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+# When Does Contrastive Learning Preserve Adversarial Robustness from Pretraining to Finetuning?
+
+Lijie Fan1, Sijia $\mathbf { L i u ^ { 2 , 3 } }$ , Pin-Yu Chen3, Gaoyuan Zhang3, Chuang Gan3
+
+1 Massachusetts Institute of Technology, 2 Michigan State University, 3 MIT-IBM Watson AI Lab, IBM Research lijiefan@mit.edu, liusiji5@msu.edu, {pin-yu.chen,gaoyuan.zhang,chuangg}@ibm.com
+
+# Abstract
+
+Contrastive learning (CL) can learn generalizable feature representations and achieve state-of-the-art performance of downstream tasks by finetuning a linear classifier on top of it. However, as adversarial robustness becomes vital in image classification, it remains unclear whether or not CL is able to preserve robustness to downstream tasks. The main challenge is that in the ‘self-supervised pretraining $^ +$ supervised finetuning’ paradigm, adversarial robustness is easily forgotten due to a learning task mismatch from pretraining to finetuning. We call such challenge ‘cross-task robustness transferability’. To address the above problem, in this paper we revisit and advance CL principles through the lens of robustness enhancement. We show that (1) the design of contrastive views matters: High-frequency components of images are beneficial to improving model robustness; (2) Augmenting CL with pseudo-supervision stimulus (e.g., resorting to feature clustering) helps preserve robustness without forgetting. Equipped with our new designs, we propose ADVCL, a novel adversarial contrastive pretraining framework. We show that ADVCL is able to enhance cross-task robustness transferability without loss of model accuracy and finetuning efficiency. With a thorough experimental study, we demonstrate that ADVCL outperforms the state-of-the-art self-supervised robust learning methods across multiple datasets (CIFAR-10, CIFAR-100 and STL-10) and finetuning schemes (linear evaluation and full model finetuning). Code is available at https://github.com/LijieFan/AdvCL.
+
+# 1 Introduction
+
+Image classification has been revolutionized by convolutional neural networks (CNNs). In spite of CNNs’ generalization power, the lack of adversarial robustness has shown to be a main weakness that gives rise to security concerns in high-stakes applications when CNNs are applied, e.g., face recognition, medical image classification, surveillance, and autonomous driving [1–5]. The brittleness of CNNs can be easily manifested by generating tiny input perturbations to completely alter the models’ decision. Such input perturbations and corresponding perturbed inputs are referred to as adversarial perturbations and adversarial examples (or attacks), respectively [6–10].
+
+One of the most powerful defensive schemes against adversarial attacks is adversarial training (AT) [11], built upon a two-player game in which an ‘attacker’ crafts input perturbations to maximize the training objective for worst-case robustness, and a ‘defender’ minimizes the maximum loss for an improved robust model against these attacks. However, AT and its many variants using min-max optimization [12–21] were restricted to supervised learning as true labels of training data are required for both supervised classifier and attack generator (that ensures misclassification). The recent work [22–24] demonstrated that with a properly-designed attacker’s objective, AT-type defenses can be generalized to the semi-supervised setting, and showed that the incorporation of additional unlabeled data could further improve adversarial robustness in image classification. Such an extension from supervised to semi-supervised defenses further inspires us to ask whether there exist unsupervised defenses that can eliminate the prerequisite of labeled data but improve model robustness.
+
+Some very recent literature [25–29] started tackling the problem of adversarial defense through the lens of self-supervised learning. Examples include augmenting a supervised task with an unsupervised ‘pretext’ task for which ground-truth label is available for ‘free’ [25, 26], or robustifying unsupervised representation learning based only on a pretext task and then finetuning the learned representations over downstream supervised tasks [27–29]. The latter scenario is of primary interest to us as a defense can then be performed at the pretraining stage without needing any label information. Meanwhile, selfsupervised contrastive learning (CL) has been outstandingly successful in the field of representation learning: It can surpass a supervised learning counterpart on downstream image classification tasks in standard accuracy [30–34]. Different from conventional self-supervised learning methods [35], CL, e.g., SimCLR [30], enforces instance discrimination by exploring multiple views of the same data and treating every instance under a specific view as a class of its own [36].
+
+The most relevant work to ours is [27, 28], which integrated adversarial training with CL. However, the achieved adversarial robustness at downstream tasks largely relies on the use of advanced finetuning techniques, either adversarial full finetuning [27] or adversarial linear finetuning [28]. Different from [27, 28], we ask:
+
+# $( Q )$ How to accomplish robustness enhancement using CL without losing its finetuning efficiency, e.g., via a standard linear finetuner?
+
+Our work attempts to make a rigorous and comprehensive study on addressing the above question. We find that self-supervised learning (including the state-of-the-art CL) suffers a new robustness challenge that we call ‘crosstask robustness transferability’, which was largely overlooked in the previous work. That is, there exists a task mismatch from pretraining to finetuning (e.g., from CL to supervised classification) so that adversarial robustness is not able to transfer across tasks even if pretraining datasets and finetuning datasets are drawn from the same distribution. Different from supervised/semi-supervised learning, this is a characteristic behavior of selfsupervision when being adapted to robust
+
+![](images/7f2ea9a79a438faed069f2c9db9cf64dabc61ba859861ba7da0ab921e88b9765.jpg)  
+Figure 1: Summary of performance for various robust pretraining methods on CIFAR-10. The covered baseline methods include AP-DPE [26], RoCL [28], ACL [27] and supervised adversarial training (AT) [11]. Upper-right indicates better performance with respect to (w.r.t.) standard accuracy and robust accuracy (under PGD attack with 20 steps and $8 / 2 5 5 \ell _ { \infty }$ -norm perturbation strength). Different colors represent different pretraining methods, and different shapes represent different finetuning settings. Circles $\mathbf { \eta } ^ { ( \bullet ) }$ indicates Standard Linear Finetuning (SLF), and Diamonds $( \bullet )$ indicates Adversarial Full Finetuning (AFF). Our method (ADVCL, red circle/diamond) has the best performance across finetuning settings. Similar improvement could be observed under Auto-Attacks, and we provide the visualization in the appendix.
+
+learning. As shown in Figure 1, our work advances CL in the adversarial context and the proposed method outperforms all state-of-the-art baseline methods, leading to a substantial improvement in both robust accuracy and standard accuracy using either the lightweight standard linear finetuning or end-to-end adversarial full finetuning.
+
+Contributions Our main contributions are summarized below.
+
+$\bullet$ We propose ADVCL, a unified adversarial CL framework, and propose to use original adversarial examples and high-frequency data components to create robustness-aware and generalization-aware views of unlabeled data.
+
+$\pmb { \varrho }$ We propose to generate proper pseudo-supervision stimulus for ADVCL to improve cross-task robustness transferability. Different from existing self-supervised defenses aided with labeled data [27], we generate pseudo-labels of unlabeled data based on their clustering information.
+
+$\otimes$ We conduct a thorough experimental study and show that ADVCL achieves state-of-the-art robust accuracies under both PGD attacks [11] and Auto-Attacks [37] using only standard linear finetuning. For example, in the case of Auto-Attack (the most powerful threat model) with $8 / 2 5 5 ~ \ell _ { \infty }$ -norm perturbation strength under ResNet-18, we achieve $3 . 4 4 \%$ and $3 . 4 5 \%$ robustness improvement on CIFAR-10 and CIFAR-100 over existing self-supervised methods. We also justify the effectiveness of ADVCL in different attack setups, dataset transferring, model explanation, and loss landscape smoothness.
+
+# 2 Background & Related Work
+
+Self-Supervised Learning Early approaches for unsupervised representation learning leverages handcrafted tasks, like prediction rotation [38] and solving the Jigsaw puzzle [39, 40], geometry prediction [41] and Selfie [42]. Recently contrastive learning (CL) [30, 33, 34, 43–45] and its variants [31, 32, 36, 46] have demonstrated superior abilities in learning generalizable features in an unsupervised manner. The main idea behind $\mathrm { C L }$ is to self-create positive samples of the same image from aggressive viewpoints, and then acquire data representations by maximizing agreement between positives while contrasts with negatives.
+
+In what follows, we elaborate on the formulation of SimCLR [30], one of the most commonly-used CL frameworks, which this paper will focus on. To be concrete, let $\mathcal { X } = \{ x _ { 1 } , x _ { 2 } , . . . , x _ { n } \}$ denote an unlabeled source dataset, SimCLR offers a learned feature encoder $f _ { \theta }$ to generate expressive deep representations of the data. To train $f _ { \theta }$ , each input $x \in \mathcal { X }$ will be transformed into two views $( \tau _ { 1 } ( x ) , \tau _ { 2 } ( x ) )$ and labels them as a positive pair. Here transformation operations $\tau _ { 1 }$ and $\tau _ { 2 }$ are randomly sampled from a pre-defined transformation set $\tau$ , which includes, e.g., random cropping and resizing, color jittering, rotation, and cutout. The positive pair is then fed in the feature encoder $f _ { \theta }$ with a projection head $g$ to acquire projected features, i.e., $z _ { i } = g \circ f _ { \theta } ( \tau _ { i } ( x ) )$ for $j \in \{ 1 , 2 \}$ . NT-Xent loss (i.e., the normalized temperature-scaled cross-entropy loss) is then applied to optimizing $f _ { \theta }$ , where the distance of projected positive features $( z _ { 1 } , z _ { 2 } )$ is minimized for each input $x$ . SimCLR follows the ‘self-supervised pretraining $^ +$ supervised finetuning’ paradigm. That is, once $f _ { \theta }$ is trained, a downstream supervised classification task can be handled by just finetuning a linear classifier $\phi$ over the fixed encoder $f _ { \theta }$ , leading to the eventual classification network $\phi \circ f _ { \theta }$ .
+
+Adversarial Training (AT) Deep neural networks are vulnerable to adversarial attacks. Various approaches have been proposed to enhance the model robustness. Given a classification model $\theta$ , AT [11] is one of the most powerful robust training methods against adversarial attacks. Different from standard training over normal data $( x , y ) \in \mathcal { D }$ (with feature $x$ and label $y$ in dataset $\mathcal { D }$ ), AT adopts a min-max training recipe, where the worst-case training loss is minimized over the adversarially perturbed data $( x + \delta , y )$ . Here $\delta$ denotes the input perturbation variable to be maximized for the worst-case training objective. The supervised $A T$ is then formally given by
+
+$$
+\operatorname* { m i n } _ { \theta } \mathbb { E } _ { ( x , y ) \in D } \ \operatorname* { m a x } _ { \| \delta \| _ { \infty } \leq \epsilon } \ell ( x + \delta , y ; \theta ) ,
+$$
+
+where $\ell$ denotes the supervised training objective, e.g., cross-entropy (CE) loss. There have been many variants of AT [19–21, 47–50, 22–25] established for supervised/semi-supervised learning.
+
+Self-supervision enabled AT Several recent works [26–29] started to study how to improve model robustness using self-supervised AT. Their idea is to apply AT (1) to a self-supervised pretraining task, e.g., SimCLR in [27, 28], such that the learned feature encoder $f _ { \theta }$ renders robust data representations. However, different from our work, the existing ones lack a systematic study on when and how self-supervised robust pretraining can preserve robustness to downstream tasks without sacrificing the efficiency of lightweight finetuning. For example, the prior work [26, 27] suggested adversarial full finetuning, where pretrained model is used as a weight initialization in finetuning downstream tasks. Yet, it requests the finetuner to update all of the weights of the pretrained model, and thus makes the advantage of self-supervised robust pretraining less significant. A more practical scenario is linear finetuning: One freezes the pretrained feature encoder for the downstream task and only partially finetunes a linear prediction head. The work [28] evaluated the performance of linear fintuning but observed a relatively large performance gap between the standard linear finetuning and adversarial linear finetuning; see more comparisons in Figure 1. Therefore, the problem–how to enhance robustness transferability from pretraining to linear finetuning–remains unexplored.
+
+# 3 Problem Statement
+
+In this section, we present the problem of our interest, together with its setup.
+
+Robust pretraining $^ +$ linear finetuning. We aim to develop robustness enhancement solutions by fully exploiting and exploring the power of CL at the pretraining phase, so that the resulting robust feature representations can seamlessly be used to generate robust predictions of downstream tasks using just a lightweight finetuning scheme. With the aid of AT (1), we formulate the ‘robust pretraining $^ +$ linear finetuning’ problem below:
+
+$$
+\begin{array} { r l } & { \mathrm { P r e t r a i n i n g : ~ } \operatorname* { m i n } _ { \theta } \mathbb { E } _ { x \in \mathcal { X } } \underset { \| \delta \| _ { \infty } \leq \epsilon } { \operatorname* { m a x } } \ell _ { \mathrm { p r e } } ( x + \delta , x ; \theta ) } \\ & { \mathrm { F i n e t u n i n g : ~ } \operatorname* { m i n } _ { \theta _ { \mathrm { c } } } \mathbb { E } _ { ( x , y ) \in \mathcal { D } } \ell _ { \mathrm { C E } } ( \phi _ { \theta _ { \mathrm { c } } } \circ f _ { \theta } ( x ) , y ) , } \end{array}
+$$
+
+where $\ell _ { \mathrm { p r e } }$ denotes a properly-designed robustness- and generalization-aware CL loss (see Sec. 4) given as a function of the adversarial example $( x + \delta )$ , original example $x$ and feature encoder parameters $\theta$ . In (2), $\phi _ { \theta _ { \mathrm { c } } } \circ f _ { \theta }$ denotes the classifier by equipping the linear prediction head $\phi _ { \theta _ { \mathrm { c } } }$ (with parameters $\theta _ { \mathrm { c } }$ to be designed) on top of the fixed feature encoder $f _ { \theta }$ , and $\ell _ { \mathrm { C E } }$ denotes the supervised CE loss over the target dataset $\mathcal { D }$ . Note that besides the standard linear finetuning (3), one can also modify (3) using the worst-case CE loss for adversarial linear/full finetuning [27, 28]. We do not consider standard full finetuning in the paper since tuning the full network weights with standard cross-entropy loss is not possible for the model to preserve robustness [26].
+
+Cross-task robustness transferability. Different from supervised/semi-supervised learning, selfsupervision enables robust pretraining over unlabeled source data. In the meantime, it also imposes a new challenge that we call ‘cross-task robustness transferability’: At the pretraining stage, a feature encoder is learned over a ‘pretext’ task for which ground-truth is available for free, while finetuning is typically carried out on a new downstream task. Spurred by the above, we ask the following questions:
+
+• Will CL improve adversarial robustness using just standard linear finetuning? • What are the principles that CL should follow to preserve robustness across tasks? • What are the insights can we acquire from self-supervised robust representation learnin
+
+# 4 Proposed Approach: Adversarial Contrastive Learning (ADVCL)
+
+In this section, we develop a new adversarial CL framework, ADVCL, which includes two main components, robustnessaware view selection and pseudosupervision stimulus generation. In particular, we advance the view selection mechanism by taking into account proper frequencybased data transformations that are beneficial to robust representation learning and pretraining generalization ability. Furthermore, we propose to design and integrate proper supervision stimulus into ADVCL so as to improve the cross-task robustness transferability since robust representations learned from self
+
+![](images/64439f7f468608e7582a2cfebf1a4bda02c24138dbb68096c8644d0018589fe2.jpg)  
+Figure 2: The overall pipeline of ADVCL. It mainly has two ingredients: robustness-aware view selection (orange box) and pseudo-supervision stimulus generation (blue box). The view selection mechanism is advanced by high frequency components, and the supervision stimulus is created by generating pseudo labels for each image through CLUSTERFIT. The pseudo label (in yellow color) can be created in an offline manner and will not increase the computation overhead.
+
+supervision may lack the class-discriminative ability required for robust predictions on downstream tasks. We provide an overview of ADVCL in Figure 2.
+
+# 4.1 View selection mechanism
+
+In contrast to standard CL, we propose two additional contrastive views: the adversarial view and the frequency view, respectively.
+
+Multi-view CL loss Prior to defining new views, we first review the NT-Xent loss and its multiview version used in CL. Following notations defined in Sec. 2, the contrastive loss with respect to (w.r.t.) a positive pair $( \tau _ { 1 } ( x ) , \tau _ { 2 } ( x ) \bar { ) }$ of each (unlabeled) data $x$ is given by
+
+$$
+\ell _ { \mathrm { C L } } ( \tau _ { 1 } ( x ) , \tau _ { 2 } ( x ) ) = - \sum _ { i = 1 } ^ { 2 } \sum _ { j \in \mathcal { P } ( i ) } \log \frac { \exp { \left( \sin ( z _ { i } , z _ { j } ) / t \right) } } { \sum _ { k \in \mathcal { N } ( i ) } \exp { \left( \sin ( z _ { i } , z _ { k } ) / t \right) } } ,
+$$
+
+where recall that $z _ { i } = g \circ f ( \tau _ { i } ( x ) )$ is the projected feature under the ith view, $\mathcal { P } ( i )$ is the set of positive views except $i$ (e.g., $\mathcal { P } ( i ) = \{ 2 \}$ if $i = 1$ ), $\mathcal { N } ( i )$ denotes the set of augmented batch data except the point $\tau _ { i } ( x )$ , the cardinality of $\mathcal { N } ( i )$ is $( 2 b - 1 )$ (for a data batch of size $b$ under 2 views), $\sin ( z _ { i 1 } , z _ { i 2 } )$ denotes the cosine similarity between representations from two views of the same data, exp denotes exponential function, $\mathrm { s i m } ( \cdot , \cdot )$ is the cosine similarity between two points, and $t > 0$ is a temperature parameter. The two-view CL objective can be further extend to the multi-view contrastive loss [51]
+
+$$
+\ell _ { \mathrm { C L } } ( \tau _ { 1 } ( x ) , \tau _ { 2 } ( x ) , \dots , \tau _ { m } ( x ) ) = - \sum _ { i = 1 } ^ { m } \sum _ { j \in \mathcal { P } ( i ) } \log \frac { \exp { \left( \sin ( z _ { i } , z _ { j } ) / t \right) } } { \displaystyle \sum _ { k \in \mathcal { N } ( i ) } \exp { \left( \sin ( z _ { i } , z _ { k } ) / t \right) } } ,
+$$
+
+where $\mathcal { P } ( i ) ~ = ~ [ m ] / \{ i \}$ denotes the $m$ positive views except $i$ , $[ m ]$ denotes the integer set $\{ 1 , 2 , \ldots , { \dot { m } } \}$ , and $\mathcal { N } ( i )$ , with cardinality $( b m - 1 )$ , denotes the set of $m$ -view augmented $b$ batch samples except the point $\tau _ { i } ( x )$ .
+
+Contrastive view from adversarial example Existing methods proposed in [27–29] can be explained based on (4): An adversarial perturbation $\delta$ w.r.t. each view of a sample $x$ is generated by maximizing the contrastive loss:
+
+$$
+\delta _ { 1 } ^ { * } , \delta _ { 2 } ^ { * } = \underset { \| \delta _ { i } \| _ { \infty } \leq \epsilon } { \mathrm { a r g m a x } } \ell _ { \mathrm { C L } } ( \tau _ { 1 } ( x ) + \delta _ { 1 } , \tau _ { 2 } ( x ) + \delta _ { 2 } ) .
+$$
+
+A solution to problem (6) eventually yields a paired perturbation view $( \tau _ { 1 } ( x ) + \delta _ { 1 } ^ { * } , \tau _ { 2 } ( x ) + \delta _ { 2 } ^ { * } )$ . However, the definition of adversarial view (6) used in [27–29] may not be proper. First, standard CL commonly uses aggressive data transformation that treats small portions of images as positive samples of the full image [36]. Despite its benefit to promoting generalization, crafting perturbations over such aggressive data transformations may not be suitable for defending adversarial attacks applied to full images in the adversarial context. Thus, a new adversarial view built upon $x$ rather than $\tau _ { i } ( x )$ is desired. Second, the contrastive loss (4) is only restricted to two views of the same data. As will be evident later, the multi-view contrastive loss is also needed when taking into account multiple robustness-promoting views. Spurred by above, we define the adversarial view over $x$ , without modifying the existing data augmentations $( \tau _ { 1 } ( x ) , \tau _ { 2 } ( x ) )$ . This leads to the following adversarial perturbation generator by maximizing a 3-view contrastive loss
+
+$$
+\delta ^ { * } = \underset { \| \delta \| \leq \epsilon } { \mathrm { a r g m a x } } \ell _ { \mathrm { C L } } ( \tau _ { 1 } ( x ) , \tau _ { 2 } ( x ) , x + \delta ) ,
+$$
+
+where $x + \delta ^ { * }$ is regarded as the third view of $x$
+
+Contrastive view from high-frequency component Next, we use the high-frequency component (HFC) of data as another additional contrastive view. The rationale arises from the facts that 1) learning over HFC of data is a main cause of achieving superior generalization ability [52] and 2) an adversary typically concentrates on HFC when manipulating an example to fool model’s decision [53]. Let $\mathcal { F }$ and $\scriptstyle { \dot { \mathcal { F } } } ^ { - 1 }$ denote Fourier transformation and its inverse. An input image $x$ can then be decomposed into its HFC $x _ { \mathrm { h } }$ and low-frequency component (LFC) $x _ { \mathrm { l } }$ :
+
+$$
+x _ { \mathrm { h } } = \mathcal { F } ^ { - 1 } ( q _ { \mathrm { h } } ) , \quad x _ { \mathrm { l } } = \mathcal { F } ^ { - 1 } ( q _ { \mathrm { l } } ) , \quad [ q _ { \mathrm { h } } , q _ { \mathrm { l } } ] = \mathcal { F } ( x ) .
+$$
+
+In (8), the distinction between $q _ { \mathrm { h } }$ and $q _ { \mathrm { l } }$ is made by a hard thresholding operation. Let $q ( i , j )$ denote the $( i , j )$ th element of $\mathcal { F } ( x )$ , and $c = ( c _ { 1 } , c _ { 2 } )$ denote the centriod of the frequency spectrum. The components $q _ { \mathrm { l } }$ and $q _ { \mathrm { h } }$ in (8) are then generated by filtering out values according to the distance from c: $q _ { h } ( i , j ) = \mathbb { 1 } _ { [ d ( ( i , j ) , ( c _ { 1 } , c _ { 2 } ) ) \geq r ] } \cdot q ( i , j )$ , and $q _ { l } ( i , j ) = \mathbb { 1 } _ { [ d ( ( i , j ) , ( c _ { 1 } , c _ { 2 } ) ) \leq r ] } \cdot q ( i , j )$ , where $d ( \cdot , \cdot )$ is the Euclidian distance between two spatial coordinates, $r$ is a pre-defined distance threshold $r = 8$ in all our experiments), and $\mathbb { 1 } _ { [ . ] } \in \{ 0 , 1 \}$ is an indicator function which equals to 1 if the condition within $[ \cdot ]$ is met and 0 otherwise.
+
+Robustness-aware contrastive learning objective By incorporating the adversarial perturbation $\delta$ and disentangling HFC $x _ { \mathrm { h } }$ from the original data $x$ , we obtain a four-view contrastive loss (5) defined over $( \tau _ { 1 } ( x ) , \tau _ { 2 } ( x ) , x + \delta , x _ { \mathrm { h } } )$ ,
+
+$$
+\ell _ { \mathrm { C L } } ^ { \mathrm { a d v } } ( \theta ; \mathcal { X } ) : = \mathbb { E } _ { x \in \mathcal { X } } \operatorname* { m a x } _ { \| \delta \| _ { \infty } \leq \epsilon } \ell _ { \mathrm { C L } } ( \tau _ { 1 } ( x ) , \tau _ { 2 } ( x ) , x + \delta , x _ { \mathrm { h } } ; \theta ) ,
+$$
+
+where recall that $\mathcal { X }$ denotes the unlabeled dataset, $\epsilon > 0$ is a perturbation tolerance during training, and for clarity, the four-view contrastive loss (5) is explicitly expressed as a function of model parameters $\theta$ . As will be evident latter, the eventual learning objective ADVCL will be built upon (9).
+
+# 4.2 Supervision stimulus generation: ADVCL empowered by CLUSTERFIT
+
+On top of (9), we further improve the robustness transferability of learned representations by generating a proper supervision stimulus. Our rationale is that robust representation could lack the class-discriminative power required by robust classification as the former is acquired by optimizing an unsupervised contrastive loss while the latter is achieved by a supervised cross-entropy CE loss. However, there is no knowledge about supervised data during pretraining. In order to improve crosstask robustness transferability but without calling for supervision, we take advantage of CLUSTERFIT [54], a pseudo-label generation method used in representation learning.
+
+To be more concrete, let $f _ { \mathrm { p r e } }$ denote a pretrained representation network that can generate latent features of unlabeled data. Note that $f _ { \mathrm { p r e } }$ can be set available beforehand and trained over either supervised or unsupervised dataset $\mathcal { D } _ { \mathrm { p r e } }$ , e.g., ImageNet using using CL in experiments. Given (normalized) pretrained data representations $\{ f _ { \mathrm { p r e } } ( x ) \} _ { x \in \mathcal { X } }$ , CLUSTERFIT uses $K$ -means clustering to find $K$ data clusters of $\mathcal { X }$ , and maps a cluster index $c$ to a pseudo-label, resulting in the pseudolabeled dataset $\{ ( x , c ) \in \hat { \mathcal { X } } \}$ . By integrating CLUSTERFIT with (9), the eventual training objective of ADVCL is then formed by
+
+$$
+\operatorname* { m i n } _ { \theta } \ \ell _ { \mathrm { { C L } } } ^ { \mathrm { a d v } } ( \theta ; \mathcal { X } ) + \lambda \operatorname* { m i n } _ { \theta , \theta _ { \mathrm { c } } } \ \mathbb { E } _ { ( x , c ) \in \hat { \mathcal { X } } } \operatorname* { m a x } _ { \| \delta _ { c e } \| _ { \infty } \leq \epsilon } \ell _ { \mathrm { C E } } ( \phi _ { \theta _ { \mathrm { c } } } \circ f _ { \theta } ( x + \delta _ { c e } ) , c ) ,
+$$
+
+Pseudo-classification enabled AT regularization
+
+where $\hat { \mathcal X }$ denotes the pseudo-labeled dataset of $\mathcal { X }$ , $\phi _ { \theta _ { \mathrm { c } } }$ denotes a prediction head over $f _ { \theta }$ , and $\lambda > 0$ is a regularization parameter that strikes a balance between adversarial contrastive training and pseudo-label stimulated AT. When the number of clusters $K$ is not known a priori, we extend (10) to an ensemble version over $n$ choices of cluster numbers $\{ K _ { 1 } , \ldots , K _ { n } \}$ . Here each cluster number $K _ { i }$ is paired with a unique linear classifier $\phi _ { i }$ to obtain the supervised prediction $\phi _ { i } \circ f$ (using cluster labels). The ensemble CE loss, given by the average of $n$ individual losses, is then used in (10). Our experiments show that the ensemble version usually leads to better generalization ability.
+
+# 5 Experiments
+
+In this section, we demonstrate the effectiveness of our proposed ADVCL from the following aspects: (1) Quantitative results, including cross-task robustness transferability, cross-dataset robustness transferability, and robustness against PGD attacks [11] and Auto-Attacks [37]; (2) Qualitative results, including representation t-SNE [55], feature inversion map visualization, and geometry of loss landscape; (3) Ablation studies of ADVCL, including finetuning schemes, view selection choices, and supervision stimulus variations.
+
+Experiment setup We consider three robustness evaluation metrics: (1) Auto-attack accuracy (AA), namely, classification accuracy over adversarially perturbed images via Auto-Attacks; (2) Robust accuracy (RA), namely, classification accuracy over adversarially perturbed images via PGD attacks; and (3) Standard accuracy (SA), namely, standard classification accuracy over benign images without perturbations. We use ResNet-18 for the encoder architecture of $f _ { \theta }$ in CL. Unless specified otherwise, we use 5-step $\ell _ { \infty }$ projected gradient descent (PGD) with $\epsilon = 8 / 2 5 5$ to generate perturbations during pretraining, and use Auto-Attack and 20-step $\ell _ { \infty }$ PGD with $\epsilon = 8 / 2 5 5$ to generate perturbations in computing AA and RA at test time. We will compare ADVCL with the CL-based adversarial pretraining baselines , ACL [27], RoCL [28], (non-CL) self-supervised adversarial learning baseline AP-DPE [26] and the supervised AT baseline [11].
+
+# 5.1 Quantitative Results
+
+Overall performance from pretraining to finetuning (across tasks) In Table 1, we evaluate the robustness of a classifier (ResNet-18) finetuned over robust representations learned by different supervised/self-supervised pretraining approaches over CIFAR-10 and CIFAR-100. We focus on two representative finetuning schemes: the simplest standard linear finetuning (SLF) and the end-to-end adversarial full finetuning (AFF). As we can see, the proposed ADVCL method yields a substantial improvement over almost all baseline methods. Moreover, ADVCL improves robustness and standard accuracy simultaneously.
+
+Table 1: Cross-task performance of ADVCL (in dark gray color), compared with supervised (in white color) and self-supervised (in light gray color) baselines, in terms of AA, RA and SA on CIFAR-10 with ResNet-18. The pretrained models are evaluated under the standard linear finetuning (SLF) setting and the adversarial full finetuning (AFF) setting. The top performance is highlighted in bold.   
+
+<table><tr><td rowspan="2">Pretraining Method</td><td rowspan="2">Finetuning Method</td><td colspan="3">CIFAR-10</td><td colspan="3">CIFAR-100</td></tr><tr><td>AA(%)</td><td>RA(%)</td><td>SA(%)</td><td>AA(%)</td><td>RA(%)</td><td>SA(%)</td></tr><tr><td>Supervised AP-DPE[26]</td><td rowspan="4">Standard linear finetuning</td><td>42.22</td><td>44.4</td><td>79.77</td><td>19.53</td><td>23.41</td><td>50.53</td></tr><tr><td>RoCL[28]</td><td>16.07</td><td>18.22</td><td>78.30</td><td>4.17</td><td>6.23</td><td>47.91</td></tr><tr><td></td><td>28.38</td><td>39.54</td><td>79.90</td><td>8.66</td><td>18.79</td><td>49.53</td></tr><tr><td>ACL[27] AdvCL (ours)</td><td>39.13</td><td>42.87</td><td>77.88</td><td>16.33</td><td>20.97</td><td>47.51</td></tr><tr><td></td><td rowspan="4">Adversarial full</td><td> 42.57</td><td> 50.45</td><td>80.85</td><td>19.78</td><td>27.67</td><td>48.34</td></tr><tr><td>Supervised</td><td>46.19</td><td>49.89</td><td>79.86</td><td>21.61</td><td>25.86</td><td>52.22</td></tr><tr><td>AP-DPE[26]</td><td>48.13</td><td>51.52</td><td>81.19</td><td>22.53</td><td>26.89</td><td>55.27</td></tr><tr><td>RoCL[28]</td><td>47.88</td><td>51.35</td><td>81.01</td><td>22.38</td><td>27.49</td><td>55.10</td></tr><tr><td>ACL[27]</td><td rowspan="3">finetuning (AFF)</td><td>49.27</td><td> 52.82</td><td>82.19</td><td>23.63</td><td>29.38</td><td>56.61</td></tr><tr><td> ADvCL (ours)</td><td>49.77</td><td> 52.77</td><td>83.62</td><td>24.72</td><td>28.73</td><td>56.77</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></table>
+
+Robustness transferability across datasets In Table 2, we next evaluate the robustness transferability across different datasets, where $A $ $B$ denotes the transferability from pretraining on dataset $A$ to finetuning on another dataset $B \left( \neq A \right)$ of representations learned by ADVCL. Here the pretraining setup is consistent with Table 1. We observe that ADVCL yields
+
+Table 2: Cross-dataset performance of ADVCL (dark gray color), compared with supervised (white color) and self-supervised (light gray) baselines, in AA, RA, SA, on STL-10 with ResNet-18.   
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">一 Fine- tuning</td><td colspan="3">CIFAR-10→STL-10</td><td colspan="3">CIFAR-100→STL-10</td></tr><tr><td>AA(%)</td><td>RA(%)</td><td>SA(%)</td><td>AA(%)</td><td>RA(%)</td><td>SA(%)</td></tr><tr><td>Supervised</td><td rowspan="4">SLF</td><td>22.26</td><td>30.45</td><td>54.70</td><td>19.54</td><td>23.63</td><td>51.11</td></tr><tr><td>RoCL[28]</td><td>18.65</td><td>28.18</td><td>54.56</td><td>12.39</td><td>21.93</td><td>47.86</td></tr><tr><td>ACL[27]</td><td>25.29</td><td>31.80</td><td>55.81</td><td>21.75</td><td>26.32</td><td>45.91</td></tr><tr><td> ADvCL (ours)</td><td>25.74</td><td>35.80</td><td>63.73</td><td>20.86</td><td>30.35</td><td>50.71</td></tr><tr><td>Supervised</td><td rowspan="4">AFF</td><td>33.10</td><td>36.7</td><td>62.78</td><td>29.18</td><td>32.43</td><td>55.85</td></tr><tr><td>RoCL[28]</td><td>29.40</td><td>34.65</td><td>61.75</td><td>27.55</td><td>31.38</td><td>57.83</td></tr><tr><td>ACL[27]</td><td>32.50</td><td>35.93</td><td>62.65</td><td>28.68</td><td>32.41</td><td>57.16</td></tr><tr><td>ADvCL (ours)</td><td>34.70</td><td>37.78</td><td>63.52</td><td>30.51</td><td>33.70</td><td>61.56</td></tr></table>
+
+better robustness as well as standard accuracy than almost all baseline approaches under both SLF and AFF finetuning settings. In the case of CIFAR- $1 0 0  \mathrm { S T L } \mathrm { - } 1 0$ , although ADVCL yields $0 . 8 9 \%$ AA drop compared to ACL [27], it yields a much better SA with $4 . 8 \%$ improvement.
+
+Robustness evaluation vs. attack strength It was shown in [56] that an adversarial defense that causes obfuscated gradients results in a false sense of model robustness. The issue of obfuscated gradients typically comes with two ‘side effects’: (a) The success rate of PGD attack ceases to be improved as the $\ell _ { \infty }$ -norm perturbation radius $\epsilon$ increases; (b) A larger number of PGD steps fails to generate stronger adversarial examples. Spurred by
+
+![](images/e5c730efe89813d6c102565477e6e1db11a1164beb2b8f69559cd73497434098.jpg)  
+Figure 3: RA of ADVCL and baseline approaches under various PGD attacks. SLF is applied to the pretrained model.
+
+the above, Figure 3 shows the finetuning performance of ADVCL (using SLF) as a function of the perturbation size $\epsilon$ and the PGD step number. As we can see, ADVCL is consistently more robust than the baselines at all different PGD settings for a significant margin.
+
+# 5.2 Qualitative Results
+
+Class discrimination of learned representations To further demonstrate the efficacy of ADVCL, Figure 4 visualizes the representations learned by self-supervision using t-SNE [55] on CIFAR-10. We color each point using its ground-truth label. The results show representations learned by ADVCL have a much clearer class boundary than those learned with baselines. This indicates that ADVCL makes an adversary difficult to successfully perturb an image, leading to a more robust prediction.
+
+![](images/97479d92663cb4be02ac05f5e83a4f2103ad791e90a19e12758e106fa172e23b.jpg)  
+Figure 4: t-SNE visualization of representations learned with different self-supervised pretraining approaches. Our ADVCL gives a much clearer separation among classes than baseline approaches.
+
+Visual interpretability of learned representations Furthermore, we demonstrate the advantage of our proposals from the perspective of model explanation, characterized by feature inversion map (FIM) [57] of internal neurons’ response. The work [18, 58, 59] showed that model robustness offered by supervised AT and its variants enforces hidden neurons to learn perceptuallyaligned data features through the lens of FIM. However, it remains unclear whether or not selfsupervised robust pretraining is able to render explainable internal response. Following [57, 58], we acquire FIM of the ith component of representation vector by solving the optimization problem $\begin{array} { r } { x _ { \mathrm { F I M } } = \operatorname* { m i n } _ { \Delta } [ f _ { \theta } ( x _ { 0 } + \Delta ) ] _ { i } } \end{array}$ , where $x _ { 0 }$ is a randomly selected seed image, and $[ \cdot ] _ { i }$ denotes the ith coordinate of a vector. Figure 5 shows that
+
+![](images/06c1fcc48298d40c5d015a0f22906b096d3dcce5827655f6dd67e88353ac4d6a.jpg)  
+Figure 5: FIM visualization of neuron 502 under CIFAR-10 using different robust training methods. Column 1 contains different seed images to generate FIM. Columns 2-5 are FIMs using models trained with different approaches.
+
+compared to other approaches, more similar texture-aligned features can be acquired from a neuron’s feature representation of the network trained with our method regardless of the choice of seed images.
+
+Flatter loss landscape implies better transferability It has been shown in [60] that the flatness of loss landscape is a good indicator for superb transferability in the pretraining $^ +$ finetuning paradigm. Motivated by that, Figure 6 presents the adversarial loss landscape of ADVCL and other self-supervised pretraining approaches under SLF, where the loss landscape is drawn using the method in [61]. Note that instead of standard CE loss, we visualize the adversarial loss w.r.t. model weights. As we can see, the loss for ADVCL has a much flatter landscape around the local optima, whereas the losses for the other approaches change more rapidly. This justifies that our proposal has a better robustness transferability than baseline approaches.
+
+![](images/d0c6b500d5ca6e86fad66f9d6e7d503ff4fdba67230a3e948a63d4ef8b39f6a5.jpg)  
+Figure 6: Visualization of adversarial loss landscape w.r.t. model weights using different self-supervised pretraining methods. ADVCL gives a much flatter landscape than the other baselines.
+
+Table 3: Performance (RA and SA) of ADVCL (in dark gray color) and baseline approaches on CIFAR-10, under different linear finetuning strategies: SLF and adversarial linear finetuning (ALF).   
+
+<table><tr><td rowspan=3 colspan=3>SLFMethodRA(%) SA(%)</td><td></td><td></td></tr><tr><td rowspan=1 colspan=2>SLF</td><td rowspan=1 colspan=2>ALF</td></tr><tr><td rowspan=1 colspan=1>RA(%)</td><td rowspan=1 colspan=1>SA(%)</td><td rowspan=1 colspan=1>RA(%)</td><td rowspan=1 colspan=1>SA(%)</td></tr><tr><td rowspan=1 colspan=1>Supervised</td><td rowspan=1 colspan=1>44.40</td><td rowspan=1 colspan=1>79.77</td><td rowspan=1 colspan=1>46.75</td><td rowspan=1 colspan=1>79.06</td></tr><tr><td rowspan=1 colspan=1>RoCL[28]ACL[27]</td><td rowspan=1 colspan=1>39.5442.87</td><td rowspan=1 colspan=1>79.9077.88</td><td rowspan=1 colspan=1>43.1145.40</td><td rowspan=1 colspan=1>77.3377.71</td></tr><tr><td rowspan=1 colspan=1>ADvCL(ours)</td><td rowspan=1 colspan=1>50.45</td><td rowspan=1 colspan=1>80.85</td><td rowspan=1 colspan=1>52.01</td><td rowspan=1 colspan=1>79.39</td></tr></table>
+
+Table 4: Performance (RA and SA) of ADVCL using different contrastive views setups. ResNet-18 is the backbone network, CIFAR-10 is the dataset, and SLF is used for classification.   
+
+<table><tr><td>Contrastive Views</td><td>RA(%)</td><td>SA(%)</td></tr><tr><td>T1(x）+01,T2(x） T1(x)+δ1,T2(x）+δ2</td><td>42.12 42.48</td><td>77.07 73.12</td></tr><tr><td>T1(x）+δ1,T2(x）+δ,T1(x）,T2(x）</td><td>43.51</td><td>74.22</td></tr><tr><td>x+δ,T1(x）,T2(x）</td><td>50.19</td><td>80.17</td></tr><tr><td>x +δ,T1(x),2(x）,x1</td><td>49.51</td><td>79.83</td></tr><tr><td>x+δ,T1(x),T2(x),x1,xh</td><td>50.03</td><td>80.14</td></tr><tr><td>x +δ,T1(x),T2(x),xh</td><td> 50.45</td><td>80.85</td></tr></table>
+
+Table 5: Performance (RA and SA) of ADVCL using various pretrained models $f _ { \mathrm { p r e } }$ and cluster numbers $K$ in CLUSTERFIT, as well as the baseline w/o using CLUSTERFIT. The setup of $f _ { \mathrm { p r e } }$ is specified by the training method (supervised training or SimCLR) and training dataset (ImageNet or CIFAR-10). ADVCL is implemented using unlabeled data from CIFAR-10 under ResNet-18, together with SLF over the acquired feature encoder for supervised CIFAR-10 classification.   
+
+<table><tr><td rowspan="2">fpre setup: (dataset, training)</td><td rowspan="2">Cluster number K</td><td rowspan="2">RA(%)</td><td rowspan="2">SA (%)</td></tr><tr><td></td></tr><tr><td>N/A</td><td>W/o CLUSTERFIT</td><td>48.89</td><td>77.73 80.34</td></tr><tr><td rowspan="2">(CIFAR-10, SimCLR)</td><td>10 100</td><td>50.10 49.21</td><td>79.52</td></tr><tr><td></td><td></td><td></td></tr><tr><td rowspan="2">(ImageNet,supervised)</td><td>10 100</td><td>50.16 49.27</td><td>78.27 78.08</td></tr><tr><td></td><td></td><td></td></tr><tr><td rowspan="6">(ImageNet, SimCLR)</td><td>2</td><td>50.09</td><td>79.72</td></tr><tr><td>10</td><td>50.12</td><td>79.93</td></tr><tr><td>50</td><td>49.27</td><td>79.55</td></tr><tr><td>100</td><td>49.16</td><td>79.07</td></tr><tr><td>500</td><td>49.03</td><td>78.96</td></tr><tr><td>Ensemble</td><td>50.45</td><td>80.85</td></tr></table>
+
+# 5.3 Ablation studies
+
+Linear finetuning types We first study the robustness difference when different linear finetuning strategies: Standard linear finetuning (SLF) and Adversarial linear finetuning (ALF) are applied. Table 3 shows the performance of models trained with different pretraining methods. As we can see, our ADVCL achieves the best performance under both linear finetuning settings and outperforms baseline approaches in a large margin. We also note the performance gap between SLF and ALF induced by our proposal ADVCL is much smaller than other approaches, and ADVCL with SLF achieves much better performance than baseline approaches with ALF. This indicates that the representations learned by ADVCL is already sufficient to yield satisfactory robustness.
+
+View selection setup We illustrate how different choices of contrastive views influence the robustness performance of ADVCL in Table 4. The first 4 rows study the effect of different types of adversarial examples in contrastive views, and our proposed 3-view contrastive loss (7) significantly outperforms the other baselines, as shown in row 4. The rows in gray show the performance of further exploring different image frequency components (8) as different contrastive views. It is clear that the use of HFC leads to the best overall performance, as shown in the last row.
+
+Supervision stimulus setup We further study the performance of ADVCL using different supervision stimulus. Specifically, we vary the pretrained model for $f _ { \mathrm { p r e } }$ and pseudo cluster number $K$ when training ADVCL and summarize the results in Table 5. The results demonstrate that adding the supervision stimulus could boost the performance of ADVCL. We also observe that the best result comes from $f _ { \mathrm { p r e } }$ pretrained on Imagenet using SimCLR. This is because such representations could generalize better. Moreover, the ensemble scheme over pseudo label categories $K \in \{ 2 , 1 0 , 5 0 , 1 0 \bar { 0 } , 5 0 0 \}$ yields better results than using a single number of clusters. The ensemble scheme also makes ADVCL less sensitive to the actual number of labels for the training dataset.
+
+# 6 Conclusion
+
+In this paper, we study the good practices in making contrastive learning robust to adversarial examples. We show that adding perturbations to original images and high-frequency components are two beneficial factors. We further show that proper supervision stimulus could improve model robustness. Our proposed approaches can achieve state-of-the-art robust accuracy as well as standard accuracy using just standard linear finetuning. Extensive experiments involving quantitative and qualitative analysis have also been made not only to demonstrate the effectiveness of our proposals but also to rationalize why it yields superior performance. Future works could be done to improve the scalability of our proposed self-supervised pretraining approach to very large datasets and models to further boost robust transferabilty across datasets.
+
+References   
+[1] Fatemeh Vakhshiteh, Raghavendra Ramachandra, and Ahmad Nickabadi, “Threat of adversarial attacks on face recognition: A comprehensive survey,” arXiv preprint arXiv:2007.11709, 2020.   
+[2] Xingjun Ma, Yuhao Niu, Lin Gu, Yisen Wang, Yitian Zhao, James Bailey, and Feng Lu, “Understanding adversarial attacks on deep learning based medical image analysis systems,” Pattern Recognition, vol. 110, pp. 107332, 2021.   
+[3] Kaidi Xu, Gaoyuan Zhang, Sijia Liu, Quanfu Fan, Mengshu Sun, Hongge Chen, Pin-Yu Chen, Yanzhi Wang, and Xue Lin, “Adversarial t-shirt! evading person detectors in a physical world,” in European Conference on Computer Vision. Springer, 2020, pp. 665–681.   
+[4] Ji Lin, Chuang Gan, and Song Han, “Defensive quantization: When efficiency meets robustness,” ICLR, 2019.   
+[5] Yulong Cao, Chaowei Xiao, Dawei Yang, Jing Fang, Ruigang Yang, Mingyan Liu, and Bo Li, “Adversarial objects against lidar-based autonomous driving systems,” arXiv preprint arXiv:1907.05418, 2019.   
+[6] Ian Goodfellow, Jonathon Shlens, and Christian Szegedy, “Explaining and harnessing adversarial examples,” International Conference on Learning Representations, vol. arXiv preprint arXiv:1412.6572, 2015.   
+[7] Nicholas Carlini and David Wagner, “Towards evaluating the robustness of neural networks,” in Security and Privacy (SP), 2017 IEEE Symposium on. IEEE, 2017, pp. 39–57.   
+[8] Nicolas Papernot, Patrick McDaniel, Somesh Jha, Matt Fredrikson, Z Berkay Celik, and Ananthram Swami, “The limitations of deep learning in adversarial settings,” in Security and Privacy (EuroS&P), 2016 IEEE European Symposium on. IEEE, 2016, pp. 372–387.   
+[9] Pin-Yu Chen, Yash Sharma, Huan Zhang, Jinfeng Yi, and Cho-Jui Hsieh, “EAD: elasticnet attacks to deep neural networks via adversarial examples,” in Proceedings of the AAAI Conference on Artificial Intelligence, 2018, pp. 10–17.   
+[10] Kaidi Xu, Sijia Liu, Pu Zhao, Pin-Yu Chen, Huan Zhang, Quanfu Fan, Deniz Erdogmus, Yanzhi Wang, and Xue Lin, “Structured adversarial attack: Towards general implementation and better interpretability,” in International Conference on Learning Representations, 2019.   
+[11] Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, and Adrian Vladu, “Towards deep learning models resistant to adversarial attacks,” 2018 ICLR, vol. arXiv preprint arXiv:1706.06083, 2018.   
+[12] Harini Kannan, Alexey Kurakin, and Ian Goodfellow, “Adversarial logit pairing,” 2018.   
+[13] Andrew Slavin Ross and Finale Doshi-Velez, “Improving the adversarial robustness and interpretability of deep neural networks by regularizing their input gradients,” in Thirty-second AAAI conference on artificial intelligence, 2018.   
+[14] Jingkang Wang, Tianyun Zhang, Sijia Liu, Pin-Yu Chen, Jiacen Xu, Makan Fardad, and Bo Li, “Towards a unified min-max framework for adversarial exploration and robustness,” arXiv preprint arXiv:1906.03563, 2019.   
+[15] Seyed-Mohsen Moosavi-Dezfooli, Alhussein Fawzi, Jonathan Uesato, and Pascal Frossard, “Robustness via curvature regularization, and vice versa,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2019, pp. 9078–9086.   
+[16] Yisen Wang, Xingjun Ma, James Bailey, Jinfeng Yi, Bowen Zhou, and Quanquan Gu, “On the convergence and robustness of adversarial training,” in International Conference on Machine Learning, 2019, pp. 6586–6595.   
+[17] Jiefeng Chen, Xi Wu, Vaibhav Rastogi, Yingyu Liang, and Somesh Jha, “Robust attribution regularization,” in Advances in Neural Information Processing Systems, 2019, pp. 14300–14310.   
+[18] Akhilan Boopathy, Sijia Liu, Gaoyuan Zhang, Cynthia Liu, Pin-Yu Chen, Shiyu Chang, and Luca Daniel, “Proper network interpretability helps adversarial robustness in classification,” in ICML, 2020.   
+[19] Ali Shafahi, Mahyar Najibi, Mohammad Amin Ghiasi, Zheng Xu, John Dickerson, Christoph Studer, Larry S Davis, Gavin Taylor, and Tom Goldstein, “Adversarial training for free!,” in Advances in Neural Information Processing Systems, 2019, pp. 3353–3364.   
+[20] Dinghuai Zhang, Tianyuan Zhang, Yiping Lu, Zhanxing Zhu, and Bin Dong, “You only propagate once: Accelerating adversarial training via maximal principle,” arXiv preprint arXiv:1905.00877, 2019.   
+[21] Eric Wong, Leslie Rice, and J. Zico Kolter, “Fast is better than free: Revisiting adversarial training,” in International Conference on Learning Representations, 2020.   
+[22] Hongyang Zhang, Yaodong Yu, Jiantao Jiao, Eric P Xing, Laurent El Ghaoui, and Michael I Jordan, “Theoretically principled trade-off between robustness and accuracy,” International Conference on Machine Learning, 2019.   
+[23] Yair Carmon, Aditi Raghunathan, Ludwig Schmidt, Percy Liang, and John C Duchi, “Unlabeled data improves adversarial robustness,” arXiv preprint arXiv:1905.13736, 2019.   
+[24] Runtian Zhai, Tianle Cai, Di He, Chen Dan, Kun He, John Hopcroft, and Liwei Wang, “Adversarially robust generalization just requires more unlabeled data,” arXiv preprint arXiv:1906.00555, 2019.   
+[25] Dan Hendrycks, Mantas Mazeika, Saurav Kadavath, and Dawn Song, “Using self-supervised learning can improve model robustness and uncertainty,” arXiv preprint arXiv:1906.12340, 2019.   
+[26] Tianlong Chen, Sijia Liu, Shiyu Chang, Yu Cheng, Lisa Amini, and Zhangyang Wang, “Adversarial robustness: From self-supervised pre-training to fine-tuning,” in Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2020, pp. 699–708.   
+[27] Ziyu Jiang, Tianlong Chen, Ting Chen, and Zhangyang Wang, “Robust pre-training by adversarial contrastive learning,” arXiv preprint arXiv:2010.13337, 2020.   
+[28] Minseon Kim, Jihoon Tack, and Sung Ju Hwang, “Adversarial self-supervised contrastive learning,” arXiv preprint arXiv:2006.07589, 2020.   
+[29] Sven Gowal, Po-Sen Huang, Aaron van den Oord, Timothy Mann, and Pushmeet Kohli, “Self-supervised adversarial robustness for the low-label, high-data regime,” in International Conference on Learning Representations, 2021.   
+[30] Ting Chen, Simon Kornblith, Mohammad Norouzi, and Geoffrey Hinton, “A simple framework for contrastive learning of visual representations,” in International conference on machine learning. PMLR, 2020, pp. 1597–1607.   
+[31] Jean-Bastien Grill, Florian Strub, Florent Altche, Corentin Tallec, Pierre H Richemond, Elena ´ Buchatskaya, Carl Doersch, Bernardo Avila Pires, Zhaohan Daniel Guo, Mohammad Gheshlaghi Azar, et al., “Bootstrap your own latent: A new approach to self-supervised learning,” arXiv preprint arXiv:2006.07733, 2020.   
+[32] Yonglong Tian, Chen Sun, Ben Poole, Dilip Krishnan, Cordelia Schmid, and Phillip Isola, “What makes for good views for contrastive learning,” arXiv preprint arXiv:2005.10243, 2020.   
+[33] Tongzhou Wang and Phillip Isola, “Understanding contrastive representation learning through alignment and uniformity on the hypersphere,” in International Conference on Machine Learning. PMLR, 2020, pp. 9929–9939.   
+[34] Xinlei Chen, Haoqi Fan, Ross Girshick, and Kaiming He, “Improved baselines with momentum contrastive learning,” arXiv preprint arXiv:2003.04297, 2020.   
+[35] Priya Goyal, Dhruv Mahajan, Abhinav Gupta, and Ishan Misra, “Scaling and benchmarking self-supervised visual representation learning,” in Proceedings of the IEEE/CVF International Conference on Computer Vision, 2019, pp. 6391–6400.   
+[36] Senthil Purushwalkam and Abhinav Gupta, “Demystifying contrastive self-supervised learning: Invariances, augmentations and dataset biases,” arXiv preprint arXiv:2007.13916, 2020.   
+[37] Francesco Croce and Matthias Hein, “Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks,” in International Conference on Machine Learning. PMLR, 2020, pp. 2206–2216.   
+[38] Spyros Gidaris, Praveer Singh, and Nikos Komodakis, “Unsupervised representation learning by predicting image rotations,” arXiv preprint arXiv:1803.07728, 2018.   
+[39] Mehdi Noroozi and Paolo Favaro, “Unsupervised learning of visual representations by solving jigsaw puzzles,” in European Conference on Computer Vision. Springer, 2016, pp. 69–84.   
+[40] Fabio M Carlucci, Antonio D’Innocente, Silvia Bucci, Barbara Caputo, and Tatiana Tommasi, “Domain generalization by solving jigsaw puzzles,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2019, pp. 2229–2238.   
+[41] Chuang Gan, Boqing Gong, Kun Liu, Hao Su, and Leonidas J Guibas, “Geometry guided convolutional neural networks for self-supervised video representation learning,” in CVPR, 2018, pp. 5589–5597.   
+[42] Trieu H Trinh, Minh-Thang Luong, and Quoc V Le, “Selfie: Self-supervised pretraining for image embedding,” arXiv preprint arXiv:1906.02940, 2019.   
+[43] Aaron van den Oord, Yazhe Li, and Oriol Vinyals, “Representation learning with contrastive predictive coding,” arXiv preprint arXiv:1807.03748, 2018.   
+[44] Kaiming He, Haoqi Fan, Yuxin Wu, Saining Xie, and Ross Girshick, “Momentum contrast for unsupervised visual representation learning,” in Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2020, pp. 9729–9738.   
+[45] Ting Chen, Simon Kornblith, Kevin Swersky, Mohammad Norouzi, and Geoffrey Hinton, “Big self-supervised models are strong semi-supervised learners,” arXiv preprint arXiv:2006.10029, 2020.   
+[46] Xinlei Chen and Kaiming He, “Exploring simple siamese representation learning,” arXiv preprint arXiv:2011.10566, 2020.   
+[47] Eric Wong and J Zico Kolter, “Provable defenses against adversarial examples via the convex outer adversarial polytope,” arXiv preprint arXiv:1711.00851, 2017.   
+[48] Krishnamurthy Dvijotham, Sven Gowal, Robert Stanforth, Relja Arandjelovic, Brendan O’Donoghue, Jonathan Uesato, and Pushmeet Kohli, “Training verified learners with learned verifiers,” arXiv preprint arXiv:1805.10265, 2018.   
+[49] Chuang Gan, Ting Yao, Kuiyuan Yang, Yi Yang, and Tao Mei, “You lead, we exceed: Laborfree video concept learning by jointly exploiting web videos and images,” in CVPR, 2016, pp. 923–932.   
+[50] Chuang Gan, Chen Sun, Lixin Duan, and Boqing Gong, “Webly-supervised video recognition by mutually voting for relevant web images and web video frames,” in ECCV, 2016, pp. 849–866.   
+[51] Prannay Khosla, Piotr Teterwak, Chen Wang, Aaron Sarna, Yonglong Tian, Phillip Isola, Aaron Maschinot, Ce Liu, and Dilip Krishnan, “Supervised contrastive learning,” arXiv preprint arXiv:2004.11362, 2020.   
+[52] Haohan Wang, Xindi Wu, Zeyi Huang, and Eric P Xing, “High-frequency component helps explain the generalization of convolutional neural networks,” in Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2020, pp. 8684–8694.   
+[53] Zifan Wang, Yilin Yang, Ankit Shrivastava, Varun Rawal, and Zihao Ding, “Towards frequencybased explanation for robust cnn,” arXiv preprint arXiv:2005.03141, 2020.   
+[54] Xueting Yan, Ishan Misra, Abhinav Gupta, Deepti Ghadiyaram, and Dhruv Mahajan, “Clusterfit: Improving generalization of visual representations,” in Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2020, pp. 6509–6518.   
+[55] Laurens Van der Maaten and Geoffrey Hinton, “Visualizing data using t-sne.,” Journal of machine learning research, vol. 9, no. 11, 2008.   
+[56] Anish Athalye, Nicholas Carlini, and David Wagner, “Obfuscated gradients give a false sense of security: Circumventing defenses to adversarial examples,” arXiv preprint arXiv:1802.00420, 2018.   
+[57] Aravindh Mahendran and Andrea Vedaldi, “Visualizing deep convolutional neural networks using natural pre-images,” International Journal of Computer Vision, vol. 120, no. 3, pp. 233–255, 2016.   
+[58] Logan Engstrom, Andrew Ilyas, Shibani Santurkar, Dimitris Tsipras, Brandon Tran, and Aleksander Madry, “Adversarial robustness as a prior for learned representations,” arXiv preprint arXiv:1906.00945, 2019.   
+[59] Simran Kaur, Jeremy Cohen, and Zachary C Lipton, “Are perceptually-aligned gradients a general property of robust classifiers?,” arXiv preprint arXiv:1910.08640, 2019.   
+[60] Hong Liu, Mingsheng Long, Jianmin Wang, and Michael I Jordan, “Towards understanding the transferability of deep representations,” arXiv preprint arXiv:1909.12031, 2019.   
+[61] Hao Li, Zheng Xu, Gavin Taylor, Christoph Studer, and Tom Goldstein, “Visualizing the loss landscape of neural nets,” arXiv preprint arXiv:1712.09913, 2017.   
+[62] Angus Galloway, Anna Golubeva, Thomas Tanay, Medhat Moussa, and Graham W Taylor, “Batch normalization is a cause of adversarial vulnerability,” arXiv preprint arXiv:1905.02161, 2019.   
+[63] Tianyu Pang, Xiao Yang, Yinpeng Dong, Hang Su, and Jun Zhu, “Bag of tricks for adversarial training,” arXiv preprint arXiv:2010.00467, 2020.

parse/train/70kOIgjKhbA/70kOIgjKhbA_content_list.json

@@ -0,0 +1,1128 @@
+[
+    {
+        "type": "text",
+        "text": "When Does Contrastive Learning Preserve Adversarial Robustness from Pretraining to Finetuning? ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Lijie Fan1, Sijia $\\mathbf { L i u ^ { 2 , 3 } }$ , Pin-Yu Chen3, Gaoyuan Zhang3, Chuang Gan3 ",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 Massachusetts Institute of Technology, 2 Michigan State University, 3 MIT-IBM Watson AI Lab, IBM Research lijiefan@mit.edu, liusiji5@msu.edu, {pin-yu.chen,gaoyuan.zhang,chuangg}@ibm.com ",
+        "bbox": [
+            274,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract ",
+        "text_level": 1,
+        "bbox": [
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+            357,
+            535,
+            375
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Contrastive learning (CL) can learn generalizable feature representations and achieve state-of-the-art performance of downstream tasks by finetuning a linear classifier on top of it. However, as adversarial robustness becomes vital in image classification, it remains unclear whether or not CL is able to preserve robustness to downstream tasks. The main challenge is that in the ‘self-supervised pretraining $^ +$ supervised finetuning’ paradigm, adversarial robustness is easily forgotten due to a learning task mismatch from pretraining to finetuning. We call such challenge ‘cross-task robustness transferability’. To address the above problem, in this paper we revisit and advance CL principles through the lens of robustness enhancement. We show that (1) the design of contrastive views matters: High-frequency components of images are beneficial to improving model robustness; (2) Augmenting CL with pseudo-supervision stimulus (e.g., resorting to feature clustering) helps preserve robustness without forgetting. Equipped with our new designs, we propose ADVCL, a novel adversarial contrastive pretraining framework. We show that ADVCL is able to enhance cross-task robustness transferability without loss of model accuracy and finetuning efficiency. With a thorough experimental study, we demonstrate that ADVCL outperforms the state-of-the-art self-supervised robust learning methods across multiple datasets (CIFAR-10, CIFAR-100 and STL-10) and finetuning schemes (linear evaluation and full model finetuning). Code is available at https://github.com/LijieFan/AdvCL. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "1 Introduction ",
+        "text_level": 1,
+        "bbox": [
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+            310,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Image classification has been revolutionized by convolutional neural networks (CNNs). In spite of CNNs’ generalization power, the lack of adversarial robustness has shown to be a main weakness that gives rise to security concerns in high-stakes applications when CNNs are applied, e.g., face recognition, medical image classification, surveillance, and autonomous driving [1–5]. The brittleness of CNNs can be easily manifested by generating tiny input perturbations to completely alter the models’ decision. Such input perturbations and corresponding perturbed inputs are referred to as adversarial perturbations and adversarial examples (or attacks), respectively [6–10]. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "One of the most powerful defensive schemes against adversarial attacks is adversarial training (AT) [11], built upon a two-player game in which an ‘attacker’ crafts input perturbations to maximize the training objective for worst-case robustness, and a ‘defender’ minimizes the maximum loss for an improved robust model against these attacks. However, AT and its many variants using min-max optimization [12–21] were restricted to supervised learning as true labels of training data are required for both supervised classifier and attack generator (that ensures misclassification). The recent work [22–24] demonstrated that with a properly-designed attacker’s objective, AT-type defenses can be generalized to the semi-supervised setting, and showed that the incorporation of additional unlabeled data could further improve adversarial robustness in image classification. Such an extension from supervised to semi-supervised defenses further inspires us to ask whether there exist unsupervised defenses that can eliminate the prerequisite of labeled data but improve model robustness. ",
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+        "type": "text",
+        "text": "",
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+    },
+    {
+        "type": "text",
+        "text": "Some very recent literature [25–29] started tackling the problem of adversarial defense through the lens of self-supervised learning. Examples include augmenting a supervised task with an unsupervised ‘pretext’ task for which ground-truth label is available for ‘free’ [25, 26], or robustifying unsupervised representation learning based only on a pretext task and then finetuning the learned representations over downstream supervised tasks [27–29]. The latter scenario is of primary interest to us as a defense can then be performed at the pretraining stage without needing any label information. Meanwhile, selfsupervised contrastive learning (CL) has been outstandingly successful in the field of representation learning: It can surpass a supervised learning counterpart on downstream image classification tasks in standard accuracy [30–34]. Different from conventional self-supervised learning methods [35], CL, e.g., SimCLR [30], enforces instance discrimination by exploring multiple views of the same data and treating every instance under a specific view as a class of its own [36]. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The most relevant work to ours is [27, 28], which integrated adversarial training with CL. However, the achieved adversarial robustness at downstream tasks largely relies on the use of advanced finetuning techniques, either adversarial full finetuning [27] or adversarial linear finetuning [28]. Different from [27, 28], we ask: ",
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+    {
+        "type": "text",
+        "text": "$( Q )$ How to accomplish robustness enhancement using CL without losing its finetuning efficiency, e.g., via a standard linear finetuner? ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Our work attempts to make a rigorous and comprehensive study on addressing the above question. We find that self-supervised learning (including the state-of-the-art CL) suffers a new robustness challenge that we call ‘crosstask robustness transferability’, which was largely overlooked in the previous work. That is, there exists a task mismatch from pretraining to finetuning (e.g., from CL to supervised classification) so that adversarial robustness is not able to transfer across tasks even if pretraining datasets and finetuning datasets are drawn from the same distribution. Different from supervised/semi-supervised learning, this is a characteristic behavior of selfsupervision when being adapted to robust ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/7f2ea9a79a438faed069f2c9db9cf64dabc61ba859861ba7da0ab921e88b9765.jpg",
+        "image_caption": [
+            "Figure 1: Summary of performance for various robust pretraining methods on CIFAR-10. The covered baseline methods include AP-DPE [26], RoCL [28], ACL [27] and supervised adversarial training (AT) [11]. Upper-right indicates better performance with respect to (w.r.t.) standard accuracy and robust accuracy (under PGD attack with 20 steps and $8 / 2 5 5 \\ell _ { \\infty }$ -norm perturbation strength). Different colors represent different pretraining methods, and different shapes represent different finetuning settings. Circles $\\mathbf { \\eta } ^ { ( \\bullet ) }$ indicates Standard Linear Finetuning (SLF), and Diamonds $( \\bullet )$ indicates Adversarial Full Finetuning (AFF). Our method (ADVCL, red circle/diamond) has the best performance across finetuning settings. Similar improvement could be observed under Auto-Attacks, and we provide the visualization in the appendix. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "learning. As shown in Figure 1, our work advances CL in the adversarial context and the proposed method outperforms all state-of-the-art baseline methods, leading to a substantial improvement in both robust accuracy and standard accuracy using either the lightweight standard linear finetuning or end-to-end adversarial full finetuning. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Contributions Our main contributions are summarized below. ",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "$\\bullet$ We propose ADVCL, a unified adversarial CL framework, and propose to use original adversarial examples and high-frequency data components to create robustness-aware and generalization-aware views of unlabeled data. ",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "$\\pmb { \\varrho }$ We propose to generate proper pseudo-supervision stimulus for ADVCL to improve cross-task robustness transferability. Different from existing self-supervised defenses aided with labeled data [27], we generate pseudo-labels of unlabeled data based on their clustering information. ",
+        "bbox": [
+            176,
+            869,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "$\\otimes$ We conduct a thorough experimental study and show that ADVCL achieves state-of-the-art robust accuracies under both PGD attacks [11] and Auto-Attacks [37] using only standard linear finetuning. For example, in the case of Auto-Attack (the most powerful threat model) with $8 / 2 5 5 ~ \\ell _ { \\infty }$ -norm perturbation strength under ResNet-18, we achieve $3 . 4 4 \\%$ and $3 . 4 5 \\%$ robustness improvement on CIFAR-10 and CIFAR-100 over existing self-supervised methods. We also justify the effectiveness of ADVCL in different attack setups, dataset transferring, model explanation, and loss landscape smoothness. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2 Background & Related Work ",
+        "text_level": 1,
+        "bbox": [
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+            212,
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+            228
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Self-Supervised Learning Early approaches for unsupervised representation learning leverages handcrafted tasks, like prediction rotation [38] and solving the Jigsaw puzzle [39, 40], geometry prediction [41] and Selfie [42]. Recently contrastive learning (CL) [30, 33, 34, 43–45] and its variants [31, 32, 36, 46] have demonstrated superior abilities in learning generalizable features in an unsupervised manner. The main idea behind $\\mathrm { C L }$ is to self-create positive samples of the same image from aggressive viewpoints, and then acquire data representations by maximizing agreement between positives while contrasts with negatives. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In what follows, we elaborate on the formulation of SimCLR [30], one of the most commonly-used CL frameworks, which this paper will focus on. To be concrete, let $\\mathcal { X } = \\{ x _ { 1 } , x _ { 2 } , . . . , x _ { n } \\}$ denote an unlabeled source dataset, SimCLR offers a learned feature encoder $f _ { \\theta }$ to generate expressive deep representations of the data. To train $f _ { \\theta }$ , each input $x \\in \\mathcal { X }$ will be transformed into two views $( \\tau _ { 1 } ( x ) , \\tau _ { 2 } ( x ) )$ and labels them as a positive pair. Here transformation operations $\\tau _ { 1 }$ and $\\tau _ { 2 }$ are randomly sampled from a pre-defined transformation set $\\tau$ , which includes, e.g., random cropping and resizing, color jittering, rotation, and cutout. The positive pair is then fed in the feature encoder $f _ { \\theta }$ with a projection head $g$ to acquire projected features, i.e., $z _ { i } = g \\circ f _ { \\theta } ( \\tau _ { i } ( x ) )$ for $j \\in \\{ 1 , 2 \\}$ . NT-Xent loss (i.e., the normalized temperature-scaled cross-entropy loss) is then applied to optimizing $f _ { \\theta }$ , where the distance of projected positive features $( z _ { 1 } , z _ { 2 } )$ is minimized for each input $x$ . SimCLR follows the ‘self-supervised pretraining $^ +$ supervised finetuning’ paradigm. That is, once $f _ { \\theta }$ is trained, a downstream supervised classification task can be handled by just finetuning a linear classifier $\\phi$ over the fixed encoder $f _ { \\theta }$ , leading to the eventual classification network $\\phi \\circ f _ { \\theta }$ . ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Adversarial Training (AT) Deep neural networks are vulnerable to adversarial attacks. Various approaches have been proposed to enhance the model robustness. Given a classification model $\\theta$ , AT [11] is one of the most powerful robust training methods against adversarial attacks. Different from standard training over normal data $( x , y ) \\in \\mathcal { D }$ (with feature $x$ and label $y$ in dataset $\\mathcal { D }$ ), AT adopts a min-max training recipe, where the worst-case training loss is minimized over the adversarially perturbed data $( x + \\delta , y )$ . Here $\\delta$ denotes the input perturbation variable to be maximized for the worst-case training objective. The supervised $A T$ is then formally given by ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/a64571ebefabc77b78096506cade79891e283492bd8f01ac41ba7a2d2f237a92.jpg",
+        "text": "$$\n\\operatorname* { m i n } _ { \\theta } \\mathbb { E } _ { ( x , y ) \\in D } \\ \\operatorname* { m a x } _ { \\| \\delta \\| _ { \\infty } \\leq \\epsilon } \\ell ( x + \\delta , y ; \\theta ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where $\\ell$ denotes the supervised training objective, e.g., cross-entropy (CE) loss. There have been many variants of AT [19–21, 47–50, 22–25] established for supervised/semi-supervised learning. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Self-supervision enabled AT Several recent works [26–29] started to study how to improve model robustness using self-supervised AT. Their idea is to apply AT (1) to a self-supervised pretraining task, e.g., SimCLR in [27, 28], such that the learned feature encoder $f _ { \\theta }$ renders robust data representations. However, different from our work, the existing ones lack a systematic study on when and how self-supervised robust pretraining can preserve robustness to downstream tasks without sacrificing the efficiency of lightweight finetuning. For example, the prior work [26, 27] suggested adversarial full finetuning, where pretrained model is used as a weight initialization in finetuning downstream tasks. Yet, it requests the finetuner to update all of the weights of the pretrained model, and thus makes the advantage of self-supervised robust pretraining less significant. A more practical scenario is linear finetuning: One freezes the pretrained feature encoder for the downstream task and only partially finetunes a linear prediction head. The work [28] evaluated the performance of linear fintuning but observed a relatively large performance gap between the standard linear finetuning and adversarial linear finetuning; see more comparisons in Figure 1. Therefore, the problem–how to enhance robustness transferability from pretraining to linear finetuning–remains unexplored. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 Problem Statement ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In this section, we present the problem of our interest, together with its setup. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Robust pretraining $^ +$ linear finetuning. We aim to develop robustness enhancement solutions by fully exploiting and exploring the power of CL at the pretraining phase, so that the resulting robust feature representations can seamlessly be used to generate robust predictions of downstream tasks using just a lightweight finetuning scheme. With the aid of AT (1), we formulate the ‘robust pretraining $^ +$ linear finetuning’ problem below: ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/2fe5a144e9853353e2cc9c7d534853d5f1c0eaa42464bd14006a2fec4657ec99.jpg",
+        "text": "$$\n\\begin{array} { r l } & { \\mathrm { P r e t r a i n i n g : ~ } \\operatorname* { m i n } _ { \\theta } \\mathbb { E } _ { x \\in \\mathcal { X } } \\underset { \\| \\delta \\| _ { \\infty } \\leq \\epsilon } { \\operatorname* { m a x } } \\ell _ { \\mathrm { p r e } } ( x + \\delta , x ; \\theta ) } \\\\ & { \\mathrm { F i n e t u n i n g : ~ } \\operatorname* { m i n } _ { \\theta _ { \\mathrm { c } } } \\mathbb { E } _ { ( x , y ) \\in \\mathcal { D } } \\ell _ { \\mathrm { C E } } ( \\phi _ { \\theta _ { \\mathrm { c } } } \\circ f _ { \\theta } ( x ) , y ) , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $\\ell _ { \\mathrm { p r e } }$ denotes a properly-designed robustness- and generalization-aware CL loss (see Sec. 4) given as a function of the adversarial example $( x + \\delta )$ , original example $x$ and feature encoder parameters $\\theta$ . In (2), $\\phi _ { \\theta _ { \\mathrm { c } } } \\circ f _ { \\theta }$ denotes the classifier by equipping the linear prediction head $\\phi _ { \\theta _ { \\mathrm { c } } }$ (with parameters $\\theta _ { \\mathrm { c } }$ to be designed) on top of the fixed feature encoder $f _ { \\theta }$ , and $\\ell _ { \\mathrm { C E } }$ denotes the supervised CE loss over the target dataset $\\mathcal { D }$ . Note that besides the standard linear finetuning (3), one can also modify (3) using the worst-case CE loss for adversarial linear/full finetuning [27, 28]. We do not consider standard full finetuning in the paper since tuning the full network weights with standard cross-entropy loss is not possible for the model to preserve robustness [26]. ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Cross-task robustness transferability. Different from supervised/semi-supervised learning, selfsupervision enables robust pretraining over unlabeled source data. In the meantime, it also imposes a new challenge that we call ‘cross-task robustness transferability’: At the pretraining stage, a feature encoder is learned over a ‘pretext’ task for which ground-truth is available for free, while finetuning is typically carried out on a new downstream task. Spurred by the above, we ask the following questions: ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "• Will CL improve adversarial robustness using just standard linear finetuning? • What are the principles that CL should follow to preserve robustness across tasks? • What are the insights can we acquire from self-supervised robust representation learnin ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4 Proposed Approach: Adversarial Contrastive Learning (ADVCL) ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In this section, we develop a new adversarial CL framework, ADVCL, which includes two main components, robustnessaware view selection and pseudosupervision stimulus generation. In particular, we advance the view selection mechanism by taking into account proper frequencybased data transformations that are beneficial to robust representation learning and pretraining generalization ability. Furthermore, we propose to design and integrate proper supervision stimulus into ADVCL so as to improve the cross-task robustness transferability since robust representations learned from self",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/64439f7f468608e7582a2cfebf1a4bda02c24138dbb68096c8644d0018589fe2.jpg",
+        "image_caption": [
+            "Figure 2: The overall pipeline of ADVCL. It mainly has two ingredients: robustness-aware view selection (orange box) and pseudo-supervision stimulus generation (blue box). The view selection mechanism is advanced by high frequency components, and the supervision stimulus is created by generating pseudo labels for each image through CLUSTERFIT. The pseudo label (in yellow color) can be created in an offline manner and will not increase the computation overhead. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "supervision may lack the class-discriminative ability required for robust predictions on downstream tasks. We provide an overview of ADVCL in Figure 2. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.1 View selection mechanism ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In contrast to standard CL, we propose two additional contrastive views: the adversarial view and the frequency view, respectively. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Multi-view CL loss Prior to defining new views, we first review the NT-Xent loss and its multiview version used in CL. Following notations defined in Sec. 2, the contrastive loss with respect to (w.r.t.) a positive pair $( \\tau _ { 1 } ( x ) , \\tau _ { 2 } ( x ) \\bar { ) }$ of each (unlabeled) data $x$ is given by ",
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+        "type": "equation",
+        "img_path": "images/20d1dee8b46d86c567946021ed37b2f20f0588580be5010312c16f95c7cc423f.jpg",
+        "text": "$$\n\\ell _ { \\mathrm { C L } } ( \\tau _ { 1 } ( x ) , \\tau _ { 2 } ( x ) ) = - \\sum _ { i = 1 } ^ { 2 } \\sum _ { j \\in \\mathcal { P } ( i ) } \\log \\frac { \\exp { \\left( \\sin ( z _ { i } , z _ { j } ) / t \\right) } } { \\sum _ { k \\in \\mathcal { N } ( i ) } \\exp { \\left( \\sin ( z _ { i } , z _ { k } ) / t \\right) } } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where recall that $z _ { i } = g \\circ f ( \\tau _ { i } ( x ) )$ is the projected feature under the ith view, $\\mathcal { P } ( i )$ is the set of positive views except $i$ (e.g., $\\mathcal { P } ( i ) = \\{ 2 \\}$ if $i = 1$ ), $\\mathcal { N } ( i )$ denotes the set of augmented batch data except the point $\\tau _ { i } ( x )$ , the cardinality of $\\mathcal { N } ( i )$ is $( 2 b - 1 )$ (for a data batch of size $b$ under 2 views), $\\sin ( z _ { i 1 } , z _ { i 2 } )$ denotes the cosine similarity between representations from two views of the same data, exp denotes exponential function, $\\mathrm { s i m } ( \\cdot , \\cdot )$ is the cosine similarity between two points, and $t > 0$ is a temperature parameter. The two-view CL objective can be further extend to the multi-view contrastive loss [51] ",
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+    {
+        "type": "equation",
+        "img_path": "images/7a1f63b4907caaf241f984653165a3696f48ca152f3a2946d815336c3f329614.jpg",
+        "text": "$$\n\\ell _ { \\mathrm { C L } } ( \\tau _ { 1 } ( x ) , \\tau _ { 2 } ( x ) , \\dots , \\tau _ { m } ( x ) ) = - \\sum _ { i = 1 } ^ { m } \\sum _ { j \\in \\mathcal { P } ( i ) } \\log \\frac { \\exp { \\left( \\sin ( z _ { i } , z _ { j } ) / t \\right) } } { \\displaystyle \\sum _ { k \\in \\mathcal { N } ( i ) } \\exp { \\left( \\sin ( z _ { i } , z _ { k } ) / t \\right) } } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $\\mathcal { P } ( i ) ~ = ~ [ m ] / \\{ i \\}$ denotes the $m$ positive views except $i$ , $[ m ]$ denotes the integer set $\\{ 1 , 2 , \\ldots , { \\dot { m } } \\}$ , and $\\mathcal { N } ( i )$ , with cardinality $( b m - 1 )$ , denotes the set of $m$ -view augmented $b$ batch samples except the point $\\tau _ { i } ( x )$ . ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Contrastive view from adversarial example Existing methods proposed in [27–29] can be explained based on (4): An adversarial perturbation $\\delta$ w.r.t. each view of a sample $x$ is generated by maximizing the contrastive loss: ",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/fa43e63fb672a71675044f7fbbc89eaedb892d928a5483203a4f55bdaa73453d.jpg",
+        "text": "$$\n\\delta _ { 1 } ^ { * } , \\delta _ { 2 } ^ { * } = \\underset { \\| \\delta _ { i } \\| _ { \\infty } \\leq \\epsilon } { \\mathrm { a r g m a x } } \\ell _ { \\mathrm { C L } } ( \\tau _ { 1 } ( x ) + \\delta _ { 1 } , \\tau _ { 2 } ( x ) + \\delta _ { 2 } ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "A solution to problem (6) eventually yields a paired perturbation view $( \\tau _ { 1 } ( x ) + \\delta _ { 1 } ^ { * } , \\tau _ { 2 } ( x ) + \\delta _ { 2 } ^ { * } )$ . However, the definition of adversarial view (6) used in [27–29] may not be proper. First, standard CL commonly uses aggressive data transformation that treats small portions of images as positive samples of the full image [36]. Despite its benefit to promoting generalization, crafting perturbations over such aggressive data transformations may not be suitable for defending adversarial attacks applied to full images in the adversarial context. Thus, a new adversarial view built upon $x$ rather than $\\tau _ { i } ( x )$ is desired. Second, the contrastive loss (4) is only restricted to two views of the same data. As will be evident later, the multi-view contrastive loss is also needed when taking into account multiple robustness-promoting views. Spurred by above, we define the adversarial view over $x$ , without modifying the existing data augmentations $( \\tau _ { 1 } ( x ) , \\tau _ { 2 } ( x ) )$ . This leads to the following adversarial perturbation generator by maximizing a 3-view contrastive loss ",
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+    {
+        "type": "equation",
+        "img_path": "images/fbe8e89e235f2d02abb0d739d454286969d78a3e2c732c93fac04180feff3648.jpg",
+        "text": "$$\n\\delta ^ { * } = \\underset { \\| \\delta \\| \\leq \\epsilon } { \\mathrm { a r g m a x } } \\ell _ { \\mathrm { C L } } ( \\tau _ { 1 } ( x ) , \\tau _ { 2 } ( x ) , x + \\delta ) ,\n$$",
+        "text_format": "latex",
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+    },
+    {
+        "type": "text",
+        "text": "where $x + \\delta ^ { * }$ is regarded as the third view of $x$ ",
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+        "type": "text",
+        "text": "Contrastive view from high-frequency component Next, we use the high-frequency component (HFC) of data as another additional contrastive view. The rationale arises from the facts that 1) learning over HFC of data is a main cause of achieving superior generalization ability [52] and 2) an adversary typically concentrates on HFC when manipulating an example to fool model’s decision [53]. Let $\\mathcal { F }$ and $\\scriptstyle { \\dot { \\mathcal { F } } } ^ { - 1 }$ denote Fourier transformation and its inverse. An input image $x$ can then be decomposed into its HFC $x _ { \\mathrm { h } }$ and low-frequency component (LFC) $x _ { \\mathrm { l } }$ : ",
+        "bbox": [
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+    {
+        "type": "equation",
+        "img_path": "images/60a1864cb53c0792c047356dde3cf478ee8b2d3ce4c09918285db4697d8952f4.jpg",
+        "text": "$$\nx _ { \\mathrm { h } } = \\mathcal { F } ^ { - 1 } ( q _ { \\mathrm { h } } ) , \\quad x _ { \\mathrm { l } } = \\mathcal { F } ^ { - 1 } ( q _ { \\mathrm { l } } ) , \\quad [ q _ { \\mathrm { h } } , q _ { \\mathrm { l } } ] = \\mathcal { F } ( x ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In (8), the distinction between $q _ { \\mathrm { h } }$ and $q _ { \\mathrm { l } }$ is made by a hard thresholding operation. Let $q ( i , j )$ denote the $( i , j )$ th element of $\\mathcal { F } ( x )$ , and $c = ( c _ { 1 } , c _ { 2 } )$ denote the centriod of the frequency spectrum. The components $q _ { \\mathrm { l } }$ and $q _ { \\mathrm { h } }$ in (8) are then generated by filtering out values according to the distance from c: $q _ { h } ( i , j ) = \\mathbb { 1 } _ { [ d ( ( i , j ) , ( c _ { 1 } , c _ { 2 } ) ) \\geq r ] } \\cdot q ( i , j )$ , and $q _ { l } ( i , j ) = \\mathbb { 1 } _ { [ d ( ( i , j ) , ( c _ { 1 } , c _ { 2 } ) ) \\leq r ] } \\cdot q ( i , j )$ , where $d ( \\cdot , \\cdot )$ is the Euclidian distance between two spatial coordinates, $r$ is a pre-defined distance threshold $r = 8$ in all our experiments), and $\\mathbb { 1 } _ { [ . ] } \\in \\{ 0 , 1 \\}$ is an indicator function which equals to 1 if the condition within $[ \\cdot ]$ is met and 0 otherwise. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Robustness-aware contrastive learning objective By incorporating the adversarial perturbation $\\delta$ and disentangling HFC $x _ { \\mathrm { h } }$ from the original data $x$ , we obtain a four-view contrastive loss (5) defined over $( \\tau _ { 1 } ( x ) , \\tau _ { 2 } ( x ) , x + \\delta , x _ { \\mathrm { h } } )$ , ",
+        "bbox": [
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+    {
+        "type": "equation",
+        "img_path": "images/6b4aa42ccf8d8f672c098d47d9b0ab2782eb9db01831952eb5176e2aa70c1313.jpg",
+        "text": "$$\n\\ell _ { \\mathrm { C L } } ^ { \\mathrm { a d v } } ( \\theta ; \\mathcal { X } ) : = \\mathbb { E } _ { x \\in \\mathcal { X } } \\operatorname* { m a x } _ { \\| \\delta \\| _ { \\infty } \\leq \\epsilon } \\ell _ { \\mathrm { C L } } ( \\tau _ { 1 } ( x ) , \\tau _ { 2 } ( x ) , x + \\delta , x _ { \\mathrm { h } } ; \\theta ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            299,
+            136,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where recall that $\\mathcal { X }$ denotes the unlabeled dataset, $\\epsilon > 0$ is a perturbation tolerance during training, and for clarity, the four-view contrastive loss (5) is explicitly expressed as a function of model parameters $\\theta$ . As will be evident latter, the eventual learning objective ADVCL will be built upon (9). ",
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+    {
+        "type": "text",
+        "text": "4.2 Supervision stimulus generation: ADVCL empowered by CLUSTERFIT ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "On top of (9), we further improve the robustness transferability of learned representations by generating a proper supervision stimulus. Our rationale is that robust representation could lack the class-discriminative power required by robust classification as the former is acquired by optimizing an unsupervised contrastive loss while the latter is achieved by a supervised cross-entropy CE loss. However, there is no knowledge about supervised data during pretraining. In order to improve crosstask robustness transferability but without calling for supervision, we take advantage of CLUSTERFIT [54], a pseudo-label generation method used in representation learning. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "To be more concrete, let $f _ { \\mathrm { p r e } }$ denote a pretrained representation network that can generate latent features of unlabeled data. Note that $f _ { \\mathrm { p r e } }$ can be set available beforehand and trained over either supervised or unsupervised dataset $\\mathcal { D } _ { \\mathrm { p r e } }$ , e.g., ImageNet using using CL in experiments. Given (normalized) pretrained data representations $\\{ f _ { \\mathrm { p r e } } ( x ) \\} _ { x \\in \\mathcal { X } }$ , CLUSTERFIT uses $K$ -means clustering to find $K$ data clusters of $\\mathcal { X }$ , and maps a cluster index $c$ to a pseudo-label, resulting in the pseudolabeled dataset $\\{ ( x , c ) \\in \\hat { \\mathcal { X } } \\}$ . By integrating CLUSTERFIT with (9), the eventual training objective of ADVCL is then formed by ",
+        "bbox": [
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+        "page_idx": 5
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+    {
+        "type": "equation",
+        "img_path": "images/dd364900f0f501c0d32b19fe01e5ad6eb3d60e62daae7a75d0347bfba52e8c65.jpg",
+        "text": "$$\n\\operatorname* { m i n } _ { \\theta } \\ \\ell _ { \\mathrm { { C L } } } ^ { \\mathrm { a d v } } ( \\theta ; \\mathcal { X } ) + \\lambda \\operatorname* { m i n } _ { \\theta , \\theta _ { \\mathrm { c } } } \\ \\mathbb { E } _ { ( x , c ) \\in \\hat { \\mathcal { X } } } \\operatorname* { m a x } _ { \\| \\delta _ { c e } \\| _ { \\infty } \\leq \\epsilon } \\ell _ { \\mathrm { C E } } ( \\phi _ { \\theta _ { \\mathrm { c } } } \\circ f _ { \\theta } ( x + \\delta _ { c e } ) , c ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Pseudo-classification enabled AT regularization ",
+        "bbox": [
+            478,
+            470,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where $\\hat { \\mathcal X }$ denotes the pseudo-labeled dataset of $\\mathcal { X }$ , $\\phi _ { \\theta _ { \\mathrm { c } } }$ denotes a prediction head over $f _ { \\theta }$ , and $\\lambda > 0$ is a regularization parameter that strikes a balance between adversarial contrastive training and pseudo-label stimulated AT. When the number of clusters $K$ is not known a priori, we extend (10) to an ensemble version over $n$ choices of cluster numbers $\\{ K _ { 1 } , \\ldots , K _ { n } \\}$ . Here each cluster number $K _ { i }$ is paired with a unique linear classifier $\\phi _ { i }$ to obtain the supervised prediction $\\phi _ { i } \\circ f$ (using cluster labels). The ensemble CE loss, given by the average of $n$ individual losses, is then used in (10). Our experiments show that the ensemble version usually leads to better generalization ability. ",
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+    {
+        "type": "text",
+        "text": "5 Experiments ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this section, we demonstrate the effectiveness of our proposed ADVCL from the following aspects: (1) Quantitative results, including cross-task robustness transferability, cross-dataset robustness transferability, and robustness against PGD attacks [11] and Auto-Attacks [37]; (2) Qualitative results, including representation t-SNE [55], feature inversion map visualization, and geometry of loss landscape; (3) Ablation studies of ADVCL, including finetuning schemes, view selection choices, and supervision stimulus variations. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Experiment setup We consider three robustness evaluation metrics: (1) Auto-attack accuracy (AA), namely, classification accuracy over adversarially perturbed images via Auto-Attacks; (2) Robust accuracy (RA), namely, classification accuracy over adversarially perturbed images via PGD attacks; and (3) Standard accuracy (SA), namely, standard classification accuracy over benign images without perturbations. We use ResNet-18 for the encoder architecture of $f _ { \\theta }$ in CL. Unless specified otherwise, we use 5-step $\\ell _ { \\infty }$ projected gradient descent (PGD) with $\\epsilon = 8 / 2 5 5$ to generate perturbations during pretraining, and use Auto-Attack and 20-step $\\ell _ { \\infty }$ PGD with $\\epsilon = 8 / 2 5 5$ to generate perturbations in computing AA and RA at test time. We will compare ADVCL with the CL-based adversarial pretraining baselines , ACL [27], RoCL [28], (non-CL) self-supervised adversarial learning baseline AP-DPE [26] and the supervised AT baseline [11]. ",
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+    {
+        "type": "text",
+        "text": "5.1 Quantitative Results ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Overall performance from pretraining to finetuning (across tasks) In Table 1, we evaluate the robustness of a classifier (ResNet-18) finetuned over robust representations learned by different supervised/self-supervised pretraining approaches over CIFAR-10 and CIFAR-100. We focus on two representative finetuning schemes: the simplest standard linear finetuning (SLF) and the end-to-end adversarial full finetuning (AFF). As we can see, the proposed ADVCL method yields a substantial improvement over almost all baseline methods. Moreover, ADVCL improves robustness and standard accuracy simultaneously. ",
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+    {
+        "type": "table",
+        "img_path": "images/1e0451dacbdc1fe4fa73974be61b2d6197817679f46f22c918b373eb70381e92.jpg",
+        "table_caption": [
+            "Table 1: Cross-task performance of ADVCL (in dark gray color), compared with supervised (in white color) and self-supervised (in light gray color) baselines, in terms of AA, RA and SA on CIFAR-10 with ResNet-18. The pretrained models are evaluated under the standard linear finetuning (SLF) setting and the adversarial full finetuning (AFF) setting. The top performance is highlighted in bold. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Pretraining Method</td><td rowspan=\"2\">Finetuning Method</td><td colspan=\"3\">CIFAR-10</td><td colspan=\"3\">CIFAR-100</td></tr><tr><td>AA(%)</td><td>RA(%)</td><td>SA(%)</td><td>AA(%)</td><td>RA(%)</td><td>SA(%)</td></tr><tr><td>Supervised AP-DPE[26]</td><td rowspan=\"4\">Standard linear finetuning</td><td>42.22</td><td>44.4</td><td>79.77</td><td>19.53</td><td>23.41</td><td>50.53</td></tr><tr><td>RoCL[28]</td><td>16.07</td><td>18.22</td><td>78.30</td><td>4.17</td><td>6.23</td><td>47.91</td></tr><tr><td></td><td>28.38</td><td>39.54</td><td>79.90</td><td>8.66</td><td>18.79</td><td>49.53</td></tr><tr><td>ACL[27] AdvCL (ours)</td><td>39.13</td><td>42.87</td><td>77.88</td><td>16.33</td><td>20.97</td><td>47.51</td></tr><tr><td></td><td rowspan=\"4\">Adversarial full</td><td> 42.57</td><td> 50.45</td><td>80.85</td><td>19.78</td><td>27.67</td><td>48.34</td></tr><tr><td>Supervised</td><td>46.19</td><td>49.89</td><td>79.86</td><td>21.61</td><td>25.86</td><td>52.22</td></tr><tr><td>AP-DPE[26]</td><td>48.13</td><td>51.52</td><td>81.19</td><td>22.53</td><td>26.89</td><td>55.27</td></tr><tr><td>RoCL[28]</td><td>47.88</td><td>51.35</td><td>81.01</td><td>22.38</td><td>27.49</td><td>55.10</td></tr><tr><td>ACL[27]</td><td rowspan=\"3\">finetuning (AFF)</td><td>49.27</td><td> 52.82</td><td>82.19</td><td>23.63</td><td>29.38</td><td>56.61</td></tr><tr><td> ADvCL (ours)</td><td>49.77</td><td> 52.77</td><td>83.62</td><td>24.72</td><td>28.73</td><td>56.77</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></table>",
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+    {
+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "Robustness transferability across datasets In Table 2, we next evaluate the robustness transferability across different datasets, where $A $ $B$ denotes the transferability from pretraining on dataset $A$ to finetuning on another dataset $B \\left( \\neq A \\right)$ of representations learned by ADVCL. Here the pretraining setup is consistent with Table 1. We observe that ADVCL yields ",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/10fcb34127e5aa5e0f1a6217554e78818df8c8afa4b3a70b7808328917cefc9a.jpg",
+        "table_caption": [
+            "Table 2: Cross-dataset performance of ADVCL (dark gray color), compared with supervised (white color) and self-supervised (light gray) baselines, in AA, RA, SA, on STL-10 with ResNet-18. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">一 Fine- tuning</td><td colspan=\"3\">CIFAR-10→STL-10</td><td colspan=\"3\">CIFAR-100→STL-10</td></tr><tr><td>AA(%)</td><td>RA(%)</td><td>SA(%)</td><td>AA(%)</td><td>RA(%)</td><td>SA(%)</td></tr><tr><td>Supervised</td><td rowspan=\"4\">SLF</td><td>22.26</td><td>30.45</td><td>54.70</td><td>19.54</td><td>23.63</td><td>51.11</td></tr><tr><td>RoCL[28]</td><td>18.65</td><td>28.18</td><td>54.56</td><td>12.39</td><td>21.93</td><td>47.86</td></tr><tr><td>ACL[27]</td><td>25.29</td><td>31.80</td><td>55.81</td><td>21.75</td><td>26.32</td><td>45.91</td></tr><tr><td> ADvCL (ours)</td><td>25.74</td><td>35.80</td><td>63.73</td><td>20.86</td><td>30.35</td><td>50.71</td></tr><tr><td>Supervised</td><td rowspan=\"4\">AFF</td><td>33.10</td><td>36.7</td><td>62.78</td><td>29.18</td><td>32.43</td><td>55.85</td></tr><tr><td>RoCL[28]</td><td>29.40</td><td>34.65</td><td>61.75</td><td>27.55</td><td>31.38</td><td>57.83</td></tr><tr><td>ACL[27]</td><td>32.50</td><td>35.93</td><td>62.65</td><td>28.68</td><td>32.41</td><td>57.16</td></tr><tr><td>ADvCL (ours)</td><td>34.70</td><td>37.78</td><td>63.52</td><td>30.51</td><td>33.70</td><td>61.56</td></tr></table>",
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+        "type": "text",
+        "text": "better robustness as well as standard accuracy than almost all baseline approaches under both SLF and AFF finetuning settings. In the case of CIFAR- $1 0 0  \\mathrm { S T L } \\mathrm { - } 1 0$ , although ADVCL yields $0 . 8 9 \\%$ AA drop compared to ACL [27], it yields a much better SA with $4 . 8 \\%$ improvement. ",
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+    {
+        "type": "text",
+        "text": "Robustness evaluation vs. attack strength It was shown in [56] that an adversarial defense that causes obfuscated gradients results in a false sense of model robustness. The issue of obfuscated gradients typically comes with two ‘side effects’: (a) The success rate of PGD attack ceases to be improved as the $\\ell _ { \\infty }$ -norm perturbation radius $\\epsilon$ increases; (b) A larger number of PGD steps fails to generate stronger adversarial examples. Spurred by ",
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+        "image_caption": [
+            "Figure 3: RA of ADVCL and baseline approaches under various PGD attacks. SLF is applied to the pretrained model. "
+        ],
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+        "type": "text",
+        "text": "the above, Figure 3 shows the finetuning performance of ADVCL (using SLF) as a function of the perturbation size $\\epsilon$ and the PGD step number. As we can see, ADVCL is consistently more robust than the baselines at all different PGD settings for a significant margin. ",
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+        "text": "5.2 Qualitative Results ",
+        "text_level": 1,
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+        "text": "Class discrimination of learned representations To further demonstrate the efficacy of ADVCL, Figure 4 visualizes the representations learned by self-supervision using t-SNE [55] on CIFAR-10. We color each point using its ground-truth label. The results show representations learned by ADVCL have a much clearer class boundary than those learned with baselines. This indicates that ADVCL makes an adversary difficult to successfully perturb an image, leading to a more robust prediction. ",
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+        "image_caption": [
+            "Figure 4: t-SNE visualization of representations learned with different self-supervised pretraining approaches. Our ADVCL gives a much clearer separation among classes than baseline approaches. "
+        ],
+        "image_footnote": [],
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+        "type": "text",
+        "text": "Visual interpretability of learned representations Furthermore, we demonstrate the advantage of our proposals from the perspective of model explanation, characterized by feature inversion map (FIM) [57] of internal neurons’ response. The work [18, 58, 59] showed that model robustness offered by supervised AT and its variants enforces hidden neurons to learn perceptuallyaligned data features through the lens of FIM. However, it remains unclear whether or not selfsupervised robust pretraining is able to render explainable internal response. Following [57, 58], we acquire FIM of the ith component of representation vector by solving the optimization problem $\\begin{array} { r } { x _ { \\mathrm { F I M } } = \\operatorname* { m i n } _ { \\Delta } [ f _ { \\theta } ( x _ { 0 } + \\Delta ) ] _ { i } } \\end{array}$ , where $x _ { 0 }$ is a randomly selected seed image, and $[ \\cdot ] _ { i }$ denotes the ith coordinate of a vector. Figure 5 shows that ",
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+        "image_caption": [
+            "Figure 5: FIM visualization of neuron 502 under CIFAR-10 using different robust training methods. Column 1 contains different seed images to generate FIM. Columns 2-5 are FIMs using models trained with different approaches. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "compared to other approaches, more similar texture-aligned features can be acquired from a neuron’s feature representation of the network trained with our method regardless of the choice of seed images. ",
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+        "type": "text",
+        "text": "Flatter loss landscape implies better transferability It has been shown in [60] that the flatness of loss landscape is a good indicator for superb transferability in the pretraining $^ +$ finetuning paradigm. Motivated by that, Figure 6 presents the adversarial loss landscape of ADVCL and other self-supervised pretraining approaches under SLF, where the loss landscape is drawn using the method in [61]. Note that instead of standard CE loss, we visualize the adversarial loss w.r.t. model weights. As we can see, the loss for ADVCL has a much flatter landscape around the local optima, whereas the losses for the other approaches change more rapidly. This justifies that our proposal has a better robustness transferability than baseline approaches. ",
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+    {
+        "type": "image",
+        "img_path": "images/d0c6b500d5ca6e86fad66f9d6e7d503ff4fdba67230a3e948a63d4ef8b39f6a5.jpg",
+        "image_caption": [
+            "Figure 6: Visualization of adversarial loss landscape w.r.t. model weights using different self-supervised pretraining methods. ADVCL gives a much flatter landscape than the other baselines. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "table",
+        "img_path": "images/2270ee83ea9b22dae59c045461805c97618f71c6f7c22e1c196cca9457ac6f12.jpg",
+        "table_caption": [
+            "Table 3: Performance (RA and SA) of ADVCL (in dark gray color) and baseline approaches on CIFAR-10, under different linear finetuning strategies: SLF and adversarial linear finetuning (ALF). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=3 colspan=3>SLFMethodRA(%) SA(%)</td><td></td><td></td></tr><tr><td rowspan=1 colspan=2>SLF</td><td rowspan=1 colspan=2>ALF</td></tr><tr><td rowspan=1 colspan=1>RA(%)</td><td rowspan=1 colspan=1>SA(%)</td><td rowspan=1 colspan=1>RA(%)</td><td rowspan=1 colspan=1>SA(%)</td></tr><tr><td rowspan=1 colspan=1>Supervised</td><td rowspan=1 colspan=1>44.40</td><td rowspan=1 colspan=1>79.77</td><td rowspan=1 colspan=1>46.75</td><td rowspan=1 colspan=1>79.06</td></tr><tr><td rowspan=1 colspan=1>RoCL[28]ACL[27]</td><td rowspan=1 colspan=1>39.5442.87</td><td rowspan=1 colspan=1>79.9077.88</td><td rowspan=1 colspan=1>43.1145.40</td><td rowspan=1 colspan=1>77.3377.71</td></tr><tr><td rowspan=1 colspan=1>ADvCL(ours)</td><td rowspan=1 colspan=1>50.45</td><td rowspan=1 colspan=1>80.85</td><td rowspan=1 colspan=1>52.01</td><td rowspan=1 colspan=1>79.39</td></tr></table>",
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+    {
+        "type": "table",
+        "img_path": "images/b5340723d71473527bf9fba21691e20020aeee56769382788b6693ff41823eed.jpg",
+        "table_caption": [
+            "Table 4: Performance (RA and SA) of ADVCL using different contrastive views setups. ResNet-18 is the backbone network, CIFAR-10 is the dataset, and SLF is used for classification. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Contrastive Views</td><td>RA(%)</td><td>SA(%)</td></tr><tr><td>T1(x）+01,T2(x） T1(x)+δ1,T2(x）+δ2</td><td>42.12 42.48</td><td>77.07 73.12</td></tr><tr><td>T1(x）+δ1,T2(x）+δ,T1(x）,T2(x）</td><td>43.51</td><td>74.22</td></tr><tr><td>x+δ,T1(x）,T2(x）</td><td>50.19</td><td>80.17</td></tr><tr><td>x +δ,T1(x),2(x）,x1</td><td>49.51</td><td>79.83</td></tr><tr><td>x+δ,T1(x),T2(x),x1,xh</td><td>50.03</td><td>80.14</td></tr><tr><td>x +δ,T1(x),T2(x),xh</td><td> 50.45</td><td>80.85</td></tr></table>",
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+    {
+        "type": "table",
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+        "table_caption": [
+            "Table 5: Performance (RA and SA) of ADVCL using various pretrained models $f _ { \\mathrm { p r e } }$ and cluster numbers $K$ in CLUSTERFIT, as well as the baseline w/o using CLUSTERFIT. The setup of $f _ { \\mathrm { p r e } }$ is specified by the training method (supervised training or SimCLR) and training dataset (ImageNet or CIFAR-10). ADVCL is implemented using unlabeled data from CIFAR-10 under ResNet-18, together with SLF over the acquired feature encoder for supervised CIFAR-10 classification. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">fpre setup: (dataset, training)</td><td rowspan=\"2\">Cluster number K</td><td rowspan=\"2\">RA(%)</td><td rowspan=\"2\">SA (%)</td></tr><tr><td></td></tr><tr><td>N/A</td><td>W/o CLUSTERFIT</td><td>48.89</td><td>77.73 80.34</td></tr><tr><td rowspan=\"2\">(CIFAR-10, SimCLR)</td><td>10 100</td><td>50.10 49.21</td><td>79.52</td></tr><tr><td></td><td></td><td></td></tr><tr><td rowspan=\"2\">(ImageNet,supervised)</td><td>10 100</td><td>50.16 49.27</td><td>78.27 78.08</td></tr><tr><td></td><td></td><td></td></tr><tr><td rowspan=\"6\">(ImageNet, SimCLR)</td><td>2</td><td>50.09</td><td>79.72</td></tr><tr><td>10</td><td>50.12</td><td>79.93</td></tr><tr><td>50</td><td>49.27</td><td>79.55</td></tr><tr><td>100</td><td>49.16</td><td>79.07</td></tr><tr><td>500</td><td>49.03</td><td>78.96</td></tr><tr><td>Ensemble</td><td>50.45</td><td>80.85</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "5.3 Ablation studies ",
+        "text_level": 1,
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+        "text": "Linear finetuning types We first study the robustness difference when different linear finetuning strategies: Standard linear finetuning (SLF) and Adversarial linear finetuning (ALF) are applied. Table 3 shows the performance of models trained with different pretraining methods. As we can see, our ADVCL achieves the best performance under both linear finetuning settings and outperforms baseline approaches in a large margin. We also note the performance gap between SLF and ALF induced by our proposal ADVCL is much smaller than other approaches, and ADVCL with SLF achieves much better performance than baseline approaches with ALF. This indicates that the representations learned by ADVCL is already sufficient to yield satisfactory robustness. ",
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+    {
+        "type": "text",
+        "text": "View selection setup We illustrate how different choices of contrastive views influence the robustness performance of ADVCL in Table 4. The first 4 rows study the effect of different types of adversarial examples in contrastive views, and our proposed 3-view contrastive loss (7) significantly outperforms the other baselines, as shown in row 4. The rows in gray show the performance of further exploring different image frequency components (8) as different contrastive views. It is clear that the use of HFC leads to the best overall performance, as shown in the last row. ",
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+        "type": "text",
+        "text": "Supervision stimulus setup We further study the performance of ADVCL using different supervision stimulus. Specifically, we vary the pretrained model for $f _ { \\mathrm { p r e } }$ and pseudo cluster number $K$ when training ADVCL and summarize the results in Table 5. The results demonstrate that adding the supervision stimulus could boost the performance of ADVCL. We also observe that the best result comes from $f _ { \\mathrm { p r e } }$ pretrained on Imagenet using SimCLR. This is because such representations could generalize better. Moreover, the ensemble scheme over pseudo label categories $K \\in \\{ 2 , 1 0 , 5 0 , 1 0 \\bar { 0 } , 5 0 0 \\}$ yields better results than using a single number of clusters. The ensemble scheme also makes ADVCL less sensitive to the actual number of labels for the training dataset. ",
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+        "type": "text",
+        "text": "6 Conclusion ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In this paper, we study the good practices in making contrastive learning robust to adversarial examples. We show that adding perturbations to original images and high-frequency components are two beneficial factors. We further show that proper supervision stimulus could improve model robustness. Our proposed approaches can achieve state-of-the-art robust accuracy as well as standard accuracy using just standard linear finetuning. Extensive experiments involving quantitative and qualitative analysis have also been made not only to demonstrate the effectiveness of our proposals but also to rationalize why it yields superior performance. Future works could be done to improve the scalability of our proposed self-supervised pretraining approach to very large datasets and models to further boost robust transferabilty across datasets. ",
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+        "text": "References   \n[1] Fatemeh Vakhshiteh, Raghavendra Ramachandra, and Ahmad Nickabadi, “Threat of adversarial attacks on face recognition: A comprehensive survey,” arXiv preprint arXiv:2007.11709, 2020.   \n[2] Xingjun Ma, Yuhao Niu, Lin Gu, Yisen Wang, Yitian Zhao, James Bailey, and Feng Lu, “Understanding adversarial attacks on deep learning based medical image analysis systems,” Pattern Recognition, vol. 110, pp. 107332, 2021.   \n[3] Kaidi Xu, Gaoyuan Zhang, Sijia Liu, Quanfu Fan, Mengshu Sun, Hongge Chen, Pin-Yu Chen, Yanzhi Wang, and Xue Lin, “Adversarial t-shirt! evading person detectors in a physical world,” in European Conference on Computer Vision. Springer, 2020, pp. 665–681.   \n[4] Ji Lin, Chuang Gan, and Song Han, “Defensive quantization: When efficiency meets robustness,” ICLR, 2019.   \n[5] Yulong Cao, Chaowei Xiao, Dawei Yang, Jing Fang, Ruigang Yang, Mingyan Liu, and Bo Li, “Adversarial objects against lidar-based autonomous driving systems,” arXiv preprint arXiv:1907.05418, 2019.   \n[6] Ian Goodfellow, Jonathon Shlens, and Christian Szegedy, “Explaining and harnessing adversarial examples,” International Conference on Learning Representations, vol. arXiv preprint arXiv:1412.6572, 2015.   \n[7] Nicholas Carlini and David Wagner, “Towards evaluating the robustness of neural networks,” in Security and Privacy (SP), 2017 IEEE Symposium on. IEEE, 2017, pp. 39–57.   \n[8] Nicolas Papernot, Patrick McDaniel, Somesh Jha, Matt Fredrikson, Z Berkay Celik, and Ananthram Swami, “The limitations of deep learning in adversarial settings,” in Security and Privacy (EuroS&P), 2016 IEEE European Symposium on. IEEE, 2016, pp. 372–387.   \n[9] Pin-Yu Chen, Yash Sharma, Huan Zhang, Jinfeng Yi, and Cho-Jui Hsieh, “EAD: elasticnet attacks to deep neural networks via adversarial examples,” in Proceedings of the AAAI Conference on Artificial Intelligence, 2018, pp. 10–17.   \n[10] Kaidi Xu, Sijia Liu, Pu Zhao, Pin-Yu Chen, Huan Zhang, Quanfu Fan, Deniz Erdogmus, Yanzhi Wang, and Xue Lin, “Structured adversarial attack: Towards general implementation and better interpretability,” in International Conference on Learning Representations, 2019.   \n[11] Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, and Adrian Vladu, “Towards deep learning models resistant to adversarial attacks,” 2018 ICLR, vol. arXiv preprint arXiv:1706.06083, 2018.   \n[12] Harini Kannan, Alexey Kurakin, and Ian Goodfellow, “Adversarial logit pairing,” 2018.   \n[13] Andrew Slavin Ross and Finale Doshi-Velez, “Improving the adversarial robustness and interpretability of deep neural networks by regularizing their input gradients,” in Thirty-second AAAI conference on artificial intelligence, 2018.   \n[14] Jingkang Wang, Tianyun Zhang, Sijia Liu, Pin-Yu Chen, Jiacen Xu, Makan Fardad, and Bo Li, “Towards a unified min-max framework for adversarial exploration and robustness,” arXiv preprint arXiv:1906.03563, 2019.   \n[15] Seyed-Mohsen Moosavi-Dezfooli, Alhussein Fawzi, Jonathan Uesato, and Pascal Frossard, “Robustness via curvature regularization, and vice versa,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2019, pp. 9078–9086.   \n[16] Yisen Wang, Xingjun Ma, James Bailey, Jinfeng Yi, Bowen Zhou, and Quanquan Gu, “On the convergence and robustness of adversarial training,” in International Conference on Machine Learning, 2019, pp. 6586–6595.   \n[17] Jiefeng Chen, Xi Wu, Vaibhav Rastogi, Yingyu Liang, and Somesh Jha, “Robust attribution regularization,” in Advances in Neural Information Processing Systems, 2019, pp. 14300–14310.   \n[18] Akhilan Boopathy, Sijia Liu, Gaoyuan Zhang, Cynthia Liu, Pin-Yu Chen, Shiyu Chang, and Luca Daniel, “Proper network interpretability helps adversarial robustness in classification,” in ICML, 2020.   \n[19] Ali Shafahi, Mahyar Najibi, Mohammad Amin Ghiasi, Zheng Xu, John Dickerson, Christoph Studer, Larry S Davis, Gavin Taylor, and Tom Goldstein, “Adversarial training for free!,” in Advances in Neural Information Processing Systems, 2019, pp. 3353–3364.   \n[20] Dinghuai Zhang, Tianyuan Zhang, Yiping Lu, Zhanxing Zhu, and Bin Dong, “You only propagate once: Accelerating adversarial training via maximal principle,” arXiv preprint arXiv:1905.00877, 2019.   \n[21] Eric Wong, Leslie Rice, and J. Zico Kolter, “Fast is better than free: Revisiting adversarial training,” in International Conference on Learning Representations, 2020.   \n[22] Hongyang Zhang, Yaodong Yu, Jiantao Jiao, Eric P Xing, Laurent El Ghaoui, and Michael I Jordan, “Theoretically principled trade-off between robustness and accuracy,” International Conference on Machine Learning, 2019.   \n[23] Yair Carmon, Aditi Raghunathan, Ludwig Schmidt, Percy Liang, and John C Duchi, “Unlabeled data improves adversarial robustness,” arXiv preprint arXiv:1905.13736, 2019.   \n[24] Runtian Zhai, Tianle Cai, Di He, Chen Dan, Kun He, John Hopcroft, and Liwei Wang, “Adversarially robust generalization just requires more unlabeled data,” arXiv preprint arXiv:1906.00555, 2019.   \n[25] Dan Hendrycks, Mantas Mazeika, Saurav Kadavath, and Dawn Song, “Using self-supervised learning can improve model robustness and uncertainty,” arXiv preprint arXiv:1906.12340, 2019.   \n[26] Tianlong Chen, Sijia Liu, Shiyu Chang, Yu Cheng, Lisa Amini, and Zhangyang Wang, “Adversarial robustness: From self-supervised pre-training to fine-tuning,” in Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2020, pp. 699–708.   \n[27] Ziyu Jiang, Tianlong Chen, Ting Chen, and Zhangyang Wang, “Robust pre-training by adversarial contrastive learning,” arXiv preprint arXiv:2010.13337, 2020.   \n[28] Minseon Kim, Jihoon Tack, and Sung Ju Hwang, “Adversarial self-supervised contrastive learning,” arXiv preprint arXiv:2006.07589, 2020.   \n[29] Sven Gowal, Po-Sen Huang, Aaron van den Oord, Timothy Mann, and Pushmeet Kohli, “Self-supervised adversarial robustness for the low-label, high-data regime,” in International Conference on Learning Representations, 2021.   \n[30] Ting Chen, Simon Kornblith, Mohammad Norouzi, and Geoffrey Hinton, “A simple framework for contrastive learning of visual representations,” in International conference on machine learning. PMLR, 2020, pp. 1597–1607.   \n[31] Jean-Bastien Grill, Florian Strub, Florent Altche, Corentin Tallec, Pierre H Richemond, Elena ´ Buchatskaya, Carl Doersch, Bernardo Avila Pires, Zhaohan Daniel Guo, Mohammad Gheshlaghi Azar, et al., “Bootstrap your own latent: A new approach to self-supervised learning,” arXiv preprint arXiv:2006.07733, 2020.   \n[32] Yonglong Tian, Chen Sun, Ben Poole, Dilip Krishnan, Cordelia Schmid, and Phillip Isola, “What makes for good views for contrastive learning,” arXiv preprint arXiv:2005.10243, 2020.   \n[33] Tongzhou Wang and Phillip Isola, “Understanding contrastive representation learning through alignment and uniformity on the hypersphere,” in International Conference on Machine Learning. PMLR, 2020, pp. 9929–9939.   \n[34] Xinlei Chen, Haoqi Fan, Ross Girshick, and Kaiming He, “Improved baselines with momentum contrastive learning,” arXiv preprint arXiv:2003.04297, 2020.   \n[35] Priya Goyal, Dhruv Mahajan, Abhinav Gupta, and Ishan Misra, “Scaling and benchmarking self-supervised visual representation learning,” in Proceedings of the IEEE/CVF International Conference on Computer Vision, 2019, pp. 6391–6400.   \n[36] Senthil Purushwalkam and Abhinav Gupta, “Demystifying contrastive self-supervised learning: Invariances, augmentations and dataset biases,” arXiv preprint arXiv:2007.13916, 2020.   \n[37] Francesco Croce and Matthias Hein, “Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks,” in International Conference on Machine Learning. PMLR, 2020, pp. 2206–2216.   \n[38] Spyros Gidaris, Praveer Singh, and Nikos Komodakis, “Unsupervised representation learning by predicting image rotations,” arXiv preprint arXiv:1803.07728, 2018.   \n[39] Mehdi Noroozi and Paolo Favaro, “Unsupervised learning of visual representations by solving jigsaw puzzles,” in European Conference on Computer Vision. Springer, 2016, pp. 69–84.   \n[40] Fabio M Carlucci, Antonio D’Innocente, Silvia Bucci, Barbara Caputo, and Tatiana Tommasi, “Domain generalization by solving jigsaw puzzles,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2019, pp. 2229–2238.   \n[41] Chuang Gan, Boqing Gong, Kun Liu, Hao Su, and Leonidas J Guibas, “Geometry guided convolutional neural networks for self-supervised video representation learning,” in CVPR, 2018, pp. 5589–5597.   \n[42] Trieu H Trinh, Minh-Thang Luong, and Quoc V Le, “Selfie: Self-supervised pretraining for image embedding,” arXiv preprint arXiv:1906.02940, 2019.   \n[43] Aaron van den Oord, Yazhe Li, and Oriol Vinyals, “Representation learning with contrastive predictive coding,” arXiv preprint arXiv:1807.03748, 2018.   \n[44] Kaiming He, Haoqi Fan, Yuxin Wu, Saining Xie, and Ross Girshick, “Momentum contrast for unsupervised visual representation learning,” in Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2020, pp. 9729–9738.   \n[45] Ting Chen, Simon Kornblith, Kevin Swersky, Mohammad Norouzi, and Geoffrey Hinton, “Big self-supervised models are strong semi-supervised learners,” arXiv preprint arXiv:2006.10029, 2020.   \n[46] Xinlei Chen and Kaiming He, “Exploring simple siamese representation learning,” arXiv preprint arXiv:2011.10566, 2020.   \n[47] Eric Wong and J Zico Kolter, “Provable defenses against adversarial examples via the convex outer adversarial polytope,” arXiv preprint arXiv:1711.00851, 2017.   \n[48] Krishnamurthy Dvijotham, Sven Gowal, Robert Stanforth, Relja Arandjelovic, Brendan O’Donoghue, Jonathan Uesato, and Pushmeet Kohli, “Training verified learners with learned verifiers,” arXiv preprint arXiv:1805.10265, 2018.   \n[49] Chuang Gan, Ting Yao, Kuiyuan Yang, Yi Yang, and Tao Mei, “You lead, we exceed: Laborfree video concept learning by jointly exploiting web videos and images,” in CVPR, 2016, pp. 923–932.   \n[50] Chuang Gan, Chen Sun, Lixin Duan, and Boqing Gong, “Webly-supervised video recognition by mutually voting for relevant web images and web video frames,” in ECCV, 2016, pp. 849–866.   \n[51] Prannay Khosla, Piotr Teterwak, Chen Wang, Aaron Sarna, Yonglong Tian, Phillip Isola, Aaron Maschinot, Ce Liu, and Dilip Krishnan, “Supervised contrastive learning,” arXiv preprint arXiv:2004.11362, 2020.   \n[52] Haohan Wang, Xindi Wu, Zeyi Huang, and Eric P Xing, “High-frequency component helps explain the generalization of convolutional neural networks,” in Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2020, pp. 8684–8694.   \n[53] Zifan Wang, Yilin Yang, Ankit Shrivastava, Varun Rawal, and Zihao Ding, “Towards frequencybased explanation for robust cnn,” arXiv preprint arXiv:2005.03141, 2020.   \n[54] Xueting Yan, Ishan Misra, Abhinav Gupta, Deepti Ghadiyaram, and Dhruv Mahajan, “Clusterfit: Improving generalization of visual representations,” in Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2020, pp. 6509–6518.   \n[55] Laurens Van der Maaten and Geoffrey Hinton, “Visualizing data using t-sne.,” Journal of machine learning research, vol. 9, no. 11, 2008.   \n[56] Anish Athalye, Nicholas Carlini, and David Wagner, “Obfuscated gradients give a false sense of security: Circumventing defenses to adversarial examples,” arXiv preprint arXiv:1802.00420, 2018.   \n[57] Aravindh Mahendran and Andrea Vedaldi, “Visualizing deep convolutional neural networks using natural pre-images,” International Journal of Computer Vision, vol. 120, no. 3, pp. 233–255, 2016.   \n[58] Logan Engstrom, Andrew Ilyas, Shibani Santurkar, Dimitris Tsipras, Brandon Tran, and Aleksander Madry, “Adversarial robustness as a prior for learned representations,” arXiv preprint arXiv:1906.00945, 2019.   \n[59] Simran Kaur, Jeremy Cohen, and Zachary C Lipton, “Are perceptually-aligned gradients a general property of robust classifiers?,” arXiv preprint arXiv:1910.08640, 2019.   \n[60] Hong Liu, Mingsheng Long, Jianmin Wang, and Michael I Jordan, “Towards understanding the transferability of deep representations,” arXiv preprint arXiv:1909.12031, 2019.   \n[61] Hao Li, Zheng Xu, Gavin Taylor, Christoph Studer, and Tom Goldstein, “Visualizing the loss landscape of neural nets,” arXiv preprint arXiv:1712.09913, 2017.   \n[62] Angus Galloway, Anna Golubeva, Thomas Tanay, Medhat Moussa, and Graham W Taylor, “Batch normalization is a cause of adversarial vulnerability,” arXiv preprint arXiv:1905.02161, 2019.   \n[63] Tianyu Pang, Xiao Yang, Yinpeng Dong, Hang Su, and Jun Zhu, “Bag of tricks for adversarial training,” arXiv preprint arXiv:2010.00467, 2020. 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parse/train/BJlAzTEKwS/BJlAzTEKwS.md

@@ -0,0 +1,383 @@
+# ATTRACTION-REPULSION ACTOR-CRITIC FOR CONTINUOUS CONTROL REINFORCEMENT LEARNING
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+In reinforcement learning, robotic control tasks are often useful for understanding how agents perform in environments with deceptive rewards where the agent can easily become trapped into suboptimal solutions. One way to avoid these local optima is to use a population of agents to ensure coverage of the policy space (a form of exploration), yet learning a population with the “best” coverage is still an open problem. In this work, we present a novel approach to population-based RL in continuous control that leverages properties of normalizing flows to perform attractive and repulsive operations between current members of the population and previously observed policies. Empirical results on the MuJoCo suite demonstrate a high performance gain for our algorithm compared to prior work, including Soft-Actor Critic (SAC).
+
+# 1 INTRODUCTION
+
+Many important reinforcement learning (RL) tasks, such as those in robotics and self-driving cars, are challenging due to large action and state spaces (Lee et al., 2018). In particular, environments with large continuous action spaces are prone to deceptive rewards, i.e. fall into local optima in learning (Conti et al., 2018). Applying traditional policy optimization algorithms to these domains often leads to locally optimal, yet globally sub-optimal policies. The agent should then explore the reward landscape more thoroughly in order to avoid falling into these local optima.
+
+Not all RL domains that require exploration are suitable for understanding how to train agents that are robust to deceptive rewards. For example, Montezuma’s Revenge, a game in the Atari Learning Environment (Bellemare et al., 2013), has sparse rewards; algorithms that perform the best on this task encourage exploration by providing a denser intrinsic reward to the agent to encourage exploration (Tang et al., 2017). On the other hand, many robotic control problems, such as those found in MuJoCo (Todorov et al., 2012), provide the agent with a dense reward signal, yet their high-dimensional action spaces induce a multimodal, often deceptive, reward landscape. For example, in the biped environments, coordinating both arms and legs is crucial for performing well on even simple tasks such as forward motion. However, simply learning to maximize the reward can be detrimental across training: agents will tend to run and fall further away from the start point rather than discovering stable and efficient walking motion. In this setting, exploration serves to provide a more reliable learning signal for the agent by covering more different types of actions during learning.
+
+One way to maximize action space coverage is the maximum entropy RL framework (Ziebart, 2010), which prevents variance collapse by adding a policy entropy auxiliary objective. One such prominent algorithm, Soft Actor-Critic (SAC,Haarnoja et al. (2018)), has been shown to excel in large continuous action spaces. To further improve on exploration properties of SAC, one can maintain a population of agents that cover non-identical sections of the policy space. To prevent premature convergence, a diversity-preserving mechanism is typically put in place; balancing the objective and the diversity term becomes key to converging to a global optimum (Hong et al., 2018). This paper studies a particular family of population-based exploration methods, which conduct coordinated local search in the policy space. Prior work on population-based strategies improves performance on robotic control domains through stochastic perturbation on a single actor’s parameter (Pourchot & Sigaud, 2019) or a set of actor’s parameters (Conti et al., 2018; Khadka & Tumer, 2018; Liu et al., 2017). We hypothesize that exploring directly in the policy space will be more effective than perturbing the parameters of the policy, as the latter does not guarantee diversity (i.e., different neural network parameterizations can approximately represent the same function).
+
+Given a population of RL agents, we enforce local exploration using an Attraction-Repulsion (AR) mechanism. The later consists in adding an auxiliary loss to encourage pairwise attraction or repulsion between members of a population, as measured by a divergence term. We make use of the KullbackLeibler (KL) divergence because of its desirable statistical properties and its easiness of computation. However, naively maximizing the KL term between two Gaussian policies can be detrimental (e.g. drives both means apart). Because of this, we parametrize the policy with a general family of distributions called Normalizing Flows (NFs, Rezende & Mohamed, 2015); this modification allows to improve upon $\mathrm { \bf A R + }$ Gaussian (see Appendix Figure 6). NFs are shown to improve the expressivity of the policies using invertible mappings while maintaining entropy guarantees (Mazoure et al., 2019; Tang & Agrawal, 2018). Nonlinear density estimators have also been previously used for deep RL problems in contexts of distributional RL (Doan et al., 2018) and reward shaping (Tang et al., 2017). The AR objective blends particularly well with SAC, since computing the KL requires stochastic policies with tractable densities for each agent.
+
+# 2 PRELIMINARIES
+
+We first formalize the RL setting in a Markov decision process (MDP). A discrete-time, finite-horizon, MDP (Bellman, 1957; Puterman, 2014) is described by a state space $s$ , an action space $\mathcal { A }$ , a transition function $\mathcal { P } : \mathcal { S } \times \mathcal { A } \times \mathcal { S } \mapsto \mathbb { R } ^ { + }$ , and a reward function $r : S \times \mathcal { A } \mapsto \mathbb { R }$ .1 On each round $t$ , an agent interacting with this MDP observes the current state $s _ { t } \in S$ , selects an action $a _ { t } \in \mathcal A$ , and observes a reward $r ( s _ { t } , a _ { t } ) \in \mathbb { R }$ upon transitioning to a new state $s _ { t + 1 } \sim \mathcal { P } ( s _ { t } , a _ { t } )$ . Let $\gamma \in [ 0 , 1 ]$ be a discount factor. The goal of an agent evolving in a discounted MDP is to learn a policy $\Dot { \pi } : \Dot { S \times A } \mapsto [ 0 , 1 ]$ such as taking action $a _ { t } \sim \pi ( \cdot | s _ { t } )$ would maximize the expected sum of discounted returns,
+
+$$
+V ^ { \pi } ( s ) = \mathbb { E } _ { \pi } \bigg [ \sum _ { t = 0 } ^ { \infty } \gamma ^ { t } r ( s _ { t } , a _ { t } ) | s _ { 0 } = s \bigg ] .
+$$
+
+In the following, we use $\rho _ { \pi }$ to denote the trajectory distribution induced by following policy $\pi$ . If $s$ or $\mathcal { A }$ are vector spaces, action and space vectors are respectively denoted by a and s.
+
+# 2.1 DISCOVERING NEW SOLUTIONS THROUGH POPULATION-BASED ATTRACTION-REPULSION
+
+Consider evolving a population of $M$ agents, also called individuals, $\lbrace \pi _ { \theta _ { m } } \rbrace _ { m = 1 } ^ { M }$ , each agent corresponding to a policy with its own parameters. In order to discover new solutions, we aim to generate agents that can mimic some target policy while following a path different from those of other policies.
+
+Let $\mathcal { G }$ denote an archive of policies encountered in previous generations of the population. A natural way of enforcing $\pi$ to be different from or similar to the policies contained in $\mathcal { G }$ is by augmenting the loss of the agent with an Attraction-Repulsion (AR) term:
+
+$$
+\begin{array} { r } { \mathcal { L } _ { \mathrm { A R } } = - \underset { \pi ^ { \prime } \sim \mathcal { G } } { \mathbb { E } } \big [ \beta _ { \pi ^ { \prime } } \mathrm { D } _ { \mathrm { K L } } [ \pi | | \pi ^ { \prime } ] \big ] , } \end{array}
+$$
+
+where $\pi ^ { \prime }$ is an archived policy and $\beta _ { \pi ^ { \prime } }$ is a coefficient weighting the relative importance of the Kullback-Leibler (KL) divergence between $\pi$ and $\pi ^ { \prime }$ , which we will choose to be a function of the average reward (see Sec. 3.2 below). Intuitively, Eq. 1 adds to the agent objective a weighted average distance between the current and the archived policies. For $\beta _ { \pi ^ { \prime } } \geq 0$ , the agent tends to move away from the archived policy’s behavior (i.e. repulsion, see Figure 1) a). On the other hand, $\beta _ { \pi ^ { \prime } } < 0$ encourages the agent $\pi$ to imitate $\pi ^ { \prime }$ (i.e. attraction).
+
+Requirements for AR In order for agents within a population to be trained using the proposed AR-based loss (Eq. 1), we have the following requirements:
+
+1. Their policies should be stochastic, so that the KL-divergence between two policies is well-defined.
+
+2. Their policies should have tractable distributions, so that the KL-divergence can be computed easily, either with closed-form solution or Monte Carlo estimation.
+
+Several RL algorithms enjoy such properties (Haarnoja et al., 2018; Schulman et al., 2015; 2017). In particular, the soft actor-critic (SAC, Haarnoja et al., 2018) is a straightforward choice, as it currently outperforms other candidates and is off-policy, thus maintains a single critic shared among all agents (instead of one critic per agent), which reduces computation costs.
+
+# 2.2 SOFT ACTOR-CRITIC
+
+SAC (Haarnoja et al., 2018) is an off-policy learning algorithm which finds the information projection of the Boltzmann Q-function onto the set of diagonal Gaussian policies $\Pi$ :
+
+$$
+\pi = \underset { \pi ^ { \prime } \in \Pi } { \arg \operatorname* { m i n } } \mathrm { D } _ { \mathrm { K L } } \bigg ( \pi ^ { \prime } ( . | \mathbf { s } _ { t } ) \bigg | \bigg | \frac { \exp \big ( \frac { 1 } { \alpha } Q ^ { \pi _ { \mathrm { o l d } } } \big ( \mathbf { s } _ { t } , . \big ) \big ) } { Z ^ { \pi _ { \mathrm { o l d } } } \big ( \mathbf { s } _ { t } \big ) } \bigg ) ,
+$$
+
+where $\alpha \in ( 0 , 1 )$ controls the temperature, i.e. the peakedness of the distribution. The policy $\pi$ , critic $Q$ , and value function $V$ are optimized according to the following loss functions:
+
+$$
+\begin{array} { r l } & { \mathcal { L } _ { \pi , \mathrm { S A C } } = \mathbb { E } _ { \mathbf { s } _ { t } \sim \mathcal { B } } [ \mathbb { E } _ { \mathbf { a } _ { t } \sim \pi } [ \alpha \log \pi ( \mathbf { a } _ { t } | \mathbf { s } _ { t } ) - Q ( \mathbf { s } _ { t } , \mathbf { a } _ { t } ) ] ] } \\ & { \qquad \mathcal { L } _ { Q } = \underset { ( s , a , r , s ^ { \prime } ) \sim \mathcal { B } } { \mathbb { E } } [ \{ Q ( s , a ) - ( r + \gamma V _ { \nu } ^ { \pi } ( s ^ { \prime } ) ) \} ^ { 2 } ] } \\ & { \qquad \mathcal { L } _ { V } = \mathbb { E } _ { \mathbf { s } _ { t } \sim \mathcal { D } } \bigg [ \frac { 1 } { 2 } \big \{ V _ { \nu } ^ { \pi } ( \mathbf { s } _ { t } ) - \mathbb { E } _ { \mathbf { a } _ { t } \sim \pi } [ Q ( \mathbf { s } _ { t } , \mathbf { a } _ { t } ) - \alpha \log \pi ( \mathbf { a } _ { t } | \mathbf { s } _ { t } ) ] \big \} ^ { 2 } \bigg ] , } \end{array}
+$$
+
+where $\boldsymbol { B }$ is the replay buffer. The policy used in SAC as introduced in Haarnoja et al. (2018) is Gaussian, which is both stochastic and tractable, thus compatible with our AR loss function in Eq. 1. Together with the AR loss in Eq. 1, the final policy loss becomes:
+
+$$
+\mathcal { L } _ { \pi } = \mathcal { L } _ { \pi , \mathrm { S A C } } + \mathcal { L } _ { \mathrm { A R } }
+$$
+
+However, Gaussian policies are arguably of limited expressibility; we can improve on the family of policy distributions without sacrificing qualities necessary for AR or SAC by using Normalizing Flows (NFs, Rezende & Mohamed, 2015).
+
+# 2.3 NORMALIZING FLOWS
+
+NFs (Rezende & Mohamed, 2015) were introduced as a means of transforming simple distributions into more complex distributions using learnable and invertible functions. Given a random variable $\mathbf { z } _ { 0 }$ sequence of with density $q _ { 0 }$ $d$ 0-dimensional random variables, , they define a set of differentiable and invertible functions, $\{ { \mathbf { z } } _ { i } \} _ { i = 1 } ^ { N }$ . $\{ f _ { i } \} _ { i = 1 } ^ { N }$ , which generate a
+
+Because SAC uses explicit, yet simple parametric policies, NFs can be used to transform the SAC policy into a richer one (e.g., multimodal) without risk loss of information. For example, Mazoure et al. (2019) enhanced SAC using a family of radial contractions around a point $\mathbf { z } _ { 0 } \in \bar { \mathbb { R } } ^ { d }$ ,
+
+$$
+f ( \mathbf { z } ) = \mathbf { z } + { \frac { \beta } { \alpha + | | \mathbf { z } - \mathbf { z } _ { 0 } | | _ { 2 } } } ( \mathbf { z } - \mathbf { z } _ { 0 } )
+$$
+
+for $\alpha \in \mathbb { R } ^ { + }$ and $\beta \in \mathbb { R }$ . This results in a rich set of policies comprised of an initial noise sample ${ \bf a } _ { 0 }$ , a state-noise embedding $h _ { \theta } ( \mathbf { a } _ { 0 } , \mathbf { s } _ { t } )$ , and a flow $\{ \dot { f } _ { \phi _ { i } } \} _ { i = 1 } ^ { N }$ of arbitrary length $N$ , parameterized by $\phi = \{ \phi _ { i } \} _ { i = 1 } ^ { N }$ . Sampling from the policy $\pi _ { \phi , \theta } ( \mathbf { a } _ { t } | \mathbf { s } _ { t } )$ can be described by the following set of equations:
+
+$$
+\begin{array} { r l } & { \mathbf { a } _ { 0 } \sim \mathcal { N } ( 0 , \mathbf { I } ) ; } \\ & { \mathbf { \Phi } \mathbf { z } = h _ { \theta } ( \mathbf { a } _ { 0 } , \mathbf { s } _ { t } ) ; } \\ & { \mathbf { a } _ { t } = f _ { \phi _ { N } } \circ f _ { \phi _ { N - 1 } } \circ \dots \circ f _ { \phi _ { 1 } } ( \mathbf { z } ) , } \end{array}
+$$
+
+where $h _ { \theta } = \mathbf { a } _ { 0 } \sigma \mathbf { I } + \mu ( \mathbf { s } _ { t } )$ depends on the state and the noise variance $\sigma > 0$ . Different SAC policies can thus be crafted by parameterizing their NFs layers.
+
+![](images/5f1e484c07b4d6aae050dd38be514b6f5d99e8200b908a2090a82327bc3e358f.jpg)  
+Figure 1: a) Augmenting the loss function with AR constraints allows an agent to reach a target policy by following different paths. Attractive and Repulsive policies represent any other agent’s policy. b) General flow of the proposed ARAC strategy.
+
+# 3 ARAC: ATTRACTION-REPULSION ACTOR-CRITIC
+
+We now detail the general procedure for training a population of agents using the proposed diversityseeking AR mechanism. More specifically, we consider here SAC agents enhanced with NFs (Mazoure et al., 2019). Figure 1 displays the general flow of the procedure. Algorithm 1 (Appendix) provides the pseudo-code of the proposed ARAC strategy, where sub-procedures for rollout and archive update can be found in the Appendix.
+
+Overview ARAC works by evolving a population of $M$ SAC agents $\{ \pi _ { \phi , \theta } ^ { m } \} _ { m = 1 } ^ { M }$ with radial NFs policies (Eq. 7) and shared critic , and by maintaining an archive of policies encountered in previous generations of the population. After performing $T$ steps per agent on the environment (Alg. 1 L8-12), individuals are evaluated by performing $R$ rollouts2 on the environment (Alg. 1 L26-28). This allows to identify the top- $K$ best agents (Alg. 1 L29), also called elites, which will be used to update the critic as they provide the most meaningful feedback (Alg. 1 L13-17). The archive is finally updated in a diversity-seeking fashion using the current population (Alg. 1 L30).
+
+The core component of the proposed approach lies within the update of the agents (Alg. 1 L18-25). During this phase, elite individuals are updated using AR operations w.r.t. policies sampled from the archive (Eq. 5), whereas non-elites are updated regularly (Eq. 2).
+
+# 3.1 ENHANCING DIVERSITY IN THE ARCHIVE
+
+Throughout the training process, we maintain an archive $\mathcal { G }$ of maximum capacity $G$ , which contains some previously encountered policies. The process goes as follow: until reaching full capacity, the archive saves a copy of the parameters of every individual in the population after the evaluation step. However, by naively adding all individuals as if the archive were just a heap, the archive could end up filled with policies leading to similar rewards, which would result in a loss of diversity (Mauldin, 1984). We mitigate this issue by keeping track of two fitness clusters (low and high) using the partition formed by running a $k$ -means algorithm on the fitness value. Hence, when $| { \mathcal { G } } | = G$ is reached and a new individual is added to the archive, it randomly replaces an archived policy from its respective cluster. This approach, also known as niching, has proved itself effective at maintaining high diversity levels (Gupta & Ghafir, 2012; Mahfoud, 1995).
+
+# 3.2 DISCOVERING NEW POLICIES THROUGH ATTRACTION-REPULSION
+
+The crux of this work lies in the explicit search for diversity in the policy space achieved using the AR mechanism. Since the KL between two base policies (i.e. input of the first flow layer) can be trivially maximized by driving their means apart, we apply attraction-repulsion only on the flow layers, while holding the mean of the base policy constant. This ensures that the KL term doesn’t depend on the difference in means and hence controls the magnitude of the AR mechanism. Every time the AR operator is applied (Alg. 1 L20-21), $n$ policies are sampled from the archive and are used for estimating the AR loss (Eq. 1). As in Hong et al. (2018), we consider two possible strategies to dictate the value of $\beta _ { \pi ^ { \prime } }$ coefficients for policies $\pi ^ { \prime } \sim \mathcal { G }$ :
+
+$$
+\begin{array} { l } { \displaystyle \beta _ { \pi ^ { \prime } } = - \biggl [ 2 \biggl ( \frac { f \bigl ( \pi ^ { \prime } \bigr ) - f _ { m i n } } { f _ { m a x } - f _ { m i n } } - 1 \biggr ) \biggr ] } \\ { \displaystyle \beta _ { \pi ^ { \prime } } = 1 - \frac { f \bigl ( \pi ^ { \prime } \bigr ) - f _ { m i n } } { f _ { m a x } - f _ { m i n } } } \end{array}
+$$
+
+where $f ( \pi ) ^ { 3 }$ represents the fitness function of policy $\pi$ (average reward in our case), and $f _ { m i n }$ and $f _ { m a x }$ are estimated based on the $n$ sampled archived policies. The proactive strategy aims to mimic high reward archived policies, while the reactive strategy is more cautious, only repulsing away the current policy from low fitness archived policies. Using this approach, the current agent policy will be attracted to some sampled policies $( \beta _ { \pi ^ { \prime } } < 0 )$ ) and will be repulsed from others $\beta _ { \pi ^ { \prime } } \geq 0 )$ ) in a more or less aggressive way, depending on the strategy.
+
+Unlike Hong et al. (2018) who applied proactive and reactive strategies on policies up to 5 timesteps back, we maintain an archive consisting of two clusters seen so far: policies with low and high fitness, respectively. Having this cluster allows to attract/repulse from a set of diverse agents, replacing high-reward policies by policies with similar performance. Indeed, without this process, elements of the archive would collapse on the most frequent policy, from which all agents would attract/repulse. To avoid performing AR against a single "average policy" , we separate low-reward and high-reward agents via clustering.
+
+# 4 RELATED WORK
+
+The challenges of exploration are well studied in the RL literature. Previously proposed approaches for overcoming hard exploration domains tend to either increase the capacity of the state-action value function (Gal & Ghahramani, 2016; Henderson et al., 2017) or the policy expressivity (Mazoure et al., 2019; Tang & Agrawal, 2018; Touati et al., 2018). This work rather tackles exploration from a diverse multi-agent perspective. Unlike prior population-based approaches for exploration (Conti et al., 2018; Khadka & Tumer, 2018; Pourchot & Sigaud, 2019), which seek diversity through the parameters space, we directly promote diversity in the policy space.
+
+The current work was inspired by Hong et al. (2018), who relied on the KL divergence to attract/repulse from a set of previous policies to discover new solutions. However, in their work, the archive is time-based (they restrict themselves to the 5 most recent policies), while our archive is built following a diversity-seeking strategy (i.e., niching and policies come from multiple agents). Notably, ARAC is different of previously discussed works in that it explores the action space in multiple regions simultaneously, a property enforced through the AR mechanism.
+
+The proposed approach bears some resemblance with Liu et al. (2017), who took advantage of a multi-agent framework in order to perform repulsion operations among agents using of similarity kernels between parameters of the agents. The AR mechanism gives rise to exploration through structured policy rather than randomized policy. This strategy has also been employed in multi-task learning (Gupta et al., 2018), where experience on previous tasks was used to explore on new tasks.
+
+# 5 EXPERIMENTS
+
+# 5.1 DIDACTIC EXAMPLE
+
+Consider a 2-dimensional multi-armed bandit problem where the actions lie in the real square $[ - 6 , 6 ] ^ { 2 }$ . We illustrate the example of using a proactive strategy where a SAC agent with radial flows policy imitates a desirable (expert) policy while simultaneously repelling from a less desirable policy. The task consists in matching the expert’s policy (blue density) while avoiding taking actions from a repulsive policy $\pi ^ { \prime }$ (red). We illustrate the properties of radial flows in Figure 2 by increasing the number of flows (where 0 flow corresponds to a Gaussian distribution).
+
+We observe that increasing the number of flows (bottom to top) leads to more complex policy’s shapes and multimodality unlike the Gaussian policy which has its variance shrinked (the KL divergence is proportional to the ratio of the two variances, hence maximizing it can lead to a reduction in the variance which can be detrimental for exploration purpose). Details are provided in Appendix.
+
+![](images/1036cd057f37e814ff6f335c0a03dd0dd10f946762eb28661267361a0bedc134.jpg)  
+Figure 2: Agent trained to imitate a target while avoiding a repulsive policy using a proactive strategy. Increasing the number of flows leads to more complex policy’s shape.
+
+![](images/85f6af52b9f366799b350719614483ad9e8170c22dac51befe8f4baebf61470b.jpg)  
+Figure 3: Average return and one standard deviation on 5 random seeds across 7 MuJoCo tasks for ARAC against single SAC agents (with and without NFs). Curves are smoothed using Savitzky-Golay filtering with window size of 7.
+
+# 5.2 MUJOCO LOCOMOTION BENCHMARKS
+
+We now compare ARAC against the CEM-TD3 (Pourchot & Sigaud, 2019), ERL (Khadka & Tumer, 2018) and CERL (Khadka et al., 2019) multi-agent baselines on seven continuous control tasks from the MuJoco suite (Duan et al., 2016): Ant-v2, HalfCheetah-v2, Humanoid-v2, HumanoidStandup-v2, Hopper-v2, Walker2d-v2 and Humanoid (rllab). We also designed a sparse reward environment SparseHumanoid-v2. All algorithms are run over 1M time steps on each environment, except Humanoid (rllab) which gets 2M time steps and SparseHumanoid-v2 on $0 . 6 { \bf M }$ time steps. We also include comparison against single-agent baselines.
+
+ARAC performs $R = 1 0$ rollouts for evaluation steps every 10, 000 interaction steps with the environment. We consider a small population of $N = 5$ individuals with $K = 2$ as elites. Every SAC agent has one feedforward hidden layer of 256 units acting as state embedding, followed by a radial flow of length $\in \{ 3 , 4 \}$ . A temperature of $\alpha = 0 . 0 5$ or 0.2 is used across all the environments (See appendix for more details). AR operations are carried out by sampling uniformly $n = 5$ archived policies from $\mathcal { G }$ . Parameters details are provided in the Appendix (Table 4). All networks are trained with Adam optimizer (Kingma & Ba, 2015) using a learning rate of $\mathrm { 3 E ^ { - 4 } }$ . Baselines CEM-TD34, $\mathrm { E R L } ^ { 5 }$ , CERL6 use the code contained in their respective repositories.
+
+<table><tr><td></td><td>ARAC</td><td>CEM-TD3</td><td>CERL</td><td>ERL</td><td>SAC-NF</td><td>SAC</td><td>TD3</td></tr><tr><td>Ant</td><td>6044</td><td>4239</td><td>1639</td><td>1442</td><td>4912</td><td>4370</td><td>4372</td></tr><tr><td>HC</td><td>10264</td><td>10659</td><td>5703</td><td>6746</td><td>8429</td><td>11 900</td><td>9543</td></tr><tr><td>Hopper</td><td>3587</td><td>3655</td><td>2970</td><td>1149</td><td>3538</td><td>2794</td><td>3564</td></tr><tr><td>Hu</td><td>5965</td><td>212</td><td>4756</td><td>551</td><td>5506</td><td>5504</td><td>71</td></tr><tr><td>Standup</td><td>175 000</td><td>29 000</td><td>117000</td><td>12 900</td><td>116 000</td><td>149 000</td><td>54000</td></tr><tr><td>Hu (rllab)</td><td>14 230</td><td>1334</td><td>3340</td><td>57</td><td>5531</td><td>1963</td><td>286</td></tr><tr><td>Walker2d</td><td>4704</td><td>4710</td><td>4386</td><td>1107</td><td>5196</td><td>3783</td><td>4682</td></tr><tr><td>Hu (Sparse)</td><td>816</td><td>0</td><td>1.32</td><td>8.65</td><td>547</td><td>88</td><td>0</td></tr></table>
+
+Table 1: Maximum average return after 1M (2M for Humanoid (rllab) and 600k for SparseHumanoid-v2) time steps 5 random seeds. Bold: best methods when the gap is less than 100 units. See appendix for average return with standard deviation. Environment short names: HC: HalfCheetah-v2, Hu: Humanoid-v2, Standup: HumanoidStandup-v2
+
+Figure 4 displays the performance of all algorithms on three environments over time steps (see Appendix Figure 7 for all environments). Results are averaged over 5 random seeds. Table 1 reports the best observed reward for each method.
+
+![](images/7c61fe7d139129b6333acea8071a346e8a481d71ecd2da64dcd95580615568ae.jpg)  
+Figure 4: Average return and one standard deviation on 5 random seeds across 8 MuJoCo tasks. Curves are smoothed using Savitzky-Golay filtering with window size of 7.
+
+Small state space environments HalfCheetah-v2, Hopper-v2, and Walker2d-v2 are low-dimensional state space environments $( d \leq 1 7 )$ . Except for HalfCheetah-v2, the proposed approach shows comparable results with its concurrent. Those results match the findings of (Plappert et al., 2018) that some environments with well-structured dynamics require little exploration. Full learning curves can be found in the Appendix.
+
+Deceptive reward and Large state space environments Humanoid-v2, HumanoidStandup-v2 and Humanoid (rllab) belong to bipedal environments with high-dimensional state space $( d = 3 7 6$ and $d = 1 4 7$ ), and are known to trap algorithms into suboptimal solutions. In addition to the legs, the agent also needs to control the arms, which may influence the walking way and hence induce deceptive rewards (Conti et al., 2018). Figure 4 shows the learning curves on MuJoCo tasks. We observe that ARAC beats both baselines in performance as well as in convergence rate.
+
+Ant-v2 is another high-dimensional state space environment $\mathit { l } \geq 1 0 0 )$ . In an unstable setup, a naive algorithm implementing an unbalanced fast walk could still generate high reward, the reward taking into account the distance from start, instead of learning to stand, stabilize, and walk (as expected).
+
+Sparse reward environment To test ARAC in a sparse reward environment, we created SparseHumanoid-v2. The dynamic is the same as Humanoid-v2 but rewards of $+ 1$ is granted only given is the center of mass of the agent is above a threshold (set to 0.6 unit in our case). The challenge not only lies in the sparse reward property but also on the complex body dynamic that can make the agent falling down and terminating the episode. As shown in Figure 4, ARAC is the only method that can achieve non zero performance. A comparison against single agent methods in the Appendix also shows better performance for ARAC.
+
+Sample efficiency compared with single agent methods Figure 3 (in Appendix) also shows that the sample efficiency of the population-based ARAC compares to a single SAC agent (with and without NFs) and other baselines methods (SAC, TD3). On Humanoid-v2 and Ant-v2 ARAC converges faster, reaching the 6k (4k, respectively) milestone performance after only 1M steps, while a single SAC agent requires 4M (3M, respectively) steps according to (Haarnoja et al., 2018). In general, ARAC achieves competitive results (no flat curves) and makes the most difference (faster convergence and better performance) in the biped environments.
+
+Attraction-repulsion ablation study To illustrate the impact of repulsive forces, we introduce a hyperparameter $\lambda$ in the overall loss (Eq. 5):
+
+$$
+\mathcal { L } _ { \theta , \phi , \lambda } = \mathcal { L } _ { \theta , \phi , \mathrm { S A C } } + \lambda \mathcal { L } _ { \phi , \mathrm { A R } }
+$$
+
+We ran an ablation analysis on Humanoid-v2 by varying that coefficient. For two random states, we sampled 500 actions from all agents and mapped these actions onto a two-dimensional space (via t-SNE). Appendix Figure 5 shows that without repulsion $\lambda = 0$ ), actions from all agents are entangled, while repulsion $( \lambda > 0$ ) forces agents to behave differently and hence explore different regions of the action space.
+
+The second ablation study is dedicated to highlight the differences between a Gaussian policy (similar to Hong et al. (2018) and an NF policy under AR operators. As one can observe in Figure 6, using a Gaussian policy deteriorates the solution as the repulsive KL term drives apart the means of agents and blows up/ shrinks the variance of the Gaussian policy. On the other hand, applying the AR term on the NF layers maximizes the KL conditioned on the mean and variance of both base policies, resulting in a solution which allows sufficient exploration. More details are provided in the Appendix.
+
+Finally, through a toy example subject to AR, we characterize the policy’s shape when increasing the number of the radial flow policy in Figure 2 (experimental setup in Appendix). Unlike the diagonal Gaussian policy (SAC) that has symmetry constraints, increasing the number of flows allows the radial policy to adopt more complex shapes (from bottom to top).
+
+# 6 CONCLUSION
+
+In this paper, we addressed the issue of RL domains with deceptive rewards by introducing a population-based search model for optimal policies using attraction-repulsion operators. Our method relies on powerful density estimators (normalizing flows), to let policies exploit the reward landscape under AR constraints. Our ablation studies showed that (1) the strength of AR and (2) the number of flows are the two factors which predominantly affect the shape of the policy. Selecting the correct AR coefficient is therefore important to obtain good performance, while at the same time preventing premature convergence.
+
+Empirical results on the MuJoCo suite demonstrate high performance of the proposed method in most settings, including with sparse rewards. Moreover, in biped environments that are known to trap algorithms into suboptimal solutions, ARAC enjoys higher sample efficiency and better performance compared to its competitors which confirms our intuitions on using AR with normalizing flows. As future steps, borrowing from multi-objective optimization literature methods could allow one to combine other diversity metrics with the performance objective, to in turn improve the coverage of the solution space among the individuals by working with the corresponding Pareto front (Horn et al., 1994).
+
+# REFERENCES
+
+Marc G Bellemare, Yavar Naddaf, Joel Veness, and Michael Bowling. The arcade learning environment: An evaluation platform for general agents. Journal of Artificial Intelligence Research, 47: 253–279, 2013.
+
+Richard Bellman. A markovian decision process. Journal of Mathematics and Mechanics, pp. 679–684, 1957.
+
+Edoardo Conti, Vashisht Madhavan, Felipe Petroski Such, Joel Lehman, Kenneth Stanley, and Jeff Clune. Improving exploration in evolution strategies for deep reinforcement learning via a population of novelty-seeking agents. In Advances in Neural Information Processing Systems (NeurIPS), pp. 5027–5038, 2018.
+
+Thang Doan, Bogdan Mazoure, and Clare Lyle. Gan q-learning. arXiv preprint arXiv:1805.04874, 2018.
+
+Yan Duan, Xi Chen, Rein Houthooft, John Schulman, and Pieter Abbeel. Benchmarking deep reinforcement learning for continuous control. In International Conference on Machine Learning (ICML), pp. 1329–1338, 2016.
+
+Yarin Gal and Zoubin Ghahramani. Dropout as a bayesian approximation: Representing model uncertainty in deep learning. In International conference on machine learning (ICML), pp. 1050– 1059, 2016.
+
+Abhishek Gupta, Russell Mendonca, YuXuan Liu, Pieter Abbeel, and Sergey Levine. Metareinforcement learning of structured exploration strategies. In Advances in Neural Information Processing Systems (NeurIPS), pp. 5302–5311, 2018.
+
+Deepti Gupta and Shabina Ghafir. An overview of methods maintaining diversity in genetic algorithms. International journal of emerging technology and advanced engineering, 2(5):56–60, 2012.
+
+Tuomas Haarnoja, Aurick Zhou, Pieter Abbeel, and Sergey Levine. Soft Actor-Critic: Off-policy maximum entropy deep reinforcement learning with a stochastic actor. In International Conference on Machine Learning (ICML), pp. 1856–1865, 2018.
+
+Peter Henderson, Thang Doan, Riashat Islam, and David Meger. Bayesian policy gradients via alpha divergence dropout inference. NIPS Bayesian Deep Learning Workshop, 2017.
+
+Zhang-Wei Hong, Tzu-Yun Shann, Shih-Yang Su, Yi-Hsiang Chang, Tsu-Jui Fu, and Chun-Yi Lee. Diversity-driven exploration strategy for deep reinforcement learning. In Advances in Neural Information Processing Systems (NeurIPS), pp. 10489–10500, 2018.
+
+Jeffrey Horn, Nicholas Nafpliotis, and David E. Goldberg. A niched pareto genetic algorithm for multiobjective optimization. In Proceedings of the 1st IEEE Conference on Evolutionary Computation, IEEE World Congress on Computational Intelligence, pp. 82–87, 1994.
+
+Shauharda Khadka and Kagan Tumer. Evolution-guided policy gradient in reinforcement learning. In Advances in Neural Information Processing Systems (NeurIPS), pp. 1188–1200, 2018.
+
+Shauharda Khadka, Somdeb Majumdar, Tarek Nassar, Zach Dwiel, Evren Tumer, Santiago Miret, Yinyin Liu, and Kagan Tumer. Collaborative evolutionary reinforcement learning. CoRR, abs/1905.00976, 2019. URL http://arxiv.org/abs/1905.00976.
+
+Diederik P. Kingma and Jimmy Ba. Adam: A method for stochastic optimization. In International Conference on Learning Representations (ICLR), 2015.
+
+Kyowoon Lee, Sol-A Kim, Jaesik Choi, and Seong-Whan Lee. Deep reinforcement learning in continuous action spaces: a case study in the game of simulated curling. In International Conference on Machine Learning, pp. 2943–2952, 2018.
+
+Yang Liu, Prajit Ramachandran, Qiang Liu, and Jian Peng. Stein variational policy gradient. In Conference on Uncertainty in Artificla Intelligence (UAI), 2017.
+
+Samir W Mahfoud. Niching methods for genetic algorithms. PhD thesis, University of Illinois at Urbana-Champaign Champaign, USA, 1995.
+
+Michael L Mauldin. Maintaining diversity in genetic search. In AAAI Conference on Artificial Intelligence (AAAI), pp. 247–250, 1984.
+
+Bogdan Mazoure, Thang Doan, Audrey Durand, R Devon Hjelm, and Joelle Pineau. Leveraging exploration in off-policy algorithms via normalizing flows. Proceedings of the 3rd Conference on Robot Learning (CoRL 2019), 2019.
+
+Joelle Pineau. The machine learning reproducibility checklist. 2018.
+
+Matthias Plappert, Rein Houthooft, Prafulla Dhariwal, Szymon Sidor, Richard Y Chen, Xi Chen, Tamim Asfour, Pieter Abbeel, and Marcin Andrychowicz. Parameter space noise for exploration. arXiv preprint arXiv:1706.01905, 2017.
+
+Matthias Plappert, Rein Houthooft, Prafulla Dhariwal, Szymon Sidor, Richard Y. Chen, Xi Chen, Tamim Asfour, Pieter Abbeel, and Marcin Andrychowicz. Parameter space noise for exploration. In International Conference on Learning Representations (ICLR), 2018.
+
+Aloïs Pourchot and Olivier Sigaud. CEM-RL: Combining evolutionary and gradient-based methods for policy search. In International Conference on Learning Representations (ICLR), 2019.
+
+Martin L Puterman. Markov decision processes: discrete stochastic dynamic programming. John Wiley & Sons, 2014.
+
+Danilo Jimenez Rezende and Shakir Mohamed. Variational inference with normalizing flows. In International Conference on Machine Learning (ICML), pp. 1530–1538, 2015.
+
+John Schulman, Sergey Levine, Pieter Abbeel, Michael Jordan, and Philipp Moritz. Trust region policy optimization. In International Conference on Machine Learning (ICML), pp. 1889–1897, 2015.
+
+John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov. Proximal policy optimization algorithms. arXiv preprint: 1707.06347, 2017.
+
+Haoran Tang, Rein Houthooft, Davis Foote, Adam Stooke, OpenAI Xi Chen, Yan Duan, John Schulman, Filip DeTurck, and Pieter Abbeel. # Exploration: A study of count-based exploration for deep reinforcement learning. In Advances in neural information processing systems (NeurIPS), pp. 2753–2762, 2017.
+
+Yunhao Tang and Shipra Agrawal. Boosting trust region policy optimization by normalizing flows policy. arXiv preprint: 1809.10326, 2018.
+
+Emanuel Todorov, Tom Erez, and Yuval Tassa. Mujoco: A physics engine for model-based control. In IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 5026–5033. IEEE, 2012.
+
+Ahmed Touati, Harsh Satija, Joshua Romoff, Joelle Pineau, and Pascal Vincent. Randomized value functions via multiplicative normalizing flows. arXiv preprint: 1806.02315, 2018.
+
+Brian D Ziebart. Modeling purposeful adaptive behavior with the principle of maximum causal entropy. PhD thesis, figshare, 2010.
+
+# APPENDIX
+
+REPRODUCIBILITY CHECKLIST
+
+We follow the reproducibility checklist (Pineau, 2018) and point to relevant sections explaining them here.
+
+For all algorithms presented, check if you include:
+
+• A clear description of the algorithm, see main paper and included codebase. The proposed approach is completely described by Alg. 1 (main paper), 2 (Appendix), and 3 (Appendix). The proposed population-based method uses attraction-repulsion operators in order to enforce a better policy space coverage by different agents. An analysis of the complexity (time, space, sample size) of the algorithm. See Appendix Figure 7 and 3. Experimentally, we demonstrate improvement in sample complexity as discussed in our main paper. In term of computation time, the proposed method scales linearly with the population size if agents are evaluated sequentially (as presented in Alg. 1 for clarity). However, this as mentioned in the paper, can be parallelized. All our results are obtained using $M$ small network architectures with $1 \times 2 5 6$ -units hidden layer followed by $f$ layers of $| A | + 2$ units each $f$ being the number of radial flows and $| A |$ being the action space dimension). A link to a downloadable source code, including all dependencies. The code is included with the Appendix as a zip file; all dependencies can be installed using Python’s package manager. Upon publication, the code would be available on Github.
+
+For all figures and tables that present empirical results, check if you include:
+
+• A complete description of the data collection process, including sample size. We use standard benchmarks provided in OpenAI Gym (Brockman et al., 2016).   
+• A link to downloadable version of the dataset or simulation environment. See: https://github.com/   
+• An explanation of how samples were allocated for training / validation / testing. We do not use a training-validation-test split, but instead report the mean performance (and one standard deviation) of the policy at evaluation time, openai/gym for OpenAI Gym benchmarks and https://www.roboti.us/index.html for MuJoCo suite. obtained with 5 random seeds. An explanation of any data that were excluded. We did not compare on easy environments (e.g. Reacher-v2) because all existing methods perform well on them. In that case, the improvement of our method upon baselines is incremental and not worth mentioning.   
+• The exact number of evaluation runs. 5 seeds for MuJoCo experiments, 1M, 2M or 3M environment steps depending on the domain.   
+• A description of how experiments were run. See Section 5 in the main paper and didactic example details in Appendix. A clear definition of the specific measure or statistics used to report results. Undiscounted returns across the whole episode are reported, and in turn averaged across 5 seeds. Clearly defined error bars. Confidence intervals and table values are always mean± 1 standard deviation over 5 seeds.   
+• A description of results with central tendency (e.g. mean) and variation (e.g. stddev). All results use the mean and standard deviation.   
+• A description of the computing infrastructure used. All runs used 1 CPU for all experiments (toy and MuJoCo) with 8Gb of memory.
+
+![](images/75d01fa4c6a294b396d495cb49a01703a056ee642fb7fd10e4b064ef53d861d8.jpg)  
+Figure 5: Mapping in two-dimension space (t-SNE) of agents’ actions for two arbitrary states. Each color represents a different agent.
+
+To illustrate the impact of the repulsive force coefficient $\lambda$ , we ran an ablation analysis by varying that coefficient (recall that the overall loss function is $\mathcal { L } _ { \pi } = \mathcal { L } _ { \pi , \mathrm { S A C } } + \lambda \mathcal { L } _ { \mathrm { A R } }$ where $\lambda = 1$ in our experiment).
+
+For two random states, we sampled 500 actions from all agents and mapped theses actions in a common 2-dimensional space (t-SNE).
+
+As shown in the Figure above, policies trained without AR $\lambda = 0$ ) result in entangled actions, while increasing the repulsive coefficient $\lambda$ forces agents to have different actions and hence explore different regions of the policy space. Note that due to the specific nature of t-SNE , the policies are shown as Gaussians in a lower-dimensional embedding, while it is not necessarily the case in the true space.
+
+# STABILIZING ATTRACTION-REPULSION WITH NORMALIZING FLOW
+
+In this section, we illustrate the consequence of the AR operators with a Gaussian policy (as in Hong et al. (2018)) and our Normalizing flow policy for Ant-v2, Humanoid-v2 and HalfCheetah-v2. As shown in the figure below, AR with Gaussian policies yield worse results. One reason is that the KL term drives apart the mean and variance of the Gaussian policy which deteriorates the main objective of maximizing the reward. On the other side, our method applies the AR only on the NF layers allows enough exploration by deviating sufficiently from the main objective function.
+
+![](images/4efc27a07944874b7749b830b2f1aa73e9d64a0e975cbc0492917b3be8aaf97e.jpg)  
+Figure 6: Comparison of ARAC agents using (1) AR with radial flows, (2) AR with only the base (Gaussian) policy and (3) no AR with radial flows.
+
+# COMPARING ARAC AGAINST BASELINES ON MUJOCO TASKS
+
+Figure 7 shows the performance of ARAC and baselines (CEM-TD3, CERL and ERL) over time steps. Learning curves are averaged over 5 random seeds and displayed with one standard deviation. Evaluation is done every 10, 000 environment steps using 10 rollouts per agent. Overall, ARAC has reasonable performance on all tasks (no flat curves) and demonstrates high performance, especially in humanoid tasks.
+
+![](images/266cfd9eb6a43128f2757b9c1b4521aa722e61184330dc539ad0fcf16fbe9337.jpg)  
+Figure 7: Average return and one standard deviation on 5 random seeds across 7 MuJoCo tasks for ARAC against baselines. Curves are smoothed using Savitzky-Golay filtering with window size of 7.
+
+BENEFITS OF POPULATION-BASED STRATEGIES: ARAC AGAINST SINGLE AGENTS
+
+In this section, we highlight the benefits of the proposed population-based strategy by comparing with single agents. Figure 3 shows the performance of ARAC against a single SAC agent (with and without normalizing flows). Learning curves are averaged over 5 random seeds and displayed with one standard deviation. Evaluation is done every 10, 000 environment steps using 10 rollouts per agent. We observe a high beneficial impact on the convergence rate as well as on the performance. ARAC outperforms single agents in almost all tasks (except for HalfCheetah-v2 and Walker-v2) with large improvement. Note the high sample efficiency on humanoid environments (Humanoid-v2 and Humanoid (rllab)), where it shows faster convergence in addition to better performance. Indeed, on Humanoid (rllab) a single SAC agent reaches the 4k milestone after 4M steps (Haarnoja et al., 2018) while ARAC achieves this performance in less than 2M steps. Also, in SparseHumanoid-v2, due to its better coordinated exploration, ARAC could find a good solution faster than SAC-NF.
+
+OVERALL PERFORMANCES ON MUJOCO TASKS   
+
+<table><tr><td rowspan="2">Ant-v2</td><td rowspan="2">ARAC 6,044 ± 216</td><td rowspan="2">CEM-TD3 4,239 ± 1,048</td><td rowspan="2">CERL</td><td rowspan="2">ERL</td><td rowspan="2">SAC - NF</td><td rowspan="2">SAC</td><td rowspan="2">TD3 4,372 ± 900</td></tr><tr><td>1,639± 564 1,442±819</td></tr><tr><td>HalfCheetah-v2</td><td>10,264± 271</td><td>10,659 ± 1,473</td><td>5,703 ± 831</td><td>6,746± 295</td><td>4,912 ± 954 8,429 ±818</td><td>4,370 ± 173 11,896 ± 574</td><td>9,543 ± 978</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Hopper-v2</td><td>3,587 ± 65</td><td>3,655 ± 82</td><td>2,970 ± 341</td><td>1,149 ±3</td><td>3,538 ± 108</td><td>2,794 ± 729</td><td>3,564 ± 114</td></tr><tr><td>Humanoid-v2 HumanoidStandup-v2</td><td>5,965 ± 51 175k±38k</td><td>212±1</td><td>4,756± 454</td><td>551± 60</td><td>5,506± 147</td><td>5,504± 116</td><td>71±10</td></tr><tr><td>Humanoid (rllab)</td><td>14,234 ± 7251</td><td>29k±4k 1,334 ± 551</td><td>117k ± 8k</td><td>129k ± 4k</td><td>116k ± 9k</td><td>149k ±7k</td><td>54k ± 24k</td></tr><tr><td>Walker2d-v2</td><td>4,704 ± 261</td><td>4,710 ± 320</td><td>3,340 ± 3,340 4,3860 ± 615</td><td>57±17 1,107 ± 60</td><td>5,531 ± 4,435</td><td>1,963 ± 1,384</td><td>286 ± 151 4,682 ± 539</td></tr><tr><td>SparseHumanoid-v2</td><td>816 ± 20</td><td>0±0</td><td>1.32 ± 2.64</td><td>8.65 ± 15.90</td><td>5,196 ± 527 547 ± 268</td><td>3,783 ± 366 88±159</td><td>0±0</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></table>
+
+Table 2: Maximum average return after 1M (2M for Humanoid (rllab) and 600k for SparseHumanoid-v2) time steps $\pm$ one standard deviation on 5 random seeds. Bold: best methods when the gap is less than 100 units.
+
+<table><tr><td></td><td>ARAC</td><td>TRPO</td><td>PPO</td><td>Trust-PCL</td><td>Plappert et al. (2017)</td><td>Touati et al. (2018)</td><td>Hong et al. (2018)</td></tr><tr><td>HalfCheetah-v2</td><td>10,264</td><td>-15</td><td>2,600</td><td>2,200</td><td>5,000</td><td>7,700</td><td>4,200</td></tr><tr><td>Walker-v2</td><td>4,764</td><td>2,400</td><td>4,050</td><td>400</td><td>850</td><td>500</td><td>N/A</td></tr><tr><td>Hopper-v2</td><td>3,588</td><td>600</td><td>3,150</td><td>280</td><td>2,500</td><td>400</td><td>N/A</td></tr><tr><td>Ant-v2</td><td>6,044</td><td>-76</td><td>1,000</td><td>1,500</td><td>N/A</td><td>N/A</td><td>N/A</td></tr><tr><td>Humanoid-v2</td><td>5,939</td><td>400</td><td>400</td><td>N/A</td><td>N/A</td><td>N/A</td><td>1,250</td></tr><tr><td>HumanoidStandup-v2</td><td>163,884</td><td>80,000</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td></tr><tr><td>Humanoid (rllab)</td><td>4,117</td><td>23</td><td>200</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td></tr></table>
+
+Table 3: Performance after 1M (except for rllab which is 2M) timesteps on 5 seeds. Values taken from their corresponding papers. N/A means the values were not available in the original paper.
+
+# EXPERIMENTAL PARAMETERS
+
+Table 4 provides the hyperparameters of ARAC used to obtain results in the MuJoCo domains. The noise input for normalizing flows in SAC policies (see Sec. 2.3) is sampled from $\mathcal { N } ( 0 , \sigma )$ , where the variance $\sigma$ is a function of the state (either fixed at a given value or learned).
+
+Table 4: ARAC parameters.   
+
+<table><tr><td colspan="7">ARAC parameters</td></tr><tr><td></td><td>#flows</td><td>0</td><td>G</td><td>p</td><td>alpha</td><td>strategy</td></tr><tr><td>Ant-v2</td><td>3</td><td>0.2</td><td>10</td><td>1</td><td>0.2</td><td>proactive</td></tr><tr><td>HalfCheetah-v2</td><td>4</td><td>0.4</td><td>20</td><td></td><td>0.2</td><td>proactive</td></tr><tr><td>Hopper-v2</td><td>4</td><td>0.8</td><td>20</td><td></td><td>0.05</td><td>proactive</td></tr><tr><td>Walker2d-v2</td><td>4</td><td>0.6</td><td>10</td><td></td><td>0.05</td><td>proactive</td></tr><tr><td>Humanoid-v2</td><td>3</td><td>0.6</td><td>10</td><td></td><td>0.05</td><td>reactive</td></tr><tr><td>HumanoidStandup-v2</td><td>3</td><td>0</td><td>20</td><td></td><td>0.2</td><td>reactive</td></tr><tr><td>Humanoid (rllab)</td><td>3</td><td>9</td><td>10</td><td></td><td>0.05</td><td>proactive</td></tr><tr><td>SparseHumanoid-v2</td><td>2</td><td>0.6</td><td>20</td><td>２１３１１１１</td><td>0.2</td><td>proactive</td></tr><tr><td colspan="7">Adam Optimizer parameters</td></tr><tr><td>αq</td><td colspan="7">3.10-4</td></tr><tr><td>αw</td><td colspan="7">3.10-4</td></tr><tr><td>α</td><td colspan="7">3.10-4</td></tr><tr><td>a</td><td colspan="7">3.10-4</td></tr><tr><td colspan="3">Algorithmparameters</td><td colspan="4"></td></tr><tr><td>Batch size m</td><td colspan="7">256</td></tr><tr><td colspan="2">Buffer size B</td><td colspan="7">106</td></tr><tr><td colspan="2">Archive sample size n</td><td colspan="7">5</td></tr></table>
+
+# IMPACT OF NUMBER OF FLOWS ON THE POLICY SHAPE
+
+We used a single SAC agent with different radial flows numbers and randomly initialized weights, starting with actions centered at $( 0 , 0 )$ . All flow parameters are $\ell _ { 1 }$ regularized with hyperparameter 2. The agent is trained with the classical evidence lower bound (ELBO) objective augmented with the AR loss (Eq. 1), where the coefficient of the repulsive policy $\pi ^ { \prime }$ is given by $\begin{array} { r } { \beta _ { t } \stackrel { \smile } { = } \frac { 1 0 } { t + 1 } } \end{array}$ . Fig. 8 shows how both the NF and learned variance Gaussian policies manage to recover the target policy. We see that NF takes advantage of its flexible parametrization to adjust its density and can show asymmetric properties unlike the Gaussian distribution. This indeed can have advantage in some non symmetric environment where the Gaussian policy would be trapped into a suboptimal behavior. Finally, increasing the number of flows (from bottom to top) can lead to more complex policy’s shape.
+
+![](images/068a6a98b0db451a89cc30af3c2408532ae00760edf2494bd89935f5c4df961e.jpg)  
+Figure 8: Single state didactic illustration of attraction-repulsion operators. Comparing behavior of NF policy against Gaussian policy with learned variance under a repulsive constraint.
+
+# 6.1 VARIANCE OF FITNESS IN THE ARCHIVE
+
+Due to the high computation time for behavioral-diversity baselines such as DIYAN, we propose to use the agent’s fitness (i.e. undiscounted returns) as a candidate to repulse/attract from.
+
+![](images/9a717f5760f116f2d1161c25e91738a390ee835da2d8bb22df1295ddab31373b.jpg)  
+Figure ?? shows the variance of the archive across three MuJoCo domains: Ant, Humanoid and HumanoidStandup. As training progresses, the clustering approach allows to maintain a high variance in the archive, preventing mode collapse to a single, "average" fitness.
+
+# 6.2 PSEUDO-CODE FOR ARAC
+
+# Algorithm 1 ARAC: Attraction-Repulsion Actor-Critic
+
+1: Input: population size $M$ ; number of elites $K$ ; maximum archive capacity $G$ ; archive samp   
+size $n$ ; number of evaluation rollouts $R$ ; actor coefficient $p$ ; strategy (either proactive or reactiv   
+2: Initialize value function network $V _ { \nu }$ and critic network $Q _ { \omega }$   
+3: Initialize population of policy networks $\{ \pi _ { \phi , \theta } ^ { m } \} _ { m = 1 } ^ { M }$   
+4: Initialize empty archive $\mathcal { G }$ and randomly assign $K$ individuals to top- $K$   
+5: total_step $ 0$   
+6: while total_step $\leq$ max_step do   
+7: step $\gets 0$   
+8: for agent $m = 1 \ldots M$ do   
+9: $( \_ , \mathsf { s t e p } s ) \gets \mathtt { r o l l o u t } ( \pi ^ { m }$ , with noise, over 1 episode)   
+10: $\mathrm { s t e p } \gets \mathrm { s t e p } + s$ Collect samples   
+11: total_step total_step + s   
+12: end for   
+13: $C = { \mathsf { s t e p } } / { K }$   
+14: for policy $\pi ^ { e }$ in top- $K$ do   
+15: Update critic with $\pi ^ { e }$ for $C$ mini-batches (Eq. 3) Update critic   
+16: Update value function (Eq. 4)   
+17: end for   
+18: for agent $m = 1 \ldots M$ do   
+19: if policy $\pi ^ { m }$ is in top- $K$ then   
+20: Sample $n$ archived policies uniformly from $\mathcal { G }$   
+21: Update actor $\pi ^ { m }$ for ${ \frac { \mathrm { s t e p } } { M } } \cdot p$ mini-batches (Eq. 5 and 8 or 9) Update actors   
+22: else   
+23: Update actor $\pi ^ { m }$ for ${ \frac { \mathrm { s t e p } } { M } } \cdot p$ mini-batches (Eq. 2)   
+24: end if   
+25: end for   
+26: for agent $m = 1 \ldots M$ do   
+27: $( \mathrm { F i t n e s s } _ { m } , \ l _ { - } ) \gets \mathtt { r o l l o u t } ( \pi ^ { m } ,$ , without noise, over $R$ episodes) Evaluate actors   
+28: end for   
+29: Rank population $\{ \pi _ { \phi , \theta } ^ { m } \} _ { m = 1 } ^ { M }$ and identify top- $K$   
+30: update_archiv $\mathsf { a } ( \mathcal { G } , \{ \pi _ { \phi , \theta } ^ { m } \} _ { m = 1 } ^ { M } , G )$   
+31: end while
+
+# COMPLEMENTARY PSEUDO-CODE FOR ARAC
+
+Algorithms 2 and 3 respectively provide the pseudo-code of functions rollout and update_archive used in Algorithm 1.
+
+# Algorithm 2 rollout
+
+Input: actor $\pi$ ; noise status; number of episodes $E$ ; replay buffer $\boldsymbol { B }$ ;   
+Fitness $ 0$   
+for episode $= 1 , \ldots , E$ do $\mathbf { s } \gets$ Initial state ${ \bf s } _ { 0 }$ from the environment for step $t = 0 \dots$ termination do if with noise then Sample noise $z$ else Set $z \gets 0$ end if $\mathbf { a } _ { t } \sim \pi ( . | \mathbf { s } _ { t } , z )$ Observe $\mathbf { s } _ { t + 1 } \sim P ( \cdot | \mathbf { s } _ { t } , \mathbf { a } _ { t } )$ and obtain reward $r _ { t }$ Fitness $\gets$ Fitness + rt Store transition $( \mathbf { s } _ { t } , \mathbf { a } _ { t } , r _ { t } , \mathbf { s } _ { t + 1 } )$ in $\boldsymbol { B }$ end for   
+end for   
+Fitness Fitness/ $E$   
+return Average fitness per episode and number of steps performed   
+Input: archive $\mathcal { G }$ ; population of size $M$ ; maximal archive capacity $G$ .   
+if $| { \mathcal { G } } | < G$ then Add all agents of current population to $\mathcal { G }$   
+else $c _ { 1 } , c _ { 2 } \gets 2$ -means(fitness of individuals in $\mathcal { G }$ ) for agent $m = 1 , \ldots , M$ do Assign agent $m$ to closest cluster $c \in \{ c _ { 1 } , c _ { 2 } \}$ based on its fitness Sample an archived agent $j \sim \mathrm { U n i f o r m } ( c )$ Replace archived individual $j$ by $m$ end for   
+end if   
+return Updated archive $\mathcal { G }$
+
+<table><tr><td>Algorithm archive</td></tr></table>

parse/train/BJlAzTEKwS/BJlAzTEKwS_content_list.json

@@ -0,0 +1,1823 @@
+[
+    {
+        "type": "text",
+        "text": "ATTRACTION-REPULSION ACTOR-CRITIC FOR CONTINUOUS CONTROL REINFORCEMENT LEARNING ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            98,
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+            146
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Anonymous authors Paper under double-blind review ",
+        "bbox": [
+            183,
+            170,
+            398,
+            198
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            234,
+            544,
+            251
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In reinforcement learning, robotic control tasks are often useful for understanding how agents perform in environments with deceptive rewards where the agent can easily become trapped into suboptimal solutions. One way to avoid these local optima is to use a population of agents to ensure coverage of the policy space (a form of exploration), yet learning a population with the “best” coverage is still an open problem. In this work, we present a novel approach to population-based RL in continuous control that leverages properties of normalizing flows to perform attractive and repulsive operations between current members of the population and previously observed policies. Empirical results on the MuJoCo suite demonstrate a high performance gain for our algorithm compared to prior work, including Soft-Actor Critic (SAC). ",
+        "bbox": [
+            233,
+            270,
+            766,
+            422
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            458,
+            336,
+            474
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Many important reinforcement learning (RL) tasks, such as those in robotics and self-driving cars, are challenging due to large action and state spaces (Lee et al., 2018). In particular, environments with large continuous action spaces are prone to deceptive rewards, i.e. fall into local optima in learning (Conti et al., 2018). Applying traditional policy optimization algorithms to these domains often leads to locally optimal, yet globally sub-optimal policies. The agent should then explore the reward landscape more thoroughly in order to avoid falling into these local optima. ",
+        "bbox": [
+            174,
+            492,
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+            577
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Not all RL domains that require exploration are suitable for understanding how to train agents that are robust to deceptive rewards. For example, Montezuma’s Revenge, a game in the Atari Learning Environment (Bellemare et al., 2013), has sparse rewards; algorithms that perform the best on this task encourage exploration by providing a denser intrinsic reward to the agent to encourage exploration (Tang et al., 2017). On the other hand, many robotic control problems, such as those found in MuJoCo (Todorov et al., 2012), provide the agent with a dense reward signal, yet their high-dimensional action spaces induce a multimodal, often deceptive, reward landscape. For example, in the biped environments, coordinating both arms and legs is crucial for performing well on even simple tasks such as forward motion. However, simply learning to maximize the reward can be detrimental across training: agents will tend to run and fall further away from the start point rather than discovering stable and efficient walking motion. In this setting, exploration serves to provide a more reliable learning signal for the agent by covering more different types of actions during learning. ",
+        "bbox": [
+            174,
+            583,
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+            750
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "One way to maximize action space coverage is the maximum entropy RL framework (Ziebart, 2010), which prevents variance collapse by adding a policy entropy auxiliary objective. One such prominent algorithm, Soft Actor-Critic (SAC,Haarnoja et al. (2018)), has been shown to excel in large continuous action spaces. To further improve on exploration properties of SAC, one can maintain a population of agents that cover non-identical sections of the policy space. To prevent premature convergence, a diversity-preserving mechanism is typically put in place; balancing the objective and the diversity term becomes key to converging to a global optimum (Hong et al., 2018). This paper studies a particular family of population-based exploration methods, which conduct coordinated local search in the policy space. Prior work on population-based strategies improves performance on robotic control domains through stochastic perturbation on a single actor’s parameter (Pourchot & Sigaud, 2019) or a set of actor’s parameters (Conti et al., 2018; Khadka & Tumer, 2018; Liu et al., 2017). We hypothesize that exploring directly in the policy space will be more effective than perturbing the parameters of the policy, as the latter does not guarantee diversity (i.e., different neural network parameterizations can approximately represent the same function). ",
+        "bbox": [
+            174,
+            757,
+            825,
+            924
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            171,
+            103,
+            823,
+            132
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Given a population of RL agents, we enforce local exploration using an Attraction-Repulsion (AR) mechanism. The later consists in adding an auxiliary loss to encourage pairwise attraction or repulsion between members of a population, as measured by a divergence term. We make use of the KullbackLeibler (KL) divergence because of its desirable statistical properties and its easiness of computation. However, naively maximizing the KL term between two Gaussian policies can be detrimental (e.g. drives both means apart). Because of this, we parametrize the policy with a general family of distributions called Normalizing Flows (NFs, Rezende & Mohamed, 2015); this modification allows to improve upon $\\mathrm { \\bf A R + }$ Gaussian (see Appendix Figure 6). NFs are shown to improve the expressivity of the policies using invertible mappings while maintaining entropy guarantees (Mazoure et al., 2019; Tang & Agrawal, 2018). Nonlinear density estimators have also been previously used for deep RL problems in contexts of distributional RL (Doan et al., 2018) and reward shaping (Tang et al., 2017). The AR objective blends particularly well with SAC, since computing the KL requires stochastic policies with tractable densities for each agent. ",
+        "bbox": [
+            173,
+            138,
+            826,
+            319
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 PRELIMINARIES ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            340,
+            339,
+            357
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We first formalize the RL setting in a Markov decision process (MDP). A discrete-time, finite-horizon, MDP (Bellman, 1957; Puterman, 2014) is described by a state space $s$ , an action space $\\mathcal { A }$ , a transition function $\\mathcal { P } : \\mathcal { S } \\times \\mathcal { A } \\times \\mathcal { S } \\mapsto \\mathbb { R } ^ { + }$ , and a reward function $r : S \\times \\mathcal { A } \\mapsto \\mathbb { R }$ .1 On each round $t$ , an agent interacting with this MDP observes the current state $s _ { t } \\in S$ , selects an action $a _ { t } \\in \\mathcal A$ , and observes a reward $r ( s _ { t } , a _ { t } ) \\in \\mathbb { R }$ upon transitioning to a new state $s _ { t + 1 } \\sim \\mathcal { P } ( s _ { t } , a _ { t } )$ . Let $\\gamma \\in [ 0 , 1 ]$ be a discount factor. The goal of an agent evolving in a discounted MDP is to learn a policy $\\Dot { \\pi } : \\Dot { S \\times A } \\mapsto [ 0 , 1 ]$ such as taking action $a _ { t } \\sim \\pi ( \\cdot | s _ { t } )$ would maximize the expected sum of discounted returns, ",
+        "bbox": [
+            173,
+            372,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "img_path": "images/2394701c30f961480407f719c1c3e2b0e8cd54caabd3407bb1e1ffc8ce2e257d.jpg",
+        "text": "$$\nV ^ { \\pi } ( s ) = \\mathbb { E } _ { \\pi } \\bigg [ \\sum _ { t = 0 } ^ { \\infty } \\gamma ^ { t } r ( s _ { t } , a _ { t } ) | s _ { 0 } = s \\bigg ] .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            369,
+            478,
+            627,
+            520
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In the following, we use $\\rho _ { \\pi }$ to denote the trajectory distribution induced by following policy $\\pi$ . If $s$ or $\\mathcal { A }$ are vector spaces, action and space vectors are respectively denoted by a and s. ",
+        "bbox": [
+            171,
+            526,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.1 DISCOVERING NEW SOLUTIONS THROUGH POPULATION-BASED ATTRACTION-REPULSION ",
+        "text_level": 1,
+        "bbox": [
+            171,
+            574,
+            821,
+            588
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Consider evolving a population of $M$ agents, also called individuals, $\\lbrace \\pi _ { \\theta _ { m } } \\rbrace _ { m = 1 } ^ { M }$ , each agent corresponding to a policy with its own parameters. In order to discover new solutions, we aim to generate agents that can mimic some target policy while following a path different from those of other policies. ",
+        "bbox": [
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+            598,
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Let $\\mathcal { G }$ denote an archive of policies encountered in previous generations of the population. A natural way of enforcing $\\pi$ to be different from or similar to the policies contained in $\\mathcal { G }$ is by augmenting the loss of the agent with an Attraction-Repulsion (AR) term: ",
+        "bbox": [
+            174,
+            648,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "img_path": "images/7af757c8ab405b8f1c79612bffc1612b211ea6df9a17755c8defe490526b179c.jpg",
+        "text": "$$\n\\begin{array} { r } { \\mathcal { L } _ { \\mathrm { A R } } = - \\underset { \\pi ^ { \\prime } \\sim \\mathcal { G } } { \\mathbb { E } } \\big [ \\beta _ { \\pi ^ { \\prime } } \\mathrm { D } _ { \\mathrm { K L } } [ \\pi | | \\pi ^ { \\prime } ] \\big ] , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            393,
+            698,
+            602,
+            722
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "where $\\pi ^ { \\prime }$ is an archived policy and $\\beta _ { \\pi ^ { \\prime } }$ is a coefficient weighting the relative importance of the Kullback-Leibler (KL) divergence between $\\pi$ and $\\pi ^ { \\prime }$ , which we will choose to be a function of the average reward (see Sec. 3.2 below). Intuitively, Eq. 1 adds to the agent objective a weighted average distance between the current and the archived policies. For $\\beta _ { \\pi ^ { \\prime } } \\geq 0$ , the agent tends to move away from the archived policy’s behavior (i.e. repulsion, see Figure 1) a). On the other hand, $\\beta _ { \\pi ^ { \\prime } } < 0$ encourages the agent $\\pi$ to imitate $\\pi ^ { \\prime }$ (i.e. attraction). ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Requirements for AR In order for agents within a population to be trained using the proposed AR-based loss (Eq. 1), we have the following requirements: ",
+        "bbox": [
+            171,
+            830,
+            823,
+            859
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "1. Their policies should be stochastic, so that the KL-divergence between two policies is well-defined. ",
+        "bbox": [
+            209,
+            871,
+            825,
+            900
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Their policies should have tractable distributions, so that the KL-divergence can be computed easily, either with closed-form solution or Monte Carlo estimation. ",
+        "bbox": [
+            204,
+            103,
+            825,
+            132
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Several RL algorithms enjoy such properties (Haarnoja et al., 2018; Schulman et al., 2015; 2017). In particular, the soft actor-critic (SAC, Haarnoja et al., 2018) is a straightforward choice, as it currently outperforms other candidates and is off-policy, thus maintains a single critic shared among all agents (instead of one critic per agent), which reduces computation costs. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.2 SOFT ACTOR-CRITIC ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            217,
+            357,
+            232
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "SAC (Haarnoja et al., 2018) is an off-policy learning algorithm which finds the information projection of the Boltzmann Q-function onto the set of diagonal Gaussian policies $\\Pi$ : ",
+        "bbox": [
+            171,
+            243,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/2f126db3046e7080aa205ca5a5625209e7e4cdaa5b94d5c905d1fab1d2d456a8.jpg",
+        "text": "$$\n\\pi = \\underset { \\pi ^ { \\prime } \\in \\Pi } { \\arg \\operatorname* { m i n } } \\mathrm { D } _ { \\mathrm { K L } } \\bigg ( \\pi ^ { \\prime } ( . | \\mathbf { s } _ { t } ) \\bigg | \\bigg | \\frac { \\exp \\big ( \\frac { 1 } { \\alpha } Q ^ { \\pi _ { \\mathrm { o l d } } } \\big ( \\mathbf { s } _ { t } , . \\big ) \\big ) } { Z ^ { \\pi _ { \\mathrm { o l d } } } \\big ( \\mathbf { s } _ { t } \\big ) } \\bigg ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            331,
+            279,
+            665,
+            316
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where $\\alpha \\in ( 0 , 1 )$ controls the temperature, i.e. the peakedness of the distribution. The policy $\\pi$ , critic $Q$ , and value function $V$ are optimized according to the following loss functions: ",
+        "bbox": [
+            174,
+            324,
+            825,
+            352
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/5d58c2c8ca0800127c9bb9bb19e622f912ca3ac0272cc1f5482402a6c745458e.jpg",
+        "text": "$$\n\\begin{array} { r l } & { \\mathcal { L } _ { \\pi , \\mathrm { S A C } } = \\mathbb { E } _ { \\mathbf { s } _ { t } \\sim \\mathcal { B } } [ \\mathbb { E } _ { \\mathbf { a } _ { t } \\sim \\pi } [ \\alpha \\log \\pi ( \\mathbf { a } _ { t } | \\mathbf { s } _ { t } ) - Q ( \\mathbf { s } _ { t } , \\mathbf { a } _ { t } ) ] ] } \\\\ & { \\qquad \\mathcal { L } _ { Q } = \\underset { ( s , a , r , s ^ { \\prime } ) \\sim \\mathcal { B } } { \\mathbb { E } } [ \\{ Q ( s , a ) - ( r + \\gamma V _ { \\nu } ^ { \\pi } ( s ^ { \\prime } ) ) \\} ^ { 2 } ] } \\\\ & { \\qquad \\mathcal { L } _ { V } = \\mathbb { E } _ { \\mathbf { s } _ { t } \\sim \\mathcal { D } } \\bigg [ \\frac { 1 } { 2 } \\big \\{ V _ { \\nu } ^ { \\pi } ( \\mathbf { s } _ { t } ) - \\mathbb { E } _ { \\mathbf { a } _ { t } \\sim \\pi } [ Q ( \\mathbf { s } _ { t } , \\mathbf { a } _ { t } ) - \\alpha \\log \\pi ( \\mathbf { a } _ { t } | \\mathbf { s } _ { t } ) ] \\big \\} ^ { 2 } \\bigg ] , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            264,
+            358,
+            733,
+            443
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where $\\boldsymbol { B }$ is the replay buffer. The policy used in SAC as introduced in Haarnoja et al. (2018) is Gaussian, which is both stochastic and tractable, thus compatible with our AR loss function in Eq. 1. Together with the AR loss in Eq. 1, the final policy loss becomes: ",
+        "bbox": [
+            176,
+            446,
+            826,
+            489
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/963a0767e1202559f840210ad31010f34ea07345530e65569ae7e34e868801c9.jpg",
+        "text": "$$\n\\mathcal { L } _ { \\pi } = \\mathcal { L } _ { \\pi , \\mathrm { S A C } } + \\mathcal { L } _ { \\mathrm { A R } }\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "However, Gaussian policies are arguably of limited expressibility; we can improve on the family of policy distributions without sacrificing qualities necessary for AR or SAC by using Normalizing Flows (NFs, Rezende & Mohamed, 2015). ",
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+    {
+        "type": "text",
+        "text": "2.3 NORMALIZING FLOWS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "NFs (Rezende & Mohamed, 2015) were introduced as a means of transforming simple distributions into more complex distributions using learnable and invertible functions. Given a random variable $\\mathbf { z } _ { 0 }$ sequence of with density $q _ { 0 }$ $d$ 0-dimensional random variables, , they define a set of differentiable and invertible functions, $\\{ { \\mathbf { z } } _ { i } \\} _ { i = 1 } ^ { N }$ . $\\{ f _ { i } \\} _ { i = 1 } ^ { N }$ , which generate a ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Because SAC uses explicit, yet simple parametric policies, NFs can be used to transform the SAC policy into a richer one (e.g., multimodal) without risk loss of information. For example, Mazoure et al. (2019) enhanced SAC using a family of radial contractions around a point $\\mathbf { z } _ { 0 } \\in \\bar { \\mathbb { R } } ^ { d }$ , ",
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+    {
+        "type": "equation",
+        "img_path": "images/78f2d2023950a3fe8d9701cea3fc796fb41b571029efcfd053ead74ff8577ae1.jpg",
+        "text": "$$\nf ( \\mathbf { z } ) = \\mathbf { z } + { \\frac { \\beta } { \\alpha + | | \\mathbf { z } - \\mathbf { z } _ { 0 } | | _ { 2 } } } ( \\mathbf { z } - \\mathbf { z } _ { 0 } )\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "for $\\alpha \\in \\mathbb { R } ^ { + }$ and $\\beta \\in \\mathbb { R }$ . This results in a rich set of policies comprised of an initial noise sample ${ \\bf a } _ { 0 }$ , a state-noise embedding $h _ { \\theta } ( \\mathbf { a } _ { 0 } , \\mathbf { s } _ { t } )$ , and a flow $\\{ \\dot { f } _ { \\phi _ { i } } \\} _ { i = 1 } ^ { N }$ of arbitrary length $N$ , parameterized by $\\phi = \\{ \\phi _ { i } \\} _ { i = 1 } ^ { N }$ . Sampling from the policy $\\pi _ { \\phi , \\theta } ( \\mathbf { a } _ { t } | \\mathbf { s } _ { t } )$ can be described by the following set of equations: ",
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/e123e5b27c6bf17fbfdf1d2e5cde202f996e672b333f249afa2aca8287252565.jpg",
+        "text": "$$\n\\begin{array} { r l } & { \\mathbf { a } _ { 0 } \\sim \\mathcal { N } ( 0 , \\mathbf { I } ) ; } \\\\ & { \\mathbf { \\Phi } \\mathbf { z } = h _ { \\theta } ( \\mathbf { a } _ { 0 } , \\mathbf { s } _ { t } ) ; } \\\\ & { \\mathbf { a } _ { t } = f _ { \\phi _ { N } } \\circ f _ { \\phi _ { N - 1 } } \\circ \\dots \\circ f _ { \\phi _ { 1 } } ( \\mathbf { z } ) , } \\end{array}\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where $h _ { \\theta } = \\mathbf { a } _ { 0 } \\sigma \\mathbf { I } + \\mu ( \\mathbf { s } _ { t } )$ depends on the state and the noise variance $\\sigma > 0$ . Different SAC policies can thus be crafted by parameterizing their NFs layers. ",
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+    {
+        "type": "image",
+        "img_path": "images/5f1e484c07b4d6aae050dd38be514b6f5d99e8200b908a2090a82327bc3e358f.jpg",
+        "image_caption": [
+            "Figure 1: a) Augmenting the loss function with AR constraints allows an agent to reach a target policy by following different paths. Attractive and Repulsive policies represent any other agent’s policy. b) General flow of the proposed ARAC strategy. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "3 ARAC: ATTRACTION-REPULSION ACTOR-CRITIC ",
+        "text_level": 1,
+        "bbox": [
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+        "type": "text",
+        "text": "We now detail the general procedure for training a population of agents using the proposed diversityseeking AR mechanism. More specifically, we consider here SAC agents enhanced with NFs (Mazoure et al., 2019). Figure 1 displays the general flow of the procedure. Algorithm 1 (Appendix) provides the pseudo-code of the proposed ARAC strategy, where sub-procedures for rollout and archive update can be found in the Appendix. ",
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+    {
+        "type": "text",
+        "text": "Overview ARAC works by evolving a population of $M$ SAC agents $\\{ \\pi _ { \\phi , \\theta } ^ { m } \\} _ { m = 1 } ^ { M }$ with radial NFs policies (Eq. 7) and shared critic , and by maintaining an archive of policies encountered in previous generations of the population. After performing $T$ steps per agent on the environment (Alg. 1 L8-12), individuals are evaluated by performing $R$ rollouts2 on the environment (Alg. 1 L26-28). This allows to identify the top- $K$ best agents (Alg. 1 L29), also called elites, which will be used to update the critic as they provide the most meaningful feedback (Alg. 1 L13-17). The archive is finally updated in a diversity-seeking fashion using the current population (Alg. 1 L30). ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The core component of the proposed approach lies within the update of the agents (Alg. 1 L18-25). During this phase, elite individuals are updated using AR operations w.r.t. policies sampled from the archive (Eq. 5), whereas non-elites are updated regularly (Eq. 2). ",
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+    {
+        "type": "text",
+        "text": "3.1 ENHANCING DIVERSITY IN THE ARCHIVE ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Throughout the training process, we maintain an archive $\\mathcal { G }$ of maximum capacity $G$ , which contains some previously encountered policies. The process goes as follow: until reaching full capacity, the archive saves a copy of the parameters of every individual in the population after the evaluation step. However, by naively adding all individuals as if the archive were just a heap, the archive could end up filled with policies leading to similar rewards, which would result in a loss of diversity (Mauldin, 1984). We mitigate this issue by keeping track of two fitness clusters (low and high) using the partition formed by running a $k$ -means algorithm on the fitness value. Hence, when $| { \\mathcal { G } } | = G$ is reached and a new individual is added to the archive, it randomly replaces an archived policy from its respective cluster. This approach, also known as niching, has proved itself effective at maintaining high diversity levels (Gupta & Ghafir, 2012; Mahfoud, 1995). ",
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+    {
+        "type": "text",
+        "text": "3.2 DISCOVERING NEW POLICIES THROUGH ATTRACTION-REPULSION ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The crux of this work lies in the explicit search for diversity in the policy space achieved using the AR mechanism. Since the KL between two base policies (i.e. input of the first flow layer) can be trivially maximized by driving their means apart, we apply attraction-repulsion only on the flow layers, while holding the mean of the base policy constant. This ensures that the KL term doesn’t depend on the difference in means and hence controls the magnitude of the AR mechanism. Every time the AR operator is applied (Alg. 1 L20-21), $n$ policies are sampled from the archive and are used for estimating the AR loss (Eq. 1). As in Hong et al. (2018), we consider two possible strategies to dictate the value of $\\beta _ { \\pi ^ { \\prime } }$ coefficients for policies $\\pi ^ { \\prime } \\sim \\mathcal { G }$ : ",
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+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/9bbbc002711d0542bb426d686a74f0370c6fb28d2354159cf46231659c3b84d4.jpg",
+        "text": "$$\n\\begin{array} { l } { \\displaystyle \\beta _ { \\pi ^ { \\prime } } = - \\biggl [ 2 \\biggl ( \\frac { f \\bigl ( \\pi ^ { \\prime } \\bigr ) - f _ { m i n } } { f _ { m a x } - f _ { m i n } } - 1 \\biggr ) \\biggr ] } \\\\ { \\displaystyle \\beta _ { \\pi ^ { \\prime } } = 1 - \\frac { f \\bigl ( \\pi ^ { \\prime } \\bigr ) - f _ { m i n } } { f _ { m a x } - f _ { m i n } } } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $f ( \\pi ) ^ { 3 }$ represents the fitness function of policy $\\pi$ (average reward in our case), and $f _ { m i n }$ and $f _ { m a x }$ are estimated based on the $n$ sampled archived policies. The proactive strategy aims to mimic high reward archived policies, while the reactive strategy is more cautious, only repulsing away the current policy from low fitness archived policies. Using this approach, the current agent policy will be attracted to some sampled policies $( \\beta _ { \\pi ^ { \\prime } } < 0 )$ ) and will be repulsed from others $\\beta _ { \\pi ^ { \\prime } } \\geq 0 )$ ) in a more or less aggressive way, depending on the strategy. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Unlike Hong et al. (2018) who applied proactive and reactive strategies on policies up to 5 timesteps back, we maintain an archive consisting of two clusters seen so far: policies with low and high fitness, respectively. Having this cluster allows to attract/repulse from a set of diverse agents, replacing high-reward policies by policies with similar performance. Indeed, without this process, elements of the archive would collapse on the most frequent policy, from which all agents would attract/repulse. To avoid performing AR against a single \"average policy\" , we separate low-reward and high-reward agents via clustering. ",
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+    {
+        "type": "text",
+        "text": "4 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The challenges of exploration are well studied in the RL literature. Previously proposed approaches for overcoming hard exploration domains tend to either increase the capacity of the state-action value function (Gal & Ghahramani, 2016; Henderson et al., 2017) or the policy expressivity (Mazoure et al., 2019; Tang & Agrawal, 2018; Touati et al., 2018). This work rather tackles exploration from a diverse multi-agent perspective. Unlike prior population-based approaches for exploration (Conti et al., 2018; Khadka & Tumer, 2018; Pourchot & Sigaud, 2019), which seek diversity through the parameters space, we directly promote diversity in the policy space. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The current work was inspired by Hong et al. (2018), who relied on the KL divergence to attract/repulse from a set of previous policies to discover new solutions. However, in their work, the archive is time-based (they restrict themselves to the 5 most recent policies), while our archive is built following a diversity-seeking strategy (i.e., niching and policies come from multiple agents). Notably, ARAC is different of previously discussed works in that it explores the action space in multiple regions simultaneously, a property enforced through the AR mechanism. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The proposed approach bears some resemblance with Liu et al. (2017), who took advantage of a multi-agent framework in order to perform repulsion operations among agents using of similarity kernels between parameters of the agents. The AR mechanism gives rise to exploration through structured policy rather than randomized policy. This strategy has also been employed in multi-task learning (Gupta et al., 2018), where experience on previous tasks was used to explore on new tasks. ",
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+    {
+        "type": "text",
+        "text": "5 EXPERIMENTS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "5.1 DIDACTIC EXAMPLE ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Consider a 2-dimensional multi-armed bandit problem where the actions lie in the real square $[ - 6 , 6 ] ^ { 2 }$ . We illustrate the example of using a proactive strategy where a SAC agent with radial flows policy imitates a desirable (expert) policy while simultaneously repelling from a less desirable policy. The task consists in matching the expert’s policy (blue density) while avoiding taking actions from a repulsive policy $\\pi ^ { \\prime }$ (red). We illustrate the properties of radial flows in Figure 2 by increasing the number of flows (where 0 flow corresponds to a Gaussian distribution). ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We observe that increasing the number of flows (bottom to top) leads to more complex policy’s shapes and multimodality unlike the Gaussian policy which has its variance shrinked (the KL divergence is proportional to the ratio of the two variances, hence maximizing it can lead to a reduction in the variance which can be detrimental for exploration purpose). Details are provided in Appendix. ",
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+    {
+        "type": "image",
+        "img_path": "images/1036cd057f37e814ff6f335c0a03dd0dd10f946762eb28661267361a0bedc134.jpg",
+        "image_caption": [
+            "Figure 2: Agent trained to imitate a target while avoiding a repulsive policy using a proactive strategy. Increasing the number of flows leads to more complex policy’s shape. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "image",
+        "img_path": "images/85f6af52b9f366799b350719614483ad9e8170c22dac51befe8f4baebf61470b.jpg",
+        "image_caption": [
+            "Figure 3: Average return and one standard deviation on 5 random seeds across 7 MuJoCo tasks for ARAC against single SAC agents (with and without NFs). Curves are smoothed using Savitzky-Golay filtering with window size of 7. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "5.2 MUJOCO LOCOMOTION BENCHMARKS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We now compare ARAC against the CEM-TD3 (Pourchot & Sigaud, 2019), ERL (Khadka & Tumer, 2018) and CERL (Khadka et al., 2019) multi-agent baselines on seven continuous control tasks from the MuJoco suite (Duan et al., 2016): Ant-v2, HalfCheetah-v2, Humanoid-v2, HumanoidStandup-v2, Hopper-v2, Walker2d-v2 and Humanoid (rllab). We also designed a sparse reward environment SparseHumanoid-v2. All algorithms are run over 1M time steps on each environment, except Humanoid (rllab) which gets 2M time steps and SparseHumanoid-v2 on $0 . 6 { \\bf M }$ time steps. We also include comparison against single-agent baselines. ",
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+    {
+        "type": "text",
+        "text": "ARAC performs $R = 1 0$ rollouts for evaluation steps every 10, 000 interaction steps with the environment. We consider a small population of $N = 5$ individuals with $K = 2$ as elites. Every SAC agent has one feedforward hidden layer of 256 units acting as state embedding, followed by a radial flow of length $\\in \\{ 3 , 4 \\}$ . A temperature of $\\alpha = 0 . 0 5$ or 0.2 is used across all the environments (See appendix for more details). AR operations are carried out by sampling uniformly $n = 5$ archived policies from $\\mathcal { G }$ . Parameters details are provided in the Appendix (Table 4). All networks are trained with Adam optimizer (Kingma & Ba, 2015) using a learning rate of $\\mathrm { 3 E ^ { - 4 } }$ . Baselines CEM-TD34, $\\mathrm { E R L } ^ { 5 }$ , CERL6 use the code contained in their respective repositories. ",
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+    {
+        "type": "table",
+        "img_path": "images/cd403724e9d9b23ce7ef79acd2a040c4516392414a5778735c01ea245d7324cd.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 1: Maximum average return after 1M (2M for Humanoid (rllab) and 600k for SparseHumanoid-v2) time steps 5 random seeds. Bold: best methods when the gap is less than 100 units. See appendix for average return with standard deviation. Environment short names: HC: HalfCheetah-v2, Hu: Humanoid-v2, Standup: HumanoidStandup-v2 "
+        ],
+        "table_body": "<table><tr><td></td><td>ARAC</td><td>CEM-TD3</td><td>CERL</td><td>ERL</td><td>SAC-NF</td><td>SAC</td><td>TD3</td></tr><tr><td>Ant</td><td>6044</td><td>4239</td><td>1639</td><td>1442</td><td>4912</td><td>4370</td><td>4372</td></tr><tr><td>HC</td><td>10264</td><td>10659</td><td>5703</td><td>6746</td><td>8429</td><td>11 900</td><td>9543</td></tr><tr><td>Hopper</td><td>3587</td><td>3655</td><td>2970</td><td>1149</td><td>3538</td><td>2794</td><td>3564</td></tr><tr><td>Hu</td><td>5965</td><td>212</td><td>4756</td><td>551</td><td>5506</td><td>5504</td><td>71</td></tr><tr><td>Standup</td><td>175 000</td><td>29 000</td><td>117000</td><td>12 900</td><td>116 000</td><td>149 000</td><td>54000</td></tr><tr><td>Hu (rllab)</td><td>14 230</td><td>1334</td><td>3340</td><td>57</td><td>5531</td><td>1963</td><td>286</td></tr><tr><td>Walker2d</td><td>4704</td><td>4710</td><td>4386</td><td>1107</td><td>5196</td><td>3783</td><td>4682</td></tr><tr><td>Hu (Sparse)</td><td>816</td><td>0</td><td>1.32</td><td>8.65</td><td>547</td><td>88</td><td>0</td></tr></table>",
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Figure 4 displays the performance of all algorithms on three environments over time steps (see Appendix Figure 7 for all environments). Results are averaged over 5 random seeds. Table 1 reports the best observed reward for each method. ",
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+    {
+        "type": "image",
+        "img_path": "images/7c61fe7d139129b6333acea8071a346e8a481d71ecd2da64dcd95580615568ae.jpg",
+        "image_caption": [
+            "Figure 4: Average return and one standard deviation on 5 random seeds across 8 MuJoCo tasks. Curves are smoothed using Savitzky-Golay filtering with window size of 7. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Small state space environments HalfCheetah-v2, Hopper-v2, and Walker2d-v2 are low-dimensional state space environments $( d \\leq 1 7 )$ . Except for HalfCheetah-v2, the proposed approach shows comparable results with its concurrent. Those results match the findings of (Plappert et al., 2018) that some environments with well-structured dynamics require little exploration. Full learning curves can be found in the Appendix. ",
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "Deceptive reward and Large state space environments Humanoid-v2, HumanoidStandup-v2 and Humanoid (rllab) belong to bipedal environments with high-dimensional state space $( d = 3 7 6$ and $d = 1 4 7$ ), and are known to trap algorithms into suboptimal solutions. In addition to the legs, the agent also needs to control the arms, which may influence the walking way and hence induce deceptive rewards (Conti et al., 2018). Figure 4 shows the learning curves on MuJoCo tasks. We observe that ARAC beats both baselines in performance as well as in convergence rate. ",
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "Ant-v2 is another high-dimensional state space environment $\\mathit { l } \\geq 1 0 0 )$ . In an unstable setup, a naive algorithm implementing an unbalanced fast walk could still generate high reward, the reward taking into account the distance from start, instead of learning to stand, stabilize, and walk (as expected). ",
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+    {
+        "type": "text",
+        "text": "Sparse reward environment To test ARAC in a sparse reward environment, we created SparseHumanoid-v2. The dynamic is the same as Humanoid-v2 but rewards of $+ 1$ is granted only given is the center of mass of the agent is above a threshold (set to 0.6 unit in our case). The challenge not only lies in the sparse reward property but also on the complex body dynamic that can make the agent falling down and terminating the episode. As shown in Figure 4, ARAC is the only method that can achieve non zero performance. A comparison against single agent methods in the Appendix also shows better performance for ARAC. ",
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+        "type": "text",
+        "text": "Sample efficiency compared with single agent methods Figure 3 (in Appendix) also shows that the sample efficiency of the population-based ARAC compares to a single SAC agent (with and without NFs) and other baselines methods (SAC, TD3). On Humanoid-v2 and Ant-v2 ARAC converges faster, reaching the 6k (4k, respectively) milestone performance after only 1M steps, while a single SAC agent requires 4M (3M, respectively) steps according to (Haarnoja et al., 2018). In general, ARAC achieves competitive results (no flat curves) and makes the most difference (faster convergence and better performance) in the biped environments. ",
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+        "type": "text",
+        "text": "Attraction-repulsion ablation study To illustrate the impact of repulsive forces, we introduce a hyperparameter $\\lambda$ in the overall loss (Eq. 5): ",
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+    {
+        "type": "equation",
+        "img_path": "images/f80d9d80506653ff593addd9c7bbb73258da29ea05f7d263e85c75031bf12940.jpg",
+        "text": "$$\n\\mathcal { L } _ { \\theta , \\phi , \\lambda } = \\mathcal { L } _ { \\theta , \\phi , \\mathrm { S A C } } + \\lambda \\mathcal { L } _ { \\phi , \\mathrm { A R } }\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "We ran an ablation analysis on Humanoid-v2 by varying that coefficient. For two random states, we sampled 500 actions from all agents and mapped these actions onto a two-dimensional space (via t-SNE). Appendix Figure 5 shows that without repulsion $\\lambda = 0$ ), actions from all agents are entangled, while repulsion $( \\lambda > 0$ ) forces agents to behave differently and hence explore different regions of the action space. ",
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+    {
+        "type": "text",
+        "text": "The second ablation study is dedicated to highlight the differences between a Gaussian policy (similar to Hong et al. (2018) and an NF policy under AR operators. As one can observe in Figure 6, using a Gaussian policy deteriorates the solution as the repulsive KL term drives apart the means of agents and blows up/ shrinks the variance of the Gaussian policy. On the other hand, applying the AR term on the NF layers maximizes the KL conditioned on the mean and variance of both base policies, resulting in a solution which allows sufficient exploration. More details are provided in the Appendix. ",
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+    {
+        "type": "text",
+        "text": "Finally, through a toy example subject to AR, we characterize the policy’s shape when increasing the number of the radial flow policy in Figure 2 (experimental setup in Appendix). Unlike the diagonal Gaussian policy (SAC) that has symmetry constraints, increasing the number of flows allows the radial policy to adopt more complex shapes (from bottom to top). ",
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+    {
+        "type": "text",
+        "text": "6 CONCLUSION ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In this paper, we addressed the issue of RL domains with deceptive rewards by introducing a population-based search model for optimal policies using attraction-repulsion operators. Our method relies on powerful density estimators (normalizing flows), to let policies exploit the reward landscape under AR constraints. Our ablation studies showed that (1) the strength of AR and (2) the number of flows are the two factors which predominantly affect the shape of the policy. Selecting the correct AR coefficient is therefore important to obtain good performance, while at the same time preventing premature convergence. ",
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+    {
+        "type": "text",
+        "text": "Empirical results on the MuJoCo suite demonstrate high performance of the proposed method in most settings, including with sparse rewards. Moreover, in biped environments that are known to trap algorithms into suboptimal solutions, ARAC enjoys higher sample efficiency and better performance compared to its competitors which confirms our intuitions on using AR with normalizing flows. As future steps, borrowing from multi-objective optimization literature methods could allow one to combine other diversity metrics with the performance objective, to in turn improve the coverage of the solution space among the individuals by working with the corresponding Pareto front (Horn et al., 1994). ",
+        "bbox": [
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+            811,
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+        ],
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+    {
+        "type": "text",
+        "text": "REFERENCES ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            103,
+            287,
+            117
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Marc G Bellemare, Yavar Naddaf, Joel Veness, and Michael Bowling. The arcade learning environment: An evaluation platform for general agents. Journal of Artificial Intelligence Research, 47: 253–279, 2013. ",
+        "bbox": [
+            173,
+            126,
+            825,
+            167
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Richard Bellman. A markovian decision process. Journal of Mathematics and Mechanics, pp. 679–684, 1957. ",
+        "bbox": [
+            171,
+            178,
+            825,
+            207
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Edoardo Conti, Vashisht Madhavan, Felipe Petroski Such, Joel Lehman, Kenneth Stanley, and Jeff Clune. Improving exploration in evolution strategies for deep reinforcement learning via a population of novelty-seeking agents. In Advances in Neural Information Processing Systems (NeurIPS), pp. 5027–5038, 2018. ",
+        "bbox": [
+            173,
+            217,
+            826,
+            273
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Thang Doan, Bogdan Mazoure, and Clare Lyle. Gan q-learning. arXiv preprint arXiv:1805.04874, 2018. ",
+        "bbox": [
+            174,
+            284,
+            823,
+            311
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Yan Duan, Xi Chen, Rein Houthooft, John Schulman, and Pieter Abbeel. Benchmarking deep reinforcement learning for continuous control. In International Conference on Machine Learning (ICML), pp. 1329–1338, 2016. ",
+        "bbox": [
+            174,
+            320,
+            826,
+            364
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Yarin Gal and Zoubin Ghahramani. Dropout as a bayesian approximation: Representing model uncertainty in deep learning. In International conference on machine learning (ICML), pp. 1050– 1059, 2016. ",
+        "bbox": [
+            174,
+            375,
+            826,
+            416
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Abhishek Gupta, Russell Mendonca, YuXuan Liu, Pieter Abbeel, and Sergey Levine. Metareinforcement learning of structured exploration strategies. In Advances in Neural Information Processing Systems (NeurIPS), pp. 5302–5311, 2018. ",
+        "bbox": [
+            173,
+            426,
+            823,
+            469
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Deepti Gupta and Shabina Ghafir. An overview of methods maintaining diversity in genetic algorithms. International journal of emerging technology and advanced engineering, 2(5):56–60, 2012. ",
+        "bbox": [
+            169,
+            478,
+            825,
+            508
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Tuomas Haarnoja, Aurick Zhou, Pieter Abbeel, and Sergey Levine. Soft Actor-Critic: Off-policy maximum entropy deep reinforcement learning with a stochastic actor. In International Conference on Machine Learning (ICML), pp. 1856–1865, 2018. ",
+        "bbox": [
+            174,
+            517,
+            823,
+            560
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Peter Henderson, Thang Doan, Riashat Islam, and David Meger. Bayesian policy gradients via alpha divergence dropout inference. NIPS Bayesian Deep Learning Workshop, 2017. ",
+        "bbox": [
+            173,
+            569,
+            821,
+            599
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Zhang-Wei Hong, Tzu-Yun Shann, Shih-Yang Su, Yi-Hsiang Chang, Tsu-Jui Fu, and Chun-Yi Lee. Diversity-driven exploration strategy for deep reinforcement learning. In Advances in Neural Information Processing Systems (NeurIPS), pp. 10489–10500, 2018. ",
+        "bbox": [
+            174,
+            608,
+            826,
+            651
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Jeffrey Horn, Nicholas Nafpliotis, and David E. Goldberg. A niched pareto genetic algorithm for multiobjective optimization. In Proceedings of the 1st IEEE Conference on Evolutionary Computation, IEEE World Congress on Computational Intelligence, pp. 82–87, 1994. ",
+        "bbox": [
+            173,
+            660,
+            826,
+            704
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Shauharda Khadka and Kagan Tumer. Evolution-guided policy gradient in reinforcement learning. In Advances in Neural Information Processing Systems (NeurIPS), pp. 1188–1200, 2018. ",
+        "bbox": [
+            173,
+            713,
+            825,
+            742
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Shauharda Khadka, Somdeb Majumdar, Tarek Nassar, Zach Dwiel, Evren Tumer, Santiago Miret, Yinyin Liu, and Kagan Tumer. Collaborative evolutionary reinforcement learning. CoRR, abs/1905.00976, 2019. URL http://arxiv.org/abs/1905.00976. ",
+        "bbox": [
+            176,
+            751,
+            825,
+            795
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Diederik P. Kingma and Jimmy Ba. Adam: A method for stochastic optimization. In International Conference on Learning Representations (ICLR), 2015. ",
+        "bbox": [
+            171,
+            804,
+            825,
+            833
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Kyowoon Lee, Sol-A Kim, Jaesik Choi, and Seong-Whan Lee. Deep reinforcement learning in continuous action spaces: a case study in the game of simulated curling. In International Conference on Machine Learning, pp. 2943–2952, 2018. ",
+        "bbox": [
+            173,
+            843,
+            823,
+            886
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Yang Liu, Prajit Ramachandran, Qiang Liu, and Jian Peng. Stein variational policy gradient. In Conference on Uncertainty in Artificla Intelligence (UAI), 2017. ",
+        "bbox": [
+            176,
+            895,
+            821,
+            924
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Samir W Mahfoud. Niching methods for genetic algorithms. PhD thesis, University of Illinois at Urbana-Champaign Champaign, USA, 1995. ",
+        "bbox": [
+            171,
+            103,
+            825,
+            132
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Michael L Mauldin. Maintaining diversity in genetic search. In AAAI Conference on Artificial Intelligence (AAAI), pp. 247–250, 1984. ",
+        "bbox": [
+            171,
+            141,
+            823,
+            170
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Bogdan Mazoure, Thang Doan, Audrey Durand, R Devon Hjelm, and Joelle Pineau. Leveraging exploration in off-policy algorithms via normalizing flows. Proceedings of the 3rd Conference on Robot Learning (CoRL 2019), 2019. ",
+        "bbox": [
+            176,
+            178,
+            823,
+            222
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Joelle Pineau. The machine learning reproducibility checklist. 2018. ",
+        "bbox": [
+            173,
+            231,
+            624,
+            246
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Matthias Plappert, Rein Houthooft, Prafulla Dhariwal, Szymon Sidor, Richard Y Chen, Xi Chen, Tamim Asfour, Pieter Abbeel, and Marcin Andrychowicz. Parameter space noise for exploration. arXiv preprint arXiv:1706.01905, 2017. ",
+        "bbox": [
+            176,
+            253,
+            826,
+            296
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Matthias Plappert, Rein Houthooft, Prafulla Dhariwal, Szymon Sidor, Richard Y. Chen, Xi Chen, Tamim Asfour, Pieter Abbeel, and Marcin Andrychowicz. Parameter space noise for exploration. In International Conference on Learning Representations (ICLR), 2018. ",
+        "bbox": [
+            174,
+            305,
+            826,
+            349
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Aloïs Pourchot and Olivier Sigaud. CEM-RL: Combining evolutionary and gradient-based methods for policy search. In International Conference on Learning Representations (ICLR), 2019. ",
+        "bbox": [
+            173,
+            357,
+            821,
+            387
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Martin L Puterman. Markov decision processes: discrete stochastic dynamic programming. John Wiley & Sons, 2014. ",
+        "bbox": [
+            173,
+            395,
+            823,
+            424
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Danilo Jimenez Rezende and Shakir Mohamed. Variational inference with normalizing flows. In International Conference on Machine Learning (ICML), pp. 1530–1538, 2015. ",
+        "bbox": [
+            174,
+            433,
+            821,
+            463
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "John Schulman, Sergey Levine, Pieter Abbeel, Michael Jordan, and Philipp Moritz. Trust region policy optimization. In International Conference on Machine Learning (ICML), pp. 1889–1897, 2015. ",
+        "bbox": [
+            174,
+            469,
+            826,
+            513
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov. Proximal policy optimization algorithms. arXiv preprint: 1707.06347, 2017. ",
+        "bbox": [
+            173,
+            522,
+            823,
+            551
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Haoran Tang, Rein Houthooft, Davis Foote, Adam Stooke, OpenAI Xi Chen, Yan Duan, John Schulman, Filip DeTurck, and Pieter Abbeel. # Exploration: A study of count-based exploration for deep reinforcement learning. In Advances in neural information processing systems (NeurIPS), pp. 2753–2762, 2017. ",
+        "bbox": [
+            174,
+            559,
+            826,
+            616
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Yunhao Tang and Shipra Agrawal. Boosting trust region policy optimization by normalizing flows policy. arXiv preprint: 1809.10326, 2018. ",
+        "bbox": [
+            173,
+            626,
+            823,
+            655
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Emanuel Todorov, Tom Erez, and Yuval Tassa. Mujoco: A physics engine for model-based control. In IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 5026–5033. IEEE, 2012. ",
+        "bbox": [
+            173,
+            662,
+            826,
+            705
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Ahmed Touati, Harsh Satija, Joshua Romoff, Joelle Pineau, and Pascal Vincent. Randomized value functions via multiplicative normalizing flows. arXiv preprint: 1806.02315, 2018. ",
+        "bbox": [
+            169,
+            714,
+            823,
+            744
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Brian D Ziebart. Modeling purposeful adaptive behavior with the principle of maximum causal entropy. PhD thesis, figshare, 2010. ",
+        "bbox": [
+            173,
+            752,
+            823,
+            781
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "APPENDIX ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            103,
+            263,
+            117
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "REPRODUCIBILITY CHECKLIST ",
+        "bbox": [
+            176,
+            133,
+            392,
+            148
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "We follow the reproducibility checklist (Pineau, 2018) and point to relevant sections explaining them here. ",
+        "bbox": [
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "For all algorithms presented, check if you include: ",
+        "bbox": [
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "• A clear description of the algorithm, see main paper and included codebase. The proposed approach is completely described by Alg. 1 (main paper), 2 (Appendix), and 3 (Appendix). The proposed population-based method uses attraction-repulsion operators in order to enforce a better policy space coverage by different agents. An analysis of the complexity (time, space, sample size) of the algorithm. See Appendix Figure 7 and 3. Experimentally, we demonstrate improvement in sample complexity as discussed in our main paper. In term of computation time, the proposed method scales linearly with the population size if agents are evaluated sequentially (as presented in Alg. 1 for clarity). However, this as mentioned in the paper, can be parallelized. All our results are obtained using $M$ small network architectures with $1 \\times 2 5 6$ -units hidden layer followed by $f$ layers of $| A | + 2$ units each $f$ being the number of radial flows and $| A |$ being the action space dimension). A link to a downloadable source code, including all dependencies. The code is included with the Appendix as a zip file; all dependencies can be installed using Python’s package manager. Upon publication, the code would be available on Github. ",
+        "bbox": [
+            215,
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "For all figures and tables that present empirical results, check if you include: ",
+        "bbox": [
+            174,
+            458,
+            673,
+            472
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "• A complete description of the data collection process, including sample size. We use standard benchmarks provided in OpenAI Gym (Brockman et al., 2016).   \n• A link to downloadable version of the dataset or simulation environment. See: https://github.com/   \n• An explanation of how samples were allocated for training / validation / testing. We do not use a training-validation-test split, but instead report the mean performance (and one standard deviation) of the policy at evaluation time, openai/gym for OpenAI Gym benchmarks and https://www.roboti.us/index.html for MuJoCo suite. obtained with 5 random seeds. An explanation of any data that were excluded. We did not compare on easy environments (e.g. Reacher-v2) because all existing methods perform well on them. In that case, the improvement of our method upon baselines is incremental and not worth mentioning.   \n• The exact number of evaluation runs. 5 seeds for MuJoCo experiments, 1M, 2M or 3M environment steps depending on the domain.   \n• A description of how experiments were run. See Section 5 in the main paper and didactic example details in Appendix. A clear definition of the specific measure or statistics used to report results. Undiscounted returns across the whole episode are reported, and in turn averaged across 5 seeds. Clearly defined error bars. Confidence intervals and table values are always mean± 1 standard deviation over 5 seeds.   \n• A description of results with central tendency (e.g. mean) and variation (e.g. stddev). All results use the mean and standard deviation.   \n• A description of the computing infrastructure used. All runs used 1 CPU for all experiments (toy and MuJoCo) with 8Gb of memory. ",
+        "bbox": [
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "image",
+        "img_path": "images/75d01fa4c6a294b396d495cb49a01703a056ee642fb7fd10e4b064ef53d861d8.jpg",
+        "image_caption": [
+            "Figure 5: Mapping in two-dimension space (t-SNE) of agents’ actions for two arbitrary states. Each color represents a different agent. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "To illustrate the impact of the repulsive force coefficient $\\lambda$ , we ran an ablation analysis by varying that coefficient (recall that the overall loss function is $\\mathcal { L } _ { \\pi } = \\mathcal { L } _ { \\pi , \\mathrm { S A C } } + \\lambda \\mathcal { L } _ { \\mathrm { A R } }$ where $\\lambda = 1$ in our experiment). ",
+        "bbox": [
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "For two random states, we sampled 500 actions from all agents and mapped theses actions in a common 2-dimensional space (t-SNE). ",
+        "bbox": [
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "As shown in the Figure above, policies trained without AR $\\lambda = 0$ ) result in entangled actions, while increasing the repulsive coefficient $\\lambda$ forces agents to have different actions and hence explore different regions of the policy space. Note that due to the specific nature of t-SNE , the policies are shown as Gaussians in a lower-dimensional embedding, while it is not necessarily the case in the true space. ",
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+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "STABILIZING ATTRACTION-REPULSION WITH NORMALIZING FLOW ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In this section, we illustrate the consequence of the AR operators with a Gaussian policy (as in Hong et al. (2018)) and our Normalizing flow policy for Ant-v2, Humanoid-v2 and HalfCheetah-v2. As shown in the figure below, AR with Gaussian policies yield worse results. One reason is that the KL term drives apart the mean and variance of the Gaussian policy which deteriorates the main objective of maximizing the reward. On the other side, our method applies the AR only on the NF layers allows enough exploration by deviating sufficiently from the main objective function. ",
+        "bbox": [
+            173,
+            128,
+            826,
+            227
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/4efc27a07944874b7749b830b2f1aa73e9d64a0e975cbc0492917b3be8aaf97e.jpg",
+        "image_caption": [
+            "Figure 6: Comparison of ARAC agents using (1) AR with radial flows, (2) AR with only the base (Gaussian) policy and (3) no AR with radial flows. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            207,
+            243,
+            789,
+            369
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "COMPARING ARAC AGAINST BASELINES ON MUJOCO TASKS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            435,
+            599,
+            450
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Figure 7 shows the performance of ARAC and baselines (CEM-TD3, CERL and ERL) over time steps. Learning curves are averaged over 5 random seeds and displayed with one standard deviation. Evaluation is done every 10, 000 environment steps using 10 rollouts per agent. Overall, ARAC has reasonable performance on all tasks (no flat curves) and demonstrates high performance, especially in humanoid tasks. ",
+        "bbox": [
+            173,
+            462,
+            825,
+            531
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/266cfd9eb6a43128f2757b9c1b4521aa722e61184330dc539ad0fcf16fbe9337.jpg",
+        "image_caption": [
+            "Figure 7: Average return and one standard deviation on 5 random seeds across 7 MuJoCo tasks for ARAC against baselines. Curves are smoothed using Savitzky-Golay filtering with window size of 7. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            176,
+            545,
+            821,
+            747
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "BENEFITS OF POPULATION-BASED STRATEGIES: ARAC AGAINST SINGLE AGENTS",
+        "bbox": [
+            174,
+            103,
+            738,
+            117
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "In this section, we highlight the benefits of the proposed population-based strategy by comparing with single agents. Figure 3 shows the performance of ARAC against a single SAC agent (with and without normalizing flows). Learning curves are averaged over 5 random seeds and displayed with one standard deviation. Evaluation is done every 10, 000 environment steps using 10 rollouts per agent. We observe a high beneficial impact on the convergence rate as well as on the performance. ARAC outperforms single agents in almost all tasks (except for HalfCheetah-v2 and Walker-v2) with large improvement. Note the high sample efficiency on humanoid environments (Humanoid-v2 and Humanoid (rllab)), where it shows faster convergence in addition to better performance. Indeed, on Humanoid (rllab) a single SAC agent reaches the 4k milestone after 4M steps (Haarnoja et al., 2018) while ARAC achieves this performance in less than 2M steps. Also, in SparseHumanoid-v2, due to its better coordinated exploration, ARAC could find a good solution faster than SAC-NF. ",
+        "bbox": [
+            173,
+            130,
+            825,
+            295
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "table",
+        "img_path": "images/e15e937fc86e4c1e07597e86a9f67ea299a575c9ca6a0ea4022b6c7457ca5589.jpg",
+        "table_caption": [
+            "OVERALL PERFORMANCES ON MUJOCO TASKS "
+        ],
+        "table_footnote": [
+            "Table 2: Maximum average return after 1M (2M for Humanoid (rllab) and 600k for SparseHumanoid-v2) time steps $\\pm$ one standard deviation on 5 random seeds. Bold: best methods when the gap is less than 100 units. "
+        ],
+        "table_body": "<table><tr><td rowspan=\"2\">Ant-v2</td><td rowspan=\"2\">ARAC 6,044 ± 216</td><td rowspan=\"2\">CEM-TD3 4,239 ± 1,048</td><td rowspan=\"2\">CERL</td><td rowspan=\"2\">ERL</td><td rowspan=\"2\">SAC - NF</td><td rowspan=\"2\">SAC</td><td rowspan=\"2\">TD3 4,372 ± 900</td></tr><tr><td>1,639± 564 1,442±819</td></tr><tr><td>HalfCheetah-v2</td><td>10,264± 271</td><td>10,659 ± 1,473</td><td>5,703 ± 831</td><td>6,746± 295</td><td>4,912 ± 954 8,429 ±818</td><td>4,370 ± 173 11,896 ± 574</td><td>9,543 ± 978</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Hopper-v2</td><td>3,587 ± 65</td><td>3,655 ± 82</td><td>2,970 ± 341</td><td>1,149 ±3</td><td>3,538 ± 108</td><td>2,794 ± 729</td><td>3,564 ± 114</td></tr><tr><td>Humanoid-v2 HumanoidStandup-v2</td><td>5,965 ± 51 175k±38k</td><td>212±1</td><td>4,756± 454</td><td>551± 60</td><td>5,506± 147</td><td>5,504± 116</td><td>71±10</td></tr><tr><td>Humanoid (rllab)</td><td>14,234 ± 7251</td><td>29k±4k 1,334 ± 551</td><td>117k ± 8k</td><td>129k ± 4k</td><td>116k ± 9k</td><td>149k ±7k</td><td>54k ± 24k</td></tr><tr><td>Walker2d-v2</td><td>4,704 ± 261</td><td>4,710 ± 320</td><td>3,340 ± 3,340 4,3860 ± 615</td><td>57±17 1,107 ± 60</td><td>5,531 ± 4,435</td><td>1,963 ± 1,384</td><td>286 ± 151 4,682 ± 539</td></tr><tr><td>SparseHumanoid-v2</td><td>816 ± 20</td><td>0±0</td><td>1.32 ± 2.64</td><td>8.65 ± 15.90</td><td>5,196 ± 527 547 ± 268</td><td>3,783 ± 366 88±159</td><td>0±0</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></table>",
+        "bbox": [
+            47,
+            132,
+            957,
+            251
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "table",
+        "img_path": "images/c626fd53e2858bf1b5a5c707eecee55372e4e55ddfc6fa96e18630afa2598053.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 3: Performance after 1M (except for rllab which is 2M) timesteps on 5 seeds. Values taken from their corresponding papers. N/A means the values were not available in the original paper. "
+        ],
+        "table_body": "<table><tr><td></td><td>ARAC</td><td>TRPO</td><td>PPO</td><td>Trust-PCL</td><td>Plappert et al. (2017)</td><td>Touati et al. (2018)</td><td>Hong et al. (2018)</td></tr><tr><td>HalfCheetah-v2</td><td>10,264</td><td>-15</td><td>2,600</td><td>2,200</td><td>5,000</td><td>7,700</td><td>4,200</td></tr><tr><td>Walker-v2</td><td>4,764</td><td>2,400</td><td>4,050</td><td>400</td><td>850</td><td>500</td><td>N/A</td></tr><tr><td>Hopper-v2</td><td>3,588</td><td>600</td><td>3,150</td><td>280</td><td>2,500</td><td>400</td><td>N/A</td></tr><tr><td>Ant-v2</td><td>6,044</td><td>-76</td><td>1,000</td><td>1,500</td><td>N/A</td><td>N/A</td><td>N/A</td></tr><tr><td>Humanoid-v2</td><td>5,939</td><td>400</td><td>400</td><td>N/A</td><td>N/A</td><td>N/A</td><td>1,250</td></tr><tr><td>HumanoidStandup-v2</td><td>163,884</td><td>80,000</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td></tr><tr><td>Humanoid (rllab)</td><td>4,117</td><td>23</td><td>200</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td></tr></table>",
+        "bbox": [
+            84,
+            324,
+            921,
+            429
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "EXPERIMENTAL PARAMETERS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            104,
+            383,
+            117
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "Table 4 provides the hyperparameters of ARAC used to obtain results in the MuJoCo domains. The noise input for normalizing flows in SAC policies (see Sec. 2.3) is sampled from $\\mathcal { N } ( 0 , \\sigma )$ , where the variance $\\sigma$ is a function of the state (either fixed at a given value or learned). ",
+        "bbox": [
+            174,
+            128,
+            823,
+            171
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "table",
+        "img_path": "images/b4fe49464be21355cd44fb57a2293cc9ef82075dadd8215f5f141ade5614269d.jpg",
+        "table_caption": [
+            "Table 4: ARAC parameters. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"7\">ARAC parameters</td></tr><tr><td></td><td>#flows</td><td>0</td><td>G</td><td>p</td><td>alpha</td><td>strategy</td></tr><tr><td>Ant-v2</td><td>3</td><td>0.2</td><td>10</td><td>1</td><td>0.2</td><td>proactive</td></tr><tr><td>HalfCheetah-v2</td><td>4</td><td>0.4</td><td>20</td><td></td><td>0.2</td><td>proactive</td></tr><tr><td>Hopper-v2</td><td>4</td><td>0.8</td><td>20</td><td></td><td>0.05</td><td>proactive</td></tr><tr><td>Walker2d-v2</td><td>4</td><td>0.6</td><td>10</td><td></td><td>0.05</td><td>proactive</td></tr><tr><td>Humanoid-v2</td><td>3</td><td>0.6</td><td>10</td><td></td><td>0.05</td><td>reactive</td></tr><tr><td>HumanoidStandup-v2</td><td>3</td><td>0</td><td>20</td><td></td><td>0.2</td><td>reactive</td></tr><tr><td>Humanoid (rllab)</td><td>3</td><td>9</td><td>10</td><td></td><td>0.05</td><td>proactive</td></tr><tr><td>SparseHumanoid-v2</td><td>2</td><td>0.6</td><td>20</td><td>２１３１１１１</td><td>0.2</td><td>proactive</td></tr><tr><td colspan=\"7\">Adam Optimizer parameters</td></tr><tr><td>αq</td><td colspan=\"7\">3.10-4</td></tr><tr><td>αw</td><td colspan=\"7\">3.10-4</td></tr><tr><td>α</td><td colspan=\"7\">3.10-4</td></tr><tr><td>a</td><td colspan=\"7\">3.10-4</td></tr><tr><td colspan=\"3\">Algorithmparameters</td><td colspan=\"4\"></td></tr><tr><td>Batch size m</td><td colspan=\"7\">256</td></tr><tr><td colspan=\"2\">Buffer size B</td><td colspan=\"7\">106</td></tr><tr><td colspan=\"2\">Archive sample size n</td><td colspan=\"7\">5</td></tr></table>",
+        "bbox": [
+            305,
+            185,
+            694,
+            405
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "IMPACT OF NUMBER OF FLOWS ON THE POLICY SHAPE ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            104,
+            547,
+            117
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "We used a single SAC agent with different radial flows numbers and randomly initialized weights, starting with actions centered at $( 0 , 0 )$ . All flow parameters are $\\ell _ { 1 }$ regularized with hyperparameter 2. The agent is trained with the classical evidence lower bound (ELBO) objective augmented with the AR loss (Eq. 1), where the coefficient of the repulsive policy $\\pi ^ { \\prime }$ is given by $\\begin{array} { r } { \\beta _ { t } \\stackrel { \\smile } { = } \\frac { 1 0 } { t + 1 } } \\end{array}$ . Fig. 8 shows how both the NF and learned variance Gaussian policies manage to recover the target policy. We see that NF takes advantage of its flexible parametrization to adjust its density and can show asymmetric properties unlike the Gaussian distribution. This indeed can have advantage in some non symmetric environment where the Gaussian policy would be trapped into a suboptimal behavior. Finally, increasing the number of flows (from bottom to top) can lead to more complex policy’s shape. ",
+        "bbox": [
+            173,
+            128,
+            826,
+            257
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "image",
+        "img_path": "images/068a6a98b0db451a89cc30af3c2408532ae00760edf2494bd89935f5c4df961e.jpg",
+        "image_caption": [
+            "Figure 8: Single state didactic illustration of attraction-repulsion operators. Comparing behavior of NF policy against Gaussian policy with learned variance under a repulsive constraint. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            181,
+            272,
+            818,
+            691
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "6.1 VARIANCE OF FITNESS IN THE ARCHIVE ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            104,
+            490,
+            117
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "Due to the high computation time for behavioral-diversity baselines such as DIYAN, we propose to use the agent’s fitness (i.e. undiscounted returns) as a candidate to repulse/attract from. ",
+        "bbox": [
+            173,
+            128,
+            825,
+            159
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "image",
+        "img_path": "images/9a717f5760f116f2d1161c25e91738a390ee835da2d8bb22df1295ddab31373b.jpg",
+        "image_caption": [
+            "Figure ?? shows the variance of the archive across three MuJoCo domains: Ant, Humanoid and HumanoidStandup. As training progresses, the clustering approach allows to maintain a high variance in the archive, preventing mode collapse to a single, \"average\" fitness. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            176,
+            176,
+            815,
+            323
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "6.2 PSEUDO-CODE FOR ARAC ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            103,
+            401,
+            117
+        ],
+        "page_idx": 18
+    },
+    {
+        "type": "text",
+        "text": "Algorithm 1 ARAC: Attraction-Repulsion Actor-Critic ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            135,
+            539,
+            150
+        ],
+        "page_idx": 18
+    },
+    {
+        "type": "text",
+        "text": "1: Input: population size $M$ ; number of elites $K$ ; maximum archive capacity $G$ ; archive samp   \nsize $n$ ; number of evaluation rollouts $R$ ; actor coefficient $p$ ; strategy (either proactive or reactiv   \n2: Initialize value function network $V _ { \\nu }$ and critic network $Q _ { \\omega }$   \n3: Initialize population of policy networks $\\{ \\pi _ { \\phi , \\theta } ^ { m } \\} _ { m = 1 } ^ { M }$   \n4: Initialize empty archive $\\mathcal { G }$ and randomly assign $K$ individuals to top- $K$   \n5: total_step $ 0$   \n6: while total_step $\\leq$ max_step do   \n7: step $\\gets 0$   \n8: for agent $m = 1 \\ldots M$ do   \n9: $( \\_ , \\mathsf { s t e p } s ) \\gets \\mathtt { r o l l o u t } ( \\pi ^ { m }$ , with noise, over 1 episode)   \n10: $\\mathrm { s t e p } \\gets \\mathrm { s t e p } + s$ Collect samples   \n11: total_step total_step + s   \n12: end for   \n13: $C = { \\mathsf { s t e p } } / { K }$   \n14: for policy $\\pi ^ { e }$ in top- $K$ do   \n15: Update critic with $\\pi ^ { e }$ for $C$ mini-batches (Eq. 3) Update critic   \n16: Update value function (Eq. 4)   \n17: end for   \n18: for agent $m = 1 \\ldots M$ do   \n19: if policy $\\pi ^ { m }$ is in top- $K$ then   \n20: Sample $n$ archived policies uniformly from $\\mathcal { G }$   \n21: Update actor $\\pi ^ { m }$ for ${ \\frac { \\mathrm { s t e p } } { M } } \\cdot p$ mini-batches (Eq. 5 and 8 or 9) Update actors   \n22: else   \n23: Update actor $\\pi ^ { m }$ for ${ \\frac { \\mathrm { s t e p } } { M } } \\cdot p$ mini-batches (Eq. 2)   \n24: end if   \n25: end for   \n26: for agent $m = 1 \\ldots M$ do   \n27: $( \\mathrm { F i t n e s s } _ { m } , \\ l _ { - } ) \\gets \\mathtt { r o l l o u t } ( \\pi ^ { m } ,$ , without noise, over $R$ episodes) Evaluate actors   \n28: end for   \n29: Rank population $\\{ \\pi _ { \\phi , \\theta } ^ { m } \\} _ { m = 1 } ^ { M }$ and identify top- $K$   \n30: update_archiv $\\mathsf { a } ( \\mathcal { G } , \\{ \\pi _ { \\phi , \\theta } ^ { m } \\} _ { m = 1 } ^ { M } , G )$   \n31: end while ",
+        "bbox": [
+            173,
+            147,
+            803,
+            683
+        ],
+        "page_idx": 18
+    },
+    {
+        "type": "text",
+        "text": "COMPLEMENTARY PSEUDO-CODE FOR ARAC ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            103,
+            491,
+            117
+        ],
+        "page_idx": 19
+    },
+    {
+        "type": "text",
+        "text": "Algorithms 2 and 3 respectively provide the pseudo-code of functions rollout and update_archive used in Algorithm 1. ",
+        "bbox": [
+            174,
+            128,
+            823,
+            159
+        ],
+        "page_idx": 19
+    },
+    {
+        "type": "text",
+        "text": "Algorithm 2 rollout ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            174,
+            331,
+            189
+        ],
+        "page_idx": 19
+    },
+    {
+        "type": "text",
+        "text": "Input: actor $\\pi$ ; noise status; number of episodes $E$ ; replay buffer $\\boldsymbol { B }$ ;   \nFitness $ 0$   \nfor episode $= 1 , \\ldots , E$ do $\\mathbf { s } \\gets$ Initial state ${ \\bf s } _ { 0 }$ from the environment for step $t = 0 \\dots$ termination do if with noise then Sample noise $z$ else Set $z \\gets 0$ end if $\\mathbf { a } _ { t } \\sim \\pi ( . | \\mathbf { s } _ { t } , z )$ Observe $\\mathbf { s } _ { t + 1 } \\sim P ( \\cdot | \\mathbf { s } _ { t } , \\mathbf { a } _ { t } )$ and obtain reward $r _ { t }$ Fitness $\\gets$ Fitness + rt Store transition $( \\mathbf { s } _ { t } , \\mathbf { a } _ { t } , r _ { t } , \\mathbf { s } _ { t + 1 } )$ in $\\boldsymbol { B }$ end for   \nend for   \nFitness Fitness/ $E$   \nreturn Average fitness per episode and number of steps performed   \nInput: archive $\\mathcal { G }$ ; population of size $M$ ; maximal archive capacity $G$ .   \nif $| { \\mathcal { G } } | < G$ then Add all agents of current population to $\\mathcal { G }$   \nelse $c _ { 1 } , c _ { 2 } \\gets 2$ -means(fitness of individuals in $\\mathcal { G }$ ) for agent $m = 1 , \\ldots , M$ do Assign agent $m$ to closest cluster $c \\in \\{ c _ { 1 } , c _ { 2 } \\}$ based on its fitness Sample an archived agent $j \\sim \\mathrm { U n i f o r m } ( c )$ Replace archived individual $j$ by $m$ end for   \nend if   \nreturn Updated archive $\\mathcal { G }$ ",
+        "bbox": [
+            179,
+            194,
+            638,
+            445
+        ],
+        "page_idx": 19
+    },
+    {
+        "type": "table",
+        "img_path": "images/2f153b688b5051609a7a9360c4e4c92197f48fd1ffc0763cf0fb6dbfbff1690e.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Algorithm archive</td></tr></table>",
+        "bbox": [
+            171,
+            479,
+            823,
+            497
+        ],
+        "page_idx": 19
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            183,
+            501,
+            651,
+            672
+        ],
+        "page_idx": 19
+    }
+]

parse/train/H1bM1fZCW/H1bM1fZCW.md

@@ -0,0 +1,205 @@
+# GRADNORM: GRADIENT NORMALIZATION FOR ADAPTIVE LOSS BALANCING IN DEEP MULTITASK NETWORKS
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+Deep multitask networks, in which one neural network produces multiple predictive outputs, are more scalable and often better regularized than their single-task counterparts. Such advantages can potentially lead to gains in both speed and performance, but multitask networks are also difficult to train without finding the right balance between tasks. We present a novel gradient normalization (GradNorm) technique which automatically balances the multitask loss function by directly tuning the gradients to equalize task training rates. We show that for various network architectures, for both regression and classification tasks, and on both synthetic and real datasets, GradNorm improves accuracy and reduces overfitting over single networks, static baselines, and other adaptive multitask loss balancing techniques. GradNorm also matches or surpasses the performance of exhaustive grid search methods, despite only involving a single asymmetry hyperparameter $\alpha$ . Thus, what was once a tedious search process which incurred exponentially more compute for each task added can now be accomplished within a few training runs, irrespective of the number of tasks. Ultimately, we hope to demonstrate that gradient manipulation affords us great control over the training dynamics of multitask networks and may be one of the keys to unlocking the potential of multitask learning.
+
+# 1 INTRODUCTION
+
+Single-task learning in computer vision has enjoyed much success in deep learning, with many models now performing at or beyond human accuracies for a wide array of tasks. However, a system that strives for full scene understanding cannot focus on one problem, but needs to perform many diverse perceptual tasks simultaneously. Such systems must also be efficient, especially within the restrictions of limited compute environments in embedded systems such as smartphones, wearable devices, and robots/drones. Multitask learning most naturally lends itself to this problem by sharing weights amongst different tasks within the same model and producing multiple predictions in one forward pass. Such networks are not only scalable, but the shared features within these networks tend to be better regularized and boost performance as a result. In the ideal limit, we can thus have the best of both worlds with multitask networks: both more efficiency and higher performance.
+
+The key difficulty in multitask learning lies in the balancing of tasks, and perhaps the simplest way to control this balance is to choose the correct joint loss function. In practice, the multitask loss function is often assumed to be linear in the single task losses, $\begin{array} { r } { L = \sum _ { i } ^ { - } w _ { i } L _ { i } } \end{array}$ , where the sum runs over $T$ tasks. The challenge is then to find the best value for each $w _ { i }$ that balances the contribution of each task for optimal model training. Our proposed method is furthermore an adaptive method, allowing $w _ { i }$ to vary with the training step $t$ , and so $w _ { i } = w _ { i } ( t )$ .
+
+Our key insight lies in the observation that these $w _ { i } ( t )$ influence training only because they control the magnitude of the gradients generated from task $i$ . As such, manipulating the gradient norms themselves would be a more direct way to control the training dynamics. More specifically, we propose a simple heuristic that penalizes the network when backpropagated gradients from any task are too large or too small. The correct balance is struck when tasks are training at similar rates; if task $i$ is training relatively quickly, then its weight $w _ { i } ( t )$ should decrease relative to other task weights $w _ { j } ( t ) | _ { j \neq i }$ to allow other tasks more influence on the network. Our method can be said to be a form of batch normalization (Ioffe & Szegedy (2015)) for backpropagation, ensuring that gradients from each task per batch lie on a common statistical scale. We will show that, when implemented, gradient normalization leads to across-the-board improvements in accuracy and suppresses overfitting.
+
+![](images/b7967b2eaf87bf5beb740b4e32f43b0678734733e83b79b85bfeb7b4b8fb6e0f.jpg)  
+Figure 1: Gradient Normalization. Imbalanced gradient norms (left) result in suboptimal training within a multitask network, so we implement a novel gradient loss $L _ { \mathrm { g r a d } }$ (right) which detects such imbalances in gradient norms amongst tasks and tunes the weights in the loss function to compensate. We illustrate here a simplified case where such balancing results in equalized gradient norms, but in general some tasks may need higher or lower gradient norms relative to other tasks for optimal task balancing (discussed further in Section 3).
+
+Our main contributions to the field of multitask learning are as follows:
+
+1. An attractively simple heuristic for multitask loss balancing involving training rate equalization, which is implemented through a novel gradient loss function. 2. A simplification to exhaustive grid search (which has compute complexity $\mathcal { O } ( N ^ { T } )$ for $N$ grid points in one dimension) that only involves tuning one robust hyperparameter. 3. Demonstration that direct interaction with gradients provides a powerful way of reasoning about multitask learning.
+
+# 2 RELATED WORK
+
+Multitask learning has existed well before the advent of deep learning (Caruana (1998); Bakker & Heskes (2003)), but the robust learned features within deep networks have spurned renewed interest. Although our primary application area is computer vision, multitask learning has applications in multiple other fields, from natural language processing (Hashimoto et al. (2016); Collobert & Weston (2008); Søgaard & Goldberg (2016)) to speech synthesis (Wu et al. (2015); Seltzer & Droppo (2013)), from very domain-specific applications like traffic prediction (Huang et al. (2014)) to very general cross-domain work (Bilen & Vedaldi (2017)).
+
+Multitask learning is very well-suited to the field of computer vision, where making multiple robust predictions is crucial for complete scene understanding. Deep networks have been used to solve various subsets of multiple vision tasks, from 3-task networks (Eigen & Fergus (2015); Teichmann et al. (2016)) to much larger subsets as in UberNet (Kokkinos (2016)). Often, single computer vision problems can even be framed as multitask problems, such as in Mask R-CNN for instance segmentation (He et al. (2017)) or YOLO-9000 for object detection (Redmon & Farhadi (2016)). Researchers often assume a fixed loss function or network architecture, but there has also been significant work on finding optimal ways to relate tasks to each other in a multitask model. Clustering methods have shown success beyond deep models (Kang et al. (2011); Jacob et al. (2009)), while constructs such as deep relationship networks (Long & Wang (2015)) and cross-stich networks (Misra et al. (2016)) search for meaningful relationships between tasks and learn which features to share between them. Work in Warde-Farley et al. (2014) and Lu et al. (2016) use groupings amongst labels to search through possible architectures for learning. Perhaps the most relevant to the current work, Kendall et al. (2017) uses a joint likelihood formulation to derive task weights based on the intrinsic uncertainty in each task.
+
+# 3 METHODOLOGY
+
+# 3.1 A GRADIENT LOSS FUNCTION BASED ON RATE BALANCING
+
+We begin with the standard multitask loss function with time dependency, $\begin{array} { r } { L ( t ) = \sum w _ { i } ( t ) L _ { i } ( t ) } \end{array}$ , and our goal is to learn the functions $w _ { i } ( t )$ . We argued in Section 1 that $w _ { i } ( t )$ is intimately related to the norm of gradients from each task backpropagated into the network. We thus must motivate a set of desirable gradient magnitudes, and use those desired magnitudes to set the task weights $w _ { i } ( t )$ .
+
+Consider the norms of gradients from task $i$ on some set of weights $W$ within the network, n $\mathsf { \Omega } ^ { \mathsf { \tiny { l o r m } } } ( \nabla _ { W } L _ { i } ( t ) )$ (specific choices for $W$ to be discussed later). Our method of gradient normalization (hereafter referred to as GradNorm) works in two steps: (1) We first scale all gradient norms to an equal value as a neutral starting point. This value is most naturally chosen to be the average gradient norm amongst tasks, $E _ { \mathrm { t a s k } } [ \mathrm { n o r m } ( \nabla _ { W } L _ { i } ( t ) ) ]$ , where we use $E _ { \mathrm { t a s k } } [ X ]$ to denote the average value of a task-dependent quantity $X$ across tasks. (2) We then modify gradient norms with a rate balancing term that ensures no task trains relatively too slowly. The gradient norms of task $i$ should grow when task $i$ trains relatively slowly, thereby boosting more sluggish tasks. Gradient norms thus should be an increasing function of the relative inverse training rate for each task.
+
+To quantify training rates, we choose the loss ratio of task $i$ at training step $t$ , $L _ { i } ^ { \prime } ( t ) : = L _ { i } ( t ) / L _ { i } ( 0 )$ , as a measure of task $i$ ’s inverse training rate; smaller values of $L _ { i } ^ { \prime } ( t )$ would mean that task $i$ has trained more. If $L _ { i } ^ { \prime } ( t )$ denotes the inverse training rate of task $i$ , then the relative inverse training rate is just $L _ { i } ^ { \prime } ( t ) / \dot { E _ { \mathrm { t a s k } } } [ L _ { i } ^ { \prime } ( t ) ]$ . Using this simple loss ratio metric is valid for both regression squared loss and classification cross-entropy loss, as we will see in Section $5 . 2 ^ { 1 }$ .
+
+Our desired gradient norms are therefore:
+
+$$
+\begin{array} { r l } & { \mathrm { n o r m } ( \nabla _ { W } L _ { i } ( t ) ) \mapsto ( \mathrm { a v e r a g e \ : g r a d i e n t \ : n o r m } ) \times ( \mathrm { r e l a t i v e \ : i n v e r s e \ : t r a i n i n g \ : r a t e \ : o f \ : t a s k \ : } i ) ^ { \alpha } } \\ & { \qquad = E _ { \mathrm { t a s k } } [ \mathrm { n o r m } ( \nabla _ { W } L ( t ) ) ] \left( \frac { L _ { i } ^ { \prime } ( t ) } { E _ { \mathrm { t a s k } } [ L _ { i } ^ { \prime } ( t ) ] } \right) ^ { \alpha } } \end{array}
+$$
+
+where $\alpha$ is an additional hyperparameter. $\alpha$ sets the strength of rate balancing in the multitask problem, and also is a measure of the asymmetry between tasks. In cases where tasks are very different in their complexity, leading to different learning dynamics, a higher value of $\alpha$ should be used to pull tasks back towards a common training rate more forcefully. When tasks are more symmetric (e.g. the synthetic examples in Section 4), a lower value of $\alpha$ is appropriate. Note that $\alpha = 0$ will always try to pin the norms of backpropped gradients from each task to be equal at $W$ .
+
+Equation 1 sets a desired target for our gradient norms, and we want to update our loss weights $w _ { i } ( t )$ to move gradient norms towards this target. To accomplish this, GradNorm is implemented as a loss function $L _ { \mathrm { g r a d } }$ which is just the L1 distance between actual gradient norms and the targets in Equation 1:
+
+$$
+L _ { \mathrm { g r a d } } ^ { ( i ) } ( t ; W ) = \left| \mathrm { n o r m } ( \nabla _ { W } L _ { i } ( t ) ) - E _ { \mathrm { t a s k } } [ \mathrm { n o r m } ( \nabla _ { W } L ( t ) ) ] \left( \frac { L _ { i } ^ { \prime } ( t ) } { E _ { \mathrm { t a s k } } [ L ^ { \prime } ( t ) ] } \right) ^ { \alpha } | . \right.
+$$
+
+The above loss is for one task; the full loss is just the mean of the individual task losses, $\begin{array} { r } { L _ { \mathrm { g r a d } } ( t ; W ) = ( 1 / T ) \sum _ { i } L _ { \mathrm { g r a d } } ^ { ( i ) } ( t ; W ) } \end{array}$ . $L _ { \mathrm { g r a d } }$ is then differentiated with respect to each $w _ { i } ( t )$ , and its gradients are applied via standard update rules to update these weights (see Figure 1 for a schematic view). In principle, it is also possible to update all network weights (not just $w _ { i } ( t ) )$ based on gradient of $L _ { \mathrm { g r a d } }$ , but in practice this adds undue complexity to the problem and often degrades performance.
+
+We can choose $W$ , the weights upon which we rate balance gradient norms, to be any subset of weights within layers of our network. In practice, in order to save on compute overhead, we choose $W$ to be the weights in the last layer which is shared amongst all three tasks. This simplification greatly shortens the number of layers $L _ { \mathrm { g r a d } }$ must be backpropagated through, and with this choice of $W$ in our experiments GradNorm only adds $\sim 5 \%$ of additional compute time. After every update step, we also renormalize the weights $w _ { i } ( t )$ so that $\begin{array} { r } { \sum _ { i } w _ { i } ( t ) = T } \end{array}$ in order to decouple gradient normalization from the global learning rate.
+
+# 4 A SIMPLE TOY EXAMPLE
+
+To illustrate GradNorm on a simple system, we consider $T$ regression tasks onto the functions
+
+$$
+f _ { i } ( { \bf x } ) = \sigma _ { i } \operatorname { t a n h } ( ( B + \epsilon _ { i } ) { \bf x } ) ,
+$$
+
+where tanh acts element-wise. We use squared loss to train each task. The matrices $B$ and $\epsilon _ { i }$ have elements generated IID from $\mathcal { N } ( 0 , 1 0 )$ and $\mathcal { N } ( 0 , 3 . 5 )$ , respectively. Our task is thus to perform regression on multiple tasks with shared information $B$ along with information specific to each task, $\epsilon _ { i }$ . The $\sigma _ { i }$ are fixed scalars which set the variance of the outputs $f _ { i }$ . Higher values of $\sigma _ { i }$ induce higher values of squared loss for that task. These tasks are harder to learn due to the higher variances in their response values, but they also backpropagate larger gradients. Classically, such a scenario can lead to suboptimal training dynamics as the higher $\sigma _ { i }$ tasks tend to dominate the training.
+
+All toy problem runs use a 4-layer fully-connected ReLU-activated network with 100 neurons per layer as a common trunk. A final affine transformation per task gives $T$ final predictions. Inputs are in $\mathbb { R } ^ { 2 5 0 }$ , and outputs lie in $\mathbb { R } ^ { 1 0 0 }$ . To ensure consistency, we only compare models initialized to the same random values and fed data generated from a fixed random seed. The asymmetry $\alpha$ is set low to 0.12 for these experiments, as the output functions $f _ { i }$ are all of the same form.
+
+In these toy problems, we measure the task-normalized test-time loss, which is the sum of the test loss ratios for each task, $\textstyle \sum _ { i } L _ { i } ^ { \prime } ( t )$ . A simple sum of losses is wholly inadequate to judge the overall performance of a multitask network, as it biases itself towards tasks with higher loss scales, and there exists no general metric by which to judge multitask performance in any setting. Luckily, our toy problem was designed with tasks which are statistically identical except for their loss scales $\sigma _ { i }$ . For this simple example, there is therefore a clear measure of overall network performance, which is the sum of losses with each loss normalized to its $\sigma _ { i }$ - precisely the sum of loss ratios.
+
+In the case of $T = 2$ , we choose the values $( \sigma _ { 0 } , \sigma _ { 1 } ) = ( 1 . 0 , 1 0 0 . 0 )$ . Classically, task 1 can suppress task 0’s influence during training due to its higher loss scale. As shown in the top panels of Figure 2, gradient normalization remedies the issue by increasing $w _ { 0 } ( t )$ to counteract the larger gradients coming from $T _ { 1 }$ , and the improved task balance results in better test-time performance.
+
+The possible benefits of gradient normalization become even clearer when the number of tasks increases. For $T = 1 0$ , we sample the $\sigma _ { i }$ from a normal distribution and plot the results in the bottom row of Figure 2. GradNorm significantly improves test time performance over naively weighting each task the same. Like $T = 2$ , for $T = 1 0$ the $w _ { i } ( t )$ grow larger for smaller $\sigma _ { i }$ tasks; GradNorm is giving tasks with smaller loss scales more breathing room.
+
+For both $T = 2$ and $T = 1 0$ , GradNorm is more stable and outperforms the uncertainty weighting proposed by Kendall et al. (2017). Uncertainty weighting, which enforces that $w _ { i } ( t ) \ \tilde { \mathbf { \Omega } } \sim 1 / \bar { L } _ { i } ( t ) \mathbf { \dot { \Omega } }$ , tends to grow weights too large and too quickly as the loss for each task drops. Although such networks train quickly at the onset, the training soon crashes as the global learning rate grows too large. This issue is exacerbated as uncertainty weighting allows $w _ { i } ( t )$ to change unconstrained (compared to GradNorm which ensures $\sum w _ { i } ( t ) = \bar { T }$ always), which pushes global learning rate up even further.
+
+Overall, the traces for each $w _ { i } ( t )$ during a single GradNorm run seem fairly stable and convergent. In fact, in Section 5.3 we will see how the time-averaged weights $E _ { t } [ w _ { i } ( t ) ]$ lie close to the optimal static weights, suggesting GradNorm can greatly simplify the tedious grid search procedure.
+
+![](images/f3bd541a017b05f81881e8b42a036a9e5d43bbaf3d46522614762465c01e336a.jpg)  
+Figure 2: Gradient Normalization on a toy 2-task (top) and 10-task (bottom) system. Diagrams of the network structure with loss scales are on the left, traces of $w _ { i } ( t )$ during training in the middle, and task-normalized test loss curves on the right. $\alpha = 0 . 1 2$ for all runs.
+
+# 5 APPLICATION TO A LARGE REAL-WORLD DATASET
+
+We primarily use NYUv2 as our dataset of choice. The standard NYUv2 dataset carries depth, surface normals, and semantic segmentation labels (which we cluster into 13 distinct classes). NYUv2 is quite small as a dataset, with a training split of ${ \sim } 8 0 0$ examples, but contains both regression and classification labels, making it a good choice to test the robustness of GradNorm.
+
+To show GradNorm in action on a more large-scale multitask dataset, we also expand NYUv2 to 40,000 images complete with pixel-wise depth, surface normals, and room keypoint labels. Keypoint labels are obtained through professional human labeling services, while surface normals are generated from camera parameters and the depth maps through standard methods.
+
+Following Lee et al. (2017), the state-of-the-art in room layout prediction, all inputs are downsampled to $3 2 0 \times 3 2 0$ pixels and outputs to $8 0 \mathrm { ~ x ~ } 8 0$ pixels. These resolutions also speed up training without compromising complexity in the inputs or labels.
+
+# 5.1 MODEL AND INDIVIDUAL TASK LOSSES
+
+We try two different models: (1) a SegNet (Badrinarayanan et al. (2015); Lee et al. (2017)) network with a symmetric VGG16 (Simonyan & Zisserman (2014)) encoder/decoder, and (2) an FCN (Long et al. (2015)) network with a modified ResNet-50 (He et al. (2016)) encoder and shallow ResNet decoder. The VGG SegNet reuses maxpool indices to perform upsampling, while the ResNet FCN learns all upsampling filters. The ResNet architecture is further thinned (both in its filters and activations) to contrast with the heavier, more complex VGG SegNet: stride-2 layers are moved earlier and all 2048-filter layers are replaced by 1024-filter layers. Ultimately, the VGG SegNet has 29M parameters versus 15M for the thin ResNet. Although we will focus on the VGG SegNet in our more in-depth analysis, by designing and testing on two extremely different network topologies we will further demonstrate that GradNorm is very robust to the choice of base model.
+
+We use standard pixel-wise loss functions for each task: cross entropy for segmentation, squared loss for depth, and cosine similarity for normals. As in Lee et al. (2017), for room layout we generate Gaussian heatmaps for each of 48 room keypoint types and predict these heatmaps with a pixel-wise squared loss. Note that all regression tasks are quadratic losses (our surface normal prediction uses a cosine loss which is quadratic to leading order), allowing us to use the loss ratio $L _ { i } ^ { \prime } ( t )$ of each task as a direct proxy for each task’s inverse training rate.
+
+Table 1: Test error, 320x320 NYUv2 for GradNorm and various baselines.   
+
+<table><tr><td>Model Type and Weighting Method</td><td>Depth Error (m)</td><td>Segmentation 100-mloU (%)</td><td>Normals Error (1-|cosl)</td></tr><tr><td>VGG SegNet, Depth Only</td><td>1.038</td><td>=</td><td></td></tr><tr><td>VGG SegNet, Segmentation Only</td><td>-</td><td>70.0</td><td>=</td></tr><tr><td>VGG SegNet, Normals Only</td><td>=</td><td>=</td><td>0.169</td></tr><tr><td>VGG SegNet, Equal Weights</td><td>0.944</td><td>70.1</td><td>0.192</td></tr><tr><td>VGG SegNet, GradNorm Converged Weights</td><td>0.939</td><td>67.5</td><td>0.171</td></tr><tr><td>VGG SegNet, GradNorm α = 1.5</td><td>0.925</td><td>67.8</td><td>0.174</td></tr></table>
+
+# 5.2 NETWORK PERFORMANCE
+
+In Table 1 we display the performance of GradNorm on the NYUv2 dataset (with input/output resolutions as described in Section 5). Specific training schemes for all NYUv2 models are detailed in Appendix A. We see that GradNorm improves the performance of all three tasks with respect to the equal-weights baseline (where $w _ { i } ( t ) = 1$ for all $^ { t , i }$ ), and that GradNorm either surpasses or matches (within statistical noise) the best performance of single networks for each task. The GradNorm Converged Weights network is derived by calculating the GradNorm time-averaged weights $E _ { t } [ w _ { i } ( t ) ]$ for each task (e.g. by averaging curves like those found in Appendix B), and retraining a network with weights fixed to those values. GradNorm thus can also be used to extract good values for static weights. We pursue this idea further in Section 5.3 and show that these weights lie very close to the optimal weights extracted from exhaustive grid search.
+
+<table><tr><td>Model Type and Weighting Method</td><td>Depth Error (m)</td><td>Keypoint Error (%)</td><td>Normals Error (1-|cos|)</td></tr><tr><td>Thin ResNet FCN, Depth Only</td><td>0.725</td><td>-</td><td>1</td></tr><tr><td>Thin ResNet FCN,Keypoint Only</td><td>1</td><td>7.90</td><td>=</td></tr><tr><td>Thin ResNet FCN, Normals Only</td><td>1</td><td>-</td><td>0.155</td></tr><tr><td>Thin ResNet FCN,Equal Weights</td><td>0.697</td><td>7.80</td><td>0.172</td></tr><tr><td>Thin ResNet FCN, Unc. Weighting (Kendall et al. (2017))</td><td>0.702</td><td>7.96</td><td>0.182</td></tr><tr><td>Thin ResNetFCN,GradNorm Converged Weights</td><td>0.695</td><td>7.63</td><td>0.156</td></tr><tr><td>Thin ResNet FCN, GradNorm α = 1.5</td><td>0.663</td><td>7.32</td><td>0.155</td></tr><tr><td>VGG SegNet, Depth Only</td><td>0.689</td><td>-</td><td>-</td></tr><tr><td>VGG SegNet, Keypoint Only</td><td>1</td><td>8.39</td><td>1</td></tr><tr><td>VGG SegNet, Normals Only</td><td>-</td><td>1</td><td>0.142</td></tr><tr><td>VGG SegNet, Equal Weights</td><td>0.658</td><td>8.39</td><td>0.155</td></tr><tr><td>VGG SegNet, Unc.Weighting (Kendall et al. (2017))</td><td>0.649</td><td>8.00</td><td>0.158</td></tr><tr><td>VGG SegNet, GradNorm Converged Weights</td><td>0.638</td><td>7.69</td><td>0.137</td></tr><tr><td>VGG SegNet, GradNorm α = 1.5</td><td>0.629</td><td>7.73</td><td>0.139</td></tr></table>
+
+# Table 2: Test error, expanded 320x320 NYUv2 for GradNorm and various baselines.
+
+To show how GradNorm can perform in the presence of a much larger dataset, we also perform extensive experiments on the expanded NYUv2 dataset, which carries a factor of $5 0 \mathrm { x }$ more data. The results are shown in Table 2. As with the standard NYUv2 runs, GradNorm networks outperform other multitask methods, and either matches (within noise) or surpasses the performance of singletask networks.
+
+Figure 3 shows test and training loss curves for GradNorm ( $\alpha = 1 . 5$ ) and baselines on the expanded NYUv2 dataset for our VGG SegNet models. GradNorm improves test-time depth error by $\sim 5 \%$ , despite ending with much higher training loss. GradNorm achieves this by aggressively rate balancing the network (enforced by a high asymmetry $\alpha = 1 . 5$ ), and ultimately suppresses the depth weight $w _ { \mathrm { d e p t h } } ( t )$ to lower than 0.10 (see Appendix B for more details). The same trend exists for keypoint regression, and is a clear signal of network regularization. In contrast, the uncertainty weighting technique (Kendall et al. (2017)) causes both test and training error to move in lockstep, and thus is not a good regularizer. Only results for the VGG SegNet are shown here, but the Thin ResNet FCN produces consistent results.
+
+![](images/c183338d678f77c294cb134b4de7a34e7b41ed89c4c169bcdca0f31b44fa7e1b.jpg)  
+Figure 3: Test and training loss curves for all tasks in expanded NYUv2, VGG16 backbone. GradNorm versus an equal weights baseline and uncertainty weighting (Kendall et al. (2017)).
+
+5.3 GRADIENT NORMALIZATION FINDS OPTIMAL GRID-SEARCH WEIGHTS IN ONE PASS
+
+For our VGG SegNet, we train 100 networks from scratch with random task weights on expanded NYUv2. Weights are sampled from a uniform distribution and renormalized to sum to $T = 3$ . For computational efficiency, we only train for 15000 iterations out of the normal 80000, and then compare the performance of that network to our GradNorm $\alpha = 1 . 5$ VGG SegNet network at the same 15000 steps. The results are shown in Figure 4.
+
+![](images/f5e0772a1680020f60b2627b1c253d7c8279499f16e65c3819998884c4bdd881.jpg)  
+Figure 4: Gridsearch performance for random task weights, expanded NYUv2. Average change in performance across three tasks for a static network with weights $w _ { i } ^ { \mathrm { s t a t i c } }$ is plotted against the $L _ { 2 }$ distance between $w _ { i } ^ { \mathrm { s t a t i c } }$ and our GradNorm network’s time-averaged weights, $E _ { t } [ w _ { i } ( t ) ]$ . All comparisons are made at 15000 steps of training.
+
+Even after 100 networks trained, grid search still falls short of our GradNorm network. But even more remarkably, there is a strong, negative correlation between network performance and task weight distance to our time-averaged GradNorm weights. At an $L _ { 2 }$ distance of $\sim 3$ , grid search networks on average have almost double the errors per task compared to our GradNorm network. GradNorm has effectively allowed us to “cheat” and immediately find the optimal grid search weights without actually performing grid search, simplifying a process that is usually notoriously laborious.
+
+![](images/93d306774aebeed67a84e1822fd4c9509658329f17e414b9f956c84f6fabc148.jpg)  
+Figure 5: Visualizations at inference time. Expanded NYUv2 with room layout labels is shown on the left, while downsampled NYUv2 with semantic segmentation labels is shown on the right.
+
+# 5.4 QUALITATIVE RESULTS
+
+Figure 5 shows visualizations of the VGG SegNet outputs on test set images along with the ground truth, for both the expanded and downsampled NYUv2 datasets. Ground truth labels are juxtaposed with outputs from the equal weights network, 3 single networks, and our best GradNorm network. The qualitative improvements are incremental, but we find the GradNorm network tends to output smoother, more detailed pixel map predictions when compared to the other two baselines.
+
+# 6 CONCLUSIONS
+
+Gradient normalization acts as a good model regularizer and leads to superb performance in multitask networks by operating directly on the gradients in the network. GradNorm is driven by the attractively simple heuristic of rate balancing, and can accommodate problems of varying complexities within the same unified model using a single hyperparameter representing task asymmetry. A GradNorm network can also be used to quickly extract optimal fixed task weights, removing the need for exhaustive grid search methods that become exponentially more expensive with the number of tasks. We hope that our work has not only introduced a new methodology for quickly balancing multitask networks, but also has shown how direct gradient manipulation can be a powerful way to reason about task relationships within a multitask framework.
+
+# REFERENCES
+
+Vijay Badrinarayanan, Alex Kendall, and Roberto Cipolla. Segnet: A deep convolutional encoder-decoder architecture for image segmentation. arXiv preprint arXiv:1511.00561, 2015.
+
+Bart Bakker and Tom Heskes. Task clustering and gating for bayesian multitask learning. Journal of Machine Learning Research, 4(May):83–99, 2003.
+
+Hakan Bilen and Andrea Vedaldi. Universal representations: The missing link between faces, text, planktons, and cat breeds. arXiv preprint arXiv:1701.07275, 2017.
+
+Rich Caruana. Multitask learning. In Learning to learn, pp. 95–133. Springer, 1998.
+
+Ronan Collobert and Jason Weston. A unified architecture for natural language processing: Deep neural networks with multitask learning. In Proceedings of the 25th international conference on Machine learning, pp. 160–167. ACM, 2008.
+
+David Eigen and Rob Fergus. Predicting depth, surface normals and semantic labels with a common multi-scale convolutional architecture. In Proceedings of the IEEE International Conference on Computer Vision, pp. 2650–2658, 2015.
+
+Kazuma Hashimoto, Caiming Xiong, Yoshimasa Tsuruoka, and Richard Socher. A joint many-task model: Growing a neural network for multiple nlp tasks. arXiv preprint arXiv:1611.01587, 2016.
+
+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, pp. 770–778, 2016.
+
+Kaiming He, Georgia Gkioxari, Piotr Dollar, and Ross Girshick. Mask r-cnn. ´ arXiv preprint arXiv:1703.06870, 2017.
+
+Wenhao Huang, Guojie Song, Haikun Hong, and Kunqing Xie. Deep architecture for traffic flow prediction: deep belief networks with multitask learning. IEEE Transactions on Intelligent Transportation Systems, 15 (5):2191–2201, 2014.
+
+Sergey Ioffe and Christian Szegedy. Batch normalization: Accelerating deep network training by reducing internal covariate shift. In International Conference on Machine Learning, pp. 448–456, 2015.
+
+Laurent Jacob, Jean-philippe Vert, and Francis R Bach. Clustered multi-task learning: A convex formulation. In Advances in neural information processing systems, pp. 745–752, 2009.
+
+Zhuoliang Kang, Kristen Grauman, and Fei Sha. Learning with whom to share in multi-task feature learning. In Proceedings of the 28th International Conference on Machine Learning (ICML-11), pp. 521–528, 2011.
+
+Alex Kendall, Yarin Gal, and Roberto Cipolla. Multi-task learning using uncertainty to weigh losses for scene geometry and semantics. arXiv preprint arXiv:1705.07115, 2017.
+
+Iasonas Kokkinos. Ubernet: Training a universal convolutional neural network for low-, mid-, and high-level vision using diverse datasets and limited memory. arXiv preprint arXiv:1609.02132, 2016.
+
+Chen-Yu Lee, Vijay Badrinarayanan, Tomasz Malisiewicz, and Andrew Rabinovich. Roomnet: End-to-end room layout estimation. arXiv preprint arXiv:1703.06241, 2017.
+
+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, pp. 3431–3440, 2015.
+
+Mingsheng Long and Jianmin Wang. Learning multiple tasks with deep relationship networks. arXiv preprint arXiv:1506.02117, 2015.
+
+Yongxi Lu, Abhishek Kumar, Shuangfei Zhai, Yu Cheng, Tara Javidi, and Rogerio Feris. Fully-adaptive feature sharing in multi-task networks with applications in person attribute classification. arXiv preprint arXiv:1611.05377, 2016.
+
+Ishan Misra, Abhinav Shrivastava, Abhinav Gupta, and Martial Hebert. Cross-stitch networks for multi-task learning. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 3994– 4003, 2016.
+
+Joseph Redmon and Ali Farhadi. Yolo9000: better, faster, stronger. arXiv preprint arXiv:1612.08242, 2016.
+
+Michael L Seltzer and Jasha Droppo. Multi-task learning in deep neural networks for improved phoneme recognition. In Acoustics, Speech and Signal Processing (ICASSP), 2013 IEEE International Conference on, pp. 6965–6969. IEEE, 2013.
+
+Karen Simonyan and Andrew Zisserman. Very deep convolutional networks for large-scale image recognition. arXiv preprint arXiv:1409.1556, 2014.
+
+Anders Søgaard and Yoav Goldberg. Deep multi-task learning with low level tasks supervised at lower layers. In Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics, volume 2, pp. 231–235, 2016.
+
+Marvin Teichmann, Michael Weber, Marius Zoellner, Roberto Cipolla, and Raquel Urtasun. Multinet: Realtime joint semantic reasoning for autonomous driving. arXiv preprint arXiv:1612.07695, 2016.
+
+David Warde-Farley, Andrew Rabinovich, and Dragomir Anguelov. Self-informed neural network structure learning. arXiv preprint arXiv:1412.6563, 2014.
+
+Zhizheng Wu, Cassia Valentini-Botinhao, Oliver Watts, and Simon King. Deep neural networks employing multi-task learning and stacked bottleneck features for speech synthesis. In Acoustics, Speech and Signal Processing (ICASSP), 2015 IEEE International Conference on, pp. 4460–4464. IEEE, 2015.
+
+# Appendices
+
+# A GENERAL TRAINING CHARACTERISTICS
+
+All runs are trained at a batch size of 24 across 4 Titan X GTX 12GB GPUs and run at 30fps on a single GPU at inference. NYUv2 runs begin with a learning rate of 2e-5. Expanded NYUv2 runs last 80000 steps with a learning rate decay of 0.2 every 25000 steps. Downsampled NYUv2 runs last 20000 steps with a learning rate decay of 0.2 every 6000 steps. Updating $w _ { i } ( t )$ is performed at a learning rate of 0.025 for both GradNorm and the uncertainty weighting (Kendall et al. (2017)) baseline. All optimizers are Adam, although we find that GradNorm is insensitive to the optimizer chosen. We implement GradNorm using TensorFlow v1.2.1.
+
+# B EFFECTS OF TUNING THE ASYMMETRY $\alpha$
+
+The only hyperparameter in our technique is the asymmetry $\alpha$ . The optimal value of $\alpha$ for NYUv2 lies near $\alpha = 1 . 5$ , while in the highly symmetric toy example in Section 4 we used $\alpha = 0 . 1 2$ . This observation reinforces why we call $\alpha$ an asymmetry parameter.
+
+![](images/2d6e46168007d433a28a97f2d802d2041bfe626eed69baf2d7a02338bbc22b14.jpg)  
+Figure 6: Weights $w _ { i } ( t )$ during training, expanded NYUv2. Traces of how the task weights $w _ { i } ( t )$ change during training for two different values of $\alpha$ . A larger value of $\alpha$ pushes weights farther apart, leading to less symmetry between tasks.
+
+Tuning $\alpha$ leads to performance gains, but we found that for NYUv2, almost any value of $0 < \alpha < 3$ will improve network performance over an equal weights baseline. Figure 6 shows that higher values of $\alpha$ tend to push the weights $w _ { i } ( t )$ further apart, which more aggressively reduces the influence of tasks which overfit or learn too quickly (in our case, depth). Remarkably, at $\alpha = 1 . 7 5$ (not shown) $w _ { \mathrm { d e p t h } } ( t )$ is suppressed to below 0.02 at no detriment to network performance on the depth task.

parse/train/H1bM1fZCW/H1bM1fZCW_content_list.json

@@ -0,0 +1,1157 @@
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+    {
+        "type": "text",
+        "text": "GRADNORM: GRADIENT NORMALIZATION FOR ADAPTIVE LOSS BALANCING IN DEEP MULTITASK NETWORKS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Anonymous authors Paper under double-blind review ",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
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+            275
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Deep multitask networks, in which one neural network produces multiple predictive outputs, are more scalable and often better regularized than their single-task counterparts. Such advantages can potentially lead to gains in both speed and performance, but multitask networks are also difficult to train without finding the right balance between tasks. We present a novel gradient normalization (GradNorm) technique which automatically balances the multitask loss function by directly tuning the gradients to equalize task training rates. We show that for various network architectures, for both regression and classification tasks, and on both synthetic and real datasets, GradNorm improves accuracy and reduces overfitting over single networks, static baselines, and other adaptive multitask loss balancing techniques. GradNorm also matches or surpasses the performance of exhaustive grid search methods, despite only involving a single asymmetry hyperparameter $\\alpha$ . Thus, what was once a tedious search process which incurred exponentially more compute for each task added can now be accomplished within a few training runs, irrespective of the number of tasks. Ultimately, we hope to demonstrate that gradient manipulation affords us great control over the training dynamics of multitask networks and may be one of the keys to unlocking the potential of multitask learning. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
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+            587
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Single-task learning in computer vision has enjoyed much success in deep learning, with many models now performing at or beyond human accuracies for a wide array of tasks. However, a system that strives for full scene understanding cannot focus on one problem, but needs to perform many diverse perceptual tasks simultaneously. Such systems must also be efficient, especially within the restrictions of limited compute environments in embedded systems such as smartphones, wearable devices, and robots/drones. Multitask learning most naturally lends itself to this problem by sharing weights amongst different tasks within the same model and producing multiple predictions in one forward pass. Such networks are not only scalable, but the shared features within these networks tend to be better regularized and boost performance as a result. In the ideal limit, we can thus have the best of both worlds with multitask networks: both more efficiency and higher performance. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The key difficulty in multitask learning lies in the balancing of tasks, and perhaps the simplest way to control this balance is to choose the correct joint loss function. In practice, the multitask loss function is often assumed to be linear in the single task losses, $\\begin{array} { r } { L = \\sum _ { i } ^ { - } w _ { i } L _ { i } } \\end{array}$ , where the sum runs over $T$ tasks. The challenge is then to find the best value for each $w _ { i }$ that balances the contribution of each task for optimal model training. Our proposed method is furthermore an adaptive method, allowing $w _ { i }$ to vary with the training step $t$ , and so $w _ { i } = w _ { i } ( t )$ . ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Our key insight lies in the observation that these $w _ { i } ( t )$ influence training only because they control the magnitude of the gradients generated from task $i$ . As such, manipulating the gradient norms themselves would be a more direct way to control the training dynamics. More specifically, we propose a simple heuristic that penalizes the network when backpropagated gradients from any task are too large or too small. The correct balance is struck when tasks are training at similar rates; if task $i$ is training relatively quickly, then its weight $w _ { i } ( t )$ should decrease relative to other task weights $w _ { j } ( t ) | _ { j \\neq i }$ to allow other tasks more influence on the network. Our method can be said to be a form of batch normalization (Ioffe & Szegedy (2015)) for backpropagation, ensuring that gradients from each task per batch lie on a common statistical scale. We will show that, when implemented, gradient normalization leads to across-the-board improvements in accuracy and suppresses overfitting. ",
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+    {
+        "type": "image",
+        "img_path": "images/b7967b2eaf87bf5beb740b4e32f43b0678734733e83b79b85bfeb7b4b8fb6e0f.jpg",
+        "image_caption": [
+            "Figure 1: Gradient Normalization. Imbalanced gradient norms (left) result in suboptimal training within a multitask network, so we implement a novel gradient loss $L _ { \\mathrm { g r a d } }$ (right) which detects such imbalances in gradient norms amongst tasks and tunes the weights in the loss function to compensate. We illustrate here a simplified case where such balancing results in equalized gradient norms, but in general some tasks may need higher or lower gradient norms relative to other tasks for optimal task balancing (discussed further in Section 3). "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "Our main contributions to the field of multitask learning are as follows: ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "1. An attractively simple heuristic for multitask loss balancing involving training rate equalization, which is implemented through a novel gradient loss function. 2. A simplification to exhaustive grid search (which has compute complexity $\\mathcal { O } ( N ^ { T } )$ for $N$ grid points in one dimension) that only involves tuning one robust hyperparameter. 3. Demonstration that direct interaction with gradients provides a powerful way of reasoning about multitask learning. ",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "2 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            676,
+            344,
+            693
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Multitask learning has existed well before the advent of deep learning (Caruana (1998); Bakker & Heskes (2003)), but the robust learned features within deep networks have spurned renewed interest. Although our primary application area is computer vision, multitask learning has applications in multiple other fields, from natural language processing (Hashimoto et al. (2016); Collobert & Weston (2008); Søgaard & Goldberg (2016)) to speech synthesis (Wu et al. (2015); Seltzer & Droppo (2013)), from very domain-specific applications like traffic prediction (Huang et al. (2014)) to very general cross-domain work (Bilen & Vedaldi (2017)). ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Multitask learning is very well-suited to the field of computer vision, where making multiple robust predictions is crucial for complete scene understanding. Deep networks have been used to solve various subsets of multiple vision tasks, from 3-task networks (Eigen & Fergus (2015); Teichmann et al. (2016)) to much larger subsets as in UberNet (Kokkinos (2016)). Often, single computer vision problems can even be framed as multitask problems, such as in Mask R-CNN for instance segmentation (He et al. (2017)) or YOLO-9000 for object detection (Redmon & Farhadi (2016)). Researchers often assume a fixed loss function or network architecture, but there has also been significant work on finding optimal ways to relate tasks to each other in a multitask model. Clustering methods have shown success beyond deep models (Kang et al. (2011); Jacob et al. (2009)), while constructs such as deep relationship networks (Long & Wang (2015)) and cross-stich networks (Misra et al. (2016)) search for meaningful relationships between tasks and learn which features to share between them. Work in Warde-Farley et al. (2014) and Lu et al. (2016) use groupings amongst labels to search through possible architectures for learning. Perhaps the most relevant to the current work, Kendall et al. (2017) uses a joint likelihood formulation to derive task weights based on the intrinsic uncertainty in each task. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "3 METHODOLOGY ",
+        "text_level": 1,
+        "bbox": [
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+            220,
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1 A GRADIENT LOSS FUNCTION BASED ON RATE BALANCING ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We begin with the standard multitask loss function with time dependency, $\\begin{array} { r } { L ( t ) = \\sum w _ { i } ( t ) L _ { i } ( t ) } \\end{array}$ , and our goal is to learn the functions $w _ { i } ( t )$ . We argued in Section 1 that $w _ { i } ( t )$ is intimately related to the norm of gradients from each task backpropagated into the network. We thus must motivate a set of desirable gradient magnitudes, and use those desired magnitudes to set the task weights $w _ { i } ( t )$ . ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Consider the norms of gradients from task $i$ on some set of weights $W$ within the network, n $\\mathsf { \\Omega } ^ { \\mathsf { \\tiny { l o r m } } } ( \\nabla _ { W } L _ { i } ( t ) )$ (specific choices for $W$ to be discussed later). Our method of gradient normalization (hereafter referred to as GradNorm) works in two steps: (1) We first scale all gradient norms to an equal value as a neutral starting point. This value is most naturally chosen to be the average gradient norm amongst tasks, $E _ { \\mathrm { t a s k } } [ \\mathrm { n o r m } ( \\nabla _ { W } L _ { i } ( t ) ) ]$ , where we use $E _ { \\mathrm { t a s k } } [ X ]$ to denote the average value of a task-dependent quantity $X$ across tasks. (2) We then modify gradient norms with a rate balancing term that ensures no task trains relatively too slowly. The gradient norms of task $i$ should grow when task $i$ trains relatively slowly, thereby boosting more sluggish tasks. Gradient norms thus should be an increasing function of the relative inverse training rate for each task. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "To quantify training rates, we choose the loss ratio of task $i$ at training step $t$ , $L _ { i } ^ { \\prime } ( t ) : = L _ { i } ( t ) / L _ { i } ( 0 )$ , as a measure of task $i$ ’s inverse training rate; smaller values of $L _ { i } ^ { \\prime } ( t )$ would mean that task $i$ has trained more. If $L _ { i } ^ { \\prime } ( t )$ denotes the inverse training rate of task $i$ , then the relative inverse training rate is just $L _ { i } ^ { \\prime } ( t ) / \\dot { E _ { \\mathrm { t a s k } } } [ L _ { i } ^ { \\prime } ( t ) ]$ . Using this simple loss ratio metric is valid for both regression squared loss and classification cross-entropy loss, as we will see in Section $5 . 2 ^ { 1 }$ . ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Our desired gradient norms are therefore: ",
+        "bbox": [
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+    {
+        "type": "equation",
+        "img_path": "images/015005484898f0f9cef818f83f9efddc0a54ed9e40fba86c239b552e2227d31f.jpg",
+        "text": "$$\n\\begin{array} { r l } & { \\mathrm { n o r m } ( \\nabla _ { W } L _ { i } ( t ) ) \\mapsto ( \\mathrm { a v e r a g e \\ : g r a d i e n t \\ : n o r m } ) \\times ( \\mathrm { r e l a t i v e \\ : i n v e r s e \\ : t r a i n i n g \\ : r a t e \\ : o f \\ : t a s k \\ : } i ) ^ { \\alpha } } \\\\ & { \\qquad = E _ { \\mathrm { t a s k } } [ \\mathrm { n o r m } ( \\nabla _ { W } L ( t ) ) ] \\left( \\frac { L _ { i } ^ { \\prime } ( t ) } { E _ { \\mathrm { t a s k } } [ L _ { i } ^ { \\prime } ( t ) ] } \\right) ^ { \\alpha } } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "where $\\alpha$ is an additional hyperparameter. $\\alpha$ sets the strength of rate balancing in the multitask problem, and also is a measure of the asymmetry between tasks. In cases where tasks are very different in their complexity, leading to different learning dynamics, a higher value of $\\alpha$ should be used to pull tasks back towards a common training rate more forcefully. When tasks are more symmetric (e.g. the synthetic examples in Section 4), a lower value of $\\alpha$ is appropriate. Note that $\\alpha = 0$ will always try to pin the norms of backpropped gradients from each task to be equal at $W$ . ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Equation 1 sets a desired target for our gradient norms, and we want to update our loss weights $w _ { i } ( t )$ to move gradient norms towards this target. To accomplish this, GradNorm is implemented as a loss function $L _ { \\mathrm { g r a d } }$ which is just the L1 distance between actual gradient norms and the targets in Equation 1: ",
+        "bbox": [
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+        "type": "equation",
+        "img_path": "images/2b921ca01451995e4a5b3dbe96bb938214a0740340cc8c1738886bacd25c9dac.jpg",
+        "text": "$$\nL _ { \\mathrm { g r a d } } ^ { ( i ) } ( t ; W ) = \\left| \\mathrm { n o r m } ( \\nabla _ { W } L _ { i } ( t ) ) - E _ { \\mathrm { t a s k } } [ \\mathrm { n o r m } ( \\nabla _ { W } L ( t ) ) ] \\left( \\frac { L _ { i } ^ { \\prime } ( t ) } { E _ { \\mathrm { t a s k } } [ L ^ { \\prime } ( t ) ] } \\right) ^ { \\alpha } | . \\right.\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The above loss is for one task; the full loss is just the mean of the individual task losses, $\\begin{array} { r } { L _ { \\mathrm { g r a d } } ( t ; W ) = ( 1 / T ) \\sum _ { i } L _ { \\mathrm { g r a d } } ^ { ( i ) } ( t ; W ) } \\end{array}$ . $L _ { \\mathrm { g r a d } }$ is then differentiated with respect to each $w _ { i } ( t )$ , and its gradients are applied via standard update rules to update these weights (see Figure 1 for a schematic view). In principle, it is also possible to update all network weights (not just $w _ { i } ( t ) )$ based on gradient of $L _ { \\mathrm { g r a d } }$ , but in practice this adds undue complexity to the problem and often degrades performance. ",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "We can choose $W$ , the weights upon which we rate balance gradient norms, to be any subset of weights within layers of our network. In practice, in order to save on compute overhead, we choose $W$ to be the weights in the last layer which is shared amongst all three tasks. This simplification greatly shortens the number of layers $L _ { \\mathrm { g r a d } }$ must be backpropagated through, and with this choice of $W$ in our experiments GradNorm only adds $\\sim 5 \\%$ of additional compute time. After every update step, we also renormalize the weights $w _ { i } ( t )$ so that $\\begin{array} { r } { \\sum _ { i } w _ { i } ( t ) = T } \\end{array}$ in order to decouple gradient normalization from the global learning rate. ",
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+    {
+        "type": "text",
+        "text": "4 A SIMPLE TOY EXAMPLE ",
+        "text_level": 1,
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "To illustrate GradNorm on a simple system, we consider $T$ regression tasks onto the functions ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/c7086989f33d3fb2215af655429503cbb89c362ec9cd842482a483014823a3ad.jpg",
+        "text": "$$\nf _ { i } ( { \\bf x } ) = \\sigma _ { i } \\operatorname { t a n h } ( ( B + \\epsilon _ { i } ) { \\bf x } ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "where tanh acts element-wise. We use squared loss to train each task. The matrices $B$ and $\\epsilon _ { i }$ have elements generated IID from $\\mathcal { N } ( 0 , 1 0 )$ and $\\mathcal { N } ( 0 , 3 . 5 )$ , respectively. Our task is thus to perform regression on multiple tasks with shared information $B$ along with information specific to each task, $\\epsilon _ { i }$ . The $\\sigma _ { i }$ are fixed scalars which set the variance of the outputs $f _ { i }$ . Higher values of $\\sigma _ { i }$ induce higher values of squared loss for that task. These tasks are harder to learn due to the higher variances in their response values, but they also backpropagate larger gradients. Classically, such a scenario can lead to suboptimal training dynamics as the higher $\\sigma _ { i }$ tasks tend to dominate the training. ",
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+    {
+        "type": "text",
+        "text": "All toy problem runs use a 4-layer fully-connected ReLU-activated network with 100 neurons per layer as a common trunk. A final affine transformation per task gives $T$ final predictions. Inputs are in $\\mathbb { R } ^ { 2 5 0 }$ , and outputs lie in $\\mathbb { R } ^ { 1 0 0 }$ . To ensure consistency, we only compare models initialized to the same random values and fed data generated from a fixed random seed. The asymmetry $\\alpha$ is set low to 0.12 for these experiments, as the output functions $f _ { i }$ are all of the same form. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In these toy problems, we measure the task-normalized test-time loss, which is the sum of the test loss ratios for each task, $\\textstyle \\sum _ { i } L _ { i } ^ { \\prime } ( t )$ . A simple sum of losses is wholly inadequate to judge the overall performance of a multitask network, as it biases itself towards tasks with higher loss scales, and there exists no general metric by which to judge multitask performance in any setting. Luckily, our toy problem was designed with tasks which are statistically identical except for their loss scales $\\sigma _ { i }$ . For this simple example, there is therefore a clear measure of overall network performance, which is the sum of losses with each loss normalized to its $\\sigma _ { i }$ - precisely the sum of loss ratios. ",
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+    {
+        "type": "text",
+        "text": "In the case of $T = 2$ , we choose the values $( \\sigma _ { 0 } , \\sigma _ { 1 } ) = ( 1 . 0 , 1 0 0 . 0 )$ . Classically, task 1 can suppress task 0’s influence during training due to its higher loss scale. As shown in the top panels of Figure 2, gradient normalization remedies the issue by increasing $w _ { 0 } ( t )$ to counteract the larger gradients coming from $T _ { 1 }$ , and the improved task balance results in better test-time performance. ",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The possible benefits of gradient normalization become even clearer when the number of tasks increases. For $T = 1 0$ , we sample the $\\sigma _ { i }$ from a normal distribution and plot the results in the bottom row of Figure 2. GradNorm significantly improves test time performance over naively weighting each task the same. Like $T = 2$ , for $T = 1 0$ the $w _ { i } ( t )$ grow larger for smaller $\\sigma _ { i }$ tasks; GradNorm is giving tasks with smaller loss scales more breathing room. ",
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+    {
+        "type": "text",
+        "text": "For both $T = 2$ and $T = 1 0$ , GradNorm is more stable and outperforms the uncertainty weighting proposed by Kendall et al. (2017). Uncertainty weighting, which enforces that $w _ { i } ( t ) \\ \\tilde { \\mathbf { \\Omega } } \\sim 1 / \\bar { L } _ { i } ( t ) \\mathbf { \\dot { \\Omega } }$ , tends to grow weights too large and too quickly as the loss for each task drops. Although such networks train quickly at the onset, the training soon crashes as the global learning rate grows too large. This issue is exacerbated as uncertainty weighting allows $w _ { i } ( t )$ to change unconstrained (compared to GradNorm which ensures $\\sum w _ { i } ( t ) = \\bar { T }$ always), which pushes global learning rate up even further. ",
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+    {
+        "type": "text",
+        "text": "Overall, the traces for each $w _ { i } ( t )$ during a single GradNorm run seem fairly stable and convergent. In fact, in Section 5.3 we will see how the time-averaged weights $E _ { t } [ w _ { i } ( t ) ]$ lie close to the optimal static weights, suggesting GradNorm can greatly simplify the tedious grid search procedure. ",
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+        "img_path": "images/f3bd541a017b05f81881e8b42a036a9e5d43bbaf3d46522614762465c01e336a.jpg",
+        "image_caption": [
+            "Figure 2: Gradient Normalization on a toy 2-task (top) and 10-task (bottom) system. Diagrams of the network structure with loss scales are on the left, traces of $w _ { i } ( t )$ during training in the middle, and task-normalized test loss curves on the right. $\\alpha = 0 . 1 2$ for all runs. "
+        ],
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+    {
+        "type": "text",
+        "text": "5 APPLICATION TO A LARGE REAL-WORLD DATASET ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We primarily use NYUv2 as our dataset of choice. The standard NYUv2 dataset carries depth, surface normals, and semantic segmentation labels (which we cluster into 13 distinct classes). NYUv2 is quite small as a dataset, with a training split of ${ \\sim } 8 0 0$ examples, but contains both regression and classification labels, making it a good choice to test the robustness of GradNorm. ",
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+        "type": "text",
+        "text": "To show GradNorm in action on a more large-scale multitask dataset, we also expand NYUv2 to 40,000 images complete with pixel-wise depth, surface normals, and room keypoint labels. Keypoint labels are obtained through professional human labeling services, while surface normals are generated from camera parameters and the depth maps through standard methods. ",
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+    {
+        "type": "text",
+        "text": "Following Lee et al. (2017), the state-of-the-art in room layout prediction, all inputs are downsampled to $3 2 0 \\times 3 2 0$ pixels and outputs to $8 0 \\mathrm { ~ x ~ } 8 0$ pixels. These resolutions also speed up training without compromising complexity in the inputs or labels. ",
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+    {
+        "type": "text",
+        "text": "5.1 MODEL AND INDIVIDUAL TASK LOSSES ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We try two different models: (1) a SegNet (Badrinarayanan et al. (2015); Lee et al. (2017)) network with a symmetric VGG16 (Simonyan & Zisserman (2014)) encoder/decoder, and (2) an FCN (Long et al. (2015)) network with a modified ResNet-50 (He et al. (2016)) encoder and shallow ResNet decoder. The VGG SegNet reuses maxpool indices to perform upsampling, while the ResNet FCN learns all upsampling filters. The ResNet architecture is further thinned (both in its filters and activations) to contrast with the heavier, more complex VGG SegNet: stride-2 layers are moved earlier and all 2048-filter layers are replaced by 1024-filter layers. Ultimately, the VGG SegNet has 29M parameters versus 15M for the thin ResNet. Although we will focus on the VGG SegNet in our more in-depth analysis, by designing and testing on two extremely different network topologies we will further demonstrate that GradNorm is very robust to the choice of base model. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We use standard pixel-wise loss functions for each task: cross entropy for segmentation, squared loss for depth, and cosine similarity for normals. As in Lee et al. (2017), for room layout we generate Gaussian heatmaps for each of 48 room keypoint types and predict these heatmaps with a pixel-wise squared loss. Note that all regression tasks are quadratic losses (our surface normal prediction uses a cosine loss which is quadratic to leading order), allowing us to use the loss ratio $L _ { i } ^ { \\prime } ( t )$ of each task as a direct proxy for each task’s inverse training rate. ",
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+    {
+        "type": "table",
+        "img_path": "images/f8ff4b1cfeb832ed1d4cddf7121510cd4607408d3f44f002eec93e3ee9dcab78.jpg",
+        "table_caption": [
+            "Table 1: Test error, 320x320 NYUv2 for GradNorm and various baselines. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model Type and Weighting Method</td><td>Depth Error (m)</td><td>Segmentation 100-mloU (%)</td><td>Normals Error (1-|cosl)</td></tr><tr><td>VGG SegNet, Depth Only</td><td>1.038</td><td>=</td><td></td></tr><tr><td>VGG SegNet, Segmentation Only</td><td>-</td><td>70.0</td><td>=</td></tr><tr><td>VGG SegNet, Normals Only</td><td>=</td><td>=</td><td>0.169</td></tr><tr><td>VGG SegNet, Equal Weights</td><td>0.944</td><td>70.1</td><td>0.192</td></tr><tr><td>VGG SegNet, GradNorm Converged Weights</td><td>0.939</td><td>67.5</td><td>0.171</td></tr><tr><td>VGG SegNet, GradNorm α = 1.5</td><td>0.925</td><td>67.8</td><td>0.174</td></tr></table>",
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+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "5.2 NETWORK PERFORMANCE ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In Table 1 we display the performance of GradNorm on the NYUv2 dataset (with input/output resolutions as described in Section 5). Specific training schemes for all NYUv2 models are detailed in Appendix A. We see that GradNorm improves the performance of all three tasks with respect to the equal-weights baseline (where $w _ { i } ( t ) = 1$ for all $^ { t , i }$ ), and that GradNorm either surpasses or matches (within statistical noise) the best performance of single networks for each task. The GradNorm Converged Weights network is derived by calculating the GradNorm time-averaged weights $E _ { t } [ w _ { i } ( t ) ]$ for each task (e.g. by averaging curves like those found in Appendix B), and retraining a network with weights fixed to those values. GradNorm thus can also be used to extract good values for static weights. We pursue this idea further in Section 5.3 and show that these weights lie very close to the optimal weights extracted from exhaustive grid search. ",
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+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model Type and Weighting Method</td><td>Depth Error (m)</td><td>Keypoint Error (%)</td><td>Normals Error (1-|cos|)</td></tr><tr><td>Thin ResNet FCN, Depth Only</td><td>0.725</td><td>-</td><td>1</td></tr><tr><td>Thin ResNet FCN,Keypoint Only</td><td>1</td><td>7.90</td><td>=</td></tr><tr><td>Thin ResNet FCN, Normals Only</td><td>1</td><td>-</td><td>0.155</td></tr><tr><td>Thin ResNet FCN,Equal Weights</td><td>0.697</td><td>7.80</td><td>0.172</td></tr><tr><td>Thin ResNet FCN, Unc. Weighting (Kendall et al. (2017))</td><td>0.702</td><td>7.96</td><td>0.182</td></tr><tr><td>Thin ResNetFCN,GradNorm Converged Weights</td><td>0.695</td><td>7.63</td><td>0.156</td></tr><tr><td>Thin ResNet FCN, GradNorm α = 1.5</td><td>0.663</td><td>7.32</td><td>0.155</td></tr><tr><td>VGG SegNet, Depth Only</td><td>0.689</td><td>-</td><td>-</td></tr><tr><td>VGG SegNet, Keypoint Only</td><td>1</td><td>8.39</td><td>1</td></tr><tr><td>VGG SegNet, Normals Only</td><td>-</td><td>1</td><td>0.142</td></tr><tr><td>VGG SegNet, Equal Weights</td><td>0.658</td><td>8.39</td><td>0.155</td></tr><tr><td>VGG SegNet, Unc.Weighting (Kendall et al. (2017))</td><td>0.649</td><td>8.00</td><td>0.158</td></tr><tr><td>VGG SegNet, GradNorm Converged Weights</td><td>0.638</td><td>7.69</td><td>0.137</td></tr><tr><td>VGG SegNet, GradNorm α = 1.5</td><td>0.629</td><td>7.73</td><td>0.139</td></tr></table>",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Table 2: Test error, expanded 320x320 NYUv2 for GradNorm and various baselines. ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "To show how GradNorm can perform in the presence of a much larger dataset, we also perform extensive experiments on the expanded NYUv2 dataset, which carries a factor of $5 0 \\mathrm { x }$ more data. The results are shown in Table 2. As with the standard NYUv2 runs, GradNorm networks outperform other multitask methods, and either matches (within noise) or surpasses the performance of singletask networks. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Figure 3 shows test and training loss curves for GradNorm ( $\\alpha = 1 . 5$ ) and baselines on the expanded NYUv2 dataset for our VGG SegNet models. GradNorm improves test-time depth error by $\\sim 5 \\%$ , despite ending with much higher training loss. GradNorm achieves this by aggressively rate balancing the network (enforced by a high asymmetry $\\alpha = 1 . 5$ ), and ultimately suppresses the depth weight $w _ { \\mathrm { d e p t h } } ( t )$ to lower than 0.10 (see Appendix B for more details). The same trend exists for keypoint regression, and is a clear signal of network regularization. In contrast, the uncertainty weighting technique (Kendall et al. (2017)) causes both test and training error to move in lockstep, and thus is not a good regularizer. Only results for the VGG SegNet are shown here, but the Thin ResNet FCN produces consistent results. ",
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+    {
+        "type": "image",
+        "img_path": "images/c183338d678f77c294cb134b4de7a34e7b41ed89c4c169bcdca0f31b44fa7e1b.jpg",
+        "image_caption": [
+            "Figure 3: Test and training loss curves for all tasks in expanded NYUv2, VGG16 backbone. GradNorm versus an equal weights baseline and uncertainty weighting (Kendall et al. (2017)). "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "5.3 GRADIENT NORMALIZATION FINDS OPTIMAL GRID-SEARCH WEIGHTS IN ONE PASS",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "For our VGG SegNet, we train 100 networks from scratch with random task weights on expanded NYUv2. Weights are sampled from a uniform distribution and renormalized to sum to $T = 3$ . For computational efficiency, we only train for 15000 iterations out of the normal 80000, and then compare the performance of that network to our GradNorm $\\alpha = 1 . 5$ VGG SegNet network at the same 15000 steps. The results are shown in Figure 4. ",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/f5e0772a1680020f60b2627b1c253d7c8279499f16e65c3819998884c4bdd881.jpg",
+        "image_caption": [
+            "Figure 4: Gridsearch performance for random task weights, expanded NYUv2. Average change in performance across three tasks for a static network with weights $w _ { i } ^ { \\mathrm { s t a t i c } }$ is plotted against the $L _ { 2 }$ distance between $w _ { i } ^ { \\mathrm { s t a t i c } }$ and our GradNorm network’s time-averaged weights, $E _ { t } [ w _ { i } ( t ) ]$ . All comparisons are made at 15000 steps of training. "
+        ],
+        "image_footnote": [],
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "Even after 100 networks trained, grid search still falls short of our GradNorm network. But even more remarkably, there is a strong, negative correlation between network performance and task weight distance to our time-averaged GradNorm weights. At an $L _ { 2 }$ distance of $\\sim 3$ , grid search networks on average have almost double the errors per task compared to our GradNorm network. GradNorm has effectively allowed us to “cheat” and immediately find the optimal grid search weights without actually performing grid search, simplifying a process that is usually notoriously laborious. ",
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/93d306774aebeed67a84e1822fd4c9509658329f17e414b9f956c84f6fabc148.jpg",
+        "image_caption": [
+            "Figure 5: Visualizations at inference time. Expanded NYUv2 with room layout labels is shown on the left, while downsampled NYUv2 with semantic segmentation labels is shown on the right. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "5.4 QUALITATIVE RESULTS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Figure 5 shows visualizations of the VGG SegNet outputs on test set images along with the ground truth, for both the expanded and downsampled NYUv2 datasets. Ground truth labels are juxtaposed with outputs from the equal weights network, 3 single networks, and our best GradNorm network. The qualitative improvements are incremental, but we find the GradNorm network tends to output smoother, more detailed pixel map predictions when compared to the other two baselines. ",
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+    {
+        "type": "text",
+        "text": "6 CONCLUSIONS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Gradient normalization acts as a good model regularizer and leads to superb performance in multitask networks by operating directly on the gradients in the network. GradNorm is driven by the attractively simple heuristic of rate balancing, and can accommodate problems of varying complexities within the same unified model using a single hyperparameter representing task asymmetry. A GradNorm network can also be used to quickly extract optimal fixed task weights, removing the need for exhaustive grid search methods that become exponentially more expensive with the number of tasks. We hope that our work has not only introduced a new methodology for quickly balancing multitask networks, but also has shown how direct gradient manipulation can be a powerful way to reason about task relationships within a multitask framework. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "REFERENCES ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            103,
+            287,
+            117
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Vijay Badrinarayanan, Alex Kendall, and Roberto Cipolla. Segnet: A deep convolutional encoder-decoder architecture for image segmentation. arXiv preprint arXiv:1511.00561, 2015. ",
+        "bbox": [
+            176,
+            125,
+            823,
+            151
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Bart Bakker and Tom Heskes. Task clustering and gating for bayesian multitask learning. Journal of Machine Learning Research, 4(May):83–99, 2003. ",
+        "bbox": [
+            173,
+            159,
+            823,
+            185
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Hakan Bilen and Andrea Vedaldi. Universal representations: The missing link between faces, text, planktons, and cat breeds. arXiv preprint arXiv:1701.07275, 2017. ",
+        "bbox": [
+            173,
+            193,
+            823,
+            219
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Rich Caruana. Multitask learning. In Learning to learn, pp. 95–133. Springer, 1998. ",
+        "bbox": [
+            173,
+            227,
+            676,
+            242
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Ronan Collobert and Jason Weston. A unified architecture for natural language processing: Deep neural networks with multitask learning. In Proceedings of the 25th international conference on Machine learning, pp. 160–167. ACM, 2008. ",
+        "bbox": [
+            173,
+            250,
+            826,
+            287
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "David Eigen and Rob Fergus. Predicting depth, surface normals and semantic labels with a common multi-scale convolutional architecture. In Proceedings of the IEEE International Conference on Computer Vision, pp. 2650–2658, 2015. ",
+        "bbox": [
+            174,
+            296,
+            823,
+            335
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Kazuma Hashimoto, Caiming Xiong, Yoshimasa Tsuruoka, and Richard Socher. A joint many-task model: Growing a neural network for multiple nlp tasks. arXiv preprint arXiv:1611.01587, 2016. ",
+        "bbox": [
+            173,
+            343,
+            821,
+            371
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "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, pp. 770–778, 2016. ",
+        "bbox": [
+            174,
+            377,
+            823,
+            405
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Kaiming He, Georgia Gkioxari, Piotr Dollar, and Ross Girshick. Mask r-cnn. ´ arXiv preprint arXiv:1703.06870, 2017. ",
+        "bbox": [
+            174,
+            411,
+            823,
+            438
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Wenhao Huang, Guojie Song, Haikun Hong, and Kunqing Xie. Deep architecture for traffic flow prediction: deep belief networks with multitask learning. IEEE Transactions on Intelligent Transportation Systems, 15 (5):2191–2201, 2014. ",
+        "bbox": [
+            174,
+            445,
+            823,
+            486
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Sergey Ioffe and Christian Szegedy. Batch normalization: Accelerating deep network training by reducing internal covariate shift. In International Conference on Machine Learning, pp. 448–456, 2015. ",
+        "bbox": [
+            173,
+            493,
+            823,
+            521
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Laurent Jacob, Jean-philippe Vert, and Francis R Bach. Clustered multi-task learning: A convex formulation. In Advances in neural information processing systems, pp. 745–752, 2009. ",
+        "bbox": [
+            173,
+            527,
+            821,
+            555
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Zhuoliang Kang, Kristen Grauman, and Fei Sha. Learning with whom to share in multi-task feature learning. In Proceedings of the 28th International Conference on Machine Learning (ICML-11), pp. 521–528, 2011. ",
+        "bbox": [
+            174,
+            561,
+            823,
+            589
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Alex Kendall, Yarin Gal, and Roberto Cipolla. Multi-task learning using uncertainty to weigh losses for scene geometry and semantics. arXiv preprint arXiv:1705.07115, 2017. ",
+        "bbox": [
+            173,
+            597,
+            821,
+            623
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Iasonas Kokkinos. Ubernet: Training a universal convolutional neural network for low-, mid-, and high-level vision using diverse datasets and limited memory. arXiv preprint arXiv:1609.02132, 2016. ",
+        "bbox": [
+            173,
+            631,
+            823,
+            659
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Chen-Yu Lee, Vijay Badrinarayanan, Tomasz Malisiewicz, and Andrew Rabinovich. Roomnet: End-to-end room layout estimation. arXiv preprint arXiv:1703.06241, 2017. ",
+        "bbox": [
+            173,
+            665,
+            823,
+            693
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "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, pp. 3431–3440, 2015. ",
+        "bbox": [
+            173,
+            699,
+            823,
+            727
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Mingsheng Long and Jianmin Wang. Learning multiple tasks with deep relationship networks. arXiv preprint arXiv:1506.02117, 2015. ",
+        "bbox": [
+            173,
+            734,
+            823,
+            761
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Yongxi Lu, Abhishek Kumar, Shuangfei Zhai, Yu Cheng, Tara Javidi, and Rogerio Feris. Fully-adaptive feature sharing in multi-task networks with applications in person attribute classification. arXiv preprint arXiv:1611.05377, 2016. ",
+        "bbox": [
+            171,
+            768,
+            823,
+            808
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Ishan Misra, Abhinav Shrivastava, Abhinav Gupta, and Martial Hebert. Cross-stitch networks for multi-task learning. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 3994– 4003, 2016. ",
+        "bbox": [
+            173,
+            815,
+            823,
+            854
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Joseph Redmon and Ali Farhadi. Yolo9000: better, faster, stronger. arXiv preprint arXiv:1612.08242, 2016. ",
+        "bbox": [
+            171,
+            862,
+            808,
+            877
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Michael L Seltzer and Jasha Droppo. Multi-task learning in deep neural networks for improved phoneme recognition. In Acoustics, Speech and Signal Processing (ICASSP), 2013 IEEE International Conference on, pp. 6965–6969. IEEE, 2013. ",
+        "bbox": [
+            174,
+            885,
+            823,
+            924
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Karen Simonyan and Andrew Zisserman. Very deep convolutional networks for large-scale image recognition. arXiv preprint arXiv:1409.1556, 2014. ",
+        "bbox": [
+            171,
+            104,
+            821,
+            131
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Anders Søgaard and Yoav Goldberg. Deep multi-task learning with low level tasks supervised at lower layers. In Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics, volume 2, pp. 231–235, 2016. ",
+        "bbox": [
+            173,
+            140,
+            821,
+            178
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Marvin Teichmann, Michael Weber, Marius Zoellner, Roberto Cipolla, and Raquel Urtasun. Multinet: Realtime joint semantic reasoning for autonomous driving. arXiv preprint arXiv:1612.07695, 2016. ",
+        "bbox": [
+            173,
+            188,
+            825,
+            213
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "David Warde-Farley, Andrew Rabinovich, and Dragomir Anguelov. Self-informed neural network structure learning. arXiv preprint arXiv:1412.6563, 2014. ",
+        "bbox": [
+            173,
+            222,
+            821,
+            250
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Zhizheng Wu, Cassia Valentini-Botinhao, Oliver Watts, and Simon King. Deep neural networks employing multi-task learning and stacked bottleneck features for speech synthesis. In Acoustics, Speech and Signal Processing (ICASSP), 2015 IEEE International Conference on, pp. 4460–4464. IEEE, 2015. ",
+        "bbox": [
+            174,
+            257,
+            823,
+            296
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Appendices ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            98,
+            341,
+            127
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "A GENERAL TRAINING CHARACTERISTICS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            148,
+            547,
+            166
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "All runs are trained at a batch size of 24 across 4 Titan X GTX 12GB GPUs and run at 30fps on a single GPU at inference. NYUv2 runs begin with a learning rate of 2e-5. Expanded NYUv2 runs last 80000 steps with a learning rate decay of 0.2 every 25000 steps. Downsampled NYUv2 runs last 20000 steps with a learning rate decay of 0.2 every 6000 steps. Updating $w _ { i } ( t )$ is performed at a learning rate of 0.025 for both GradNorm and the uncertainty weighting (Kendall et al. (2017)) baseline. All optimizers are Adam, although we find that GradNorm is insensitive to the optimizer chosen. We implement GradNorm using TensorFlow v1.2.1. ",
+        "bbox": [
+            174,
+            180,
+            825,
+            279
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "B EFFECTS OF TUNING THE ASYMMETRY $\\alpha$ ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            299,
+            547,
+            314
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "The only hyperparameter in our technique is the asymmetry $\\alpha$ . The optimal value of $\\alpha$ for NYUv2 lies near $\\alpha = 1 . 5$ , while in the highly symmetric toy example in Section 4 we used $\\alpha = 0 . 1 2$ . This observation reinforces why we call $\\alpha$ an asymmetry parameter. ",
+        "bbox": [
+            174,
+            330,
+            825,
+            372
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "image",
+        "img_path": "images/2d6e46168007d433a28a97f2d802d2041bfe626eed69baf2d7a02338bbc22b14.jpg",
+        "image_caption": [
+            "Figure 6: Weights $w _ { i } ( t )$ during training, expanded NYUv2. Traces of how the task weights $w _ { i } ( t )$ change during training for two different values of $\\alpha$ . A larger value of $\\alpha$ pushes weights farther apart, leading to less symmetry between tasks. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            179,
+            387,
+            808,
+            553
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Tuning $\\alpha$ leads to performance gains, but we found that for NYUv2, almost any value of $0 < \\alpha < 3$ will improve network performance over an equal weights baseline. Figure 6 shows that higher values of $\\alpha$ tend to push the weights $w _ { i } ( t )$ further apart, which more aggressively reduces the influence of tasks which overfit or learn too quickly (in our case, depth). Remarkably, at $\\alpha = 1 . 7 5$ (not shown) $w _ { \\mathrm { d e p t h } } ( t )$ is suppressed to below 0.02 at no detriment to network performance on the depth task. ",
+        "bbox": [
+            174,
+            623,
+            825,
+            693
+        ],
+        "page_idx": 10
+    }
+]

parse/train/H1gEP6NFwr/H1gEP6NFwr.md

@@ -0,0 +1,371 @@
+# ON THE TUNABILITY OF OPTIMIZERS IN DEEP LEARNING
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+There is no consensus yet on the question whether adaptive gradient methods like Adam are easier to use than non-adaptive optimization methods like SGD. In this work, we fill in the important, yet ambiguous concept of ‘ease-of-use’ by defining an optimizer’s tunability: How easy is it to find good hyperparameter configurations using automatic random hyperparameter search? We propose a practical evaluation protocol for optimizer tunability that can form the basis for a fair optimizer benchmark. Evaluating a variety of optimizers on an extensive set of standard datasets and architectures, we find that Adam is the most tunable for the majority of problems, especially with a low budget for hyperparameter tuning.
+
+# 1 INTRODUCTION
+
+With the ubiquity of deep learning in various applications, a multitude of first-order stochastic optimizers (Robbins & Monro, 1951) have been in vogue. They have varying algorithmic components like momentum (Sutskever et al., 2013) and adaptive learning rates (Tieleman & Hinton, 2012; Duchi et al., 2011; Kingma & Ba, 2015). With all these choices, picking the optimizer is among the most important design decisions for machine learning practitioners. For this decision, the best possible generalization performance is certainly an important characteristic to be taken into account. However, we argue that in practice, an even more important characteristic is whether the best possible performance can be reached with the available resources.
+
+The performance of optimizers strongly depends on the choice of hyperparameter values such as the learning rate. In the machine learning research community, the sensitivity of models to hyperparameters has been of great debate recently, where in multiple cases, reported model advances did not stand the test of time because they can be explained by better hyperparameter tuning (Lucic et al., 2018; Melis et al., 2018; Henderson et al., 2018). This has led to calls for using automatic hyperparameter optimization methods with a fixed budget for a fairer comparison of models (Sculley et al., 2018; Feurer & Hutter, 2019; Eggensperger et al., 2019). For industrial applications, automated machine learning (AutoML, Hutter et al., 2019), which has automatic hyperparameter optimization as one of its key concepts, is becoming increasingly more important. In both cases, an optimization algorithm that achieves good performances with relatively little tuning effort is arguably substantially more useful than an optimization algorithm that achieves top performances, but reaches it only with a lot of careful tuning effort. Hence, we advocate that the performance obtained by an optimizer is not only the best performance obtained when using that optimizer, but also has to account for the cost of tuning its hyperparameters to obtain that performance, thus being dichotomous. We term this concept tunability in this paper.
+
+Despite the importance of this concept, there is no standard way of measuring tunability. Works that propose optimization techniques show their performance on various tasks as depicted in Table 1. It is apparent that the experimental settings, as well as the network architectures tested, widely vary, hindering a fair comparison. The introduction of benchmarking suites like DEEPOBS (Schneider et al., 2019) have standardized the tested architectures, however, this does not fix the problem of selecting the hyperparameters themselves, and the effort expended in doing so. Previous studies treat tunability to be the best performance obtained on varying a hyperparameter (Schneider et al., 2019) or by measuring the improvement in performance by tuning a hyperparameter (Probst et al., 2019), but do not take any cognizance to the intermediate performance during the tuning process.
+
+Table 1: Experimental settings shown in the original papers of popular optimizers. The large differences in test problems and tuning methods make them difficult to compare. $\gamma$ denotes learning rate, $\mu$ denotes momentum, $\lambda$ is the weight decay coefficient.   
+
+<table><tr><td>Method</td><td>Datasets</td><td>Network architecture</td><td>Parameter tuning methods</td></tr><tr><td>SGD with momentum (Sutskever et al., 2013)</td><td>Artificial datasets MNIST</td><td>Fully-connected LSTM</td><td>μ = 0.9 for first 1000 updates then μ ∈ {0,0.9,0.98,0.995}. other schedules for μ are used &amp; log1o(γ)∈{-3,-4,-5,-6}</td></tr><tr><td>Adagrad (Duchi et al., 2011)</td><td>ImageNet ranking Reuter RCV1 MNIST KDD Census</td><td>Single layer Handcrafted features Histogram features</td><td>Perfomance on dev-set</td></tr><tr><td>Adam (Kingma &amp; Ba, 2015)</td><td>IMDb MNIST CIFAR10</td><td>Logistic regression Multi-layer perceptron Convolutional network</td><td>β1∈{0,0.9} β∈{0.99,0.999,0.9999} log10(γ)∈{-5,-4,-3,-2,-1}</td></tr><tr><td>AdamW (Loshchilov &amp; Hutter,2019)</td><td>CIFAR 10 ImageNet 32×32</td><td>ResNet CNN</td><td>log2(γ) ∈{-11,-10.-1,0} log2(λ)∈ log2(10-3)+{-5,-4,...,4}</td></tr></table>
+
+In this paper, we introduce a fair evaluation protocol for tunability based on automatic hyperparameter optimization, and simple evaluation measures that allow to compare the performance of optimizers under varying resource constraints. By evaluating on a wide range of 9 diverse tasks, we aim to contribute to the debate of adaptive vs. non-adaptive optimizers (Wilson et al., 2017; Shah et al., 2018; Chen & Gu, 2018) . To reach a fair comparison, we experiment with several SGD variants that are often needed to reach good performance. Although a well-tuned SGD variant is able to reach the top performance in some cases, our overall results clearly favor adaptive gradient methods. We therefore conclude that there is substantial value in adaptive gradient methods.
+
+# 2 MEASURING TUNABILITY
+
+Given the dichotomy of the problem of tunability, we argue that it needs to take into account
+
+1. how difficult it is to find a good hyperparameter configuration for the optimizer,   
+2. the absolute performance of the optimizer.
+
+To see why both are needed, consider Figure 1.a, which shows the performance in terms of loss of four different optimizers as a function of its only hyperparameter $\theta$ (by assumption). If we only consider requirement #1, optimizer C would be considered the best, since every hyperparameter value is the optimum. However, its absolute performance is poor, making it of low practical value. Moreover, due to the same shape, optimizers A and B would be considered equally good, although optimizer A clearly outperforms B. On the other hand, if we only consider requirement #2, optimizers B and D would be considered equally good, although optimizer D’s optimum is harder to find.
+
+As we show in Section 5, no existing definition of tunability takes both requirements into account. In the following, we present a formulation that does so.
+
+# 2.1 PRELIMINARIES: HYPERPARAMETER OPTIMIZATION
+
+We define hyperparameter optimization (HPO) (Feurer & Hutter, 2019) as follows:
+
+Definition. Let $\mathcal { M }$ be an optimization algorithm with $N$ hyperparameters $( \theta _ { 1 } , \ldots , \theta _ { N } ) \in \Theta$ . Let $a$ specific instantiation of $\mathcal { M }$ with $\pmb \theta \in \Theta$ be denoted by $\mathcal { M } _ { \theta }$ . Thus, given a dataset $D = D _ { t r a i n } \bigcup D _ { v a l }$ , the following objective is minimized
+
+$$
+\pmb { \theta } ^ { \star } = \arg \operatorname* { m i n } _ { \pmb { \theta } \in \Theta } \mathcal { L } ( \mathcal { M } _ { \pmb { \theta } } , D _ { v a l } )
+$$
+
+where $\mathcal { M } _ { \theta }$ is trained on $D _ { t r a i n }$ . In our work, we use $\mathcal { L }$ to be validation loss.
+
+We use $\mathcal { L } ( \pmb { \theta } )$ to refer to $\mathcal { L } ( \mathcal { M } _ { \theta } , D _ { v a l } )$ for brevity. In our experiments, we use the time-tested Random Search (Bergstra & Bengio, 2012) algorithm for HPO for simplicity.
+
+The ability to easily find good minima depends on the loss surface $\mathcal { L }$ itself. Thus, tunability is a characterization of the HPO’s loss function $\mathcal { L }$ . Here we present a quantification of this idea, which we illustrate with Figure 1.b.
+
+Let us assume that there are two optimizers E & F, both with hyperparameter $\theta$ , both of them used to minimize a function (e.g. train a neural network). Let the loss functions of HPO be $\mathcal { L } _ { E }$ and $\mathcal { L } _ { F }$ respectively. As the figure shows, the minimum of $\mathcal { L } _ { E }$ is lower than that of $\mathcal { L } _ { F }$ (denoted by $\theta _ { E } ^ { \star }$ and $\theta _ { F } ^ { \star } .$ ) i.e. $\mathcal { L } _ { E } ( \theta _ { E } ^ { \star } ) < \mathcal { L } _ { F } ( \theta _ { F } ^ { \star } )$ . However, the minimum of $\mathcal { L } _ { E }$ is much sharper than that of $\mathcal { L } _ { F }$ , and in most regions of the parameter space F performs much better than E. This makes it easier to find configurations that already perform well. This makes optimizer F an attractive option when we have no prior knowledge of the good parameter settings.
+
+![](images/e23b0ccbb293a18f6a1db6c084466c5253e59cc3b80bdd3822b44d9f98c145d2.jpg)  
+1.a: Illustration. It is important to consider both the absolute performance of optimizers as well as the tuning effort to get to good performances.
+
+![](images/1b5b7c856204f84cee6dd94985a20853400f67d375d9ac8122ea6d45cfa55388.jpg)  
+1.b: Illustration. While optimizer E can achieve the best performance after careful tuning, optimizer F is likely to provide better performance under a constrained HPO budget.
+
+The key-difference between the two interpretations is whether one prefers a ‘good enough’ performance through fewer hyperparameter configuration searches (in the case of optimizer F), or whether one is willing to spend computational time to get the best possible performance $\left( \theta _ { E } ^ { \star } \right)$ in the case of optimizer E). In this work, we search for the hyperparameter through an HPO like Random Search. Thus, the difference of the two interpretations of tunability lies whether one values results from late stages of the HPO process (i.e. optimizer $\mathrm { E }$ is preferable due to better optimum) more than results from early stages of the HPO process (i.e. optimizer F is preferable).
+
+Motivated by these observations, we propose the following metric for tunability.
+
+$\omega$ -tunability’s Definition. Let $( \mathbf { \boldsymbol { \theta } } _ { t } , \mathbf { \mathcal { L } } ( \mathbf { \boldsymbol { \theta } } _ { t } ) )$ be the incumbents (best performance attained till $t$ ) of the HPO algorithm at iteration $t$ and $T$ be the hyperparameter tuning budget. For $w _ { t } > 0 \forall t$ and $\textstyle \sum _ { t } w _ { t } < \infty$ , we define $\omega$ -tunability as
+
+$$
+\omega \ – t u n a b i l i t y = \sum _ { t = 1 } ^ { T } \omega _ { t } \mathcal { L } _ { t }
+$$
+
+i.e, $\omega$ -tunability is a weighted sum of the incumbents $\mathcal { L } ( \pmb { \theta } _ { t } )$ . In our experiments we use $\textstyle \sum _ { t } \omega _ { t } = 1$
+
+By appropriately choosing the weights $\left\{ \omega _ { t } \right\}$ , we can interpolate between our two notions of tunability. In the extreme case where we are only interested in the peak performance of the optimizer, we can set $\omega _ { T } = 1$ and set the other weights to zero. In the opposite extreme case where we are interested in the "one-shot tunability" of the optimizer, we can set $\omega _ { 1 } = 1$ . In general, we can answer the question of "How well does the optimizer perform with a budget of $K$ iterations?" by setting $\omega _ { i } = { \bf 1 } _ { \mathrm { i = K } }$ .
+
+While the above weighting scheme is intuitive, merely computing the performance after expending HPO budget of $K$ does not consider the performance obtained after the previous $K - 1$ iterations i.e. we would like to differentiate the cases where a requisite performance is attained by tuning an optimizer for $K$ iterations and another for $K _ { 1 }$ iterations, where $K _ { 1 } \gg K$ . Therefore, we employ three additional weighting schemes. By setting $\omega _ { i } \propto ( T - i )$ , our first one puts more emphasis on the earlier stages of the hyperparameter tuning process. We term this weighting scheme Cumulative Performance-Early $( C P E )$ . In contrast, the second weighting scheme, Cumulative Performance-Late $( C P L )$ puts more emphasis on late stages of tuning, and thus on obtaining a better performance at a higher tuning cost: $\omega _ { i } \propto i$ . As a intermediate of the two, we also report a uniform weighting Cumulative Performance-Uniform $( C P U ) : \omega _ { i } = 1 / T$ .
+
+# 3 OPTIMIZERS AND THEIR HYPERPARAMETERS
+
+# 3.1 PARAMETERS OF THE OPTIMIZERS
+
+To compare the tunability of adaptive gradient methods to non-adaptive methods, we choose the most commonly used optimizers from both the strata; SGD and SGD with momentum for non-adaptive methods, and Adagrad and Adam for adaptive gradient methods. Since adaptive gradient methods are said to work well with their default hyperparameter values already, we additionally employ a default version of Adam where we only tune the initial learning rate and set the other hyperparameters to the values recommended in the original paper (Kingma & Ba, 2015) (termed AdamLR). Such a scheme has been used by Schneider et al. too. A similar argument can be made for SGD with momentum (termed SGDM): thus we experiment with a fixed momentum value of 0.9 (termed SGDMC).
+
+In addition to standard parameters in all optimizers, we consider weight decay with SGD too. SGD with weight decay can be considered as an optimizer with two steps where the first step is to scale current weights with the decay value, followed by a normal descent step (Loshchilov & Hutter, 2019). Thus we devise two additional experiments for SGD with weight-decay where we tune weight-decay along with momentum (termed SGDMW), and one where we fix it to $1 0 ^ { - 5 }$ (termed $\mathbf { S G D M ^ { C } W } ^ { \dot { \mathbf { C } } } ,$ ) along with the momentum being fixed to 0.9, which is the value for weight decay we found to be consistently better through HPO. The full list of optimizers we consider is provided in Table 4
+
+Manually defining a specific number of epochs can be biased towards one optimizer, as one optimizer may reach good performance in the early epochs of a single HPO iteration, whereas another may reach higher peaks more slowly. In order to alleviate this, it would be possible to add the number of training epochs as an additional hyperparameter to be searched. Since this would incur even higher computational cost, we instead use a validation set performance as stopping criterion. Thus we stop training when the validation loss plateaus for more than 2 epochs or if the number of epochs exceeds the predetermined maximum number as set in DEEPOBS.
+
+# 3.2 CALIBRATION OF HYPERPARAMETER DISTRIBUTIONS
+
+As mentioned previously, we use Random Search for optimizing the hyperparameters, which requires distributions of random variables to sample from. Choosing poor distributions to sample from impacts the performance, and may break requisite properties (e.g. learning rate is non-negative). For some of the parameters listed in Table 2, obvious bounds exist due their mathematical properties, or have been prescribed by the optimizer designers themselves. For example, Kingma & Ba (2015) bound $\beta _ { 1 } , \beta _ { 2 }$ to $[ 0 , 1 )$ and specify that they are close to 1. In the absence of such prior knowledge, we devise a simple method to determine the priors.
+
+We train each task specified in the DEEPOBS with a large number of hyperparameter samplings and retain the hyperparameters which resulted in performance within $2 0 \%$ of the best performance obtained. For each of the hyperparameters in this set, we fit the distributions in the third column of Table 2 using maximum likelihood estimation. In doing so, we make a simplifying assumption that all the hyperparameters are independent of each other. We argue that these distributions are appropriate; the only condition on learning rate is non-negativity that is inherent to the log-normal distribution, momentum is non-negative with a usual upper bound of 1, $\beta \mathrm { { s } }$ in Adam have been prescribed to be less than 1 but close to it, $\epsilon$ is used to avoid divide-by-zero error and thus is a small positive value close to 0. We report the parameters of the distributions obtained after the fitting in Table 2. The calibration procedure’s performance is not included in the tunability computation.
+
+Table 2: Optimizers evaluated. For each hyperparameter, we calibrated a ‘sampling distribution’ to give good results across tasks (Section 3.2). $\boldsymbol { \bar { \mathcal { U } } } [ \boldsymbol { a } , \boldsymbol { b } ]$ is the continuous uniform distribution on $[ a , b ]$ . Log-uniform $( a , b )$ is a distribution whose logarithm is $\mathcal { U } [ a , b ]$ . Log-normal $( \mu , \sigma )$ is a distribution whose logarithm is normally distributed with mean $\mu$ and standard deviation $\sigma$ .   
+
+<table><tr><td>Optimizer</td><td>Tunable parameters</td><td>Sampling distribution</td></tr><tr><td rowspan="3">Stochastic Gradient Descent</td><td>Learning rate</td><td>Log-normal(-2.09,1.312)</td></tr><tr><td>Momentum</td><td>u[0,1]</td></tr><tr><td>Weight decay</td><td>Log-uniform(-5,-1)</td></tr><tr><td>Adagrad</td><td>Learning rate</td><td>Log-normal(-2.004,1.20)</td></tr><tr><td rowspan="3">Adam</td><td>Learning rate</td><td>Log-normal(-2.69,1.42)</td></tr><tr><td>β1,β</td><td>Log-uniform(-5, -1)</td></tr><tr><td>E</td><td>Log-uniform(-8,0)</td></tr></table>
+
+Table 3: Models and datasets used. We use the DeepOBS benchmark set (Schneider et al., 2019). Details are provided in Appendix A.   
+
+<table><tr><td>Architecture</td><td>Datasets</td></tr><tr><td>Convolutional net</td><td>FMNIST, CIFAR10/100</td></tr><tr><td>Variational autoencoder</td><td>FMNIST,I</td></tr><tr><td>Wide residual network</td><td>SVHN</td></tr><tr><td>CharacterRNN</td><td>Tolstoi&#x27;s War and Peace</td></tr><tr><td>Quadratic function</td><td>Artificial datatset</td></tr><tr><td>LSTM</td><td>IMDb</td></tr></table>
+
+Table 4: Optimizers and tunable parameters. $\gamma$ is learning rate, $\mu$ is momentum, $\lambda$ is the weight decay coefficient.   
+
+<table><tr><td>Optimizer</td><td>Tunable parameters</td></tr><tr><td>SGD</td><td>γ(μ=0,λ=0)</td></tr><tr><td>SGDM</td><td>Y,μ(入=0)</td></tr><tr><td>SGDMC SGDMCWC</td><td>γ (μ=0.9,λ=0) γ (μ=0.9,λ=10-5)</td></tr><tr><td>SGDMW</td><td>Y，μ,入</td></tr><tr><td>Adagrad</td><td>Y</td></tr><tr><td>AdamLR Adam</td><td>γ (β1=0.9,β2=0.999,∈=10-8) Y,β1,β2,E</td></tr></table>
+
+# 4 EXPERIMENTS AND RESULTS
+
+To assess the tunability of optimizers’ hyperparameters for the training of deep neural networks, we benchmark using the open-source suite DEEPOBS (Schneider et al., 2019). The architectures and datasets we experiment are given in Table 3. We refer the reader to Schneider et al. (2019) for specific details of the architectures. To obtain a better balance between vision and NLP applications, we added an LSTM network with the task of sentiment classification in the IMDB dataset (Maas et al., 2011), details for which are provided in Appendix A.
+
+# 4.1 HYPERPARAMETERS AND IMPLEMENTATION
+
+The performance of automatic hyperparameter search methods is dependent on its own hyperparameters, which play an important role in the outcome, e.g number of configurations to test. In our experiments, we evaluate 100 configurations with each of the hyperparameter optimization methods. As we use random search, we simulate multiple runs of these 100 configurations through shuffling. This gives us the variance of performance at each step.
+
+# 4.2 ANALYSIS OF TUNABILITY
+
+We analyze the tunability for the various weighting schemes proposed. For the weighting scheme $\omega _ { i } = { \bf 1 } _ { \mathrm { i = K } }$ , for increasing values of $K$ , we show the performance as well as its variance in Figure 3. For readability, we show only results for Adam, AdamLR, Adagrad and SGDMW, and the rest are given in Appendix C. It is quite apparent that in most of the tasks, a well tuned SGD with momentum and weight decay is as good as Adam (for large $K$ ). However, the gap in the performance is quite noticeable when AdamLR outperforms SGD in the VAE tasks and the IMDB task. In the case of image classification problems, SGD variants fare the best, as it has been reported before (Keskar & Socher, 2017). It is interesting to notice that for $K { = } 4$ , the decreasing order of variance is nearly always SGDMW, Adam, Adagrad, AdamLR (10 out of 11 cases), even if AdamLR marginally underperforms as it is in the case of Quadratic Deep. Given this formulation, we ask the following question: given an HPO budget of $K$ , what is the best choice for optimizer? We answer this in Appendix D.
+
+For the other weighting schemes, tunability scores are reported in Table 5. We see that there is no one optimizer that is best across three schemes, and tasks presented. A similar trend of SGD doing better than the adaptive gradient methods on image classification tasks is evident. Considering CPE, we observe that AdamLR performs the best in 6 out 9 tasks, where as the other three times $\mathrm { \Delta S G D M ^ { C } W ^ { C } }$ performs the best. The trend is not very obvious for CPU and CPL. In the case of CPU, AdamLR wins 5 out of 9 tasks, $\mathbf { S G D M ^ { C } W ^ { C } }$ wins twice, and SGDM wins once. For CPL, AdamLR wins 4 out of 9, and the $\mathbf { S G D M ^ { C } W ^ { C } }$ wins once, and SGDM and $\mathbf { S G D M ^ { C } }$ win twice each. Summarizing, if peak-performance or even evolving to better performance at a larger hyperparameter search cost, SGD variants are better 5 out 9 times. However, if a good performance is expected in the earlier iterations of hyperparameter search, AdamLR is very competitive. Also, the default parameters of $\beta _ { 1 } , \beta _ { 2 } , \epsilon$ of Adam optimizer result in quite good performance, to the point that Adam is rarely the better alternative over AdamLR. A known exception is training Inception networks (Abadi et al., 2015), where $\epsilon$ is recommended to be set to 0.1.
+
+For some of the cases, the tunablities reported are very similar for the AdamLR and SGD variants. However, tuning Adam is very different from tuning SGD from a wall-clock time measurement. For example, we find that for the case of CIFAR-10, AdamLR requires on average $39 \%$ fewer epochs to complete training than $\mathbf { S G D M ^ { C } }$ (the top perfomer); thus being that much faster than $\mathrm { S G D M ^ { C } }$ in wall-clock time. It can be argued that a more practical form of hyperparameter tuning budget is wall-clock time i.e. if a wall-clock time budget of $K$ minutes is given, how do our findings vary? In short, we find similar trends as we noticed before. We provide the details in Appendix E.
+
+# 4.3 SUMMARIZING ACROSS DATASETS
+
+To get a better understanding of an optimizer’s aggregate tunability across datasets compared to the rest, we compute summary statistics for an optimizer $o$ ’s performance after $k$ iterations in the following way:
+
+$$
+S ( o , k ) = \frac { 1 } { | \mathcal { P } | } \sum _ { p \in \mathcal { P } } \frac { o ( k , p ) } { \operatorname* { m a x } _ { o ^ { \prime } \in \mathcal { O } } o ^ { \prime } ( k , p ) } ,
+$$
+
+where $o ( k , p )$ denotes the performance of optimizer $o \in \mathcal { O }$ on test problem $p \in \mathcal P$ after $k$ iterations of the HPO process (i.e. $\omega$ -tunability with $\omega _ { i } = \mathbf { 1 } _ { \mathrm { i = k } }$ ). In other words, we compute the average relative performance of an optimizer to the best performance of any optimizer over all tasks.
+
+![](images/49a91c72fa4f42bd73f6a4d510b838b41da14b1747ddb982287a49add13f2d19.jpg)  
+Figure 2: Aggregated relative tunability of each optimizer across datasets
+
+The results are in Figure 2 and show that AdamLR performs very close to the best optimizer throughout the HPO process and is the best till about the $6 0 ^ { \mathrm { t h } }$ iteration. In early stages of HPO, the SGD variants perform $10 \mathrm { - } 2 0 \%$ worse than Adam, but improve as the HPO progresses.
+
+# 5 RELATED WORK
+
+There exist few works that have tried to define and investigate tunability formally. Assessing the impact of hyperparameter tuning for decision tree models, Mantovani et al. (2018) count the number of times the tuned hyperparameter values are (statistically significantly) better than the default values. Probst et al. (2019) define tunability of an ML algorithm as the performance difference between a reference configuration (e.g., the default hyperparameters of the algorithm) and the best possible configuration on each dataset. This metric is comparable across ML algorithms, but it disregards entirely the absolute performance of ML algorithms. Schneider et al. (2019) recently released a benchmark for optimizers that evaluates their peak performance and speed. Tunability is assessed as the sensitivity of the performance to changes of the learning rate. In all three aforementioned studies, the definitions of tunability would fail to identify the superiority of optimizer A over optimizer B in Figure 1.a.
+
+The study by Wilson et al. (2017) finds SGD-based methods as easy to tune as adaptive gradient methods. However, their study lacks a clear definition of tunability and tunes the algorithms on manually selected, dataset dependent grid values. The study by Shah et al. (2018) applies a similar methodology and comes to similar conclusions regarding tunability. Since both studies only consider the best parameter configuration, their approach would be unable to identify the better optimizer among B and D in Figure 1.a. In contrast, the methodology in our study is able to distinguish all the cases depicted in Figure 1.a.
+
+Table 5: Performance of various experiments.   
+
+<table><tr><td>Optimizer</td><td>CPE</td><td>CPU</td><td>CPL</td></tr><tr><td>Adagrad</td><td>91.3</td><td>91.4</td><td>91.6</td></tr><tr><td>Adam</td><td>91.3</td><td>91.5</td><td>91.8</td></tr><tr><td>AdamLR</td><td>91.3</td><td>91.6</td><td>91.9</td></tr><tr><td>SGD</td><td>90.4</td><td>90.8</td><td>91.2</td></tr><tr><td>SGDM</td><td>90.5</td><td>90.9</td><td>91.3</td></tr><tr><td>SGDMC</td><td>90.7</td><td>90.9</td><td>91.1</td></tr><tr><td>SGDMCWC</td><td>90.7</td><td>90.9</td><td>91.1</td></tr><tr><td>SGDMW</td><td>90.4</td><td>90.8</td><td>91.3</td></tr></table>
+
+5.a: FMNIST 2C2D. Higher is better
+
+<table><tr><td>Optimizer</td><td>CPE</td><td>CPU</td><td>CPL</td></tr><tr><td>Adagrad</td><td>76.4</td><td>77.1</td><td>77.9</td></tr><tr><td>Adam</td><td>77.2</td><td>78.4</td><td>79.5</td></tr><tr><td>AdamLR</td><td>78.8</td><td>79.4</td><td>80.0</td></tr><tr><td>SGD</td><td>77.0</td><td>77.8</td><td>78.6</td></tr><tr><td>SGDM</td><td>77.8</td><td>78.6</td><td>79.5</td></tr><tr><td>SGDMC</td><td>78.6</td><td>79.4</td><td>80.1</td></tr><tr><td>SGDMCWC</td><td>81.1</td><td>81.6</td><td>82.0</td></tr><tr><td>SGDMW</td><td>79.7</td><td>80.4</td><td>81.2</td></tr></table>
+
+5.b: CIFAR 10. Higher is better
+
+<table><tr><td>Optimizer</td><td>CPE</td><td>CPU</td><td>CPL</td></tr><tr><td>Adagrad</td><td>30.4</td><td>31.8</td><td>33.1</td></tr><tr><td>Adam</td><td>39.4</td><td>42.2</td><td>45.1</td></tr><tr><td>AdamLR</td><td>42.2</td><td>43.0</td><td>43.8</td></tr><tr><td>SGD</td><td>31.8</td><td>34.2</td><td>36.6</td></tr><tr><td>SGDM</td><td>40.6</td><td>43.3</td><td>46.0</td></tr><tr><td>SGDMC</td><td>42.1</td><td>43.3</td><td>44.5</td></tr><tr><td>SGDMCWC</td><td>39.2</td><td>40.3</td><td>41.5</td></tr><tr><td>SGDMW</td><td>33.5</td><td>37.2</td><td>41.0</td></tr></table>
+
+5.c: CIFAR 100. Higher the better
+
+<table><tr><td>Optimizer</td><td>CPE</td><td>CPU</td><td>CPL</td></tr><tr><td>Adagrad</td><td>84.3</td><td>84.8</td><td>85.3</td></tr><tr><td>Adam</td><td>83.6</td><td>84.5</td><td>85.5</td></tr><tr><td>AdamLR</td><td>85.8</td><td>86.0</td><td>86.3</td></tr><tr><td>SGD</td><td>68.1</td><td>69.3</td><td>70.5</td></tr><tr><td>SGDM</td><td>74.3</td><td>75.9</td><td>77.5</td></tr><tr><td>SGDMC</td><td>79.3</td><td>80.1</td><td>81.0</td></tr><tr><td>SGDMCWC</td><td>78.8</td><td>79.4</td><td>80.0</td></tr><tr><td>SGDMW</td><td>75.7</td><td>77.1</td><td>78.6</td></tr></table>
+
+5.d: IMDB. Higher is better
+
+<table><tr><td>Optimizer</td><td>CPE</td><td>CPU</td><td>CPL</td></tr><tr><td>Adagrad</td><td>94.8</td><td>94.9</td><td>95.0</td></tr><tr><td>Adam</td><td>94.5</td><td>94.8</td><td>95.2</td></tr><tr><td>AdamLR</td><td>95.1</td><td>95.3</td><td>95.4</td></tr><tr><td>SGD</td><td>94.6</td><td>94.9</td><td>95.2</td></tr><tr><td>SGDM</td><td>94.8</td><td>95.2</td><td>95.6</td></tr><tr><td>SGDMC</td><td>94.9</td><td>95.1</td><td>95.3</td></tr><tr><td>SGDMCWC</td><td>95.2</td><td>95.4</td><td>95.5</td></tr><tr><td>SGDMW</td><td>95.0</td><td>95.2</td><td>95.3</td></tr></table>
+
+5.e: WRN-16(4). Higher is better
+
+<table><tr><td>Optimizer</td><td>CPE</td><td>CPU</td><td>CPL</td></tr><tr><td>Adagrad</td><td>55.6</td><td>56.2</td><td>56.7</td></tr><tr><td>Adam</td><td>54.4</td><td>55.7</td><td>57.0</td></tr><tr><td>AdamLR</td><td>56.9</td><td>57.2</td><td>57.5</td></tr><tr><td>SGD</td><td>40.3</td><td>42.5</td><td>44.6</td></tr><tr><td>SGDM</td><td>51.4</td><td>54.0</td><td>56.5</td></tr><tr><td>SGDMC</td><td>55.6</td><td>57.0</td><td>58.3</td></tr><tr><td>SGDMCWC</td><td>54.2</td><td>55.6</td><td>57.0</td></tr><tr><td>SGDMW</td><td>45.1</td><td>48.2</td><td>51.2</td></tr></table>
+
+5.f: Char-RNN. Higher is better
+
+<table><tr><td>Optimizer</td><td>CPE</td><td>CPU</td><td>CPL</td></tr><tr><td>Adagrad</td><td>30.3</td><td>29.4</td><td>28.4</td></tr><tr><td>Adam</td><td>33.2</td><td>31.2</td><td>29.1</td></tr><tr><td>AdamLR</td><td>29.2</td><td>28.6</td><td>27.9</td></tr><tr><td>SGD</td><td>53.3</td><td>53.1</td><td>52.9</td></tr><tr><td>SGDM</td><td>36.0</td><td>32.9</td><td>29.9</td></tr><tr><td>SGDMC</td><td>54.1</td><td>53.5</td><td>53.0</td></tr><tr><td>SGDMCWC</td><td>54.0</td><td>53.5</td><td>53.0</td></tr><tr><td>SGDMW</td><td>34.6</td><td>32.2</td><td>29.8</td></tr></table>
+
+<table><tr><td>Optimizer</td><td>CPE</td><td>CPU</td><td>CPL</td></tr><tr><td>Adagrad</td><td>25.5</td><td>24.7</td><td>24.0</td></tr><tr><td>Adam</td><td>26.0</td><td>24.8</td><td>23.7</td></tr><tr><td>AdamLR</td><td>24.6</td><td>24.0</td><td>23.5</td></tr><tr><td>SGD</td><td>26.2</td><td>25.5</td><td>24.8</td></tr><tr><td>SGDM</td><td>26.2</td><td>25.4</td><td>24.6</td></tr><tr><td>SGDMC</td><td>28.6</td><td>26.7</td><td>24.9</td></tr><tr><td>SGDMCWC</td><td>27.9</td><td>26.4</td><td>24.8</td></tr><tr><td></td><td></td><td></td><td></td></tr><tr><td>SGDMW</td><td>26.5</td><td>25.7</td><td>24.8</td></tr></table>
+
+5.g: FMNIST-VAE. Lower is better. 5.h: MNIST-VAE. Lower is better
+
+<table><tr><td>Optimizer</td><td>CPE</td><td>CPU</td><td>CPL</td></tr><tr><td>Adagrad</td><td>91.5</td><td>89.6</td><td>87.6</td></tr><tr><td>Adam</td><td>94.8</td><td>92.1</td><td>89.4</td></tr><tr><td>AdamLR</td><td>91.2</td><td>89.5</td><td>87.7</td></tr><tr><td>SGD</td><td>90.5</td><td>89.6</td><td>88.7</td></tr><tr><td>SGDM</td><td>89.5</td><td>88.7</td><td>87.9</td></tr><tr><td>SGDMC</td><td>89.6</td><td>88.6</td><td>87.5</td></tr><tr><td>SGDMCWC</td><td>88.6</td><td>88.4</td><td>88.1</td></tr><tr><td>SGDMW</td><td>89.3</td><td>88.9</td><td>88.4</td></tr></table>
+
+5.i: Quadratic deep. Lower is better
+
+In a concurrent study, Choi et al. (2019) show that there exist a hierarchy among optimizers that such some can be viewed as specific cases of others e.g. SGDM is shown to be a special case of Adam as its $\epsilon \to \infty$ , and thus Adam should never underperform SGDM with appropriate hyperparameter search). Like in our study, they suggest that the performance comparison of optimizers strongly depends on the hyperparameter tuning protocol. They also argue that the search space needs to be chosen optimizer specific. However, their focus is on the best possible performance achievable by an optimizer and does not take into account the tuning process. Moreover, while the authors claim their search protocol to be relevant for practitioners, the search spaces are manually chosen per dataset, constituting a significant difference to the AutoML scenario considered in our paper.
+
+Tunability is related to measuring hyperparameter importance (Hutter et al., 2013), where van Rijn & Hutter (2018) have recently shown that learning the priors for hyperparameter distributions can yield to better HPO performance, akin to the calibration phase in our study.
+
+There has been recent interest in building optimizers termed the APROX family (Asi & Duchi, 2019a;b) that are provably robust to hyperparameter choices. Asi & Duchi experimentally find that, training a Residual network (He et al., 2016) on CIFAR-10, SGD converges only for a small range of initial learning rate choices, whereas Adam exhibits better robustness to learning rate choices. This is inline with our findings of tunability.
+
+# 6 CONCLUSION
+
+Our work proposes a new notion of tunability for optimizers that takes into account the tuning efforts of an HPO. The results of our experiments support the hypothesis that adaptive gradient methods are easier to tune than non-adaptive methods: In a setting with low budget for hyperparameter tuning, tuning only Adam optimizer’s learning rate is likely to be a very good choice; it doesn’t guarantee the best possible performance, but it is evidently the easiest to find well-performing hyperparameter configurations for. While SGD yields the best performance in some cases, its best configuration is tedious to find, and Adam often performs close to it. We, thus, state that the substantial value of the adaptive gradient methods, specifically Adam, is its amenability to hyperparameter search. This is in contrast to the findings of Wilson et al. (2017) who observe no advantage in tunabilty for adaptive gradient methods, and thus deem them to be of ‘marginal value’. Unlike them, we base our experiments on a standard hyperparameter optimization method that allows for an arguably fairer comparison.
+
+![](images/a6a328ac8956d13a356ce3cd78118cadaef5aaeea2be8387efb7945b6d603628.jpg)  
+3.a: CIFAR 10   
+3.c: SVHN WRN-16-4
+
+![](images/37fa782ff72d6c3cf69d86b7bd1bf2925155a46897c634641a8aafccf461ecb4.jpg)  
+3.b: CIFAR 100   
+3.d: IMDb LSTM
+
+![](images/e59c891fc2344e65b1e84273272d32d8febae7cc9a8d8a365967a1a77934fa9a.jpg)  
+3.e: FMNIST 2C2D CNN
+
+![](images/bb206c4e3b713dfa1b45b309a8f55d8dcbfc4dd9ea7cd3c6a4aac0182bda7c7d.jpg)  
+3.f: Tolstoi Char-RNN
+
+![](images/6bdf6b9d68c3d0c673e056db52c9ba789a12343641b39d2f56bfc440064906ac.jpg)  
+3.g: MNIST VAE
+
+![](images/fa18ce6d21356460daa8eb8cc9e764f75e8757afc08162235afa854744667933.jpg)  
+3.h: F-MNIST VAE
+
+![](images/a078543749ba6f7edf8a8a44d7004986e18f4c4dea570d019b6e6567ab23eee0.jpg)  
+3.i: Quadratic Deep
+
+![](images/05eab81f16ad917d949b166f6ff68db46a6643578bfd7be2228473acb6ff3bf1.jpg)
+
+![](images/72c08104c5d2ffc1ab91f210834a909ccc4020c306e77796c46c8c5d68c88a97.jpg)  
+Figure 3: $\omega$ -tunability with $\omega _ { i } = { \bf 1 } _ { \mathrm { i = K } }$ for various experiments. We plot the on the $\mathbf { X }$ -axis the number of the hyperparameter configuration searches, on the y-axis the appropriate performance on a log scale. Figures a-f: higher is better and g-i: lower is better.
+
+Our study is certainly not exhaustive: We do not study the effect of the inclusion of a learning rate schedule, or using a different HPO algorithm on the results. However, their inclusion would result in a large increase the number of experiments, and constitutes our future work.
+
+We hope that this paper encourages other researchers to conduct future studies on the performance of optimizers from a more holistic perspective, where the cost of the hyperparameter search is included.
+
+# REFERENCES
+
+Martín Abadi, Ashish Agarwal, Paul Barham, Eugene Brevdo, Zhifeng Chen, Craig Citro, Greg S. Corrado, Andy Davis, Jeffrey Dean, Matthieu Devin, Sanjay Ghemawat, Ian Goodfellow, Andrew Harp, Geoffrey Irving, Michael Isard, Yangqing Jia, Rafal Jozefowicz, Lukasz Kaiser, Manjunath Kudlur, Josh Levenberg, Dandelion Mané, Rajat Monga, Sherry Moore, Derek Murray, Chris Olah, Mike Schuster, Jonathon Shlens, Benoit Steiner, Ilya Sutskever, Kunal Talwar, Paul Tucker, Vincent Vanhoucke, Vijay Vasudevan, Fernanda Viégas, Oriol Vinyals, Pete Warden, Martin Wattenberg, Martin Wicke, Yuan Yu, and Xiaoqiang Zheng. TensorFlow: Large-scale machine learning on heterogeneous systems, 2015. URL https://www.tensorflow.org/. Software available from tensorflow.org.
+
+Hilal Asi and John C. Duchi. The importance of better models in stochastic optimization. Proceedings of the National Academy of Sciences, 2019a. ISSN 0027-8424. doi: 10.1073/pnas.1908018116. URL https://www.pnas.org/content/early/2019/10/29/1908018116.
+
+Hilal Asi and John C Duchi. Stochastic (approximate) proximal point methods: Convergence, optimality, and adaptivity. SIAM Journal on Optimization, 29(3):2257–2290, 2019b.
+
+James Bergstra and Yoshua Bengio. Random search for hyper-parameter optimization. Journal of Machine Learning Research, 13(Feb):281–305, 2012.
+
+Jinghui Chen and Quanquan Gu. Closing the generalization gap of adaptive gradient methods in training deep neural networks. CoRR, abs/1806.06763, 2018. URL http://arxiv.org/ abs/1806.06763.
+
+Dami Choi, Christopher J Shallue, Zachary Nado, Jaehoon Lee, Chris J Maddison, and George E Dahl. On empirical comparisons of optimizers for deep learning. arXiv preprint arXiv:1910.05446, 2019.
+
+John Duchi, Elad Hazan, and Yoram Singer. Adaptive subgradient methods for online learning and stochastic optimization. Journal of Machine Learning Research, 12(Jul):2121–2159, 2011.
+
+Katharina Eggensperger, Marius Lindauer, and Frank Hutter. Pitfalls and best practices in algorithm configuration. Journal of Artificial Intelligence Research, 64:861–893, 2019.
+
+Matthias Feurer and Frank Hutter. Hyperparameter Optimization, pp. 3–33. Springer International Publishing, Cham, 2019. ISBN 978-3-030-05318-5. doi: 10.1007/978-3-030-05318-5_1. URL https://doi.org/10.1007/978-3-030-05318-5_1.
+
+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, pp. 770–778, 2016.
+
+Peter Henderson, Riashat Islam, Philip Bachman, Joelle Pineau, Doina Precup, and David Meger. Deep reinforcement learning that matters. In Thirty-Second AAAI Conference on Artificial Intelligence, 2018.
+
+Frank Hutter, Holger H Hoos, and Kevin Leyton-Brown. Identifying key algorithm parameters and instance features using forward selection. In International Conference on Learning and Intelligent Optimization, pp. 364–381. Springer, 2013.
+
+Frank Hutter, Lars Kotthoff, and Joaquin Vanschoren. Automated machine learning-methods, systems, challenges, 2019.
+
+Nitish Shirish Keskar and Richard Socher. Improving generalization performance by switching from adam to sgd. arXiv preprint arXiv:1712.07628, 2017.
+
+Diederik Kingma and Jimmy Ba. Adam: A method for stochastic optimization. In International Conference on Learning Representations, 2015.
+
+Ilya Loshchilov and Frank Hutter. Decoupled weight decay regularization. In International Conference on Learning Representations, 2019. URL https://openreview.net/forum?id= Bkg6RiCqY7.
+
+Mario Lucic, Karol Kurach, Marcin Michalski, Sylvain Gelly, and Olivier Bousquet. Are gans created equal? a large-scale study. In Advances in neural information processing systems, pp. 700–709, 2018.
+
+Andrew L. Maas, Raymond E. Daly, Peter T. Pham, Dan Huang, Andrew Y. Ng, and Christopher Potts. Learning word vectors for sentiment analysis. In Proceedings of the 49th Annual Meeting of the Association for Computational Linguistics: Human Language Technologies, pp. 142–150, Portland, Oregon, USA, June 2011. Association for Computational Linguistics. URL http: //www.aclweb.org/anthology/P11-1015.
+
+Rafael Gomes Mantovani, Tomáš Horváth, Ricardo Cerri, Sylvio Barbon Junior, Joaquin Vanschoren, André Carlos Ponce de de Carvalho, and Leon Ferreira. An empirical study on hyperparameter tuning of decision trees. arXiv preprint arXiv:1812.02207, 2018.
+
+Gábor Melis, Chris Dyer, and Phil Blunsom. On the state of the art of evaluation in neural language models. In International Conference on Learning Representations, 2018. URL https:// openreview.net/forum?id $=$ ByJHuTgA-.
+
+Philipp Probst, Anne-Laure Boulesteix, and Bernd Bischl. Tunability: Importance of hyperparameters of machine learning algorithms. Journal of Machine Learning Research, 20(53):1–32, 2019. URL http://jmlr.org/papers/v20/18-444.html.
+
+Herbert Robbins and Sutton Monro. A stochastic approximation method. The annals of mathematical statistics, pp. 400–407, 1951.
+
+Frank Schneider, Lukas Balles, and Philipp Hennig. DeepOBS: A deep learning optimizer benchmark suite. In International Conference on Learning Representations, 2019. URL https://openreview.net/forum?id ${ \underline { { \underline { { \mathbf { \Pi } } } } } } =$ rJg6ssC5Y7.
+
+D. Sculley, Jasper Snoek, Alexander B. Wiltschko, and Ali Rahimi. Winner’s curse? on pace, progress, and empirical rigor. In 6th International Conference on Learning Representations, ICLR 2018, Vancouver, BC, Canada, April 30 - May 3, 2018, Workshop Track Proceedings, 2018. URL https://openreview.net/forum?id ${ \underline { { \underline { { \mathbf { \Pi } } } } } } =$ rJWF0Fywf.
+
+Vatsal Shah, Anastasios Kyrillidis, and Sujay Sanghavi. Minimum norm solutions do not always generalize well for over-parameterized problems. arXiv preprint arXiv:1811.07055, 2018.
+
+Ilya Sutskever, James Martens, George Dahl, and Geoffrey Hinton. On the importance of initialization and momentum in deep learning. In Sanjoy Dasgupta and David McAllester (eds.), Proceedings of the 30th International Conference on Machine Learning, volume 28 of Proceedings of Machine Learning Research, pp. 1139–1147, Atlanta, Georgia, USA, 17–19 Jun 2013. PMLR. URL http://proceedings.mlr.press/v28/sutskever13.html.
+
+T. Tieleman and G. Hinton. Lecture 6.5—RmsProp: Divide the gradient by a running average of its recent magnitude. COURSERA: Neural Networks for Machine Learning, 2012.
+
+Jan N van Rijn and Frank Hutter. Hyperparameter importance across datasets. In Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pp. 2367–2376. ACM, 2018.
+
+Ashia C Wilson, Rebecca Roelofs, Mitchell Stern, Nati Srebro, and Benjamin Recht. The marginal value of adaptive gradient methods in machine learning. In Advances in Neural Information Processing Systems, pp. 4148–4158, 2017.
+
+# A ARCHITECTURES OF THE MODELS USED IN EXPERIMENTS
+
+Along with the architectures examined by Schneider et al. (2019), we experiment with an additional network and dataset. We included an additional network into our experimental setup, as DEEPOBS does not contain an word level LSTM model. Our model uses a 32-dimensional word embedding table and a single layer LSTM with memory cell size 128, the exact architecture is given in Table 6. We experiment with the IMDB sentiment classification dataset (Maas et al., 2011). The dataset contains 50, 000 movie reviews collected from movie rating website IMDB. The training set has 25, 000 reviews, each labeled as positive or negative. The rest 25, 000 form the test set. We split $2 0 \%$ of the training set to use as the development set. We refer the readers to DEEPOBS (Schneider et al., 2019) for the exact details of the other architectures used in this work.
+
+Table 6: Architecture of the LSTM network used for IMDb experiments   
+
+<table><tr><td>Layer name</td><td>Description</td></tr><tr><td>Emb</td><td>Embedding Layer Vocabulary of 10000 [Embedding dimension: 32]</td></tr><tr><td>LSTM_1</td><td>LSTM Input size: 32 [Hidden dimension:128]</td></tr><tr><td>FC Layer</td><td>Linear(128 → 2)</td></tr><tr><td>Classifier</td><td>Softmax(2)</td></tr></table>
+
+# B $\alpha$ - TUNABILITY
+
+We provide additional methods to analyze tunability here. Let $p ( t )$ denote the best performance observed after using budget $t$ of hyperparameter optimization algorithm. We call an optimizer $\alpha$ -tunable $( \alpha \in [ 0 , 1 ] )$ at $t$ if $p ( t ) \geq \alpha \cdot p ( T )$ . Thus $\alpha$ −tunability is the ratio of number of times the neural network needs to be retrained with optimizer’s hyperparameters being provided by an automatic method, to the total budget $T$ (maximum number of configurations tested).
+
+For each optimizer, we define its $\alpha$ -tunability $\zeta ( \alpha ) = \textstyle { \frac { t } { T } }$ for $\alpha \in \{ 0 . 9 , 0 . 9 5 , 0 . 9 9 \}$ . This metric provides an intuitive and simple quantification of how easy it is to tune an optimizer to reach requisite performance. We extend $\alpha$ –tunability to indicate the sharpness of the minima by computing the difference $\Delta = \zeta ( \alpha _ { 1 } ) - \zeta ( \alpha _ { 2 } )$ where $\alpha _ { 1 } > \alpha _ { 2 }$ and term it Sharpness. In our experiments, we choose $\alpha _ { 1 } = 0 . 9 9$ and $\alpha _ { 2 } = 0 . 9$ . Sharpness $( \Delta )$ is the relative time taken by the HPO to improve from $\alpha _ { 2 }$ to $\alpha _ { 1 }$ and thus quantifies the flatness of the minima in the space of hyperparameters. If the minima is sharper, then we expect random-search also takes a longer time to find it, thus the time required to go from $\alpha _ { 1 }$ and $\alpha _ { 2 }$ is higher. We provide Sharpness for our optimizers in table:7.
+
+Table 7: Sharpness for various optimizers examined.   
+
+<table><tr><td></td><td>MNIST VAE</td><td>FMNIST2C2D</td><td>CIFAR100</td><td>CIFAR10</td><td>SVHN WRN</td><td>IMDBLSTM</td><td>FMNIST VAE</td><td>Quadratic Deep</td><td>Char RNN</td></tr><tr><td>Adagrad</td><td>92.0</td><td>99.0</td><td>63.0</td><td>95.0</td><td>10.0</td><td>97.0</td><td>91.0</td><td>66.0</td><td>95.0</td></tr><tr><td>Adam</td><td>80.0</td><td>98.0</td><td>40.0</td><td>91.0</td><td>71.0</td><td>93.0</td><td>90.0</td><td>75.0</td><td>87.0</td></tr><tr><td>Adam LR</td><td>83.0</td><td>96.0</td><td>71.0</td><td>94.0</td><td>98.0</td><td>70.0</td><td>95.0</td><td>93.0</td><td>97.0</td></tr><tr><td>SGD</td><td>98.0</td><td>95.0</td><td>35.0</td><td>93.0</td><td>98.0</td><td>81.0</td><td>94.0</td><td>6.0</td><td>47.0</td></tr><tr><td>SGDM</td><td>58.0</td><td>97.0</td><td>50.0</td><td>91.0</td><td>59.0</td><td>72.0</td><td>90.0</td><td>30.0</td><td>59.0</td></tr><tr><td>SGDMC</td><td>95.0</td><td>83.0</td><td>82.0</td><td>94.0</td><td>52.0</td><td>88.0</td><td>75.0</td><td>95.0</td><td>87.0</td></tr><tr><td>SGDMCWC</td><td>94.0</td><td>45.0</td><td>78.0</td><td>95.0</td><td>98.0</td><td>68.0</td><td>88.0</td><td>16.0</td><td>85.0</td></tr><tr><td>SGDMW</td><td>65.0</td><td>97.0</td><td>23.0</td><td>94.0</td><td>36.0</td><td>86.0</td><td>91.0</td><td>14.0</td><td>32.0</td></tr></table>
+
+The above definition is not without faults. An optimizer’s $\alpha$ -tunability depends only on how fast it can get close to its own best performance, a pitfall it shares with Probst et al. (2019). That is, an optimizer that peaks at the performance of a random classifier may be considered well-tunable because it reaches its peak performance in the first iteration. It is apparent from tables 7 and 4 that the top performance does not imply lower sharpness. Take the case of IMDB Bi-LSTM, the lowest sharpness is for $\mathrm { S G D M ^ { C } W ^ { C } }$ , while the best performance is attained by AdamLR, implying that $\mathrm { S G D M ^ { C } W ^ { C } }$ settled to a minima faster which isn’t necessarily better than the one AdamLR found. In other terms, the flatness of the minima does not indicate how deep it is.
+
+# C PERFORMANCE ANALYSIS
+
+We show the full performance plots of all variants of SGD experimented with, in figures 5, 6, 7.
+
+# D HOW LIKELY ARE WE TO FIND GOOD CONFIGURATIONS?
+
+A natural question that arises is: given a budget $K$ , what is the best optimizer one can pick? In other words, for a given budget what is probability of each optimizer finding the best configuration? We answer this with a simple procedure. We repeat the runs of HPO for a budget $K$ , and collect the optimizer that gave the best result in each of those runs. Using the classical definition of probability, we compute the required quantity. We plot the computed probability in Figure 8. It is very evident for nearly all budgets, AdamLR is always the best option for 4 of the problems. SGD variants emerge to be better options for CIFAR-100 and Char-RNN at later stages of HPO. For some of the problems like VAEs, LSTM, it is very obvious that AdamLR is nearly always the best choice. Thus further strengthens our hypothesis that adaptive gradient methods are more tunable, especially in constrained HPO budget scenarios.
+
+# E TUNABILITY BY COMPUTATION BUDGET
+
+In our experiments so far, we defined tunability in terms of number of hyperparameter configurations. However, due to varying convergence speeds, different optimizers require varying amounts of time/epochs per configuration. We choose to work with number of epochs per configuration, as it is a hardware agnostic measure, but still indicates the relative time required. To incorporate epochs into our definition of tunability, we conduct the following analysis: For each dataset, we consider minimum total epochs for running all 100 trials across all optimizers, and consider it as the (virtual) maximum epoch budget $e _ { \mathrm { m a x } }$ , i.e., we disregard all trials after this point. We divide this maximum into $K = 1 0 0$ intervals $\begin{array} { r } { I _ { i } = \frac { e _ { \mathrm { m a x } } \cdot i } { K } , 1 \le i \le K } \end{array}$ . We modify the definition of $\omega$ -tunability from Section 2.2 as follows:
+
+$\omega ^ { e p o c h }$ -tunability’s Definition. Let $( \mathbf { \boldsymbol { \theta } } _ { t } , \mathbf { \mathcal { L } } ( \mathbf { \boldsymbol { \theta } } _ { t } ) )$ be the incumbents (best performance attained till $t$ ) of the HPO algorithm at iteration $t$ , $e _ { t }$ be the total number of epochs required until iteration $t$ has finished. We define $\tilde { \mathcal { L } } _ { i } = \operatorname* { m a x } _ { e _ { t } \leq I _ { i } } \mathcal { L } _ { t }$ as the maximum performance among all configurations that have finished before interval $I _ { t }$ , where $\mathcal { L } _ { 0 } = e _ { 0 } = 0 .$ . For $w _ { i } > 0 \forall t$ and $\textstyle \sum _ { t } w _ { i } < \infty$ , we define $\omega ^ { e p o c h }$ -tunability as
+
+$$
+\omega ^ { e p o c h } \ – t u n a b i l i t y = \sum _ { i = 1 } ^ { K } \omega _ { i } \tilde { \mathcal { L } } _ { i }
+$$
+
+Please note that due to the case where no trial has finished before the first interval has concluded, we assign a performance of 0 for that task to that interval (bin). The above definition does not lend itself to VAE tasks, as an appropriate value there is $\infty$ . We, therefore, report the results for all classification problems in Table 8, where we use the same weighting schemes (CPE, CPU, and CPL) as before. To better understand the results, we also report the average number of epochs each configuration takes on average. Comparing the relative performances of optimizers to the results from Table 5, we can observe that considering $\omega ^ { e p o c h }$ yields to the same conclusions as before, and even amplifies Adam’s strengths: The performance gap to SGD variants widens in the cases where Adam(LR) was already better (FMNIST, IMDB, Char-RNN), and narrows considerably in the cases where an SGD variant was previously better (CIFAR-10, CIFAR-100, WRN-16). On CIFAR-100 and WRN-16, this even results in Adam outperforming the SGD variants slightly. Considering the average number of epochs, the results can easily be explained by the fact that the adaptive gradient methods tend to take less time to converge.
+
+Table 8: $\omega ^ { e p o c h }$ -tunability performance of optimizers on the classification tasks for CPE, CPU, and CPL weighting schemes. We additionally provide the average number of epochs required by each optimizer for a single configuration.   
+
+<table><tr><td>Optimizer</td><td>CPE</td><td>CPU</td><td>CPL</td><td>Epochs</td></tr><tr><td>Adagrad</td><td>89.2</td><td>90.3</td><td>91.4</td><td>33.0</td></tr><tr><td>Adam</td><td>90.2</td><td>91.0</td><td>91.8</td><td>24.1</td></tr><tr><td>AdamLR</td><td>90.4</td><td>91.1</td><td>91.9</td><td>19.5</td></tr><tr><td>SGD</td><td>87.4</td><td>89.2</td><td>90.9</td><td>34.5</td></tr><tr><td>SGDM</td><td>88.1</td><td>89.6</td><td>91.1</td><td>33.6</td></tr><tr><td>SGDMC</td><td>88.6</td><td>89.8</td><td>91.0</td><td>28.2</td></tr><tr><td>SGDMCWC</td><td>89.1</td><td>90.1</td><td>91.1</td><td>27.4</td></tr><tr><td>SGDMW</td><td>88.0</td><td>89.5</td><td>91.0</td><td>32.4</td></tr></table>
+
+<table><tr><td>Optimizer</td><td>CPE</td><td>CPU</td><td>CPL</td><td>Epochs</td></tr><tr><td>Adagrad</td><td>30.1</td><td>31.6</td><td>33.1</td><td>23.7</td></tr><tr><td>Adam</td><td>36.0</td><td>39.4</td><td>42.8</td><td>36.8</td></tr><tr><td>AdamLR</td><td>41.8</td><td>42.8</td><td>43.8</td><td>24.6</td></tr><tr><td>SGD</td><td>23.3</td><td>26.6</td><td>29.9</td><td>91.8</td></tr><tr><td>SGDM</td><td>30.5</td><td>34.7</td><td>39.0</td><td>80.6</td></tr><tr><td>SGDMC</td><td>36.9</td><td>39.8</td><td>42.7</td><td>68.7</td></tr><tr><td>SGDMCWC</td><td>34.1</td><td>36.8</td><td>39.4</td><td>71.7</td></tr><tr><td>SGDMW</td><td>21.5</td><td>25.6</td><td>29.7</td><td>102.3</td></tr></table>
+
+8.c: CIFAR 100. Higher the better
+
+8.a: FMNIST 2C2D. Higher is better   
+8.b: CIFAR 10. Higher is better   
+
+<table><tr><td>Optimizer</td><td>CPE</td><td>CPU</td><td>CPL</td><td>Epochs</td></tr><tr><td>Adagrad</td><td>74.2</td><td>75.9</td><td>77.5</td><td>36.9</td></tr><tr><td>Adam</td><td>75.6</td><td>77.5</td><td>79.3</td><td>27.7</td></tr><tr><td>AdamLR</td><td>78.2</td><td>79.1</td><td>80.0</td><td>24.9</td></tr><tr><td>SGD</td><td>73.4</td><td>75.6</td><td>77.9</td><td>49.6</td></tr><tr><td>SGDM</td><td>74.3</td><td>76.5</td><td>78.8</td><td>46.9</td></tr><tr><td>SGDMC</td><td>75.6</td><td>77.6</td><td>79.6</td><td>44.4</td></tr><tr><td>SGDMCWC</td><td>78.2</td><td>79.9</td><td>81.7</td><td>47.6</td></tr><tr><td>SGDMW</td><td>75.5</td><td>78.1</td><td>80.6</td><td>52.4</td></tr></table>
+
+<table><tr><td>Optimizer</td><td>CPE</td><td>CPU</td><td>CPL</td><td>Epochs</td></tr><tr><td>Adagrad</td><td>83.1</td><td>84.1</td><td>85.2</td><td>34.4</td></tr><tr><td>Adam</td><td>82.1</td><td>83.7</td><td>85.2</td><td>31.2</td></tr><tr><td>AdamLR</td><td>84.8</td><td>85.5</td><td>86.2</td><td>28.6</td></tr><tr><td>SGD</td><td>65.8</td><td>67.7</td><td>69.6</td><td>42.2</td></tr><tr><td>SGDM</td><td>72.2</td><td>74.5</td><td>76.9</td><td>37.2</td></tr><tr><td>SGDMC</td><td>77.9</td><td>79.3</td><td>80.8</td><td>32.3</td></tr><tr><td>SGDMCWC</td><td>71.3</td><td>75.0</td><td>78.6</td><td>109.7</td></tr><tr><td>SGDMW</td><td>64.6</td><td>69.6</td><td>74.6</td><td>119.0</td></tr></table>
+
+8.d: IMDB. Higher is better
+
+<table><tr><td>Optimizer</td><td>CPE</td><td>CPU</td><td>CPL</td><td>Epochs</td></tr><tr><td>Adagrad</td><td>93.8</td><td>94.4</td><td>95.0</td><td>19.7</td></tr><tr><td>Adam</td><td>92.0</td><td>93.5</td><td>95.1</td><td>24.3</td></tr><tr><td>AdamLR</td><td>94.5</td><td>95.0</td><td>95.4</td><td>17.2</td></tr><tr><td>SGD</td><td>92.6</td><td>93.8</td><td>95.1</td><td>29.9</td></tr><tr><td>SGDM</td><td>91.9</td><td>93.6</td><td>95.3</td><td>29.2</td></tr><tr><td>SGDMC</td><td>93.3</td><td>94.2</td><td>95.2</td><td>26.0</td></tr><tr><td>SGDMCWC</td><td>92.5</td><td>94.0</td><td>95.4</td><td>31.8</td></tr><tr><td>SGDMW</td><td>91.6</td><td>93.4</td><td>95.3</td><td>33.5</td></tr></table>
+
+8.e: WRN-16(4). Higher is better
+
+<table><tr><td>Optimizer</td><td>CPE</td><td>CPU</td><td>CPL Epochs</td></tr><tr><td>Adagrad</td><td>54.5</td><td>55.5</td><td>56.6 166.6</td></tr><tr><td>Adam</td><td>53.7</td><td>55.3</td><td>57.0 131.0</td></tr><tr><td>AdamLR</td><td>55.9</td><td>56.7</td><td>57.4 170.9</td></tr><tr><td>SGD</td><td>38.1</td><td>40.8</td><td>43.4 183.2</td></tr><tr><td>SGDM</td><td>48.5</td><td>51.8</td><td>55.2 188.3</td></tr><tr><td>SGDMC</td><td>53.3</td><td>55.6</td><td>58.0 194.5</td></tr><tr><td>SGDMCWC</td><td>51.7</td><td>54.2</td><td>56.6 197.3</td></tr><tr><td>SGDMW</td><td>42.2</td><td>45.6</td><td>49.1 184.0</td></tr></table>
+
+8.f: Char-RNN. Higher is better
+
+![](images/1638032d7d15d84e395e0faa09da5b7438cc54ad9d1aeb688caa6a26c9879864.jpg)  
+Figure 4: Performance analysis of various experiments. We plot the on the $\mathbf { X }$ -axis the number of the hyperparameter configuration searches, on the y-axis the appropriate performance.   
+4.a: CIFAR-10 evolution
+
+![](images/84dcfcf92124dfc11105f29ebc9b20accf8298aebe9565b74e6f5a71ac46bc85.jpg)  
+4.b: CIFAR-100 evolution
+
+![](images/b57494dc15a0b20c175961de79e9089054bc521b0b7fe4af1900ef95ac8bff49.jpg)  
+Figure 5: Performance analysis of various experiments. We plot the on the $\mathbf { X } ^ { } -$ -axis the number of the hyperparameter configuration searches, on the y-axis the appropriate performance on a log scale
+
+![](images/6fc13ff033e20baef240f395612d759fafce569eab04436ea8f39c39121c080b.jpg)  
+6.a: Bi-LSTM evolution
+
+![](images/108350007f0e2d6fee04b87a5a958acacad0e5df60ea42e53d3cdf68e741896f.jpg)  
+6.c: Tolstoi Char-RNN evolution   
+Figure 6: Performance analysis of various experiments. We plot the on the $\mathbf { X }$ -axis the number of the hyperparameter configuration searches, on the y-axis the appropriate performance on a log scale
+
+![](images/31d69d1c9650e9afbef7b1ae9e0ddd3bb8cebab8351627a42fc678cf71fc52e5.jpg)
+
+![](images/d4a03ff2add522127f868a9ad798425c2e1eac934abf07a87607853110ed674c.jpg)  
+7.a: MNIST-VAE evolution
+
+![](images/94fc6587ea0272557615517ed8879a09bd2ef787bc3d6f9306e31029aaba6363.jpg)  
+7.b: MNIST-VAE evolution   
+7.c: Quadratic deep evolution
+
+Figure 7: Performance analysis of various experiments. We plot the on the $\mathbf { X }$ -axis the number of the hyperparameter configuration searches, on the y-axis the appropriate performance on a log scale
+
+![](images/f40a5ba4ff8ec878621de75cb452f9ebfd5499757561a53052e0f6724f2eecc7.jpg)  
+Figure 8: Which optimizer for which budget? Given a tuning budget $K$ $\scriptstyle { \dot { x } }$ -axis), the stacked area plots above show how likely each optimizer (colored bands) is to yield the best result after $K$ steps of hyperparameter optimization. For example, for the IMDB LSTM problem, for a small budget, ‘AdamLR’ is the best choice (with $\sim 0 . 8$ probability), whereas for a larger search budget $> 5 0$ , tuning the additional parameters of ‘Adam’ is likely to pay off.

parse/train/H1gEP6NFwr/H1gEP6NFwr_content_list.json

@@ -0,0 +1,1915 @@
+[
+    {
+        "type": "text",
+        "text": "ON THE TUNABILITY OF OPTIMIZERS IN DEEP LEARNING ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            99,
+            660,
+            146
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Anonymous authors Paper under double-blind review ",
+        "bbox": [
+            183,
+            170,
+            398,
+            198
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            234,
+            544,
+            250
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "There is no consensus yet on the question whether adaptive gradient methods like Adam are easier to use than non-adaptive optimization methods like SGD. In this work, we fill in the important, yet ambiguous concept of ‘ease-of-use’ by defining an optimizer’s tunability: How easy is it to find good hyperparameter configurations using automatic random hyperparameter search? We propose a practical evaluation protocol for optimizer tunability that can form the basis for a fair optimizer benchmark. Evaluating a variety of optimizers on an extensive set of standard datasets and architectures, we find that Adam is the most tunable for the majority of problems, especially with a low budget for hyperparameter tuning. ",
+        "bbox": [
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+            270,
+            766,
+            395
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            430,
+            334,
+            446
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "With the ubiquity of deep learning in various applications, a multitude of first-order stochastic optimizers (Robbins & Monro, 1951) have been in vogue. They have varying algorithmic components like momentum (Sutskever et al., 2013) and adaptive learning rates (Tieleman & Hinton, 2012; Duchi et al., 2011; Kingma & Ba, 2015). With all these choices, picking the optimizer is among the most important design decisions for machine learning practitioners. For this decision, the best possible generalization performance is certainly an important characteristic to be taken into account. However, we argue that in practice, an even more important characteristic is whether the best possible performance can be reached with the available resources. ",
+        "bbox": [
+            174,
+            465,
+            825,
+            577
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "The performance of optimizers strongly depends on the choice of hyperparameter values such as the learning rate. In the machine learning research community, the sensitivity of models to hyperparameters has been of great debate recently, where in multiple cases, reported model advances did not stand the test of time because they can be explained by better hyperparameter tuning (Lucic et al., 2018; Melis et al., 2018; Henderson et al., 2018). This has led to calls for using automatic hyperparameter optimization methods with a fixed budget for a fairer comparison of models (Sculley et al., 2018; Feurer & Hutter, 2019; Eggensperger et al., 2019). For industrial applications, automated machine learning (AutoML, Hutter et al., 2019), which has automatic hyperparameter optimization as one of its key concepts, is becoming increasingly more important. In both cases, an optimization algorithm that achieves good performances with relatively little tuning effort is arguably substantially more useful than an optimization algorithm that achieves top performances, but reaches it only with a lot of careful tuning effort. Hence, we advocate that the performance obtained by an optimizer is not only the best performance obtained when using that optimizer, but also has to account for the cost of tuning its hyperparameters to obtain that performance, thus being dichotomous. We term this concept tunability in this paper. ",
+        "bbox": [
+            174,
+            584,
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+            791
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Despite the importance of this concept, there is no standard way of measuring tunability. Works that propose optimization techniques show their performance on various tasks as depicted in Table 1. It is apparent that the experimental settings, as well as the network architectures tested, widely vary, hindering a fair comparison. The introduction of benchmarking suites like DEEPOBS (Schneider et al., 2019) have standardized the tested architectures, however, this does not fix the problem of selecting the hyperparameters themselves, and the effort expended in doing so. Previous studies treat tunability to be the best performance obtained on varying a hyperparameter (Schneider et al., 2019) or by measuring the improvement in performance by tuning a hyperparameter (Probst et al., 2019), but do not take any cognizance to the intermediate performance during the tuning process. ",
+        "bbox": [
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+            799,
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+            924
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+        "page_idx": 0
+    },
+    {
+        "type": "table",
+        "img_path": "images/78e18d432f854cb11323e4b494d131dd4f5389378766531608d05da05189bf48.jpg",
+        "table_caption": [
+            "Table 1: Experimental settings shown in the original papers of popular optimizers. The large differences in test problems and tuning methods make them difficult to compare. $\\gamma$ denotes learning rate, $\\mu$ denotes momentum, $\\lambda$ is the weight decay coefficient. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Datasets</td><td>Network architecture</td><td>Parameter tuning methods</td></tr><tr><td>SGD with momentum (Sutskever et al., 2013)</td><td>Artificial datasets MNIST</td><td>Fully-connected LSTM</td><td>μ = 0.9 for first 1000 updates then μ ∈ {0,0.9,0.98,0.995}. other schedules for μ are used &amp; log1o(γ)∈{-3,-4,-5,-6}</td></tr><tr><td>Adagrad (Duchi et al., 2011)</td><td>ImageNet ranking Reuter RCV1 MNIST KDD Census</td><td>Single layer Handcrafted features Histogram features</td><td>Perfomance on dev-set</td></tr><tr><td>Adam (Kingma &amp; Ba, 2015)</td><td>IMDb MNIST CIFAR10</td><td>Logistic regression Multi-layer perceptron Convolutional network</td><td>β1∈{0,0.9} β∈{0.99,0.999,0.9999} log10(γ)∈{-5,-4,-3,-2,-1}</td></tr><tr><td>AdamW (Loshchilov &amp; Hutter,2019)</td><td>CIFAR 10 ImageNet 32×32</td><td>ResNet CNN</td><td>log2(γ) ∈{-11,-10.-1,0} log2(λ)∈ log2(10-3)+{-5,-4,...,4}</td></tr></table>",
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+        "type": "text",
+        "text": "In this paper, we introduce a fair evaluation protocol for tunability based on automatic hyperparameter optimization, and simple evaluation measures that allow to compare the performance of optimizers under varying resource constraints. By evaluating on a wide range of 9 diverse tasks, we aim to contribute to the debate of adaptive vs. non-adaptive optimizers (Wilson et al., 2017; Shah et al., 2018; Chen & Gu, 2018) . To reach a fair comparison, we experiment with several SGD variants that are often needed to reach good performance. Although a well-tuned SGD variant is able to reach the top performance in some cases, our overall results clearly favor adaptive gradient methods. We therefore conclude that there is substantial value in adaptive gradient methods. ",
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+    {
+        "type": "text",
+        "text": "2 MEASURING TUNABILITY ",
+        "text_level": 1,
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+        "text": "Given the dichotomy of the problem of tunability, we argue that it needs to take into account ",
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+        "type": "text",
+        "text": "1. how difficult it is to find a good hyperparameter configuration for the optimizer,   \n2. the absolute performance of the optimizer. ",
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+        "type": "text",
+        "text": "To see why both are needed, consider Figure 1.a, which shows the performance in terms of loss of four different optimizers as a function of its only hyperparameter $\\theta$ (by assumption). If we only consider requirement #1, optimizer C would be considered the best, since every hyperparameter value is the optimum. However, its absolute performance is poor, making it of low practical value. Moreover, due to the same shape, optimizers A and B would be considered equally good, although optimizer A clearly outperforms B. On the other hand, if we only consider requirement #2, optimizers B and D would be considered equally good, although optimizer D’s optimum is harder to find. ",
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+        "text": "As we show in Section 5, no existing definition of tunability takes both requirements into account. In the following, we present a formulation that does so. ",
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+        "type": "text",
+        "text": "2.1 PRELIMINARIES: HYPERPARAMETER OPTIMIZATION ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We define hyperparameter optimization (HPO) (Feurer & Hutter, 2019) as follows: ",
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+        "text": "Definition. Let $\\mathcal { M }$ be an optimization algorithm with $N$ hyperparameters $( \\theta _ { 1 } , \\ldots , \\theta _ { N } ) \\in \\Theta$ . Let $a$ specific instantiation of $\\mathcal { M }$ with $\\pmb \\theta \\in \\Theta$ be denoted by $\\mathcal { M } _ { \\theta }$ . Thus, given a dataset $D = D _ { t r a i n } \\bigcup D _ { v a l }$ , the following objective is minimized ",
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+        "type": "equation",
+        "img_path": "images/f1d517e3861cea858ed50d3ec978cebf181fcc8b63e4b360e13506b861d99235.jpg",
+        "text": "$$\n\\pmb { \\theta } ^ { \\star } = \\arg \\operatorname* { m i n } _ { \\pmb { \\theta } \\in \\Theta } \\mathcal { L } ( \\mathcal { M } _ { \\pmb { \\theta } } , D _ { v a l } )\n$$",
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+    {
+        "type": "text",
+        "text": "where $\\mathcal { M } _ { \\theta }$ is trained on $D _ { t r a i n }$ . In our work, we use $\\mathcal { L }$ to be validation loss. ",
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+        "type": "text",
+        "text": "We use $\\mathcal { L } ( \\pmb { \\theta } )$ to refer to $\\mathcal { L } ( \\mathcal { M } _ { \\theta } , D _ { v a l } )$ for brevity. In our experiments, we use the time-tested Random Search (Bergstra & Bengio, 2012) algorithm for HPO for simplicity. ",
+        "bbox": [
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+        "type": "text",
+        "text": "The ability to easily find good minima depends on the loss surface $\\mathcal { L }$ itself. Thus, tunability is a characterization of the HPO’s loss function $\\mathcal { L }$ . Here we present a quantification of this idea, which we illustrate with Figure 1.b. ",
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+    {
+        "type": "text",
+        "text": "Let us assume that there are two optimizers E & F, both with hyperparameter $\\theta$ , both of them used to minimize a function (e.g. train a neural network). Let the loss functions of HPO be $\\mathcal { L } _ { E }$ and $\\mathcal { L } _ { F }$ respectively. As the figure shows, the minimum of $\\mathcal { L } _ { E }$ is lower than that of $\\mathcal { L } _ { F }$ (denoted by $\\theta _ { E } ^ { \\star }$ and $\\theta _ { F } ^ { \\star } .$ ) i.e. $\\mathcal { L } _ { E } ( \\theta _ { E } ^ { \\star } ) < \\mathcal { L } _ { F } ( \\theta _ { F } ^ { \\star } )$ . However, the minimum of $\\mathcal { L } _ { E }$ is much sharper than that of $\\mathcal { L } _ { F }$ , and in most regions of the parameter space F performs much better than E. This makes it easier to find configurations that already perform well. This makes optimizer F an attractive option when we have no prior knowledge of the good parameter settings. ",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/e23b0ccbb293a18f6a1db6c084466c5253e59cc3b80bdd3822b44d9f98c145d2.jpg",
+        "image_caption": [
+            "1.a: Illustration. It is important to consider both the absolute performance of optimizers as well as the tuning effort to get to good performances. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/1b5b7c856204f84cee6dd94985a20853400f67d375d9ac8122ea6d45cfa55388.jpg",
+        "image_caption": [
+            "1.b: Illustration. While optimizer E can achieve the best performance after careful tuning, optimizer F is likely to provide better performance under a constrained HPO budget. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "",
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+        "type": "text",
+        "text": "The key-difference between the two interpretations is whether one prefers a ‘good enough’ performance through fewer hyperparameter configuration searches (in the case of optimizer F), or whether one is willing to spend computational time to get the best possible performance $\\left( \\theta _ { E } ^ { \\star } \\right)$ in the case of optimizer E). In this work, we search for the hyperparameter through an HPO like Random Search. Thus, the difference of the two interpretations of tunability lies whether one values results from late stages of the HPO process (i.e. optimizer $\\mathrm { E }$ is preferable due to better optimum) more than results from early stages of the HPO process (i.e. optimizer F is preferable). ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Motivated by these observations, we propose the following metric for tunability. ",
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+    {
+        "type": "text",
+        "text": "$\\omega$ -tunability’s Definition. Let $( \\mathbf { \\boldsymbol { \\theta } } _ { t } , \\mathbf { \\mathcal { L } } ( \\mathbf { \\boldsymbol { \\theta } } _ { t } ) )$ be the incumbents (best performance attained till $t$ ) of the HPO algorithm at iteration $t$ and $T$ be the hyperparameter tuning budget. For $w _ { t } > 0 \\forall t$ and $\\textstyle \\sum _ { t } w _ { t } < \\infty$ , we define $\\omega$ -tunability as ",
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+    {
+        "type": "equation",
+        "img_path": "images/5a01001ac3cc9597dd73fde03b7f269dfc5bcf8b9770569e2ba032dc1cd391c2.jpg",
+        "text": "$$\n\\omega \\ – t u n a b i l i t y = \\sum _ { t = 1 } ^ { T } \\omega _ { t } \\mathcal { L } _ { t }\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "i.e, $\\omega$ -tunability is a weighted sum of the incumbents $\\mathcal { L } ( \\pmb { \\theta } _ { t } )$ . In our experiments we use $\\textstyle \\sum _ { t } \\omega _ { t } = 1$ ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "By appropriately choosing the weights $\\left\\{ \\omega _ { t } \\right\\}$ , we can interpolate between our two notions of tunability. In the extreme case where we are only interested in the peak performance of the optimizer, we can set $\\omega _ { T } = 1$ and set the other weights to zero. In the opposite extreme case where we are interested in the \"one-shot tunability\" of the optimizer, we can set $\\omega _ { 1 } = 1$ . In general, we can answer the question of \"How well does the optimizer perform with a budget of $K$ iterations?\" by setting $\\omega _ { i } = { \\bf 1 } _ { \\mathrm { i = K } }$ . ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "While the above weighting scheme is intuitive, merely computing the performance after expending HPO budget of $K$ does not consider the performance obtained after the previous $K - 1$ iterations i.e. we would like to differentiate the cases where a requisite performance is attained by tuning an optimizer for $K$ iterations and another for $K _ { 1 }$ iterations, where $K _ { 1 } \\gg K$ . Therefore, we employ three additional weighting schemes. By setting $\\omega _ { i } \\propto ( T - i )$ , our first one puts more emphasis on the earlier stages of the hyperparameter tuning process. We term this weighting scheme Cumulative Performance-Early $( C P E )$ . In contrast, the second weighting scheme, Cumulative Performance-Late $( C P L )$ puts more emphasis on late stages of tuning, and thus on obtaining a better performance at a higher tuning cost: $\\omega _ { i } \\propto i$ . As a intermediate of the two, we also report a uniform weighting Cumulative Performance-Uniform $( C P U ) : \\omega _ { i } = 1 / T$ . ",
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+    {
+        "type": "text",
+        "text": "3 OPTIMIZERS AND THEIR HYPERPARAMETERS ",
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+    {
+        "type": "text",
+        "text": "3.1 PARAMETERS OF THE OPTIMIZERS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "To compare the tunability of adaptive gradient methods to non-adaptive methods, we choose the most commonly used optimizers from both the strata; SGD and SGD with momentum for non-adaptive methods, and Adagrad and Adam for adaptive gradient methods. Since adaptive gradient methods are said to work well with their default hyperparameter values already, we additionally employ a default version of Adam where we only tune the initial learning rate and set the other hyperparameters to the values recommended in the original paper (Kingma & Ba, 2015) (termed AdamLR). Such a scheme has been used by Schneider et al. too. A similar argument can be made for SGD with momentum (termed SGDM): thus we experiment with a fixed momentum value of 0.9 (termed SGDMC). ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In addition to standard parameters in all optimizers, we consider weight decay with SGD too. SGD with weight decay can be considered as an optimizer with two steps where the first step is to scale current weights with the decay value, followed by a normal descent step (Loshchilov & Hutter, 2019). Thus we devise two additional experiments for SGD with weight-decay where we tune weight-decay along with momentum (termed SGDMW), and one where we fix it to $1 0 ^ { - 5 }$ (termed $\\mathbf { S G D M ^ { C } W } ^ { \\dot { \\mathbf { C } } } ,$ ) along with the momentum being fixed to 0.9, which is the value for weight decay we found to be consistently better through HPO. The full list of optimizers we consider is provided in Table 4 ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Manually defining a specific number of epochs can be biased towards one optimizer, as one optimizer may reach good performance in the early epochs of a single HPO iteration, whereas another may reach higher peaks more slowly. In order to alleviate this, it would be possible to add the number of training epochs as an additional hyperparameter to be searched. Since this would incur even higher computational cost, we instead use a validation set performance as stopping criterion. Thus we stop training when the validation loss plateaus for more than 2 epochs or if the number of epochs exceeds the predetermined maximum number as set in DEEPOBS. ",
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+    {
+        "type": "text",
+        "text": "3.2 CALIBRATION OF HYPERPARAMETER DISTRIBUTIONS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "As mentioned previously, we use Random Search for optimizing the hyperparameters, which requires distributions of random variables to sample from. Choosing poor distributions to sample from impacts the performance, and may break requisite properties (e.g. learning rate is non-negative). For some of the parameters listed in Table 2, obvious bounds exist due their mathematical properties, or have been prescribed by the optimizer designers themselves. For example, Kingma & Ba (2015) bound $\\beta _ { 1 } , \\beta _ { 2 }$ to $[ 0 , 1 )$ and specify that they are close to 1. In the absence of such prior knowledge, we devise a simple method to determine the priors. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We train each task specified in the DEEPOBS with a large number of hyperparameter samplings and retain the hyperparameters which resulted in performance within $2 0 \\%$ of the best performance obtained. For each of the hyperparameters in this set, we fit the distributions in the third column of Table 2 using maximum likelihood estimation. In doing so, we make a simplifying assumption that all the hyperparameters are independent of each other. We argue that these distributions are appropriate; the only condition on learning rate is non-negativity that is inherent to the log-normal distribution, momentum is non-negative with a usual upper bound of 1, $\\beta \\mathrm { { s } }$ in Adam have been prescribed to be less than 1 but close to it, $\\epsilon$ is used to avoid divide-by-zero error and thus is a small positive value close to 0. We report the parameters of the distributions obtained after the fitting in Table 2. The calibration procedure’s performance is not included in the tunability computation. ",
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+    {
+        "type": "table",
+        "img_path": "images/3134f4766ed1aa87bce7dc3b98966bf793782045a8591bc7036cf4ebd0969f4d.jpg",
+        "table_caption": [
+            "Table 2: Optimizers evaluated. For each hyperparameter, we calibrated a ‘sampling distribution’ to give good results across tasks (Section 3.2). $\\boldsymbol { \\bar { \\mathcal { U } } } [ \\boldsymbol { a } , \\boldsymbol { b } ]$ is the continuous uniform distribution on $[ a , b ]$ . Log-uniform $( a , b )$ is a distribution whose logarithm is $\\mathcal { U } [ a , b ]$ . Log-normal $( \\mu , \\sigma )$ is a distribution whose logarithm is normally distributed with mean $\\mu$ and standard deviation $\\sigma$ . "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Optimizer</td><td>Tunable parameters</td><td>Sampling distribution</td></tr><tr><td rowspan=\"3\">Stochastic Gradient Descent</td><td>Learning rate</td><td>Log-normal(-2.09,1.312)</td></tr><tr><td>Momentum</td><td>u[0,1]</td></tr><tr><td>Weight decay</td><td>Log-uniform(-5,-1)</td></tr><tr><td>Adagrad</td><td>Learning rate</td><td>Log-normal(-2.004,1.20)</td></tr><tr><td rowspan=\"3\">Adam</td><td>Learning rate</td><td>Log-normal(-2.69,1.42)</td></tr><tr><td>β1,β</td><td>Log-uniform(-5, -1)</td></tr><tr><td>E</td><td>Log-uniform(-8,0)</td></tr></table>",
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+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/d3f247c1961e3318032b5df3e591818758d12d3c536b5064ea83275d253746df.jpg",
+        "table_caption": [
+            "Table 3: Models and datasets used. We use the DeepOBS benchmark set (Schneider et al., 2019). Details are provided in Appendix A. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Architecture</td><td>Datasets</td></tr><tr><td>Convolutional net</td><td>FMNIST, CIFAR10/100</td></tr><tr><td>Variational autoencoder</td><td>FMNIST,I</td></tr><tr><td>Wide residual network</td><td>SVHN</td></tr><tr><td>CharacterRNN</td><td>Tolstoi&#x27;s War and Peace</td></tr><tr><td>Quadratic function</td><td>Artificial datatset</td></tr><tr><td>LSTM</td><td>IMDb</td></tr></table>",
+        "bbox": [
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+    {
+        "type": "table",
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+        "table_caption": [
+            "Table 4: Optimizers and tunable parameters. $\\gamma$ is learning rate, $\\mu$ is momentum, $\\lambda$ is the weight decay coefficient. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Optimizer</td><td>Tunable parameters</td></tr><tr><td>SGD</td><td>γ(μ=0,λ=0)</td></tr><tr><td>SGDM</td><td>Y,μ(入=0)</td></tr><tr><td>SGDMC SGDMCWC</td><td>γ (μ=0.9,λ=0) γ (μ=0.9,λ=10-5)</td></tr><tr><td>SGDMW</td><td>Y，μ,入</td></tr><tr><td>Adagrad</td><td>Y</td></tr><tr><td>AdamLR Adam</td><td>γ (β1=0.9,β2=0.999,∈=10-8) Y,β1,β2,E</td></tr></table>",
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+        "page_idx": 4
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+    {
+        "type": "text",
+        "text": "4 EXPERIMENTS AND RESULTS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
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+    {
+        "type": "text",
+        "text": "To assess the tunability of optimizers’ hyperparameters for the training of deep neural networks, we benchmark using the open-source suite DEEPOBS (Schneider et al., 2019). The architectures and datasets we experiment are given in Table 3. We refer the reader to Schneider et al. (2019) for specific details of the architectures. To obtain a better balance between vision and NLP applications, we added an LSTM network with the task of sentiment classification in the IMDB dataset (Maas et al., 2011), details for which are provided in Appendix A. ",
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+    {
+        "type": "text",
+        "text": "4.1 HYPERPARAMETERS AND IMPLEMENTATION ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "The performance of automatic hyperparameter search methods is dependent on its own hyperparameters, which play an important role in the outcome, e.g number of configurations to test. In our experiments, we evaluate 100 configurations with each of the hyperparameter optimization methods. As we use random search, we simulate multiple runs of these 100 configurations through shuffling. This gives us the variance of performance at each step. ",
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+    {
+        "type": "text",
+        "text": "4.2 ANALYSIS OF TUNABILITY ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We analyze the tunability for the various weighting schemes proposed. For the weighting scheme $\\omega _ { i } = { \\bf 1 } _ { \\mathrm { i = K } }$ , for increasing values of $K$ , we show the performance as well as its variance in Figure 3. For readability, we show only results for Adam, AdamLR, Adagrad and SGDMW, and the rest are given in Appendix C. It is quite apparent that in most of the tasks, a well tuned SGD with momentum and weight decay is as good as Adam (for large $K$ ). However, the gap in the performance is quite noticeable when AdamLR outperforms SGD in the VAE tasks and the IMDB task. In the case of image classification problems, SGD variants fare the best, as it has been reported before (Keskar & Socher, 2017). It is interesting to notice that for $K { = } 4$ , the decreasing order of variance is nearly always SGDMW, Adam, Adagrad, AdamLR (10 out of 11 cases), even if AdamLR marginally underperforms as it is in the case of Quadratic Deep. Given this formulation, we ask the following question: given an HPO budget of $K$ , what is the best choice for optimizer? We answer this in Appendix D. ",
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+    },
+    {
+        "type": "text",
+        "text": "",
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+    },
+    {
+        "type": "text",
+        "text": "For the other weighting schemes, tunability scores are reported in Table 5. We see that there is no one optimizer that is best across three schemes, and tasks presented. A similar trend of SGD doing better than the adaptive gradient methods on image classification tasks is evident. Considering CPE, we observe that AdamLR performs the best in 6 out 9 tasks, where as the other three times $\\mathrm { \\Delta S G D M ^ { C } W ^ { C } }$ performs the best. The trend is not very obvious for CPU and CPL. In the case of CPU, AdamLR wins 5 out of 9 tasks, $\\mathbf { S G D M ^ { C } W ^ { C } }$ wins twice, and SGDM wins once. For CPL, AdamLR wins 4 out of 9, and the $\\mathbf { S G D M ^ { C } W ^ { C } }$ wins once, and SGDM and $\\mathbf { S G D M ^ { C } }$ win twice each. Summarizing, if peak-performance or even evolving to better performance at a larger hyperparameter search cost, SGD variants are better 5 out 9 times. However, if a good performance is expected in the earlier iterations of hyperparameter search, AdamLR is very competitive. Also, the default parameters of $\\beta _ { 1 } , \\beta _ { 2 } , \\epsilon$ of Adam optimizer result in quite good performance, to the point that Adam is rarely the better alternative over AdamLR. A known exception is training Inception networks (Abadi et al., 2015), where $\\epsilon$ is recommended to be set to 0.1. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "For some of the cases, the tunablities reported are very similar for the AdamLR and SGD variants. However, tuning Adam is very different from tuning SGD from a wall-clock time measurement. For example, we find that for the case of CIFAR-10, AdamLR requires on average $39 \\%$ fewer epochs to complete training than $\\mathbf { S G D M ^ { C } }$ (the top perfomer); thus being that much faster than $\\mathrm { S G D M ^ { C } }$ in wall-clock time. It can be argued that a more practical form of hyperparameter tuning budget is wall-clock time i.e. if a wall-clock time budget of $K$ minutes is given, how do our findings vary? In short, we find similar trends as we noticed before. We provide the details in Appendix E. ",
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+    {
+        "type": "text",
+        "text": "4.3 SUMMARIZING ACROSS DATASETS ",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "To get a better understanding of an optimizer’s aggregate tunability across datasets compared to the rest, we compute summary statistics for an optimizer $o$ ’s performance after $k$ iterations in the following way: ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/d30ddaf093016aa7078fb9f9f0a2553ba2e0f57dd8dd18a26ea8e9e7a419eeb3.jpg",
+        "text": "$$\nS ( o , k ) = \\frac { 1 } { | \\mathcal { P } | } \\sum _ { p \\in \\mathcal { P } } \\frac { o ( k , p ) } { \\operatorname* { m a x } _ { o ^ { \\prime } \\in \\mathcal { O } } o ^ { \\prime } ( k , p ) } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+            564
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where $o ( k , p )$ denotes the performance of optimizer $o \\in \\mathcal { O }$ on test problem $p \\in \\mathcal P$ after $k$ iterations of the HPO process (i.e. $\\omega$ -tunability with $\\omega _ { i } = \\mathbf { 1 } _ { \\mathrm { i = k } }$ ). In other words, we compute the average relative performance of an optimizer to the best performance of any optimizer over all tasks. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/49a91c72fa4f42bd73f6a4d510b838b41da14b1747ddb982287a49add13f2d19.jpg",
+        "image_caption": [
+            "Figure 2: Aggregated relative tunability of each optimizer across datasets "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The results are in Figure 2 and show that AdamLR performs very close to the best optimizer throughout the HPO process and is the best till about the $6 0 ^ { \\mathrm { t h } }$ iteration. In early stages of HPO, the SGD variants perform $10 \\mathrm { - } 2 0 \\%$ worse than Adam, but improve as the HPO progresses. ",
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+    {
+        "type": "text",
+        "text": "5 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "There exist few works that have tried to define and investigate tunability formally. Assessing the impact of hyperparameter tuning for decision tree models, Mantovani et al. (2018) count the number of times the tuned hyperparameter values are (statistically significantly) better than the default values. Probst et al. (2019) define tunability of an ML algorithm as the performance difference between a reference configuration (e.g., the default hyperparameters of the algorithm) and the best possible configuration on each dataset. This metric is comparable across ML algorithms, but it disregards entirely the absolute performance of ML algorithms. Schneider et al. (2019) recently released a benchmark for optimizers that evaluates their peak performance and speed. Tunability is assessed as the sensitivity of the performance to changes of the learning rate. In all three aforementioned studies, the definitions of tunability would fail to identify the superiority of optimizer A over optimizer B in Figure 1.a. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The study by Wilson et al. (2017) finds SGD-based methods as easy to tune as adaptive gradient methods. However, their study lacks a clear definition of tunability and tunes the algorithms on manually selected, dataset dependent grid values. The study by Shah et al. (2018) applies a similar methodology and comes to similar conclusions regarding tunability. Since both studies only consider the best parameter configuration, their approach would be unable to identify the better optimizer among B and D in Figure 1.a. In contrast, the methodology in our study is able to distinguish all the cases depicted in Figure 1.a. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/4299e710803323da6d2a6452267f075e1e7f49811fcaa2695768cb85e1791fb1.jpg",
+        "table_caption": [
+            "Table 5: Performance of various experiments. "
+        ],
+        "table_footnote": [
+            "5.a: FMNIST 2C2D. Higher is better "
+        ],
+        "table_body": "<table><tr><td>Optimizer</td><td>CPE</td><td>CPU</td><td>CPL</td></tr><tr><td>Adagrad</td><td>91.3</td><td>91.4</td><td>91.6</td></tr><tr><td>Adam</td><td>91.3</td><td>91.5</td><td>91.8</td></tr><tr><td>AdamLR</td><td>91.3</td><td>91.6</td><td>91.9</td></tr><tr><td>SGD</td><td>90.4</td><td>90.8</td><td>91.2</td></tr><tr><td>SGDM</td><td>90.5</td><td>90.9</td><td>91.3</td></tr><tr><td>SGDMC</td><td>90.7</td><td>90.9</td><td>91.1</td></tr><tr><td>SGDMCWC</td><td>90.7</td><td>90.9</td><td>91.1</td></tr><tr><td>SGDMW</td><td>90.4</td><td>90.8</td><td>91.3</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/0bcb9c856a2c279d086fc2134671dc731d425f55cb6ae2cadcd86553bbf0d43f.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "5.b: CIFAR 10. Higher is better "
+        ],
+        "table_body": "<table><tr><td>Optimizer</td><td>CPE</td><td>CPU</td><td>CPL</td></tr><tr><td>Adagrad</td><td>76.4</td><td>77.1</td><td>77.9</td></tr><tr><td>Adam</td><td>77.2</td><td>78.4</td><td>79.5</td></tr><tr><td>AdamLR</td><td>78.8</td><td>79.4</td><td>80.0</td></tr><tr><td>SGD</td><td>77.0</td><td>77.8</td><td>78.6</td></tr><tr><td>SGDM</td><td>77.8</td><td>78.6</td><td>79.5</td></tr><tr><td>SGDMC</td><td>78.6</td><td>79.4</td><td>80.1</td></tr><tr><td>SGDMCWC</td><td>81.1</td><td>81.6</td><td>82.0</td></tr><tr><td>SGDMW</td><td>79.7</td><td>80.4</td><td>81.2</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/3506076fc88d5e46b9b1a97405f132150300155c1c006ef6054c3de11b91e66e.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "5.c: CIFAR 100. Higher the better "
+        ],
+        "table_body": "<table><tr><td>Optimizer</td><td>CPE</td><td>CPU</td><td>CPL</td></tr><tr><td>Adagrad</td><td>30.4</td><td>31.8</td><td>33.1</td></tr><tr><td>Adam</td><td>39.4</td><td>42.2</td><td>45.1</td></tr><tr><td>AdamLR</td><td>42.2</td><td>43.0</td><td>43.8</td></tr><tr><td>SGD</td><td>31.8</td><td>34.2</td><td>36.6</td></tr><tr><td>SGDM</td><td>40.6</td><td>43.3</td><td>46.0</td></tr><tr><td>SGDMC</td><td>42.1</td><td>43.3</td><td>44.5</td></tr><tr><td>SGDMCWC</td><td>39.2</td><td>40.3</td><td>41.5</td></tr><tr><td>SGDMW</td><td>33.5</td><td>37.2</td><td>41.0</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/ddca109efdcc63d5a17b795d2cf3bfe161c9f9b5d7d1724a73c4c69949d877e7.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "5.d: IMDB. Higher is better "
+        ],
+        "table_body": "<table><tr><td>Optimizer</td><td>CPE</td><td>CPU</td><td>CPL</td></tr><tr><td>Adagrad</td><td>84.3</td><td>84.8</td><td>85.3</td></tr><tr><td>Adam</td><td>83.6</td><td>84.5</td><td>85.5</td></tr><tr><td>AdamLR</td><td>85.8</td><td>86.0</td><td>86.3</td></tr><tr><td>SGD</td><td>68.1</td><td>69.3</td><td>70.5</td></tr><tr><td>SGDM</td><td>74.3</td><td>75.9</td><td>77.5</td></tr><tr><td>SGDMC</td><td>79.3</td><td>80.1</td><td>81.0</td></tr><tr><td>SGDMCWC</td><td>78.8</td><td>79.4</td><td>80.0</td></tr><tr><td>SGDMW</td><td>75.7</td><td>77.1</td><td>78.6</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/58c15fcf9fb495d19280d9f3f46e2ae5ae91424073959902b5ebe19fc06616fa.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "5.e: WRN-16(4). Higher is better "
+        ],
+        "table_body": "<table><tr><td>Optimizer</td><td>CPE</td><td>CPU</td><td>CPL</td></tr><tr><td>Adagrad</td><td>94.8</td><td>94.9</td><td>95.0</td></tr><tr><td>Adam</td><td>94.5</td><td>94.8</td><td>95.2</td></tr><tr><td>AdamLR</td><td>95.1</td><td>95.3</td><td>95.4</td></tr><tr><td>SGD</td><td>94.6</td><td>94.9</td><td>95.2</td></tr><tr><td>SGDM</td><td>94.8</td><td>95.2</td><td>95.6</td></tr><tr><td>SGDMC</td><td>94.9</td><td>95.1</td><td>95.3</td></tr><tr><td>SGDMCWC</td><td>95.2</td><td>95.4</td><td>95.5</td></tr><tr><td>SGDMW</td><td>95.0</td><td>95.2</td><td>95.3</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/156ca9e88353671860efb2ac2cf18007519e13e4b6b6a41fe809ed9f39f6aefb.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "5.f: Char-RNN. Higher is better "
+        ],
+        "table_body": "<table><tr><td>Optimizer</td><td>CPE</td><td>CPU</td><td>CPL</td></tr><tr><td>Adagrad</td><td>55.6</td><td>56.2</td><td>56.7</td></tr><tr><td>Adam</td><td>54.4</td><td>55.7</td><td>57.0</td></tr><tr><td>AdamLR</td><td>56.9</td><td>57.2</td><td>57.5</td></tr><tr><td>SGD</td><td>40.3</td><td>42.5</td><td>44.6</td></tr><tr><td>SGDM</td><td>51.4</td><td>54.0</td><td>56.5</td></tr><tr><td>SGDMC</td><td>55.6</td><td>57.0</td><td>58.3</td></tr><tr><td>SGDMCWC</td><td>54.2</td><td>55.6</td><td>57.0</td></tr><tr><td>SGDMW</td><td>45.1</td><td>48.2</td><td>51.2</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/5184c76a6e84d3b7509d8f16a25d680fc6c5e25a0515f0c20f71bd2e787e4319.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Optimizer</td><td>CPE</td><td>CPU</td><td>CPL</td></tr><tr><td>Adagrad</td><td>30.3</td><td>29.4</td><td>28.4</td></tr><tr><td>Adam</td><td>33.2</td><td>31.2</td><td>29.1</td></tr><tr><td>AdamLR</td><td>29.2</td><td>28.6</td><td>27.9</td></tr><tr><td>SGD</td><td>53.3</td><td>53.1</td><td>52.9</td></tr><tr><td>SGDM</td><td>36.0</td><td>32.9</td><td>29.9</td></tr><tr><td>SGDMC</td><td>54.1</td><td>53.5</td><td>53.0</td></tr><tr><td>SGDMCWC</td><td>54.0</td><td>53.5</td><td>53.0</td></tr><tr><td>SGDMW</td><td>34.6</td><td>32.2</td><td>29.8</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/b3d31dc19ec1c07e54593e17ae930aa0586c9da9f4f14eb21306afba1d8aa35f.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "5.g: FMNIST-VAE. Lower is better. 5.h: MNIST-VAE. Lower is better "
+        ],
+        "table_body": "<table><tr><td>Optimizer</td><td>CPE</td><td>CPU</td><td>CPL</td></tr><tr><td>Adagrad</td><td>25.5</td><td>24.7</td><td>24.0</td></tr><tr><td>Adam</td><td>26.0</td><td>24.8</td><td>23.7</td></tr><tr><td>AdamLR</td><td>24.6</td><td>24.0</td><td>23.5</td></tr><tr><td>SGD</td><td>26.2</td><td>25.5</td><td>24.8</td></tr><tr><td>SGDM</td><td>26.2</td><td>25.4</td><td>24.6</td></tr><tr><td>SGDMC</td><td>28.6</td><td>26.7</td><td>24.9</td></tr><tr><td>SGDMCWC</td><td>27.9</td><td>26.4</td><td>24.8</td></tr><tr><td></td><td></td><td></td><td></td></tr><tr><td>SGDMW</td><td>26.5</td><td>25.7</td><td>24.8</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/026c96190f4ca7b7e1d5788cd265b949b5630dfd9116158179bfbbdbd449f149.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "5.i: Quadratic deep. Lower is better "
+        ],
+        "table_body": "<table><tr><td>Optimizer</td><td>CPE</td><td>CPU</td><td>CPL</td></tr><tr><td>Adagrad</td><td>91.5</td><td>89.6</td><td>87.6</td></tr><tr><td>Adam</td><td>94.8</td><td>92.1</td><td>89.4</td></tr><tr><td>AdamLR</td><td>91.2</td><td>89.5</td><td>87.7</td></tr><tr><td>SGD</td><td>90.5</td><td>89.6</td><td>88.7</td></tr><tr><td>SGDM</td><td>89.5</td><td>88.7</td><td>87.9</td></tr><tr><td>SGDMC</td><td>89.6</td><td>88.6</td><td>87.5</td></tr><tr><td>SGDMCWC</td><td>88.6</td><td>88.4</td><td>88.1</td></tr><tr><td>SGDMW</td><td>89.3</td><td>88.9</td><td>88.4</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In a concurrent study, Choi et al. (2019) show that there exist a hierarchy among optimizers that such some can be viewed as specific cases of others e.g. SGDM is shown to be a special case of Adam as its $\\epsilon \\to \\infty$ , and thus Adam should never underperform SGDM with appropriate hyperparameter search). Like in our study, they suggest that the performance comparison of optimizers strongly depends on the hyperparameter tuning protocol. They also argue that the search space needs to be chosen optimizer specific. However, their focus is on the best possible performance achievable by an optimizer and does not take into account the tuning process. Moreover, while the authors claim their search protocol to be relevant for practitioners, the search spaces are manually chosen per dataset, constituting a significant difference to the AutoML scenario considered in our paper. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Tunability is related to measuring hyperparameter importance (Hutter et al., 2013), where van Rijn & Hutter (2018) have recently shown that learning the priors for hyperparameter distributions can yield to better HPO performance, akin to the calibration phase in our study. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "There has been recent interest in building optimizers termed the APROX family (Asi & Duchi, 2019a;b) that are provably robust to hyperparameter choices. Asi & Duchi experimentally find that, training a Residual network (He et al., 2016) on CIFAR-10, SGD converges only for a small range of initial learning rate choices, whereas Adam exhibits better robustness to learning rate choices. This is inline with our findings of tunability. ",
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "6 CONCLUSION ",
+        "text_level": 1,
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Our work proposes a new notion of tunability for optimizers that takes into account the tuning efforts of an HPO. The results of our experiments support the hypothesis that adaptive gradient methods are easier to tune than non-adaptive methods: In a setting with low budget for hyperparameter tuning, tuning only Adam optimizer’s learning rate is likely to be a very good choice; it doesn’t guarantee the best possible performance, but it is evidently the easiest to find well-performing hyperparameter configurations for. While SGD yields the best performance in some cases, its best configuration is tedious to find, and Adam often performs close to it. We, thus, state that the substantial value of the adaptive gradient methods, specifically Adam, is its amenability to hyperparameter search. This is in contrast to the findings of Wilson et al. (2017) who observe no advantage in tunabilty for adaptive gradient methods, and thus deem them to be of ‘marginal value’. Unlike them, we base our experiments on a standard hyperparameter optimization method that allows for an arguably fairer comparison. ",
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+        "page_idx": 7
+    },
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+            "3.a: CIFAR 10 ",
+            "3.c: SVHN WRN-16-4 "
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+            "Figure 3: $\\omega$ -tunability with $\\omega _ { i } = { \\bf 1 } _ { \\mathrm { i = K } }$ for various experiments. We plot the on the $\\mathbf { X }$ -axis the number of the hyperparameter configuration searches, on the y-axis the appropriate performance on a log scale. Figures a-f: higher is better and g-i: lower is better. "
+        ],
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+        "text": "",
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+    {
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+        "text": "Our study is certainly not exhaustive: We do not study the effect of the inclusion of a learning rate schedule, or using a different HPO algorithm on the results. However, their inclusion would result in a large increase the number of experiments, and constitutes our future work. ",
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+    {
+        "type": "text",
+        "text": "We hope that this paper encourages other researchers to conduct future studies on the performance of optimizers from a more holistic perspective, where the cost of the hyperparameter search is included. ",
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+    {
+        "type": "text",
+        "text": "REFERENCES ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            279,
+            285,
+            292
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Martín Abadi, Ashish Agarwal, Paul Barham, Eugene Brevdo, Zhifeng Chen, Craig Citro, Greg S. Corrado, Andy Davis, Jeffrey Dean, Matthieu Devin, Sanjay Ghemawat, Ian Goodfellow, Andrew Harp, Geoffrey Irving, Michael Isard, Yangqing Jia, Rafal Jozefowicz, Lukasz Kaiser, Manjunath Kudlur, Josh Levenberg, Dandelion Mané, Rajat Monga, Sherry Moore, Derek Murray, Chris Olah, Mike Schuster, Jonathon Shlens, Benoit Steiner, Ilya Sutskever, Kunal Talwar, Paul Tucker, Vincent Vanhoucke, Vijay Vasudevan, Fernanda Viégas, Oriol Vinyals, Pete Warden, Martin Wattenberg, Martin Wicke, Yuan Yu, and Xiaoqiang Zheng. TensorFlow: Large-scale machine learning on heterogeneous systems, 2015. URL https://www.tensorflow.org/. Software available from tensorflow.org. ",
+        "bbox": [
+            176,
+            301,
+            826,
+            426
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Hilal Asi and John C. Duchi. The importance of better models in stochastic optimization. Proceedings of the National Academy of Sciences, 2019a. ISSN 0027-8424. doi: 10.1073/pnas.1908018116. URL https://www.pnas.org/content/early/2019/10/29/1908018116. ",
+        "bbox": [
+            174,
+            434,
+            825,
+            477
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Hilal Asi and John C Duchi. Stochastic (approximate) proximal point methods: Convergence, optimality, and adaptivity. SIAM Journal on Optimization, 29(3):2257–2290, 2019b. ",
+        "bbox": [
+            174,
+            484,
+            821,
+            513
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "James Bergstra and Yoshua Bengio. Random search for hyper-parameter optimization. Journal of Machine Learning Research, 13(Feb):281–305, 2012. ",
+        "bbox": [
+            174,
+            520,
+            823,
+            549
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Jinghui Chen and Quanquan Gu. Closing the generalization gap of adaptive gradient methods in training deep neural networks. CoRR, abs/1806.06763, 2018. URL http://arxiv.org/ abs/1806.06763. ",
+        "bbox": [
+            173,
+            556,
+            825,
+            599
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Dami Choi, Christopher J Shallue, Zachary Nado, Jaehoon Lee, Chris J Maddison, and George E Dahl. On empirical comparisons of optimizers for deep learning. arXiv preprint arXiv:1910.05446, 2019. ",
+        "bbox": [
+            174,
+            607,
+            825,
+            650
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "John Duchi, Elad Hazan, and Yoram Singer. Adaptive subgradient methods for online learning and stochastic optimization. Journal of Machine Learning Research, 12(Jul):2121–2159, 2011. ",
+        "bbox": [
+            174,
+            657,
+            821,
+            686
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Katharina Eggensperger, Marius Lindauer, and Frank Hutter. Pitfalls and best practices in algorithm configuration. Journal of Artificial Intelligence Research, 64:861–893, 2019. ",
+        "bbox": [
+            174,
+            694,
+            823,
+            723
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Matthias Feurer and Frank Hutter. Hyperparameter Optimization, pp. 3–33. Springer International Publishing, Cham, 2019. ISBN 978-3-030-05318-5. doi: 10.1007/978-3-030-05318-5_1. URL https://doi.org/10.1007/978-3-030-05318-5_1. ",
+        "bbox": [
+            176,
+            731,
+            823,
+            773
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "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, pp. 770–778, 2016. ",
+        "bbox": [
+            174,
+            780,
+            825,
+            823
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Peter Henderson, Riashat Islam, Philip Bachman, Joelle Pineau, Doina Precup, and David Meger. Deep reinforcement learning that matters. In Thirty-Second AAAI Conference on Artificial Intelligence, 2018. ",
+        "bbox": [
+            173,
+            830,
+            825,
+            873
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Frank Hutter, Holger H Hoos, and Kevin Leyton-Brown. Identifying key algorithm parameters and instance features using forward selection. In International Conference on Learning and Intelligent Optimization, pp. 364–381. Springer, 2013. ",
+        "bbox": [
+            176,
+            882,
+            825,
+            924
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Frank Hutter, Lars Kotthoff, and Joaquin Vanschoren. Automated machine learning-methods, systems, challenges, 2019. ",
+        "bbox": [
+            173,
+            103,
+            825,
+            132
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Nitish Shirish Keskar and Richard Socher. Improving generalization performance by switching from adam to sgd. arXiv preprint arXiv:1712.07628, 2017. ",
+        "bbox": [
+            174,
+            138,
+            825,
+            167
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Diederik Kingma and Jimmy Ba. Adam: A method for stochastic optimization. In International Conference on Learning Representations, 2015. ",
+        "bbox": [
+            174,
+            174,
+            823,
+            203
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Ilya Loshchilov and Frank Hutter. Decoupled weight decay regularization. In International Conference on Learning Representations, 2019. URL https://openreview.net/forum?id= Bkg6RiCqY7. ",
+        "bbox": [
+            174,
+            209,
+            825,
+            252
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Mario Lucic, Karol Kurach, Marcin Michalski, Sylvain Gelly, and Olivier Bousquet. Are gans created equal? a large-scale study. In Advances in neural information processing systems, pp. 700–709, 2018. ",
+        "bbox": [
+            176,
+            258,
+            826,
+            301
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Andrew L. Maas, Raymond E. Daly, Peter T. Pham, Dan Huang, Andrew Y. Ng, and Christopher Potts. Learning word vectors for sentiment analysis. In Proceedings of the 49th Annual Meeting of the Association for Computational Linguistics: Human Language Technologies, pp. 142–150, Portland, Oregon, USA, June 2011. Association for Computational Linguistics. URL http: //www.aclweb.org/anthology/P11-1015. ",
+        "bbox": [
+            173,
+            308,
+            826,
+            380
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Rafael Gomes Mantovani, Tomáš Horváth, Ricardo Cerri, Sylvio Barbon Junior, Joaquin Vanschoren, André Carlos Ponce de de Carvalho, and Leon Ferreira. An empirical study on hyperparameter tuning of decision trees. arXiv preprint arXiv:1812.02207, 2018. ",
+        "bbox": [
+            178,
+            385,
+            823,
+            428
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Gábor Melis, Chris Dyer, and Phil Blunsom. On the state of the art of evaluation in neural language models. In International Conference on Learning Representations, 2018. URL https:// openreview.net/forum?id $=$ ByJHuTgA-. ",
+        "bbox": [
+            176,
+            434,
+            823,
+            477
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Philipp Probst, Anne-Laure Boulesteix, and Bernd Bischl. Tunability: Importance of hyperparameters of machine learning algorithms. Journal of Machine Learning Research, 20(53):1–32, 2019. URL http://jmlr.org/papers/v20/18-444.html. ",
+        "bbox": [
+            173,
+            483,
+            826,
+            526
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Herbert Robbins and Sutton Monro. A stochastic approximation method. The annals of mathematical statistics, pp. 400–407, 1951. ",
+        "bbox": [
+            173,
+            532,
+            823,
+            563
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Frank Schneider, Lukas Balles, and Philipp Hennig. DeepOBS: A deep learning optimizer benchmark suite. In International Conference on Learning Representations, 2019. URL https://openreview.net/forum?id ${ \\underline { { \\underline { { \\mathbf { \\Pi } } } } } } =$ rJg6ssC5Y7. ",
+        "bbox": [
+            176,
+            568,
+            821,
+            611
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "D. Sculley, Jasper Snoek, Alexander B. Wiltschko, and Ali Rahimi. Winner’s curse? on pace, progress, and empirical rigor. In 6th International Conference on Learning Representations, ICLR 2018, Vancouver, BC, Canada, April 30 - May 3, 2018, Workshop Track Proceedings, 2018. URL https://openreview.net/forum?id ${ \\underline { { \\underline { { \\mathbf { \\Pi } } } } } } =$ rJWF0Fywf. ",
+        "bbox": [
+            173,
+            617,
+            825,
+            674
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Vatsal Shah, Anastasios Kyrillidis, and Sujay Sanghavi. Minimum norm solutions do not always generalize well for over-parameterized problems. arXiv preprint arXiv:1811.07055, 2018. ",
+        "bbox": [
+            171,
+            680,
+            823,
+            710
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Ilya Sutskever, James Martens, George Dahl, and Geoffrey Hinton. On the importance of initialization and momentum in deep learning. In Sanjoy Dasgupta and David McAllester (eds.), Proceedings of the 30th International Conference on Machine Learning, volume 28 of Proceedings of Machine Learning Research, pp. 1139–1147, Atlanta, Georgia, USA, 17–19 Jun 2013. PMLR. URL http://proceedings.mlr.press/v28/sutskever13.html. ",
+        "bbox": [
+            173,
+            715,
+            826,
+            786
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "T. Tieleman and G. Hinton. Lecture 6.5—RmsProp: Divide the gradient by a running average of its recent magnitude. COURSERA: Neural Networks for Machine Learning, 2012. ",
+        "bbox": [
+            169,
+            792,
+            825,
+            821
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Jan N van Rijn and Frank Hutter. Hyperparameter importance across datasets. In Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pp. 2367–2376. ACM, 2018. ",
+        "bbox": [
+            171,
+            829,
+            825,
+            871
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Ashia C Wilson, Rebecca Roelofs, Mitchell Stern, Nati Srebro, and Benjamin Recht. The marginal value of adaptive gradient methods in machine learning. In Advances in Neural Information Processing Systems, pp. 4148–4158, 2017. ",
+        "bbox": [
+            174,
+            877,
+            825,
+            921
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "A ARCHITECTURES OF THE MODELS USED IN EXPERIMENTS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            103,
+            689,
+            118
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Along with the architectures examined by Schneider et al. (2019), we experiment with an additional network and dataset. We included an additional network into our experimental setup, as DEEPOBS does not contain an word level LSTM model. Our model uses a 32-dimensional word embedding table and a single layer LSTM with memory cell size 128, the exact architecture is given in Table 6. We experiment with the IMDB sentiment classification dataset (Maas et al., 2011). The dataset contains 50, 000 movie reviews collected from movie rating website IMDB. The training set has 25, 000 reviews, each labeled as positive or negative. The rest 25, 000 form the test set. We split $2 0 \\%$ of the training set to use as the development set. We refer the readers to DEEPOBS (Schneider et al., 2019) for the exact details of the other architectures used in this work. ",
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+        "page_idx": 10
+    },
+    {
+        "type": "table",
+        "img_path": "images/0c7e44d06b38fb2b2803fbaa20cc41643df41397d559494ff942319fecaaa33d.jpg",
+        "table_caption": [
+            "Table 6: Architecture of the LSTM network used for IMDb experiments "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Layer name</td><td>Description</td></tr><tr><td>Emb</td><td>Embedding Layer Vocabulary of 10000 [Embedding dimension: 32]</td></tr><tr><td>LSTM_1</td><td>LSTM Input size: 32 [Hidden dimension:128]</td></tr><tr><td>FC Layer</td><td>Linear(128 → 2)</td></tr><tr><td>Classifier</td><td>Softmax(2)</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "B $\\alpha$ - TUNABILITY ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "We provide additional methods to analyze tunability here. Let $p ( t )$ denote the best performance observed after using budget $t$ of hyperparameter optimization algorithm. We call an optimizer $\\alpha$ -tunable $( \\alpha \\in [ 0 , 1 ] )$ at $t$ if $p ( t ) \\geq \\alpha \\cdot p ( T )$ . Thus $\\alpha$ −tunability is the ratio of number of times the neural network needs to be retrained with optimizer’s hyperparameters being provided by an automatic method, to the total budget $T$ (maximum number of configurations tested). ",
+        "bbox": [
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+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "For each optimizer, we define its $\\alpha$ -tunability $\\zeta ( \\alpha ) = \\textstyle { \\frac { t } { T } }$ for $\\alpha \\in \\{ 0 . 9 , 0 . 9 5 , 0 . 9 9 \\}$ . This metric provides an intuitive and simple quantification of how easy it is to tune an optimizer to reach requisite performance. We extend $\\alpha$ –tunability to indicate the sharpness of the minima by computing the difference $\\Delta = \\zeta ( \\alpha _ { 1 } ) - \\zeta ( \\alpha _ { 2 } )$ where $\\alpha _ { 1 } > \\alpha _ { 2 }$ and term it Sharpness. In our experiments, we choose $\\alpha _ { 1 } = 0 . 9 9$ and $\\alpha _ { 2 } = 0 . 9$ . Sharpness $( \\Delta )$ is the relative time taken by the HPO to improve from $\\alpha _ { 2 }$ to $\\alpha _ { 1 }$ and thus quantifies the flatness of the minima in the space of hyperparameters. If the minima is sharper, then we expect random-search also takes a longer time to find it, thus the time required to go from $\\alpha _ { 1 }$ and $\\alpha _ { 2 }$ is higher. We provide Sharpness for our optimizers in table:7. ",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/a2bc9d68e6002bc7abd68cc4114b87e3b83f9edfb4213f4043faf628080e832b.jpg",
+        "table_caption": [
+            "Table 7: Sharpness for various optimizers examined. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>MNIST VAE</td><td>FMNIST2C2D</td><td>CIFAR100</td><td>CIFAR10</td><td>SVHN WRN</td><td>IMDBLSTM</td><td>FMNIST VAE</td><td>Quadratic Deep</td><td>Char RNN</td></tr><tr><td>Adagrad</td><td>92.0</td><td>99.0</td><td>63.0</td><td>95.0</td><td>10.0</td><td>97.0</td><td>91.0</td><td>66.0</td><td>95.0</td></tr><tr><td>Adam</td><td>80.0</td><td>98.0</td><td>40.0</td><td>91.0</td><td>71.0</td><td>93.0</td><td>90.0</td><td>75.0</td><td>87.0</td></tr><tr><td>Adam LR</td><td>83.0</td><td>96.0</td><td>71.0</td><td>94.0</td><td>98.0</td><td>70.0</td><td>95.0</td><td>93.0</td><td>97.0</td></tr><tr><td>SGD</td><td>98.0</td><td>95.0</td><td>35.0</td><td>93.0</td><td>98.0</td><td>81.0</td><td>94.0</td><td>6.0</td><td>47.0</td></tr><tr><td>SGDM</td><td>58.0</td><td>97.0</td><td>50.0</td><td>91.0</td><td>59.0</td><td>72.0</td><td>90.0</td><td>30.0</td><td>59.0</td></tr><tr><td>SGDMC</td><td>95.0</td><td>83.0</td><td>82.0</td><td>94.0</td><td>52.0</td><td>88.0</td><td>75.0</td><td>95.0</td><td>87.0</td></tr><tr><td>SGDMCWC</td><td>94.0</td><td>45.0</td><td>78.0</td><td>95.0</td><td>98.0</td><td>68.0</td><td>88.0</td><td>16.0</td><td>85.0</td></tr><tr><td>SGDMW</td><td>65.0</td><td>97.0</td><td>23.0</td><td>94.0</td><td>36.0</td><td>86.0</td><td>91.0</td><td>14.0</td><td>32.0</td></tr></table>",
+        "bbox": [
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+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "The above definition is not without faults. An optimizer’s $\\alpha$ -tunability depends only on how fast it can get close to its own best performance, a pitfall it shares with Probst et al. (2019). That is, an optimizer that peaks at the performance of a random classifier may be considered well-tunable because it reaches its peak performance in the first iteration. It is apparent from tables 7 and 4 that the top performance does not imply lower sharpness. Take the case of IMDB Bi-LSTM, the lowest sharpness is for $\\mathrm { S G D M ^ { C } W ^ { C } }$ , while the best performance is attained by AdamLR, implying that $\\mathrm { S G D M ^ { C } W ^ { C } }$ settled to a minima faster which isn’t necessarily better than the one AdamLR found. In other terms, the flatness of the minima does not indicate how deep it is. ",
+        "bbox": [
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+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "C PERFORMANCE ANALYSIS ",
+        "text_level": 1,
+        "bbox": [
+            176,
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+            195
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "We show the full performance plots of all variants of SGD experimented with, in figures 5, 6, 7. ",
+        "bbox": [
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "D HOW LIKELY ARE WE TO FIND GOOD CONFIGURATIONS? ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "A natural question that arises is: given a budget $K$ , what is the best optimizer one can pick? In other words, for a given budget what is probability of each optimizer finding the best configuration? We answer this with a simple procedure. We repeat the runs of HPO for a budget $K$ , and collect the optimizer that gave the best result in each of those runs. Using the classical definition of probability, we compute the required quantity. We plot the computed probability in Figure 8. It is very evident for nearly all budgets, AdamLR is always the best option for 4 of the problems. SGD variants emerge to be better options for CIFAR-100 and Char-RNN at later stages of HPO. For some of the problems like VAEs, LSTM, it is very obvious that AdamLR is nearly always the best choice. Thus further strengthens our hypothesis that adaptive gradient methods are more tunable, especially in constrained HPO budget scenarios. ",
+        "bbox": [
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+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "E TUNABILITY BY COMPUTATION BUDGET ",
+        "text_level": 1,
+        "bbox": [
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+            438,
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+            454
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "In our experiments so far, we defined tunability in terms of number of hyperparameter configurations. However, due to varying convergence speeds, different optimizers require varying amounts of time/epochs per configuration. We choose to work with number of epochs per configuration, as it is a hardware agnostic measure, but still indicates the relative time required. To incorporate epochs into our definition of tunability, we conduct the following analysis: For each dataset, we consider minimum total epochs for running all 100 trials across all optimizers, and consider it as the (virtual) maximum epoch budget $e _ { \\mathrm { m a x } }$ , i.e., we disregard all trials after this point. We divide this maximum into $K = 1 0 0$ intervals $\\begin{array} { r } { I _ { i } = \\frac { e _ { \\mathrm { m a x } } \\cdot i } { K } , 1 \\le i \\le K } \\end{array}$ . We modify the definition of $\\omega$ -tunability from Section 2.2 as follows: ",
+        "bbox": [
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+            468,
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "$\\omega ^ { e p o c h }$ -tunability’s Definition. Let $( \\mathbf { \\boldsymbol { \\theta } } _ { t } , \\mathbf { \\mathcal { L } } ( \\mathbf { \\boldsymbol { \\theta } } _ { t } ) )$ be the incumbents (best performance attained till $t$ ) of the HPO algorithm at iteration $t$ , $e _ { t }$ be the total number of epochs required until iteration $t$ has finished. We define $\\tilde { \\mathcal { L } } _ { i } = \\operatorname* { m a x } _ { e _ { t } \\leq I _ { i } } \\mathcal { L } _ { t }$ as the maximum performance among all configurations that have finished before interval $I _ { t }$ , where $\\mathcal { L } _ { 0 } = e _ { 0 } = 0 .$ . For $w _ { i } > 0 \\forall t$ and $\\textstyle \\sum _ { t } w _ { i } < \\infty$ , we define $\\omega ^ { e p o c h }$ -tunability as ",
+        "bbox": [
+            173,
+            597,
+            825,
+            679
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "equation",
+        "img_path": "images/d8ef7f74732f8027c5138dc9d14fe988e70163e8b780a4783bd8eda51df62a3f.jpg",
+        "text": "$$\n\\omega ^ { e p o c h } \\ – t u n a b i l i t y = \\sum _ { i = 1 } ^ { K } \\omega _ { i } \\tilde { \\mathcal { L } } _ { i }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            400,
+            676,
+            598,
+            720
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Please note that due to the case where no trial has finished before the first interval has concluded, we assign a performance of 0 for that task to that interval (bin). The above definition does not lend itself to VAE tasks, as an appropriate value there is $\\infty$ . We, therefore, report the results for all classification problems in Table 8, where we use the same weighting schemes (CPE, CPU, and CPL) as before. To better understand the results, we also report the average number of epochs each configuration takes on average. Comparing the relative performances of optimizers to the results from Table 5, we can observe that considering $\\omega ^ { e p o c h }$ yields to the same conclusions as before, and even amplifies Adam’s strengths: The performance gap to SGD variants widens in the cases where Adam(LR) was already better (FMNIST, IMDB, Char-RNN), and narrows considerably in the cases where an SGD variant was previously better (CIFAR-10, CIFAR-100, WRN-16). On CIFAR-100 and WRN-16, this even results in Adam outperforming the SGD variants slightly. Considering the average number of epochs, the results can easily be explained by the fact that the adaptive gradient methods tend to take less time to converge. ",
+        "bbox": [
+            173,
+            729,
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "table",
+        "img_path": "images/ac340fa76c075be54b72d2b6715bb9c569dccc0a852d43abf0d551a148208dfd.jpg",
+        "table_caption": [
+            "Table 8: $\\omega ^ { e p o c h }$ -tunability performance of optimizers on the classification tasks for CPE, CPU, and CPL weighting schemes. We additionally provide the average number of epochs required by each optimizer for a single configuration. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Optimizer</td><td>CPE</td><td>CPU</td><td>CPL</td><td>Epochs</td></tr><tr><td>Adagrad</td><td>89.2</td><td>90.3</td><td>91.4</td><td>33.0</td></tr><tr><td>Adam</td><td>90.2</td><td>91.0</td><td>91.8</td><td>24.1</td></tr><tr><td>AdamLR</td><td>90.4</td><td>91.1</td><td>91.9</td><td>19.5</td></tr><tr><td>SGD</td><td>87.4</td><td>89.2</td><td>90.9</td><td>34.5</td></tr><tr><td>SGDM</td><td>88.1</td><td>89.6</td><td>91.1</td><td>33.6</td></tr><tr><td>SGDMC</td><td>88.6</td><td>89.8</td><td>91.0</td><td>28.2</td></tr><tr><td>SGDMCWC</td><td>89.1</td><td>90.1</td><td>91.1</td><td>27.4</td></tr><tr><td>SGDMW</td><td>88.0</td><td>89.5</td><td>91.0</td><td>32.4</td></tr></table>",
+        "bbox": [
+            176,
+            422,
+            387,
+            516
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "table",
+        "img_path": "images/16463771dde50267dc24d6f185dfacd203e181c8bcd4ad9d016ee3529cea546a.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "8.c: CIFAR 100. Higher the better "
+        ],
+        "table_body": "<table><tr><td>Optimizer</td><td>CPE</td><td>CPU</td><td>CPL</td><td>Epochs</td></tr><tr><td>Adagrad</td><td>30.1</td><td>31.6</td><td>33.1</td><td>23.7</td></tr><tr><td>Adam</td><td>36.0</td><td>39.4</td><td>42.8</td><td>36.8</td></tr><tr><td>AdamLR</td><td>41.8</td><td>42.8</td><td>43.8</td><td>24.6</td></tr><tr><td>SGD</td><td>23.3</td><td>26.6</td><td>29.9</td><td>91.8</td></tr><tr><td>SGDM</td><td>30.5</td><td>34.7</td><td>39.0</td><td>80.6</td></tr><tr><td>SGDMC</td><td>36.9</td><td>39.8</td><td>42.7</td><td>68.7</td></tr><tr><td>SGDMCWC</td><td>34.1</td><td>36.8</td><td>39.4</td><td>71.7</td></tr><tr><td>SGDMW</td><td>21.5</td><td>25.6</td><td>29.7</td><td>102.3</td></tr></table>",
+        "bbox": [
+            611,
+            422,
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+            516
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "table",
+        "img_path": "images/6c13e698224bd9b905ffd5029c94fb260d8a7aaecf00cf5c96b09fd4da5adc61.jpg",
+        "table_caption": [
+            "8.a: FMNIST 2C2D. Higher is better ",
+            "8.b: CIFAR 10. Higher is better "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Optimizer</td><td>CPE</td><td>CPU</td><td>CPL</td><td>Epochs</td></tr><tr><td>Adagrad</td><td>74.2</td><td>75.9</td><td>77.5</td><td>36.9</td></tr><tr><td>Adam</td><td>75.6</td><td>77.5</td><td>79.3</td><td>27.7</td></tr><tr><td>AdamLR</td><td>78.2</td><td>79.1</td><td>80.0</td><td>24.9</td></tr><tr><td>SGD</td><td>73.4</td><td>75.6</td><td>77.9</td><td>49.6</td></tr><tr><td>SGDM</td><td>74.3</td><td>76.5</td><td>78.8</td><td>46.9</td></tr><tr><td>SGDMC</td><td>75.6</td><td>77.6</td><td>79.6</td><td>44.4</td></tr><tr><td>SGDMCWC</td><td>78.2</td><td>79.9</td><td>81.7</td><td>47.6</td></tr><tr><td>SGDMW</td><td>75.5</td><td>78.1</td><td>80.6</td><td>52.4</td></tr></table>",
+        "bbox": [
+            393,
+            422,
+            602,
+            516
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "table",
+        "img_path": "images/d24d5b25a8e33121dc99e7c69b53396638107807c969e5d001c7276937b8f39b.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "8.d: IMDB. Higher is better "
+        ],
+        "table_body": "<table><tr><td>Optimizer</td><td>CPE</td><td>CPU</td><td>CPL</td><td>Epochs</td></tr><tr><td>Adagrad</td><td>83.1</td><td>84.1</td><td>85.2</td><td>34.4</td></tr><tr><td>Adam</td><td>82.1</td><td>83.7</td><td>85.2</td><td>31.2</td></tr><tr><td>AdamLR</td><td>84.8</td><td>85.5</td><td>86.2</td><td>28.6</td></tr><tr><td>SGD</td><td>65.8</td><td>67.7</td><td>69.6</td><td>42.2</td></tr><tr><td>SGDM</td><td>72.2</td><td>74.5</td><td>76.9</td><td>37.2</td></tr><tr><td>SGDMC</td><td>77.9</td><td>79.3</td><td>80.8</td><td>32.3</td></tr><tr><td>SGDMCWC</td><td>71.3</td><td>75.0</td><td>78.6</td><td>109.7</td></tr><tr><td>SGDMW</td><td>64.6</td><td>69.6</td><td>74.6</td><td>119.0</td></tr></table>",
+        "bbox": [
+            176,
+            539,
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "table",
+        "img_path": "images/6f225ccd52c014e054510b9bbb12bf311ddd15733edd19c0fc79ac4865fc9866.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "8.e: WRN-16(4). Higher is better "
+        ],
+        "table_body": "<table><tr><td>Optimizer</td><td>CPE</td><td>CPU</td><td>CPL</td><td>Epochs</td></tr><tr><td>Adagrad</td><td>93.8</td><td>94.4</td><td>95.0</td><td>19.7</td></tr><tr><td>Adam</td><td>92.0</td><td>93.5</td><td>95.1</td><td>24.3</td></tr><tr><td>AdamLR</td><td>94.5</td><td>95.0</td><td>95.4</td><td>17.2</td></tr><tr><td>SGD</td><td>92.6</td><td>93.8</td><td>95.1</td><td>29.9</td></tr><tr><td>SGDM</td><td>91.9</td><td>93.6</td><td>95.3</td><td>29.2</td></tr><tr><td>SGDMC</td><td>93.3</td><td>94.2</td><td>95.2</td><td>26.0</td></tr><tr><td>SGDMCWC</td><td>92.5</td><td>94.0</td><td>95.4</td><td>31.8</td></tr><tr><td>SGDMW</td><td>91.6</td><td>93.4</td><td>95.3</td><td>33.5</td></tr></table>",
+        "bbox": [
+            395,
+            539,
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+            631
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "table",
+        "img_path": "images/a91933f11699460917f4f2e7c20ca787b527a53e29917d966f174f1459e56ed0.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "8.f: Char-RNN. Higher is better "
+        ],
+        "table_body": "<table><tr><td>Optimizer</td><td>CPE</td><td>CPU</td><td>CPL Epochs</td></tr><tr><td>Adagrad</td><td>54.5</td><td>55.5</td><td>56.6 166.6</td></tr><tr><td>Adam</td><td>53.7</td><td>55.3</td><td>57.0 131.0</td></tr><tr><td>AdamLR</td><td>55.9</td><td>56.7</td><td>57.4 170.9</td></tr><tr><td>SGD</td><td>38.1</td><td>40.8</td><td>43.4 183.2</td></tr><tr><td>SGDM</td><td>48.5</td><td>51.8</td><td>55.2 188.3</td></tr><tr><td>SGDMC</td><td>53.3</td><td>55.6</td><td>58.0 194.5</td></tr><tr><td>SGDMCWC</td><td>51.7</td><td>54.2</td><td>56.6 197.3</td></tr><tr><td>SGDMW</td><td>42.2</td><td>45.6</td><td>49.1 184.0</td></tr></table>",
+        "bbox": [
+            612,
+            539,
+            820,
+            631
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/1638032d7d15d84e395e0faa09da5b7438cc54ad9d1aeb688caa6a26c9879864.jpg",
+        "image_caption": [
+            "Figure 4: Performance analysis of various experiments. We plot the on the $\\mathbf { X }$ -axis the number of the hyperparameter configuration searches, on the y-axis the appropriate performance. ",
+            "4.a: CIFAR-10 evolution "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            178,
+            167,
+            820,
+            380
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "image",
+        "img_path": "images/84dcfcf92124dfc11105f29ebc9b20accf8298aebe9565b74e6f5a71ac46bc85.jpg",
+        "image_caption": [
+            "4.b: CIFAR-100 evolution "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            176,
+            410,
+            820,
+            621
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "image",
+        "img_path": "images/b57494dc15a0b20c175961de79e9089054bc521b0b7fe4af1900ef95ac8bff49.jpg",
+        "image_caption": [
+            "Figure 5: Performance analysis of various experiments. We plot the on the $\\mathbf { X } ^ { } -$ -axis the number of the hyperparameter configuration searches, on the y-axis the appropriate performance on a log scale "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            178,
+            650,
+            820,
+            845
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "image",
+        "img_path": "images/6fc13ff033e20baef240f395612d759fafce569eab04436ea8f39c39121c080b.jpg",
+        "image_caption": [
+            "6.a: Bi-LSTM evolution "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            176,
+            138,
+            820,
+            351
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "image",
+        "img_path": "images/108350007f0e2d6fee04b87a5a958acacad0e5df60ea42e53d3cdf68e741896f.jpg",
+        "image_caption": [
+            "6.c: Tolstoi Char-RNN evolution ",
+            "Figure 6: Performance analysis of various experiments. We plot the on the $\\mathbf { X }$ -axis the number of the hyperparameter configuration searches, on the y-axis the appropriate performance on a log scale "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            173,
+            376,
+            821,
+            829
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "image",
+        "img_path": "images/31d69d1c9650e9afbef7b1ae9e0ddd3bb8cebab8351627a42fc678cf71fc52e5.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            174,
+            138,
+            820,
+            351
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "image",
+        "img_path": "images/d4a03ff2add522127f868a9ad798425c2e1eac934abf07a87607853110ed674c.jpg",
+        "image_caption": [
+            "7.a: MNIST-VAE evolution "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            173,
+            375,
+            820,
+            587
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "image",
+        "img_path": "images/94fc6587ea0272557615517ed8879a09bd2ef787bc3d6f9306e31029aaba6363.jpg",
+        "image_caption": [
+            "7.b: MNIST-VAE evolution ",
+            "7.c: Quadratic deep evolution "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            176,
+            612,
+            820,
+            824
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "Figure 7: Performance analysis of various experiments. We plot the on the $\\mathbf { X }$ -axis the number of the hyperparameter configuration searches, on the y-axis the appropriate performance on a log scale ",
+        "bbox": [
+            171,
+            856,
+            825,
+            885
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "image",
+        "img_path": "images/f40a5ba4ff8ec878621de75cb452f9ebfd5499757561a53052e0f6724f2eecc7.jpg",
+        "image_caption": [
+            "Figure 8: Which optimizer for which budget? Given a tuning budget $K$ $\\scriptstyle { \\dot { x } }$ -axis), the stacked area plots above show how likely each optimizer (colored bands) is to yield the best result after $K$ steps of hyperparameter optimization. For example, for the IMDB LSTM problem, for a small budget, ‘AdamLR’ is the best choice (with $\\sim 0 . 8$ probability), whereas for a larger search budget $> 5 0$ , tuning the additional parameters of ‘Adam’ is likely to pay off. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            173,
+            311,
+            820,
+            625
+        ],
+        "page_idx": 16
+    }
+]

parse/train/HJGkisCcKm/HJGkisCcKm.md

@@ -0,0 +1,260 @@
+# A UNIVERSAL MUSIC TRANSLATION NETWORK
+
+Noam Mor Facebook AI Research noam.mor@gmail.com
+
+Lior Wolf & Adam Polyak Facebook AI Research & Tel Aviv Uni. wolf,adampolyak@fb.com
+
+Yaniv Taigman Facebook AI Research yaniv@fb.com
+
+# ABSTRACT
+
+We present a method for translating music across musical instruments and styles. This method is based on unsupervised training of a multi-domain wavenet autoencoder, with a shared encoder and a domain-independent latent space that is trained end-to-end on waveforms. Employing a diverse training dataset and large net capacity, the single encoder allows us to translate also from musical domains that were not seen during training. We evaluate our method on a dataset collected from professional musicians, and achieve convincing translations. We also study the properties of the obtained translation and demonstrate translating even from a whistle, potentially enabling the creation of instrumental music by untrained humans.
+
+# 1 INTRODUCTION
+
+Humans have always created music and replicated it – whether it is by singing, whistling, clapping, or, after some training, playing improvised or standard musical instruments. This ability is not unique to us, and there are many other vocal mimicking species that are able to repeat music from hearing. Music is also one of the first domains to be digitized and processed by modern computers and algorithms. It is, therefore, somewhat surprising that in the core music task of mimicry, AI is still much inferior to biological systems.
+
+In this work, we present a novel way to produce convincing musical translation between instruments and styles. For example1, we convert the audio of a Mozart symphony performed by an orchestra to an audio in the style of a pianist playing Beethoven. Our ability builds upon two technologies that have recently become available: (i) the ability to synthesize high quality audio using autoregressive models, and (ii) the recent advent of methods that transform between domains in an unsupervised way. The first technology allows us to generate high quality and realistic audio and thanks to the teacher forcing technique, autoregressive models are efficiently trained as decoders. The second family of technologies contributes to the practicality of the solution, since posing the learning problem in the supervised setting, would require a parallel dataset of different musical instruments.
+
+In our architecture, we employ a single, universal, encoder and apply it to all inputs (universal here means that a single encoder can address all input music, allowing us to achieve capabilities that are known as universal translation). In addition to the advantage of training fewer networks, this also enables us to convert from musical domains that were not heard during training to any of the domains encountered.
+
+The key to being able to train a single encoder architecture, is making sure that the domain-specific information is not encoded. We do this using a domain confusion network that provides an adversarial signal to the encoder. In addition, it is important for the encoder not to memorize the input signal but to encode it in a semantic way. We achieve this by distorting the input audio by random local pitch modulation. During training, the network is trained as a denoising autoencoder, which recovers the undistorted version of the original input. Since the distorted input is no longer in the musical domain of the output, the network learns to project out-of-domain inputs to the desired output domain. In addition, the network no longer benefits from memorizing the input signal and employs a higher-level encoding.
+
+Asked to convert one musical instrument to another, our network shows a level of performance that seems to approach that of musicians. When controlling for audio quality, which is still lower for generated music, it is many times hard to tell which is the original audio file and which is the output of the conversion that mimics a completely different instrument. The network is also able to successfully process unseen musical instruments such as drums, or other sources, such as whistles.
+
+# 2 PREVIOUS WORK
+
+Domain Transfer Recently, there has been a considerable amount of work, mostly on images and text, which performs unsupervised translation between domains $\mathcal { A }$ and $\boldsymbol { B }$ , without being shown any matching pairs, i.e., in a completely unsupervised way. Almost all of this work employs GAN constraints (Goodfellow et al., 2014), in order to ensure a high level of indistinguishability between the translations of samples in $A$ and samples from the domain $B$ . In our work, the output is generated by an autoregressive model and training takes place using the ground truth output of the previous time steps (“teacher forcing”), instead of the predicted ones. A complete autoregressive inference is only done during test time, and it is not practical to apply such inference during training in order to get a realistic generated (“fake”) sample for the purpose of training the GAN.
+
+Another popular constraint is that of circularity, namely that by mapping from $\mathcal { A }$ to $\boldsymbol { B }$ and back to $\mathcal { A }$ a reconstruction of the original sample is obtained (Kim et al., 2017; Zhu et al., 2017; Yi et al., 2017). In our work, for the same reason mentioned above, the output during training does not represent the future test time output, and such a constraint is unrealistic. An application of circularity in audio was present in (Kaneko & Kameoka, 2017), where a non-autoregressive model between vocoder features is used to convert between voices in an unsupervised way.
+
+Cross domain translation is not restricted to a single pair of domains. The recent StarGAN (Choi et al., 2017) method creates multiple cycles for mapping between multiple (more than two) domains. The method employs a single generator that receives as input the source image as well as the specification of the target domain. It then produces the analog “fake” image from the target domain. Our work employs multiple decoders, one per domain, and attempts to condition a single decoder on the selection of the output domain failed to produce convincing results.
+
+UNIT (Liu et al., 2017) employs an encoder-decoder pair per each domain, where the latent spaces of the domains are assumed to be shared. This is achieved by sharing the network layers that are distant from the image (the top layers of the encoder and the bottom layers of the decoder), similarly to CoGAN (Liu & Tuzel, 2016). Cycle-consistency is also added, and structure is added to the latent space using a variational autoencoder (Kingma & Welling, 2014) loss terms. Our method employs a single encoder, which eliminates the need for many of the associated constraints. In addition, we do not impose a VAE loss term (Kingma & Welling, 2014) on the latent space of the encodings and instead employ a domain confusion loss (Ganin et al., 2016). The work of Louizos et al. (2015) investigates the problem of learning invariant representations by employing the Maximum Mean Discrepancy (MMD), which we do not use.
+
+Audio Synthesis WaveNet (van den Oord et al., 2016) is an autoregressive model that predicts the probability distribution of the next sample, given the previous samples and an input conditioning signal. Its generated output is currently considered of the highest naturalness, and is applied in a range of tasks. In (Rethage et al., 2017), the authors have used it for denoising waveforms by predicting the middle ground-truth sample from its noisy input support. Recent contributions in Text-To-Speech(TTS) (Ping et al., 2018; Shen et al., 2018) have successfully conditioned wavenet on linguistic and acoustic features to obtain state of the art performance.
+
+In VQ-VAE (van den Oord et al., 2017), voice conversion was obtained by employing a variational autoencoder that produces a quantized latent space that is conditioned on the speaker identity. Similar to our work, the decoder is based on WaveNet. However, we impose a greater constraint on the latent space by (a) having a universal encoder, forcing the embeddings of all domains to lie in the same space, yet (b) training a separate reconstructing decoder for each domain, provided that (c) the latent space is domain independent, thereby reducing source-target pathways memorization, which is also accomplished by (d) employing augmentation to distort the input signal. Invariance is achieved in VQ-VAE through the strong bottleneck effect achieved by discretization. Despite some effort, we were not able to use a discrete latent space here.
+
+![](images/8b9792730bd1bbfaf4808011743662447a7857a2b456112cf8a61abcd73a70b2.jpg)  
+Figure 1: (a) The schematic architecture of our translation network. The confusion term (marked by the dashed line) is employed only during training. $E$ is the shared encoder, $C$ is the domain classification network employed in the domain confusion term, $D ^ { i }$ are the various decoders. (b) A detailed depiction of our architecture. ‘NC’ indicates non-causal convolution. ‘1x1’ indicates a 1-D convolution with kernel size 1.
+
+Recently, Dieleman et al. (2018) explored discretization as a method to capture long-range dependencies in unconditioned music generation, for up to 24 seconds. We focus on translation, and the conditioning on the source signal carries some long-range information on the development of the music. Consider an analogy to a myopic language translation system, where the input is a story in English and the output is a story in Spanish. Even if the translation occurs one sentence at a time, the main theme of the story is carried by the “conditioning” on the source text.
+
+The architecture of the autoencoder we employ is the wavenet-autoencoder presented in (Engel et al., 2017). In comparison to this work, our inputs are not controlled and are collected from consumer media. Our overall architecture differs in that multiple decoders and an additional auxiliary network, which is used for disentangling the domain information from the other aspects of the music representation, are trained and by the addition of an important augmentation step.
+
+In the supervised learning domain, an audio style transfer between source and target spectrograms was performed with sequence-to-sequence recurrent networks (Haque et al., 2018). This method requires matching pairs of samples played on different instruments. In another fully supervised work (Hadjeres & Pachet, 2017), a graphical model aimed at modeling polyphonic tones of Bach was trained on notes, capturing the specificity of Bach’s chorales. This model is based on RNNs and requires a large corpus of notes of a particular instrument produced with a music editor.
+
+Style Transfer Style transfer is often confused with domain translation and the distinction is not always clear. In the task of style transfer, the “content” remains the same between the input and the output, but the ”style” is modified. Notable contributions in the field include (Gatys et al., 2016; Ulyanov et al., 2016; Johnson et al., 2016), which synthesize a new image that minimizes the content loss with respect to the content-donor sample and the style loss with respect to one or more samples of a certain style. The content loss is based on comparing the activations of a network training for an image categorization task. The style loss compares the statistics of the activations in various layers of the categorization layer. An attempt at audio style transfer is described in (Barry & Kim, 2018).
+
+Concatenative Synthesis In the computer music and audio effects literature, the conversion task we aim to solve is tackled by concatenating together short pieces of audio from the target domain, such that the output audio resembles the input audio from the source domain Verfaille & Arfib (2000); Schwarz (2006); Zils & Pachet (2001); Simon et al. (2005). The method has been extensively researched, see the previous work section of Nuanain et al. (2017) and the online resource of Schwarz ´ (2018). A direct comparison to such methods is challenging, since many of the methods have elaborate interfaces with many tunable parameters that vary from one conversion task to the next. To the extent possible, we compare with some of the published results in Sec. 4.2, obtaining what we believe to be clearly superior results.
+
+# 3 METHOD
+
+Our domain translation method is based on training multiple autoencoder pathways, one per musical domain, such that the encoders are shared. During training, a softmax-based reconstruction loss is applied to each domain separately. The input data is randomly augmented, prior to applying the encoder, in order to force the network to extract high-level semantic features, instead of simply memorizing the data. In addition, a domain confusion loss (Ganin et al., 2016) is applied to the latent space to ensure that the encoding is not domain-specific. A diagram of the translation architecture is shown in Fig. 1 (a).
+
+# 3.1 WAVENET AUTOENCODER
+
+We reuse an existing autoencoder architecture that is based on a WaveNet decoder and a WaveNetlike dilated convolution encoder (Engel et al., 2017). The WaveNet of each decoder is conditioned on the latent representation produced by the encoder. In order to reduce the inferencetime, the nv-wavenet CUDA kernels provided by NVIDIA ( https://github.com/NVIDIA/ nv-wavenet) were used after modification to better match the architecture suggested by van den Oord et al. (2016), as described below.
+
+The encoder is a fully convolutional network that can be applied to any sequence length. The network has three blocks of ten residual-layers, a total of thirty layers. Each residual-layer contains a RELU nonlinearity, a non-causal dilated convolution with an increasing kernel size, a second RELU, and a $1 \times 1$ convolution followed by the residual summation of the activations before the first RELU. There is a fixed width of 128 channels. After the three blocks, there is an additional $1 \times 1$ layer. An average pooling with a kernel size of 50 milliseconds (800 samples) follows in order to obtain an encoding in $\mathbb { R } ^ { 6 \bar { 4 } }$ , which implies a temporal down sampling by a factor of $\times 1 2 . 5$ .
+
+The encoding is upsampled temporally to the original audio rate, using nearest neighbor interpolation and is used to condition a WaveNet decoder. The conditioning signal is passed through a $1 \times 1$ layer that is different for each WaveNet layer. The audio (both input and output) is quantized using 8-bit mu-law encoding, similarly to both (van den Oord et al., 2016; Engel et al., 2017), which results in some inherent loss of quality. The WaveNet decoder has either four blocks of 10 residual-layers and a resulting receptive field of 250 milliseconds (4,093 samples), as in Engel et al. (2017), or 14 layer blocks and a much larger receptive field of 4 seconds. Each residual-layer contains a causal dilated convolution with an increasing kernel size, a gated hyperbolic tangent activation, a $1 \times 1$ convolution followed by the residual summation of the layer input, and a $1 \times 1$ convolution layer which introduces a skip connection. Each residual-layer is conditioned on the encoding described above. The summed skip connections are passed through two fully connected layers and a softmax activation to output the next timestep probability. A detailed diagram of the WaveNet autoencoder is shown in Fig. 1 (b).
+
+We modify the fast nv-wavenet CUDA inference kernels, which implement the architecture suggested by Ping et al. (2018), and create efficient WaveNet kernels that implement the WaveNet architecture suggested by Engel et al. (2017). Specifically, we make the following modifications to nv-wavenet: (i) we add initialization of skip connections with previous WAV samples, (ii) we increase the kernel capacity to support 128 residual channels and (iii) we also add the conditioning to the last fully connected layer.
+
+# 3.2 AUDIO INPUT AUGMENTATION
+
+In order to improve the generalization capability of the encoder, as well as to enforce it to maintain higher-level information, we employ a dedicated augmentation procedure that changes the pitch locally. The resulting audio is of a similar quality but is slightly out of tune.
+
+Specifically, we perform our training on segments of one second length. For augmentation, we uniformly select a segment of length between 0.25 and 0.5 seconds, and modulate its pitch by a random number between -0.5 and 0.5 of half-steps, using librosa (McFee et al., 2015).
+
+# 3.3 TRAINING AND THE LOSSES USED
+
+Let $s ^ { j }$ be an input sample from domain $j = 1 , 2 , \dots , k ,$ $k$ being the number of domains employed during training. Let $E$ be the shared encoder, and $D ^ { j }$ the WaveNet decoder for domain $j$ . Let $C$ be the domain classification network, and $O ( s , r )$ be the random augmentation procedure applied to a sample $s$ with a random seed $r$ .
+
+The network $C$ predicts which domain the input data came from, based on the latent vectors. It applies three 1D-convolution layers, with the ELU (Clevert et al., 2017) nonlinearity. The last layer projects the vectors to dimension $k$ and the vectors are subsequently averaged to a single $\mathbb { R } ^ { k }$ vector. A detailed diagram of network $C$ is shown as part of Fig. 1 (b).
+
+During training, the domain classification network $C$ minimizes the classification loss
+
+$$
+\Omega = \sum _ { j } \sum _ { s ^ { j } } \operatorname { \mathbb { E } } _ { r } \mathcal { L } ( C ( E ( O ( s ^ { j } , r ) ) ) , j ) ,
+$$
+
+and the music to music autoencoders $j = 1 , 2 , \dots$ are trained with the loss
+
+$$
+- \lambda \Omega + \sum _ { j } \sum _ { s ^ { j } } \operatorname { \mathbb { E } } \mathcal { L } ( D ^ { j } ( E ( O ( s ^ { j } , r ) ) ) , s ^ { j } )
+$$
+
+where $\mathcal { L } ( o , y )$ is the cross entropy loss applied to each element of the output $o$ and the corresponding element of the target $y$ separately. Note that the decoder $D ^ { j }$ is an autoregressive model that is conditioned on the output of $E$ . During training, the autoregressive model is fed the target output $s ^ { j }$ from the previous time-step, instead of the generated output.
+
+# 3.4 NETWORK DURING INFERENCE
+
+To perform the actual transformation from a sample $s$ from any domain, even from an unseen musical domain, to output domain $j$ , we apply the autoencoder of domain $j$ to it, without applying the distortion. The new sample $\hat { s } ^ { j }$ is, therefore, given as $D ^ { j } ( E ( s ) )$ . The bottleneck during inference is the WaveNet autoregressive process, which is optimized by the dedicated CUDA kernels.
+
+# 4 EXPERIMENTS
+
+We conduct music translation experiments, using a mix of human evaluation and qualitative analysis, in order to overcome the challenges of evaluating generative models. The experiments were done in two phases. In the first phase, described in an earlier technical report (Mor et al., 2018), we train our network on six arbitrary classical musical domains: (i) Mozart’s symphonies conducted by Karl Bohm, (ii) Haydn’s string quartets, performed by the Amadeus Quartet, (iii) J.S Bach’s cantatas for ¨ orchestra, chorus and soloists, (iv) J.S Bach’s organ works, (v) Beethoven’s piano sonatas, performed by Daniel Barenboim, and (vi) J.S Bach’s keyboard works, played on Harpsichord. The music recordings by Bach (iii,iv,vi) are from the Teldec 2000 Complete Bach collection.
+
+In the second phase, in order to allow reproducibility and sharing of the code and models, we train on audio data from MusicNET (Thickstun et al., 2017). Domains were chosen as the largest domains that show variability between composers and instruments. The following six domains were selected: (i) J.S Bach’s suites for cello, (ii) Beethoven’s piano sonatas, (iii) Cambini’s Wind Quintet, (iv) J.S Bach’s fugues, played on piano, (v) Beethoven’s violin sonatas and (vi) Beethoven’s string quartet. This public dataset is somewhat smaller than the data used in phase one.
+
+The phases differ in the depth of the decoders: in the first phase, we employed blocks of ten layers, while in the second, we shifted to larger receptive fields and blocks of 14. The training and test splits are strictly separated by dividing the tracks (or audio files) between the two sets. The segments used in the evaluation experiments below were not seen during training. During training, we iterate over the training domains, such that each training batch contains 16 randomly sampled one second samples from a single domain. Each batch is first used to train the domain classification network $C$ , and then to train the universal encoder and the domain decoder, given the updated discriminator.
+
+The method was implemented in the PyTorch framework, and trained on eight Tesla V100 GPUs for a total of 6 days. We used the ADAM optimization algorithm with a learning rate of $1 0 ^ { - 3 }$ and a decay factor of 0.98 every 10,000 samples. We weighted the confusion loss with $\lambda = 1 0 ^ { - 2 }$ .
+
+Table 1: MOS scores (mean $\pm$ SD) for the conversion tasks.   
+
+<table><tr><td rowspan="2">Converter</td><td colspan="2">Harpsichord→Piano</td><td colspan="2">Orchestra-→ Piano</td><td colspan="2">New domains-→ Piano</td></tr><tr><td>Audio quality</td><td>Translation success</td><td>Audio quality</td><td>Translation success</td><td>Audio quality</td><td>Translation success</td></tr><tr><td>Musician E</td><td>3.89 ± 1.06</td><td>4.10± 0.94</td><td>4.02± 0.81</td><td>4.12± 0.97</td><td>4.44±0.82</td><td>4.13± 0.83</td></tr><tr><td>Musician M</td><td>3.82 ± 1.18</td><td>3.75± 1.17</td><td>4.13± 0.89</td><td>4.12± 0.98</td><td>4.48±0.72</td><td>3.97± 0.88</td></tr><tr><td>Musician A</td><td>3.69 ± 1.08</td><td>3.91± 1.16</td><td>4.06± 0.86</td><td>3.99± 1.08</td><td>4.53±0.79</td><td>3.93± 0.95</td></tr><tr><td>Our</td><td>2.95 ± 1.18</td><td>3.07± 1.30</td><td>2.56± 1.04</td><td>2.86± 1.16</td><td>2.36±1.17</td><td>3.18± 1.14</td></tr></table>
+
+# 4.1 EVALUATION OF TRANSLATION QUALITY
+
+The first set of experiments compared the method to human musicians using the phase one network. Since human musicians, are equipped by evolution with music skills, selected among their peers according to their talent, and who have trained for decades, we do not expect to do better than humans at this point. To perform this comparsion, music from domain $X$ was converted to piano, for various $X$ . The piano was selected for practical reasons: pianists are in higher availability than other musicians and a piano is easier to produce than, e.g., an orchestra.
+
+Three professional musicians with a diverse background were employed for the conversion task: E, who is a conservatory graduate with an extensive background in music theory and piano performance, and also specializes in transcribing music; M, who is a professional producer, composer, pianist and audio engineer, who is an expert in musical transcription; and A who is a music producer, editor, and a skilled player of keyboards and other instruments.
+
+The task used for comparison was to convert 60 segments of five seconds each to piano. Three varied sources were used. 20 of the segments were from Bach’s keyboard works, played on a Harpsichord, and 20 others were from Mozart’s 46 symphonies conducted by Karl Bohm, which are ¨ orchestral works. The last group of 20 segments was a mix of three different domains that were not encountered during training – Swing Jazz, metal guitar riffs, and instrumental Chinese music. The 60 music segments were encoded by the universal encoder and decoded by the WaveNet trained on Beethoven’s piano sonatas, as performed by Daniel Barenboim.
+
+In order to compare between the conversions, we employed human evaluation, which is subjective and could be a mix of the assessment of the audio quality and the assessment of the translation itself. This limits the success of the automatic method, since the quality of the algorithm’s output is upper bounded by the neural network architecture and cannot match that of a high quality recording.
+
+Since there is a trade-off between the fidelity to the original piece and the ability to create audio in the target domain, we present two scores: audio quality of the output piano and a matching score for the translation. While one can argue that style is hard to define and, therefore, such subjective experiments are not well founded, there are many similar MOS experiments in image to image translation, e.g., (Lample et al., 2017), and indeed MOS studies are used exactly where the translation metric is perceptual and subjective.
+
+Specifically, Mean Opinion Scores (MOS) were collected using the CrowdMOS (Ribeiro et al., 2011) package. Two questions were asked: (1) what is the quality of the audio, and (2) how well does the converted version match the original. The results are shown in Tab. 1. It shows that our audio quality is considerably lower than the results produced by humans, using a keyboard connected to a computer (which should be rated as near perfect and makes any other audio quality in the MOS experiment pale in comparison). Regarding the translation success, the conversion from Harpsichord is better than the conversion from Orchestra. Surprisingly, the conversion from unseen domains is more successful than both these domains. In all three cases, our system is outperformed by the human musicians, whose conversions will soon be released to form a public benchmark.
+
+Lineup experiment In another set of experiments, we evaluate the ability of persons to identify the source musical segment from the conversions. We present, in each test, a set of six segments. One segment is a real segment from a random domain out of the ones used to train our network, and five are the associated translations. We shuffle the segments and ask which is the original one and which are conversions. To equate the quality of the source to that of the translations and prevent identification by quality, we attach the source after passing it through its domain’s autoencoder.
+
+![](images/293098298e93b1a6e0ff4c825ebfca2e556ed1d935525d1d4f333f50890f2a8e.jpg)  
+Figure 2: Results of the lineup experiment. (a) listeners from the general population tend to select the same domain as the source regardless of the actual source. (b) the musician A failed to identify the source most of the time. (c) the amateurs T and (d) S failed most of the time.
+
+The translation is perfectly authentic, if the distribution of answers is uniform. However, the task is hard to define. In a first attempt, Amazon Mechanical Turk (AMT) freelancers tended to choose the Mozart domain as the source, regardless of the real source and the presentation order, probably due to its relatively complex nature in comparison to the other domains. This is shown in the confusion matrix of Fig. 2(a). We, therefore, asked two amateur musicians (T, a guitarist, and S a dancer and a drummer with a background in piano) and the professional musician A (from the first experiment) to identify the source sample out of the six options, based on authenticity.
+
+The results, in Fig. 2(b-d) show that there is a great amount of confusion. T and A failed in most cases, and A tended to show a similar bias to the AMT freelancers. S also failed to identify the majority of the cases, but showed coherent confusion patterns between pairs of instruments.
+
+NSynth pitch experiments NSynth (Engel et al., 2017) is an audio dataset containing samples of 1,006 instruments, each sample labeled with a unique pitch, timbre, and envelope. Each sample is a four second monophonic 16kHz snippet, ranging over every pitch of a standard MIDI piano (21-108) as well as five different velocities. It was not seen during training of our system.
+
+We measure the correlation of embeddings retrieved using the encoder of our network across pitch for multiple instruments. The first two columns (from the left hand side) of Fig. 3 show selfcorrelations, while the third column shows correlation across instruments. As can be seen, the embedding encodes pitch information very clearly, despite being trained on complex polyphonic audio. The cosine similarity between the two instruments for the same pitch is, on average, 0.90-0.95 (mean of the diagonal), depending on the pair of instruments.
+
+# 4.2 EXPLORATORY EXPERIMENTS
+
+In order to freely share our trained models and allow for maximal reproducibility, we have retrained the network with data from MusicNet (Thickstun et al., 2017). The following experiments are based on this network and are focused on understanding the properties of the conversion. The description is based on the supplementary media available at musictranslation.github.io.
+
+Are we doing more than timbral transfer? Is our system equivalent to pitch estimation followed by rendering with a different instrument, or can it capture stylistic musical elements? We demonstrate that our system does more than timbral transfer in two ways. Consider the conversions presented in supplementary S1, which consist of many conversion examples from each of the domains to every other domain. There are many samples where it is clear that more than timbral transfer is happening. For example, when converting Beethoven’s string quartet music to a wind quintet (Sample #30), an ornamentation note is added in the output that is nowhere to be found in the input music; when converting Beethoven’s violin sonata to Beethoven’s solo piano (Samples $\# 2 4$ and $\# 2 3$ ), the violin line seamlessly integrated into the piano part; when converting Beethoven’s solo piano music to Bach’s solo cello (Sample #9), the bass line of the piano is converted to cello. It is perhaps most evident when converting solo piano to piano and violin; an identity transformation would have been a valid translation, but the network adds a violin part to better match the output distribution.
+
+![](images/f0d11ae8c94a6609dda271d7e0f52ae9c63c2c0eb4bb65d8e3c358b93bc58141.jpg)  
+Figure 3: Correlation of embeddings across pitch. (a) Self-correlation for NSynth’s flute-acoustic027. (b) Self-correlation for keyboard-electronic-019. (c) The correlation between the electronic keyboard (y-axis) and the flute. (d) Self-correlation for brass-acoustic-018. (e) Self-correlation for string-acoustic-029. (f) The correlation between the brass instrument (y-axis) and the string.
+
+To further demonstrate the capabilities of our system, we train a network on two piano domains: MusicNet solo piano recordings of Bach and Beethoven. We reduce the size of the latent space to 8 to limit the ability of the original input to be repeated exactly, thereby encouraging the decoders to be more ”creative” than they normally would, with the goal of observing how decoders trained on different training data will use their freedom of expression. The input we employ is a simple MIDI synthesized as a piano. Supplementary S2 presents a clear stylistic difference: one can hear some counterpoint in the Bach sample, whereas the Beethoven output exhibits a more “Sturm und Drang” feeling, indicating that the network learns stylistic elements from the training data.
+
+Comparison with previous methods We compare our results with those of Concatenative Synthesis methods in supplementary S3. To do that, we use our system to translate target files from published results of two works in that field, and present the methods’ results side-by-side. Samples 1 and 2 are compared with the published results of Coleman (2016), a work comparing several Concatenative Synthesis methods, and uses a violin passage as source audio input. Sample 3 is compared with MATConcat (Sturm, 2006), which uses a corpus of string quartets as a source material. Sample 1 is a fugue performed on a piano. We show that we are able to convincingly produce string quartet and wind ensemble renditions of the piece. To push our model to its boundaries, we also attempt to convert the polyphonic fugue to solo cello, obtaining a rather convincing result. We believe that our results surpass in naturalness those obtained by concatenative methods. Sample 2 is an orchestra piece, which for our system is data that has never been seen during training. We convert it to piano, solo cello and a wind quintet, achieving convincing results, that we believe surpass the concatenative synthesis results. Sample 3 is another orchestra piece, which includes a long drum roll, followed by brass instruments. It is not quite well-defined how to convert a drum roll to a string quartet, but we believe our rendition is more coherent. Our method is able to render the brass instruments and orchestral music after the drum roll more convincingly than MATConcat, which mimics the audio volume but loses most musical content.
+
+Universality Note that our network has never observed drums, brass instruments or an entire orchestra during training, and, therefore, the results of supplementary S3 also serve to demonstrate the versatility of the encoder module resulting from our training procedure (and so do those of S2). Supplementary S4 presents more out-of-domain conversion results, including other domains from MusicNet, whistles, and even spontaneous hand clapping.
+
+The universality property hinges on the success of training a domain-independent representation. As can be seen in the confusion matrices given in Fig. 4, the domain classification network does not do considerably better than chance when the networks converge.
+
+Ablation Analysis We conducted three ablation studies. In the first study, the training procedure did not use the augmentation procedure of Sec. 3.2. This resulted in a learning divergence during training, and we were unable to obtain a working model trained without augmentation, despite considerable effort.
+
+In order to investigate the option of not using augmentation in a domain where training without it converges, we have applied our method to the task of voice conversion. Our experiments show a clear advantage for applying augmentation, see Appendix A. Additional experiments were conducted, for voice conversion, using the VQ-VAE method of van den Oord et al. (2017).
+
+In the second ablation study, the domain classification network was not used $\lambda = 0$ ). Without requiring that the shared encoder remove domain-specific information from the latent representation of the input, the network learned to simply encode all information in the latent vectors, and all decoders learned to turn this information back to the original waveform. This resulted in a model that does not do any conversion at all.
+
+Finally, we performed an ablation study on the latent code size, in which we convert a simple MIDI clip to the Beethoven domain and the Bach domain. Samples are available as supplementary S6. As can be heard, a latent dimensionality of 64 tends to reconstruct the input (unwanted memorization). A model with a latent space of 8 (used in S2) performs well. A model with a latent dimensionality of 4 is more creative, less related to the input midi, and also suffers from a reduction in quality.
+
+Semantic blending We blend two encoded musical segments linearly in order to check the additivity of the embedding space. For that, we have selected two random five second segments $i$ and $j$ from each domain and embedded both using the encoder, obtaining $e _ { i }$ and $e _ { j }$ . We then combine the embeddings as follows: starting with 3.5 seconds from $e _ { i }$ , we combine the next 1.5 seconds of $e _ { i }$ with the first 1.5 seconds of $e _ { j }$ using a linear weighting with weights $1 - t / 1 . 5$ and $t / 1 . 5$ respectively, where $t \in [ 0 , 1 . 5 ]$ . We then use the various decoders to generate audio. The results are natural and the shift is completely seamless, as far as we observe. See supplementary S5 for samples.
+
+The samples also demonstrate that in the scenario we tested, one can alternatively use fade-in and fade-out to create a similar effect. We therefore employ a second network that is used for a related task of voice conversion (see Appendix A) and demonstrate that in the case of voice conversion, latent space embedding is clearly superior to converting the audio itself. These samples can also be found in supplementary S5 for details and samples.
+
+# 5 DISCUSSION
+
+Our work demonstrates capabilities in music conversion, which is a high-level task (a terminology that means that they are more semantic than low-level audio processing tasks), and could open the door to other high-level tasks, such as composition. We have initial results that we find interesting: by reducing the size of the latent space, the decoders become more “creative” and produce outputs that are natural yet novel, in the sense that the exact association with the original input is lost.
+
+# ACKNOWLEDGMENTS
+
+This work is part of Adam Polyak’s Ph.D thesis research conducted at Tel Aviv University.
+
+![](images/97bfcf7f6456a18cd5c56163146ca7fee1bd8ddc8d766e43a47d611f03e524aa.jpg)  
+Figure 4: Accuracy of the domain classification network. (a) A confusion matrix of the domain classification network at the end of training on the private dataset used in the first phase of experiments. The mean accuracy is 0.30. (b) The confusion matrix for the MusicNet dataset used in the second phase of experiments. The mean accuracy is 0.24.
+
+# REFERENCES
+
+Shaun Barry and Youngmoo Kim. style transfer for musical audio using multiple time-frequency representations, 2018. URL https://openreview.net/forum?id $\underline { { \underline { { \mathbf { \Pi } } } } }$ BybQ7zWCb.
+
+Yunjey Choi, Min-Je Choi, Munyoung Kim, Jung-Woo Ha, Sunghun Kim, and Jaegul Choo. StarGAN: Unified generative adversarial networks for multi-domain image-to-image translation. In arXiv preprint 1711.09020, 2017.
+
+Djork-Arne Clevert, Thomas Unterthiner, and Sepp Hochreiter. Fast and accurate deep network ´ learning by exponential linear units (elus). In International Conference on Learning Representations (ICLR), 2017.
+
+G Coleman. Descriptor Control of Sound Transformations and Mosaicing Synthesis. PhD thesis, Universitat Pompeu Fabra, Barcelona, 2016.
+
+Sander Dieleman, Aaron van den Oord, and Karen Simonyan. The challenge of realistic music ¨ generation: modelling raw audio at scale. In Advances in Neural Information Processing Systems, 2018.
+
+Jesse Engel, Cinjon Resnick, Adam Roberts, Sander Dieleman, Mohammad Norouzi, Douglas Eck, and Karen Simonyan. Neural audio synthesis of musical notes with WaveNet autoencoders. In ICML, 2017.
+
+Yaroslav Ganin, Evgeniya Ustinova, Hana Ajakan, Pascal Germain, Hugo Larochelle, Franc¸ois Laviolette, Mario Marchand, and Victor Lempitsky. Domain-adversarial training of neural networks. J. Mach. Learn. Res., 17(1):2096–2030, 2016.
+
+Leon A. Gatys, Alexander S. Ecker, and Matthias Bethge. Image style transfer using convolutional neural networks. In CVPR, 2016.
+
+Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial nets. In NIPS. 2014.
+
+Gaetan Hadjeres and Franc¸ois Pachet. DeepBach: a steerable model for bach chorales generation.¨ In ICML, 2017.
+
+Albert Haque, Michelle Guo, and Prateek Verma. Conditional end-to-end audio transforms. In Arxiv preprint 1804.00047, 2018.
+
+Keith Ito. The lj speech dataset, 2017. URL ttps://keithito.com/ LJ-Speech-Dataset.   
+Justin Johnson, Alexandre Alahi, and Li Fei-Fei. Perceptual losses for real-time style transfer and super-resolution. In ECCV, 2016.   
+Takuhiro Kaneko and Hirokazu Kameoka. Parallel-data-free voice conversion using cycle-consistent adversarial networks. arXiv preprint arXiv:1711.11293, 2017.   
+Taeksoo Kim, Moonsu Cha, Hyunsoo Kim, Jungkwon Lee, and Jiwon Kim. Learning to Discover Cross-Domain Relations with Generative Adversarial Networks. In ICML, 2017.   
+Simon King and Vasilis Karaiskos. The blizzard challenge 2011. In Blizzard Challenge workshop, 2011.   
+Simon King and Vasilis Karaiskos. The blizzard challenge 2013. In Blizzard Challenge workshop, 2013.   
+Diederik P Kingma and Max Welling. Auto-encoding variational bayes. Stat, 2014.   
+Guillaume Lample, Neil Zeghidour, Nicolas Usunier, Antoine Bordes, Ludovic Denoyer, et al. Fader networks: Manipulating images by sliding attributes. In Advances in Neural Information Processing Systems, pp. 5967–5976, 2017.   
+Ming-Yu Liu and Oncel Tuzel. Coupled generative adversarial networks. In NIPS, pp. 469–477. 2016.   
+Ming-Yu Liu, Thomas Breuel, and Jan Kautz. Unsupervised image-to-image translation networks. In NIPS. 2017.   
+Christos Louizos, Kevin Swersky, Yujia Li, Max Welling, and Richard Zemel. The variational fair autoencoder. arXiv preprint arXiv:1511.00830, 2015.   
+Brian McFee, Colin Raffel, Dawen Liang, Daniel PW Ellis, Matt McVicar, Eric Battenberg, and Oriol Nieto. librosa: Audio and music signal analysis in python. 2015.   
+Noam Mor, Lior Wolf, Adam Polyak, and Yaniv Taigman. A universal music translation network. arXiv preprint arXiv:1805.07848, 2018.   
+Carthach ´ O Nuan ´ ain, Perfecto Herrera, and Sergi Jord ´ a. Rhythmic concatenative synthesis for elec- \` tronic music: Techniques, implementation, and evaluation. Computer Music Journal, 41(2):21– 37, June 2017. ISSN 0148-9267. doi: 10.1162/COMJ a 00412.   
+Wei Ping, Kainan Peng, Andrew Gibiansky, Sercan Omer Arik, Ajay Kannan, Sharan Narang, ¨ Jonathan Raiman, and John Miller. Deep Voice 3: 2000-speaker neural text-to-speech. In ICLR, 2018.   
+Dario Rethage, Jordi Pons, and Xavier Serra. A wavenet for speech denoising. arXiv preprint arXiv:1706.07162, 2017.   
+Flavio Ribeiro, Dinei Flor ´ encio, Cha Zhang, and Michael Seltzer. Crowdmos: An approach for ˆ crowdsourcing mean opinion score studies. In Acoustics, Speech and Signal Processing (ICASSP), IEEE International Conference, pp. 2416–2419. IEEE, 2011.   
+Diemo Schwarz. Concatenative sound synthesis: The early years. Journal of New Music Research, 35(1):3–22, 2006.   
+Diemo Schwarz. Corpus-based sound synthesis survey, 2018. URL http://imtr.ircam.fr/ imtr/Corpus-Based_Sound_Synthesis_Survey.   
+Jonathan Shen, Ruoming Pang, Ron J. Weiss, Mike Schuster, Navdeep Jaitly, Zongheng Yang, Zhifeng Chen, Yu Zhang, Yuxuan Wang, R. J. Skerry-Ryan, Rif A. Saurous, Yannis Agiomyrgiannakis, and Yonghui Wu. Natural TTS synthesis by conditioning wavenet on mel spectrogram predictions. In ICASSP, 2018.
+
+Ian Simon, Sumit Basu, David Salesin, and Maneesh Agrawala. Audio analogies: Creating new music from an existing performance by concatenative synthesis. In Int. Computer Music Conference, 2005.
+
+Bob L Sturm. Adaptive concatenative sound synthesis and its application to micromontage composition. Computer Music Journal, 30(4):46–66, 2006.
+
+John Thickstun, Zaid Harchaoui, and Sham Kakade. Learning Features of Music From Scratch. In ICLR, 2017.
+
+D. Ulyanov, V. Lebedev, A. Vedaldi, and V. Lempitsky. Texture networks: Feed-forward synthesis of textures and stylized images. In ICML, 2016.
+
+Aaron van den Oord, Oriol Vinyals, and Koray Kavukcuoglu. Neural Discrete Representation Learning. In NIPS, 2017.
+
+Aron van den Oord, Sander Dieleman, Heiga Zen, Karen Simonyan, Oriol Vinyals, Alexander Graves, Nal Kalchbrenner, Andrew Senior, and Koray Kavukcuoglu. Wavenet: A generative model for raw audio. In Arxiv preprint 1609.03499, 2016.
+
+V Verfaille and D Arfib. A-dafx: Adaptive digital audio effects. energy, 2000.
+
+Zili Yi, Hao Zhang, Ping Tan, and Minglun Gong. DualGAN: Unsupervised dual learning for image-to-image translation. In ICCV, 2017.
+
+Jun-Yan Zhu, Taesung Park, Phillip Isola, and Alexei A Efros. Unpaired image-to-image translation using cycle-consistent adversarial networks. In ICCV, 2017.
+
+Aymeric Zils and Franc¸ois Pachet. Musical mosaicing. In Digital Audio Effects $( D A F x )$ , volume 2, pp. 135, 2001.
+
+# A VOICE CONVERSION EXPERIMENTS
+
+We further evaluate our method on the task of voice conversion, which is not as challenging as the music conversion task explored in this work. It is, therefore, a convenient test bed when comparing to the VQ-VAE (van den Oord et al., 2017) method, which, as we mention in the paper, did not perform well in our music-based experiments, and which was shown by the authors to work on voice conversion.
+
+In addition, as mentioned in Sec. 4.2, successful training on the music domains requires data augmentation. In voice conversion, we were able to successfully train our network even without data augmentation, and we can therefore perform a direction comparison.
+
+We apply our method, a variant without data augmentation, and the VQVQE method on three publicly available datasets: “Nancy” from Blizzard 2011 (King & Karaiskos, 2011), Blizzard 2013 (King & Karaiskos, 2013) and LJ (Ito, 2017) dataset. The generated samples are obtained by converting an audio produced by the Google Cloud TTS robot to these three voices. The models are evaluated by their quality using the Mean Opinion Score, as obtained with the CrowdMOS (Ribeiro et al., 2011) package.
+
+As can be seen in Tab. 2, samples generated by our WaveNet autoencoder based method are of higher quality than those of VQ-VAE. A second results is that the method trains well in voice conversion, even without the data augmentation. However, this leads to inferior results.
+
+# A.1 VOICE CONVERSION ARCHITECTURES
+
+We slightly modify the WaveNet autoencoder used in our method for the voice conversion task. Specifically, we modify the size of the latent encoding to be in $\mathbb { R } ^ { 4 8 }$ , instead of $\mathbb { R } ^ { 6 4 }$ . The rest of the model details remain the same as in the music translation task.
+
+In our implementation of the VQ-VAE, the encoder was composed of 6 one-dimensional convolution layer with a ReLU activation. As in the original paper, the convolutions were with a stride of 2 and kernel size of 4. Therefore, the mu-law quantized waveform is temporally downsampled by $\times 6 4$ . We used a dictionary of 512 vectors in $\mathbb { R } ^ { 1 2 8 }$ . The obtained quantized encoding is upsampled and serves to condition a decoder which reconstructs the input waveform. Here as well, we follow the original paper and implement a single WaveNet decoder for all three speaker domains, this is achieved by concatenating the quantized encoding with a learned speaker embedding. We train the VQ-VAE using dictionary updates with Exponential Moving Averages (EMA) with a decay parameter of $\gamma = 0 . 9 9$ and a commitment parameter of $\beta = 1$ .
+
+Table 2: MOS scores (mean $\pm$ SD) for the unseen speaker conversion.   
+
+<table><tr><td></td><td>Blizzard 2013</td><td>Nancy</td><td>LJ</td></tr><tr><td>Our method</td><td>3.16 ± 0.79</td><td>3.85 ± 0.84</td><td>3.40± 0.77</td></tr><tr><td>Our method - without augmentation</td><td>3.07 ± 0.79</td><td>3.87 ± 0.85</td><td>2.85± 0.92</td></tr><tr><td>VQ-VAE</td><td>2.53 ± 1.08</td><td>2.92 ± 0.92</td><td>2.22± 0.96</td></tr></table>

parse/train/HJGkisCcKm/HJGkisCcKm_content_list.json

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+    {
+        "type": "text",
+        "text": "A UNIVERSAL MUSIC TRANSLATION NETWORK ",
+        "text_level": 1,
+        "bbox": [
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+            98,
+            753,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Noam Mor Facebook AI Research noam.mor@gmail.com ",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Lior Wolf & Adam Polyak Facebook AI Research & Tel Aviv Uni. wolf,adampolyak@fb.com ",
+        "bbox": [
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+        ],
+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "Yaniv Taigman Facebook AI Research yaniv@fb.com ",
+        "bbox": [
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+            145,
+            812,
+            188
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            452,
+            224,
+            544,
+            239
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "We present a method for translating music across musical instruments and styles. This method is based on unsupervised training of a multi-domain wavenet autoencoder, with a shared encoder and a domain-independent latent space that is trained end-to-end on waveforms. Employing a diverse training dataset and large net capacity, the single encoder allows us to translate also from musical domains that were not seen during training. We evaluate our method on a dataset collected from professional musicians, and achieve convincing translations. We also study the properties of the obtained translation and demonstrate translating even from a whistle, potentially enabling the creation of instrumental music by untrained humans. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
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+            433,
+            336,
+            448
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Humans have always created music and replicated it – whether it is by singing, whistling, clapping, or, after some training, playing improvised or standard musical instruments. This ability is not unique to us, and there are many other vocal mimicking species that are able to repeat music from hearing. Music is also one of the first domains to be digitized and processed by modern computers and algorithms. It is, therefore, somewhat surprising that in the core music task of mimicry, AI is still much inferior to biological systems. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In this work, we present a novel way to produce convincing musical translation between instruments and styles. For example1, we convert the audio of a Mozart symphony performed by an orchestra to an audio in the style of a pianist playing Beethoven. Our ability builds upon two technologies that have recently become available: (i) the ability to synthesize high quality audio using autoregressive models, and (ii) the recent advent of methods that transform between domains in an unsupervised way. The first technology allows us to generate high quality and realistic audio and thanks to the teacher forcing technique, autoregressive models are efficiently trained as decoders. The second family of technologies contributes to the practicality of the solution, since posing the learning problem in the supervised setting, would require a parallel dataset of different musical instruments. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In our architecture, we employ a single, universal, encoder and apply it to all inputs (universal here means that a single encoder can address all input music, allowing us to achieve capabilities that are known as universal translation). In addition to the advantage of training fewer networks, this also enables us to convert from musical domains that were not heard during training to any of the domains encountered. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "The key to being able to train a single encoder architecture, is making sure that the domain-specific information is not encoded. We do this using a domain confusion network that provides an adversarial signal to the encoder. In addition, it is important for the encoder not to memorize the input signal but to encode it in a semantic way. We achieve this by distorting the input audio by random local pitch modulation. During training, the network is trained as a denoising autoencoder, which recovers the undistorted version of the original input. Since the distorted input is no longer in the musical domain of the output, the network learns to project out-of-domain inputs to the desired output domain. In addition, the network no longer benefits from memorizing the input signal and employs a higher-level encoding. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Asked to convert one musical instrument to another, our network shows a level of performance that seems to approach that of musicians. When controlling for audio quality, which is still lower for generated music, it is many times hard to tell which is the original audio file and which is the output of the conversion that mimics a completely different instrument. The network is also able to successfully process unseen musical instruments such as drums, or other sources, such as whistles. ",
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+    {
+        "type": "text",
+        "text": "2 PREVIOUS WORK ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Domain Transfer Recently, there has been a considerable amount of work, mostly on images and text, which performs unsupervised translation between domains $\\mathcal { A }$ and $\\boldsymbol { B }$ , without being shown any matching pairs, i.e., in a completely unsupervised way. Almost all of this work employs GAN constraints (Goodfellow et al., 2014), in order to ensure a high level of indistinguishability between the translations of samples in $A$ and samples from the domain $B$ . In our work, the output is generated by an autoregressive model and training takes place using the ground truth output of the previous time steps (“teacher forcing”), instead of the predicted ones. A complete autoregressive inference is only done during test time, and it is not practical to apply such inference during training in order to get a realistic generated (“fake”) sample for the purpose of training the GAN. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Another popular constraint is that of circularity, namely that by mapping from $\\mathcal { A }$ to $\\boldsymbol { B }$ and back to $\\mathcal { A }$ a reconstruction of the original sample is obtained (Kim et al., 2017; Zhu et al., 2017; Yi et al., 2017). In our work, for the same reason mentioned above, the output during training does not represent the future test time output, and such a constraint is unrealistic. An application of circularity in audio was present in (Kaneko & Kameoka, 2017), where a non-autoregressive model between vocoder features is used to convert between voices in an unsupervised way. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Cross domain translation is not restricted to a single pair of domains. The recent StarGAN (Choi et al., 2017) method creates multiple cycles for mapping between multiple (more than two) domains. The method employs a single generator that receives as input the source image as well as the specification of the target domain. It then produces the analog “fake” image from the target domain. Our work employs multiple decoders, one per domain, and attempts to condition a single decoder on the selection of the output domain failed to produce convincing results. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "UNIT (Liu et al., 2017) employs an encoder-decoder pair per each domain, where the latent spaces of the domains are assumed to be shared. This is achieved by sharing the network layers that are distant from the image (the top layers of the encoder and the bottom layers of the decoder), similarly to CoGAN (Liu & Tuzel, 2016). Cycle-consistency is also added, and structure is added to the latent space using a variational autoencoder (Kingma & Welling, 2014) loss terms. Our method employs a single encoder, which eliminates the need for many of the associated constraints. In addition, we do not impose a VAE loss term (Kingma & Welling, 2014) on the latent space of the encodings and instead employ a domain confusion loss (Ganin et al., 2016). The work of Louizos et al. (2015) investigates the problem of learning invariant representations by employing the Maximum Mean Discrepancy (MMD), which we do not use. ",
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+    {
+        "type": "text",
+        "text": "Audio Synthesis WaveNet (van den Oord et al., 2016) is an autoregressive model that predicts the probability distribution of the next sample, given the previous samples and an input conditioning signal. Its generated output is currently considered of the highest naturalness, and is applied in a range of tasks. In (Rethage et al., 2017), the authors have used it for denoising waveforms by predicting the middle ground-truth sample from its noisy input support. Recent contributions in Text-To-Speech(TTS) (Ping et al., 2018; Shen et al., 2018) have successfully conditioned wavenet on linguistic and acoustic features to obtain state of the art performance. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In VQ-VAE (van den Oord et al., 2017), voice conversion was obtained by employing a variational autoencoder that produces a quantized latent space that is conditioned on the speaker identity. Similar to our work, the decoder is based on WaveNet. However, we impose a greater constraint on the latent space by (a) having a universal encoder, forcing the embeddings of all domains to lie in the same space, yet (b) training a separate reconstructing decoder for each domain, provided that (c) the latent space is domain independent, thereby reducing source-target pathways memorization, which is also accomplished by (d) employing augmentation to distort the input signal. Invariance is achieved in VQ-VAE through the strong bottleneck effect achieved by discretization. Despite some effort, we were not able to use a discrete latent space here. ",
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+    {
+        "type": "image",
+        "img_path": "images/8b9792730bd1bbfaf4808011743662447a7857a2b456112cf8a61abcd73a70b2.jpg",
+        "image_caption": [
+            "Figure 1: (a) The schematic architecture of our translation network. The confusion term (marked by the dashed line) is employed only during training. $E$ is the shared encoder, $C$ is the domain classification network employed in the domain confusion term, $D ^ { i }$ are the various decoders. (b) A detailed depiction of our architecture. ‘NC’ indicates non-causal convolution. ‘1x1’ indicates a 1-D convolution with kernel size 1. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "Recently, Dieleman et al. (2018) explored discretization as a method to capture long-range dependencies in unconditioned music generation, for up to 24 seconds. We focus on translation, and the conditioning on the source signal carries some long-range information on the development of the music. Consider an analogy to a myopic language translation system, where the input is a story in English and the output is a story in Spanish. Even if the translation occurs one sentence at a time, the main theme of the story is carried by the “conditioning” on the source text. ",
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+        "type": "text",
+        "text": "The architecture of the autoencoder we employ is the wavenet-autoencoder presented in (Engel et al., 2017). In comparison to this work, our inputs are not controlled and are collected from consumer media. Our overall architecture differs in that multiple decoders and an additional auxiliary network, which is used for disentangling the domain information from the other aspects of the music representation, are trained and by the addition of an important augmentation step. ",
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+    {
+        "type": "text",
+        "text": "In the supervised learning domain, an audio style transfer between source and target spectrograms was performed with sequence-to-sequence recurrent networks (Haque et al., 2018). This method requires matching pairs of samples played on different instruments. In another fully supervised work (Hadjeres & Pachet, 2017), a graphical model aimed at modeling polyphonic tones of Bach was trained on notes, capturing the specificity of Bach’s chorales. This model is based on RNNs and requires a large corpus of notes of a particular instrument produced with a music editor. ",
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+    {
+        "type": "text",
+        "text": "Style Transfer Style transfer is often confused with domain translation and the distinction is not always clear. In the task of style transfer, the “content” remains the same between the input and the output, but the ”style” is modified. Notable contributions in the field include (Gatys et al., 2016; Ulyanov et al., 2016; Johnson et al., 2016), which synthesize a new image that minimizes the content loss with respect to the content-donor sample and the style loss with respect to one or more samples of a certain style. The content loss is based on comparing the activations of a network training for an image categorization task. The style loss compares the statistics of the activations in various layers of the categorization layer. An attempt at audio style transfer is described in (Barry & Kim, 2018). ",
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+    },
+    {
+        "type": "text",
+        "text": "Concatenative Synthesis In the computer music and audio effects literature, the conversion task we aim to solve is tackled by concatenating together short pieces of audio from the target domain, such that the output audio resembles the input audio from the source domain Verfaille & Arfib (2000); Schwarz (2006); Zils & Pachet (2001); Simon et al. (2005). The method has been extensively researched, see the previous work section of Nuanain et al. (2017) and the online resource of Schwarz ´ (2018). A direct comparison to such methods is challenging, since many of the methods have elaborate interfaces with many tunable parameters that vary from one conversion task to the next. To the extent possible, we compare with some of the published results in Sec. 4.2, obtaining what we believe to be clearly superior results. ",
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+        "type": "text",
+        "text": "3 METHOD ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Our domain translation method is based on training multiple autoencoder pathways, one per musical domain, such that the encoders are shared. During training, a softmax-based reconstruction loss is applied to each domain separately. The input data is randomly augmented, prior to applying the encoder, in order to force the network to extract high-level semantic features, instead of simply memorizing the data. In addition, a domain confusion loss (Ganin et al., 2016) is applied to the latent space to ensure that the encoding is not domain-specific. A diagram of the translation architecture is shown in Fig. 1 (a). ",
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+    {
+        "type": "text",
+        "text": "3.1 WAVENET AUTOENCODER ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We reuse an existing autoencoder architecture that is based on a WaveNet decoder and a WaveNetlike dilated convolution encoder (Engel et al., 2017). The WaveNet of each decoder is conditioned on the latent representation produced by the encoder. In order to reduce the inferencetime, the nv-wavenet CUDA kernels provided by NVIDIA ( https://github.com/NVIDIA/ nv-wavenet) were used after modification to better match the architecture suggested by van den Oord et al. (2016), as described below. ",
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+        "type": "text",
+        "text": "The encoder is a fully convolutional network that can be applied to any sequence length. The network has three blocks of ten residual-layers, a total of thirty layers. Each residual-layer contains a RELU nonlinearity, a non-causal dilated convolution with an increasing kernel size, a second RELU, and a $1 \\times 1$ convolution followed by the residual summation of the activations before the first RELU. There is a fixed width of 128 channels. After the three blocks, there is an additional $1 \\times 1$ layer. An average pooling with a kernel size of 50 milliseconds (800 samples) follows in order to obtain an encoding in $\\mathbb { R } ^ { 6 \\bar { 4 } }$ , which implies a temporal down sampling by a factor of $\\times 1 2 . 5$ . ",
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+    {
+        "type": "text",
+        "text": "The encoding is upsampled temporally to the original audio rate, using nearest neighbor interpolation and is used to condition a WaveNet decoder. The conditioning signal is passed through a $1 \\times 1$ layer that is different for each WaveNet layer. The audio (both input and output) is quantized using 8-bit mu-law encoding, similarly to both (van den Oord et al., 2016; Engel et al., 2017), which results in some inherent loss of quality. The WaveNet decoder has either four blocks of 10 residual-layers and a resulting receptive field of 250 milliseconds (4,093 samples), as in Engel et al. (2017), or 14 layer blocks and a much larger receptive field of 4 seconds. Each residual-layer contains a causal dilated convolution with an increasing kernel size, a gated hyperbolic tangent activation, a $1 \\times 1$ convolution followed by the residual summation of the layer input, and a $1 \\times 1$ convolution layer which introduces a skip connection. Each residual-layer is conditioned on the encoding described above. The summed skip connections are passed through two fully connected layers and a softmax activation to output the next timestep probability. A detailed diagram of the WaveNet autoencoder is shown in Fig. 1 (b). ",
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+        "type": "text",
+        "text": "We modify the fast nv-wavenet CUDA inference kernels, which implement the architecture suggested by Ping et al. (2018), and create efficient WaveNet kernels that implement the WaveNet architecture suggested by Engel et al. (2017). Specifically, we make the following modifications to nv-wavenet: (i) we add initialization of skip connections with previous WAV samples, (ii) we increase the kernel capacity to support 128 residual channels and (iii) we also add the conditioning to the last fully connected layer. ",
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+    {
+        "type": "text",
+        "text": "3.2 AUDIO INPUT AUGMENTATION ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In order to improve the generalization capability of the encoder, as well as to enforce it to maintain higher-level information, we employ a dedicated augmentation procedure that changes the pitch locally. The resulting audio is of a similar quality but is slightly out of tune. ",
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+    {
+        "type": "text",
+        "text": "Specifically, we perform our training on segments of one second length. For augmentation, we uniformly select a segment of length between 0.25 and 0.5 seconds, and modulate its pitch by a random number between -0.5 and 0.5 of half-steps, using librosa (McFee et al., 2015). ",
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+    {
+        "type": "text",
+        "text": "3.3 TRAINING AND THE LOSSES USED ",
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+    {
+        "type": "text",
+        "text": "Let $s ^ { j }$ be an input sample from domain $j = 1 , 2 , \\dots , k ,$ $k$ being the number of domains employed during training. Let $E$ be the shared encoder, and $D ^ { j }$ the WaveNet decoder for domain $j$ . Let $C$ be the domain classification network, and $O ( s , r )$ be the random augmentation procedure applied to a sample $s$ with a random seed $r$ . ",
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+        "type": "text",
+        "text": "The network $C$ predicts which domain the input data came from, based on the latent vectors. It applies three 1D-convolution layers, with the ELU (Clevert et al., 2017) nonlinearity. The last layer projects the vectors to dimension $k$ and the vectors are subsequently averaged to a single $\\mathbb { R } ^ { k }$ vector. A detailed diagram of network $C$ is shown as part of Fig. 1 (b). ",
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+        "type": "text",
+        "text": "During training, the domain classification network $C$ minimizes the classification loss ",
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+        "type": "equation",
+        "img_path": "images/56c5c10cc2d464c17f7a1eaabb1dcb588c1a56a664f872f8c3bb117c7617826e.jpg",
+        "text": "$$\n\\Omega = \\sum _ { j } \\sum _ { s ^ { j } } \\operatorname { \\mathbb { E } } _ { r } \\mathcal { L } ( C ( E ( O ( s ^ { j } , r ) ) ) , j ) ,\n$$",
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+        "type": "text",
+        "text": "and the music to music autoencoders $j = 1 , 2 , \\dots$ are trained with the loss ",
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+        "type": "equation",
+        "img_path": "images/2ab6ac46e60383587a1930a5d6deac90ac8c08401b1890a0192f20f3a6f2d377.jpg",
+        "text": "$$\n- \\lambda \\Omega + \\sum _ { j } \\sum _ { s ^ { j } } \\operatorname { \\mathbb { E } } \\mathcal { L } ( D ^ { j } ( E ( O ( s ^ { j } , r ) ) ) , s ^ { j } )\n$$",
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+    {
+        "type": "text",
+        "text": "where $\\mathcal { L } ( o , y )$ is the cross entropy loss applied to each element of the output $o$ and the corresponding element of the target $y$ separately. Note that the decoder $D ^ { j }$ is an autoregressive model that is conditioned on the output of $E$ . During training, the autoregressive model is fed the target output $s ^ { j }$ from the previous time-step, instead of the generated output. ",
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+    {
+        "type": "text",
+        "text": "3.4 NETWORK DURING INFERENCE ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "To perform the actual transformation from a sample $s$ from any domain, even from an unseen musical domain, to output domain $j$ , we apply the autoencoder of domain $j$ to it, without applying the distortion. The new sample $\\hat { s } ^ { j }$ is, therefore, given as $D ^ { j } ( E ( s ) )$ . The bottleneck during inference is the WaveNet autoregressive process, which is optimized by the dedicated CUDA kernels. ",
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+        "text": "4 EXPERIMENTS ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We conduct music translation experiments, using a mix of human evaluation and qualitative analysis, in order to overcome the challenges of evaluating generative models. The experiments were done in two phases. In the first phase, described in an earlier technical report (Mor et al., 2018), we train our network on six arbitrary classical musical domains: (i) Mozart’s symphonies conducted by Karl Bohm, (ii) Haydn’s string quartets, performed by the Amadeus Quartet, (iii) J.S Bach’s cantatas for ¨ orchestra, chorus and soloists, (iv) J.S Bach’s organ works, (v) Beethoven’s piano sonatas, performed by Daniel Barenboim, and (vi) J.S Bach’s keyboard works, played on Harpsichord. The music recordings by Bach (iii,iv,vi) are from the Teldec 2000 Complete Bach collection. ",
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+    {
+        "type": "text",
+        "text": "In the second phase, in order to allow reproducibility and sharing of the code and models, we train on audio data from MusicNET (Thickstun et al., 2017). Domains were chosen as the largest domains that show variability between composers and instruments. The following six domains were selected: (i) J.S Bach’s suites for cello, (ii) Beethoven’s piano sonatas, (iii) Cambini’s Wind Quintet, (iv) J.S Bach’s fugues, played on piano, (v) Beethoven’s violin sonatas and (vi) Beethoven’s string quartet. This public dataset is somewhat smaller than the data used in phase one. ",
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+        "type": "text",
+        "text": "The phases differ in the depth of the decoders: in the first phase, we employed blocks of ten layers, while in the second, we shifted to larger receptive fields and blocks of 14. The training and test splits are strictly separated by dividing the tracks (or audio files) between the two sets. The segments used in the evaluation experiments below were not seen during training. During training, we iterate over the training domains, such that each training batch contains 16 randomly sampled one second samples from a single domain. Each batch is first used to train the domain classification network $C$ , and then to train the universal encoder and the domain decoder, given the updated discriminator. ",
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+    {
+        "type": "text",
+        "text": "The method was implemented in the PyTorch framework, and trained on eight Tesla V100 GPUs for a total of 6 days. We used the ADAM optimization algorithm with a learning rate of $1 0 ^ { - 3 }$ and a decay factor of 0.98 every 10,000 samples. We weighted the confusion loss with $\\lambda = 1 0 ^ { - 2 }$ . ",
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+    {
+        "type": "table",
+        "img_path": "images/61f4810ea7717b8a7e04910707125d1ca9b8da10585fa39053b42d7ccb5e658f.jpg",
+        "table_caption": [
+            "Table 1: MOS scores (mean $\\pm$ SD) for the conversion tasks. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Converter</td><td colspan=\"2\">Harpsichord→Piano</td><td colspan=\"2\">Orchestra-→ Piano</td><td colspan=\"2\">New domains-→ Piano</td></tr><tr><td>Audio quality</td><td>Translation success</td><td>Audio quality</td><td>Translation success</td><td>Audio quality</td><td>Translation success</td></tr><tr><td>Musician E</td><td>3.89 ± 1.06</td><td>4.10± 0.94</td><td>4.02± 0.81</td><td>4.12± 0.97</td><td>4.44±0.82</td><td>4.13± 0.83</td></tr><tr><td>Musician M</td><td>3.82 ± 1.18</td><td>3.75± 1.17</td><td>4.13± 0.89</td><td>4.12± 0.98</td><td>4.48±0.72</td><td>3.97± 0.88</td></tr><tr><td>Musician A</td><td>3.69 ± 1.08</td><td>3.91± 1.16</td><td>4.06± 0.86</td><td>3.99± 1.08</td><td>4.53±0.79</td><td>3.93± 0.95</td></tr><tr><td>Our</td><td>2.95 ± 1.18</td><td>3.07± 1.30</td><td>2.56± 1.04</td><td>2.86± 1.16</td><td>2.36±1.17</td><td>3.18± 1.14</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "4.1 EVALUATION OF TRANSLATION QUALITY ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "The first set of experiments compared the method to human musicians using the phase one network. Since human musicians, are equipped by evolution with music skills, selected among their peers according to their talent, and who have trained for decades, we do not expect to do better than humans at this point. To perform this comparsion, music from domain $X$ was converted to piano, for various $X$ . The piano was selected for practical reasons: pianists are in higher availability than other musicians and a piano is easier to produce than, e.g., an orchestra. ",
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+    {
+        "type": "text",
+        "text": "Three professional musicians with a diverse background were employed for the conversion task: E, who is a conservatory graduate with an extensive background in music theory and piano performance, and also specializes in transcribing music; M, who is a professional producer, composer, pianist and audio engineer, who is an expert in musical transcription; and A who is a music producer, editor, and a skilled player of keyboards and other instruments. ",
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+    {
+        "type": "text",
+        "text": "The task used for comparison was to convert 60 segments of five seconds each to piano. Three varied sources were used. 20 of the segments were from Bach’s keyboard works, played on a Harpsichord, and 20 others were from Mozart’s 46 symphonies conducted by Karl Bohm, which are ¨ orchestral works. The last group of 20 segments was a mix of three different domains that were not encountered during training – Swing Jazz, metal guitar riffs, and instrumental Chinese music. The 60 music segments were encoded by the universal encoder and decoded by the WaveNet trained on Beethoven’s piano sonatas, as performed by Daniel Barenboim. ",
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+    {
+        "type": "text",
+        "text": "In order to compare between the conversions, we employed human evaluation, which is subjective and could be a mix of the assessment of the audio quality and the assessment of the translation itself. This limits the success of the automatic method, since the quality of the algorithm’s output is upper bounded by the neural network architecture and cannot match that of a high quality recording. ",
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+    {
+        "type": "text",
+        "text": "Since there is a trade-off between the fidelity to the original piece and the ability to create audio in the target domain, we present two scores: audio quality of the output piano and a matching score for the translation. While one can argue that style is hard to define and, therefore, such subjective experiments are not well founded, there are many similar MOS experiments in image to image translation, e.g., (Lample et al., 2017), and indeed MOS studies are used exactly where the translation metric is perceptual and subjective. ",
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+    {
+        "type": "text",
+        "text": "Specifically, Mean Opinion Scores (MOS) were collected using the CrowdMOS (Ribeiro et al., 2011) package. Two questions were asked: (1) what is the quality of the audio, and (2) how well does the converted version match the original. The results are shown in Tab. 1. It shows that our audio quality is considerably lower than the results produced by humans, using a keyboard connected to a computer (which should be rated as near perfect and makes any other audio quality in the MOS experiment pale in comparison). Regarding the translation success, the conversion from Harpsichord is better than the conversion from Orchestra. Surprisingly, the conversion from unseen domains is more successful than both these domains. In all three cases, our system is outperformed by the human musicians, whose conversions will soon be released to form a public benchmark. ",
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+    {
+        "type": "text",
+        "text": "Lineup experiment In another set of experiments, we evaluate the ability of persons to identify the source musical segment from the conversions. We present, in each test, a set of six segments. One segment is a real segment from a random domain out of the ones used to train our network, and five are the associated translations. We shuffle the segments and ask which is the original one and which are conversions. To equate the quality of the source to that of the translations and prevent identification by quality, we attach the source after passing it through its domain’s autoencoder. ",
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+    {
+        "type": "image",
+        "img_path": "images/293098298e93b1a6e0ff4c825ebfca2e556ed1d935525d1d4f333f50890f2a8e.jpg",
+        "image_caption": [
+            "Figure 2: Results of the lineup experiment. (a) listeners from the general population tend to select the same domain as the source regardless of the actual source. (b) the musician A failed to identify the source most of the time. (c) the amateurs T and (d) S failed most of the time. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "The translation is perfectly authentic, if the distribution of answers is uniform. However, the task is hard to define. In a first attempt, Amazon Mechanical Turk (AMT) freelancers tended to choose the Mozart domain as the source, regardless of the real source and the presentation order, probably due to its relatively complex nature in comparison to the other domains. This is shown in the confusion matrix of Fig. 2(a). We, therefore, asked two amateur musicians (T, a guitarist, and S a dancer and a drummer with a background in piano) and the professional musician A (from the first experiment) to identify the source sample out of the six options, based on authenticity. ",
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+    {
+        "type": "text",
+        "text": "The results, in Fig. 2(b-d) show that there is a great amount of confusion. T and A failed in most cases, and A tended to show a similar bias to the AMT freelancers. S also failed to identify the majority of the cases, but showed coherent confusion patterns between pairs of instruments. ",
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+    {
+        "type": "text",
+        "text": "NSynth pitch experiments NSynth (Engel et al., 2017) is an audio dataset containing samples of 1,006 instruments, each sample labeled with a unique pitch, timbre, and envelope. Each sample is a four second monophonic 16kHz snippet, ranging over every pitch of a standard MIDI piano (21-108) as well as five different velocities. It was not seen during training of our system. ",
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+    {
+        "type": "text",
+        "text": "We measure the correlation of embeddings retrieved using the encoder of our network across pitch for multiple instruments. The first two columns (from the left hand side) of Fig. 3 show selfcorrelations, while the third column shows correlation across instruments. As can be seen, the embedding encodes pitch information very clearly, despite being trained on complex polyphonic audio. The cosine similarity between the two instruments for the same pitch is, on average, 0.90-0.95 (mean of the diagonal), depending on the pair of instruments. ",
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+    {
+        "type": "text",
+        "text": "4.2 EXPLORATORY EXPERIMENTS ",
+        "text_level": 1,
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+        "text": "In order to freely share our trained models and allow for maximal reproducibility, we have retrained the network with data from MusicNet (Thickstun et al., 2017). The following experiments are based on this network and are focused on understanding the properties of the conversion. The description is based on the supplementary media available at musictranslation.github.io. ",
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+        "text": "Are we doing more than timbral transfer? Is our system equivalent to pitch estimation followed by rendering with a different instrument, or can it capture stylistic musical elements? We demonstrate that our system does more than timbral transfer in two ways. Consider the conversions presented in supplementary S1, which consist of many conversion examples from each of the domains to every other domain. There are many samples where it is clear that more than timbral transfer is happening. For example, when converting Beethoven’s string quartet music to a wind quintet (Sample #30), an ornamentation note is added in the output that is nowhere to be found in the input music; when converting Beethoven’s violin sonata to Beethoven’s solo piano (Samples $\\# 2 4$ and $\\# 2 3$ ), the violin line seamlessly integrated into the piano part; when converting Beethoven’s solo piano music to Bach’s solo cello (Sample #9), the bass line of the piano is converted to cello. It is perhaps most evident when converting solo piano to piano and violin; an identity transformation would have been a valid translation, but the network adds a violin part to better match the output distribution. ",
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+        "image_caption": [
+            "Figure 3: Correlation of embeddings across pitch. (a) Self-correlation for NSynth’s flute-acoustic027. (b) Self-correlation for keyboard-electronic-019. (c) The correlation between the electronic keyboard (y-axis) and the flute. (d) Self-correlation for brass-acoustic-018. (e) Self-correlation for string-acoustic-029. (f) The correlation between the brass instrument (y-axis) and the string. "
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+        "text": "To further demonstrate the capabilities of our system, we train a network on two piano domains: MusicNet solo piano recordings of Bach and Beethoven. We reduce the size of the latent space to 8 to limit the ability of the original input to be repeated exactly, thereby encouraging the decoders to be more ”creative” than they normally would, with the goal of observing how decoders trained on different training data will use their freedom of expression. The input we employ is a simple MIDI synthesized as a piano. Supplementary S2 presents a clear stylistic difference: one can hear some counterpoint in the Bach sample, whereas the Beethoven output exhibits a more “Sturm und Drang” feeling, indicating that the network learns stylistic elements from the training data. ",
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+        "text": "Comparison with previous methods We compare our results with those of Concatenative Synthesis methods in supplementary S3. To do that, we use our system to translate target files from published results of two works in that field, and present the methods’ results side-by-side. Samples 1 and 2 are compared with the published results of Coleman (2016), a work comparing several Concatenative Synthesis methods, and uses a violin passage as source audio input. Sample 3 is compared with MATConcat (Sturm, 2006), which uses a corpus of string quartets as a source material. Sample 1 is a fugue performed on a piano. We show that we are able to convincingly produce string quartet and wind ensemble renditions of the piece. To push our model to its boundaries, we also attempt to convert the polyphonic fugue to solo cello, obtaining a rather convincing result. We believe that our results surpass in naturalness those obtained by concatenative methods. Sample 2 is an orchestra piece, which for our system is data that has never been seen during training. We convert it to piano, solo cello and a wind quintet, achieving convincing results, that we believe surpass the concatenative synthesis results. Sample 3 is another orchestra piece, which includes a long drum roll, followed by brass instruments. It is not quite well-defined how to convert a drum roll to a string quartet, but we believe our rendition is more coherent. Our method is able to render the brass instruments and orchestral music after the drum roll more convincingly than MATConcat, which mimics the audio volume but loses most musical content. ",
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+        "text": "",
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+        "type": "text",
+        "text": "Universality Note that our network has never observed drums, brass instruments or an entire orchestra during training, and, therefore, the results of supplementary S3 also serve to demonstrate the versatility of the encoder module resulting from our training procedure (and so do those of S2). Supplementary S4 presents more out-of-domain conversion results, including other domains from MusicNet, whistles, and even spontaneous hand clapping. ",
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+        "type": "text",
+        "text": "The universality property hinges on the success of training a domain-independent representation. As can be seen in the confusion matrices given in Fig. 4, the domain classification network does not do considerably better than chance when the networks converge. ",
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+    {
+        "type": "text",
+        "text": "Ablation Analysis We conducted three ablation studies. In the first study, the training procedure did not use the augmentation procedure of Sec. 3.2. This resulted in a learning divergence during training, and we were unable to obtain a working model trained without augmentation, despite considerable effort. ",
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+        "type": "text",
+        "text": "In order to investigate the option of not using augmentation in a domain where training without it converges, we have applied our method to the task of voice conversion. Our experiments show a clear advantage for applying augmentation, see Appendix A. Additional experiments were conducted, for voice conversion, using the VQ-VAE method of van den Oord et al. (2017). ",
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+    {
+        "type": "text",
+        "text": "In the second ablation study, the domain classification network was not used $\\lambda = 0$ ). Without requiring that the shared encoder remove domain-specific information from the latent representation of the input, the network learned to simply encode all information in the latent vectors, and all decoders learned to turn this information back to the original waveform. This resulted in a model that does not do any conversion at all. ",
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+        "type": "text",
+        "text": "Finally, we performed an ablation study on the latent code size, in which we convert a simple MIDI clip to the Beethoven domain and the Bach domain. Samples are available as supplementary S6. As can be heard, a latent dimensionality of 64 tends to reconstruct the input (unwanted memorization). A model with a latent space of 8 (used in S2) performs well. A model with a latent dimensionality of 4 is more creative, less related to the input midi, and also suffers from a reduction in quality. ",
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+        "type": "text",
+        "text": "Semantic blending We blend two encoded musical segments linearly in order to check the additivity of the embedding space. For that, we have selected two random five second segments $i$ and $j$ from each domain and embedded both using the encoder, obtaining $e _ { i }$ and $e _ { j }$ . We then combine the embeddings as follows: starting with 3.5 seconds from $e _ { i }$ , we combine the next 1.5 seconds of $e _ { i }$ with the first 1.5 seconds of $e _ { j }$ using a linear weighting with weights $1 - t / 1 . 5$ and $t / 1 . 5$ respectively, where $t \\in [ 0 , 1 . 5 ]$ . We then use the various decoders to generate audio. The results are natural and the shift is completely seamless, as far as we observe. See supplementary S5 for samples. ",
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+        "type": "text",
+        "text": "The samples also demonstrate that in the scenario we tested, one can alternatively use fade-in and fade-out to create a similar effect. We therefore employ a second network that is used for a related task of voice conversion (see Appendix A) and demonstrate that in the case of voice conversion, latent space embedding is clearly superior to converting the audio itself. These samples can also be found in supplementary S5 for details and samples. ",
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+    {
+        "type": "text",
+        "text": "5 DISCUSSION ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Our work demonstrates capabilities in music conversion, which is a high-level task (a terminology that means that they are more semantic than low-level audio processing tasks), and could open the door to other high-level tasks, such as composition. We have initial results that we find interesting: by reducing the size of the latent space, the decoders become more “creative” and produce outputs that are natural yet novel, in the sense that the exact association with the original input is lost. ",
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+    {
+        "type": "text",
+        "text": "ACKNOWLEDGMENTS ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "This work is part of Adam Polyak’s Ph.D thesis research conducted at Tel Aviv University. ",
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+        "image_caption": [
+            "Figure 4: Accuracy of the domain classification network. (a) A confusion matrix of the domain classification network at the end of training on the private dataset used in the first phase of experiments. The mean accuracy is 0.30. (b) The confusion matrix for the MusicNet dataset used in the second phase of experiments. The mean accuracy is 0.24. "
+        ],
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+    {
+        "type": "text",
+        "text": "REFERENCES ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            425,
+            285,
+            440
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Shaun Barry and Youngmoo Kim. style transfer for musical audio using multiple time-frequency representations, 2018. URL https://openreview.net/forum?id $\\underline { { \\underline { { \\mathbf { \\Pi } } } } }$ BybQ7zWCb. ",
+        "bbox": [
+            174,
+            448,
+            823,
+            477
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Yunjey Choi, Min-Je Choi, Munyoung Kim, Jung-Woo Ha, Sunghun Kim, and Jaegul Choo. StarGAN: Unified generative adversarial networks for multi-domain image-to-image translation. In arXiv preprint 1711.09020, 2017. ",
+        "bbox": [
+            174,
+            484,
+            825,
+            529
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Djork-Arne Clevert, Thomas Unterthiner, and Sepp Hochreiter. Fast and accurate deep network ´ learning by exponential linear units (elus). In International Conference on Learning Representations (ICLR), 2017. ",
+        "bbox": [
+            173,
+            537,
+            823,
+            580
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "G Coleman. Descriptor Control of Sound Transformations and Mosaicing Synthesis. PhD thesis, Universitat Pompeu Fabra, Barcelona, 2016. ",
+        "bbox": [
+            178,
+            588,
+            823,
+            618
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Sander Dieleman, Aaron van den Oord, and Karen Simonyan. The challenge of realistic music ¨ generation: modelling raw audio at scale. In Advances in Neural Information Processing Systems, 2018. ",
+        "bbox": [
+            176,
+            627,
+            823,
+            669
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Jesse Engel, Cinjon Resnick, Adam Roberts, Sander Dieleman, Mohammad Norouzi, Douglas Eck, and Karen Simonyan. Neural audio synthesis of musical notes with WaveNet autoencoders. In ICML, 2017. ",
+        "bbox": [
+            173,
+            678,
+            823,
+            720
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Yaroslav Ganin, Evgeniya Ustinova, Hana Ajakan, Pascal Germain, Hugo Larochelle, Franc¸ois Laviolette, Mario Marchand, and Victor Lempitsky. Domain-adversarial training of neural networks. J. Mach. Learn. Res., 17(1):2096–2030, 2016. ",
+        "bbox": [
+            176,
+            729,
+            821,
+            773
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Leon A. Gatys, Alexander S. Ecker, and Matthias Bethge. Image style transfer using convolutional neural networks. In CVPR, 2016. ",
+        "bbox": [
+            171,
+            781,
+            821,
+            810
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial nets. In NIPS. 2014. ",
+        "bbox": [
+            173,
+            819,
+            821,
+            848
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Gaetan Hadjeres and Franc¸ois Pachet. DeepBach: a steerable model for bach chorales generation.¨ In ICML, 2017. ",
+        "bbox": [
+            174,
+            857,
+            821,
+            886
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Albert Haque, Michelle Guo, and Prateek Verma. Conditional end-to-end audio transforms. In Arxiv preprint 1804.00047, 2018. ",
+        "bbox": [
+            173,
+            895,
+            820,
+            924
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Keith Ito. The lj speech dataset, 2017. URL ttps://keithito.com/ LJ-Speech-Dataset.   \nJustin Johnson, Alexandre Alahi, and Li Fei-Fei. Perceptual losses for real-time style transfer and super-resolution. In ECCV, 2016.   \nTakuhiro Kaneko and Hirokazu Kameoka. Parallel-data-free voice conversion using cycle-consistent adversarial networks. arXiv preprint arXiv:1711.11293, 2017.   \nTaeksoo Kim, Moonsu Cha, Hyunsoo Kim, Jungkwon Lee, and Jiwon Kim. Learning to Discover Cross-Domain Relations with Generative Adversarial Networks. In ICML, 2017.   \nSimon King and Vasilis Karaiskos. The blizzard challenge 2011. In Blizzard Challenge workshop, 2011.   \nSimon King and Vasilis Karaiskos. The blizzard challenge 2013. In Blizzard Challenge workshop, 2013.   \nDiederik P Kingma and Max Welling. Auto-encoding variational bayes. Stat, 2014.   \nGuillaume Lample, Neil Zeghidour, Nicolas Usunier, Antoine Bordes, Ludovic Denoyer, et al. Fader networks: Manipulating images by sliding attributes. In Advances in Neural Information Processing Systems, pp. 5967–5976, 2017.   \nMing-Yu Liu and Oncel Tuzel. Coupled generative adversarial networks. In NIPS, pp. 469–477. 2016.   \nMing-Yu Liu, Thomas Breuel, and Jan Kautz. Unsupervised image-to-image translation networks. In NIPS. 2017.   \nChristos Louizos, Kevin Swersky, Yujia Li, Max Welling, and Richard Zemel. The variational fair autoencoder. arXiv preprint arXiv:1511.00830, 2015.   \nBrian McFee, Colin Raffel, Dawen Liang, Daniel PW Ellis, Matt McVicar, Eric Battenberg, and Oriol Nieto. librosa: Audio and music signal analysis in python. 2015.   \nNoam Mor, Lior Wolf, Adam Polyak, and Yaniv Taigman. A universal music translation network. arXiv preprint arXiv:1805.07848, 2018.   \nCarthach ´ O Nuan ´ ain, Perfecto Herrera, and Sergi Jord ´ a. Rhythmic concatenative synthesis for elec- \\` tronic music: Techniques, implementation, and evaluation. Computer Music Journal, 41(2):21– 37, June 2017. ISSN 0148-9267. doi: 10.1162/COMJ a 00412.   \nWei Ping, Kainan Peng, Andrew Gibiansky, Sercan Omer Arik, Ajay Kannan, Sharan Narang, ¨ Jonathan Raiman, and John Miller. Deep Voice 3: 2000-speaker neural text-to-speech. In ICLR, 2018.   \nDario Rethage, Jordi Pons, and Xavier Serra. A wavenet for speech denoising. arXiv preprint arXiv:1706.07162, 2017.   \nFlavio Ribeiro, Dinei Flor ´ encio, Cha Zhang, and Michael Seltzer. Crowdmos: An approach for ˆ crowdsourcing mean opinion score studies. In Acoustics, Speech and Signal Processing (ICASSP), IEEE International Conference, pp. 2416–2419. IEEE, 2011.   \nDiemo Schwarz. Concatenative sound synthesis: The early years. Journal of New Music Research, 35(1):3–22, 2006.   \nDiemo Schwarz. Corpus-based sound synthesis survey, 2018. URL http://imtr.ircam.fr/ imtr/Corpus-Based_Sound_Synthesis_Survey.   \nJonathan Shen, Ruoming Pang, Ron J. Weiss, Mike Schuster, Navdeep Jaitly, Zongheng Yang, Zhifeng Chen, Yu Zhang, Yuxuan Wang, R. J. Skerry-Ryan, Rif A. Saurous, Yannis Agiomyrgiannakis, and Yonghui Wu. Natural TTS synthesis by conditioning wavenet on mel spectrogram predictions. In ICASSP, 2018. ",
+        "bbox": [
+            171,
+            66,
+            828,
+            929
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Ian Simon, Sumit Basu, David Salesin, and Maneesh Agrawala. Audio analogies: Creating new music from an existing performance by concatenative synthesis. In Int. Computer Music Conference, 2005. ",
+        "bbox": [
+            174,
+            103,
+            821,
+            146
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Bob L Sturm. Adaptive concatenative sound synthesis and its application to micromontage composition. Computer Music Journal, 30(4):46–66, 2006. ",
+        "bbox": [
+            173,
+            155,
+            823,
+            184
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "John Thickstun, Zaid Harchaoui, and Sham Kakade. Learning Features of Music From Scratch. In ICLR, 2017. ",
+        "bbox": [
+            176,
+            194,
+            821,
+            223
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "D. Ulyanov, V. Lebedev, A. Vedaldi, and V. Lempitsky. Texture networks: Feed-forward synthesis of textures and stylized images. In ICML, 2016. ",
+        "bbox": [
+            174,
+            232,
+            821,
+            262
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Aaron van den Oord, Oriol Vinyals, and Koray Kavukcuoglu. Neural Discrete Representation Learning. In NIPS, 2017. ",
+        "bbox": [
+            174,
+            270,
+            823,
+            300
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Aron van den Oord, Sander Dieleman, Heiga Zen, Karen Simonyan, Oriol Vinyals, Alexander Graves, Nal Kalchbrenner, Andrew Senior, and Koray Kavukcuoglu. Wavenet: A generative model for raw audio. In Arxiv preprint 1609.03499, 2016. ",
+        "bbox": [
+            176,
+            309,
+            825,
+            352
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "V Verfaille and D Arfib. A-dafx: Adaptive digital audio effects. energy, 2000. ",
+        "bbox": [
+            174,
+            361,
+            686,
+            377
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Zili Yi, Hao Zhang, Ping Tan, and Minglun Gong. DualGAN: Unsupervised dual learning for image-to-image translation. In ICCV, 2017. ",
+        "bbox": [
+            176,
+            386,
+            825,
+            415
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Jun-Yan Zhu, Taesung Park, Phillip Isola, and Alexei A Efros. Unpaired image-to-image translation using cycle-consistent adversarial networks. In ICCV, 2017. ",
+        "bbox": [
+            173,
+            424,
+            823,
+            454
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Aymeric Zils and Franc¸ois Pachet. Musical mosaicing. In Digital Audio Effects $( D A F x )$ , volume 2, pp. 135, 2001. ",
+        "bbox": [
+            174,
+            463,
+            823,
+            492
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "A VOICE CONVERSION EXPERIMENTS ",
+        "text_level": 1,
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+            529
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "We further evaluate our method on the task of voice conversion, which is not as challenging as the music conversion task explored in this work. It is, therefore, a convenient test bed when comparing to the VQ-VAE (van den Oord et al., 2017) method, which, as we mention in the paper, did not perform well in our music-based experiments, and which was shown by the authors to work on voice conversion. ",
+        "bbox": [
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+        ],
+        "page_idx": 11
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+    {
+        "type": "text",
+        "text": "In addition, as mentioned in Sec. 4.2, successful training on the music domains requires data augmentation. In voice conversion, we were able to successfully train our network even without data augmentation, and we can therefore perform a direction comparison. ",
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+    {
+        "type": "text",
+        "text": "We apply our method, a variant without data augmentation, and the VQVQE method on three publicly available datasets: “Nancy” from Blizzard 2011 (King & Karaiskos, 2011), Blizzard 2013 (King & Karaiskos, 2013) and LJ (Ito, 2017) dataset. The generated samples are obtained by converting an audio produced by the Google Cloud TTS robot to these three voices. The models are evaluated by their quality using the Mean Opinion Score, as obtained with the CrowdMOS (Ribeiro et al., 2011) package. ",
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+    {
+        "type": "text",
+        "text": "As can be seen in Tab. 2, samples generated by our WaveNet autoencoder based method are of higher quality than those of VQ-VAE. A second results is that the method trains well in voice conversion, even without the data augmentation. However, this leads to inferior results. ",
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+    {
+        "type": "text",
+        "text": "A.1 VOICE CONVERSION ARCHITECTURES ",
+        "text_level": 1,
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+        "text": "We slightly modify the WaveNet autoencoder used in our method for the voice conversion task. Specifically, we modify the size of the latent encoding to be in $\\mathbb { R } ^ { 4 8 }$ , instead of $\\mathbb { R } ^ { 6 4 }$ . The rest of the model details remain the same as in the music translation task. ",
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+        "text": "In our implementation of the VQ-VAE, the encoder was composed of 6 one-dimensional convolution layer with a ReLU activation. As in the original paper, the convolutions were with a stride of 2 and kernel size of 4. Therefore, the mu-law quantized waveform is temporally downsampled by $\\times 6 4$ . We used a dictionary of 512 vectors in $\\mathbb { R } ^ { 1 2 8 }$ . The obtained quantized encoding is upsampled and serves to condition a decoder which reconstructs the input waveform. Here as well, we follow the original paper and implement a single WaveNet decoder for all three speaker domains, this is achieved by concatenating the quantized encoding with a learned speaker embedding. We train the VQ-VAE using dictionary updates with Exponential Moving Averages (EMA) with a decay parameter of $\\gamma = 0 . 9 9$ and a commitment parameter of $\\beta = 1$ . ",
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+        "table_caption": [
+            "Table 2: MOS scores (mean $\\pm$ SD) for the unseen speaker conversion. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Blizzard 2013</td><td>Nancy</td><td>LJ</td></tr><tr><td>Our method</td><td>3.16 ± 0.79</td><td>3.85 ± 0.84</td><td>3.40± 0.77</td></tr><tr><td>Our method - without augmentation</td><td>3.07 ± 0.79</td><td>3.87 ± 0.85</td><td>2.85± 0.92</td></tr><tr><td>VQ-VAE</td><td>2.53 ± 1.08</td><td>2.92 ± 0.92</td><td>2.22± 0.96</td></tr></table>",
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parse/train/iEEAPq3TUEZ/iEEAPq3TUEZ.md

@@ -0,0 +1,244 @@
+# UFC-BERT: Unifying Multi-Modal Controls for Conditional Image Synthesis
+
+Zhu Zhang†, Jianxin $\mathbf { M } \mathbf { a } ^ { \dagger }$ , Chang Zhou†, Rui Men†, Zhikang Li†, Ming Ding‡, Jie Tang‡, Jingren Zhou†, and Hongxia Yang† †DAMO Academy, Alibaba Group, ‡Tsinghua University {zhangzhu950310}@gmail.com {jason.mjx, ericzhou.zc, yang.yhx}@alibaba-inc.com
+
+# Abstract
+
+Conditional image synthesis aims to create an image according to some multi-modal guidance in the forms of textual descriptions, reference images, and image blocks to preserve, as well as their combinations. In this paper, instead of investigating these control signals separately, we propose a new two-stage architecture, UFC-BERT, to unify any number of multi-modal controls. In UFC-BERT, both the diverse control signals and the synthesized image are uniformly represented as a sequence of discrete tokens to be processed by Transformer. Different from existing two-stage autoregressive approaches such as DALL-E and VQGAN, UFC-BERT adopts non-autoregressive generation (NAR) at the second stage to enhance the holistic consistency of the synthesized image, to support preserving specified image blocks, and to improve the synthesis speed. Further, we design a progressive algorithm that iteratively improves the non-autoregressively generated image, with the help of two estimators developed for evaluating the compliance with the controls and evaluating the fidelity of the synthesized image, respectively. Extensive experiments on a newly collected large-scale clothing dataset M2C-Fashion and a facial dataset MultiModal CelebA-HQ verify that UFC-BERT can synthesize high-fidelity images that comply with flexible multi-modal controls.
+
+# 1 Introduction
+
+Conditional image synthesis aims to create an image according to the given control signals. With the increasing demand for flexible conditional image synthesis, various kinds of control signals have been introduced into this field, which can be divided into three main modalities: (i) textual controls (TC), including the class labels [1] and natural language descriptions [62, 54]; (ii) visual controls $( V C )$ , such as a spatially-aligned sketch map for reference [17, 60] or another image for style transfer [15, 27]; (iii) preservation controls $( P C )$ , which require the synthesized image to preserve some given image blocks, e.g., image outpainting and inpainting [63, 69].
+
+However, control signals of various modalities possess different characteristics. Existing works [62, 26, 61] hence typically design separate methods customized for each control modality. Moreover, most of these approaches only utilize one type of control signal and cannot simultaneously combine multiple types of controls in a concise and versatile model. This begs the question: can we integrate any number of multi-modal control signals into a unified framework for flexible conditional image synthesis? There are two inevitable challenges in this setting: (i) how to unify the multi-modal controls and represent them in a unified form, especial when employing multiple control signals from different modalities concurrently; (ii) how to guarantee the fulfillment of the multi-modal controls while ensuring the fidelity of the synthesized image.
+
+![](images/05896f0fbfafe0f337aaac313cea867f65a8bcee6717c204d7869da2de03448b.jpg)  
+Figure 1: The three main modalities of control signals for conditional image synthesis: Textual Controls (TC), Visual Controls (VC), and Preservation Controls (PC).
+
+Recently, two-stage image synthesis [42, 48, 3, 13, 47] has made great progress. The first stage learns a convolutional autoencoder with quantized latent representations for converting an image into a sequence of discrete tokens, e.g., for compressing a $2 5 6 \times 2 5 6$ image into a sequence of $3 2 \times 3 2$ tokens where each token correlates mainly with an $8 \times 8$ block of the image. Converting a sequence of tokens back into an image is also supported. The second stage then typically adopts an autoregressive model, e.g., PixelCNN [41] or a unidirectional Transformer decoder [55], to capture the distribution over sequences of tokens. Particularly, the Transformer-based methods [3, 13, 47] exploit the global expressivity of Transformer to capture long-range relationships between local constituents.
+
+In this paper, we make two key observations about the two-stage framework. First, the two-stage framework has the advantage that it can potentially unify the multi-modal control signals and the generated image into a single sequence of discrete tokens. However, existing works [42, 48, 13, 47] largely neglect this advantage of the two-stage framework over the traditional one-stage approaches such as those based mainly on the generative adversarial networks (GAN) [18]. Second, the autoregressive $( A R )$ approach to sequence generation, adopted by the existing two-stage methods such as DALL-E [47] and VQGAN [13], brings undesirable shortcomings: (i) the token-by-token synthesis procedure leads to slow generation speed, especially for the heavyweight Transformer [3, 13, 47]; (ii) each generated token can only catch sight of the previously generated tokens and cannot incorporate bidirectional contexts, which may affect the holistic consistency of image synthesis; (iii) the fixed left-to-right order of autoregressive decoding cannot respond to the preservation control signals unless the image blocks to be preserved are at the beginning of the sequence. Notably, different from AR generation, non-autoregressive (NAR) sequence generation with bidirectional Transformer, i.e., BERT [9], can naturally avoid the three shortcomings.
+
+Based on the aforementioned observations, we propose UFC-BERT, a novel BERT-based two-stage framework to UniFy any number of multi-modal Controls for conditional image synthesis. Concretely, the textual, visual, and preservation control signals, as well as the generated image, are uniformly represented as a sequence of discrete tokens, as shown in Figure 2. The textual control consists of word tokens for class labels or natural language descriptions. The visual control(s) and the generated image are both represented as discrete tokens due to the first stage, where each token corresponds to a block within the reference image(s) or the generated image. Zero, one, or more reference images are supported. To preserve a given image block within the generated image, we encode the given image block into discrete tokens and fix corresponding parts of the generated sequence to the tokens.
+
+We train UFC-BERT via the masked sequence modeling task, which predicts a masked subset of the target image’s tokens conditioned on both the multi-modal control signals and the generation target’s unmasked tokens. During inference, we adopt Mask-Predict, a NAR generation algorithm [16, 21, 7], which predicts all target tokens at the first iteration and then iteratively re-mask and re-predict a subset of tokens with low confidence scores. To further improve upon the NAR generation algorithm, we exploit the discriminative capability of the BERT architecture [11, 70] and add two estimators (see Figure 2), where one estimator estimates the relevance between the generated image and the control signals, and the other one estimates the image’s fidelity. The two estimators help improve the quality of the synthesized image, because at each iteration we can generate multiple samples and keep only the highly-scored one before starting the next iteration. The two estimators also help save the number of iterations needed, since the algorithm can dynamically terminate if running for more iterations no longer improves the scores.
+
+The extensive experiments on M2C-Fashion, a newly collected clothing dataset with tens of millions of image-text pairs, as well as on Multi-Modal CelebA-HQ [28, 61], a public facial dataset, demonstrate UFC-BERT can synthesize high-quality images that comply with various multi-modal controls.
+
+# 2 Related Works
+
+We have discussed the connection between our work and Two-Stage Image Synthesis in the Introduction. In this section, we further discuss related works from other fields.
+
+Conditional Image Synthesis. A variety of control signals have been introduced into conditional image synthesis. The class-conditional generation task [1, 39] adopts class labels as control signals. The text-to-image synthesis task [64, 65, 30, 62, 72, 54] further employs natural language descriptions as controls. The image-to-image translation task generates photo-realism images from visual controls, such as a sketch map [17, 60], semantic label map [26, 4, 58], human pose [37] or another image for style transfer [15, 27]. Moreover, image outpainting and inpainting [25, 63] can be regarded as image synthesis conditioned on preservation control signals, where some image blocks of the desired image are already specified and need to be preserved in the generated image. However, these works only utilize one kind of control signal and design their methods customized for each kind of control. Text-guided image manipulation [10, 40, 69, 31, 61] semantically edits an image, where the text description and the original image serve as control signals. But they still fail to unify multiple modalities in a universal form and cannot easily extend to more control modalities. To promote versatility and extensibility, we propose UFC-BERT to unify any number of multi-modal controls.
+
+Visual-Language Transformer. With great progress in language tasks [55, 44, 45, 2], the transformer architecture is being rapidly transferred to other fields such as vision [3, 68, 12] and audio [6]. Recently, pretraining visual-language transformer [43, 24, 70, 7, 35, 53, 67] (e.g. multi-modal BERT) has achieved significant improvements on a variety of downstream tasks, e.g. visual question answering, image captioning [70], and text-to-image generation [7]. Among them, the single-stream architecture [52, 32, 46, 5, 43, 24] uses a single transformer to jointly model a pair of text and image, while the two-stream architecture [35, 36, 53] applies two transformers to separately learn the representations of the text and the image, respectively. Our UFC-BERT is also a variant of the single-stream visual-language transformer, but focuses on flexible multi-modal image synthesis instead of multi-modal pretraining.
+
+Non-Autoregressive Sequence Generation. Though it is natural to autoregressively predict tokens from left to right when generating a sequence, autoregressive decoding suffers from the slow speed and sequential error accumulation. Thus, the non-autoregressive generation (NAR) paradigm is proposed to avoid these drawbacks in neural machine translation [19, 20, 29, 16], image captioning [14, 22, 70], and speech synthesis [50, 49]. These approaches often employ the bidirectional Transformer (i.e. BERT) as it is not trained with a specific generation order. Our progressive NAR generation algorithm improves upon the Mask-Predict non-autoregressive algorithm [57, 16, 38, 33], by introducing the relevance estimator and the fidelity estimator to facilitate sample selection and dynamic termination.
+
+# 3 UFC-BERT For Multi-Modal Image Synthesis
+
+# 3.1 Background: Two-Stage Image Synthesis
+
+In this section, we review the two-stage architecture [42, 48, 13, 47] for image synthesis.
+
+At the first stage, a codebook $\mathcal { Z } = \{ \mathbf { z } _ { k } \} _ { k = 1 } ^ { K }$ for vector quantization is learned, where $\mathbf { z } _ { k } \in \mathbb { R } ^ { n _ { z } }$ is the $k$ -th code-word in the codebook and $K$ is the number of code-words. An image $\mathbf { X } \in \mathbb { R } ^ { H \times W \times 3 }$ can be transformed into (or from) a collection of code-words $\mathbf { Z } \in \mathbb { R } ^ { h \times w \times n _ { z } }$ . Concretely, a convolutional encoder $E$ first encodes the original image $\mathbf { X }$ as $\hat { \mathbf { Z } } = E ( \mathbf { X } ) \in \mathbb { R } ^ { h \times w \times n _ { z } }$ . Then an element-wise quantization step $\mathbf { q } ( \cdot )$ is applied to each element $\hat { \mathbf { Z } } _ { i j }$ to obtain the element’s closest code-word $\mathbf { z } _ { k }$ , i.e., $\begin{array} { r } { \mathbf q ( \hat { \mathbf Z } _ { i j } ) = \arg \operatorname* { m i n } _ { { \mathbf z } _ { k } \in { \mathcal Z } } \| \hat { \mathbf Z } _ { i j } - { \mathbf z } _ { k } \| } \end{array}$ . For reconstruction, a convolutional decoder $D$ is also learned for recovering image $\hat { \mathbf { X } } \in \mathbb { R } ^ { H \times W \times 3 }$ from $\mathbf { Z }$ such that $\hat { \bf X }$ is close to $\mathbf { X }$ . The first stage can be denoted by
+
+![](images/a477c09f0665712f866aecce069439db279ed3cfb382c98f7ba6a3e714ef3dc4.jpg)  
+Figure 2: The framework of UFC-BERT, where the textual control (TC), vsiual control (VC), and preservation control (PC), as well as the image to generate, collectively form a sequence of tokens.
+
+$$
+\mathbf { Z } = \mathbf { q } ( E ( \mathbf { X } ) ) , \hat { \mathbf { X } } = D ( \mathbf { Z } ) .
+$$
+
+Due to the convolutional layers, each of the $h \times w$ elements of $\hat { \mathbf { Z } }$ mainly correlates with an $\textstyle { \frac { H } { h } } \times { \frac { W } { w } }$ block of the image, though its receptive field may be larger if multiple convolutions are stacked.
+
+At the second stage, image $\mathbf { X }$ ’s quantized representation $\mathbf { Z }$ can be rewritten as a sequence of codes $\mathbf { I } \in$ $\{ 0 , \ldots , | \mathcal { Z } | - 1 \} ^ { \overline { { N } } _ { I } }$ , composed of $N _ { I } \left( = h \times w \right)$ indices from the codebook $\mathcal { Z }$ . Thus, image synthesis can be formulated as autoregressive sequence generation, i.e. predicting the distribution $\mathrm { P } \mathrm { \bar { r } } ( I _ { i } | \mathbf { I } _ { < i } , \mathbf { C } )$ of the next token $I _ { i }$ conditioned on the preceding tokens $\mathbf { I } _ { < i }$ and the control signals $\mathbf { C }$ . The distribution is typically modeled using a unidirectional Transformer. The likelihood is then $\mathrm { P r } ( { \bf I } | { \bf C } ) =$ $\begin{array} { r } { \prod _ { i } \operatorname* { P r } ( I _ { i } | \mathbf { I } _ { < i } , \mathbf { \dot { C } } ) } \end{array}$ . Parameters are learned by minimizing $\mathcal { L } _ { \mathrm { A R } } = \mathbb { E } _ { \mathbf { I } \sim d a t a } \left[ - \log \operatorname* { P r } ( \mathbf { I } | \mathbf { C } ) \right]$ .
+
+We focus on improving the second stage. Specifically, the autoregressive paradigm adopted by the existing two-stage works [42, 48, 13, 47] suffers from slow generation speed, fails to capture bidirectional contexts, and cannot fully support preservation control signals. We thus propose UFCBERT, a novel NAR approach for stage two, to unify any number of multi-modal controls and tackle the shortcomings of AR. As for stage one, we directly follow VQGAN’s design [47], which improves upon VQVAE [42] by incorporating a perceptual loss [27] and patch-based adversarial training [26].
+
+# 3.2 Problem Formulation
+
+Conditional image synthesis aims to generate an image that satisfies a set of control signals C. We consider three major modalities of control signals. A Textual Control $( T C )$ consists of a sequence of words $\mathbf { T } \in \{ 0 , \dot { \mathbf { \Omega } } . . . , | \mathcal { W } | - 1 \} ^ { N _ { T } }$ , where $\mathcal { W }$ is the vocabulary and $N _ { T }$ is the number of words in the text. In the two-stage framework, an image can be converted into a sequence of code-words (i.e. tokens) based on stage one’s encoder $E$ and codebook $\mathcal { Z }$ . Thus, a Visual Control $( V C )$ is denoted by a sequence $\mathbf { V } \in \{ 0 , \overline { { \mathbf { \Omega } } } , \mathbf { \Omega } , | \mathcal { Z } | - 1 \} ^ { N _ { V } }$ consisting of code-words from the codebook $\mathcal { Z }$ , where $N _ { V }$ is the sequence length. Similarly, the target (i.e., the image to generate) is a sequence of code-words $\mathbf { I } \in \{ \bar { 0 , } . . . , | \mathcal { Z } | \overset { - } { - } 1 \} ^ { N _ { I } }$ . We support zero, one, or multiple visual controls for flexibility. As for the Preservation Control $( P C )$ , it is a sequence of binary masks $\mathbf { P } \in \{ 0 , 1 \} ^ { N _ { I } }$ with the same length as $\mathbf { I }$ , where 1 means that the token is known (i.e., $I _ { i }$ is ground-truth if $P _ { i } = 1$ ) while 0 means the token needs to be predicted. We aim to design a model at the second stage to synthesize the target image’s sequence I conditioned on $\mathbf { C }$ , i.e., a combination of any number of control signals from $\mathbf { \bar { \{ T } } , V , \bar { P } \}$ .
+
+# 3.3 Model Inputs
+
+As shown in Figure 2, our UFC-BERT modifies the original BERT model [9] to accommodate any number of multi-modal controls. Similar to BERT, the backbone is a multi-layer bidirectional Transformer encoder, enabling the dependency modeling between all input elements. The input sequence of UFC-BERT always starts with two special tokens [REL] and [FDL] for relevance estimation and fidelity estimation, then goes on with the word sequence $\mathbf { T }$ of textual controls, code sequence V of visual controls, and ends with the code sequence I of the target image to generate. Two special separation tokens [EOT] and [EOV] are appended to the end of the textual and the visual control sequences, respectively. If there are multiple visual controls, another special token [SEP] is inserted to separate them. The sequence I of the target image to generate may be partially or fully masked by a special token [MASK]. When the preservation control $\mathbf { P }$ is present and $P _ { i } = 1$ , token $I _ { i }$ in I is always set to the code-word corresponding to the given image block to be preserved.
+
+Each input token’s representation is the sum of the position and token embeddings:
+
+Position Embedding. Our UFC-BERT learns independent sets of position embeddings for the different kinds of the inputs to achieve better distinguishment between the various modalities. The position embeddings for the word sequence are the same as BERT, i.e., we use sequential position embeddings. For a visual control or the target image, the position embedding of each token is decided according to where this token lies on the $h \times w$ grid, i.e., we use spatial position embeddings.
+
+Token Embedding. For textual controls, we use Byte-Pair Encoding [51] to segment each word into sub-words and then learn sub-word embeddings. Each special token, e.g., [REL] or [MASK], is assigned a dedicated embedding. For visual controls and the target image, we learn an embedding for each code-word. We do not directly use the embeddings from stage one’s codebook due to the decoupling of the two stages.
+
+# 3.4 Training: Masked Sequence Modeling with Relevance and Fidelity Estimation
+
+As shown in Figure 2, we train UFC-BERT via masked sequence modeling, i.e., predicting the masked tokens in the target image conditioned on the controls. A relevance estimator and a fidelity estimator are also trained in the process, and will be key to our progressive NAR generation algorithm.
+
+Task 1: Masked Sequence Modeling. This task is similar to Masked Language Modeling (MLM) in BERT, but incorporates multi-modal control signals when predicting the masked tokens. To construct training samples, we mask parts of the target image I to predict using four strategies: (1) randomly decide the number of tokens to mask, and then randomly mask the desired number of tokens; (2) mask all tokens; (3) mask the tokens within some boxed areas of the image, where the number of boxes and the box sizes are randomly decided; (4) mask the tokens outside some random boxed areas of the image. We use the four strategies with probability 0.70, 0.10, 0.10, and 0.10, respectively. To construct multi-modal control signal $\mathbf { C }$ for each training sample, there are four different combinations: ${ < } T C$ , $V C >$ , ${ < } T C >$ , ${ < } V C >$ , <empty>, where ${ < } T C$ , $V C >$ means the textual and visual controls are simultaneously employed, ${ < } T C >$ or ${ < } V C >$ means only a textual or visual signal is used, and <empty> means no textual or visual control is present. Note that the preservation control is already included in the masked sequence modeling task. Since our dataset does not contain ground-truth pairs of visual controls and target images, we crop one or multiple regions of a target image to construct VC for the target image. Because image synthesis from solely textual controls is more challenging than from other signals, we use the four combinations with probability 0.20, 0.55, 0.20, 0.05, respectively, where textual controls get more attention. We feed UFC-BERT’s outputs at each position of I into a softmax classifier over the codebook $\mathcal { Z }$ , which produces a probability score $Y _ { i } = \mathrm { \bar { P r } } ( I _ { i } | \mathbf { I } _ { U } , \mathbf { C } )$ for each position $i \in M$ , where $M$ is the set of masked positions and $U$ is the unmasked set. Finally, the masked sequence modeling task minimizes the softmax cross-entropy loss $\mathcal { L } _ { \mathrm { M S M } } = \mathbb { E } _ { \mathbf { I } _ { M } , \mathbf { I } _ { U } } \left[ - \log \operatorname* { P r } ( \mathbf { I } _ { M } | \mathbf { I } _ { U } , \mathbf { C } ) \right]$ , where $\begin{array} { r } { \mathrm { P r } ( \mathbf { I } _ { M } ^ { \mathbf { - } } | \mathbf { I } _ { U } , \mathbf { C } ) = \prod _ { i \in M } Y _ { i } } \end{array}$ .
+
+Task 2: Relevance Estimation. This task is to learn a binary classifier that judges whether the generated image is relevant or irrelevant to the given multi-modal control $\mathbf { C }$ . Briefly, we add a linear layer on the output corresponding to the special token [REL]. The linear layer outputs a scalar representing the logit, and a binary cross-entropy loss $\mathcal { L } _ { \mathrm { R E L } }$ is added. During training, the training samples from Task 1 serve as the positive instances (i.e. relevant pairs). We construct negative instances (i.e. irrelevant pairs) by swapping the control signals of two training samples.
+
+Task 3: Fidelity Estimation. This task aims to distinguish whether the generated image is realistic from the view of human visual cognition. Similar to relevance estimation, we feed the output corresponding to [FDL] into a linear layer for binary classification and add another binary crossentropy loss ${ \mathcal { L } } _ { \mathrm { F D L } }$ . Since the low-fidelity images (i.e. negative instances) do not exist in the dataset, we run UFC-BERT from previous epochs to synthesize images based solely on textual control signals, and use the synthesized images as negative instances.
+
+We combine the three tasks’ losses to train UFC-BERT, i.e.,
+
+$$
+\begin{array} { r } { \mathcal { L } _ { \mathrm { U F C - B E R T } } = \lambda _ { 1 } \mathcal { L } _ { \mathrm { M S M } } + \lambda _ { 2 } \mathcal { L } _ { \mathrm { R E L } } + \lambda _ { 3 } \mathcal { L } _ { \mathrm { F D L } } , } \end{array}
+$$
+
+where $\lambda _ { 1 }$ , $\lambda _ { 2 }$ and $\lambda _ { 3 }$ are set to 1.0, 0.5, and 0.5 to balance the three losses. The masked sequence modeling task ignores the negative instances from the other two tasks, i.e., irrelevant pairs or unrealistic instances. And the fidelity estimation task is added only after a certain number of epochs.
+
+# 3.5 Inference: Progressive Non-Autoregressive Generation
+
+We design a Progressive Non-Autoregressive Generation (PNAG) algorithm for conditional image synthesis after training, which improves upon Mask-Predict [16, 21, 7]. Mask-Predict predicts all target tokens when given a fully-masked sequence at the first iteration, and then iteratively re-mask and re-predict a subset of tokens with low probability scores for a constant number of iterations. However, Mask-Predict cannot ensure the efficacy of multi-modal controls and the fidelity of the synthesized images, and requires determining the number of iterations. Our PNAG tackles its drawbacks via sample selection and dynamic termination, based on the relevance and fidelity estimators.
+
+Each iteration of our PNAG algorithm consists of a Mask step and then a Predict step. Let $\mathbf { I } ^ { ( t , i n ) } =$ (I (t,in)1 , . $( I _ { 1 } ^ { ( t , i n ) } , \ldots , I _ { N _ { I } } ^ { ( t , i n ) } )$ and $\mathbf { I } ^ { ( t , o u t ) } = ( I _ { 1 } ^ { ( t , o u t ) } , \dots , I _ { N _ { I } } ^ { ( t , o u t ) } )$ , I (t,out)N ) be the state of the target image’s sequence before and after the $t$ -th iteration, respectively. The tokens in $\mathbf { I } ^ { ( 0 , o u t ) }$ for $t = 0$ is all set to [MASK] except for the positions that are controlled by the preservation signals, i.e., except for I(0,out)i t hat has $P _ { i } = 1$ . If a preservation control is present, i.e. $P _ { i } = 1$ , we always set $I _ { i } ^ { ( t , i n ) }$ and $I _ { i } ^ { ( t , o u t ) }$ for all $t$ to be the code-word that corresponds to the provided image block to be preserved.
+
+Mask Step. At the beginning of iteration $t$ $\left( t \geq 1 \right)$ ), we construct the input sequence $\mathbf { I } ^ { ( t , i n ) }$ by (re-)masking a subset of tokens in the generated sequence $\mathbf { I } ^ { ( t - 1 , o u t ) }$ from the last iteration. Similar to beam search, we construct $B$ parallel input sequences $\{ \mathbf { I } _ { 1 } ^ { ( t , i n ) } , \ldots , \mathbf { I } _ { B } ^ { ( t , i n ) } \}$ at each iteration. Specifically, we re-mask $n$ tokens of $\mathbf { I } ^ { ( t - 1 , o u t ) }$ to produce each $\mathbf { I } _ { b } ^ { ( t , i n ) }$ . We first sample $N _ { I } - n$ tokens from a multinomial distribution $\mathrm { P r } ^ { ( t , i n ) }$ proportional to the probability scores $\mathbf { Y } ^ { ( t - 1 ) } = \{ Y _ { i } ^ { ( t - 1 ) } \} _ { i = 1 } ^ { N _ { I } }$ (see Equation 3), computed by $\mathrm { P r } ^ { ( t , i n ) } = \mathrm { S o f t m a x } ( \mathbf { Y } ^ { ( t - 1 ) } )$ . And other tokens are re-masked and re-predicted at the next Predict Step. Here $\begin{array} { r } { n = N _ { I } \cdot ( \beta + \frac { T - t } { T - 1 } \cdot ( \alpha - \beta ) ) } \end{array}$ , where $\alpha$ is the initial mask ratio, $\beta$ is the minimum mask ratio, and $T$ is the maximum possible number of iterations, such that the number of tokens to re-mask gradually decreases after every iteration.
+
+Predict Step. Given the control $\mathbf { C }$ and an input sequence $\mathbf { I } _ { b } ^ { ( t , i n ) }$ , UFC-BERT estimates a distribution $\mathrm { P r } ( \hat { I } _ { i } | \mathbf { I } _ { b } ^ { ( t , i n ) } , \mathbf { C } )$ for each masked position $i$ . UFC-BERT also estimates the relevance score $S _ { b } ^ { R }$ and fidelity score $S _ { b } ^ { F }$ regarding the image that it is about to synthesize, and summarizes the scores into a comprehensive score $S _ { b } ^ { ( t ) } = \sigma S _ { b } ^ { R } + ( 1 - \sigma ) S _ { b } ^ { F }$ , where $\sigma$ is a coefficient for adjusting the importance of the two. We perform sample selection based on $S _ { b } ^ { ( t ) }$ , i.e., we select the $b$ -th sequen ce I(t,in)b w ith the highest $S _ { b } ^ { ( t ) }$ , discard the others, and then generate $\mathbf { I } ^ { ( t , o u t ) }$ based on the selected $\mathbf { I } _ { b } ^ { ( t , i n ) }$ as follows:
+
+$$
+I _ { i } ^ { ( t , o u t ) } \sim \mathrm { P r } ( \hat { I } _ { i } | \mathbf { I } _ { b } ^ { ( t , i n ) } , \mathbf { C } ) , \qquad Y _ { i } ^ { ( t ) } \gets \mathrm { P r } ( \hat { I } _ { i } = I _ { i } ^ { ( t , o u t ) } | \mathbf { I } _ { b } ^ { ( t , i n ) } , \mathbf { C } ) ,
+$$
+
+where each token $I _ { i } ^ { ( t , o u t ) }$ is sampled from the multinomial distribution $\mathrm { P r } ( \hat { I } _ { i } | \mathbf { I } _ { b } ^ { ( t , i n ) } , \mathbf { C } )$ and the corresponding probability is assigned to $Y _ { i } ^ { ( t ) }$ . Note that we predict tokens for all masked positions regardless of the predictions’ confidence. We also implement dynamic termination based on $S _ { b } ^ { ( t ) }$ . Specifically, if the current iteration’s score $S _ { b } ^ { ( t ) }$ is higher than $S _ { m a x }$ (initialized as zero), we set $S _ { m a x }$ to $S _ { b } ^ { ( t ) }$ and record the current iteration as $t _ { m a x }$ . If $S _ { m a x }$ does not increase after three consecutive iterations, we select $\mathbf { I } ^ { ( t _ { m a x } , o u t ) }$ as the final result and terminate our generation algorithm.
+
+![](images/93edd2d5d3aff83da7f00a082c45b0340506c523bc72098992f460bfeadc1bec.jpg)  
+Figure 3: Images generated by our UFC-BERT under various combinations of textual controls (TC), visual controls (VC), and preservation controls (PC). Please see the supplemental material for more showcases, where we also include a study on the diversity of the images generated by UFC-BERT and analyze how the multiple control signals interfere with each other.
+
+# 4 Experiments
+
+# 4.1 Datasets and Hyperparameters
+
+In experiments, we focus on two practical fields of image synthesis: fashionable clothing and human faces. We collect a very large-scale clothing dataset M2C-Fashion with Chinese text descriptions, which contains tens of millions of image-text pairs, much larger than the commonly used text-to-image datasets COCO [34] and CUB [56]. Details of the dataset are provided in the supplementary material. We additionally use another high-resolution facial dataset Multi-Modal CelebA-HQ [28, 61].
+
+Following the model setting of VQGAN [13], we use the $2 5 6 \times 2 5 6$ image size on the two datasets and transform each image to a discrete sequence of $1 6 \times 1 6$ codes, where the codebook size $| { \mathcal { Z } } |$ is set to 1024. For the BERT model, we set the number of layers, hidden size, and the number of attention heads to 24, 1024, and 16, respectively. Our UFC-BERT has 307M parameters, same as the Transformer used by VQGAN. As for hyper-parameters of PNAG, we set the parallel decoding number $B$ to 5 and the balance coefficient $\sigma$ to 0.5. We set the initial mask ratio $\alpha$ , the minimum mask ratio $\beta$ , and the maximum iteration number $T$ to 0.8, 0.2, and 10, respectively.
+
+![](images/5a13f76b34d1717dd6eb50b4d3c2e9780dd310cab6091849fdb547a10501aeca.jpg)
+
+Figure 4: Image synthesis with multiple visual controls, where we crop regions from $2 \sim 3$ images to serve as the visual controls. UFC-BERT synthesizes images that naturally fuse the visual elements.
+
+Table 1: Comparisons with GAN baselines for text-to-image synthesis on Multi-Modal CelebA-HQ.   
+
+<table><tr><td>Method</td><td>AttnGAN [62]</td><td>ControlGAN [30]</td><td>DF-GAN [54]</td><td>DM-GAN [71]</td><td>TediGAN [61]</td><td>UFC-BERT (our)</td></tr><tr><td>FID↓</td><td>125.98</td><td>116.32</td><td>137.60</td><td>131.05</td><td>106.37</td><td>66.72</td></tr><tr><td>LPIPS↓</td><td>0.512</td><td>0.522</td><td>0.581</td><td>0.544</td><td>0.456</td><td>0.448</td></tr></table>
+
+Table 2: Comparisons with the autoregressive two-stage method VQGAN for text-to-image synthesis. ↓ means the lower the better, while $\uparrow$ means the opposite. We evaluate speed on the same V100 GPU.   
+
+<table><tr><td rowspan="2">Datasets</td><td rowspan="2">Methods</td><td colspan="4">Automatic Metrics</td><td colspan="2">Human Pairwise Study</td><td rowspan="2">Inference Speed</td></tr><tr><td>FID↓</td><td>LPIPS↓</td><td>PSNR↑</td><td>SSIM↑</td><td>Relevance</td><td>Fidelity</td></tr><tr><td rowspan="2">M2C-Fashion</td><td>VQGAN (AR)</td><td>12.48</td><td>0.483</td><td>10.80</td><td>0.56</td><td>38.6%</td><td>44.2%</td><td>8.73 sec/sample</td></tr><tr><td>UFC-BERT (NAR)</td><td>11.53</td><td>0.461</td><td>13.14</td><td>0.58</td><td>61.4%</td><td>55.8%</td><td>0.81 sec/sample</td></tr><tr><td rowspan="2">Multi-Modal CelebA-HQ</td><td>VQGAN (AR)</td><td>52.63</td><td>0.503</td><td>8.98</td><td>0.28</td><td>42.7%</td><td>46.9%</td><td>8.66 sec/sample</td></tr><tr><td>UFC-BERT (NAR)</td><td>66.72</td><td>0.448</td><td>9.56</td><td>0.29</td><td>57.3%</td><td>53.1%</td><td>0.79 sec/sample</td></tr></table>
+
+# 4.2 Flexibility of Multi-Modal Controls for Conditional Image Synthesis
+
+In this section, we qualitatively verify the synthesis ability of UFC-BERT with three modalities of control signals, i.e., textual, visual, and preservation controls. The textual controls are the texts paired with the images, which are already provided by the two datasets, while the visual controls are code sequences of cropped regions, e.g. regions that represent logos or texture of clothes.
+
+In Figure 3, we synthesize images conditioned on combinations of the three types of control signals. The results demonstrate UFC-BERT can unify any number of multi-modal controls to synthesize high-quality images. Further, UFC-BERT supports one or multiple visual controls for more flexible synthesis, as shown in Figure 4 where we generate images given $2 { \sim } 3$ visual controls. We observe that UFC-BERT can reasonably fuse multiple visual elements and produce a harmonious image.
+
+# 4.3 Quantitative Comparison to Existing Methods for Text-to-Image Synthesis
+
+In this section, we investigate how our UFC-BERT quantitatively compares to existing models. Considering most existing methods only utilize one control signal, we select the most common and challenging task text-to-image synthesis to compare the synthesis ability.
+
+First, we compare our UFC-BERT with GAN-based text-to-image models AttnGAN [62], ControlGAN [30], DF-GAN [54], DM-GAN [71] and TediGAN [61] on the Multi-Modal CelebA-HQ dataset. For evalution, we adopt two automatic metrics FID [23] and LPIPS [66]. We report the results on Table 1 and our UFC-BERT achieves the best performance on the two metrics, even outperforming the TediGAN that uses slow and complex instance-level optimization. This demonstrates the two-stage architecture and non-autoregressive generation of UFC-BERT are suitable for text-to-image synthesis.
+
+![](images/1d08458dedaac9faaf6b73ca6ee658a8e85190ea957f3c4271e84dbf31086c91.jpg)
+
+This woman has wavy hair and is wearing earrings, and lipstick.
+
+![](images/9d2a3197362c142ec2df400999d14750954a6da27378d00895af4eda427a44b5.jpg)  
+Figure 6: The iterative inference process of our PNAG algorithm. The red bounding box means the image has the highest comprehensive score and is selected as the final output result.
+
+Besides, we compare our UFC-BERT with the autoregressive two-stage method VQGAN from three aspects: (i) the automatic metrics FID for image quality, as well as LPIPS, PSNR [59] and SSIM [59] for the similarity between the generated image and the ground truth; (ii) the Relevance and Fidelity metrics are evaluated through a user study, where the users are asked to judge which model’s output is more relevant to the textual descriptions, and more photorealistic; (iii) the synthesis speed of the two approaches. Note that the autoregressive inference implementation of VQGAN has been optimized by caching the preceding computation as in Transformer-XL [8], and UFCBERT and VQGAN have the same parameter number (307M) for fair com
+
+![](images/39a4b0e8cd6b09b597ea30d66c7ff01259cf6892713f421054bd3094d3fec779.jpg)  
+Figure 5: Typical examples of UFC-BERT and VQGAN for text-to-image synthesis, including a counterfactual case.
+
+parison. For the user study, the two models receive the same textual signals, and each generates 50 images. We collect the pairwise comparison results from five volunteers.
+
+As shown in Table 2, our UFC-BERT achieves better performance for almost all criteria with about $1 1 \times$ speedup. This suggests our non-autoregressive UFC-BERT with progressive NAR generation algorithm can synthesize high-fidelity images relevant to textual descriptions. As for the FID metric, UFC-BERT outperforms VQGAN on M2C-Fashion, but has worse performance on Multi-Modal CelebA-HQ, it may be due to the fact that the autoregressive VQGAN can more easily memorize the pattern of a small dataset (only 30,000 facial images). In Figure 5, we further show typical generated examples to intuitively display the difference between the two approaches, including a case of counterfactual generation. We find that UFC-BERT can synthesize high-quality images, even for the counterfactual case.
+
+# 4.4 The Effectiveness of Our Progressive NAR Generation Algorithm
+
+In this section, we first visualize in Figure 6 the iterative process of our PNAG inference method based on the relevance and fidelity estimators. The images with red bounding boxes are the final outputs that match the textual control signals. We can find that the fidelity and relevance of the images increase after a few iterations, verifying our PNAG algorithm can guide the inference process towards a better direction and synthesize more realistic images that match the control signals.
+
+Table 3: Ablation studies of our PNAG inference algorithm. PNAG(w/o. REF) and PNAG(w/o. FDL) set $B$ to the default value 5. MNAG is the original Mask-Predict algorithm [16].   
+
+<table><tr><td>Dataset</td><td>Metrics</td><td>MNAG [16]</td><td>PNAG(w/o.REF)</td><td>PNAG(w/o.FDL)</td><td>PNAG(B=1)</td><td>PNAG(B=5)</td><td>PNAG(B=10)</td></tr><tr><td rowspan="2">M2C-Fashion</td><td>FID↓</td><td>14.77</td><td>12.17</td><td>13.14</td><td>12.72</td><td>11.53</td><td>11.14</td></tr><tr><td>LPIPS↓</td><td>0.488</td><td>0.477</td><td>0.469</td><td>0.479</td><td>0.461</td><td>0.456</td></tr><tr><td rowspan="2">Multi-Modal CelebA-HQ</td><td>FID↓</td><td>72.04</td><td>68.90</td><td>70.32</td><td>69.49</td><td>66.72</td><td>65.30</td></tr><tr><td>LPIPS↓</td><td>0.514</td><td>0.469</td><td>0.463</td><td>0.475</td><td>0.448</td><td>0.445</td></tr></table>
+
+We then conduct ablation studies of PNAG. As shown in Table 3, we develop three ablated inference methods PNAG(w/o. REF), PNAG(w/o. FDL) and MNAG, where PNAG(w/o. REF) and PNAG(w/o. FDL) discard the relevance estimator and the fidelity estimator, respectively, and MNAG is the original Mask-Predict method [16] without any estimator. The results demonstrate that the two estimators effectively utilize the discriminative capability of UFC-BERT and do help improve the synthesis quality. Additionally, we vary the crucial hyper-parameter of PNAG $B$ (i.e. the parallel decoding number during inference) from 1 to 10, and the results in Table 3 show that a larger $B$ is beneficial to the synthesis quality.
+
+# 5 Conclusions
+
+We proposed UFC-BERT to unify any number of multi-modal controls in a universal form for conditional image synthesis. We utilized non-autoregressive generation to improve inference speed, enhance holistic consistency, and support preservation controls. Further, we designed a progressive generation algorithm based on relevance and fidelity estimators to ensure relevance and fidelity.
+
+# References
+
+[1] Andrew Brock, Jeff Donahue, and Karen Simonyan. Large scale gan training for high fidelity natural image synthesis. arXiv preprint arXiv:1809.11096, 2018.   
+[2] 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.   
+[3] 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.   
+[4] Qifeng Chen and Vladlen Koltun. Photographic image synthesis with cascaded refinement networks. In Proceedings of the IEEE International Conference on Computer Vision, pages 1511–1520, 2017.   
+[5] Yen-Chun Chen, Linjie Li, Licheng Yu, Ahmed El Kholy, Faisal Ahmed, Zhe Gan, Yu Cheng, and Jingjing Liu. Uniter: Learning universal image-text representations. 2019.   
+[6] Rewon Child, Scott Gray, Alec Radford, and Ilya Sutskever. Generating long sequences with sparse transformers. arXiv preprint arXiv:1904.10509, 2019.   
+[7] Jaemin Cho, Jiasen Lu, Dustin Schwenk, Hannaneh Hajishirzi, and Aniruddha Kembhavi. X-lxmert: Paint, caption and answer questions with multi-modal transformers. arXiv preprint arXiv:2009.11278, 2020.   
+[8] Zihang Dai, Zhilin Yang, Yiming Yang, Jaime Carbonell, Quoc V Le, and Ruslan Salakhutdinov. Transformer-xl: Attentive language models beyond a fixed-length context. arXiv preprint arXiv:1901.02860, 2019.   
+[9] Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. Bert: Pre-training of deep bidirectional transformers for language understanding. In Proceedings of the Conference on The North American Chapter of the Association for Computational Linguistics, 2019.   
+[10] Hao Dong, Simiao Yu, Chao Wu, and Yike Guo. Semantic image synthesis via adversarial learning. In Proceedings of the IEEE International Conference on Computer Vision, pages 5706–5714, 2017.   
+[11] Li Dong, Nan Yang, Wenhui Wang, Furu Wei, Xiaodong Liu, Yu Wang, Jianfeng Gao, Ming Zhou, and Hsiao-Wuen Hon. Unified language model pre-training for natural language understanding and generation. arXiv preprint arXiv:1905.03197, 2019.   
+[12] 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.   
+[13] Patrick Esser, Robin Rombach, and Björn Ommer. Taming transformers for high-resolution image synthesis. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2021.   
+[14] Junlong Gao, Xi Meng, Shiqi Wang, Xia Li, Shanshe Wang, Siwei Ma, and Wen Gao. Masked nonautoregressive image captioning. arXiv preprint arXiv:1906.00717, 2019.   
+[15] Leon A Gatys, Alexander S Ecker, and Matthias Bethge. Image style transfer using convolutional neural networks. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 2414–2423, 2016.   
+[16] Marjan Ghazvininejad, Omer Levy, Yinhan Liu, and Luke Zettlemoyer. Mask-predict: Parallel decoding of conditional masked language models. arXiv preprint arXiv:1904.09324, 2019.   
+[17] Arnab Ghosh, Richard Zhang, Puneet K Dokania, Oliver Wang, Alexei A Efros, Philip HS Torr, and Eli Shechtman. Interactive sketch & fill: Multiclass sketch-to-image translation. In Proceedings of the IEEE International Conference on Computer Vision, pages 1171–1180, 2019.   
+[18] Ian J Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial networks. arXiv preprint arXiv:1406.2661, 2014.   
+[19] Jiatao Gu, James Bradbury, Caiming Xiong, Victor OK Li, and Richard Socher. Non-autoregressive neural machine translation. arXiv preprint arXiv:1711.02281, 2017.   
+[20] Junliang Guo, Xu Tan, Di He, Tao Qin, Linli Xu, and Tie-Yan Liu. Non-autoregressive neural machine translation with enhanced decoder input. In Proceedings of the American Association for Artificial Intelligence, volume 33, pages 3723–3730, 2019.   
+[21] Junliang Guo, Zhirui Zhang, Linli Xu, Hao-Ran Wei, Boxing Chen, and Enhong Chen. Incorporating bert into parallel sequence decoding with adapters. In Advances in Neural Information Processing Systems, 2020.   
+[22] Longteng Guo, Jing Liu, Xinxin Zhu, Xingjian He, Jie Jiang, and Hanqing Lu. Non-autoregressive image captioning with counterfactuals-critical multi-agent learning. arXiv preprint arXiv:2005.04690, 2020.   
+[23] Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, Günter Klambauer, and Sepp Hochreiter. Gans trained by a two time-scale update rule converge to a nash equilibrium. 2017.   
+[24] Zhicheng Huang, Zhaoyang Zeng, Bei Liu, Dongmei Fu, and Jianlong Fu. Pixel-bert: Aligning image pixels with text by deep multi-modal transformers. arXiv preprint arXiv:2004.00849, 2020.   
+[25] Satoshi Iizuka, Edgar Simo-Serra, and Hiroshi Ishikawa. Let there be color! joint end-to-end learning of global and local image priors for automatic image colorization with simultaneous classification. ACM Transactions on Graphics (ToG), 35(4):1–11, 2016.   
+[26] Phillip Isola, Jun-Yan Zhu, Tinghui Zhou, and Alexei A Efros. Image-to-image translation with conditional adversarial networks. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 1125–1134, 2017.   
+[27] Justin Johnson, Alexandre Alahi, and Li Fei-Fei. Perceptual losses for real-time style transfer and superresolution. In Proceedings of the European Conference on Computer Vision, pages 694–711. Springer, 2016.   
+[28] Tero Karras, Timo Aila, Samuli Laine, and Jaakko Lehtinen. Progressive growing of gans for improved quality, stability, and variation. arXiv preprint arXiv:1710.10196, 2017.   
+[29] Jason Lee, Elman Mansimov, and Kyunghyun Cho. Deterministic non-autoregressive neural sequence modeling by iterative refinement. arXiv preprint arXiv:1802.06901, 2018.   
+[30] Bowen Li, Xiaojuan Qi, Thomas Lukasiewicz, and Philip HS Torr. Controllable text-to-image generation. arXiv preprint arXiv:1909.07083, 2019.   
+[31] Bowen Li, Xiaojuan Qi, Thomas Lukasiewicz, and Philip HS Torr. Manigan: Text-guided image manipulation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 7880–7889, 2020.   
+[32] Gen Li, Nan Duan, Yuejian Fang, Ming Gong, and Daxin Jiang. Unicoder-vl: A universal encoder for vision and language by cross-modal pre-training. In Proceedings of the American Association for Artificial Intelligence, volume 34, pages 11336–11344, 2020.   
+[33] Yi Liao, Xin Jiang, and Qun Liu. Probabilistically masked language model capable of autoregressive generation in arbitrary word order. arXiv preprint arXiv:2004.11579, 2020.   
+[34] Tsung-Yi Lin, Michael Maire, Serge Belongie, James Hays, Pietro Perona, Deva Ramanan, Piotr Dollár, and C Lawrence Zitnick. Microsoft coco: Common objects in context. In Proceedings of the European Conference on Computer Vision, pages 740–755. Springer, 2014.   
+[35] Jiasen Lu, Dhruv Batra, Devi Parikh, and Stefan Lee. Vilbert: Pretraining task-agnostic visiolinguistic representations for vision-and-language tasks. arXiv preprint arXiv:1908.02265, 2019.   
+[36] Jiasen Lu, Vedanuj Goswami, Marcus Rohrbach, Devi Parikh, and Stefan Lee. 12-in-1: Multi-task vision and language representation learning. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 10437–10446, 2020.   
+[37] Liqian Ma, Xu Jia, Qianru Sun, Bernt Schiele, Tinne Tuytelaars, and Luc Van Gool. Pose guided person image generation. arXiv preprint arXiv:1705.09368, 2017.   
+[38] Elman Mansimov, Alex Wang, Sean Welleck, and Kyunghyun Cho. A generalized framework of sequence generation with application to undirected sequence models. arXiv preprint arXiv:1905.12790, 2019.   
+[40] Seonghyeon Nam, Yunji Kim, and Seon Joo Kim. Text-adaptive generative adversarial networks: manipulating images with natural language. arXiv preprint arXiv:1810.11919, 2018.   
+[41] Aaron van den Oord, Nal Kalchbrenner, Oriol Vinyals, Lasse Espeholt, Alex Graves, and Koray Kavukcuoglu. Conditional image generation with pixelcnn decoders. arXiv preprint arXiv:1606.05328, 2016.   
+[42] Aaron van den Oord, Oriol Vinyals, and Koray Kavukcuoglu. Neural discrete representation learning. arXiv preprint arXiv:1711.00937, 2017.   
+[43] Di Qi, Lin Su, Jia Song, Edward Cui, Taroon Bharti, and Arun Sacheti. Imagebert: Cross-modal pre-training with large-scale weak-supervised image-text data. arXiv preprint arXiv:2001.07966, 2020.   
+[44] Alec Radford, Karthik Narasimhan, Tim Salimans, and Ilya Sutskever. Improving language understanding by generative pre-training. 2018.   
+[45] Alec Radford, Jeffrey Wu, Rewon Child, David Luan, Dario Amodei, and Ilya Sutskever. Language models are unsupervised multitask learners. OpenAI blog, 1(8):9, 2019.   
+[46] Wasifur Rahman, Md Kamrul Hasan, Amir Zadeh, Louis-Philippe Morency, and Mohammed Ehsan Hoque. M-bert: Injecting multimodal information in the bert structure. arXiv preprint arXiv:1908.05787, 2019.   
+[47] Aditya Ramesh, Mikhail Pavlov, Gabriel Goh, Scott Gray, Chelsea Voss, Alec Radford, Mark Chen, and Ilya Sutskever. Zero-shot text-to-image generation. arXiv preprint arXiv:2102.12092, 2021.   
+[48] Ali Razavi, Aaron van den Oord, and Oriol Vinyals. Generating diverse high-fidelity images with vq-vae-2. arXiv preprint arXiv:1906.00446, 2019.   
+[49] Yi Ren, Chenxu Hu, Xu Tan, Tao Qin, Sheng Zhao, Zhou Zhao, and Tie-Yan Liu. Fastspeech 2: Fast and high-quality end-to-end text to speech. arXiv preprint arXiv:2006.04558, 2020.   
+[50] Yi Ren, Yangjun Ruan, Xu Tan, Tao Qin, Sheng Zhao, Zhou Zhao, and Tie-Yan Liu. Fastspeech: Fast, robust and controllable text to speech. arXiv preprint arXiv:1905.09263, 2019.   
+[51] Rico Sennrich, Barry Haddow, and Alexandra Birch. Neural machine translation of rare words with subword units. arXiv preprint arXiv:1508.07909, 2015.   
+[52] Weijie Su, Xizhou Zhu, Yue Cao, Bin Li, Lewei Lu, Furu Wei, and Jifeng Dai. Vl-bert: Pre-training of generic visual-linguistic representations. arXiv preprint arXiv:1908.08530, 2019.   
+[53] Hao Tan and Mohit Bansal. Lxmert: Learning cross-modality encoder representations from transformers. arXiv preprint arXiv:1908.07490, 2019.   
+[54] Ming Tao, Hao Tang, Songsong Wu, Nicu Sebe, Xiao-Yuan Jing, Fei Wu, and Bingkun Bao. Df-gan: Deep fusion generative adversarial networks for text-to-image synthesis. arXiv preprint arXiv:2008.05865, 2020.   
+[55] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin. Attention is all you need. In Advances in Neural Information Processing Systems, pages 5998–6008, 2017.   
+[56] Catherine Wah, Steve Branson, Peter Welinder, Pietro Perona, and Serge Belongie. The caltech-ucsd birds-200-2011 dataset. 2011.   
+[57] Alex Wang and Kyunghyun Cho. Bert has a mouth, and it must speak: Bert as a markov random field language model. arXiv preprint arXiv:1902.04094, 2019.   
+[58] Ting-Chun Wang, Ming-Yu Liu, Jun-Yan Zhu, Andrew Tao, Jan Kautz, and Bryan Catanzaro. Highresolution image synthesis and semantic manipulation with conditional gans. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 8798–8807, 2018.   
+[59] Zhou Wang, Alan C Bovik, Hamid R Sheikh, and Eero P Simoncelli. Image quality assessment: from error visibility to structural similarity. IEEE transactions on image processing, 13(4):600–612, 2004.   
+[60] Weihao Xia, Yujiu Yang, and Jing-Hao Xue. Cali-sketch: Stroke calibration and completion for high-quality face image generation from poorly-drawn sketches. arXiv preprint arXiv:1911.00426, 2019.   
+[61] Weihao Xia, Yujiu Yang, Jing-Hao Xue, and Baoyuan Wu. Tedigan: Text-guided diverse image generation and manipulation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2021.   
+[62] Tao Xu, Pengchuan Zhang, Qiuyuan Huang, Han Zhang, Zhe Gan, Xiaolei Huang, and Xiaodong He. Attngan: Fine-grained text to image generation with attentional generative adversarial networks. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 1316–1324, 2018.   
+[63] Jiahui Yu, Zhe Lin, Jimei Yang, Xiaohui Shen, Xin Lu, and Thomas S Huang. Free-form image inpainting with gated convolution. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 4471–4480, 2019.   
+[64] Han Zhang, Tao Xu, Hongsheng Li, Shaoting Zhang, Xiaogang Wang, Xiaolei Huang, and Dimitris N Metaxas. Stackgan: Text to photo-realistic image synthesis with stacked generative adversarial networks. In Proceedings of the IEEE International Conference on Computer Vision, pages 5907–5915, 2017.   
+[65] Han Zhang, Tao Xu, Hongsheng Li, Shaoting Zhang, Xiaogang Wang, Xiaolei Huang, and Dimitris N Metaxas. Stackgan $^ { + + }$ : Realistic image synthesis with stacked generative adversarial networks. IEEE transactions on pattern analysis and machine intelligence, 41(8):1947–1962, 2018.   
+[66] Richard Zhang, Phillip Isola, Alexei A Efros, Eli Shechtman, and Oliver Wang. The unreasonable effectiveness of deep features as a perceptual metric. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 586–595, 2018.   
+[67] Shengyu Zhang, Tan Jiang, Tan Wang, Kun Kuang, Zhou Zhao, Jianke Zhu, Jin Yu, Hongxia Yang, and Fei Wu. Devlbert: Learning deconfounded visio-linguistic representations. In Proceedings of the 28th ACM International Conference on Multimedia, pages 4373–4382, 2020.   
+[68] Shengyu Zhang, Ziqi Tan, Zhou Zhao, Jin Yu, Kun Kuang, Tan Jiang, Jingren Zhou, Hongxia Yang, and Fei Wu. Comprehensive information integration modeling framework for video titling. In Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pages 2744–2754, 2020.   
+[69] Zijian Zhang, Zhou Zhao, Zhu Zhang, Baoxing Huai, and Jing Yuan. Text-guided image inpainting. In Proceedings of the ACM International Conference on Multimedia, pages 4079–4087, 2020.   
+[70] Luowei Zhou, Hamid Palangi, Lei Zhang, Houdong Hu, Jason Corso, and Jianfeng Gao. Unified visionlanguage pre-training for image captioning and vqa. In Proceedings of the American Association for Artificial Intelligence, volume 34, pages 13041–13049, 2020.   
+[71] Minfeng Zhu, Pingbo Pan, Wei Chen, and Yi Yang. Dm-gan: Dynamic memory generative adversarial networks for text-to-image synthesis. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 5802–5810, 2019.   
+[72] Peihao Zhu, Rameen Abdal, Yipeng Qin, and Peter Wonka. Sean: Image synthesis with semantic region-adaptive normalization. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 5104–5113, 2020.

parse/train/iEEAPq3TUEZ/iEEAPq3TUEZ_content_list.json

@@ -0,0 +1,977 @@
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+    {
+        "type": "text",
+        "text": "UFC-BERT: Unifying Multi-Modal Controls for Conditional Image Synthesis ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Zhu Zhang†, Jianxin $\\mathbf { M } \\mathbf { a } ^ { \\dagger }$ , Chang Zhou†, Rui Men†, Zhikang Li†, Ming Ding‡, Jie Tang‡, Jingren Zhou†, and Hongxia Yang† †DAMO Academy, Alibaba Group, ‡Tsinghua University {zhangzhu950310}@gmail.com {jason.mjx, ericzhou.zc, yang.yhx}@alibaba-inc.com ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Abstract ",
+        "text_level": 1,
+        "bbox": [
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+            333,
+            535,
+            349
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Conditional image synthesis aims to create an image according to some multi-modal guidance in the forms of textual descriptions, reference images, and image blocks to preserve, as well as their combinations. In this paper, instead of investigating these control signals separately, we propose a new two-stage architecture, UFC-BERT, to unify any number of multi-modal controls. In UFC-BERT, both the diverse control signals and the synthesized image are uniformly represented as a sequence of discrete tokens to be processed by Transformer. Different from existing two-stage autoregressive approaches such as DALL-E and VQGAN, UFC-BERT adopts non-autoregressive generation (NAR) at the second stage to enhance the holistic consistency of the synthesized image, to support preserving specified image blocks, and to improve the synthesis speed. Further, we design a progressive algorithm that iteratively improves the non-autoregressively generated image, with the help of two estimators developed for evaluating the compliance with the controls and evaluating the fidelity of the synthesized image, respectively. Extensive experiments on a newly collected large-scale clothing dataset M2C-Fashion and a facial dataset MultiModal CelebA-HQ verify that UFC-BERT can synthesize high-fidelity images that comply with flexible multi-modal controls. ",
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+    {
+        "type": "text",
+        "text": "1 Introduction ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Conditional image synthesis aims to create an image according to the given control signals. With the increasing demand for flexible conditional image synthesis, various kinds of control signals have been introduced into this field, which can be divided into three main modalities: (i) textual controls (TC), including the class labels [1] and natural language descriptions [62, 54]; (ii) visual controls $( V C )$ , such as a spatially-aligned sketch map for reference [17, 60] or another image for style transfer [15, 27]; (iii) preservation controls $( P C )$ , which require the synthesized image to preserve some given image blocks, e.g., image outpainting and inpainting [63, 69]. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "However, control signals of various modalities possess different characteristics. Existing works [62, 26, 61] hence typically design separate methods customized for each control modality. Moreover, most of these approaches only utilize one type of control signal and cannot simultaneously combine multiple types of controls in a concise and versatile model. This begs the question: can we integrate any number of multi-modal control signals into a unified framework for flexible conditional image synthesis? There are two inevitable challenges in this setting: (i) how to unify the multi-modal controls and represent them in a unified form, especial when employing multiple control signals from different modalities concurrently; (ii) how to guarantee the fulfillment of the multi-modal controls while ensuring the fidelity of the synthesized image. ",
+        "bbox": [
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+    {
+        "type": "image",
+        "img_path": "images/05896f0fbfafe0f337aaac313cea867f65a8bcee6717c204d7869da2de03448b.jpg",
+        "image_caption": [
+            "Figure 1: The three main modalities of control signals for conditional image synthesis: Textual Controls (TC), Visual Controls (VC), and Preservation Controls (PC). "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "Recently, two-stage image synthesis [42, 48, 3, 13, 47] has made great progress. The first stage learns a convolutional autoencoder with quantized latent representations for converting an image into a sequence of discrete tokens, e.g., for compressing a $2 5 6 \\times 2 5 6$ image into a sequence of $3 2 \\times 3 2$ tokens where each token correlates mainly with an $8 \\times 8$ block of the image. Converting a sequence of tokens back into an image is also supported. The second stage then typically adopts an autoregressive model, e.g., PixelCNN [41] or a unidirectional Transformer decoder [55], to capture the distribution over sequences of tokens. Particularly, the Transformer-based methods [3, 13, 47] exploit the global expressivity of Transformer to capture long-range relationships between local constituents. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we make two key observations about the two-stage framework. First, the two-stage framework has the advantage that it can potentially unify the multi-modal control signals and the generated image into a single sequence of discrete tokens. However, existing works [42, 48, 13, 47] largely neglect this advantage of the two-stage framework over the traditional one-stage approaches such as those based mainly on the generative adversarial networks (GAN) [18]. Second, the autoregressive $( A R )$ approach to sequence generation, adopted by the existing two-stage methods such as DALL-E [47] and VQGAN [13], brings undesirable shortcomings: (i) the token-by-token synthesis procedure leads to slow generation speed, especially for the heavyweight Transformer [3, 13, 47]; (ii) each generated token can only catch sight of the previously generated tokens and cannot incorporate bidirectional contexts, which may affect the holistic consistency of image synthesis; (iii) the fixed left-to-right order of autoregressive decoding cannot respond to the preservation control signals unless the image blocks to be preserved are at the beginning of the sequence. Notably, different from AR generation, non-autoregressive (NAR) sequence generation with bidirectional Transformer, i.e., BERT [9], can naturally avoid the three shortcomings. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Based on the aforementioned observations, we propose UFC-BERT, a novel BERT-based two-stage framework to UniFy any number of multi-modal Controls for conditional image synthesis. Concretely, the textual, visual, and preservation control signals, as well as the generated image, are uniformly represented as a sequence of discrete tokens, as shown in Figure 2. The textual control consists of word tokens for class labels or natural language descriptions. The visual control(s) and the generated image are both represented as discrete tokens due to the first stage, where each token corresponds to a block within the reference image(s) or the generated image. Zero, one, or more reference images are supported. To preserve a given image block within the generated image, we encode the given image block into discrete tokens and fix corresponding parts of the generated sequence to the tokens. ",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "We train UFC-BERT via the masked sequence modeling task, which predicts a masked subset of the target image’s tokens conditioned on both the multi-modal control signals and the generation target’s unmasked tokens. During inference, we adopt Mask-Predict, a NAR generation algorithm [16, 21, 7], which predicts all target tokens at the first iteration and then iteratively re-mask and re-predict a subset of tokens with low confidence scores. To further improve upon the NAR generation algorithm, we exploit the discriminative capability of the BERT architecture [11, 70] and add two estimators (see Figure 2), where one estimator estimates the relevance between the generated image and the control signals, and the other one estimates the image’s fidelity. The two estimators help improve the quality of the synthesized image, because at each iteration we can generate multiple samples and keep only the highly-scored one before starting the next iteration. The two estimators also help save the number of iterations needed, since the algorithm can dynamically terminate if running for more iterations no longer improves the scores. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The extensive experiments on M2C-Fashion, a newly collected clothing dataset with tens of millions of image-text pairs, as well as on Multi-Modal CelebA-HQ [28, 61], a public facial dataset, demonstrate UFC-BERT can synthesize high-quality images that comply with various multi-modal controls. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2 Related Works ",
+        "text_level": 1,
+        "bbox": [
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+            189,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We have discussed the connection between our work and Two-Stage Image Synthesis in the Introduction. In this section, we further discuss related works from other fields. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Conditional Image Synthesis. A variety of control signals have been introduced into conditional image synthesis. The class-conditional generation task [1, 39] adopts class labels as control signals. The text-to-image synthesis task [64, 65, 30, 62, 72, 54] further employs natural language descriptions as controls. The image-to-image translation task generates photo-realism images from visual controls, such as a sketch map [17, 60], semantic label map [26, 4, 58], human pose [37] or another image for style transfer [15, 27]. Moreover, image outpainting and inpainting [25, 63] can be regarded as image synthesis conditioned on preservation control signals, where some image blocks of the desired image are already specified and need to be preserved in the generated image. However, these works only utilize one kind of control signal and design their methods customized for each kind of control. Text-guided image manipulation [10, 40, 69, 31, 61] semantically edits an image, where the text description and the original image serve as control signals. But they still fail to unify multiple modalities in a universal form and cannot easily extend to more control modalities. To promote versatility and extensibility, we propose UFC-BERT to unify any number of multi-modal controls. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Visual-Language Transformer. With great progress in language tasks [55, 44, 45, 2], the transformer architecture is being rapidly transferred to other fields such as vision [3, 68, 12] and audio [6]. Recently, pretraining visual-language transformer [43, 24, 70, 7, 35, 53, 67] (e.g. multi-modal BERT) has achieved significant improvements on a variety of downstream tasks, e.g. visual question answering, image captioning [70], and text-to-image generation [7]. Among them, the single-stream architecture [52, 32, 46, 5, 43, 24] uses a single transformer to jointly model a pair of text and image, while the two-stream architecture [35, 36, 53] applies two transformers to separately learn the representations of the text and the image, respectively. Our UFC-BERT is also a variant of the single-stream visual-language transformer, but focuses on flexible multi-modal image synthesis instead of multi-modal pretraining. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Non-Autoregressive Sequence Generation. Though it is natural to autoregressively predict tokens from left to right when generating a sequence, autoregressive decoding suffers from the slow speed and sequential error accumulation. Thus, the non-autoregressive generation (NAR) paradigm is proposed to avoid these drawbacks in neural machine translation [19, 20, 29, 16], image captioning [14, 22, 70], and speech synthesis [50, 49]. These approaches often employ the bidirectional Transformer (i.e. BERT) as it is not trained with a specific generation order. Our progressive NAR generation algorithm improves upon the Mask-Predict non-autoregressive algorithm [57, 16, 38, 33], by introducing the relevance estimator and the fidelity estimator to facilitate sample selection and dynamic termination. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "3 UFC-BERT For Multi-Modal Image Synthesis ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1 Background: Two-Stage Image Synthesis ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this section, we review the two-stage architecture [42, 48, 13, 47] for image synthesis. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "At the first stage, a codebook $\\mathcal { Z } = \\{ \\mathbf { z } _ { k } \\} _ { k = 1 } ^ { K }$ for vector quantization is learned, where $\\mathbf { z } _ { k } \\in \\mathbb { R } ^ { n _ { z } }$ is the $k$ -th code-word in the codebook and $K$ is the number of code-words. An image $\\mathbf { X } \\in \\mathbb { R } ^ { H \\times W \\times 3 }$ can be transformed into (or from) a collection of code-words $\\mathbf { Z } \\in \\mathbb { R } ^ { h \\times w \\times n _ { z } }$ . Concretely, a convolutional encoder $E$ first encodes the original image $\\mathbf { X }$ as $\\hat { \\mathbf { Z } } = E ( \\mathbf { X } ) \\in \\mathbb { R } ^ { h \\times w \\times n _ { z } }$ . Then an element-wise quantization step $\\mathbf { q } ( \\cdot )$ is applied to each element $\\hat { \\mathbf { Z } } _ { i j }$ to obtain the element’s closest code-word $\\mathbf { z } _ { k }$ , i.e., $\\begin{array} { r } { \\mathbf q ( \\hat { \\mathbf Z } _ { i j } ) = \\arg \\operatorname* { m i n } _ { { \\mathbf z } _ { k } \\in { \\mathcal Z } } \\| \\hat { \\mathbf Z } _ { i j } - { \\mathbf z } _ { k } \\| } \\end{array}$ . For reconstruction, a convolutional decoder $D$ is also learned for recovering image $\\hat { \\mathbf { X } } \\in \\mathbb { R } ^ { H \\times W \\times 3 }$ from $\\mathbf { Z }$ such that $\\hat { \\bf X }$ is close to $\\mathbf { X }$ . The first stage can be denoted by ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/a477c09f0665712f866aecce069439db279ed3cfb382c98f7ba6a3e714ef3dc4.jpg",
+        "image_caption": [
+            "Figure 2: The framework of UFC-BERT, where the textual control (TC), vsiual control (VC), and preservation control (PC), as well as the image to generate, collectively form a sequence of tokens. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/6b619ec264a30e6029c9005e409b630ceff6a043f2d2d444a504460d23317f7e.jpg",
+        "text": "$$\n\\mathbf { Z } = \\mathbf { q } ( E ( \\mathbf { X } ) ) , \\hat { \\mathbf { X } } = D ( \\mathbf { Z } ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Due to the convolutional layers, each of the $h \\times w$ elements of $\\hat { \\mathbf { Z } }$ mainly correlates with an $\\textstyle { \\frac { H } { h } } \\times { \\frac { W } { w } }$ block of the image, though its receptive field may be larger if multiple convolutions are stacked. ",
+        "bbox": [
+            173,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "At the second stage, image $\\mathbf { X }$ ’s quantized representation $\\mathbf { Z }$ can be rewritten as a sequence of codes $\\mathbf { I } \\in$ $\\{ 0 , \\ldots , | \\mathcal { Z } | - 1 \\} ^ { \\overline { { N } } _ { I } }$ , composed of $N _ { I } \\left( = h \\times w \\right)$ indices from the codebook $\\mathcal { Z }$ . Thus, image synthesis can be formulated as autoregressive sequence generation, i.e. predicting the distribution $\\mathrm { P } \\mathrm { \\bar { r } } ( I _ { i } | \\mathbf { I } _ { < i } , \\mathbf { C } )$ of the next token $I _ { i }$ conditioned on the preceding tokens $\\mathbf { I } _ { < i }$ and the control signals $\\mathbf { C }$ . The distribution is typically modeled using a unidirectional Transformer. The likelihood is then $\\mathrm { P r } ( { \\bf I } | { \\bf C } ) =$ $\\begin{array} { r } { \\prod _ { i } \\operatorname* { P r } ( I _ { i } | \\mathbf { I } _ { < i } , \\mathbf { \\dot { C } } ) } \\end{array}$ . Parameters are learned by minimizing $\\mathcal { L } _ { \\mathrm { A R } } = \\mathbb { E } _ { \\mathbf { I } \\sim d a t a } \\left[ - \\log \\operatorname* { P r } ( \\mathbf { I } | \\mathbf { C } ) \\right]$ . ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We focus on improving the second stage. Specifically, the autoregressive paradigm adopted by the existing two-stage works [42, 48, 13, 47] suffers from slow generation speed, fails to capture bidirectional contexts, and cannot fully support preservation control signals. We thus propose UFCBERT, a novel NAR approach for stage two, to unify any number of multi-modal controls and tackle the shortcomings of AR. As for stage one, we directly follow VQGAN’s design [47], which improves upon VQVAE [42] by incorporating a perceptual loss [27] and patch-based adversarial training [26]. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2 Problem Formulation ",
+        "text_level": 1,
+        "bbox": [
+            176,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Conditional image synthesis aims to generate an image that satisfies a set of control signals C. We consider three major modalities of control signals. A Textual Control $( T C )$ consists of a sequence of words $\\mathbf { T } \\in \\{ 0 , \\dot { \\mathbf { \\Omega } } . . . , | \\mathcal { W } | - 1 \\} ^ { N _ { T } }$ , where $\\mathcal { W }$ is the vocabulary and $N _ { T }$ is the number of words in the text. In the two-stage framework, an image can be converted into a sequence of code-words (i.e. tokens) based on stage one’s encoder $E$ and codebook $\\mathcal { Z }$ . Thus, a Visual Control $( V C )$ is denoted by a sequence $\\mathbf { V } \\in \\{ 0 , \\overline { { \\mathbf { \\Omega } } } , \\mathbf { \\Omega } , | \\mathcal { Z } | - 1 \\} ^ { N _ { V } }$ consisting of code-words from the codebook $\\mathcal { Z }$ , where $N _ { V }$ is the sequence length. Similarly, the target (i.e., the image to generate) is a sequence of code-words $\\mathbf { I } \\in \\{ \\bar { 0 , } . . . , | \\mathcal { Z } | \\overset { - } { - } 1 \\} ^ { N _ { I } }$ . We support zero, one, or multiple visual controls for flexibility. As for the Preservation Control $( P C )$ , it is a sequence of binary masks $\\mathbf { P } \\in \\{ 0 , 1 \\} ^ { N _ { I } }$ with the same length as $\\mathbf { I }$ , where 1 means that the token is known (i.e., $I _ { i }$ is ground-truth if $P _ { i } = 1$ ) while 0 means the token needs to be predicted. We aim to design a model at the second stage to synthesize the target image’s sequence I conditioned on $\\mathbf { C }$ , i.e., a combination of any number of control signals from $\\mathbf { \\bar { \\{ T } } , V , \\bar { P } \\}$ . ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3 Model Inputs ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "As shown in Figure 2, our UFC-BERT modifies the original BERT model [9] to accommodate any number of multi-modal controls. Similar to BERT, the backbone is a multi-layer bidirectional Transformer encoder, enabling the dependency modeling between all input elements. The input sequence of UFC-BERT always starts with two special tokens [REL] and [FDL] for relevance estimation and fidelity estimation, then goes on with the word sequence $\\mathbf { T }$ of textual controls, code sequence V of visual controls, and ends with the code sequence I of the target image to generate. Two special separation tokens [EOT] and [EOV] are appended to the end of the textual and the visual control sequences, respectively. If there are multiple visual controls, another special token [SEP] is inserted to separate them. The sequence I of the target image to generate may be partially or fully masked by a special token [MASK]. When the preservation control $\\mathbf { P }$ is present and $P _ { i } = 1$ , token $I _ { i }$ in I is always set to the code-word corresponding to the given image block to be preserved. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Each input token’s representation is the sum of the position and token embeddings: ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Position Embedding. Our UFC-BERT learns independent sets of position embeddings for the different kinds of the inputs to achieve better distinguishment between the various modalities. The position embeddings for the word sequence are the same as BERT, i.e., we use sequential position embeddings. For a visual control or the target image, the position embedding of each token is decided according to where this token lies on the $h \\times w$ grid, i.e., we use spatial position embeddings. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Token Embedding. For textual controls, we use Byte-Pair Encoding [51] to segment each word into sub-words and then learn sub-word embeddings. Each special token, e.g., [REL] or [MASK], is assigned a dedicated embedding. For visual controls and the target image, we learn an embedding for each code-word. We do not directly use the embeddings from stage one’s codebook due to the decoupling of the two stages. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "3.4 Training: Masked Sequence Modeling with Relevance and Fidelity Estimation ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
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+    {
+        "type": "text",
+        "text": "As shown in Figure 2, we train UFC-BERT via masked sequence modeling, i.e., predicting the masked tokens in the target image conditioned on the controls. A relevance estimator and a fidelity estimator are also trained in the process, and will be key to our progressive NAR generation algorithm. ",
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+    {
+        "type": "text",
+        "text": "Task 1: Masked Sequence Modeling. This task is similar to Masked Language Modeling (MLM) in BERT, but incorporates multi-modal control signals when predicting the masked tokens. To construct training samples, we mask parts of the target image I to predict using four strategies: (1) randomly decide the number of tokens to mask, and then randomly mask the desired number of tokens; (2) mask all tokens; (3) mask the tokens within some boxed areas of the image, where the number of boxes and the box sizes are randomly decided; (4) mask the tokens outside some random boxed areas of the image. We use the four strategies with probability 0.70, 0.10, 0.10, and 0.10, respectively. To construct multi-modal control signal $\\mathbf { C }$ for each training sample, there are four different combinations: ${ < } T C$ , $V C >$ , ${ < } T C >$ , ${ < } V C >$ , <empty>, where ${ < } T C$ , $V C >$ means the textual and visual controls are simultaneously employed, ${ < } T C >$ or ${ < } V C >$ means only a textual or visual signal is used, and <empty> means no textual or visual control is present. Note that the preservation control is already included in the masked sequence modeling task. Since our dataset does not contain ground-truth pairs of visual controls and target images, we crop one or multiple regions of a target image to construct VC for the target image. Because image synthesis from solely textual controls is more challenging than from other signals, we use the four combinations with probability 0.20, 0.55, 0.20, 0.05, respectively, where textual controls get more attention. We feed UFC-BERT’s outputs at each position of I into a softmax classifier over the codebook $\\mathcal { Z }$ , which produces a probability score $Y _ { i } = \\mathrm { \\bar { P r } } ( I _ { i } | \\mathbf { I } _ { U } , \\mathbf { C } )$ for each position $i \\in M$ , where $M$ is the set of masked positions and $U$ is the unmasked set. Finally, the masked sequence modeling task minimizes the softmax cross-entropy loss $\\mathcal { L } _ { \\mathrm { M S M } } = \\mathbb { E } _ { \\mathbf { I } _ { M } , \\mathbf { I } _ { U } } \\left[ - \\log \\operatorname* { P r } ( \\mathbf { I } _ { M } | \\mathbf { I } _ { U } , \\mathbf { C } ) \\right]$ , where $\\begin{array} { r } { \\mathrm { P r } ( \\mathbf { I } _ { M } ^ { \\mathbf { - } } | \\mathbf { I } _ { U } , \\mathbf { C } ) = \\prod _ { i \\in M } Y _ { i } } \\end{array}$ . ",
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+    {
+        "type": "text",
+        "text": "Task 2: Relevance Estimation. This task is to learn a binary classifier that judges whether the generated image is relevant or irrelevant to the given multi-modal control $\\mathbf { C }$ . Briefly, we add a linear layer on the output corresponding to the special token [REL]. The linear layer outputs a scalar representing the logit, and a binary cross-entropy loss $\\mathcal { L } _ { \\mathrm { R E L } }$ is added. During training, the training samples from Task 1 serve as the positive instances (i.e. relevant pairs). We construct negative instances (i.e. irrelevant pairs) by swapping the control signals of two training samples. ",
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+        "type": "text",
+        "text": "Task 3: Fidelity Estimation. This task aims to distinguish whether the generated image is realistic from the view of human visual cognition. Similar to relevance estimation, we feed the output corresponding to [FDL] into a linear layer for binary classification and add another binary crossentropy loss ${ \\mathcal { L } } _ { \\mathrm { F D L } }$ . Since the low-fidelity images (i.e. negative instances) do not exist in the dataset, we run UFC-BERT from previous epochs to synthesize images based solely on textual control signals, and use the synthesized images as negative instances. ",
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+    {
+        "type": "text",
+        "text": "We combine the three tasks’ losses to train UFC-BERT, i.e., ",
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+    {
+        "type": "equation",
+        "img_path": "images/fcd45a99e78db65de140e10215af1a7eb0e4e5f978d2794718c1fce2962e7848.jpg",
+        "text": "$$\n\\begin{array} { r } { \\mathcal { L } _ { \\mathrm { U F C - B E R T } } = \\lambda _ { 1 } \\mathcal { L } _ { \\mathrm { M S M } } + \\lambda _ { 2 } \\mathcal { L } _ { \\mathrm { R E L } } + \\lambda _ { 3 } \\mathcal { L } _ { \\mathrm { F D L } } , } \\end{array}\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where $\\lambda _ { 1 }$ , $\\lambda _ { 2 }$ and $\\lambda _ { 3 }$ are set to 1.0, 0.5, and 0.5 to balance the three losses. The masked sequence modeling task ignores the negative instances from the other two tasks, i.e., irrelevant pairs or unrealistic instances. And the fidelity estimation task is added only after a certain number of epochs. ",
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+        "type": "text",
+        "text": "3.5 Inference: Progressive Non-Autoregressive Generation ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We design a Progressive Non-Autoregressive Generation (PNAG) algorithm for conditional image synthesis after training, which improves upon Mask-Predict [16, 21, 7]. Mask-Predict predicts all target tokens when given a fully-masked sequence at the first iteration, and then iteratively re-mask and re-predict a subset of tokens with low probability scores for a constant number of iterations. However, Mask-Predict cannot ensure the efficacy of multi-modal controls and the fidelity of the synthesized images, and requires determining the number of iterations. Our PNAG tackles its drawbacks via sample selection and dynamic termination, based on the relevance and fidelity estimators. ",
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+    {
+        "type": "text",
+        "text": "Each iteration of our PNAG algorithm consists of a Mask step and then a Predict step. Let $\\mathbf { I } ^ { ( t , i n ) } =$ (I (t,in)1 , . $( I _ { 1 } ^ { ( t , i n ) } , \\ldots , I _ { N _ { I } } ^ { ( t , i n ) } )$ and $\\mathbf { I } ^ { ( t , o u t ) } = ( I _ { 1 } ^ { ( t , o u t ) } , \\dots , I _ { N _ { I } } ^ { ( t , o u t ) } )$ , I (t,out)N ) be the state of the target image’s sequence before and after the $t$ -th iteration, respectively. The tokens in $\\mathbf { I } ^ { ( 0 , o u t ) }$ for $t = 0$ is all set to [MASK] except for the positions that are controlled by the preservation signals, i.e., except for I(0,out)i t hat has $P _ { i } = 1$ . If a preservation control is present, i.e. $P _ { i } = 1$ , we always set $I _ { i } ^ { ( t , i n ) }$ and $I _ { i } ^ { ( t , o u t ) }$ for all $t$ to be the code-word that corresponds to the provided image block to be preserved. ",
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+    {
+        "type": "text",
+        "text": "Mask Step. At the beginning of iteration $t$ $\\left( t \\geq 1 \\right)$ ), we construct the input sequence $\\mathbf { I } ^ { ( t , i n ) }$ by (re-)masking a subset of tokens in the generated sequence $\\mathbf { I } ^ { ( t - 1 , o u t ) }$ from the last iteration. Similar to beam search, we construct $B$ parallel input sequences $\\{ \\mathbf { I } _ { 1 } ^ { ( t , i n ) } , \\ldots , \\mathbf { I } _ { B } ^ { ( t , i n ) } \\}$ at each iteration. Specifically, we re-mask $n$ tokens of $\\mathbf { I } ^ { ( t - 1 , o u t ) }$ to produce each $\\mathbf { I } _ { b } ^ { ( t , i n ) }$ . We first sample $N _ { I } - n$ tokens from a multinomial distribution $\\mathrm { P r } ^ { ( t , i n ) }$ proportional to the probability scores $\\mathbf { Y } ^ { ( t - 1 ) } = \\{ Y _ { i } ^ { ( t - 1 ) } \\} _ { i = 1 } ^ { N _ { I } }$ (see Equation 3), computed by $\\mathrm { P r } ^ { ( t , i n ) } = \\mathrm { S o f t m a x } ( \\mathbf { Y } ^ { ( t - 1 ) } )$ . And other tokens are re-masked and re-predicted at the next Predict Step. Here $\\begin{array} { r } { n = N _ { I } \\cdot ( \\beta + \\frac { T - t } { T - 1 } \\cdot ( \\alpha - \\beta ) ) } \\end{array}$ , where $\\alpha$ is the initial mask ratio, $\\beta$ is the minimum mask ratio, and $T$ is the maximum possible number of iterations, such that the number of tokens to re-mask gradually decreases after every iteration. ",
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+    {
+        "type": "text",
+        "text": "Predict Step. Given the control $\\mathbf { C }$ and an input sequence $\\mathbf { I } _ { b } ^ { ( t , i n ) }$ , UFC-BERT estimates a distribution $\\mathrm { P r } ( \\hat { I } _ { i } | \\mathbf { I } _ { b } ^ { ( t , i n ) } , \\mathbf { C } )$ for each masked position $i$ . UFC-BERT also estimates the relevance score $S _ { b } ^ { R }$ and fidelity score $S _ { b } ^ { F }$ regarding the image that it is about to synthesize, and summarizes the scores into a comprehensive score $S _ { b } ^ { ( t ) } = \\sigma S _ { b } ^ { R } + ( 1 - \\sigma ) S _ { b } ^ { F }$ , where $\\sigma$ is a coefficient for adjusting the importance of the two. We perform sample selection based on $S _ { b } ^ { ( t ) }$ , i.e., we select the $b$ -th sequen ce I(t,in)b w ith the highest $S _ { b } ^ { ( t ) }$ , discard the others, and then generate $\\mathbf { I } ^ { ( t , o u t ) }$ based on the selected $\\mathbf { I } _ { b } ^ { ( t , i n ) }$ as follows: ",
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+        "type": "equation",
+        "img_path": "images/06e7f30d33c86d1433e41886ea9f1d9cb6957396f3313c4e0a709b84ccaa4c41.jpg",
+        "text": "$$\nI _ { i } ^ { ( t , o u t ) } \\sim \\mathrm { P r } ( \\hat { I } _ { i } | \\mathbf { I } _ { b } ^ { ( t , i n ) } , \\mathbf { C } ) , \\qquad Y _ { i } ^ { ( t ) } \\gets \\mathrm { P r } ( \\hat { I } _ { i } = I _ { i } ^ { ( t , o u t ) } | \\mathbf { I } _ { b } ^ { ( t , i n ) } , \\mathbf { C } ) ,\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where each token $I _ { i } ^ { ( t , o u t ) }$ is sampled from the multinomial distribution $\\mathrm { P r } ( \\hat { I } _ { i } | \\mathbf { I } _ { b } ^ { ( t , i n ) } , \\mathbf { C } )$ and the corresponding probability is assigned to $Y _ { i } ^ { ( t ) }$ . Note that we predict tokens for all masked positions regardless of the predictions’ confidence. We also implement dynamic termination based on $S _ { b } ^ { ( t ) }$ . Specifically, if the current iteration’s score $S _ { b } ^ { ( t ) }$ is higher than $S _ { m a x }$ (initialized as zero), we set $S _ { m a x }$ to $S _ { b } ^ { ( t ) }$ and record the current iteration as $t _ { m a x }$ . If $S _ { m a x }$ does not increase after three consecutive iterations, we select $\\mathbf { I } ^ { ( t _ { m a x } , o u t ) }$ as the final result and terminate our generation algorithm. ",
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+    {
+        "type": "image",
+        "img_path": "images/93edd2d5d3aff83da7f00a082c45b0340506c523bc72098992f460bfeadc1bec.jpg",
+        "image_caption": [
+            "Figure 3: Images generated by our UFC-BERT under various combinations of textual controls (TC), visual controls (VC), and preservation controls (PC). Please see the supplemental material for more showcases, where we also include a study on the diversity of the images generated by UFC-BERT and analyze how the multiple control signals interfere with each other. "
+        ],
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+    {
+        "type": "text",
+        "text": "4 Experiments ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "4.1 Datasets and Hyperparameters ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In experiments, we focus on two practical fields of image synthesis: fashionable clothing and human faces. We collect a very large-scale clothing dataset M2C-Fashion with Chinese text descriptions, which contains tens of millions of image-text pairs, much larger than the commonly used text-to-image datasets COCO [34] and CUB [56]. Details of the dataset are provided in the supplementary material. We additionally use another high-resolution facial dataset Multi-Modal CelebA-HQ [28, 61]. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Following the model setting of VQGAN [13], we use the $2 5 6 \\times 2 5 6$ image size on the two datasets and transform each image to a discrete sequence of $1 6 \\times 1 6$ codes, where the codebook size $| { \\mathcal { Z } } |$ is set to 1024. For the BERT model, we set the number of layers, hidden size, and the number of attention heads to 24, 1024, and 16, respectively. Our UFC-BERT has 307M parameters, same as the Transformer used by VQGAN. As for hyper-parameters of PNAG, we set the parallel decoding number $B$ to 5 and the balance coefficient $\\sigma$ to 0.5. We set the initial mask ratio $\\alpha$ , the minimum mask ratio $\\beta$ , and the maximum iteration number $T$ to 0.8, 0.2, and 10, respectively. ",
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+    {
+        "type": "image",
+        "img_path": "images/5a13f76b34d1717dd6eb50b4d3c2e9780dd310cab6091849fdb547a10501aeca.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "Figure 4: Image synthesis with multiple visual controls, where we crop regions from $2 \\sim 3$ images to serve as the visual controls. UFC-BERT synthesizes images that naturally fuse the visual elements. ",
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+    {
+        "type": "table",
+        "img_path": "images/bc8cc6545840e29fdfcba71a14c5e3b7d1ca6dbbf87ab7d71365fbb4a2d37ba5.jpg",
+        "table_caption": [
+            "Table 1: Comparisons with GAN baselines for text-to-image synthesis on Multi-Modal CelebA-HQ. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>AttnGAN [62]</td><td>ControlGAN [30]</td><td>DF-GAN [54]</td><td>DM-GAN [71]</td><td>TediGAN [61]</td><td>UFC-BERT (our)</td></tr><tr><td>FID↓</td><td>125.98</td><td>116.32</td><td>137.60</td><td>131.05</td><td>106.37</td><td>66.72</td></tr><tr><td>LPIPS↓</td><td>0.512</td><td>0.522</td><td>0.581</td><td>0.544</td><td>0.456</td><td>0.448</td></tr></table>",
+        "bbox": [
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+    {
+        "type": "table",
+        "img_path": "images/aa2be92a3ce5cdf4d74e840448d88aa2a3d320a24c50984efef7edfe6b90839d.jpg",
+        "table_caption": [
+            "Table 2: Comparisons with the autoregressive two-stage method VQGAN for text-to-image synthesis. ↓ means the lower the better, while $\\uparrow$ means the opposite. We evaluate speed on the same V100 GPU. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Datasets</td><td rowspan=\"2\">Methods</td><td colspan=\"4\">Automatic Metrics</td><td colspan=\"2\">Human Pairwise Study</td><td rowspan=\"2\">Inference Speed</td></tr><tr><td>FID↓</td><td>LPIPS↓</td><td>PSNR↑</td><td>SSIM↑</td><td>Relevance</td><td>Fidelity</td></tr><tr><td rowspan=\"2\">M2C-Fashion</td><td>VQGAN (AR)</td><td>12.48</td><td>0.483</td><td>10.80</td><td>0.56</td><td>38.6%</td><td>44.2%</td><td>8.73 sec/sample</td></tr><tr><td>UFC-BERT (NAR)</td><td>11.53</td><td>0.461</td><td>13.14</td><td>0.58</td><td>61.4%</td><td>55.8%</td><td>0.81 sec/sample</td></tr><tr><td rowspan=\"2\">Multi-Modal CelebA-HQ</td><td>VQGAN (AR)</td><td>52.63</td><td>0.503</td><td>8.98</td><td>0.28</td><td>42.7%</td><td>46.9%</td><td>8.66 sec/sample</td></tr><tr><td>UFC-BERT (NAR)</td><td>66.72</td><td>0.448</td><td>9.56</td><td>0.29</td><td>57.3%</td><td>53.1%</td><td>0.79 sec/sample</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "4.2 Flexibility of Multi-Modal Controls for Conditional Image Synthesis ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In this section, we qualitatively verify the synthesis ability of UFC-BERT with three modalities of control signals, i.e., textual, visual, and preservation controls. The textual controls are the texts paired with the images, which are already provided by the two datasets, while the visual controls are code sequences of cropped regions, e.g. regions that represent logos or texture of clothes. ",
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+    {
+        "type": "text",
+        "text": "In Figure 3, we synthesize images conditioned on combinations of the three types of control signals. The results demonstrate UFC-BERT can unify any number of multi-modal controls to synthesize high-quality images. Further, UFC-BERT supports one or multiple visual controls for more flexible synthesis, as shown in Figure 4 where we generate images given $2 { \\sim } 3$ visual controls. We observe that UFC-BERT can reasonably fuse multiple visual elements and produce a harmonious image. ",
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+    {
+        "type": "text",
+        "text": "4.3 Quantitative Comparison to Existing Methods for Text-to-Image Synthesis ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In this section, we investigate how our UFC-BERT quantitatively compares to existing models. Considering most existing methods only utilize one control signal, we select the most common and challenging task text-to-image synthesis to compare the synthesis ability. ",
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+        "type": "text",
+        "text": "First, we compare our UFC-BERT with GAN-based text-to-image models AttnGAN [62], ControlGAN [30], DF-GAN [54], DM-GAN [71] and TediGAN [61] on the Multi-Modal CelebA-HQ dataset. For evalution, we adopt two automatic metrics FID [23] and LPIPS [66]. We report the results on Table 1 and our UFC-BERT achieves the best performance on the two metrics, even outperforming the TediGAN that uses slow and complex instance-level optimization. This demonstrates the two-stage architecture and non-autoregressive generation of UFC-BERT are suitable for text-to-image synthesis. ",
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+    {
+        "type": "image",
+        "img_path": "images/1d08458dedaac9faaf6b73ca6ee658a8e85190ea957f3c4271e84dbf31086c91.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "This woman has wavy hair and is wearing earrings, and lipstick. ",
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+        "page_idx": 8
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+    {
+        "type": "image",
+        "img_path": "images/9d2a3197362c142ec2df400999d14750954a6da27378d00895af4eda427a44b5.jpg",
+        "image_caption": [
+            "Figure 6: The iterative inference process of our PNAG algorithm. The red bounding box means the image has the highest comprehensive score and is selected as the final output result. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Besides, we compare our UFC-BERT with the autoregressive two-stage method VQGAN from three aspects: (i) the automatic metrics FID for image quality, as well as LPIPS, PSNR [59] and SSIM [59] for the similarity between the generated image and the ground truth; (ii) the Relevance and Fidelity metrics are evaluated through a user study, where the users are asked to judge which model’s output is more relevant to the textual descriptions, and more photorealistic; (iii) the synthesis speed of the two approaches. Note that the autoregressive inference implementation of VQGAN has been optimized by caching the preceding computation as in Transformer-XL [8], and UFCBERT and VQGAN have the same parameter number (307M) for fair com",
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+    {
+        "type": "image",
+        "img_path": "images/39a4b0e8cd6b09b597ea30d66c7ff01259cf6892713f421054bd3094d3fec779.jpg",
+        "image_caption": [
+            "Figure 5: Typical examples of UFC-BERT and VQGAN for text-to-image synthesis, including a counterfactual case. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "parison. For the user study, the two models receive the same textual signals, and each generates 50 images. We collect the pairwise comparison results from five volunteers. ",
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+    {
+        "type": "text",
+        "text": "As shown in Table 2, our UFC-BERT achieves better performance for almost all criteria with about $1 1 \\times$ speedup. This suggests our non-autoregressive UFC-BERT with progressive NAR generation algorithm can synthesize high-fidelity images relevant to textual descriptions. As for the FID metric, UFC-BERT outperforms VQGAN on M2C-Fashion, but has worse performance on Multi-Modal CelebA-HQ, it may be due to the fact that the autoregressive VQGAN can more easily memorize the pattern of a small dataset (only 30,000 facial images). In Figure 5, we further show typical generated examples to intuitively display the difference between the two approaches, including a case of counterfactual generation. We find that UFC-BERT can synthesize high-quality images, even for the counterfactual case. ",
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+    {
+        "type": "text",
+        "text": "4.4 The Effectiveness of Our Progressive NAR Generation Algorithm ",
+        "text_level": 1,
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+        "text": "In this section, we first visualize in Figure 6 the iterative process of our PNAG inference method based on the relevance and fidelity estimators. The images with red bounding boxes are the final outputs that match the textual control signals. We can find that the fidelity and relevance of the images increase after a few iterations, verifying our PNAG algorithm can guide the inference process towards a better direction and synthesize more realistic images that match the control signals. ",
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+    {
+        "type": "table",
+        "img_path": "images/4372df104d5e90ebfc4928059da8b15658f94dc3665d27bc68df7a5c2a608218.jpg",
+        "table_caption": [
+            "Table 3: Ablation studies of our PNAG inference algorithm. PNAG(w/o. REF) and PNAG(w/o. FDL) set $B$ to the default value 5. MNAG is the original Mask-Predict algorithm [16]. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset</td><td>Metrics</td><td>MNAG [16]</td><td>PNAG(w/o.REF)</td><td>PNAG(w/o.FDL)</td><td>PNAG(B=1)</td><td>PNAG(B=5)</td><td>PNAG(B=10)</td></tr><tr><td rowspan=\"2\">M2C-Fashion</td><td>FID↓</td><td>14.77</td><td>12.17</td><td>13.14</td><td>12.72</td><td>11.53</td><td>11.14</td></tr><tr><td>LPIPS↓</td><td>0.488</td><td>0.477</td><td>0.469</td><td>0.479</td><td>0.461</td><td>0.456</td></tr><tr><td rowspan=\"2\">Multi-Modal CelebA-HQ</td><td>FID↓</td><td>72.04</td><td>68.90</td><td>70.32</td><td>69.49</td><td>66.72</td><td>65.30</td></tr><tr><td>LPIPS↓</td><td>0.514</td><td>0.469</td><td>0.463</td><td>0.475</td><td>0.448</td><td>0.445</td></tr></table>",
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+        "type": "text",
+        "text": "We then conduct ablation studies of PNAG. As shown in Table 3, we develop three ablated inference methods PNAG(w/o. REF), PNAG(w/o. FDL) and MNAG, where PNAG(w/o. REF) and PNAG(w/o. FDL) discard the relevance estimator and the fidelity estimator, respectively, and MNAG is the original Mask-Predict method [16] without any estimator. The results demonstrate that the two estimators effectively utilize the discriminative capability of UFC-BERT and do help improve the synthesis quality. Additionally, we vary the crucial hyper-parameter of PNAG $B$ (i.e. the parallel decoding number during inference) from 1 to 10, and the results in Table 3 show that a larger $B$ is beneficial to the synthesis quality. ",
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+    {
+        "type": "text",
+        "text": "5 Conclusions ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "We proposed UFC-BERT to unify any number of multi-modal controls in a universal form for conditional image synthesis. We utilized non-autoregressive generation to improve inference speed, enhance holistic consistency, and support preservation controls. Further, we designed a progressive generation algorithm based on relevance and fidelity estimators to ensure relevance and fidelity. ",
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+    {
+        "type": "text",
+        "text": "References ",
+        "text_level": 1,
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+            174,
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+    },
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+        "type": "text",
+        "text": "[1] Andrew Brock, Jeff Donahue, and Karen Simonyan. Large scale gan training for high fidelity natural image synthesis. arXiv preprint arXiv:1809.11096, 2018.   \n[2] 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[3] 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[4] Qifeng Chen and Vladlen Koltun. Photographic image synthesis with cascaded refinement networks. In Proceedings of the IEEE International Conference on Computer Vision, pages 1511–1520, 2017.   \n[5] Yen-Chun Chen, Linjie Li, Licheng Yu, Ahmed El Kholy, Faisal Ahmed, Zhe Gan, Yu Cheng, and Jingjing Liu. Uniter: Learning universal image-text representations. 2019.   \n[6] Rewon Child, Scott Gray, Alec Radford, and Ilya Sutskever. Generating long sequences with sparse transformers. arXiv preprint arXiv:1904.10509, 2019.   \n[7] Jaemin Cho, Jiasen Lu, Dustin Schwenk, Hannaneh Hajishirzi, and Aniruddha Kembhavi. X-lxmert: Paint, caption and answer questions with multi-modal transformers. arXiv preprint arXiv:2009.11278, 2020.   \n[8] Zihang Dai, Zhilin Yang, Yiming Yang, Jaime Carbonell, Quoc V Le, and Ruslan Salakhutdinov. Transformer-xl: Attentive language models beyond a fixed-length context. arXiv preprint arXiv:1901.02860, 2019.   \n[9] Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. Bert: Pre-training of deep bidirectional transformers for language understanding. In Proceedings of the Conference on The North American Chapter of the Association for Computational Linguistics, 2019.   \n[10] Hao Dong, Simiao Yu, Chao Wu, and Yike Guo. Semantic image synthesis via adversarial learning. In Proceedings of the IEEE International Conference on Computer Vision, pages 5706–5714, 2017.   \n[11] Li Dong, Nan Yang, Wenhui Wang, Furu Wei, Xiaodong Liu, Yu Wang, Jianfeng Gao, Ming Zhou, and Hsiao-Wuen Hon. Unified language model pre-training for natural language understanding and generation. arXiv preprint arXiv:1905.03197, 2019.   \n[12] 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[13] Patrick Esser, Robin Rombach, and Björn Ommer. Taming transformers for high-resolution image synthesis. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2021.   \n[14] Junlong Gao, Xi Meng, Shiqi Wang, Xia Li, Shanshe Wang, Siwei Ma, and Wen Gao. Masked nonautoregressive image captioning. arXiv preprint arXiv:1906.00717, 2019.   \n[15] Leon A Gatys, Alexander S Ecker, and Matthias Bethge. Image style transfer using convolutional neural networks. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 2414–2423, 2016.   \n[16] Marjan Ghazvininejad, Omer Levy, Yinhan Liu, and Luke Zettlemoyer. Mask-predict: Parallel decoding of conditional masked language models. arXiv preprint arXiv:1904.09324, 2019.   \n[17] Arnab Ghosh, Richard Zhang, Puneet K Dokania, Oliver Wang, Alexei A Efros, Philip HS Torr, and Eli Shechtman. Interactive sketch & fill: Multiclass sketch-to-image translation. In Proceedings of the IEEE International Conference on Computer Vision, pages 1171–1180, 2019.   \n[18] Ian J Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial networks. arXiv preprint arXiv:1406.2661, 2014.   \n[19] Jiatao Gu, James Bradbury, Caiming Xiong, Victor OK Li, and Richard Socher. Non-autoregressive neural machine translation. arXiv preprint arXiv:1711.02281, 2017.   \n[20] Junliang Guo, Xu Tan, Di He, Tao Qin, Linli Xu, and Tie-Yan Liu. Non-autoregressive neural machine translation with enhanced decoder input. In Proceedings of the American Association for Artificial Intelligence, volume 33, pages 3723–3730, 2019.   \n[21] Junliang Guo, Zhirui Zhang, Linli Xu, Hao-Ran Wei, Boxing Chen, and Enhong Chen. Incorporating bert into parallel sequence decoding with adapters. In Advances in Neural Information Processing Systems, 2020.   \n[22] Longteng Guo, Jing Liu, Xinxin Zhu, Xingjian He, Jie Jiang, and Hanqing Lu. Non-autoregressive image captioning with counterfactuals-critical multi-agent learning. arXiv preprint arXiv:2005.04690, 2020.   \n[23] Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, Günter Klambauer, and Sepp Hochreiter. Gans trained by a two time-scale update rule converge to a nash equilibrium. 2017.   \n[24] Zhicheng Huang, Zhaoyang Zeng, Bei Liu, Dongmei Fu, and Jianlong Fu. Pixel-bert: Aligning image pixels with text by deep multi-modal transformers. arXiv preprint arXiv:2004.00849, 2020.   \n[25] Satoshi Iizuka, Edgar Simo-Serra, and Hiroshi Ishikawa. Let there be color! joint end-to-end learning of global and local image priors for automatic image colorization with simultaneous classification. ACM Transactions on Graphics (ToG), 35(4):1–11, 2016.   \n[26] Phillip Isola, Jun-Yan Zhu, Tinghui Zhou, and Alexei A Efros. Image-to-image translation with conditional adversarial networks. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 1125–1134, 2017.   \n[27] Justin Johnson, Alexandre Alahi, and Li Fei-Fei. Perceptual losses for real-time style transfer and superresolution. In Proceedings of the European Conference on Computer Vision, pages 694–711. Springer, 2016.   \n[28] Tero Karras, Timo Aila, Samuli Laine, and Jaakko Lehtinen. Progressive growing of gans for improved quality, stability, and variation. arXiv preprint arXiv:1710.10196, 2017.   \n[29] Jason Lee, Elman Mansimov, and Kyunghyun Cho. Deterministic non-autoregressive neural sequence modeling by iterative refinement. arXiv preprint arXiv:1802.06901, 2018.   \n[30] Bowen Li, Xiaojuan Qi, Thomas Lukasiewicz, and Philip HS Torr. Controllable text-to-image generation. arXiv preprint arXiv:1909.07083, 2019.   \n[31] Bowen Li, Xiaojuan Qi, Thomas Lukasiewicz, and Philip HS Torr. Manigan: Text-guided image manipulation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 7880–7889, 2020.   \n[32] Gen Li, Nan Duan, Yuejian Fang, Ming Gong, and Daxin Jiang. Unicoder-vl: A universal encoder for vision and language by cross-modal pre-training. In Proceedings of the American Association for Artificial Intelligence, volume 34, pages 11336–11344, 2020.   \n[33] Yi Liao, Xin Jiang, and Qun Liu. Probabilistically masked language model capable of autoregressive generation in arbitrary word order. arXiv preprint arXiv:2004.11579, 2020.   \n[34] Tsung-Yi Lin, Michael Maire, Serge Belongie, James Hays, Pietro Perona, Deva Ramanan, Piotr Dollár, and C Lawrence Zitnick. Microsoft coco: Common objects in context. In Proceedings of the European Conference on Computer Vision, pages 740–755. Springer, 2014.   \n[35] Jiasen Lu, Dhruv Batra, Devi Parikh, and Stefan Lee. Vilbert: Pretraining task-agnostic visiolinguistic representations for vision-and-language tasks. arXiv preprint arXiv:1908.02265, 2019.   \n[36] Jiasen Lu, Vedanuj Goswami, Marcus Rohrbach, Devi Parikh, and Stefan Lee. 12-in-1: Multi-task vision and language representation learning. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 10437–10446, 2020.   \n[37] Liqian Ma, Xu Jia, Qianru Sun, Bernt Schiele, Tinne Tuytelaars, and Luc Van Gool. Pose guided person image generation. arXiv preprint arXiv:1705.09368, 2017.   \n[38] Elman Mansimov, Alex Wang, Sean Welleck, and Kyunghyun Cho. A generalized framework of sequence generation with application to undirected sequence models. arXiv preprint arXiv:1905.12790, 2019.   \n[40] Seonghyeon Nam, Yunji Kim, and Seon Joo Kim. Text-adaptive generative adversarial networks: manipulating images with natural language. arXiv preprint arXiv:1810.11919, 2018.   \n[41] Aaron van den Oord, Nal Kalchbrenner, Oriol Vinyals, Lasse Espeholt, Alex Graves, and Koray Kavukcuoglu. Conditional image generation with pixelcnn decoders. arXiv preprint arXiv:1606.05328, 2016.   \n[42] Aaron van den Oord, Oriol Vinyals, and Koray Kavukcuoglu. Neural discrete representation learning. arXiv preprint arXiv:1711.00937, 2017.   \n[43] Di Qi, Lin Su, Jia Song, Edward Cui, Taroon Bharti, and Arun Sacheti. Imagebert: Cross-modal pre-training with large-scale weak-supervised image-text data. arXiv preprint arXiv:2001.07966, 2020.   \n[44] Alec Radford, Karthik Narasimhan, Tim Salimans, and Ilya Sutskever. Improving language understanding by generative pre-training. 2018.   \n[45] Alec Radford, Jeffrey Wu, Rewon Child, David Luan, Dario Amodei, and Ilya Sutskever. Language models are unsupervised multitask learners. OpenAI blog, 1(8):9, 2019.   \n[46] Wasifur Rahman, Md Kamrul Hasan, Amir Zadeh, Louis-Philippe Morency, and Mohammed Ehsan Hoque. M-bert: Injecting multimodal information in the bert structure. arXiv preprint arXiv:1908.05787, 2019.   \n[47] Aditya Ramesh, Mikhail Pavlov, Gabriel Goh, Scott Gray, Chelsea Voss, Alec Radford, Mark Chen, and Ilya Sutskever. Zero-shot text-to-image generation. arXiv preprint arXiv:2102.12092, 2021.   \n[48] Ali Razavi, Aaron van den Oord, and Oriol Vinyals. Generating diverse high-fidelity images with vq-vae-2. arXiv preprint arXiv:1906.00446, 2019.   \n[49] Yi Ren, Chenxu Hu, Xu Tan, Tao Qin, Sheng Zhao, Zhou Zhao, and Tie-Yan Liu. Fastspeech 2: Fast and high-quality end-to-end text to speech. arXiv preprint arXiv:2006.04558, 2020.   \n[50] Yi Ren, Yangjun Ruan, Xu Tan, Tao Qin, Sheng Zhao, Zhou Zhao, and Tie-Yan Liu. Fastspeech: Fast, robust and controllable text to speech. arXiv preprint arXiv:1905.09263, 2019.   \n[51] Rico Sennrich, Barry Haddow, and Alexandra Birch. Neural machine translation of rare words with subword units. arXiv preprint arXiv:1508.07909, 2015.   \n[52] Weijie Su, Xizhou Zhu, Yue Cao, Bin Li, Lewei Lu, Furu Wei, and Jifeng Dai. Vl-bert: Pre-training of generic visual-linguistic representations. arXiv preprint arXiv:1908.08530, 2019.   \n[53] Hao Tan and Mohit Bansal. Lxmert: Learning cross-modality encoder representations from transformers. arXiv preprint arXiv:1908.07490, 2019.   \n[54] Ming Tao, Hao Tang, Songsong Wu, Nicu Sebe, Xiao-Yuan Jing, Fei Wu, and Bingkun Bao. Df-gan: Deep fusion generative adversarial networks for text-to-image synthesis. arXiv preprint arXiv:2008.05865, 2020.   \n[55] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin. Attention is all you need. In Advances in Neural Information Processing Systems, pages 5998–6008, 2017.   \n[56] Catherine Wah, Steve Branson, Peter Welinder, Pietro Perona, and Serge Belongie. The caltech-ucsd birds-200-2011 dataset. 2011.   \n[57] Alex Wang and Kyunghyun Cho. Bert has a mouth, and it must speak: Bert as a markov random field language model. arXiv preprint arXiv:1902.04094, 2019.   \n[58] Ting-Chun Wang, Ming-Yu Liu, Jun-Yan Zhu, Andrew Tao, Jan Kautz, and Bryan Catanzaro. Highresolution image synthesis and semantic manipulation with conditional gans. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 8798–8807, 2018.   \n[59] Zhou Wang, Alan C Bovik, Hamid R Sheikh, and Eero P Simoncelli. Image quality assessment: from error visibility to structural similarity. IEEE transactions on image processing, 13(4):600–612, 2004.   \n[60] Weihao Xia, Yujiu Yang, and Jing-Hao Xue. Cali-sketch: Stroke calibration and completion for high-quality face image generation from poorly-drawn sketches. arXiv preprint arXiv:1911.00426, 2019.   \n[61] Weihao Xia, Yujiu Yang, Jing-Hao Xue, and Baoyuan Wu. Tedigan: Text-guided diverse image generation and manipulation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2021.   \n[62] Tao Xu, Pengchuan Zhang, Qiuyuan Huang, Han Zhang, Zhe Gan, Xiaolei Huang, and Xiaodong He. Attngan: Fine-grained text to image generation with attentional generative adversarial networks. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 1316–1324, 2018.   \n[63] Jiahui Yu, Zhe Lin, Jimei Yang, Xiaohui Shen, Xin Lu, and Thomas S Huang. Free-form image inpainting with gated convolution. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 4471–4480, 2019.   \n[64] Han Zhang, Tao Xu, Hongsheng Li, Shaoting Zhang, Xiaogang Wang, Xiaolei Huang, and Dimitris N Metaxas. Stackgan: Text to photo-realistic image synthesis with stacked generative adversarial networks. In Proceedings of the IEEE International Conference on Computer Vision, pages 5907–5915, 2017.   \n[65] Han Zhang, Tao Xu, Hongsheng Li, Shaoting Zhang, Xiaogang Wang, Xiaolei Huang, and Dimitris N Metaxas. Stackgan $^ { + + }$ : Realistic image synthesis with stacked generative adversarial networks. IEEE transactions on pattern analysis and machine intelligence, 41(8):1947–1962, 2018.   \n[66] Richard Zhang, Phillip Isola, Alexei A Efros, Eli Shechtman, and Oliver Wang. The unreasonable effectiveness of deep features as a perceptual metric. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 586–595, 2018.   \n[67] Shengyu Zhang, Tan Jiang, Tan Wang, Kun Kuang, Zhou Zhao, Jianke Zhu, Jin Yu, Hongxia Yang, and Fei Wu. Devlbert: Learning deconfounded visio-linguistic representations. In Proceedings of the 28th ACM International Conference on Multimedia, pages 4373–4382, 2020.   \n[68] Shengyu Zhang, Ziqi Tan, Zhou Zhao, Jin Yu, Kun Kuang, Tan Jiang, Jingren Zhou, Hongxia Yang, and Fei Wu. Comprehensive information integration modeling framework for video titling. In Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pages 2744–2754, 2020.   \n[69] Zijian Zhang, Zhou Zhao, Zhu Zhang, Baoxing Huai, and Jing Yuan. Text-guided image inpainting. In Proceedings of the ACM International Conference on Multimedia, pages 4079–4087, 2020.   \n[70] Luowei Zhou, Hamid Palangi, Lei Zhang, Houdong Hu, Jason Corso, and Jianfeng Gao. Unified visionlanguage pre-training for image captioning and vqa. In Proceedings of the American Association for Artificial Intelligence, volume 34, pages 13041–13049, 2020.   \n[71] Minfeng Zhu, Pingbo Pan, Wei Chen, and Yi Yang. Dm-gan: Dynamic memory generative adversarial networks for text-to-image synthesis. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 5802–5810, 2019.   \n[72] Peihao Zhu, Rameen Abdal, Yipeng Qin, and Peter Wonka. Sean: Image synthesis with semantic region-adaptive normalization. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 5104–5113, 2020. ",
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parse/train/r1eIiCNYwS/r1eIiCNYwS.md

@@ -0,0 +1,421 @@
+# TRANSFORMER-XH: MULTI-EVIDENCE REASONING WITH EXTRA HOP ATTENTION
+
+Chen Zhao∗   
+University of Maryland, College Park   
+chenz@cs.umd.edu
+
+Chenyan Xiong, Corby Rosset, Xia Song, Paul Bennett, and Saurabh Tiwary
+
+Microsoft AI & Research cxiong, corosset, xiaso, pauben, satiwary $@$ microsoft.com
+
+# ABSTRACT
+
+Transformers have achieved new heights modeling natural language as a sequence of text tokens. However, in many real world scenarios, textual data inherently exhibits structures beyond a linear sequence such as trees and graphs; many tasks require reasoning with evidence scattered across multiple pieces of texts. This paper presents Transformer-XH, which uses eXtra Hop attention to enable intrinsic modeling of structured texts in a fully data-driven way. Its new attention mechanism naturally “hops” across the connected text sequences in addition to attending over tokens within each sequence. Thus, Transformer-XH better conducts joint multi-evidence reasoning by propagating information between documents and constructing global contextualized representations. On multi-hop question answering, Transformer-XH leads to a simpler multi-hop QA system which outperforms previous state-of-the-art on the HotpotQA FullWiki setting. On FEVER fact verification, applying Transformer-XH provides state-of-the-art accuracy and excels on claims whose verification requires multiple evidence.
+
+# 1 INTRODUCTION
+
+Transformers effectively model natural language in sequential form (Vaswani et al., 2017; Dai et al., 2019; Devlin et al., 2019; Yang et al., 2019). Nevertheless, in many NLP tasks, text does not simply appear as a linear sequence of tokens but rather carries meaningful structure in the form of paragraphs, headings, and hyperlinks. These structures can be represented abstractly as trees or graphs with nodes and edges; and the tasks can be performed as joint reasoning on these more general structures as input. Multi-hop question answering (Yang et al., 2018) is one such task in which structure plays an important role, since the evidence required to formulate the answer is scattered across multiple documents, requiring systems to jointly reason across links between them.
+
+Recent approaches leverage pre-trained Transformers (e.g., BERT) for multi-hop question answering (QA) by converting the structural reasoning task into sub-tasks that model flat sequences. For example, Min et al. (2019b) decompose a multi-hop question into a series of single-hop questions; Ding et al. (2019) conduct several steps of single-hop reading comprehension to simulate the multihop reasoning. The hope is that additional processing to fuse the outputs of the sub-models can recover all the necessary information from the original structure. While pre-trained Transformer language models have shown improvements on multi-hop QA, manipulating the inherent structure of the problem to fit the rigid requirements of out-of-the-box models can introduce problematic assumptions or information loss.
+
+This paper presents Transformer-XH (meaning eXtra Hop), which upgrades Transformers with the ability to natively represent structured texts. Transformer-XH introduces extra hop attention in its layers that connects different text pieces following their inherent structure while also maintaining the powerful pre-trained Transformer abilities over each textual piece individually. Our extra hop attention enables 1) a more global representation of the evidence contributed by each piece of text as it relates to the other evidence, and 2) a more natural way to jointly reason over an evidence graph by propagating information along edges necessary to complete the task at hand.
+
+We apply Transformer-XH to two multi-evidence reasoning tasks: Hotpot QA, the multi-hop question answering task (Yang et al., 2018), and FEVER, the fact verification benchmark whose claims often require multiple pieces of evidence to support (Thorne et al., 2018). Rather than decomposing the task into a series of sub-tasks to fit the constraints of pre-trained Transformers, TransformerXH is a solution that fits the problem as it naturally occurs. It is a single model that represents and combines evidence from multiple documents to conduct the reasoning process. On HotpotQA’s FullWiki setting, which requires strong multi-hop reasoning capability (Min et al., 2019b; Jiang & Bansal, 2019), Transformer-XH outperforms CogQA (Ding et al., 2019), the previous start-of-theart, by 12 points on answer F1. On FEVER 1.0 shared task, Transformer-XH outperforms GEAR, the Graph Neural Network based approach significantly. On both applications, Transformer-XH beats the contemporary BERT based pipeline SR-MRS (Nie et al., 2019), by 2-3 points.
+
+The results follow from our simple yet effective design, with one unified model operating over the inherent structure of the task, rather than melding the outputs from disparate sub-tasks adapted to the sequential constraints of pre-trained Transformers. Our ablation studies demonstrate TransformerXH’s efficacy on questions that are known to require multi-hop reasoning (Min et al., 2019b) and on verifying multi-evidence claims (Liu et al., 2019b). Our analyses confirm that the source of Transformer-XH’s effectiveness success is due to the eXtra Hop attention’s ability to fuse and propagate information across multiple documents.1
+
+# 2 MODEL
+
+This section first discusses preliminaries on sequential Transformers, then we show how we incorporate eXtra hop attention to create Transformer-XH.
+
+# 2.1 PRELIMINARIES
+
+Transformers represent a sequence of input text tokens $X = \{ x _ { 1 } , . . . , x _ { i } , . . . , x _ { n } \}$ as contextualized distributed representations $H = \{ h _ { 1 } , . . . , h _ { i } , . . . , h _ { n } \}$ (Vaswani et al., 2017). This process involves multiple stacked self-attention layers that converts the input $X$ into $\{ H ^ { 0 } , H ^ { 1 } , . . . , \dot { H } ^ { l } , . . . H ^ { L } \}$ , starting from $H ^ { 0 }$ , the embeddings, to the final layer of depth $L$ .
+
+The key idea of Transformer is its attention mechanism, which calculates the $l$ -th layer output $H ^ { l }$ using the input $H ^ { l - 1 }$ from the previous layer:
+
+$$
+\begin{array} { c } { { H ^ { l } = \mathrm { s o f t m a x } ( \frac { \boldsymbol { Q } \cdot \boldsymbol { K } ^ { T } } { \sqrt { d _ { k } } } ) \cdot \boldsymbol { V } ^ { T } , } } \\ { { Q ^ { T } ; \boldsymbol { K } ^ { T } ; \boldsymbol { V } ^ { T } = W ^ { q } \cdot H ^ { l - 1 } ; W ^ { k } \cdot H ^ { l - 1 } ; W ^ { v } \cdot H ^ { l - 1 } . } } \end{array}
+$$
+
+It includes three projections on the input $H ^ { l - 1 }$ : Query (Q), Key (K), and Value (V).
+
+Specifically, the slices of token $h _ { i } ^ { l }$ in Eqn.(2) is:
+
+$$
+h _ { i } ^ { l } = \sum _ { j } \mathrm { s o f t m a x } _ { j } ( \frac { q _ { i } ^ { T } \cdot k _ { j } } { \sqrt { d _ { k } } } ) \cdot v _ { j } ,
+$$
+
+which first calculates its attention to all other tokens $j$ in the sequence and then combines the token values $v _ { j }$ into a new representation $h _ { i } ^ { l }$ , using the normalized attention weights. Multiple attentions can be used in one Transformer layer and concatenated as multi-head attention (Vaswani et al., 2017). The architecture is stacked to form rather deep networks, which leads to significant success of large pre-trained Transformer models (Devlin et al., 2019; Liu et al., 2019a).
+
+A challenge of Transformer is that its attention is calculated over all token pairs (Eqn. 3), which is hard to scale to long text sequences. Transformer-XL (eXtra Long) addresses this challenge by breaking down longer texts, e.g., a multi-paragraph document, into a sequence of text segments: $\{ X _ { 1 } , . . . , \bar { X } _ { \tau } , . . . , X _ { \zeta } \}$ , and propagates the information between adjacent text segments using the following attention:
+
+$$
+\tilde { H } _ { \tau } ^ { l - 1 } = [ \mathrm { F r e e z e } ( H _ { \tau - 1 } ^ { l - 1 } ) \circ H _ { \tau } ^ { l - 1 } ] .
+$$
+
+![](images/8baba74743e8e0ad5cde2c86e9cf6d36bd451afabad7f781dfa9d0e1d0a6d335.jpg)  
+(a) Hop attention on the path   
+(b) Transformer-XH in Multi-hop QA   
+Figure 1: The eXtra Hop attention in Transformer-XH (a) and its application to multi-hop QA (b).
+
+It concatenates (◦) the representation of the previous segment $H _ { \tau - 1 } ^ { l - 1 }$ to the current segment as segment level recurrences. The new representation $\tilde { H } _ { \tau } ^ { l - 1 }$ includes the information from previous segment and is integrated in the new attention mechanism:
+
+$$
+\tilde { Q } ^ { T } ; \tilde { K } ^ { T } ; \tilde { V } ^ { T } = W ^ { q } \cdot H _ { \tau } ^ { l - 1 } ; W ^ { k } \cdot \tilde { H } _ { \tau } ^ { l - 1 } ; W ^ { v } \cdot \tilde { H } _ { \tau } ^ { l - 1 } .
+$$
+
+The attention over the previous segment allows Transformer-XL to effectively model long form text data recurrently as a sequence of text chunks (Dai et al., 2019).
+
+Nevertheless, in many scenarios, the text segments are organized in nontrivial structures beyond a linear sequence. For example, documents are connected by hyperlinks in a graphical structure that does not readily simplify to form a linear sequence, prohibiting Transformer-XL’s recurrent approach.
+
+# 2.2 TRANSFORMER-XH WITH EXTRA HOP ATTENTION
+
+Transformer-XH models structured text sequence by linking them with eXtra Hop attention following their original structure. As illustrated in Figure 1a, to model three connected documents $d _ { 2 }  d _ { 1 }  d _ { 3 }$ , Transformer-XH uses eXtra Hop attention to propagate information along the graph edges, enabling information sharing between connected text sequence.
+
+Formally, the structured text data includes a set of nodes, $\mathcal { X } = \{ X _ { 1 } , . . . , X _ { \tau } , . . . X _ { \zeta } \}$ , each corresponding to a text sequence, and an edge matrix $E$ , which includes the connections (e.g., links) between them. The goal is to learn representations $\mathcal { H } = \{ \tilde { H } _ { 1 } , . . . , \tilde { H } _ { \tau } , . . . \tilde { H } _ { \zeta } \}$ , that incorporate not only the local information in each sequence $X$ , but also the global contexts on the entire structured text $\{ \mathcal { X } , E \}$ .
+
+Transformer-XH achieves this by two attention mechanisms: in-sequence attention and eXtra Hop attention. The in-sequence attention is the same as vanilla Transformer: in layer $l$ , token $i$ gathers information from other tokens inside the same text piece $\tau$ :
+
+$$
+h _ { \tau , i } ^ { l } = \sum _ { j } \mathrm { s o f t m a x } _ { j } ( \frac { q _ { \tau , i } ^ { T } \cdot k _ { \tau , j } } { \sqrt { d _ { k } } } ) \cdot v _ { \tau , j } .
+$$
+
+The eXtra Hop attention uses the first token in each sequence – the added special token “[CLS]” – as an “attention hub”, which attends on all other connected nodes’ hub token. In layer $l$ , the $\tau$ -th text sequence attends over another text sequence $\eta$ if there is an edge between them $e _ { \tau \eta } = 1$ ):
+
+$$
+\hat { h } _ { \tau , 0 } ^ { l } = \sum _ { \eta ; e _ { \tau \eta } = 1 } \mathrm { s o f t m a x } _ { \eta } ( \frac { \hat { q } _ { \tau , 0 } ^ { T } \cdot \hat { k } _ { \eta , 0 } } { \sqrt { d _ { k } } } ) \cdot \hat { v } _ { \eta , 0 } .
+$$
+
+Node $\tau$ calculates the attention weight on its neighbor $\eta$ using hop query $\hat { q } _ { \tau , 0 }$ and key $\hat { k } _ { \eta , 0 }$ . Then it uses the weights to combine its neighbors’ value $\hat { v } _ { \eta , 0 }$ and forms a globalized representation $\hat { h } _ { \tau , 0 } ^ { l }$ .
+
+The two attention mechanism are combined to form the new representation of layer $l$
+
+$$
+\begin{array} { r l } & { \tilde { h } _ { \tau , 0 } ^ { l } = \mathrm { L i n e a r } ( [ h _ { \tau , 0 } ^ { l } \circ \hat { h } _ { \tau , 0 } ^ { l } ] ) , } \\ & { \tilde { h } _ { \tau , i } ^ { l } = h _ { \tau , i } ^ { l } ; \forall i \neq 0 . } \end{array}
+$$
+
+Note that the non-hub tokens $( i \neq 0 )$ ) still have access to the hop attention in the previous layer through Eqn. (6).
+
+One layer of eXtra Hop attention can be viewed as single-step of information propagation along edges $E$ . For example, in Figure 1a, the document node $d _ { 3 }$ updates its representation by gathering information from its neighbor $d _ { 1 }$ using the hop attention $d _ { 1 }  d _ { 3 }$ . When multiple TransformerXH layers are stacked, this information in $d _ { 1 }$ includes both $d _ { 1 }$ ’s local contexts from its in-sequence attention, and cross-sequence information from the hop attention $d _ { 2 } \to d _ { 1 }$ of the $l - 1$ layer. Hence, an L-layer Transformer-XH can attend over information from up to $\mathrm { L }$ hops away.
+
+Together, three main properties equip Transformer-XH to effectively model raw structured text data: the propagation of information (values) along edges, the importance of that information (hop attention weights), and the balance of in-sequence and cross-sequence information (attention combination). The representations learned in $\mathcal { H }$ can innately express nuances in structured text that are required for complex reasoning tasks such as multi-hop QA and natural language inference.
+
+# 3 APPLICATION TO MULTI-HOP QUESTION ANSWERING
+
+This section describes how Transformer-XH applies to multi-hop QA. Given a question $q$ , the task is to find an answer span $a$ in a large open-domain document corpus, e.g. the first paragraph of all Wikipedia pages. By design, the questions are complex and often require information from multiple documents to answer. For example, in the case shown in Figure 1b, the correct answer “Cambridge” requires combining the information from both the Wikipedia pages “Facebook” and “Harvard University”. To apply Transformer-XH in the open domain multi-hop QA task, we first construct an evidence graph and then apply Transformer-XH on the graph to find the answer.
+
+Evidence Graph Construction. The first step is to find the relevant candidate documents $D$ for the question $q$ and connect them with edges $E$ to form the graph $G$ . Our set $D$ consists of three sources. The first two sources are from canonical information retrieval and entity linking techniques:
+
+$D _ { i r }$ : the top 100 documents retrieved by DrQA’s TF-IDF on the question (Chen et al., 2017).
+
+$D _ { e l }$ : the Wikipedia documents associated with the entities that appear in the question, annotated by entity linking systems: TagMe (Ferragina & Scaiella, 2010) and CMNS (Hasibi et al., 2017).
+
+For better retrieval quality, we use a BERT ranker (Nogueira & Cho, 2019) on the set $D _ { i r } \cup D _ { e l }$ and keep the top two ranked ones in $D _ { i r }$ and top one per question entity in $D _ { e l }$ . Then the third source $D _ { e x p }$ includes all documents connected to or from any top ranked documents via Wikipedia hyperlinks (e.g., “Facebook” “Harvard University”).
+
+The final graph comprises all documents from the three sources as nodes $\mathcal { X }$ . The edge matrix $E$ is flexible. We experiment with various edge matrix settings, including directed edges along Wikipedia links, i.e. $e _ { i j } = 1$ if there is a hyperlink from document $i$ to $j$ , bidirectional edges along Wiki links, and fully-connected graphs, which rely on Transformer-XH to learns the edge importance.
+
+Similar to previous work (Ding et al., 2019), the textual representation for each node in the graph is the [SEP]-delimited concatenation of the question, anchor text (the text in the hyperlink in parent nodes pointing to the child node), and the paragraph itself. More details on the evidence graph construction are in Appendix A.1.
+
+Transformer-XH on Evidence Graph. Transformer-XH takes the input nodes $\mathcal { X }$ and edges $E$ , and produces the global representation of all text sequences:
+
+$$
+\mathcal { H } ^ { L } = \mathrm { T r a n s f o r m e r - X H } ( \mathcal { X } , E ) .
+$$
+
+Then we add two task-specific layers upon the last layer’s representation $\mathcal { H } ^ { L }$ : one auxiliary layer to predict the relevance score of the evidence node, and one layer to extract the answer span within it:
+
+$$
+\begin{array} { r l } & { p ( \mathrm { r e l e v a n c e } | \tau ) = \mathrm { s o f t m a x } ( \mathrm { L i n e a r } ( \tilde { h } _ { \tau , 0 } ^ { L } ) ) ; } \\ & { p ( \mathrm { s t a r t } | \tau , i ) , p ( \mathrm { e n d } | \tau , j ) = \mathrm { s o f t m a x } ( \mathrm { L i n e a r } ( \tilde { h } _ { \tau , i } ^ { L } ) ) , \mathrm { s o f t m a x } ( \mathrm { L i n e a r } ( \tilde { h } _ { \tau , j } ^ { L } ) ) . } \end{array}
+$$
+
+The final model is trained end-to-end with cross-entropy loss for both tasks in a multi-task setting. During inference, we first select the document with the highest relevance score, and then the start and end positions of the answer within that document.
+
+# 4 APPLICATION TO FACT VERIFICATION
+
+This section describes how Transformer-XH applies to the fact verification task in FEVER Thorne et al. (2018). Given a claim and a trustworthy background corpus, i.e. Wikipedia, the task is to verify whether the evidence in the corpus SUPPORTS, REFUTES, or there is NOT ENOUGH INFO to verify the claim. Similar to multi-hop QA, the first step is to construct an evidence graph using the text pieces in the background corpus and then Transformer-XH can be easily applied to conduct reasoning on these evidence pieces.
+
+Evidence Graph Construction. Many previous FEVER systems first retrieve the evidence sentences for the claim and then reason verify it (Nie et al., 2019; Zhou et al., 2019). This first step is similar as the retrieval stage in Hotpot QA. And the second step is a multi-evidence reasoning task, where Transformer-XH is applied.
+
+We keep the evidence sentence retrieval step consistent with previous methods. The sentence retrieval results of SR-MRS is not yet released at the time of our experiments, thus we instead use the BERT-based retrieval results from another contemporary work (Liu et al., 2019b).
+
+We construct the evidence graph using the top five sentences from Liu et al. (2019b) as the nodes $\mathcal { X }$ and fully connected edges $E$ . Following Liu et al. (2019b), the representation of each node is the concatenation of the claim, the Wikipedia title (entity name) of the document that includes the sentence, and the evidence sentence.
+
+Transformer-XH on Evidence Graph. Transformer-XH takes the evidence graph $\{ X , E \}$ and learns to verify the claim to three categories: $y \in \{ \mathrm { S U P P O R T }$ , REFUSE, NOT ENOUGH EVIDENCE}. Similar to the application in Hotpot QA, it first produces the global representation of the graph:
+
+$$
+\mathcal { H } ^ { L } = \mathrm { T r a n s f o r m e r - X H } ( \mathcal { X } , E ) .
+$$
+
+Then two task-specific layers are added upon the last layer. The first layer conducts the fact prediction per node using the “[CLS]” token:
+
+$$
+p ( y | \tau ) = \mathrm { s o f t m a x } ( \mathrm { L i n e a r } ( \tilde { h } _ { \tau , 0 } ^ { L } ) ) .
+$$
+
+The second layer learns to measure the importance of each node in the graph:
+
+$$
+p ( s | \tau ) = \mathrm { s o f t m a x } ( \mathrm { L i n e a r } ( \tilde { h } _ { \tau , 0 } ^ { L } ) ) ,
+$$
+
+The node level predictions and node importance are combined to the final prediction for the claim:
+
+$$
+p ( y | \mathcal { X } , E ) = \sum _ { \tau } p ( s | \tau ) \cdot p ( y | \tau ) .
+$$
+
+Similar to the Hotpot QA scenario, we use multi-task learning that combines the node prediction task and the claim verification task. The first task uses the evidence sentence label provided by FEVER and cross-entropy loss on Eqn. 15. The second task uses the final verification label with cross-entropy loss on Eqn. 16.
+
+# 5 EXPERIMENTAL METHODOLOGIES
+
+Our experiments are conducted on Hotpot QA, the multi-hop question answering benchmark Yang et al. (2018), and FEVER, the fact verfication benchmark Thorne et al. (2018).
+
+# 5.1 MULTI-HOP QUESTION ANSWERING ON HOTPOT QA
+
+Dataset. HotpotQA includes $1 1 2 \mathrm { k }$ crowd-sourced questions designed to require multiple pieces of textual evidence, which are the first paragraphs of Wikipedia pages. It has two type of questions: bridge question require hopping via an outside entity, and comparison question compare a property of two entities. There are two settings in HotpotQA. The Distractor setting provides golden evidence paragraphs together with TF-IDF retrieved negatives. The FullWiki setting requires systems to retrieve evidence paragraphs from the full set of Wikipedia articles.
+
+We focus on FullWiki setting since previous research found that the negative documents in Distractor may be too weak and mitigate the need for multi-hop reasoning (Min et al., 2019b). There are 90k Train, 7k Dev and 7k Test questions. The ground truth answer and supporting evidence sentences in Train and Dev sets are provided. Test labels are hidden; only one submission is allowed to the leaderboard per $3 0 \mathrm { d a y s } ^ { 2 }$ . We evaluate our final model on Test and conduct ablations on Dev.
+
+Metrics. We use official evaluation metrics of HotpotQA: exact match (EM) and F1 on answer (Ans), supporting facts (Supp), and the combination (Joint). The supporting facts prediction is an auxiliary task that evaluates model’s ability to find the evidence sentences. Joint EM is the product of the two EM result. Joint F1 first multiplies the precision and recall from Ans and Supp, then combines the Joint precision and recall to F1.
+
+Baseline. The main baselines include Cognitive QA (CogQA, Ding et al. (2019)) and Semantic Retrieval MRS (SR-MRS, Nie et al. (2019)). CogQA uses several fine-tuned BERT machine reading comprehension (MRC) models to find hop entities and candidate spans, and then uses a BERT based Graph Convolution Network to rank the candidate spans. SR-MRS is a contemporary work and was the previous leaderboard rank one. It is a BERT based pipeline and uses fine-tuned BERT models to first rank the documents (twice), then to rank sentences to find supporting facts, and finally conducts BERT MRC on the concatenated evidence sentences.
+
+We also re-implement $\mathrm { C o g Q A }$ and upgrade its IR with our BERT IR model (BERT on $D _ { i r } \cup D _ { e l }$ , same as Transformer-XH), for fair comparisons. We include other approaches on the FullWiki setting: Official Baseline (Yang et al., 2018), MUPPET (Feldman & El-Yaniv, 2019), QFE (Nishida et al., 2019), and DecompRC (Min et al., 2019a),
+
+Implementation Details. The in-sequence attention and other standard Transformer components in Transformer-XH are initialized by the pre-trained BERT base model (Devlin et al., 2019). The extra hop attention parameters are initialized randomly and trained from scratch. The final model uses three hop steps. For bridge questions, we build the evidence graph described in Section 3. And for comparison questions, we build the fully-connected graph on the set $D _ { i r } \cup D _ { e l }$ and train Transformer-XH separately. We leave more implementation details in the Appendix.
+
+# 5.2 FACT VERIFICATION ON FEVER
+
+Dataset. The FEVER task provides a claim sentence and requires the system to classify it into three categories: SUPPORTS, REFUTES, and NOT ENOUGH INFO, using the Wikipedia corpus as the evidence source. It provides 185,455 claims with manual labels and uses the Wikipedia dump in June 2017 which includes 5.4 million documents.
+
+Metrics. There are two official evaluation metrics in FEVER: Label Accuracy (LA), which evaluates the classification accuracy of the verification labels, and FEVER Score, which evaluates both the correctness of the evidence sentences used in verification and the LA. The latter is close to Joint EM in Hotpot QA and is the main metric. We use the official evaluation scripts from FEVER task and we refer to Thorne et al. (2018) for more details of this task.
+
+Experimental Setups. We follow the experiment settings used by previous research in FEVER 1.0 shared task, i.e. Nie et al. (2019), Zhou et al. (2019), and Liu et al. (2019b). Similar as Liu et al. (2019b), we also split the data into single and multi evidence categories and evaluate TransformerXH on the two splits.
+
+Table 1: Results $( \% )$ on HotpotQA FullWiki Setting. Dev results of previous methods are reported in their papers. Test results are from the leaderboard. Contemporary method is marked by ∗.   
+
+<table><tr><td rowspan="3"></td><td colspan="5">Dev</td><td colspan="5">Test</td></tr><tr><td colspan="2">Ans</td><td colspan="2">Supp</td><td colspan="2">Joint</td><td>Ans</td><td colspan="2">Supp</td><td colspan="2">Joint</td></tr><tr><td>EMF1</td><td></td><td>EMF1</td><td></td><td>EM F1</td><td>EM</td><td>F1</td><td>EMF1</td><td></td><td>EMF1</td></tr><tr><td>Official Baseline (Yang et al.,2018)</td><td>23.9 32.9</td><td></td><td>5.140.9</td><td></td><td>47.240.8</td><td>24.0 32.9</td><td></td><td>3.9</td><td>37.7</td><td>1.9 16.2</td></tr><tr><td>DecompRC (Min et al.,2019a)</td><td></td><td>43.3</td><td>1</td><td>1</td><td>-</td><td>30.0</td><td>40.7 -</td><td>1</td><td>-</td><td>-</td></tr><tr><td>QFE (Nishida et al., 2019)</td><td></td><td></td><td></td><td>=</td><td></td><td>28.7</td><td>38.1</td><td>14.2 44.4</td><td>8.7</td><td>23.1</td></tr><tr><td>MUPPET(Feldman &amp;El-Yaniv,2019)</td><td>31.1 40.4</td><td></td><td>17.0 47.7</td><td></td><td>11.8 27.6</td><td>30.6 40.3</td><td></td><td>16.7 47.3</td><td></td><td>10.9 27.0</td></tr><tr><td>CogQA (Ding et al., 2019)</td><td>37.6 49.4</td><td></td><td>23.1 58.5</td><td></td><td>12.2 35.3</td><td>37.1</td><td>48.9 22.8</td><td>57.7</td><td></td><td>12.4 34.9</td></tr><tr><td>SR-MRS* (Nie et al., 2019)</td><td>46.5</td><td>58.8</td><td>39.9</td><td>71.5</td><td>26.6 49.2</td><td>45.3 57.3</td><td>38.7</td><td>70.8</td><td>25.1</td><td>47.6</td></tr><tr><td>CogQA(w. BERT IR) [Ours]</td><td>44.8 57.7</td><td></td><td></td><td>29.262.8</td><td>18.543.4</td><td>1</td><td>- -</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Transformer-XH</td><td>54.0 66.2</td><td></td><td></td><td>41.7 72.1</td><td>27.7 52.9</td><td>51.6 64.1</td><td></td><td>40.9 71.4</td><td></td><td>26.1 51.3</td></tr></table>
+
+<table><tr><td rowspan="3"></td><td colspan="4">Question Type</td><td colspan="4">Reasoning Type</td></tr><tr><td colspan="2">Comparison (1487)</td><td colspan="2">Bridge (5918)</td><td colspan="2">Single-Hop(3426)</td><td colspan="2">Multi-Hop (3979)</td></tr><tr><td>EM</td><td>F1</td><td>EM</td><td>F1</td><td>EM</td><td>F1</td><td>EM</td><td>F1</td></tr><tr><td>CogQA</td><td>43.3</td><td>51.1</td><td>36.1</td><td>49.0</td><td>45.1</td><td>61.1</td><td>31.1</td><td>39.4</td></tr><tr><td>SR-MRS*</td><td>62.0</td><td>68.9</td><td>42.4</td><td>56.1</td><td>52.3</td><td>68.4</td><td>41.3</td><td>50.3</td></tr><tr><td>CogQA (w. BERT IR)</td><td>54.1</td><td>60.9</td><td>42.4</td><td>56.9</td><td>52.0</td><td>69.3</td><td>38.6</td><td>47.8</td></tr><tr><td>Transformer-XH(w.BERT IR)</td><td>59.9</td><td>65.8</td><td>52.4</td><td>66.3</td><td>62.2</td><td>78.3</td><td>46.8</td><td>55.7</td></tr><tr><td>Transformer-XH(w. SR-MRS)</td><td>64.3</td><td>70.7</td><td>47.9</td><td>62.3</td><td>58.1</td><td>74.3</td><td>45.3</td><td>55.2</td></tr></table>
+
+Table 2: Dev Ans $( \% )$ on different scenarios. Reasoning Types are estimated by Min et al. (2019b) via whether single-hop BERT has non-zero Ans F1. The numbers of questions are shown in brackets.
+
+Baselines. The baselines include GEAR (Zhou et al., 2019) and two contemporary work, SRMRS (Nie et al., 2019) and KGAT (Liu et al., 2019b). SR-MRS uses similar adaptations as Transformer-XH from Hotpot QA to FEVER. GEAR is a graph attention network based approach specially designed for fact verification. KGAT further improves GEAR’s GAT by adding the kernel information, and is the previous STOA with BERT base. We also include the BERT Concat baseline Liu et al. (2019b) which concatenates the evidence sentences to a text sequence and applies BERT on it.
+
+Implementation Details. We use the retrieval result from Liu et al. (2019b) and connect all sentences as a fully connected graph. We follow similar parameter settings as Hothot QA. We use pre-trained BERT base model to initialize the Transformer components. The extra hop attention parameters are initialized randomly and trained from scratch, and three hop steps are used. We train Transformer-XH for two epochs.
+
+# 6 EVALUATION RESULTS
+
+This section first presents the evaluation results on HotpotQA and FEVER. Then it conducts ablation studies, analyses, and case studies on HotpotQA to understand the effectiveness of Transformer-XH.
+
+# 6.1 OVERALL RESULT
+
+HotpotQA FullWiki results are presented in Table 1. Transformer-XH outperforms all previous methods by significant margins. Besides strong results, Transformer-XH’s ability to natively represent structured data leads to much simpler QA system. Previously, in order to utilize pre-trained BERT, Hotpot QA approaches adapted the multi-hop reasoning task to comprise multiple sub-tasks. For example, given the retrieved documents, CogQA (w. BERT IR) first leverages one BERT MRC model to find hop entities and then another BERT MRC to find candidate answer spans. After that, it ranks the candidate spans using a BERT based GAT, which is the only structure modeling step. In comparison, Transformer-XH is a unified model which directly represents structured texts and integrates BERT weights.
+
+<table><tr><td rowspan="2"></td><td colspan="2">Dev</td><td colspan="2">Test</td><td colspan="2">Single Evidence</td><td colspan="2">Multi Evidence</td></tr><tr><td>LA</td><td>FEVER</td><td>LA</td><td>FEVER</td><td>LA</td><td>FEVER</td><td>LA</td><td>FEVER</td></tr><tr><td>BERT Concat (Liu et al., 2019b)</td><td>73.67</td><td>68.89</td><td>71.01</td><td>65.64</td><td>1</td><td>1</td><td>1</td><td>-</td></tr><tr><td>GEAR/GAT (Zhou et al.,2019)</td><td>74.84</td><td>70.69</td><td>71.60</td><td>67.10</td><td>79.79</td><td>77.42</td><td>66.12</td><td>38.21</td></tr><tr><td>SR-MRS* (Nie et al., 2019)</td><td>75.12</td><td>70.18</td><td>72.56</td><td>67.26</td><td>1</td><td>1</td><td>1</td><td>1</td></tr><tr><td>KGAT* (Liu et al.,2019b)</td><td>78.02</td><td>75.88</td><td>72.81</td><td>69.40</td><td>80.33</td><td>78.07</td><td>65.92</td><td>39.23</td></tr><tr><td>Transformer-XH</td><td>78.05</td><td>74.98</td><td>72.39</td><td>69.07</td><td>81.84</td><td>81.31</td><td>86.58</td><td>58.47</td></tr></table>
+
+Table 3: FEVER Results. Contemporary work is marked by ∗. Single and Multi Evidence are results on Dev claims on which one or multiple sentences are labeled as evidence.
+
+Table 2 further inspects model performances on the Dev set by question types and reasoning types. Transformer-XH significantly outperforms all baselines on bridge questions which require more multi-hop reasoning. And on the “multi-hop” questions, Transformer-XH has higher relative gains $3 9 \%$ over $\mathrm { C o g Q A }$ on EM) than the “single-hop” questions $( 2 7 \% )$ , demonstrating its stronger multihop reasoning capability. We further study this in Section 6.3.
+
+To further investigate the reasoning ability of Transformer-XH, we replace our retrieval pipeline with the top retrieved documents from the SR-MRS pipeline. More specifically, we use the top retrieved documents from SR-MRS to construct Transformer-XH’s evidence graph while keeping all else constant. The resulting system, Transformer-XH (w. SR-MRS), outperforms SR-MRS’s multi-step BERT based reasoning on all metrics and question types. Transformer-XH’s effectiveness is robust with multiple IR systems.
+
+FEVER fact verification results are shown in Table 3. Transformer-XH outperforms SR-MRS by 4 FEVER score on Dev and 1.8 on Test. It performs on par with KGAT. More importantly, Transformer-XH excels at verifying claims that require multiple pieces of evidence–outperforming the contemporary work KGAT by 20 FEVER scores on the multi-evidence claims, a $49 \%$ relative improvement. Compared to KGAT, Transformer-XH mainly loses on the ”not enough evidence” category which is neither single nor multi evidence. This is an artifact the FEVER task which our system is not specifically designed for.
+
+This result also demonstrates Transformer-XH’s generality on tasks with multiple text inputs not in sequential formats. The only difference between Transformer-XH when applied on multi-hop QA and FEVER is the last (linear) task specific layer; it provides similar or better performances over contemporary approaches that were specifically designed for the fact verification task. Due to space constraints and the consistent effectiveness of Transformer-XH on the two applications, the rest experiments mainly used HotpotQA to analyze the behavior of Transformer-XH.
+
+# 6.2 ABLATION STUDIES
+
+Model Variations. We show the results of different model variations on the top left of Table 4. Single-Hop BERT uses BERT MRC model on each document individually, which significantly decreases the accuracy, confirming the importance of multi-hop reasoning in FullWiki setting (Min et al., 2019a). $G A T + B E R T$ first uses Graph Attention Network (Velickovi ˇ c et al., 2018) on the evi- ´ dence graph to predict the best node; then it uses BERT MRC on the best document. It is $10 \%$ worse than Transformer-XH since the MRC model has no access to the information from other documents. No Node Prediction eliminates the node prediction task and only trains on span prediction task; the accuracy difference shows node prediction task helps the model training.
+
+Graph Structures. We show Transformer-XH’s performance with different graph structures on the bottom left of Table 4. Bidirectional Edges adds reverse edges along the hyperlinks; Fully Connected Graph connects all document pairs; Node Sequence randomly permutes the documents and connects them into a sequence to simulate the Transformer-XL setting. Both Bidirectional Links and Fully Connected Graph have comparable performance with the original graph structure. Transformer-XH is able to learn meaningful connections using its hop attentions and is less dependent on the pre-existing graph structural. The fully connected graph can be used if there is no strong edge patterns available in the task. However, the performance drops significantly on Node Sequence, showing that structured texts cannot be treated as a linear sequence which cuts off many connections.
+
+Table 4: Ablation studies on the bridge questions on Dev answer accuracy $( \% )$ , including model components (top left), graph structures (bottom left), and hop steps (right). Transformer-XH’s full model uses three hop step and unidirectional Wiki link graph.   
+
+<table><tr><td rowspan="2">Model Ablation</td><td colspan="2">Dev Ans</td><td rowspan="2">Hop Steps</td><td colspan="2">Dev Ans</td></tr><tr><td>EM</td><td>F1</td><td>EM</td><td>F1</td></tr><tr><td>Single-Hop BERT MRC on Individual Documents</td><td>31.3</td><td>42.2</td><td>One Hop</td><td>50.3</td><td>64.6</td></tr><tr><td>GAT (Node Prediction) + BERT (MRC on Best Node)</td><td>48.9</td><td>61.9</td><td>Two Hops</td><td>51.6</td><td>66.4</td></tr><tr><td>No Node Prediction Multi-Task</td><td>43.2</td><td>55.3</td><td>Four Hops</td><td>51.4</td><td>66.1</td></tr><tr><td>Bidirectional Edges on Hyperlinks</td><td>50.6</td><td>65.0</td><td>Five Hops</td><td>50.6</td><td>64.7</td></tr><tr><td>Fully Connected Graph</td><td>51.0</td><td>65.5</td><td>Six Hops</td><td>50.1</td><td>64.2</td></tr><tr><td>Node Sequence (Bidirectional Transformer-XL)</td><td>14.1</td><td>20.7</td><td>Transformer-XH</td><td>52.4</td><td>66.3</td></tr></table>
+
+![](images/937abe87ea803a9f533d860bb7ad6f79103c7adf93ed6ab6fb080b78abf1871c.jpg)  
+Figure 2: Distributions of learned attention weights of three hops on three groups: From All (Node) (to) All, $\mathbf { A l l } $ (to) Ans (ground truth answer node), and Supp (nodes with the supporting facts) (to) Ans. X-axes are attention values scaled by number of nodes.
+
+Hop Steps. Recall that a Transformer-XH layer with extra hop attention corresponds to one information propagation (hop) step in the graph. Thus Transformer-XH with last K layers conducts K-step attention hops in the graph. We show results with different K on the right side of Table 4. Transformer-XH reaches its peak performance with three hops (our full-model). This is expected as most Hotpot QA questions can be answered by two documents (Yang et al., 2018).
+
+# 6.3 HOP ATTENTION ANALYSIS
+
+This experiment analyzes the hop attentions using our full-model (three-hop) on the fully connected graph to study their behavior without pre-defined structure. Figure 2 plots the distributions of the learned hop attentions on the Dev set. It shows a strong shift away from the normal distribution with more hops. Transformer-XH learns to distinguish different nodes after multi-hop attention: the attention score becomes a bimodal distribution after three hops, ignoring some non-useful nodes. Transformer-XH also learns to focus on meaningful edges: the score is higher on the path Supp Ans than All $ .$ Ans. And the margin is larger as the hop step increases from one to three.
+
+# 6.4 CASE STUDY
+
+Table 5 lists two examples from Transformer-XH and CogQA (w. BERT IR). The first case has a clear evidence chain “2011/S/S” “Winner” “YG Entertainment”; both methods find the correct answer. However, the second case has too many distractors in the first document. Without additional clues from document 2, it is likely that the single-hop hop entity extraction component in CogQA (w. BERT IR) misses the correct answer document in its candidate sets; and the later structural reasoning component can not recover from this cascade error. In comparison, Transformer-XH finds the correct answer by combining the evidence with the hop attentions between the two evidence pieces. We leave more positive and negative cases in Appendix A.5.
+
+Table 5: Examples of Transformer-XH and BERT pipeline results in Hotpot QA.   
+
+<table><tr><td rowspan="2">Q:2014 S/S is the debut album of a South Ko- rean boy group that was formed by who? Document 1: 2014 S/S is the debut album of South Korean group Winner. Document 2: Winner is a South Korean boy group formed in 2013 by YG Entertainment. Transformer-XH:YG Entertainment√ CogQA(w.BERTIR): YG Entertainment√</td><td>Q:Which man who presented 2022FIFA World Cup bid was born on October 22,1930? Document 1: 2022 FIFA World Cup bid was presented by Quentin Bryce and Elle Macpherson. Document 2:FrankLowy (born 22 October</td></tr><tr><td>Frank Lowy, Ben_Buckley, 1930),is an Australian-Israeli businessman and Chairman of Westfield Corporation. Transformer-XH:FrankLowy√ CogQA(w. BERT IR): Quentin Bryce X</td></tr></table>
+
+# 7 RELATED WORK
+
+HotpotQA’s FullWiki task is a combination of open-domain QA (Chen et al., 2017) and multi-hop QA (Yang et al., 2018): the questions are designed to require multiple pieces of evidence and these evidence pieces are documents to retrieve from Wikipedia. It is a challenging combination: The retrieved documents are inevitably noisy and include much stronger distractors than the TF-IDF retrieved documents in the Distractor setting (Min et al., 2019a; Jiang & Bansal, 2019).
+
+Various solutions have been proposed for Hotpot QA (Min et al., 2019b; Feldman & El-Yaniv, 2019; Nishida et al., 2019). These solutions often use complicated pipelines to adapt the multi-hop task into a combination of single-hop tasks, in order to leverage the advantage of pre-trained models. For example, CogQA (Ding et al., 2019) uses two BERT based MRC model to find candidate spans and then another BERT initialized Graph Neural Network (GNN) to rank spans; SR-MRS (Nie et al., 2019) uses three BERT based rankers to find supporting sentences, and then another BERT MRC model on the concatenated sentences to get the answer span. Transformer-XH is a simpler model that directly represents and reasons with multiple pieces of evidence using extra hop attentions.
+
+Fact verification is a natural language inference task while also requires retrieving (“open-domain”) and reasoning with multiple text pieces (“multi-evidence”) (Thorne et al., 2018; Nie et al., 2019; Liu et al., 2019b). Many recent FEVER systems leverage Graph Neural Networks to combine information from multiple text nodes, while each node text is represented by BERT encodings (Zhou et al., 2019; Liu et al., 2019b). Transformer-XH is a more unified solution that simply includes language modeling as part of its joint reasoning.
+
+In addition to Transformer-XL (Dai et al., 2019), other work is proposed to improve the Transformer architecture on long text sequence. For example, T-DMCA (Liu et al., 2018) splits the sequence into blocks and then the attention merges different blocks. Sparse Transformer (Child et al., 2019) introduces the sparse factorizations of the attention matrix. Transformer-XH shares similar motivation and focuses on multiple pieces of text that are not in sequential forms.
+
+Transformer-XH is also inspired by GNN (Kipf & Welling, 2017; Schlichtkrull et al., 2017; Velickovi ˇ c et al., 2018), which leverages neural networks to model graph structured data for down- ´ stream tasks (Sun et al., 2018; Zhao et al., 2020). The key difference is that a “node” in TransformerXH is a text sequence, and modeling of the structure is conducted jointly with the representation of the text. Transformer-XH combines the Transformer’s advantages in understanding text with the power that GNN has in modeling structure.
+
+# 8 CONCLUSION
+
+Transformer-XH and its eXtra Hop attention mechanism is a simple yet powerful adaptation of Transformer to learn better representations of structured text data as it naturally occurs. It innately integrates with pre-trained language models to allow for complex reasoning across multiple textual evidence pieces. When applied to HotpotQA, Transformer-XH significantly shrinks the typical multi-hop QA pipeline, eliminating many cascading errors that arise from the linear sequence input constraints of pre-trained Transformers. The same simplicity also applies to FEVER, with one Transformer-XH all we needed to obtain a much stronger answer accuracy. With its simplicity and efficacy, we envision Transformer-XH will benefit many applications in the near future.
+
+# REFERENCES
+
+Danqi Chen, Adam Fisch, Jason Weston, and Antoine Bordes. Reading Wikipedia to Answer OpenDomain Questions. In Proceedings of the 55th Annual Meeting of the Association for Computational Linguistics, pp. 1870–1879, 2017.
+
+Rewon Child, Scott Gray, Alec Radford, and Ilya Sutskever. Generating Long Sequences with Sparse Transformers. arXiv preprint arXiv:1904.10509, 2019.
+
+Zihang Dai, Zhilin Yang, Yiming Yang, Jaime Carbonell, Quoc Le, and Ruslan Salakhutdinov. Transformer-XL: Attentive Language Models beyond a Fixed-Length Context. In Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics, pp. 2978–2988, 2019.
+
+Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding. In Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, pp. 4171–4186, 2019.
+
+Ming Ding, Chang Zhou, Qibin Chen, Hongxia Yang, and Jie Tang. Cognitive Graph for Multi-Hop Reading Comprehension at Scale. In Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics, pp. 2694–2703, 2019.
+
+Yair Feldman and Ran El-Yaniv. Multi-Hop Paragraph Retrieval for Open-Domain Question Answering. In Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics, pp. 2296–2309, 2019.
+
+Paolo Ferragina and Ugo Scaiella. Tagme: On-the-fly Annotation of Short Text Fragments (by Wikipedia Entities). In Proceedings of the 19th ACM international conference on Information and knowledge management, pp. 1625–1628, 2010.
+
+Faegheh Hasibi, Krisztian Balog, and Svein Erik Bratsberg. Entity Linking in Queries: Efficiency vs.Effectiveness. In European Conference on Information Retrieval, pp. 40–53, 2017.
+
+Yichen Jiang and Mohit Bansal. Avoiding Reasoning Shortcuts: Adversarial Evaluation, Training, and Model Development for Multi-Hop QA. In Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics, pp. 2726–2736, 2019.
+
+Thomas N Kipf and Max Welling. Semi-supervised Classification with Graph Convolutional Networks. In International Conference on Learning Representations, 2017.
+
+Peter J Liu, Mohammad Saleh, Etienne Pot, Ben Goodrich, Ryan Sepassi, Lukasz Kaiser, and Noam Shazeer. Generating Wikipedia by Summarizing Long Sequences. In International Conference on Learning Representations, 2018.
+
+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, 2019a.
+
+Zhenghao Liu, Chenyan Xiong, and Maosong Sun. Kernel Graph Attention Network for Fact Verification. arXiv preprint arXiv:1910.09796, 2019b.
+
+Sewon Min, Eric Wallace, Sameer Singh, Matt Gardner, Hannaneh Hajishirzi, and Luke Zettlemoyer. Compositional Questions Do Not Necessitate Multi-hop Reasoning. In Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics, pp. 4249–4257, 2019a.
+
+Sewon Min, Victor Zhong, Luke Zettlemoyer, and Hannaneh Hajishirzi. Multi-hop Reading Comprehension through Question Decomposition and Rescoring. In Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics, pp. 6097–6109, 2019b.
+
+Yixin Nie, Songhe Wang, and Mohit Bansal. Revealing the Importance of Semantic Retrieval for Machine Reading at Scale. In Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing, 2019.
+
+Kosuke Nishida, Kyosuke Nishida, Masaaki Nagata, Atsushi Otsuka, Itsumi Saito, Hisako Asano, and Junji Tomita. Answering while Summarizing: Multi-task Learning for Multi-hop QA with Evidence Extraction. In Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics, pp. 2335–2345, 2019.
+
+Rodrigo Nogueira and Kyunghyun Cho. Passage Re-ranking with BERT. arXiv preprint arXiv:1901.04085, 2019.
+
+Michael Schlichtkrull, Thomas N Kipf, Peter Bloem, Rianne van den Berg, Ivan Titov, and Max Welling. Modeling Relational Data with Graph Convolutional Networks. arXiv preprint arXiv:1703.06103, 2017.
+
+Haitian Sun, Bhuwan Dhingra, Manzil Zaheer, Kathryn Mazaitis, Ruslan Salakhutdinov, and William Cohen. Open domain question answering using early fusion of knowledge bases and text. In Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing, pp. 4231–4242, 2018.
+
+James Thorne, Andreas Vlachos, Oana Cocarascu, Christos Christodoulopoulos, and Arpit Mittal. The Fact Extraction and VERification (FEVER) Shared Task. In Proceedings of the First Workshop on Fact Extraction and VERification (FEVER), pp. 1–9, 2018.
+
+Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin. Attention is All You Need. In Advances in neural information processing systems, pp. 5998–6008, 2017.
+
+Petar Velickovi ˇ c, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Lio, and Yoshua ´ Bengio. Graph Attention Networks. In International Conference on Learning Representations, 2018.
+
+Minjie Wang, Lingfan Yu, Da Zheng, Quan Gan, Yu Gai, Zihao Ye, Mufei Li, Jinjing Zhou, Qi Huang, Chao Ma, Ziyue Huang, Qipeng Guo, Hao Zhang, Haibin Lin, Junbo Zhao, Jinyang Li, Alexander J Smola, and Zheng Zhang. Deep Graph Library: Towards Efficient and Scalable Deep Learning on Graphs. In ICLR Workshop on Representation Learning on Graphs and Manifolds, 2019.
+
+Zhilin Yang, Peng Qi, Saizheng Zhang, Yoshua Bengio, William W. Cohen, Ruslan Salakhutdinov, and Christopher D. Manning. HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering. In Proceedings of the Conference on Empirical Methods in Natural Language Processing, pp. 2369–2380, 2018.
+
+Zhilin Yang, Zihang Dai, Yiming Yang, Jaime Carbonell, Russ R Salakhutdinov, and Quoc V Le. XLNet: Generalized Autoregressive Pretraining for Language Understanding. In Advances in Neural Information Processing Systems, pp. 5754–5764, 2019.
+
+Chen Zhao, Chenyan Xiong, Xin Qian, and Jordan Boyd-Graber. Complex factoid question answering with a free-text knowledge graph. In The Web Conference, 2020.
+
+Jie Zhou, Xu Han, Cheng Yang, Zhiyuan Liu, Lifeng Wang, Changcheng Li, and Maosong Sun. GEAR: Graph-based Evidence Aggregating and Reasoning for Fact Verification. In Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics, pp. 892–901, 2019.
+
+# A APPENDIX
+
+The appendix includes details of the evidence graph construction for Hotpot QA, ablation studies in the BERT IR component, more details and results on Hotpot QA.
+
+# A.1 HOTPOTQA EVIDENCE GRAPH CONSTRUCTION DETAILS
+
+The evidence graph construction includes two stages. The first stage is BERT IR, which extract related documents directly from question. The second stage expands the related documents along Wikipedia links. The first is applied on all questions while the second is only required by Bridge questions.
+
+The first stage uses two methods to find documents. The first method uses DrQA’s retrieval system (Chen et al., 2017), which is unsupervised TF-IDF. We keep the top $1 0 0 \ \mathrm { { D r Q A } }$ retrieved ones $D _ { i r }$ for each question. The second method uses TagMe (Ferragina & Scaiella, 2010) and CMNS (Hasibi et al., 2017), two commonly used entity linkers, to annotate questions. We keep the TagMe output entity and three highest scored entities per surface form (a phrase in the question linked with entities) from CMNS, and use its corresponding Wikipedia document as $D _ { e l }$ .
+
+We use BERT ranker (Nogueira & Cho, 2019) to re-rank the initial set $D _ { i r } \cup D _ { e l }$ . The input to the BERT is the concatenation of question and first paragraph of document:
+
+[CLS] Question [SEP] First Paragraph of Document.
+
+Then a linear layer is added on the last layer’s [CLS] representation to score the relevance of the document. We use BERT base and fine-tune it using the relevance label (from supporting facts) with cross-entropy loss. The top two highest scored documents from $D _ { i r }$ and the top one document per entity position (surface form) in $D _ { e l }$ are kept as the first stage BERT IR documents.
+
+The second stage expands the first stage BERT IR documents by Wikipedia hyperlinks to obtain $D _ { e x p }$ . A document is included if it is linked to or links to a document in the first stage. We use the same BERT ranker to rank $D _ { e x p }$ and keep the top 15 documents in $D _ { e x p }$ .
+
+The final evidence graph nodes per question includes the top two highest ranked documents in $D _ { i r }$ top one per entity name in $D _ { e l }$ , and top 15 from the expanded documents $D _ { e x p }$ .
+
+The comparison questions only require information from two question entities; thus when building the evidence graph we do not expand them (i.e. there is no $D _ { e x p , }$ ).
+
+The retrieval pipeline is a multi-stage retrieval enhanced with entity linking. It is close to the retrieval system used in SR-MRS (Nie et al., 2019). When using SR-MRS retrieved documents for documents, we use top 10 documents on bridge questions and top two documents on comparison questions.
+
+In the next section, we show that Transformer-XH is robust to different number of documents kept in the evidence graph and performs similarly using the documents retrieved from SR-MRS.
+
+# A.2 ABLATION STUDIES ON DOCUMENT RETRIEVAL
+
+This experiment studies the effectiveness and influence of different retrieval settings. We use different numbers of top K ranked documents from the BERT ranker, run Transformer-XH in the corresponding evidence graph, and evaluate its performance on Bridge questions in the Dev set. We also evaluate the Supporting facts Recall and Answer Recall. Supp Recall evaluates whether the document with the supporting fact is included in the first stage retrieved documents. Ans Recall evaluates whether their exists a document in the evidence graph that includes the ground truth answer. The results are in Table 6.
+
+Our BERT IR system performs better than CogQA’s TF-IDF and on par with SR-MRS, as expected. The latter uses a similar retrieval pipeline with our BERT IR system; Transformer-XH is robust on different retrieval settings and keeps its effectiveness when applied on Top 10 documents from SR-MRS (including both stages).
+
+<table><tr><td>Method</td><td>Supp Recall</td><td>Ans Recall</td><td>Dev AnsEM</td><td>Dev Ans F1</td></tr><tr><td>Top 10 TFIDF (CogQA)</td><td>70.8</td><td>n.a.</td><td>1</td><td>1</td></tr><tr><td>Top 2 w. BERT IR + Q Entites</td><td>72.3</td><td>88.1</td><td>48.7</td><td>62.6</td></tr><tr><td>Top 5 w. BERT IR +QEntites</td><td>76.5</td><td>89.6</td><td>47.1</td><td>60.8</td></tr><tr><td>Top 10 w.BERTIR+Q Entites</td><td>78.9</td><td>91.1</td><td>46.6</td><td>60.3</td></tr><tr><td>SR-MRS Top 10 (All Together)</td><td>n.a.</td><td>86.1</td><td>47.9</td><td>62.3</td></tr></table>
+
+Table 6: Ablation study on the retrieval systems. Top-10 TFIDF is the one used by $\mathrm { C o g Q A }$ (Ding et al., 2019). BERT IR is the retrieval system used by $\mathrm { C o g Q A }$ (w. BERT IR) and Transformer-XH. Top K refers to using the 2/5/10 highest ranked documents from the BERT ranker in the first stage. SR-MRS Top 10 uses the 10 retrieved documents per question provided by Nie et al. (2019). All retrieval methods include entities linked in the question and are expanded along Wiki links, except when evaluating the 1st stage Supp Recall.
+
+# A.3 OTHER HOTPOT QA COMPONENTS
+
+This section describes the other components for HotpotQA dataset. The whole QA system starts with question type classification. We train transformer-XH separately on each type of questions over their evidence graph. Besides answer prediction, we also adopt BERT based model for predicting supporting sentences.
+
+# A.3.1 QUESTION CLASSIFICATION
+
+The first component of our system is to classify the question to bridge and comparison types. We adopt BERT classification fine-tuning setting on HotpotQA questions using the question type labels provided in HotpotQA. The classifier achieves $9 9 . 1 \%$ accuracy on the dev set. We use the classifier to split the questions into Comparison and Bridge.
+
+# A.3.2 SUPPORTING FACTS CLASSIFICATION
+
+The supporting facts prediction task is to extract all sentences that help get the answer. For bridge question, these sentences usually cover different pieces of questions. And for comparison questions, the supporting facts are the properties of two question entities. We design one model architecture for this task, but we train two models on each type to reflect the inherent difference.
+
+We use BERT as our base model and on top of BERT, we conduct multi-task learning scheme. The first task is document relevance prediction, similar as Transformer-XH, we add a linear layer on the [CLS] token of BERT to predict the relevance score. The other task is sentence binary classification, we concatenate the first and last token representation of each sentence in the document through a linear layer, the binary output decides whether this sentence is supporting sentence.
+
+Bridge question supporting facts prediction For bridge questions, we predict supporting facts after answer prediction from Transformer-XH to resume the inference chain. We start by predicting supporting facts in the answer document. The other document is chosen from the parents of the answer document in the evidence graph. 3. Compare with the contemporary model Nie et al. (2019), which does not limit the search space along the inference chain (i.e., the answer document may not be relevant to the other supporting page), our method more naturally fits the task purpose.
+
+Comparison question supporting facts prediction For comparison questions, after extracting the first step documents $D$ , we simply run this supporting facts prediction model to select the top-2 documents, and predict the corresponding supporting facts.
+
+# A.3.3 TRAINING DETAILS
+
+We use DGL (Wang et al., 2019) for implementing Transformer-XH and CogQA (w. BERT IR) with batch size 1 (i.e., one graph for each batch), and keep the other parameters same as default BERT setting. We train Transformer-XH separately on two different types of questions, following previous
+
+Table 7: Additional examples for model prediction on HotpotQA dataset, the first example is the correct prediction $( + )$ , the other two examples are the wrong predictions (-).   
+
+<table><tr><td>id</td><td>Example</td><td>Explanation</td></tr><tr><td>1(+)</td><td>Q:In which year was the King who made the 1925 Birthday Honours born? P: 1865√ Document 1: The 1925 Birthday Honours were ap- pointments by King George V to various orders and honours. Document 2: GeorgeV (3 June 1865- 20 January 1936)was King of the United Kingdom.</td><td>Withnecessary evidenceavailable, Transformer-XH conducts multi-hop reasoning,and extracts the correct span.</td></tr><tr><td>2(-)</td><td>Q:Where was the world cup hosted that Algeria quali- fied for the first time into the round of 16? A:Brazil P: Spain X Document 1 (Algeria at the FIFA World Cup):In 2014,Algeria qualified for the first time into the round of 16. Document 2 (2014 FIFA CUP): It took place in Brazil from 12 June to 13 July 2O14,after the country was awarded the hosting rights in 2007.</td><td>Transformer-XH does not predict the correct answer, since document 1 does not link to any other docu- ments.Thus,the information does not propagate to the correct answer docu- ment 2014 FIFA CUP.</td></tr><tr><td>3(-)</td><td>Q:What government position was held by the woman who portrayed Corliss Archer in the film Kiss and Tell? A:Chief of ProtocolP:ambassador X Document 1: Kiss and Tell is a 1945 American comedy film starring then 17-year-old Shirley Temple as Corliss Archer. Document 2:As an adult, Shirley Temple was named United States ambassador to Ghana and to Czechoslo- vakia,and also servedas Chief ofProtocol of theUnited States.</td><td>Transformer-XH predicts the correct answer document Shirley Temple. However it could not distinguish from the wrong answer ambassador which she was named but not held that position.</td></tr></table>
+
+research (Ding et al., 2019). We train Transformer-XH and the GNN of CogQA (w. BERT IR) for 2 epochs. All other BERT based models use the default BERT parameters and train the model for 1 epoch.
+
+# A.4 IMPLEMENTATION DETAILS OF COGQA (W. BERT IR)
+
+This section discusses our implementation of CogQA (W. BERT IR). We start with the same documents from BERT IR, the one used by Transformer-XH, and then implement the following steps:
+
+# A.4.1 HOP ENTITY EXTRACTION
+
+For each document from the previous step, we run BERT MRC model and limit the span candidates as hyperlinked entities for hop entity extraction (e.g., in Figure 1, “Harvard University” is a hop entity). Following Ding et al. (2019), we predict the top three entities that above the relative threshold that is the start span probability of [CLS] position.
+
+# A.4.2 ANSWER SPAN EXTRACTION
+
+For each document (add the hop entity document), following Ding et al. (2019), we run BERT MRC model to extract spans (e.g., “Combridge” in Figure 1.). We predict the top one span that above the threshold that is the start span probability of [CLS] position.
+
+We train both hop entity extraction and span extraction tasks with same BERT model but different prediction layers. For each training example, we extract the link between two given supporting pages. The page includes the link (e.g., “Harvard University” in Figure 1.) is the supporting page
+
+for hop entity extraction, while the other page is the answer page (e.g., “Combridge” in Figure 1.) for answer span extraction.
+
+# A.4.3 GAT MODELING
+
+All the entities and answer spans form the final graph. The nodes are the entities and spans, and edges are the connections from the entities to the extracted hop entities or spans.
+
+We use BERT for each node representation with question, anchor sentences and context, following Ding et al. (2019). We run GAT (Velickovi ˇ c et al., 2018) on top of BERT to predict the correct ´ answer span node.
+
+# A.4.4 COMPARISON QUESTIONS
+
+After predicting supporting facts, we concatenate the sentences and follow Min et al. (2019b) to run a BERT MRC model to predict either span or yes/no as the answer.
+
+# A.5 ADDITIONAL CASE STUDY
+
+We provide addition case studies in Table 7. The first case can be directly predicted through the clear evidence chain ”the 1925 Birthday Honours” ”George $\mathrm { V } ^ { \prime \prime }  ^ { \prime \prime } 1 8 6 5 ^ { \prime \prime }$ . In the second case, the first document (”Algeria at the FIFA World Cup”) has no link to any other documents, therefore the model can not access the correct answer. The third case is more reading comprehension oriented, where the model can not distinguish the correct and wrong spans inside one sentence.