, and Bootstrapped DQN in the categories of Human Optimal, Score Explicit, and Dense Reward. In Sparse Reward, both ucb exploration and Ensemble Voting achieve best performance in 2 games out of total of 5. Thus, we conclude that ucb exploration improves prior methods consistently across different game categories within the Arcade Learning Environment. ",
+        "bbox": [
+            174,
+            785,
+            825,
+            924
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/755944a1fbb499ae90c0dbc15edc278a059fe19214caa71c8855f17a85eb8094.jpg",
+        "image_caption": [
+            "Figure 1: Comparison of algorithms in normalized learning curve. The normalized learning curve is calculated as follows: first, we normalize learning curves for all algorithms in the same game to the interval [0, 1]; next, average the normalized learning curve from all games for each algorithm. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            187,
+            133,
+            849,
+            426
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/187b14c9628fc4f8130883728517c533abd226a73264ac629bbd4c497df9fc9f.jpg",
+        "image_caption": [
+            "Figure 2: Comparison of UCB Exploration and Ensemble Voting against Double DQN and Bootstrapped DQN. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            173,
+            551,
+            862,
+            847
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "6 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            102,
+            318,
+            118
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We proposed a $Q$ -ensemble approach to deep $Q$ -learning, a computationally practical algorithm inspired by Bayesian reinforcement learning that outperforms Double DQN and bootstrapped DQN, as evaluated on Atari. The key ingredient is the UCB exploration strategy, inspired by bandit algorithms. Our experiments show that the exploration strategy achieves improved learning performance on the majority of Atari games. ",
+        "bbox": [
+            174,
+            132,
+            825,
+            204
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "REFERENCES ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            224,
+            285,
+            239
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Jean-Yves Audibert, Rémi Munos, and Csaba Szepesvári. Exploration–exploitation tradeoff using variance estimates in multi-armed bandits. Theor. Comput. Sci., 410(19):1876–1902, 2009. ",
+        "bbox": [
+            173,
+            247,
+            825,
+            276
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Peter Auer, Nicolo Cesa-Bianchi, and Paul Fischer. Finite-time analysis of the multiarmed bandit problem. Mach. Learn., 47(2-3):235–256, 2002. ",
+        "bbox": [
+            174,
+            284,
+            821,
+            313
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Marc Bellemare, Sriram Srinivasan, Georg Ostrovski, Tom Schaul, David Saxton, and Remi Munos. Unifying count-based exploration and intrinsic motivation. In NIPS, pages 1471–1479, 2016. ",
+        "bbox": [
+            173,
+            320,
+            823,
+            351
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Marc G Bellemare, Yavar Naddaf, Joel Veness, and Michael Bowling. The arcade learning environment: An evaluation platform for general agents. J. Artif. Intell. Res., 47:253–279, 2013. ",
+        "bbox": [
+            173,
+            358,
+            825,
+            388
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Ronen I Brafman and Moshe Tennenholtz. R-max-a general polynomial time algorithm for nearoptimal reinforcement learning. J. Mach. Learn. Res., 3(Oct):213–231, 2002. ",
+        "bbox": [
+            174,
+            396,
+            823,
+            425
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Greg Brockman, Vicki Cheung, Ludwig Pettersson, Jonas Schneider, John Schulman, Jie Tang, and Wojciech Zaremba. OpenAI Gym. arXiv preprint arXiv:1606.01540, 2016. ",
+        "bbox": [
+            176,
+            433,
+            823,
+            463
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Richard Dearden, Nir Friedman, and Stuart Russell. Bayesian Q-learning. In AAAI/IAAI, pages 761–768, 1998. ",
+        "bbox": [
+            176,
+            469,
+            823,
+            500
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Richard Dearden, Nir Friedman, and David Andre. Model based Bayesian exploration. In UAI, pages 150–159, 1999. ",
+        "bbox": [
+            174,
+            507,
+            823,
+            536
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Justin Fu, John D Co-Reyes, and Sergey Levine. EX2: Exploration with exemplar models for deep reinforcement learning. arXiv preprint arXiv:1703.01260, 2017. ",
+        "bbox": [
+            173,
+            545,
+            823,
+            575
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Rein Houthooft, Xi Chen, Yan Duan, John Schulman, Filip De Turck, and Pieter Abbeel. VIME: Variational information maximizing exploration. In NIPS, pages 1109–1117, 2016. ",
+        "bbox": [
+            174,
+            582,
+            821,
+            612
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Michael Kearns and Satinder Singh. Near-optimal reinforcement learning in polynomial time. Mach. Learn., 49(2-3):209–232, 2002. ",
+        "bbox": [
+            174,
+            619,
+            823,
+            648
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Diederik Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014. ",
+        "bbox": [
+            174,
+            656,
+            821,
+            685
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Balaji Lakshminarayanan, Alexander Pritzel, and Charles Blundell. Simple and scalable predictive uncertainty estimation using deep ensembles. arXiv preprint arXiv:1612.01474, 2016. ",
+        "bbox": [
+            173,
+            694,
+            821,
+            723
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Stefan Lee, Senthil Purushwalkam, Michael Cogswell, David Crandall, and Dhruv Batra. Why M heads are better than one: Training a diverse ensemble of deep networks. arXiv preprint arXiv:1511.06314, 2015. ",
+        "bbox": [
+            173,
+            732,
+            825,
+            775
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Xiuyuan Lu and Benjamin Van Roy. Ensemble sampling. 2017. ",
+        "bbox": [
+            173,
+            784,
+            593,
+            799
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Volodymyr Mnih, Koray Kavukcuoglu, David Silver, Andrei A Rusu, Joel Veness, Marc G Bellemare, Alex Graves, Martin Riedmiller, Andreas K Fidjeland, Georg Ostrovski, et al. Human-level control through deep reinforcement learning. Nature, 518(7540):529–533, 2015. ",
+        "bbox": [
+            176,
+            806,
+            823,
+            849
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Ian Osband and Benjamin Van Roy. Why is posterior sampling better than optimism for reinforcement learning. arXiv preprint arXiv:1607.00215, 2016. ",
+        "bbox": [
+            173,
+            858,
+            821,
+            887
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Ian Osband, Dan Russo, and Benjamin Van Roy. (More) efficient reinforcement learning via posterior sampling. In NIPS, pages 3003–3011, 2013. ",
+        "bbox": [
+            174,
+            895,
+            821,
+            924
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Ian Osband, Benjamin Van Roy, and Zheng Wen. Generalization and exploration via randomized value functions. arXiv preprint arXiv:1402.0635, 2014.   \nIan Osband, Charles Blundell, Alexander Pritzel, and Benjamin Van Roy. Deep exploration via bootstrapped DQN. In NIPS, pages 4026–4034, 2016.   \nGeorg Ostrovski, Marc G Bellemare, Aaron van den Oord, and Remi Munos. Count-based exploration with neural density models. arXiv preprint arXiv:1703.01310, 2017.   \nJonathan Sorg, Satinder Singh, and Richard L Lewis. Variance-based rewards for approximate bayesian reinforcement learning. arXiv preprint arXiv:1203.3518, 2012.   \nAlexander L Strehl, Lihong Li, Eric Wiewiora, John Langford, and Michael L Littman. Pac model-free reinforcement learning. In ICML, pages 881–888. ACM, 2006.   \nMalcolm Strens. A Bayesian framework for reinforcement learning. In ICML, pages 943–950, 2000.   \nYi Sun, Faustino Gomez, and Jürgen Schmidhuber. Planning to be surprised: Optimal Bayesian exploration in dynamic environments. In ICAGI, pages 41–51. Springer, 2011.   \nHaoran Tang, Rein Houthooft, Davis Foote, Adam Stooke, Xi Chen, Yan Duan, John Schulman, Filip De Turck, and Pieter Abbeel. # Exploration: A study of count-based exploration for deep reinforcement learning. arXiv preprint arXiv:1611.04717, 2016.   \nHado Van Hasselt, Arthur Guez, and David Silver. Deep reinforcement learning with double Qlearning. In AAAI, pages 2094–2100, 2016.   \nChristopher JCH Watkins and Peter Dayan. Q-learning. Mach. Learn., 8(3-4):279–292, 1992.   \nChristopher John Cornish Hellaby Watkins. Learning from delayed rewards. PhD thesis, University of Cambridge England, 1989. ",
+        "bbox": [
+            169,
+            103,
+            828,
+            497
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "A HYPERPARAMETERS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            102,
+            382,
+            118
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We tabulate the hyperparameters in our well-tuned implementation of double DQN in Table 1: ",
+        "bbox": [
+            173,
+            143,
+            789,
+            159
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/896390fffca83112777cedcbd8f03dd31ff87650868945a92d74639f978326d5.jpg",
+        "table_caption": [
+            "Table 1: Double DQN hyperparameters. These hyperparameters are selected based on performances of seven Atari games: Beam Rider, Breakout, Pong, Enduro, Qbert, Seaquest, and Space Invaders. $I n t e r p ( \\cdot , \\cdot )$ is linear interpolation between two values. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"4\">value</td></tr><tr><td>hyperparameter total training frames</td><td>40 million</td><td>descriptions</td><td>Length of training for each game.</td></tr><tr><td>minibatch size</td><td colspan=\"3\">32</td></tr><tr><td>replay buffer size</td><td>1000000</td><td>parameter update.</td><td>The number of most recent frames</td></tr><tr><td>agent history length</td><td colspan=\"3\">4</td></tr><tr><td></td><td></td><td>length.</td><td>concatenated as input to the Q net- work. Total number of iterations = total training frames /agent history</td></tr><tr><td>target network update10000 frequency</td><td colspan=\"3\"></td></tr><tr><td>discount factor</td><td colspan=\"3\">0.99</td></tr><tr><td>action repeat</td><td colspan=\"3\">4</td></tr><tr><td>update frequency 4</td><td colspan=\"3\"></td></tr><tr><td>optimizer</td><td colspan=\"2\">Adam</td><td>Optimizer for parameter updates.</td></tr><tr><td>β1 0.9</td><td colspan=\"3\">Adam optimizer parameter.</td></tr><tr><td>β</td><td colspan=\"2\">0.99</td><td>Adam optimizer parameter.</td></tr><tr><td>E 10-4</td><td colspan=\"2\"></td><td>Adam optimizer parameter.</td></tr><tr><td>learning rate schedule 2</td><td>10-4 Interp(10-4,5 * 10-5) 5*10-5</td><td>t≤106 otherwise t&gt;5*106</td><td>Learning rate for Adam optimizer, as a function of iteration t.</td></tr><tr><td>exploration schedule</td><td>Interp(1,0.1) Interp(0.1,0.01) 0.01</td><td colspan=\"2\">t&lt;106 otherwise Probability of random action in e- t&gt;5*106</td></tr><tr><td></td><td></td><td colspan=\"2\">greedy exploration, as a function of the iteration t . Number of uniform random ac- tions taken before learning starts.</td></tr><tr><td>replay start size</td><td colspan=\"3\">50000</td></tr></table>",
+        "bbox": [
+            178,
+            176,
+            859,
+            875
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "B RESULTS TABLES ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            103,
+            352,
+            117
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "table",
+        "img_path": "images/4eb43f40bc33336067ff917a144de986a4192279d3974d786f0bb7f1c6ae1bcd.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 2: Comparison of maximal mean rewards achieved by agents. Maximal mean reward is calculated in a window of 100 consecutive episodes. Bold denotes the highest value in each row. "
+        ],
+        "table_body": "<table><tr><td colspan=\"4\"></td><td rowspan=\"2\">UCB-Exploration</td></tr><tr><td></td><td>Bootstrapped DQN</td><td>DoubleDQN</td><td>Ensemble Voting 2282.8</td></tr><tr><td>Alien</td><td>1445.1</td><td>2059.7</td><td></td><td>2817.6</td></tr><tr><td>Amidar</td><td>430.58</td><td>667.5</td><td>683.72</td><td>663.8</td></tr><tr><td>Assault</td><td>2519.06</td><td>2820.61</td><td>3213.58</td><td>3702.76</td></tr><tr><td>Asterix</td><td>3829.0</td><td>7639.5</td><td>8740.0</td><td>8732.0</td></tr><tr><td>Asteroids</td><td>1009.5</td><td>1002.3</td><td>1149.3</td><td>1007.8</td></tr><tr><td>Atlantis</td><td>1314058.0</td><td>1982677.0</td><td>1786305.0</td><td>2016145.0</td></tr><tr><td>Bank Heist</td><td>795.1</td><td>789.9</td><td>869.4</td><td>906.9</td></tr><tr><td>Battle Zone</td><td>26230.0</td><td>24880.0</td><td>27430.0</td><td>26770.0</td></tr><tr><td>Beam Rider</td><td>8006.58</td><td>7743.74</td><td>7991.9</td><td>9188.26</td></tr><tr><td>Bowling</td><td>28.62</td><td>30.92</td><td>32.92</td><td>38.06</td></tr><tr><td>Boxing</td><td>85.91</td><td>94.07</td><td>94.47</td><td>98.08</td></tr><tr><td>Breakout</td><td>400.22</td><td>467.45</td><td>426.78</td><td>411.31</td></tr><tr><td>Centipede</td><td>5328.77</td><td>5177.51</td><td>6153.28</td><td>6237.18</td></tr><tr><td>Chopper Command</td><td>2153.0</td><td>3260.0</td><td>3544.0</td><td>3677.0</td></tr><tr><td>Crazy Climber</td><td>110926.0</td><td>124456.0</td><td>126677.0</td><td>127754.0</td></tr><tr><td>Demon Attack</td><td>9811.45</td><td>23562.55</td><td>30004.4</td><td>59861.9</td></tr><tr><td>Double Dunk</td><td>-10.82</td><td>-14.58</td><td>-11.94</td><td>-4.08</td></tr><tr><td>Enduro</td><td>1314.31</td><td>1439.59</td><td>1999.88</td><td>2752.55</td></tr><tr><td>Fishing Derby</td><td>21.89</td><td>23.69</td><td>30.02</td><td>29.71</td></tr><tr><td>Freeway</td><td>33.57</td><td>32.93</td><td>33.92</td><td>33.96</td></tr><tr><td>Frostbite</td><td>1284.8</td><td>529.2</td><td>1196.0</td><td>1903.0</td></tr><tr><td>Gopher</td><td>7652.2</td><td>12030.0</td><td>10993.2</td><td>12910.8</td></tr><tr><td>Gravitar</td><td>227.5</td><td>279.5</td><td>371.5</td><td>318.0</td></tr><tr><td>Ice Hockey</td><td>-4.62</td><td>-4.63</td><td>-1.73</td><td>-4.71</td></tr><tr><td>Jamesbond</td><td>594.5</td><td>594.0</td><td>602.0</td><td>710.0</td></tr><tr><td>Kangaroo</td><td>8186.0</td><td>7787.0</td><td>8174.0</td><td>14196.0</td></tr><tr><td>Krull</td><td>8537.52</td><td>8517.91</td><td>8669.17</td><td>9171.61</td></tr><tr><td>Kung Fu Master</td><td>24153.0</td><td>32896.0</td><td>30988.0</td><td>31291.0</td></tr><tr><td>Montezuma Revenge</td><td>2.0</td><td>4.0</td><td>1.0</td><td>4.0</td></tr><tr><td>Ms Pacman</td><td>2508.7</td><td>2498.1</td><td>3039.7</td><td>3425.4</td></tr><tr><td>Name This Game</td><td>8212.4</td><td>9806.9</td><td>9255.1</td><td>9570.5</td></tr><tr><td>Pitfall</td><td>-5.99</td><td>-7.57</td><td>-3.37</td><td>-1.47</td></tr><tr><td>Pong</td><td>21.0</td><td>20.67</td><td>21.0</td><td>20.95</td></tr><tr><td>Private Eye</td><td>1815.19</td><td>788.63</td><td>1845.28</td><td>1252.01</td></tr><tr><td>Qbert</td><td>10557.25</td><td>6529.5</td><td>12036.5</td><td>14198.25</td></tr><tr><td>Riverraid</td><td>11528.0</td><td>11834.7</td><td>12785.8</td><td>15622.2</td></tr><tr><td>Road Runner</td><td>52489.0</td><td>49039.0</td><td>54768.0</td><td>53596.0</td></tr><tr><td>Robotank</td><td>21.03</td><td>29.8</td><td>31.83</td><td>41.04</td></tr><tr><td>Seaquest</td><td>9320.7</td><td>18056.4</td><td>20458.6</td><td>24001.6</td></tr><tr><td>Space Invaders</td><td>1549.9</td><td>1917.5</td><td>1890.8</td><td>2626.55</td></tr><tr><td>Star Gunner</td><td>20115.0</td><td>52283.0</td><td>41684.0</td><td>47367.0</td></tr><tr><td>Tennis</td><td>-15.11</td><td>-14.04</td><td>-11.63</td><td>-7.8</td></tr><tr><td>Time Pilot</td><td>5088.0</td><td>5548.0</td><td>6153.0</td><td>6490.0</td></tr><tr><td>Tutankham</td><td>167.47</td><td>223.43</td><td>208.61</td><td>200.76</td></tr><tr><td>Up N Down</td><td>9049.1</td><td>11815.3</td><td>19528.3</td><td>19827.3</td></tr><tr><td>Venture</td><td>115.0</td><td>96.0</td><td>78.0</td><td>67.0</td></tr><tr><td>Video Pinball</td><td>364600.85</td><td>374686.89</td><td>343380.29</td><td>372564.11</td></tr><tr><td>Wizard Of Wor</td><td>2860.0</td><td>3877.0</td><td>5451.0</td><td>5873.0</td></tr><tr><td>Zaxxon</td><td>592.0</td><td>8903.0</td><td>3901.0</td><td>3695.0</td></tr><tr><td>Times best</td><td>1</td><td>7</td><td>9</td><td>30</td></tr></table>",
+        "bbox": [
+            179,
+            155,
+            854,
+            880
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "table",
+        "img_path": "images/27e3fba1891440807533f9b61b3ee4160ebb19c8a6f9c4e7e5bbc0ef5a241f83.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 3: Comparison of Ensemble Voting, UCB Exploration, both trained with 40 million frames and ${ \\bf A } 3 { \\bf C } +$ of Bellemare et al. (2016), trained with 200 million frames "
+        ],
+        "table_body": "<table><tr><td colspan=\"2\">Ensemble Voting</td><td>UCB-Exploration</td><td>A3C+</td></tr><tr><td>Alien</td><td>2282.8</td><td>2817.6</td><td>1848.33</td></tr><tr><td>Amidar</td><td>683.72</td><td>663.8</td><td>964.77</td></tr><tr><td>Assault</td><td>3213.58</td><td>3702.76</td><td>2607.28</td></tr><tr><td>Asterix</td><td>8740.0</td><td>8732.0</td><td>7262.77</td></tr><tr><td>Asteroids</td><td>1149.3</td><td>1007.8</td><td>2257.92</td></tr><tr><td>Atlantis</td><td>1786305.0</td><td>2016145.0</td><td>1733528.71</td></tr><tr><td>Bank Heist</td><td>869.4</td><td>906.9</td><td>991.96</td></tr><tr><td>Battle Zone</td><td>27430.0</td><td>26770.0</td><td>7428.99</td></tr><tr><td>Beam Rider</td><td>7991.9</td><td>9188.26</td><td>5992.08</td></tr><tr><td>Bowling</td><td>32.92</td><td>38.06</td><td>68.72</td></tr><tr><td>Boxing</td><td>94.47</td><td>98.08</td><td>13.82</td></tr><tr><td>Breakout</td><td>426.78</td><td>411.31</td><td>323.21</td></tr><tr><td>Centipede</td><td>6153.28</td><td>6237.18</td><td>5338.24</td></tr><tr><td>Chopper Command</td><td>3544.0</td><td>3677.0</td><td>5388.22</td></tr><tr><td>Crazy Climber</td><td>126677.0</td><td>127754.0</td><td>104083.51</td></tr><tr><td>Demon Attack</td><td>30004.4</td><td>59861.9</td><td>19589.95</td></tr><tr><td>Double Dunk</td><td>-11.94</td><td>-4.08</td><td>-8.88</td></tr><tr><td>Enduro</td><td>1999.88</td><td>2752.55</td><td>749.11</td></tr><tr><td>Fishing Derby</td><td>30.02</td><td>29.71</td><td>29.46</td></tr><tr><td>Freeway</td><td>33.92</td><td>33.96</td><td>27.33</td></tr><tr><td>Frostbite</td><td>1196.0</td><td>1903.0</td><td>506.61</td></tr><tr><td>Gopher</td><td>10993.2</td><td>12910.8</td><td>5948.40</td></tr><tr><td>Gravitar</td><td>371.5</td><td>318.0</td><td>246.02</td></tr><tr><td>Ice Hockey</td><td>-1.73</td><td>-4.71</td><td>-7.05</td></tr><tr><td>Jamesbond</td><td>602.0</td><td>710.0</td><td>1024.16</td></tr><tr><td>Kangaroo</td><td>8174.0</td><td>14196.0</td><td>5475.73</td></tr><tr><td>Krull</td><td>8669.17</td><td>9171.61</td><td>7587.58</td></tr><tr><td>Kung Fu Master</td><td>30988.0</td><td>31291.0</td><td>26593.67</td></tr><tr><td>Montezuma Revenge</td><td>1.0</td><td>4.0</td><td>142.50</td></tr><tr><td>Ms Pacman</td><td>3039.7</td><td>3425.4</td><td>2380.58</td></tr><tr><td>Name This Game</td><td>9255.1</td><td>9570.5</td><td>6427.51</td></tr><tr><td>Pitfall</td><td>-3.37</td><td>-1.47</td><td>-155.97</td></tr><tr><td>Pong</td><td>21.0</td><td>20.95</td><td>17.33</td></tr><tr><td>Private Eye</td><td>1845.28</td><td>1252.01</td><td>100.0</td></tr><tr><td>Qbert</td><td>12036.5</td><td>14198.25</td><td>15804.72</td></tr><tr><td>Riverraid</td><td>12785.8</td><td>15622.2</td><td>10331.56</td></tr><tr><td>Road Runner</td><td>54768.0</td><td>53596.0</td><td>49029.74</td></tr><tr><td>Robotank</td><td>31.83</td><td>41.04</td><td>6.68</td></tr><tr><td>Seaquest</td><td>20458.6</td><td>24001.6</td><td>2274.06</td></tr><tr><td>Space Invaders</td><td>1890.8</td><td>2626.55</td><td>1466.01</td></tr><tr><td> Star Gunner</td><td>41684.0</td><td>47367.0</td><td>52466.84</td></tr><tr><td>Tennis</td><td>-11.63</td><td>-7.8</td><td>-20.49</td></tr><tr><td>Time Pilot</td><td>6153.0</td><td>6490.0</td><td>3816.38</td></tr><tr><td>Tutankham</td><td>208.61</td><td>200.76</td><td>132.67</td></tr><tr><td>Up N Down</td><td>19528.3</td><td>19827.3</td><td>8705.64</td></tr><tr><td>Venture</td><td>78.0</td><td>67.0</td><td>0.00</td></tr><tr><td>Video Pinball</td><td>343380.29</td><td>372564.11</td><td>35515.92</td></tr><tr><td>Wizard Of Wor</td><td>5451.0</td><td>5873.0</td><td>3657.65</td></tr><tr><td>Zaxxon</td><td>3901.0</td><td>3695.0</td><td>7956.05</td></tr><tr><td>Times Best</td><td>10</td><td>28</td><td>10</td></tr></table>",
+        "bbox": [
+            243,
+            94,
+            758,
+            818
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "table",
+        "img_path": "images/005571787932de1656c370acfee80aa9b5104f24d15ee5200d9347b27ed2a0d1.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Category</td><td>Total</td><td>Bootstrapped DQN</td><td>Double DQN</td><td>Ensemble Voting</td><td>UCB-Exploration</td></tr><tr><td>Human Optimal</td><td>23</td><td>0</td><td>3</td><td>5</td><td>15</td></tr><tr><td>Score Explicit</td><td>8</td><td>0</td><td>2</td><td>1</td><td>5</td></tr><tr><td>Dense Reward</td><td>8</td><td>0</td><td>1</td><td>1</td><td>6</td></tr><tr><td>Sparse Reward</td><td>5</td><td>1</td><td>0</td><td>2</td><td>2</td></tr></table>",
+        "bbox": [
+            173,
+            99,
+            872,
+            174
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Table 4: Comparison of each method across different game categories. The Atari games are separated into four categories: human optimal, score explicit, dense reward, and sparse reward. In each row, we present the number of games in this category, the total number of games where each algorithm achieves the optimal performance according to Table 2. The game categories follow the taxonomy in Table 1 of Ostrovski et al. (2017) ",
+        "bbox": [
+            173,
+            189,
+            826,
+            260
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "C APPROXIMATING BAYESIAN $Q$ -LEARNING WITH $Q$ -ENSEMBLES ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            284,
+            743,
+            301
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "In this section, we first derive a posterior update formula for the $Q ^ { * }$ -function under full exploration assumption and this formula turns out to depend on the transition Markov chain. Next, we approximate the posterior update with $Q$ -ensembles $\\{ { \\bar { Q } } _ { k } \\}$ and demonstrate that the Bellman equation emerges as the approximate update rule for each $Q _ { k }$ . ",
+        "bbox": [
+            173,
+            314,
+            825,
+            372
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "C.1 POSTERIOR UPDATE FOR THE $Q ^ { * }$ -FUNCTION ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            387,
+            526,
+            402
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "An MDP is specified by the transition probability $T$ and the reward function $R$ . Unlike prior works outlined in Section 2.3 which learned the posterior of the MDP, we will consider the joint distribution over $( Q ^ { * } , T )$ . Note that $R$ can be recovered from $Q ^ { * }$ given $T$ . So $( Q ^ { * } , T )$ determines a unique MDP. In this section, we assume that the agent samples $( s , a )$ according to a fixed distribution. The corresponding reward $r$ and next state $s ^ { \\prime }$ given by the MDP append to $( s , a )$ to form a transition ${ \\boldsymbol \\tau } = ( s , a , r , s ^ { \\prime } )$ , for updating the posterior of $( Q ^ { * } , T )$ . Recall that the $Q ^ { * }$ -function satisfies the Bellman equation ",
+        "bbox": [
+            173,
+            412,
+            825,
+            511
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "equation",
+        "img_path": "images/a6677133076ccab2959a65d94d7e4fb0872abfdf9ae434ebc50645522db14b11.jpg",
+        "text": "$$\nQ ( s , a ) = r + \\mathbb { E } _ { s ^ { \\prime } \\sim T ( \\cdot | s , a ) } \\left[ \\gamma \\operatorname* { m a x } _ { a ^ { \\prime } } Q ( s ^ { \\prime } , a ^ { \\prime } ) \\right] .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            344,
+            510,
+            651,
+            536
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Denote the joint prior distribution as $p ( Q ^ { * } , T )$ and the posterior as $\\tilde { p }$ . We apply Bayes’ formula to expand the posterior: ",
+        "bbox": [
+            174,
+            539,
+            823,
+            566
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "equation",
+        "img_path": "images/49c85f5489553a7e3afb98aca65933136c3196eb0e7aba19aecddb350c6c2167.jpg",
+        "text": "$$\n\\begin{array} { r l } & { \\tilde { p } ( Q ^ { * } , T | \\tau ) = \\frac { p ( \\tau | Q ^ { * } , T ) \\cdot p ( Q ^ { * } , T ) } { Z ( \\tau ) } } \\\\ & { \\qquad = \\frac { p ( Q ^ { * } , T ) \\cdot p ( s ^ { \\prime } | Q ^ { * } , T , ( s , a ) ) \\cdot p ( r | Q ^ { * } , T , ( s , a , s ^ { \\prime } ) ) \\cdot p ( s , a ) } { Z ( \\tau ) } , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            246,
+            569,
+            748,
+            641
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "where $Z ( \\tau )$ is a normalizing constant and the second equality is because $s$ and $a$ are sampled randomly from $s$ and $\\mathcal { A }$ . Next, we calculate the two conditional probabilities in (1). First, ",
+        "bbox": [
+            176,
+            643,
+            823,
+            672
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "equation",
+        "img_path": "images/602cdad18535c501841b89ecb1826559681ee676df0c9a35d39a813d615bf0be.jpg",
+        "text": "$$\np ( s ^ { \\prime } | Q ^ { * } , T , ( s , a ) ) = p ( s ^ { \\prime } | T , ( s , a ) ) = T ( s ^ { \\prime } | s , a ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            334,
+            675,
+            661,
+            694
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "where the first equality is because given $T$ , $Q ^ { * }$ does not influence the transition. Second, ",
+        "bbox": [
+            173,
+            696,
+            751,
+            712
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "equation",
+        "img_path": "images/fb0955c02f65e1e496f065faeae25ba9c05cbf13f12d277ebac49da28a4215c6.jpg",
+        "text": "$$\n\\begin{array} { r l } & { p ( r | Q ^ { * } , T , ( s , a , s ^ { \\prime } ) ) = p ( r | Q ^ { * } , T , ( s , a ) ) } \\\\ & { \\phantom { p s p a c e } = \\mathbb { 1 } _ { \\{ Q ^ { * } ( s , a ) = r + \\gamma \\cdot \\mathbb { E } _ { s ^ { \\prime \\prime } \\sim T ( \\cdot \\cdot \\vert s , a ) } \\operatorname* { m a x } _ { a ^ { \\prime } } Q ^ { * } ( s ^ { \\prime \\prime } , a ^ { \\prime } ) \\} } } \\\\ & { \\phantom { p s p a c e } : = \\mathbb { 1 } ( Q ^ { * } , T ) , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            282,
+            714,
+            715,
+            773
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "where $\\mathbb { 1 } _ { \\{ \\cdot \\} }$ is the indicator function and in the last equation we abbreviate it as $\\mathbb { 1 } ( Q ^ { * } , T )$ . Substituting (2) and (3) into (1), we obtain the joint posterior of $Q ^ { * }$ and $T$ after observing an additional randomly sampled transition $\\tau$ ",
+        "bbox": [
+            176,
+            775,
+            825,
+            818
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "equation",
+        "img_path": "images/9e1f8436cc01293f7e533e96b6775e8cf9531c631fae4a8f68650d6cb6ddb3a0.jpg",
+        "text": "$$\n\\tilde { p } ( Q ^ { * } , T | \\tau ) = \\frac { p ( Q ^ { * } , T ) \\cdot T ( s ^ { \\prime } | s , a ) \\cdot p ( s , a ) } { Z ( \\tau ) } \\cdot \\mathbb { 1 } ( Q ^ { * } , T ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            310,
+            820,
+            686,
+            854
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "C.2 APPROXIMATIONS WITH $Q$ -ENSEMBLES ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            869,
+            493,
+            885
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "The exact $Q ^ { * }$ -posterior update (4) is intractable in high-dimensional RL due to the large space of $( Q ^ { * } , T )$ . Thus, we make several approximations to the $Q ^ { * }$ -posterior update. First, we approximate the prior of $Q ^ { * }$ by sampling $K \\in \\mathbb { N } _ { + }$ independently initialized $Q ^ { * }$ -functions $\\{ Q _ { k } \\} _ { k = 1 } ^ { K }$ . Next, we update them as more transitions are sampled. The resulting $\\left\\{ Q _ { k } \\right\\}$ approximate samples drawn from the posterior. The agent chooses the action by taking a majority vote from the actions determined by each $Q _ { k }$ . ",
+        "bbox": [
+            173,
+            895,
+            825,
+            924
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            173,
+            102,
+            825,
+            160
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "We derive the update rule for $\\left\\{ Q _ { k } \\right\\}$ after observing a new transition $\\tau = ( s , a , r , s ^ { \\prime } )$ . At iteration $i$ , given $Q ^ { * } = Q _ { k , i } ( \\cdot ; \\theta _ { k } )$ parametrized by $\\theta _ { k }$ the joint probability of $( Q ^ { * } , T )$ factors into ",
+        "bbox": [
+            174,
+            165,
+            825,
+            195
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "equation",
+        "img_path": "images/a9e3490d38f1df33eee5e4e8f26512fd49304477b682900ff7783bd506bbe021.jpg",
+        "text": "$$\np ( Q _ { k , i } , T ) = p ( Q ^ { * } , T | Q ^ { * } = Q _ { k , i } ) = p ( T | Q _ { k , i } ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            336,
+            200,
+            661,
+            219
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Substitute (5) into (4) and we obtain the corresponding posterior for each $Q _ { k , i + 1 }$ at iteration $i + 1$ as ",
+        "bbox": [
+            174,
+            223,
+            820,
+            239
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "equation",
+        "img_path": "images/2161b1d580d9c2964aed6a05d3774e58926355fa4fa34b423c443d47e0cad512.jpg",
+        "text": "$$\n\\begin{array} { r l r } {  { \\tilde { p } ( Q _ { k , i + 1 } , T | \\tau ) = \\frac { p ( T | Q _ { k , i } ) \\cdot T ( s ^ { \\prime } | s , a ) \\cdot p ( s , a ) } { Z ( \\tau ) } \\cdot \\mathbb { 1 } ( Q _ { k , i + 1 } , T ) . } } \\\\ & { } & { \\tilde { p } ( Q _ { k , i + 1 } | \\tau ) = \\int _ { T } \\tilde { p } ( Q _ { k , i + 1 } , T | \\tau ) \\mathrm { d } T = p ( s , a ) \\cdot \\int _ { T } \\tilde { p } ( T | Q _ { k , i } , \\tau ) \\cdot \\mathbb { 1 } ( Q _ { k , i + 1 } , T ) \\mathrm { d } T . } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            210,
+            244,
+            784,
+            314
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "We update $Q _ { k , i }$ to $Q _ { k , i + 1 }$ according to ",
+        "bbox": [
+            174,
+            318,
+            431,
+            334
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "equation",
+        "img_path": "images/3572d2c11640739b572990e946c494fde34c0c4e2420f4edaef3189bc4796174.jpg",
+        "text": "$$\nQ _ { k , i + 1 }  \\operatorname * { a r g m a x } _ { Q _ { k , i + 1 } } \\tilde { p } ( Q _ { k , i + 1 } | \\tau ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            390,
+            338,
+            607,
+            366
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "We first derive a lower bound of the the posterior $\\tilde { p } ( Q _ { k , i + 1 } | \\tau )$ : ",
+        "bbox": [
+            173,
+            372,
+            584,
+            388
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "equation",
+        "img_path": "images/aadb27b42c7df13b92fe96ca8b2bd2e3c4f0eb84124981ebf634d4b0c43dae83.jpg",
+        "text": "$$\n\\begin{array} { r l r } {  { \\operatorname { i } ( Q _ { k , i + 1 } \\lvert \\tau \\rangle = p ( s , a ) \\cdot \\mathbb { E } _ { T \\sim \\tilde { p } ( T \\lvert Q _ { k , i } , \\tau ) } \\mathbb { 1 } ( Q _ { k , i + 1 } , T ) } } \\\\ & { = p ( s , a ) \\cdot \\mathbb { E } _ { T \\sim \\tilde { p } ( T \\lvert Q _ { k , i } , \\tau ) } \\underset { c \\to + \\infty } { \\operatorname { i m } } \\exp ( - c [ Q _ { k , i + 1 } ( s , a ) - r - \\gamma \\mathbb { E } _ { s ^ { \\prime \\prime } \\sim T ( \\cdot \\lvert s , a ) } \\underset { a ^ { \\prime } } { \\operatorname { m a x } } Q _ { k , i + 1 } ( s ^ { \\prime \\prime } , a ^ { \\prime } ) ] ^ { 2 } ) } \\\\ & { = p ( s , a ) \\cdot \\underset { c \\to + \\infty } { \\operatorname* { i m } } \\mathbb { E } _ { T \\sim \\tilde { p } ( T \\lvert Q _ { k , i } , \\tau ) } \\exp ( - c [ Q _ { k , i + 1 } ( s , a ) - r - \\gamma \\mathbb { E } _ { s ^ { \\prime \\prime } \\sim T ( \\cdot \\lvert s , a ) } \\underset { a ^ { \\prime } } { \\operatorname { m a x } } Q _ { k , i + 1 } ( s ^ { \\prime \\prime } , a ^ { \\prime } ) ] ^ { 2 } ) } \\\\ & { \\geq p ( s , a ) \\cdot \\underset { c \\to + \\infty } { \\operatorname* { i m } } \\exp ( - c \\mathbb { E } _ { T \\sim \\tilde { p } ( T \\lvert Q _ { k , i } , \\tau ) } [ Q _ { k , i + 1 } ( s , a ) - r - \\gamma \\mathbb { E } _ { s ^ { \\prime \\prime } \\sim T ( \\cdot \\lvert s , a ) } \\underset { a ^ { \\prime } } { \\operatorname { m a x } } Q _ { k , i + 1 } ( s ^ { \\prime \\prime } , a ^ { \\prime } ) ] ^ { 2 } ) } \\\\ & { = p ( s , a ) \\cdot \\underset { c \\to + \\infty } { \\operatorname* { l i m } } \\underset { c \\to \\tau ( \\tau \\lvert Q _ { k , i } , \\tau ) } { \\operatorname* { i m } } [ Q _ { k , i + 1 } ( s , a ) - r - \\gamma \\mathbb { E } _ { s ^ { \\prime \\prime } \\sim T ( \\cdot \\lvert s , a ) } \\underset { a ^ { \\prime } } { \\operatorname* { m a x } } Q _ { k , i + 1 } ( s ^ { \\prime \\prime } , a ^ { \\prime } ) ] ^ { 2 } } \\\\ &  = p ( s , a ) \\cdot \\mathbb { E } _ { T \\sim \\tilde { p } ( T \\lvert Q _ { k , i } , \\tau ) } [ Q _  k , \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            181,
+            392,
+            838,
+            512
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "where we apply a limit representation of the indicator function in the third equation. The fourth equation is due to the bounded convergence theorem. The inequality is Jensen’s inequality. The last equation (9) replaces the limit with an indicator function. ",
+        "bbox": [
+            174,
+            516,
+            826,
+            559
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "A sufficient condition for (8) is to maximize the lower-bound of the posterior distribution in (9) by ensuring the indicator function in (9) to hold. We can replace (8) with the following update ",
+        "bbox": [
+            171,
+            565,
+            823,
+            594
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "equation",
+        "img_path": "images/1cc85ed7d62f85ce8d16545a0958e89d101ba108cc4e25fe6629d2e2ecef62f7.jpg",
+        "text": "$$\nQ _ { k , i + 1 }  \\underset { Q _ { k , i + 1 } } { \\mathrm { a r g m i n } } \\mathbb { E } _ { T \\sim \\tilde { p } ( T | Q _ { k , i } , \\tau ) } [ Q _ { k , i + 1 } ( s , a ) - ( r + \\gamma \\cdot \\mathbb { E } _ { s ^ { \\prime \\prime } \\sim T ( \\cdot | s , a ) } \\operatorname* { m a x } _ { a ^ { \\prime } } Q _ { k , i + 1 } ( s ^ { \\prime \\prime } , a ^ { \\prime } ) ) ] ^ { 2 } .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            183,
+            601,
+            813,
+            632
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "However, (10) is not tractable because the expectation in (10) is taken with respect to the posterior $\\tilde { p } ( T | Q _ { k , i } , \\tau )$ of the transition $T$ . To overcome this challenge, we approximate the posterior update by reusing the one-sample next state $s ^ { \\prime }$ from $\\tau$ . Solving the exact minimal for each $Q _ { k , i + 1 }$ is impractical, thus we take a gradient step on $Q _ { k , i + 1 }$ according to the following gradient ",
+        "bbox": [
+            173,
+            642,
+            825,
+            700
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "equation",
+        "img_path": "images/4bea0dec3faa79e0caee8d86ff93eb1847812a86435a690e5db1076c1a7d9095.jpg",
+        "text": "$$\n\\theta _ { k }  \\theta _ { k } + \\eta \\cdot ( Q _ { k } ( s , a ; \\theta _ { k } ) - ( r + \\gamma \\cdot \\operatorname* { m a x } _ { a ^ { \\prime } } Q _ { k } ( s ^ { \\prime } , a ^ { \\prime } ; \\theta _ { k } ) ) ) \\nabla _ { \\theta _ { k } } Q _ { k } ( s , a ; \\theta _ { k } ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            243,
+            705,
+            753,
+            729
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "where $\\eta$ is the step size. Instead of updating $Q _ { k }$ after each transition, we use an experience replay buffer $B$ to store observed transitions and sample a minibatch $B _ { \\mathrm { m i n i } }$ of transitions $( s , a , r , s ^ { \\prime } )$ for each update. In this case, the batched update of each $Q _ { k , i }$ to $Q _ { k , i + 1 }$ becomes a standard Bellman update ",
+        "bbox": [
+            173,
+            734,
+            825,
+            791
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "equation",
+        "img_path": "images/d70b3f36248f6004e8bc44efa652a042d00c1404f0bb9b03800759a5a683cd41.jpg",
+        "text": "$$\n\\theta _ { k } \\gets \\theta _ { k } + \\eta \\cdot \\mathbb { E } _ { ( s , a , r , s ^ { \\prime } ) \\in B _ { \\operatorname* { m i n } } } \\big [ \\big ( Q _ { k } \\big ( s , a ; \\theta _ { k } \\big ) - \\big ( r + \\gamma \\cdot \\operatorname* { m a x } _ { a ^ { \\prime } } Q _ { k } \\big ( s ^ { \\prime } , a ^ { \\prime } ; \\theta _ { k } \\big ) \\big ) \\big ) \\nabla _ { \\theta _ { k } } Q _ { k } \\big ( s , a ; \\theta _ { k } \\big ) \\big ] .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            183,
+            795,
+            812,
+            819
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "D INFOGAIN EXPLORATION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            837,
+            421,
+            853
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "In this section, we also studied an “InfoGain” exploration bonus, which encourages agents to gain information about the $Q ^ { * }$ -function and examine its effectiveness. We found it had some benefits on top of Ensemble Voting, but no uniform additional benefits once already using Q-ensembles on top of Double DQN. We describe the approach and our experimental findings. ",
+        "bbox": [
+            174,
+            867,
+            825,
+            924
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Similar to Sun et al. (2011), we define the information gain from observing an additional transition $\\tau _ { n }$ as ",
+        "bbox": [
+            171,
+            103,
+            823,
+            132
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "equation",
+        "img_path": "images/92d0a80953a40c9a25364420585521da683a2bbc55554267f030e06126cf824a.jpg",
+        "text": "$$\nH _ { \\tau _ { t } | \\tau _ { 1 } , \\dots , \\tau _ { n - 1 } } = D _ { K L } ( \\tilde { p } ( Q ^ { * } | \\tau _ { 1 } , \\dots , \\tau _ { n } ) | | \\tilde { p } ( Q ^ { * } | \\tau _ { 1 } , \\dots , \\tau _ { n - 1 } ) )\n$$",
+        "text_format": "latex",
+        "bbox": [
+            290,
+            132,
+            704,
+            151
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "where $\\tilde { p } ( Q ^ { * } | \\tau _ { 1 } , \\dots , \\tau _ { n } )$ is the posterior distribution of $Q ^ { * }$ after observing a sequence of transitions $\\left( \\tau _ { 1 } , \\dots , \\tau _ { n } \\right)$ . The total information gain is ",
+        "bbox": [
+            173,
+            156,
+            820,
+            185
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "equation",
+        "img_path": "images/f989e42d3a3df5cd3eacb6baeb2a0fdf4ed66ccb011a106b222986f026240b2d.jpg",
+        "text": "$$\nH _ { \\tau _ { 1 } , \\dots , \\tau _ { N } } = \\sum _ { n = 1 } ^ { N } H _ { \\tau _ { n } | \\tau _ { 1 } , \\dots , \\tau _ { n - 1 } } .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            379,
+            194,
+            617,
+            223
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "Our Ensemble Voting, Algorithm 1, does not maintain the posterior $\\tilde { p }$ , thus we cannot calculate (11) explicitly. Instead, inspired by Lakshminarayanan et al. (2016), we define an InfoGain exploration bonus that measures the disagreement among $\\left\\{ Q _ { k } \\right\\}$ . Note that ",
+        "bbox": [
+            173,
+            229,
+            825,
+            273
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "equation",
+        "img_path": "images/da85240ec8e2f545f5e402235f477ab4c68b55ff03768b899da2490a4bc78ae3.jpg",
+        "text": "$$\nH _ { \\tau _ { 1 } , \\dots , \\tau _ { N } } + \\mathsf { H } ( \\tilde { p } ( Q ^ { * } | \\tau _ { 1 } , \\dots , \\tau _ { N } ) ) = \\mathsf { H } ( p ( Q ^ { * } ) ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            339,
+            281,
+            656,
+            299
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "where $\\mathsf { H } ( \\cdot )$ is the entropy. If $H _ { \\tau _ { 1 } , \\dots , \\tau _ { N } }$ is small, then the posterior distribution has high entropy and high residual information. Since $\\left\\{ Q _ { k } \\right\\}$ are approximate samples from the posterior, high entropy of the posterior leads to large discrepancy among $\\left\\{ Q _ { k } \\right\\}$ . Thus, the exploration bonus is monotonous with respect to the residual information in the posterior $\\mathsf { H } ( \\tilde { p } ( Q ^ { * } | \\tau _ { 1 } , \\dots , \\tau _ { N } ) )$ . We first compute the Boltzmann distribution for each $Q _ { k }$ ",
+        "bbox": [
+            173,
+            306,
+            825,
+            377
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "equation",
+        "img_path": "images/24be8a27e56f39b989b40f301208b39a1e67cb305d0df0b0a77cb478192364bf.jpg",
+        "text": "$$\nP _ { \\mathsf { T } , k } ( a | s ) = \\frac { \\exp \\left( Q _ { k } ( s , a ) / \\mathsf { T } \\right) } { \\sum _ { a ^ { \\prime } } \\exp \\left( Q _ { k } ( s , a ^ { \\prime } ) / \\mathsf { T } \\right) } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            370,
+            385,
+            625,
+            424
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "where $\\mathsf T > 0$ is a temperature parameter. Next, calculate the average Boltzmann distribution ",
+        "bbox": [
+            169,
+            431,
+            776,
+            445
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "equation",
+        "img_path": "images/fd7f46f57b39c6d76b6ea0551a04fbcf7f0fff4f0f12971f16ea7d9371731d99.jpg",
+        "text": "$$\nP _ { \\mathsf { T } , \\mathrm { a v g } } = \\frac { 1 } { K } \\cdot \\sum _ { k = 1 } ^ { K } P _ { \\mathsf { T } , k } ( a | s ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            388,
+            454,
+            607,
+            484
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "The InfoGain exploration bonus is the average KL-divergence from $\\{ P _ { \\mathsf { T } , k } \\} _ { k = 1 } ^ { K }$ to $P _ { \\mathrm { { T , a v g } } }$ ",
+        "bbox": [
+            171,
+            492,
+            754,
+            510
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "equation",
+        "img_path": "images/0b2a7fedeb71301cadf9a63b4396515b553a6a5e5eaf3244c7354a20783153fb.jpg",
+        "text": "$$\nb _ { \\mathsf { T } } ( s ) = \\frac { 1 } { K } \\cdot \\sum _ { k = 1 } ^ { K } \\mathrm { D } _ { K L } [ P _ { \\mathsf { T } , k } | | P _ { \\mathsf { T } , \\mathrm { a v g } } ] .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            361,
+            517,
+            637,
+            547
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "The modified reward is ",
+        "bbox": [
+            174,
+            555,
+            326,
+            569
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "equation",
+        "img_path": "images/2271a374b1bd2f8522eea625ab54732f3037b9931d39f79a368d1c20741583c3.jpg",
+        "text": "$$\n\\hat { r } ( s , a , s ^ { \\prime } ) = r ( s , a ) + \\rho \\cdot b \\tau ( s ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            392,
+            570,
+            606,
+            588
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "where $\\rho \\in \\mathbb { R } _ { + }$ is a hyperparameter that controls the degree of exploration. ",
+        "bbox": [
+            174,
+            593,
+            658,
+            608
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "The exploration bonus $b _ { \\mathsf { T } } ( s _ { t } )$ encourages the agent to explore where $\\left\\{ Q _ { k } \\right\\}$ disagree. The temperature parameter $\\top$ controls the sensitivity to discrepancies among $\\{ Q _ { k } \\}$ . When $\\mathsf { T } \\to + \\infty$ , $\\{ P _ { \\top , k } \\}$ converge to the uniform distribution on the action space and $b _ { \\mathsf { T } } ( s ) \\to 0$ . When $\\top$ is small, the differences among $\\left\\{ Q _ { k } \\right\\}$ are magnified and $b _ { \\mathsf { T } } ( s )$ is large. ",
+        "bbox": [
+            173,
+            614,
+            825,
+            671
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "We display Algorithrim 3, which incorporates our InfoGain exploration bonus into Algorithm 2. The hyperparameters $\\lambda$ , $\\top$ and $\\rho$ vary for each game. ",
+        "bbox": [
+            171,
+            676,
+            823,
+            707
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "Algorithm 3 UCB + InfoGain Exploration with $Q$ -Ensembles ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            723,
+            581,
+            738
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "1: Input: Value function networks $Q$ with $K$ outputs $\\{ Q _ { k } \\} _ { k = 1 } ^ { K }$ . Hyperparameters $\\tau , \\lambda$ , and $\\rho$ .   \n2: Let $B$ be a replay buffer storing experience for training.   \n3: for each episode do   \n4: Obtain initial state from environment $s _ { 0 }$   \n5: for step $t = 1 , \\dots$ until end of episode do   \n6: Pick an action according to $\\begin{array} { r } { \\grave { a _ { t } } \\in \\mathrm { a r g m a x } _ { a } \\left\\{ \\tilde { \\mu } ( s _ { t } , a ) + \\lambda \\cdot \\tilde { \\sigma } ( s _ { t } , a ) \\right\\} } \\end{array}$   \n7: Receive state $s _ { t + 1 }$ and reward $r _ { t }$ from environment, having taken action $a _ { t }$   \n8: Calculate exploration bonus $b _ { \\mathsf { T } } ( s _ { t } )$ according to (12)   \n9: Add $( s _ { t } , a _ { t } , r _ { t } + \\rho \\cdot b _ { \\mathsf { T } } ( s _ { t } ) , s _ { t + 1 } )$ to replay buffer $B$   \n10: At learning interval, sample random minibatch and update $\\left\\{ Q _ { k } \\right\\}$   \n11: end for   \n12: end for ",
+        "bbox": [
+            178,
+            741,
+            808,
+            911
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "image",
+        "img_path": "images/939ce04cb216d1efd18ae513f715268a3148f6d9a0bb94bd5582028e5311ce05.jpg",
+        "image_caption": [
+            "Figure 3: Comparison of all algorithms in normalized curve. The normalized learning curve is calculated as follows: first, we normalize learning curves for all algorithms in the same game to the interval [0, 1]; next, average the normalized learning curve from all games for each algorithm. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            186,
+            102,
+            849,
+            414
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "D.1 PERFORMANCE OF UCB $^ +$ INFOGAIN EXPLORATION ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            502,
+            573,
+            517
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "We demonstrate the performance of the combined UCB+InfoGain exploration in Figure 3 and Figure 3. We augment the previous figures in Section 5 with the performance of ucb+infogain exploration, where we set $\\lambda = 0 . 1 , \\rho = 1$ , and ${ \\mathsf T } = 1$ in Algorithm 3. ",
+        "bbox": [
+            174,
+            529,
+            823,
+            571
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Figure 3 shows that combining UCB and InfoGain exploration does not lead to uniform improvement in the normalized learning curve. ",
+        "bbox": [
+            171,
+            577,
+            823,
+            606
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "At the individual game level, Figure 3 shows that the impact of InfoGain exploration varies. UCB exploration achieves sufficient exploration in games including Demon Attack and Kangaroo and Riverraid, while InfoGain exploration further improves learning on Enduro, Seaquest, and Up N Down. The effect of InfoGain exploration depends on the choice of the temperature $\\top$ . The optimal temperature parameter varies across games. In Figure 5, we display the behavior of ucb+infogain exploration with different temperature values. Thus, we see the InfoGain exploration bonus, tuned with the appropriate temperature parameter, can lead to improved learning for games that require extra exploration, such as ChopperCommand, KungFuMaster, Seaquest, UpNDown. ",
+        "bbox": [
+            173,
+            613,
+            825,
+            738
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "image",
+        "img_path": "images/298f295b77aa13e16d25b06d19768431fd0cd7bebf49664568a091f6ffef1383.jpg",
+        "image_caption": [
+            "Figure 4: Comparison of algorithms against Double DQN and bootstrapped DQN. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            174,
+            349,
+            864,
+            641
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "image",
+        "img_path": "images/bb37003bba1e0413ac880ed76c095033248f764b2a5e78eee9d9c0b3878a47c9.jpg",
+        "image_caption": [
+            "D.2 UCB $^ +$ INFOGAIN EXPLORATION WITH DIFFERENT TEMPERATURES",
+            "Figure 5: Comparison of UCB+InfoGain exploration with different temperatures versus UCB exploration. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            202,
+            126,
+            782,
+            792
+        ],
+        "page_idx": 16
+    }
+]