diff --git a/parse/train/-iu9-C_lan/-iu9-C_lan.md b/parse/train/-iu9-C_lan/-iu9-C_lan.md new file mode 100644 index 0000000000000000000000000000000000000000..e744073e9dd199c4f800b30f34c63046d9c86c27 --- /dev/null +++ b/parse/train/-iu9-C_lan/-iu9-C_lan.md @@ -0,0 +1,373 @@ +# Cycle Self-Training for Domain Adaptation + +Hong Liu Dept of Electronic Engineering Tsinghua University hongliu9903@gmail.com + +Jianmin Wang +School of Software, BNRist +Tsinghua University +jimwang@tsinghua.edu.cn Mingsheng Long⇤ +School of Software, BNRist Tsinghua University +mingsheng@tsinghua.edu.cn + +# Abstract + +Mainstream approaches for unsupervised domain adaptation (UDA) learn domaininvariant representations to narrow the domain shift, which are empirically effective but theoretically challenged by the hardness or impossibility theorems. Recently, self-training has been gaining momentum in UDA, which exploits unlabeled target data by training with target pseudo-labels. However, as corroborated in this work, under distributional shift, the pseudo-labels can be unreliable in terms of their large discrepancy from target ground truth. In this paper, we propose Cycle Self-Training (CST), a principled self-training algorithm that explicitly enforces pseudo-labels to generalize across domains. CST cycles between a forward step and a reverse step until convergence. In the forward step, CST generates target pseudo-labels with a source-trained classifier. In the reverse step, CST trains a target classifier using target pseudo-labels, and then updates the shared representations to make the target classifier perform well on the source data. We introduce the Tsallis entropy as a confidence-friendly regularization to improve the quality of target pseudo-labels. We analyze CST theoretically under realistic assumptions, and provide hard cases where CST recovers target ground truth, while both invariant feature learning and vanilla self-training fail. Empirical results indicate that CST significantly improves over the state-of-the-arts on visual recognition and sentiment analysis benchmarks. + +# 1 Introduction + +Transferring knowledge from a source domain with rich supervision to an unlabeled target domain is an important yet challenging problem. Since deep neural networks are known to be sensitive to subtle change in underlying distributions [70], models trained on one labeled dataset often fail to generalize to another unlabeled dataset [58, 1]. Unsupervised domain adaptation (UDA) addresses the challenge of distributional shift by adapting the source model to the unlabeled target data [50, 43]. + +The mainstream paradigm for UDA is feature adaptation, a.k.a. domain alignment. By reducing the distance of the source and target feature distributions, these methods learn invariant representations to facilitate knowledge transfer between domains [34, 22, 36, 54, 37, 73], with successful applications in various areas such as computer vision [63, 27, 77] and natural language processing [75, 49]. Despite their popularity, the impossibility theories [6] uncovered intrinsic limitations of learning invariant representations when it comes to label shift [74, 32] and shift in the support of domains [29]. + +Recently, self-training (a.k.a. pseudo-labeling) [21, 78, 30, 32, 47, 68] has been gaining momentum as a promising alternative to feature adaptation. Originally tailored to semi-supervised learning, self-training generates pseudo-labels of unlabeled data, and jointly trains the model with source labels and target pseudo-labels [31, 39, 30]. However, the distributional shift in UDA makes pseudo-labeling more difficult. Directly using all pseudo-labels is risky due to accumulated error and even trivial solution [14]. Thus previous works tailor self-training to UDA by selecting trustworthy pseudo-labels. Using confidence threshold or reweighting, recent works try to alleviate the negative effect of domain shift in standard self-training [78, 47], but they can be brittle and require expensive tweaking of the threshold or weight for different tasks, and their performance gain is still inconsistent. + +![](images/a98d2d44c2b974a909fc041a6f8726476f59f9bdcb19e5febe93a6d25e86dd55.jpg) +Figure 1: Standard self-training vs. cycle self-training. In standard self-training, we generate target pseudolabels with a source model, and then train the model with both source ground-truths and target pseudo-labels. In cycle self-training, we train a target classifier with target pseudo-labels in the inner loop, and make the target classifier perform well on the source domain by updating the shared representations in the outer loop. + +In this work, we first analyze the quality of pseudo-labels with or without domain shift to delve deeper into the difficulty of standard self-training in UDA. On popular benchmark datasets, when the source and target are the same, our analysis indicates that the pseudo-label distribution is almost identical to the ground-truth distribution. However, with distributional shift, their discrepancy can be very large with examples of several classes mostly misclassified into other classes. We also study the difficulty of selecting correct pseudo-labels with popular criteria under domain shift. Although entropy and confidence are reasonable selection criteria for correct pseudo-labels without domain shift, the domain shift makes their accuracy decrease sharply. + +Our analysis shows that domain shift makes pseudo-labels unreliable and that self-training on selected target instances with accurate pseudo-labels is less successful. Thereby, more principled improvement of standard self-training should be tailored to UDA and address the domain shift explicitly. In this work, we propose Cycle Self-Training (CST), a principled self-training approach to UDA, which overcomes the limitations of standard self-training (see Figure 1). Different from previous works to select target pseudo-labels with hard-to-tweak protocols, CST learns to generalize the pseudo-labels across domains. Specifically, CST cycles between the use of target pseudo-labels to train a target classifier, and the update of shared representations to make the target classifier perform well on the source data. In contrast to the standard Gibbs entropy that makes the target predictions over-confident, we propose a confidence-friendly uncertainty measure based on the Tsallis entropy in information theory, which adaptively minimizes the uncertainty without manually tuning or setting thresholds. Our method is simple and generally applicable to vision and language tasks with various backbones. + +We empirically evaluate our method on a series of standard UDA benchmarks. Results indicate that CST outperforms previous state-of-the-art methods in 21 out of 25 tasks for object recognition and sentiment classification. Theoretically, we prove that the minimizer of CST objective is endowed with general guarantees of target performance. We also study hard cases on specific distributions, showing that CST recovers target ground-truths while both feature adaptation and standard self-training fail. + +# 2 Preliminaries + +We study unsupervised domain adaptation (UDA). Consider a source distribution $P$ and a target distribution $Q$ over the input-label space $\mathcal { X } \times \mathcal { V }$ . We have access to $n _ { s }$ labeled i.i.d. samples $\widehat { P } = \{ x _ { i } ^ { s } , y _ { i } ^ { s } \} _ { i = 1 } ^ { n _ { s } }$ from $P$ and $n _ { t }$ unlabeled i.i.d. samples $\widehat { Q } = \{ x _ { i } ^ { t } \} _ { i = 1 } ^ { n _ { t } }$ from $Q$ . The model $f$ comprises a feature extractor $h _ { \phi }$ parametrized by $\phi$ and a head (linear classifier) $g _ { \theta }$ parametrized by $\theta$ , i.e. $\bar { f } _ { \theta , \phi } ( x ) = g _ { \theta } ( h _ { \phi } ( x ) )$ . The loss function is $\ell ( \cdot , \cdot )$ . Denote by $L _ { P } ( \theta , \phi ) : = \mathbb { E } _ { ( x , y ) \sim P } \ell ( f _ { \theta , \phi } ( x ) , y )$ the expected error on $P$ . Similarly, we use ${ \cal L } _ { \widehat { P } } ( \theta , \phi )$ to denote the empirical error on dataset $\widehat { P }$ . + +We discuss two mainstream UDA methods and their formulations: feature adaptation and self-training. + +Feature Adaptation trains the model $f$ on the source dataset $\widehat { P }$ , and simultaneously matches the source and target distributions in the representation space $\mathcal { Z } = h ( \mathcal { X } )$ : + +$$ +\operatorname* { m i n } _ { \theta , \phi } L _ { \widehat { P } } ( \theta , \phi ) + d ( h _ { \sharp } \widehat { P } , h _ { \sharp } \widehat { Q } ) . +$$ + +![](images/b47a38073ca7224e33f9ab2c301d27144b2711ff9fb5bf238f28f0fb56f3274f.jpg) +Figure 2: Analysis of pseudo-labels under domain shift on VisDA-2017. Left: Pseudo-label distributions with and without domain shift. Middle: Changes of pseudo-label distributions throughout training. Right: Quality of pseudo-labels under different pseudo-label selection criteria. + +Here, $h _ { \sharp } \widehat { P }$ denotes the pushforward distribution of $\widehat { P }$ , and $d ( \cdot , \cdot )$ is some distribution distance. For instance, Long et al. [34] used maximum mean discrepancy $d _ { \mathrm { M M D } }$ , and Ganin et al. [22] approximated the $\mathcal { H } \Delta \mathcal { H }$ -distance $d _ { \mathcal { H } \Delta \mathcal { H } }$ [7] with adversarial training. Despite its pervasiveness, recent works have shown the intrinsic limitations of feature adaptation under real-world situations [6, 74, 33, 32, 29]. + +Self-Training is considered a promising alternative to feature adaptation. In this work we mainly focus on pseudo-labeling [31, 30]. Stemming from semi-supervised learning, standard self-training trains a source model $f _ { s }$ on the source dataset $\widehat { P }$ $: \mathrm { m i n } _ { \theta _ { s } , \phi _ { s } } L _ { \widehat { P } } ( \theta _ { s } , \phi _ { s } )$ . The target pseudo-labels are then generated by $f _ { s }$ on the target dataset $\widehat { Q }$ . To leverage unlabeled target data, self-training trains the model on the source and target datasets together with source ground-truths and target pseudo-labels: + +$$ +\operatorname* { m i n } _ { \theta , \phi } L _ { \widehat { P } } ( \theta , \phi ) + \mathbb { E } _ { x \sim \widehat { Q } } \ell ( f _ { \theta , \phi } ( x ) , \arg \operatorname* { m a x } _ { i } \{ f _ { \theta , \phi _ { s } } ( x ) _ { [ i ] } \} ) . +$$ + +Self-training also uses label-sharpening as a standard protocol [31, 57]. Another popular variant of pseudo-labeling is the teacher-student model [4, 61], which iteratively improves the quality of pseudo-labels via alternatively replacing $\theta _ { s }$ and $\phi _ { s }$ with $\theta$ and $\phi$ of the previous iteration. + +# 2.1 Limitations of Standard Self-Training + +Standard self-training with pseudo-labels uses unlabeled data efficiently for semi-supervised learning [31, 39, 57]. Here we carry out exploratory studies on the popular VisDA-2017 [45] dataset using ResNet-50 backbones. We find that domain shift makes the pseudo-labels biased towards several classes and thereby unreliable in UDA. See Appendix C.1 for details and results on more datasets. + +Pseudo-label distributions with or without domain shift. We resample the original VisDA-2017 to simulate different relationship between source and target domains: 1) i.i.d., 2) covariate shift, and 3) label shift. We train the model on the three variants of source dataset and use it to generate target pseudo-labels. We show the distributions of target ground-truths and pseudo-labels in Figure 2 (Left). When the source and target distributions are identical, the distribution of pseudo-labels is almost the same as ground-truths, indicating the reliability of pseudo-labels. In contrast, when exposed to label shift or covariate shift, the distribution of pseudo-labels is significantly different from target ground-truths. Note that classes 2, 7, 8 and 12 appear rarely in the target pseudo-labels in the covariate shift setting, indicating that the pseudo-labels are biased towards several classes due to domain shift. Self-training with these pseudo-labels is risky since it may lead to misalignment of distributions and misclassify many examples of classes 2, 7, 8 and 12. + +Change of pseudo-label distributions throughout training. To further study the change of pseudolabels in standard self-training, we compute the total variation (TV) distance between target groundtruths and target pseudo-labels: $\begin{array} { r } { d _ { \mathrm { T V } } ( c , \dot { c ^ { \prime } } ) = \frac { 1 } { 2 } \sum _ { i } \| c _ { i } - c _ { i } ^ { \prime } \| } \end{array}$ , where $c _ { i }$ is the ratio of class $i$ . We plot its change during training in Figure 2 (Middle). Although the error rate of pseudo-labels continues to decrease, $d _ { \mathrm { T V } }$ remains almost unchanged at 0.26 throughout training. Note that $d _ { \mathrm { T V } }$ is the lower bound of the error rate of the pseudo-labels (shown in Appendix C.1). If $d _ { \mathrm { T V } }$ converges to 0.26, then the accuracy of pseudo-labels is upper-bounded by 0.74. This indicates that the important denoising ability [66] of pseudo-labels in standard self-training is hindered by domain shift. + +Difficulty of selecting reliable pseudo-labels under domain shift. To mitigate the negative effect of false pseudo-labels, recent works proposed to select correct pseudo-labels based on thresholding the entropy or confidence criteria [35, 21, 37, 57]. However, it remains unclear whether these strategies are still effective under domain shift. Here we compare the quality of pseudo-labels selected by different strategies with or without domain shift. For each strategy, we compute False Positive Rate and True Positive Rate for different thresholds and plot its ROC curve in Figure 2 (Right). When the source and target distributions are identical, both entropy and confidence are reasonable strategies for selecting correct pseudo-labels $( \mathrm { A U C } { = } 0 . 8 9 )$ ). However, when the target pseudo-labels are generated by the source model, the quality of pseudo-labels decreases sharply under domain shift $\mathrm { \Delta A U C { = } 0 . 7 8 }$ ). + +# 3 Approach + +We present Cycle Self-Training (CST) to improve pseudo-labels under domain shift. An overview of our method is given in Figure 1. Cycle Self-Training iterates between a forward step and a reverse step to make self-trained classifiers generalize well on both target and source domains. + +# 3.1 Cycle Self-Training + +Forward Step. Similar to standard self-training, we have a source classifier $\theta _ { s }$ trained on top of the shared representations $\phi$ on the labeled source domain, and use it to generate target pseudo-labels as + +$$ +y ^ { \prime } = \arg \operatorname* { m a x } _ { i } \{ f _ { \theta _ { s } , \phi } ( x ) _ { [ i ] } \} , +$$ + +for each $x$ in the target dataset $\widehat { Q }$ . Traditional self-training methods use confidence thresholding or reweighting to select reliable pseudo-labels. For example, Sohn et al. [57] select pseudo-labels with softmax value and Long et al. [37] add entropy reweighting to rely on examples with more confidence prediction. However, the output of deep networks is usually miscalibrated [25], and is not necessarily related to the ground-truth confidence even on the same distribution. In domain adaptation, as shown in Section 2.1, the discrepancy between the source and target domains makes pseudo-labels even more unreliable, and the performance of commonly used selection strategies is also unsatisfactory. Another drawback is the expensive tweaking in order to find the optimal confidence threshold for new tasks. To better apply self-training to domain adaptation, we expect that the model can gradually refine the pseudo-labels by itself without the cumbersome selection or thresholding. + +Reverse Step. We design a complementary step with the following insights to improve self-training. Intuitively, the labels on the source domain contain both useful information that can transfer to the target domain and harmful information that can make pseudo-labels incorrect. Similarly, reliable pseudo-labels on the target domain can transfer to the source domain in turn, while models trained with incorrect pseudo-labels on the target domain cannot transfer to the source domain. In this sense, if we explicitly train the model to make target pseudo-labels informative of the source domain, we can gradually make the pseudo-labels more accurate and learn to generalize to the target domain. + +Specifically, with the pseudo-labels $y ^ { \prime }$ generated by the source classifier $\theta _ { s }$ at hand as in equation 3, we train a target head $\hat { \theta } _ { t } ( \phi )$ on top of the representation $\phi$ with pseudo-labels on the target domain $\widehat { Q }$ + +$$ +\hat { \theta } _ { t } ( \phi ) = \underset { \theta } { \arg \operatorname* { m i n } } \mathbb { E } _ { \boldsymbol { x } \sim \hat { \boldsymbol { Q } } } \ell ( f _ { \theta , \phi } ( \boldsymbol { x } ) , y ^ { \prime } ) . +$$ + +We wish to make the target pseudo-labels informative of the source domain and gradually refine them. To this end, we update the shared feature extractor $\phi$ to predict accurately on the source domain and jointly enforce the target classifier $\hat { \theta } _ { t } ( \phi )$ to perform well on the source domain. This naturally leads to the objective of Cycle Self-Training: + +$$ +\operatorname* { m i n i m i z e } _ { \theta _ { s } , \phi } L _ { \mathrm { C y c l e } } ( \theta _ { s } , \phi ) : = L _ { \hat { P } } ( \theta _ { s } , \phi ) + L _ { \hat { P } } ( \hat { \theta } _ { t } ( \phi ) , \phi ) . +$$ + +Bi-level Optimization. The objective in equation 5 relies on the solution $\hat { \theta } _ { t } ( \phi )$ to the objective in equation 4. Thus, CST formulates a bi-level optimization problem. In the inner loop we generate target pseudo-labels with the source classifier (equation 3), and train a target classifier with target pseudo-labels (equation 4). After each inner loop, we update the feature extractor $\phi$ for one step in the outer loop (equation 5), and start a new inner loop again. However, since the inner loop of the optimization in equation 4 only involves the light-weight linear head $\theta _ { t }$ , we propose to calculate the analytical form of $\hat { \theta } _ { t } ( \phi )$ and directly back-propagate to the feature extractor $\phi$ instead of calculating the second-order derivatives as in MAML [18]. The resulting framework is as fast as training two heads jointly. Also note that the solution $\hat { \theta } _ { t } ( \phi )$ relies on $\theta _ { s }$ implicitly through $y ^ { \prime }$ . However, both standard self-training and our implementation use label sharpening, making $y ^ { \prime }$ not differentiable. Thus we follow vanilla self-training and do not consider the gradient of $\hat { \theta } _ { t } ( \phi )$ w.r.t. $y ^ { \prime }$ in the outer loop optimization. We defer the derivation and implementation of bi-level optimization to Appendix B.2. + +# 3.2 Tsallis Entropy Minimization + +Gibbs entropy is widely used by existing semi-supervised learning methods to regularize the model output and minimize the uncertainty of predictions on unlabeled data [24]. In this work, we generalize Gibbs entropy to Tsallis entropy [62] in information theory. Suppose the softmax output of a model is $\boldsymbol { y } \in \mathbb { R } ^ { K }$ , then the $\alpha$ -Tsallis entropy is defined as + +$$ +S _ { \alpha } ( y ) = \frac { 1 } { \alpha - 1 } \left( 1 - \sum y _ { [ i ] } ^ { \alpha } \right) , +$$ + +where $\alpha > 0$ is the entropic-index. Note that $\begin{array} { r } { \operatorname* { l i m } _ { \alpha \to 1 } S _ { \alpha } ( y ) = \sum _ { i } - y _ { [ i ] } \mathrm { l o g } ( y _ { [ i ] } ) } \end{array}$ which exactly recovers the Gibbs entropy. When $\alpha = 2$ , $S _ { \alpha } ( y )$ becomes the Gini impurity $1 - \textstyle \sum _ { i } y _ { [ i ] } ^ { 2 }$ . + +We propose to control the uncertainty of target pseudo-labels based on Tsallis entropy minimization: + +$$ +L _ { \widehat { Q } , \mathrm { T s a l l i s } , \alpha } ( \theta , \phi ) : = \mathbb { E } _ { \boldsymbol { x } \sim \widehat { Q } } S _ { \alpha } ( f _ { \theta , \phi } ( \boldsymbol { x } ) ) . +$$ + +Figure 3 shows the change of Tsallis entropy with different entropic-indices $\alpha$ for binary problems. Intuitively, smaller $\alpha$ exerts more penalization on uncertain predictions and larger $\alpha$ allows several scores $y _ { i }$ ’s to be similar. This is critical in self-training since an overly small $\alpha$ (as in Gibbs entropy) will make the incorrect dimension of pseudo-labels close to 1 and have no chance to be corrected throughout training. In Section 5.4, we further verify this property with experiments. + +![](images/1ee6c84356d7e7a52e7c51e6a8539defd26596a9b539b8488d28b38233853582.jpg) +Figure 3: Tsallis entropy vs. entropic-index $\alpha$ + +An important improvement of the Tsallis entropy over Gibbs entropy is that it can choose the suitable measure of uncertainty for different systems to avoid over-confidence caused by overly penalizing the uncertain pseudo-labels. To automatically find the suitable $\alpha$ , we adopt a similar strategy as Section 3.1. The intuition is that if we use the suitable entropic-index $\alpha$ to train the source classifier $\theta _ { s , \alpha }$ , the target pseudo-labels generated by $\theta _ { s , \alpha }$ will contain desirable knowledge of the source dataset, i.e. a target classifier $\theta _ { t , \alpha }$ trained with these pseudo-labels will perform well on the source domain. Therefore, we semi-supervisedly train a classifier $\widehat { \theta } _ { s , \alpha }$ on the source domain with the $\alpha$ -Tsallis entropy regularization $L _ { \widehat { Q } , \mathrm { T s a l l i s } , \alpha }$ on the target domain as: $\hat { \theta } _ { s , \alpha } = \arg \operatorname* { m i n } _ { \theta } L _ { \widehat { P } } ( \theta , \phi ) + L _ { \widehat { Q } , \mathrm { T s a l l i s } , \alpha } ( \theta , \phi )$ , from which we obtain the target pseudo-labels. Then we train another head $\widehat { \theta } _ { t , \alpha }$ with target pseudo-labels. We automatically find $\alpha$ by minimizing the loss of $\widehat { \theta } _ { t , \alpha }$ on the source data: + +$$ +\hat { \alpha } = \underset { \alpha \in [ 1 , 2 ] } { \arg \operatorname* { m i n } } L _ { \widehat { P } } ( \widehat { \theta } _ { t , \alpha } , \phi ) +$$ + +To solve equation 10, we discretize the feasible region [1, 2] of $\alpha$ and use discrete optimization to lower computational cost. We also update $\alpha$ at the start of each epoch, since we found more frequent + +# Algorithm 1 Cycle Self-Training (CST) + +1: Input: source dataset $\widehat { P }$ and target dataset $\widehat { Q }$ . +2: for epoch $= 0$ to MaxEpoch do +3: Select $\hat { \alpha }$ as equation 10 at the start of each epoch. +4: for $t = 0$ to MaxIter do +5: Forward Step +6: Generate pseudo-labels on the target domain with $\phi$ and $\theta _ { s }$ ${ \mathrm { ~ \mu ~ } } _ { 3 } \colon y ^ { \prime } = \arg \operatorname* { m a x } _ { i } \{ f _ { \theta _ { s } , \phi } ( x ) _ { [ i ] } \}$ . +7: Reverse Step +8: Train a target head $\hat { \theta } _ { t } ( \phi )$ with target pseudo-labels $y ^ { \prime }$ on the feature extractor $\phi$ : +$\hat { \theta } _ { t } ( \phi ) = \underset { \theta } { \arg \operatorname* { m i n } } \mathbb { E } _ { x \sim \hat { Q } } \ell ( f _ { \theta , \phi } ( x ) , y ^ { \prime } ) .$ +9: Update the feature extractor $\phi$ and the source head $\theta _ { s }$ to make $\hat { \theta } _ { t } ( \phi )$ perform well on the +source dataset and minimize the $\hat { \alpha }$ -Tsallis entropy on the target dataset: + +$$ +\begin{array} { r l } & { \phi \phi - \eta \nabla _ { \phi } [ L _ { \widehat { P } } ( \theta _ { s } , \phi ) + L _ { \widehat { P } } ( \widehat { \theta } _ { t } ( \phi ) , \phi ) + L _ { \widehat { Q } , \mathrm { T s a l l i s } , \widehat { \alpha } } ( \theta _ { s } , \phi ) ] . } \\ & { \qquad \theta _ { s } \theta _ { s } - \eta \nabla _ { \theta _ { s } } [ L _ { \widehat { P } } ( \theta _ { s } , \phi ) + L _ { \widehat { Q } , \mathrm { T s a l l i s } , \widehat { \alpha } } ( \theta _ { s } , \phi ) ] . } \end{array} +$$ + +10: end for +11: end for + +update leads to no performance gain. Details are deferred to Appendix B.3. Finally, with the optimal $\hat { \alpha }$ found, we add the $\hat { \alpha }$ -Tsallis entropy minimization term $L _ { \widehat { Q } , \mathrm { T s a l l i s } , \widehat { \alpha } }$ to the overall objective: + +$$ +\operatorname* { m i n i m i z e } _ { \theta _ { s } , \phi } L _ { \mathrm { C y c l e } } ( \theta _ { s } , \phi ) + L _ { \hat { Q } , \mathrm { T s a l l i s } , \hat { \alpha } } ( \theta _ { s } , \phi ) . +$$ + +In summary, Algorithm 1 depicts the complete training procedure of Cycle Self-Training (CST). + +# 4 Theoretical Analysis + +We analyze the properties of CST theoretically. First, we prove that the minimizer of the CST loss $L _ { \mathrm { C S T } } ( f _ { s } , f _ { t } )$ will lead to small target loss $\mathrm { E r r } _ { Q } ( f _ { s } )$ under a simple but realistic expansion assumption. Then, we further demonstrate a concrete instantiation where cycle self-training provably recovers the target ground truth, but both feature adaptation and standard self-training fail. Due to space limit, we state the main results here and defer all proof details to Appendix $A$ . + +# 4.1 CST Provably Works under the Expansion Assumption + +We start from a $K$ -way classification model, $f : \mathcal { X } \to [ 0 , 1 ] ^ { K } \in \mathcal { F }$ and ${ \tilde { f } } ( x ) : = \arg \operatorname* { m a x } _ { i } f ( x ) _ { [ i ] }$ denotes the prediction. Denote by $P _ { i }$ the conditional distribution of $P$ given $y = i$ . Assume the supports of $P _ { i }$ and $P _ { j }$ are disjoint for $i \neq j$ . The definition is similar for $Q _ { i }$ . We further Assume $P ( y = i ) = Q ( y = i )$ . For any $x \in \mathcal { X }$ , $\mathcal { N } ( x )$ is defined as the neighboring set of $x$ with a proper metric $d ( \cdot , \cdot )$ $\vert , \mathcal { N } ( x ) = \{ x ^ { \prime } : d ( x , x ^ { \prime } ) \leq \xi \}$ . ${ \mathcal { N } } ( A ) : = \cup _ { x \in A } { \mathcal { N } } ( x )$ . Denote the expected error on the target domain by $\mathrm { E r r } _ { Q } ( f ) : = \mathbb { E } _ { ( x , y ) \sim Q } \mathbb { I } ( \tilde { f } ( x ) \neq y )$ . + +We study the CST algorithm under the expansion assumption of the mixture distribution [66, 11]. Intuitively, this assumption indicates that the conditional distributions $P _ { i }$ and $Q _ { i }$ are closely located and regularly shaped, enabling knowledge transfer from the source domain to the target domain. + +Definition 1 $[ q , \epsilon )$ -constant expansion [66]). We say $P$ and $Q$ satisfy $( q , \epsilon )$ -constant expansion for some constant $q , \epsilon \in ( 0 , 1 )$ , if for any set $A \in { \mathcal { X } }$ and any $i \in [ K ]$ with ${ \textstyle \frac { 1 } { 2 } } > P _ { \frac { 1 } { 2 } ( P _ { i } + Q _ { i } ) } ( A ) > q$ , we have $P _ { \frac { 1 } { 2 } ( P _ { i } + Q _ { i } ) } ( { \mathcal { N } } ( A ) \backslash A ) > \operatorname* { m i n } \{ \epsilon , P _ { \frac { 1 } { 2 } ( P _ { i } + Q _ { i } ) } ( A ) \} .$ . + +Based on this expansion assumption, we consider a robustness-constrained version of CST. Later we will show that the robustness is closely related to the uncertainty. Denote by $f _ { s }$ the source model and $f _ { t }$ the model trained on the target with pseudo-labels. Let $R ( f _ { t } ) : = P _ { \frac { 1 } { 2 } ( P + Q ) } ( \{ x : \exists x ^ { \prime } \in$ $\mathcal { N } ( x ) , \tilde { f } _ { t } ( x ) \neq \tilde { f } _ { t } ( x ^ { \prime } ) \} )$ represent the robustness [66] of $f _ { t }$ on $P$ and $Q$ . Suppose $\mathbb { E } _ { ( x , y ) \sim Q } \mathbb { I } ( \tilde { f } _ { s } ( x ) \neq$ $\tilde { f } _ { t } ( x ) ) \leq c$ and $R ( f _ { t } ) \leq \rho$ . The following theorem states that when $f _ { s }$ and $f _ { t }$ behave similarly on the target domain $Q$ and $f _ { t }$ is robust to local changes in input, the minimizer of the cycle source error $\mathrm { E r r } _ { P } ( f _ { t } )$ will guarantee low error of $f _ { s }$ on the target domain $Q$ . + +Theorem 1. Suppose Definition 1 holds for $P$ and $Q$ . For any $f _ { s } , f _ { t }$ satisfying $\mathbb { E } _ { ( x , y ) \sim Q } \mathbb { I } ( \tilde { f } _ { s } ( x ) \neq$ $\tilde { f } _ { t } ( x ) ) \leq c$ and $R ( f _ { t } ) \leq \rho _ { : }$ , the expected error of $f _ { s }$ on the target domain $Q$ is bounded, + +$$ +\mathrm { E r r } _ { Q } ( f _ { s } ) \le \mathrm { E r r } _ { P } ( f _ { t } ) + c + 2 q + \frac { \rho } { \mathrm { m i n } \{ \epsilon , q \} } . +$$ + +To further relate the expected error with the CST training objective and obtain finite-sample guarantee, we use the multi-class margin loss: $l _ { \gamma } ( f ( x ) , y ) : = \bar { \psi _ { \gamma } } ( - { \cal M } ( f ( x ) , y ) )$ , where $\mathcal { M } ( v , y ) =$ $v _ { [ y ] } - \operatorname* { m a x } _ { y ^ { \prime } \ne y } v _ { [ y ^ { \prime } ] }$ and $\psi _ { \gamma }$ is the ramp function. We then extend the margin loss: $\mathcal { M } ( v ) =$ $\begin{array} { r } { \operatorname* { m a x } _ { y } \big ( v _ { [ y ] } - \operatorname* { m a x } _ { y ^ { \prime } \neq y } v _ { [ y ^ { \prime } ] } \big ) } \end{array}$ (The difference between the largest and the second largest scores in $v )$ , and $\dot { l } _ { \gamma } ( f _ { t } ( x ) , f _ { s } ( x ) ) : = \psi _ { \gamma } ( - \mathcal { M } ( f _ { t } ( x ) , \tilde { f } _ { s } ( x ) ) )$ . Further suppose $f _ { [ i ] }$ is $L _ { f }$ -Lipschitz w.r.t. the metric $d ( \cdot , \cdot )$ and $\tau : = 1 - 2 L _ { f } \xi \operatorname* { m i n } \{ \epsilon , q \} > 0$ . Consider the following training objective for CST, denoted by $L _ { \mathrm { C S T } } ( f _ { s } , f _ { t } )$ , where $\mathcal { L } _ { \widehat { P } , \gamma } ( f _ { t } ) : = \mathbb { E } _ { ( x , y ) \sim \widehat { P } } l _ { \gamma } ( f _ { t } ( x ) , y )$ corresponds to the cycle source loss in equation 5, $L _ { \widehat { Q } , \gamma } ( f _ { t } , f _ { s } ) : = \mathbb { E } _ { ( x , y ) \sim \widehat { Q } } l _ { \gamma } ( f _ { t } ( x ) , f _ { s } ( x ) )$ is consistent with the target loss in equation 4, and $\mathcal { M } ( f _ { t } ( x ) )$ is closely related to the uncertainty of predictions in equation 11. + +$$ +\operatorname* { m i n } L _ { \mathrm { C S T } } ( f _ { s } , f _ { t } ) : = L _ { \widehat { P } , \gamma } ( f _ { t } ) + L _ { \widehat { Q } , \gamma } ( f _ { t } , f _ { s } ) + \frac { 1 - \mathbb { E } _ { ( x , y ) \sim \frac { 1 } { 2 } ( \widehat { P } + \widehat { Q } ) } \mathcal { M } ( f _ { t } ( x ) ) } { \tau } . +$$ + +The following theorem shows that the minimizer of the training objective $L _ { \mathrm { C S T } } ( f _ { s } , f _ { t } )$ guarantees low population error of $f _ { s }$ on the target domain $Q$ . + +Theorem 2. $ { \widehat { \mathcal { R } } } ( \mathcal { F } | _ { { \widehat { P } } } )$ denotes the empirical Rademacher complexity of function class $\mathcal { F }$ on dataset $\widehat { P }$ . For any solution of equation $^ { 1 3 }$ and $\gamma > 0$ , with probability larger than $1 - \delta$ , + +$\mathrm { E r r } _ { Q } ( f _ { s } ) \leq L _ { \mathrm { C S T } } ( f _ { s } , f _ { t } ) + 2 q + \frac { 4 K } { \gamma } \left[ \widehat { R } ( \mathcal { F } | _ { \widehat { P } } ) + \widehat { \mathcal { R } } ( \tilde { \mathcal { F } } \times \mathcal { F } | _ { \widehat { Q } } ) \right] + \frac { 2 } { \tau } \left[ \widehat { R } ( \mathcal { F } | _ { \widehat { P } } ) + \widehat { \mathcal { R } } ( \mathcal { F } | _ { \widehat { Q } } ) \right] + \zeta ,$ where $\zeta = O \left( \sqrt { \log ( 1 / \delta ) / n _ { s } } + \sqrt { \log ( 1 / \delta ) / n _ { t } } \right)$ is a low-order term. $\tilde { \mathcal { F } } \times \mathcal { F }$ refers to the function class $\{ x f ( \overleftarrow { x } ) _ { [ \tilde { f } ^ { \prime } ( x ) ] } : f , f ^ { \prime } \in \mathcal { F } \} _ { }$ . + +Main insights. Theorem 2 justifies CST under the expansion assumption. The generalization error of the classifier $f _ { s }$ on the target domain is bounded with the CST loss objective $L _ { \mathrm { C S T } } ( f _ { s } , f _ { t } )$ , the intrinsic property of the data distribution $q$ , and the complexity of the function classes. In our algorithm, $\bar { L _ { \mathrm { C S T } } } ( f _ { s } , f _ { t } )$ is minimized by the neural networks and $q$ is a constant. The complexity of the function class can be controlled with proper regularization. + +# 4.2 Hard Case for Feature Adaptation and Standard Self-Training + +To gain more insight, we study UDA in a quadratic neural network $f _ { \theta , \phi } ( x ) = \theta ^ { \top } ( \phi ^ { \top } x ) ^ { \odot 2 }$ , where $\odot$ is element-wise power. In UDA, the source can have multiple solutions but we aim to learn the one working on the target [34]. We design the underlying distributions $p$ and $q$ in Table 6 to reflect this. Consider the following $P$ and $Q$ . $x _ { [ 1 ] }$ and $x _ { [ 2 ] }$ are sampled i.i.d. from distribution $p$ on $P$ , and from $q$ on $Q$ . For $i \in [ 3 , d ]$ , $x _ { [ i ] } = \sigma _ { i } x _ { [ 2 ] }$ on $P$ and $x _ { [ i ] } = \sigma _ { i } x _ { [ 1 ] }$ on $Q$ . $\sigma _ { i } \in \{ \pm 1 \}$ are i.i.d. and uniform. We also assume realizability: for all $y = x _ { [ 1 ] } ^ { 2 } - x _ { [ 2 ] } ^ { 2 }$ $i \in [ 2 , d ]$ for both source and target. Note that are solutions to $P$ but only $y = x _ { [ 1 ] } ^ { 2 } - x _ { [ 2 ] } ^ { 2 }$ $y = x _ { [ 1 ] } ^ { 2 } - x _ { [ i ] } ^ { 2 }$ [1] [i]works on $Q$ . We visualize this specialized setting in Figure 4. + +Table 1: The design of $p$ and $q$ . + +
Distribution-1+10
Source p[0.050.050.90
Target q0.250.250.50
+ +![](images/c5b098da78c5868e7858cc364d018d8dfcb55a8acb4b0000cd134653d0e02a42.jpg) +Figure 4: The hard case where $d = 3$ . Green dots for $y = 1$ , red dots for $y = 0$ , and blue dots for $y = - 1$ . The grey curve is the classification boundary of different features. The good feature $x _ { [ 1 ] } ^ { 2 } - x _ { [ 2 ] } ^ { 2 }$ works on the target domain (shown in (a) and (c)), whereas the spurious feature $x _ { [ 1 ] } ^ { 2 } - x _ { [ 3 ] } ^ { 2 }$ only works on the source domain (shown in (b) andwhile CST learns tion 4.2, we show that feature adaptation and standard self-training learn . $x _ { [ 1 ] } ^ { 2 } - x _ { [ 3 ] } ^ { 2 }$ , $x _ { [ 1 ] } ^ { 2 } - x _ { [ 2 ] } ^ { 2 }$ + +To make the features more tractable, we study the norm-constrained version of the algorithms (details are deferred to Section A.3.2). We compare the features learned by feature adaptation, standard selftraining, and CST. Intuitively, feature adaptation fails because the ideal target solution $y = x _ { [ 1 ] } ^ { 2 } - x _ { [ 2 ] } ^ { 2 }$ has larger distance in the feature space than other spurious solutions y = x2[1] $y = x _ { [ 1 ] } ^ { 2 } - x _ { [ i ] } ^ { 2 }$ x2[i] . Standard selftraining also fails since it will choose randomly among all solutions. In comparison, CST can recover the ground truth, because it can distinguish the spurious solution resulting in bad pseudo-labels. A classifier trained with those pseudo-labels cannot work on the source domain in turn. This intuition is rigorously justified in the following two theorems. + +Theorem 3. For $\epsilon \in ( 0 , 0 . 5 )$ , the following statements hold for feature adaptation and self-training: + +• For failure rate $\xi > 0$ , and target dataset size $n _ { t } > \Theta ( \log { \frac { 1 } { \xi } } )$ , with probability at least $1 - \xi$ over the sampling of target data, the solution $( \hat { \theta } _ { \mathrm { F A } } , \hat { \phi } _ { \mathrm { F A } } )$ found by feature adaptation satisfies + +$$ +\mathrm { E r r } _ { Q } ( \hat { \theta } _ { \mathrm { F A } } , \hat { \phi } _ { \mathrm { F A } } ) \geq \epsilon . +$$ + +• With probability at least $1 - { \frac { 1 } { d - 1 } }$ , the solution $( \hat { \theta } _ { \mathrm { S T } } , \hat { \phi } _ { \mathrm { S T } } )$ of standard self-training satisfies + +$$ +\mathrm { E r r } _ { Q } ( \hat { \theta } _ { \mathrm { S T } } , \hat { \phi } _ { \mathrm { S T } } ) \geq \epsilon . +$$ + +Theorem 4. For failure rate $\xi > 0$ , and target dataset size $\begin{array} { r } { n _ { t } > \Theta ( \log { \frac { 1 } { \xi } } ) } \end{array}$ , with probability at least $1 - \xi ,$ , the solution of $C S T ( \hat { \phi } _ { \mathrm { C S T } } , \hat { \theta } _ { \mathrm { C S T } } )$ recovers the ground truth of the target dataset: + +$$ +\mathrm { E r r } _ { Q } ( \hat { \theta } _ { \mathrm { C S T } } , \hat { \phi } _ { \mathrm { C S T } } ) = 0 . +$$ + +# 5 Experiments + +We test the performance of the proposed method on both vision and language datasets. Cycle SelfTraining (CST) consistently outperforms state-of-the-art feature adaptation and self-training methods. Code is available at https://github.com/Liuhong99/CST. + +# 5.1 Setup + +Datasets. We experiment on visual object recognition and linguistic sentiment classification tasks: Office-Home [64] has 65 classes from four kinds of environment with large domain gap: Artistic (Ar), Clip Art (Cl), Product $( \mathbf { P r } )$ , and Real-World (Rw); VisDA-2017 [45] is a large-scale UDA dataset with two domains named Synthetic and Real. The datasets consist of over $2 0 0 \mathrm { k }$ images from 12 categories of objects; Amazon Review [10] is a linguistic sentiment classification dataset of product reviews in four products: Books $\mathbf { ( B ) }$ , DVDs (D), Electronics (E), and Kitchen $\mathbf { \eta } ( \mathbf { K } )$ . + +Implementation. We use ResNet-50 [26] (pretrained on ImageNet [53]) as feature extractors for vision tasks, and BERT [16] for linguistic tasks. On VisDA-2017, we also provide results of ResNet101 to include more baselines. We use cross-entropy loss for classification on the source domain. When training the target head $\widehat { \theta } _ { t }$ and updating the feature extractor with CST, we use squared loss to get the analytical solution of $\widehat { \theta } _ { t }$ directly and avoid calculating second order derivatives as metalearning [18]. Details on adapting squared loss to multi-class classification are deferred to Appendix B. We adopt SGD with initial learning rate $\eta _ { 0 } = 2 e - 3$ for image classification and $\eta _ { 0 } = 5 e - 4$ for sentiment classification. Following standard protocol in [26], we decay the learning rate by 0.1 each 50 epochs until 150 epochs. We run all the tasks 3 times and report mean and deviation in top-1 accuracy. For VisDA-2017, we report the mean class accuracy. Following Theorem 2, we also enhance CST with sharpness-aware regularization [19] $( \mathbf { C S T + S A M } )$ , which help regularize the Lipschitzness of the function class. Due to space limit, we report mean accuracies in Tables 2 and 3 and defer standard deviation to Appendix C. + +# 5.2 Baselines + +We compare with two lines of works in domain adaptation: feature adaptation and self-training. We also compare with more complex state-of-the-arts and create stronger baselines by combining feature adaptation and self-training. + +Feature Adaptation: DANN [22], MCD [54], CDAN [37] (which improves DANN with pseudolabel conditioning), MDD [73] (which improves previous domain adaptation with margin theory), Implicit Alignment (IA) [28] (which improves MDD to deal with label shift). + +Self-Training. We include VAT [40], MixMatch [8] and FixMatch [57] in the semi-supervised learning literature as self-training methods. We also compare with self-training methods for UDA: CBST [77], which considers class imbalance in standard self-training, and KLD [78], which improves CBST with label regularization. However, these methods involve tricks specified for convolutional networks. Thus, in sentiment classification tasks where we use BERT backbones, we compare with other consistency regularization baselines: VAT [40], VAT $^ { \cdot } +$ Entropy Minimization. + +Feature Adaptation $^ +$ Self-Training. DIRT-T [56] combines DANN, VAT, and entropy minimization. We also create more powerful baselines: CDAN $^ +$ VAT $^ +$ Entropy and MDD $+$ Fixmatch. + +Other SOTA. AFN [69] boosts transferability by large norm. STAR [38] aligns domains with stochastic classifiers. SENTRY [48] selects confident examples with a committee of random augmentations. + +# 5.3 Results + +Results on 12 pairs of Office-Home tasks are shown in Table 2. When domain shift is large, standard self-training methods such as VAT and FixMatch suffer from the decay in pseudo-label quality. CST outperforms feature adaptation and self-training methods significantly in 9 out of 12 tasks. Note that CST does not involve manually setting confidence threshold or reweighting. + +Table 2: Accuracy $( \% )$ on Office-Home for unsupervised domain adaptation (ResNet-50). + +
Method|Ar-Cl Ar-Pr Ar-Rw Cl-Ar Cl-Pr Cl-Rw Pr-Ar Pr-CIPr-Rw Rw-Ar Rw-Cl Rw-Pr|Avg.
DANN [22]45.659.370.147.058.560.946.143.768.563.251.876.857.6
CDAN [37]50.770.676.057.670.070.057.450.977.370.956.781.665.8
CDAN+VAT+Entropy52.271.576.461.170.367.859.554.478.673.259.082.767.3
FixMatch [57]51.874.280.163.573.861.364.751.480.073.356.881.767.7
MDD [73]54.973.777.860.071.471.861.253.678.172.560.282.368.1
MDD+IA [28]56.277.979.264.473.174.464.254.279.971.258.183.169.5
SENTRY [48]61.877.480.166.371.674.766.863.080.974.066.384.172.2
CST59.079.683.468.477.176.768.956.483.075.362.285.1|73.0
+ +Table 3: Accuracy $( \% )$ on Multi-Domain Sentiment Dataset for domain adaptation with BERT. + +
MethodB-DB-EB-KD-BD-ED-KE-BE-DE-KK-BK-DK-EAvg.
Source-only89.788.490.990.188.590.286.988.591.587.687.391.289.2
DANN [22]90.289.590.991.090.690.287.187.592.887.887.693.289.9
VAT[40]90.691.091.790.890.892.087.286.992.686.987.792.990.1
VAT+Entropy90.491.391.591.091.192.487.586.392.486.587.593.190.1
MDD [73]90.490.491.890.290.991.087.586.392.589.087.992.190.0
CST91.592.992.691.992.693.590.289.493.887.988.393.591.5
+ +Table 4 shows the results on VisDA-2017. CST surpasses state-of-the-arts with ResNet-50 and ResNet101 backbones. We also combine feature adaptation and self-training (DIRT-T, CDAN+VAT+entropy and MDD $^ { + }$ FixMatch) to test if feature adaptation alleviates the negative effect of domain shift in standard self-training. Results indicate that CST is a better solution than simple combination. + +While most traditional self-training methods include techniques specified for ConvNets such as Mixup [72], CST is a universal method and can directly work on sentiment classification by simply replacing the head and training objective of BERT [16]. In Table 3, most feature adaptation baselines improve over source only marginally, but CST outperforms all baselines on most tasks significantly. + +# 5.4 Analysis + +Ablation Study. We study the role of each part of CST in self-training. CST w/o Tsallis removes the Tsallis entropy $L _ { \mathrm { T s a l l i s } , \alpha }$ . CST $+$ Entropy replaces the Tsallis entropy with standard entropy. FixMatch+Tsallis adds $L _ { \mathrm { T s a l l i s } , \alpha }$ to standard self-training. Observations are shown in Table 5. $\mathrm { C S T + l }$ Entropy performs $3 . 7 \%$ worse than CST, indicating that Tsallis entropy is a better regularization for pseudolabels than standard entropy. CST performs $5 . 4 \%$ better than FixMatch, indicating that CST is better adapted to domain shift than standard self-training. While FixMatch+Tsallis outperforms FixMatch, it is still $3 . 6 \%$ behind CST, with much larger total variation distance $d _ { \mathrm { T V } }$ between pseudo-labels and ground-truths, indicating that CST makes pseudo-labels more reliable than standard self-training under domain shift. + +Table 5: Ablation on VisDA-2017. + +
MethodAccuracy ↑|drv↓
FixMatch [57]74.5 ± 0.20.22
Fixmatch+Tsallis76.3 ± 0.80.15
CST w/o Tsallis72.0 ± 0.40.16
CST+Entropy76.2 ± 0.60.20
CST79.9 ± 0.50.12
+ +Quality of Pseudo-labels. We visualize the error of pseudo-labels during training on VisDA-2017 in Figure 5 (Left). The error of target classifier $\theta _ { t }$ on the source domain decreases quickly in training, when both the error of pseudo-labels (error of $\theta _ { s }$ on $Q$ ) and the total variation (TV) distance between pseudo-labels and ground-truths continue to decay, indicating that CST gradually refines pseudolabels. This forms a clear contrast to standard self-training as visualized in Figure 2 (Middle), where the distance $d _ { \mathrm { T V } }$ remains nearly unchanged throughout training. + +Comparison of Gibbs entropy and Tsallis entropy. We compare the pseudo-labels learned with standard Gibbs entropy and Tsallis entropy on $\mathbf { A r { } C l }$ with ResNet-50 at epoch 40. We compute the difference between the largest and the second largest softmax scores of each target example and plot the histogram in Figure 5 (Right). Gibbs entropy makes the largest softmax output close to 1, indicating over-confidence. In this case, if the prediction is wrong, it can be hard to correct it using self-training. In contrast, Tsallis entropy allows the largest and the second largest scores to be similar. + +Table 4: Mean Class Accuracy $( \% )$ for unsupervised domain adaptation on VisDA-2017. + +
MethodResNet-50ResNet-101MethodResNet-50ResNet-101
DANN [22]69.379.5CBST[77]176.4 ± 0.9
VAT [40]68.0±0.373.4 ± 0.5KLD [78]178.1 ± 0.2
DIRT-T [56]68.2 ± 0.377.2 ± 0.5MDD[73]74.681.6 ± 0.3
MCD [54]69.277.7AFN [69]176.1
CDAN [37]70.080.1MDD+IA [28]75.81
CDAN+VAT+Entropy76.5 ± 0.580.4± 0.7MDD+FixMatch77.8 ± 0.382.4 ± 0.4
MixMatch69.3 ± 0.477.0 ± 0.5STAR [38]182.7
FixMatch [57]74.5 ± 0.279.5 ± 0.3SENTRY [48]76.71
CST79.9 ± 0.584.8± 0.6CST+SAM80.6 ± 0.586.5 ± 0.7
+ +![](images/b438078399476e8bc688a6c6252f161f15cda1ea9f72241d501cd24f973a4fac.jpg) +Figure 5: Analysis. Left: Error of pseudo-labels and reverse pseudo-labels. The error of target classifier $\theta _ { t }$ on the source domain decreases, indicating the quality of pseudo-labels is refined. Right: Histograms of the difference between the largest and the second largest softmax scores. Tsallis entropy avoids over-confidence. + +# 6 Related Work + +Self-Training. Self-training is a mainstream technique for semi-supervised learning [13]. In this work, we focus on pseudo-labeling [52, 31, 2], which uses unlabeled data by training on pseudo-labels generated by a source model. Other lines of work study consistency regularization [4, 51, 55, 40]. Recent works demonstrate the power of such methods [67, 57, 23]. Equipped with proper training techniques, these methods can achieve comparable results as standard training that uses much more labeled examples [17]. Zoph et al. [76] compare self-training to pre-training and joint training. Vu et al. [65], Mukherjee & Awadallah [42] show that task-level self-training works well in few-shot learning. These methods are tailored to semi-supervised learning or general representation learning and do not take domain shift into consideration explicitly. Wei et al. [66], Frei et al. [20] provide the first nice theoretical analysis of self-training based on the expansion assumption. + +Domain Adaptation. Inspired by the generalization error bound of Ben-David et al. [7], Long et al. [34], Zellinger et al. [71] minimize distance measures between source and target distributions to learn domain-invariant features. Ganin et al. [22] (DANN) proposed to approximate the domain distance by adversarial learning. Follow-up works proposed various improvement upon DANN [63, 54, 37, 73, 28]. Popular as they are, failure cases exist in situation like label shift [74, 32], shift in support of domains [29], and large discrepancy between source and target [33]. Another line of works try to address domain adaptation with self-training. Shu et al. [56] improves DANN with VAT and entropy minimization. French et al. [21], Zou et al. [78], Li et al. [32] incorporated various semi-supervised learning techniques to boost domain adaptation performance. Kumar et al. [30], Chen et al. [15] and Cai et al. [11] showed self-training provably works in domain adaptation under certain assumptions. + +# 7 Conclusion + +We propose cycle self-training in place of standard self-training to explicitly address the distribution shift in domain adaptation. We show that our method provably works under the expansion assumption and demonstrate hard cases for feature adaptation and standard self-training. Self-training (or pseudolabeling) is only one line of works in the semi-supervised learning literature. Future work can delve into the behaviors of other semi-supervised learning techniques including consistency regularization and data augmentation under distribution shift, and exploit them extensively for domain adaptation. + +# Acknowledgements + +This work was supported by the National Natural Science Foundation of China under Grants 62022050 and 62021002, Beijing Nova Program under Grant Z201100006820041, China’s Ministry of Industry and Information Technology, the MOE Innovation Plan and the BNRist Innovation Fund. + +# References + +[1] Albadawy, E. A., Saha, A., and Mazurowski, M. A. Deep learning for segmentation of brain tumors: Impact of cross-institutional training and testing. Medical Physics, 45(3), 2018. +[2] Arazo, E., Ortego, D., Albert, P., O’Connor, N. E., and McGuinness, K. Pseudo-labeling and confirmation bias in deep semi-supervised learning. 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In ICCV, October 2019. \ No newline at end of file diff --git a/parse/train/-iu9-C_lan/-iu9-C_lan_content_list.json b/parse/train/-iu9-C_lan/-iu9-C_lan_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..682b4bcc338d8877faa5aaabfc8465cda1e43bc8 --- /dev/null +++ b/parse/train/-iu9-C_lan/-iu9-C_lan_content_list.json @@ -0,0 +1,1484 @@ +[ + { + "type": "text", + "text": "Cycle Self-Training for Domain Adaptation ", + "text_level": 1, + "bbox": [ + 235, + 122, + 763, + 147 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Hong Liu Dept of Electronic Engineering Tsinghua University hongliu9903@gmail.com ", + "bbox": [ + 186, + 202, + 392, + 257 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jianmin Wang \nSchool of Software, BNRist \nTsinghua University \njimwang@tsinghua.edu.cn Mingsheng Long⇤ \nSchool of Software, BNRist Tsinghua University \nmingsheng@tsinghua.edu.cn ", + "bbox": [ + 411, + 202, + 598, + 257 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "", + "bbox": [ + 617, + 202, + 810, + 257 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract ", + "text_level": 1, + "bbox": [ + 462, + 292, + 535, + 309 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Mainstream approaches for unsupervised domain adaptation (UDA) learn domaininvariant representations to narrow the domain shift, which are empirically effective but theoretically challenged by the hardness or impossibility theorems. Recently, self-training has been gaining momentum in UDA, which exploits unlabeled target data by training with target pseudo-labels. However, as corroborated in this work, under distributional shift, the pseudo-labels can be unreliable in terms of their large discrepancy from target ground truth. In this paper, we propose Cycle Self-Training (CST), a principled self-training algorithm that explicitly enforces pseudo-labels to generalize across domains. CST cycles between a forward step and a reverse step until convergence. In the forward step, CST generates target pseudo-labels with a source-trained classifier. In the reverse step, CST trains a target classifier using target pseudo-labels, and then updates the shared representations to make the target classifier perform well on the source data. We introduce the Tsallis entropy as a confidence-friendly regularization to improve the quality of target pseudo-labels. We analyze CST theoretically under realistic assumptions, and provide hard cases where CST recovers target ground truth, while both invariant feature learning and vanilla self-training fail. Empirical results indicate that CST significantly improves over the state-of-the-arts on visual recognition and sentiment analysis benchmarks. ", + "bbox": [ + 232, + 324, + 766, + 571 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 Introduction ", + "text_level": 1, + "bbox": [ + 174, + 590, + 310, + 607 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Transferring knowledge from a source domain with rich supervision to an unlabeled target domain is an important yet challenging problem. Since deep neural networks are known to be sensitive to subtle change in underlying distributions [70], models trained on one labeled dataset often fail to generalize to another unlabeled dataset [58, 1]. Unsupervised domain adaptation (UDA) addresses the challenge of distributional shift by adapting the source model to the unlabeled target data [50, 43]. ", + "bbox": [ + 174, + 616, + 825, + 685 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The mainstream paradigm for UDA is feature adaptation, a.k.a. domain alignment. By reducing the distance of the source and target feature distributions, these methods learn invariant representations to facilitate knowledge transfer between domains [34, 22, 36, 54, 37, 73], with successful applications in various areas such as computer vision [63, 27, 77] and natural language processing [75, 49]. Despite their popularity, the impossibility theories [6] uncovered intrinsic limitations of learning invariant representations when it comes to label shift [74, 32] and shift in the support of domains [29]. ", + "bbox": [ + 174, + 691, + 825, + 775 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, self-training (a.k.a. pseudo-labeling) [21, 78, 30, 32, 47, 68] has been gaining momentum as a promising alternative to feature adaptation. Originally tailored to semi-supervised learning, self-training generates pseudo-labels of unlabeled data, and jointly trains the model with source labels and target pseudo-labels [31, 39, 30]. However, the distributional shift in UDA makes pseudo-labeling more difficult. Directly using all pseudo-labels is risky due to accumulated error and even trivial solution [14]. Thus previous works tailor self-training to UDA by selecting trustworthy pseudo-labels. Using confidence threshold or reweighting, recent works try to alleviate the negative effect of domain shift in standard self-training [78, 47], but they can be brittle and require expensive tweaking of the threshold or weight for different tasks, and their performance gain is still inconsistent. ", + "bbox": [ + 174, + 780, + 825, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a98d2d44c2b974a909fc041a6f8726476f59f9bdcb19e5febe93a6d25e86dd55.jpg", + "image_caption": [ + "Figure 1: Standard self-training vs. cycle self-training. In standard self-training, we generate target pseudolabels with a source model, and then train the model with both source ground-truths and target pseudo-labels. In cycle self-training, we train a target classifier with target pseudo-labels in the inner loop, and make the target classifier perform well on the source domain by updating the shared representations in the outer loop. " + ], + "image_footnote": [], + "bbox": [ + 209, + 87, + 789, + 208 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 281, + 821, + 310 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we first analyze the quality of pseudo-labels with or without domain shift to delve deeper into the difficulty of standard self-training in UDA. On popular benchmark datasets, when the source and target are the same, our analysis indicates that the pseudo-label distribution is almost identical to the ground-truth distribution. However, with distributional shift, their discrepancy can be very large with examples of several classes mostly misclassified into other classes. We also study the difficulty of selecting correct pseudo-labels with popular criteria under domain shift. Although entropy and confidence are reasonable selection criteria for correct pseudo-labels without domain shift, the domain shift makes their accuracy decrease sharply. ", + "bbox": [ + 173, + 315, + 825, + 428 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our analysis shows that domain shift makes pseudo-labels unreliable and that self-training on selected target instances with accurate pseudo-labels is less successful. Thereby, more principled improvement of standard self-training should be tailored to UDA and address the domain shift explicitly. In this work, we propose Cycle Self-Training (CST), a principled self-training approach to UDA, which overcomes the limitations of standard self-training (see Figure 1). Different from previous works to select target pseudo-labels with hard-to-tweak protocols, CST learns to generalize the pseudo-labels across domains. Specifically, CST cycles between the use of target pseudo-labels to train a target classifier, and the update of shared representations to make the target classifier perform well on the source data. In contrast to the standard Gibbs entropy that makes the target predictions over-confident, we propose a confidence-friendly uncertainty measure based on the Tsallis entropy in information theory, which adaptively minimizes the uncertainty without manually tuning or setting thresholds. Our method is simple and generally applicable to vision and language tasks with various backbones. ", + "bbox": [ + 174, + 433, + 825, + 599 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We empirically evaluate our method on a series of standard UDA benchmarks. Results indicate that CST outperforms previous state-of-the-art methods in 21 out of 25 tasks for object recognition and sentiment classification. Theoretically, we prove that the minimizer of CST objective is endowed with general guarantees of target performance. We also study hard cases on specific distributions, showing that CST recovers target ground-truths while both feature adaptation and standard self-training fail. ", + "bbox": [ + 174, + 606, + 825, + 676 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2 Preliminaries ", + "text_level": 1, + "bbox": [ + 174, + 693, + 318, + 710 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We study unsupervised domain adaptation (UDA). Consider a source distribution $P$ and a target distribution $Q$ over the input-label space $\\mathcal { X } \\times \\mathcal { V }$ . We have access to $n _ { s }$ labeled i.i.d. samples $\\widehat { P } = \\{ x _ { i } ^ { s } , y _ { i } ^ { s } \\} _ { i = 1 } ^ { n _ { s } }$ from $P$ and $n _ { t }$ unlabeled i.i.d. samples $\\widehat { Q } = \\{ x _ { i } ^ { t } \\} _ { i = 1 } ^ { n _ { t } }$ from $Q$ . The model $f$ comprises a feature extractor $h _ { \\phi }$ parametrized by $\\phi$ and a head (linear classifier) $g _ { \\theta }$ parametrized by $\\theta$ , i.e. $\\bar { f } _ { \\theta , \\phi } ( x ) = g _ { \\theta } ( h _ { \\phi } ( x ) )$ . The loss function is $\\ell ( \\cdot , \\cdot )$ . Denote by $L _ { P } ( \\theta , \\phi ) : = \\mathbb { E } _ { ( x , y ) \\sim P } \\ell ( f _ { \\theta , \\phi } ( x ) , y )$ the expected error on $P$ . Similarly, we use ${ \\cal L } _ { \\widehat { P } } ( \\theta , \\phi )$ to denote the empirical error on dataset $\\widehat { P }$ . ", + "bbox": [ + 173, + 722, + 826, + 814 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We discuss two mainstream UDA methods and their formulations: feature adaptation and self-training. ", + "bbox": [ + 173, + 818, + 825, + 833 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Feature Adaptation trains the model $f$ on the source dataset $\\widehat { P }$ , and simultaneously matches the source and target distributions in the representation space $\\mathcal { Z } = h ( \\mathcal { X } )$ : ", + "bbox": [ + 171, + 839, + 823, + 871 + ], + "page_idx": 1 + }, + { + "type": "equation", + "img_path": "images/08c3281134353cdfc0b467df0091b2073698e29eaba7544d4dbb027d50f15236.jpg", + "text": "$$\n\\operatorname* { m i n } _ { \\theta , \\phi } L _ { \\widehat { P } } ( \\theta , \\phi ) + d ( h _ { \\sharp } \\widehat { P } , h _ { \\sharp } \\widehat { Q } ) .\n$$", + "text_format": "latex", + "bbox": [ + 398, + 881, + 599, + 909 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/b47a38073ca7224e33f9ab2c301d27144b2711ff9fb5bf238f28f0fb56f3274f.jpg", + "image_caption": [ + "Figure 2: Analysis of pseudo-labels under domain shift on VisDA-2017. Left: Pseudo-label distributions with and without domain shift. Middle: Changes of pseudo-label distributions throughout training. Right: Quality of pseudo-labels under different pseudo-label selection criteria. " + ], + "image_footnote": [], + "bbox": [ + 202, + 97, + 790, + 214 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here, $h _ { \\sharp } \\widehat { P }$ denotes the pushforward distribution of $\\widehat { P }$ , and $d ( \\cdot , \\cdot )$ is some distribution distance. For instance, Long et al. [34] used maximum mean discrepancy $d _ { \\mathrm { M M D } }$ , and Ganin et al. [22] approximated the $\\mathcal { H } \\Delta \\mathcal { H }$ -distance $d _ { \\mathcal { H } \\Delta \\mathcal { H } }$ [7] with adversarial training. Despite its pervasiveness, recent works have shown the intrinsic limitations of feature adaptation under real-world situations [6, 74, 33, 32, 29]. ", + "bbox": [ + 174, + 270, + 825, + 329 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Self-Training is considered a promising alternative to feature adaptation. In this work we mainly focus on pseudo-labeling [31, 30]. Stemming from semi-supervised learning, standard self-training trains a source model $f _ { s }$ on the source dataset $\\widehat { P }$ $: \\mathrm { m i n } _ { \\theta _ { s } , \\phi _ { s } } L _ { \\widehat { P } } ( \\theta _ { s } , \\phi _ { s } )$ . The target pseudo-labels are then generated by $f _ { s }$ on the target dataset $\\widehat { Q }$ . To leverage unlabeled target data, self-training trains the model on the source and target datasets together with source ground-truths and target pseudo-labels: ", + "bbox": [ + 173, + 335, + 825, + 412 + ], + "page_idx": 2 + }, + { + "type": "equation", + "img_path": "images/7eb4ed6be74b99db248b902505b5c093a12694a3b85b7d17df4c597e37de3e0f.jpg", + "text": "$$\n\\operatorname* { m i n } _ { \\theta , \\phi } L _ { \\widehat { P } } ( \\theta , \\phi ) + \\mathbb { E } _ { x \\sim \\widehat { Q } } \\ell ( f _ { \\theta , \\phi } ( x ) , \\arg \\operatorname* { m a x } _ { i } \\{ f _ { \\theta , \\phi _ { s } } ( x ) _ { [ i ] } \\} ) .\n$$", + "text_format": "latex", + "bbox": [ + 308, + 417, + 689, + 441 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Self-training also uses label-sharpening as a standard protocol [31, 57]. Another popular variant of pseudo-labeling is the teacher-student model [4, 61], which iteratively improves the quality of pseudo-labels via alternatively replacing $\\theta _ { s }$ and $\\phi _ { s }$ with $\\theta$ and $\\phi$ of the previous iteration. ", + "bbox": [ + 174, + 446, + 825, + 489 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.1 Limitations of Standard Self-Training ", + "text_level": 1, + "bbox": [ + 174, + 498, + 477, + 513 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Standard self-training with pseudo-labels uses unlabeled data efficiently for semi-supervised learning [31, 39, 57]. Here we carry out exploratory studies on the popular VisDA-2017 [45] dataset using ResNet-50 backbones. We find that domain shift makes the pseudo-labels biased towards several classes and thereby unreliable in UDA. See Appendix C.1 for details and results on more datasets. ", + "bbox": [ + 173, + 517, + 825, + 574 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Pseudo-label distributions with or without domain shift. We resample the original VisDA-2017 to simulate different relationship between source and target domains: 1) i.i.d., 2) covariate shift, and 3) label shift. We train the model on the three variants of source dataset and use it to generate target pseudo-labels. We show the distributions of target ground-truths and pseudo-labels in Figure 2 (Left). When the source and target distributions are identical, the distribution of pseudo-labels is almost the same as ground-truths, indicating the reliability of pseudo-labels. In contrast, when exposed to label shift or covariate shift, the distribution of pseudo-labels is significantly different from target ground-truths. Note that classes 2, 7, 8 and 12 appear rarely in the target pseudo-labels in the covariate shift setting, indicating that the pseudo-labels are biased towards several classes due to domain shift. Self-training with these pseudo-labels is risky since it may lead to misalignment of distributions and misclassify many examples of classes 2, 7, 8 and 12. ", + "bbox": [ + 173, + 579, + 825, + 732 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Change of pseudo-label distributions throughout training. To further study the change of pseudolabels in standard self-training, we compute the total variation (TV) distance between target groundtruths and target pseudo-labels: $\\begin{array} { r } { d _ { \\mathrm { T V } } ( c , \\dot { c ^ { \\prime } } ) = \\frac { 1 } { 2 } \\sum _ { i } \\| c _ { i } - c _ { i } ^ { \\prime } \\| } \\end{array}$ , where $c _ { i }$ is the ratio of class $i$ . We plot its change during training in Figure 2 (Middle). Although the error rate of pseudo-labels continues to decrease, $d _ { \\mathrm { T V } }$ remains almost unchanged at 0.26 throughout training. Note that $d _ { \\mathrm { T V } }$ is the lower bound of the error rate of the pseudo-labels (shown in Appendix C.1). If $d _ { \\mathrm { T V } }$ converges to 0.26, then the accuracy of pseudo-labels is upper-bounded by 0.74. This indicates that the important denoising ability [66] of pseudo-labels in standard self-training is hindered by domain shift. ", + "bbox": [ + 173, + 738, + 825, + 849 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Difficulty of selecting reliable pseudo-labels under domain shift. To mitigate the negative effect of false pseudo-labels, recent works proposed to select correct pseudo-labels based on thresholding the entropy or confidence criteria [35, 21, 37, 57]. However, it remains unclear whether these strategies are still effective under domain shift. Here we compare the quality of pseudo-labels selected by different strategies with or without domain shift. For each strategy, we compute False Positive Rate and True Positive Rate for different thresholds and plot its ROC curve in Figure 2 (Right). When the source and target distributions are identical, both entropy and confidence are reasonable strategies for selecting correct pseudo-labels $( \\mathrm { A U C } { = } 0 . 8 9 )$ ). However, when the target pseudo-labels are generated by the source model, the quality of pseudo-labels decreases sharply under domain shift $\\mathrm { \\Delta A U C { = } 0 . 7 8 }$ ). ", + "bbox": [ + 174, + 856, + 825, + 911 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 90, + 825, + 161 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3 Approach ", + "text_level": 1, + "bbox": [ + 174, + 174, + 289, + 191 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We present Cycle Self-Training (CST) to improve pseudo-labels under domain shift. An overview of our method is given in Figure 1. Cycle Self-Training iterates between a forward step and a reverse step to make self-trained classifiers generalize well on both target and source domains. ", + "bbox": [ + 174, + 198, + 825, + 241 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1 Cycle Self-Training ", + "text_level": 1, + "bbox": [ + 174, + 246, + 349, + 261 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Forward Step. Similar to standard self-training, we have a source classifier $\\theta _ { s }$ trained on top of the shared representations $\\phi$ on the labeled source domain, and use it to generate target pseudo-labels as ", + "bbox": [ + 173, + 265, + 823, + 294 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/f320bf246563b81f6d2648d2fdd1228bfad0d9c84e43d970ceea81de6211fd67.jpg", + "text": "$$\ny ^ { \\prime } = \\arg \\operatorname* { m a x } _ { i } \\{ f _ { \\theta _ { s } , \\phi } ( x ) _ { [ i ] } \\} ,\n$$", + "text_format": "latex", + "bbox": [ + 406, + 299, + 589, + 324 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "for each $x$ in the target dataset $\\widehat { Q }$ . Traditional self-training methods use confidence thresholding or reweighting to select reliable pseudo-labels. For example, Sohn et al. [57] select pseudo-labels with softmax value and Long et al. [37] add entropy reweighting to rely on examples with more confidence prediction. However, the output of deep networks is usually miscalibrated [25], and is not necessarily related to the ground-truth confidence even on the same distribution. In domain adaptation, as shown in Section 2.1, the discrepancy between the source and target domains makes pseudo-labels even more unreliable, and the performance of commonly used selection strategies is also unsatisfactory. Another drawback is the expensive tweaking in order to find the optimal confidence threshold for new tasks. To better apply self-training to domain adaptation, we expect that the model can gradually refine the pseudo-labels by itself without the cumbersome selection or thresholding. ", + "bbox": [ + 173, + 330, + 825, + 473 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Reverse Step. We design a complementary step with the following insights to improve self-training. Intuitively, the labels on the source domain contain both useful information that can transfer to the target domain and harmful information that can make pseudo-labels incorrect. Similarly, reliable pseudo-labels on the target domain can transfer to the source domain in turn, while models trained with incorrect pseudo-labels on the target domain cannot transfer to the source domain. In this sense, if we explicitly train the model to make target pseudo-labels informative of the source domain, we can gradually make the pseudo-labels more accurate and learn to generalize to the target domain. ", + "bbox": [ + 173, + 478, + 825, + 575 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, with the pseudo-labels $y ^ { \\prime }$ generated by the source classifier $\\theta _ { s }$ at hand as in equation 3, we train a target head $\\hat { \\theta } _ { t } ( \\phi )$ on top of the representation $\\phi$ with pseudo-labels on the target domain $\\widehat { Q }$ ", + "bbox": [ + 173, + 580, + 821, + 613 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/03699fae3f7b59b86374fb91a0f3d780b856c7a8778a428e47452fb369f5cccb.jpg", + "text": "$$\n\\hat { \\theta } _ { t } ( \\phi ) = \\underset { \\theta } { \\arg \\operatorname* { m i n } } \\mathbb { E } _ { \\boldsymbol { x } \\sim \\hat { \\boldsymbol { Q } } } \\ell ( f _ { \\theta , \\phi } ( \\boldsymbol { x } ) , y ^ { \\prime } ) .\n$$", + "text_format": "latex", + "bbox": [ + 374, + 619, + 624, + 646 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We wish to make the target pseudo-labels informative of the source domain and gradually refine them. To this end, we update the shared feature extractor $\\phi$ to predict accurately on the source domain and jointly enforce the target classifier $\\hat { \\theta } _ { t } ( \\phi )$ to perform well on the source domain. This naturally leads to the objective of Cycle Self-Training: ", + "bbox": [ + 173, + 651, + 825, + 710 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/ed81524779eb8a44184f8a5fa701e5693bc66a771d5cf2175c8b352bbc8f7bc8.jpg", + "text": "$$\n\\operatorname* { m i n i m i z e } _ { \\theta _ { s } , \\phi } L _ { \\mathrm { C y c l e } } ( \\theta _ { s } , \\phi ) : = L _ { \\hat { P } } ( \\theta _ { s } , \\phi ) + L _ { \\hat { P } } ( \\hat { \\theta } _ { t } ( \\phi ) , \\phi ) .\n$$", + "text_format": "latex", + "bbox": [ + 320, + 715, + 676, + 742 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Bi-level Optimization. The objective in equation 5 relies on the solution $\\hat { \\theta } _ { t } ( \\phi )$ to the objective in equation 4. Thus, CST formulates a bi-level optimization problem. In the inner loop we generate target pseudo-labels with the source classifier (equation 3), and train a target classifier with target pseudo-labels (equation 4). After each inner loop, we update the feature extractor $\\phi$ for one step in the outer loop (equation 5), and start a new inner loop again. However, since the inner loop of the optimization in equation 4 only involves the light-weight linear head $\\theta _ { t }$ , we propose to calculate the analytical form of $\\hat { \\theta } _ { t } ( \\phi )$ and directly back-propagate to the feature extractor $\\phi$ instead of calculating the second-order derivatives as in MAML [18]. The resulting framework is as fast as training two heads jointly. Also note that the solution $\\hat { \\theta } _ { t } ( \\phi )$ relies on $\\theta _ { s }$ implicitly through $y ^ { \\prime }$ . However, both standard self-training and our implementation use label sharpening, making $y ^ { \\prime }$ not differentiable. Thus we follow vanilla self-training and do not consider the gradient of $\\hat { \\theta } _ { t } ( \\phi )$ w.r.t. $y ^ { \\prime }$ in the outer loop optimization. We defer the derivation and implementation of bi-level optimization to Appendix B.2. ", + "bbox": [ + 173, + 744, + 826, + 919 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2 Tsallis Entropy Minimization ", + "text_level": 1, + "bbox": [ + 174, + 90, + 418, + 106 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Gibbs entropy is widely used by existing semi-supervised learning methods to regularize the model output and minimize the uncertainty of predictions on unlabeled data [24]. In this work, we generalize Gibbs entropy to Tsallis entropy [62] in information theory. Suppose the softmax output of a model is $\\boldsymbol { y } \\in \\mathbb { R } ^ { K }$ , then the $\\alpha$ -Tsallis entropy is defined as ", + "bbox": [ + 173, + 109, + 825, + 165 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/b95e1c346e23f4b85a1a6f60a6af5ce0f86164604ee0f7976ebba75830a25b7b.jpg", + "text": "$$\nS _ { \\alpha } ( y ) = \\frac { 1 } { \\alpha - 1 } \\left( 1 - \\sum y _ { [ i ] } ^ { \\alpha } \\right) ,\n$$", + "text_format": "latex", + "bbox": [ + 392, + 162, + 604, + 194 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\alpha > 0$ is the entropic-index. Note that $\\begin{array} { r } { \\operatorname* { l i m } _ { \\alpha \\to 1 } S _ { \\alpha } ( y ) = \\sum _ { i } - y _ { [ i ] } \\mathrm { l o g } ( y _ { [ i ] } ) } \\end{array}$ which exactly recovers the Gibbs entropy. When $\\alpha = 2$ , $S _ { \\alpha } ( y )$ becomes the Gini impurity $1 - \\textstyle \\sum _ { i } y _ { [ i ] } ^ { 2 }$ . ", + "bbox": [ + 174, + 196, + 826, + 229 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We propose to control the uncertainty of target pseudo-labels based on Tsallis entropy minimization: ", + "bbox": [ + 173, + 236, + 825, + 251 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/9217f3dc045a29db80f7156064abccd6aedaffed583742fa94bbd6774795f66a.jpg", + "text": "$$\nL _ { \\widehat { Q } , \\mathrm { T s a l l i s } , \\alpha } ( \\theta , \\phi ) : = \\mathbb { E } _ { \\boldsymbol { x } \\sim \\widehat { Q } } S _ { \\alpha } ( f _ { \\theta , \\phi } ( \\boldsymbol { x } ) ) .\n$$", + "text_format": "latex", + "bbox": [ + 367, + 253, + 629, + 275 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Figure 3 shows the change of Tsallis entropy with different entropic-indices $\\alpha$ for binary problems. Intuitively, smaller $\\alpha$ exerts more penalization on uncertain predictions and larger $\\alpha$ allows several scores $y _ { i }$ ’s to be similar. This is critical in self-training since an overly small $\\alpha$ (as in Gibbs entropy) will make the incorrect dimension of pseudo-labels close to 1 and have no chance to be corrected throughout training. In Section 5.4, we further verify this property with experiments. ", + "bbox": [ + 173, + 284, + 531, + 409 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/1ee6c84356d7e7a52e7c51e6a8539defd26596a9b539b8488d28b38233853582.jpg", + "image_caption": [ + "Figure 3: Tsallis entropy vs. entropic-index $\\alpha$ " + ], + "image_footnote": [], + "bbox": [ + 545, + 286, + 816, + 388 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "An important improvement of the Tsallis entropy over Gibbs entropy is that it can choose the suitable measure of uncertainty for different systems to avoid over-confidence caused by overly penalizing the uncertain pseudo-labels. To automatically find the suitable $\\alpha$ , we adopt a similar strategy as Section 3.1. The intuition is that if we use the suitable entropic-index $\\alpha$ to train the source classifier $\\theta _ { s , \\alpha }$ , the target pseudo-labels generated by $\\theta _ { s , \\alpha }$ will contain desirable knowledge of the source dataset, i.e. a target classifier $\\theta _ { t , \\alpha }$ trained with these pseudo-labels will perform well on the source domain. Therefore, we semi-supervisedly train a classifier $\\widehat { \\theta } _ { s , \\alpha }$ on the source domain with the $\\alpha$ -Tsallis entropy regularization $L _ { \\widehat { Q } , \\mathrm { T s a l l i s } , \\alpha }$ on the target domain as: $\\hat { \\theta } _ { s , \\alpha } = \\arg \\operatorname* { m i n } _ { \\theta } L _ { \\widehat { P } } ( \\theta , \\phi ) + L _ { \\widehat { Q } , \\mathrm { T s a l l i s } , \\alpha } ( \\theta , \\phi )$ , from which we obtain the target pseudo-labels. Then we train another head $\\widehat { \\theta } _ { t , \\alpha }$ with target pseudo-labels. We automatically find $\\alpha$ by minimizing the loss of $\\widehat { \\theta } _ { t , \\alpha }$ on the source data: ", + "bbox": [ + 173, + 415, + 826, + 569 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/8049a6e65f36582e37ae51ea79dc307021193480cbdf85b180862acbd25d47dc.jpg", + "text": "$$\n\\hat { \\alpha } = \\underset { \\alpha \\in [ 1 , 2 ] } { \\arg \\operatorname* { m i n } } L _ { \\widehat { P } } ( \\widehat { \\theta } _ { t , \\alpha } , \\phi )\n$$", + "text_format": "latex", + "bbox": [ + 413, + 573, + 584, + 603 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To solve equation 10, we discretize the feasible region [1, 2] of $\\alpha$ and use discrete optimization to lower computational cost. We also update $\\alpha$ at the start of each epoch, since we found more frequent ", + "bbox": [ + 174, + 606, + 823, + 636 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Algorithm 1 Cycle Self-Training (CST) ", + "text_level": 1, + "bbox": [ + 174, + 659, + 437, + 672 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "1: Input: source dataset $\\widehat { P }$ and target dataset $\\widehat { Q }$ . \n2: for epoch $= 0$ to MaxEpoch do \n3: Select $\\hat { \\alpha }$ as equation 10 at the start of each epoch. \n4: for $t = 0$ to MaxIter do \n5: Forward Step \n6: Generate pseudo-labels on the target domain with $\\phi$ and $\\theta _ { s }$ ${ \\mathrm { ~ \\mu ~ } } _ { 3 } \\colon y ^ { \\prime } = \\arg \\operatorname* { m a x } _ { i } \\{ f _ { \\theta _ { s } , \\phi } ( x ) _ { [ i ] } \\}$ . \n7: Reverse Step \n8: Train a target head $\\hat { \\theta } _ { t } ( \\phi )$ with target pseudo-labels $y ^ { \\prime }$ on the feature extractor $\\phi$ : \n$\\hat { \\theta } _ { t } ( \\phi ) = \\underset { \\theta } { \\arg \\operatorname* { m i n } } \\mathbb { E } _ { x \\sim \\hat { Q } } \\ell ( f _ { \\theta , \\phi } ( x ) , y ^ { \\prime } ) .$ \n9: Update the feature extractor $\\phi$ and the source head $\\theta _ { s }$ to make $\\hat { \\theta } _ { t } ( \\phi )$ perform well on the \nsource dataset and minimize the $\\hat { \\alpha }$ -Tsallis entropy on the target dataset: ", + "bbox": [ + 178, + 676, + 823, + 848 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/6d875ecdfd62ea38ad6b27593a76ee5f7927e127b3756c92fd9a5c61070856d5.jpg", + "text": "$$\n\\begin{array} { r l } & { \\phi \\phi - \\eta \\nabla _ { \\phi } [ L _ { \\widehat { P } } ( \\theta _ { s } , \\phi ) + L _ { \\widehat { P } } ( \\widehat { \\theta } _ { t } ( \\phi ) , \\phi ) + L _ { \\widehat { Q } , \\mathrm { T s a l l i s } , \\widehat { \\alpha } } ( \\theta _ { s } , \\phi ) ] . } \\\\ & { \\qquad \\theta _ { s } \\theta _ { s } - \\eta \\nabla _ { \\theta _ { s } } [ L _ { \\widehat { P } } ( \\theta _ { s } , \\phi ) + L _ { \\widehat { Q } , \\mathrm { T s a l l i s } , \\widehat { \\alpha } } ( \\theta _ { s } , \\phi ) ] . } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 318, + 847, + 738, + 891 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "10: end for \n11: end for ", + "bbox": [ + 174, + 877, + 271, + 905 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "update leads to no performance gain. Details are deferred to Appendix B.3. Finally, with the optimal $\\hat { \\alpha }$ found, we add the $\\hat { \\alpha }$ -Tsallis entropy minimization term $L _ { \\widehat { Q } , \\mathrm { T s a l l i s } , \\widehat { \\alpha } }$ to the overall objective: ", + "bbox": [ + 171, + 90, + 823, + 122 + ], + "page_idx": 5 + }, + { + "type": "equation", + "img_path": "images/2cceee179cc3a3be90b0ab3de021cb3447406ac386ba4aec8ca271ad95f039c1.jpg", + "text": "$$\n\\operatorname* { m i n i m i z e } _ { \\theta _ { s } , \\phi } L _ { \\mathrm { C y c l e } } ( \\theta _ { s } , \\phi ) + L _ { \\hat { Q } , \\mathrm { T s a l l i s } , \\hat { \\alpha } } ( \\theta _ { s } , \\phi ) .\n$$", + "text_format": "latex", + "bbox": [ + 352, + 128, + 643, + 154 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In summary, Algorithm 1 depicts the complete training procedure of Cycle Self-Training (CST). ", + "bbox": [ + 169, + 159, + 802, + 174 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4 Theoretical Analysis ", + "text_level": 1, + "bbox": [ + 174, + 185, + 377, + 203 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We analyze the properties of CST theoretically. First, we prove that the minimizer of the CST loss $L _ { \\mathrm { C S T } } ( f _ { s } , f _ { t } )$ will lead to small target loss $\\mathrm { E r r } _ { Q } ( f _ { s } )$ under a simple but realistic expansion assumption. Then, we further demonstrate a concrete instantiation where cycle self-training provably recovers the target ground truth, but both feature adaptation and standard self-training fail. Due to space limit, we state the main results here and defer all proof details to Appendix $A$ . ", + "bbox": [ + 173, + 210, + 826, + 281 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1 CST Provably Works under the Expansion Assumption ", + "text_level": 1, + "bbox": [ + 173, + 287, + 598, + 304 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We start from a $K$ -way classification model, $f : \\mathcal { X } \\to [ 0 , 1 ] ^ { K } \\in \\mathcal { F }$ and ${ \\tilde { f } } ( x ) : = \\arg \\operatorname* { m a x } _ { i } f ( x ) _ { [ i ] }$ denotes the prediction. Denote by $P _ { i }$ the conditional distribution of $P$ given $y = i$ . Assume the supports of $P _ { i }$ and $P _ { j }$ are disjoint for $i \\neq j$ . The definition is similar for $Q _ { i }$ . We further Assume $P ( y = i ) = Q ( y = i )$ . For any $x \\in \\mathcal { X }$ , $\\mathcal { N } ( x )$ is defined as the neighboring set of $x$ with a proper metric $d ( \\cdot , \\cdot )$ $\\vert , \\mathcal { N } ( x ) = \\{ x ^ { \\prime } : d ( x , x ^ { \\prime } ) \\leq \\xi \\}$ . ${ \\mathcal { N } } ( A ) : = \\cup _ { x \\in A } { \\mathcal { N } } ( x )$ . Denote the expected error on the target domain by $\\mathrm { E r r } _ { Q } ( f ) : = \\mathbb { E } _ { ( x , y ) \\sim Q } \\mathbb { I } ( \\tilde { f } ( x ) \\neq y )$ . ", + "bbox": [ + 173, + 309, + 825, + 397 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We study the CST algorithm under the expansion assumption of the mixture distribution [66, 11]. Intuitively, this assumption indicates that the conditional distributions $P _ { i }$ and $Q _ { i }$ are closely located and regularly shaped, enabling knowledge transfer from the source domain to the target domain. ", + "bbox": [ + 174, + 401, + 823, + 444 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Definition 1 $[ q , \\epsilon )$ -constant expansion [66]). We say $P$ and $Q$ satisfy $( q , \\epsilon )$ -constant expansion for some constant $q , \\epsilon \\in ( 0 , 1 )$ , if for any set $A \\in { \\mathcal { X } }$ and any $i \\in [ K ]$ with ${ \\textstyle \\frac { 1 } { 2 } } > P _ { \\frac { 1 } { 2 } ( P _ { i } + Q _ { i } ) } ( A ) > q$ , we have $P _ { \\frac { 1 } { 2 } ( P _ { i } + Q _ { i } ) } ( { \\mathcal { N } } ( A ) \\backslash A ) > \\operatorname* { m i n } \\{ \\epsilon , P _ { \\frac { 1 } { 2 } ( P _ { i } + Q _ { i } ) } ( A ) \\} .$ . ", + "bbox": [ + 173, + 446, + 825, + 497 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Based on this expansion assumption, we consider a robustness-constrained version of CST. Later we will show that the robustness is closely related to the uncertainty. Denote by $f _ { s }$ the source model and $f _ { t }$ the model trained on the target with pseudo-labels. Let $R ( f _ { t } ) : = P _ { \\frac { 1 } { 2 } ( P + Q ) } ( \\{ x : \\exists x ^ { \\prime } \\in$ $\\mathcal { N } ( x ) , \\tilde { f } _ { t } ( x ) \\neq \\tilde { f } _ { t } ( x ^ { \\prime } ) \\} )$ represent the robustness [66] of $f _ { t }$ on $P$ and $Q$ . Suppose $\\mathbb { E } _ { ( x , y ) \\sim Q } \\mathbb { I } ( \\tilde { f } _ { s } ( x ) \\neq$ $\\tilde { f } _ { t } ( x ) ) \\leq c$ and $R ( f _ { t } ) \\leq \\rho$ . The following theorem states that when $f _ { s }$ and $f _ { t }$ behave similarly on the target domain $Q$ and $f _ { t }$ is robust to local changes in input, the minimizer of the cycle source error $\\mathrm { E r r } _ { P } ( f _ { t } )$ will guarantee low error of $f _ { s }$ on the target domain $Q$ . ", + "bbox": [ + 173, + 505, + 826, + 613 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Theorem 1. Suppose Definition 1 holds for $P$ and $Q$ . For any $f _ { s } , f _ { t }$ satisfying $\\mathbb { E } _ { ( x , y ) \\sim Q } \\mathbb { I } ( \\tilde { f } _ { s } ( x ) \\neq$ $\\tilde { f } _ { t } ( x ) ) \\leq c$ and $R ( f _ { t } ) \\leq \\rho _ { : }$ , the expected error of $f _ { s }$ on the target domain $Q$ is bounded, ", + "bbox": [ + 173, + 617, + 826, + 651 + ], + "page_idx": 5 + }, + { + "type": "equation", + "img_path": "images/3767b419c5d7590bcb91c5aa576cdb2e8a221e8b675b0cb2270ca20aa270faad.jpg", + "text": "$$\n\\mathrm { E r r } _ { Q } ( f _ { s } ) \\le \\mathrm { E r r } _ { P } ( f _ { t } ) + c + 2 q + \\frac { \\rho } { \\mathrm { m i n } \\{ \\epsilon , q \\} } .\n$$", + "text_format": "latex", + "bbox": [ + 348, + 656, + 648, + 686 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To further relate the expected error with the CST training objective and obtain finite-sample guarantee, we use the multi-class margin loss: $l _ { \\gamma } ( f ( x ) , y ) : = \\bar { \\psi _ { \\gamma } } ( - { \\cal M } ( f ( x ) , y ) )$ , where $\\mathcal { M } ( v , y ) =$ $v _ { [ y ] } - \\operatorname* { m a x } _ { y ^ { \\prime } \\ne y } v _ { [ y ^ { \\prime } ] }$ and $\\psi _ { \\gamma }$ is the ramp function. We then extend the margin loss: $\\mathcal { M } ( v ) =$ $\\begin{array} { r } { \\operatorname* { m a x } _ { y } \\big ( v _ { [ y ] } - \\operatorname* { m a x } _ { y ^ { \\prime } \\neq y } v _ { [ y ^ { \\prime } ] } \\big ) } \\end{array}$ (The difference between the largest and the second largest scores in $v )$ , and $\\dot { l } _ { \\gamma } ( f _ { t } ( x ) , f _ { s } ( x ) ) : = \\psi _ { \\gamma } ( - \\mathcal { M } ( f _ { t } ( x ) , \\tilde { f } _ { s } ( x ) ) )$ . Further suppose $f _ { [ i ] }$ is $L _ { f }$ -Lipschitz w.r.t. the metric $d ( \\cdot , \\cdot )$ and $\\tau : = 1 - 2 L _ { f } \\xi \\operatorname* { m i n } \\{ \\epsilon , q \\} > 0$ . Consider the following training objective for CST, denoted by $L _ { \\mathrm { C S T } } ( f _ { s } , f _ { t } )$ , where $\\mathcal { L } _ { \\widehat { P } , \\gamma } ( f _ { t } ) : = \\mathbb { E } _ { ( x , y ) \\sim \\widehat { P } } l _ { \\gamma } ( f _ { t } ( x ) , y )$ corresponds to the cycle source loss in equation 5, $L _ { \\widehat { Q } , \\gamma } ( f _ { t } , f _ { s } ) : = \\mathbb { E } _ { ( x , y ) \\sim \\widehat { Q } } l _ { \\gamma } ( f _ { t } ( x ) , f _ { s } ( x ) )$ is consistent with the target loss in equation 4, and $\\mathcal { M } ( f _ { t } ( x ) )$ is closely related to the uncertainty of predictions in equation 11. ", + "bbox": [ + 173, + 696, + 826, + 838 + ], + "page_idx": 5 + }, + { + "type": "equation", + "img_path": "images/c6d24ce0adbf8cbbf84bc22d55ac6324f6f73dadd0fed6d9251d5b91d46526cc.jpg", + "text": "$$\n\\operatorname* { m i n } L _ { \\mathrm { C S T } } ( f _ { s } , f _ { t } ) : = L _ { \\widehat { P } , \\gamma } ( f _ { t } ) + L _ { \\widehat { Q } , \\gamma } ( f _ { t } , f _ { s } ) + \\frac { 1 - \\mathbb { E } _ { ( x , y ) \\sim \\frac { 1 } { 2 } ( \\widehat { P } + \\widehat { Q } ) } \\mathcal { M } ( f _ { t } ( x ) ) } { \\tau } .\n$$", + "text_format": "latex", + "bbox": [ + 233, + 842, + 763, + 877 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The following theorem shows that the minimizer of the training objective $L _ { \\mathrm { C S T } } ( f _ { s } , f _ { t } )$ guarantees low population error of $f _ { s }$ on the target domain $Q$ . ", + "bbox": [ + 171, + 882, + 823, + 912 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Theorem 2. $ { \\widehat { \\mathcal { R } } } ( \\mathcal { F } | _ { { \\widehat { P } } } )$ denotes the empirical Rademacher complexity of function class $\\mathcal { F }$ on dataset $\\widehat { P }$ . For any solution of equation $^ { 1 3 }$ and $\\gamma > 0$ , with probability larger than $1 - \\delta$ , ", + "bbox": [ + 173, + 88, + 823, + 125 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "$\\mathrm { E r r } _ { Q } ( f _ { s } ) \\leq L _ { \\mathrm { C S T } } ( f _ { s } , f _ { t } ) + 2 q + \\frac { 4 K } { \\gamma } \\left[ \\widehat { R } ( \\mathcal { F } | _ { \\widehat { P } } ) + \\widehat { \\mathcal { R } } ( \\tilde { \\mathcal { F } } \\times \\mathcal { F } | _ { \\widehat { Q } } ) \\right] + \\frac { 2 } { \\tau } \\left[ \\widehat { R } ( \\mathcal { F } | _ { \\widehat { P } } ) + \\widehat { \\mathcal { R } } ( \\mathcal { F } | _ { \\widehat { Q } } ) \\right] + \\zeta ,$ where $\\zeta = O \\left( \\sqrt { \\log ( 1 / \\delta ) / n _ { s } } + \\sqrt { \\log ( 1 / \\delta ) / n _ { t } } \\right)$ is a low-order term. $\\tilde { \\mathcal { F } } \\times \\mathcal { F }$ refers to the function class $\\{ x f ( \\overleftarrow { x } ) _ { [ \\tilde { f } ^ { \\prime } ( x ) ] } : f , f ^ { \\prime } \\in \\mathcal { F } \\} _ { }$ . ", + "bbox": [ + 174, + 126, + 825, + 205 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Main insights. Theorem 2 justifies CST under the expansion assumption. The generalization error of the classifier $f _ { s }$ on the target domain is bounded with the CST loss objective $L _ { \\mathrm { C S T } } ( f _ { s } , f _ { t } )$ , the intrinsic property of the data distribution $q$ , and the complexity of the function classes. In our algorithm, $\\bar { L _ { \\mathrm { C S T } } } ( f _ { s } , f _ { t } )$ is minimized by the neural networks and $q$ is a constant. The complexity of the function class can be controlled with proper regularization. ", + "bbox": [ + 173, + 212, + 826, + 282 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2 Hard Case for Feature Adaptation and Standard Self-Training ", + "text_level": 1, + "bbox": [ + 173, + 294, + 650, + 309 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To gain more insight, we study UDA in a quadratic neural network $f _ { \\theta , \\phi } ( x ) = \\theta ^ { \\top } ( \\phi ^ { \\top } x ) ^ { \\odot 2 }$ , where $\\odot$ is element-wise power. In UDA, the source can have multiple solutions but we aim to learn the one working on the target [34]. We design the underlying distributions $p$ and $q$ in Table 6 to reflect this. Consider the following $P$ and $Q$ . $x _ { [ 1 ] }$ and $x _ { [ 2 ] }$ are sampled i.i.d. from distribution $p$ on $P$ , and from $q$ on $Q$ . For $i \\in [ 3 , d ]$ , $x _ { [ i ] } = \\sigma _ { i } x _ { [ 2 ] }$ on $P$ and $x _ { [ i ] } = \\sigma _ { i } x _ { [ 1 ] }$ on $Q$ . $\\sigma _ { i } \\in \\{ \\pm 1 \\}$ are i.i.d. and uniform. We also assume realizability: for all $y = x _ { [ 1 ] } ^ { 2 } - x _ { [ 2 ] } ^ { 2 }$ $i \\in [ 2 , d ]$ for both source and target. Note that are solutions to $P$ but only $y = x _ { [ 1 ] } ^ { 2 } - x _ { [ 2 ] } ^ { 2 }$ $y = x _ { [ 1 ] } ^ { 2 } - x _ { [ i ] } ^ { 2 }$ [1] \u0000 [i]works on $Q$ . We visualize this specialized setting in Figure 4. ", + "bbox": [ + 171, + 315, + 823, + 372 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/dec7d5c5c265fa3517e125f23204bae6b6328a41a793093a8f16e95e56e7c393.jpg", + "table_caption": [ + "Table 1: The design of $p$ and $q$ . " + ], + "table_footnote": [], + "table_body": "
Distribution-1+10
Source p[0.050.050.90
Target q0.250.250.50
", + "bbox": [ + 630, + 393, + 823, + 445 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "", + "bbox": [ + 173, + 378, + 620, + 457 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c5b098da78c5868e7858cc364d018d8dfcb55a8acb4b0000cd134653d0e02a42.jpg", + "image_caption": [ + "Figure 4: The hard case where $d = 3$ . Green dots for $y = 1$ , red dots for $y = 0$ , and blue dots for $y = - 1$ . The grey curve is the classification boundary of different features. The good feature $x _ { [ 1 ] } ^ { 2 } - x _ { [ 2 ] } ^ { 2 }$ works on the target domain (shown in (a) and (c)), whereas the spurious feature $x _ { [ 1 ] } ^ { 2 } - x _ { [ 3 ] } ^ { 2 }$ only works on the source domain (shown in (b) andwhile CST learns tion 4.2, we show that feature adaptation and standard self-training learn . $x _ { [ 1 ] } ^ { 2 } - x _ { [ 3 ] } ^ { 2 }$ , $x _ { [ 1 ] } ^ { 2 } - x _ { [ 2 ] } ^ { 2 }$ " + ], + "image_footnote": [], + "bbox": [ + 196, + 470, + 789, + 559 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To make the features more tractable, we study the norm-constrained version of the algorithms (details are deferred to Section A.3.2). We compare the features learned by feature adaptation, standard selftraining, and CST. Intuitively, feature adaptation fails because the ideal target solution $y = x _ { [ 1 ] } ^ { 2 } - x _ { [ 2 ] } ^ { 2 }$ has larger distance in the feature space than other spurious solutions y = x2[1] $y = x _ { [ 1 ] } ^ { 2 } - x _ { [ i ] } ^ { 2 }$ \u0000 x2[i] . Standard selftraining also fails since it will choose randomly among all solutions. In comparison, CST can recover the ground truth, because it can distinguish the spurious solution resulting in bad pseudo-labels. A classifier trained with those pseudo-labels cannot work on the source domain in turn. This intuition is rigorously justified in the following two theorems. ", + "bbox": [ + 173, + 650, + 826, + 767 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Theorem 3. For $\\epsilon \\in ( 0 , 0 . 5 )$ , the following statements hold for feature adaptation and self-training: ", + "bbox": [ + 173, + 770, + 825, + 785 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "• For failure rate $\\xi > 0$ , and target dataset size $n _ { t } > \\Theta ( \\log { \\frac { 1 } { \\xi } } )$ , with probability at least $1 - \\xi$ over the sampling of target data, the solution $( \\hat { \\theta } _ { \\mathrm { F A } } , \\hat { \\phi } _ { \\mathrm { F A } } )$ found by feature adaptation satisfies ", + "bbox": [ + 176, + 790, + 825, + 825 + ], + "page_idx": 6 + }, + { + "type": "equation", + "img_path": "images/afe6482f8253d3cdc0a14cb5eb569c010b4413eaf5d99d1cc896456d1e87bf37.jpg", + "text": "$$\n\\mathrm { E r r } _ { Q } ( \\hat { \\theta } _ { \\mathrm { F A } } , \\hat { \\phi } _ { \\mathrm { F A } } ) \\geq \\epsilon .\n$$", + "text_format": "latex", + "bbox": [ + 439, + 835, + 573, + 856 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "• With probability at least $1 - { \\frac { 1 } { d - 1 } }$ , the solution $( \\hat { \\theta } _ { \\mathrm { S T } } , \\hat { \\phi } _ { \\mathrm { S T } } )$ of standard self-training satisfies ", + "bbox": [ + 171, + 864, + 784, + 885 + ], + "page_idx": 6 + }, + { + "type": "equation", + "img_path": "images/fd18edd7a8a42cef00255f76e999ade6cbb72cc6851eacd590e343946e6c4f62.jpg", + "text": "$$\n\\mathrm { E r r } _ { Q } ( \\hat { \\theta } _ { \\mathrm { S T } } , \\hat { \\phi } _ { \\mathrm { S T } } ) \\geq \\epsilon .\n$$", + "text_format": "latex", + "bbox": [ + 441, + 893, + 573, + 912 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Theorem 4. For failure rate $\\xi > 0$ , and target dataset size $\\begin{array} { r } { n _ { t } > \\Theta ( \\log { \\frac { 1 } { \\xi } } ) } \\end{array}$ , with probability at least $1 - \\xi ,$ , the solution of $C S T ( \\hat { \\phi } _ { \\mathrm { C S T } } , \\hat { \\theta } _ { \\mathrm { C S T } } )$ recovers the ground truth of the target dataset: ", + "bbox": [ + 171, + 90, + 825, + 126 + ], + "page_idx": 7 + }, + { + "type": "equation", + "img_path": "images/a687f52493667af53742d40a8ef8dff8469302111c5c6a72746feb742d9f3911.jpg", + "text": "$$\n\\mathrm { E r r } _ { Q } ( \\hat { \\theta } _ { \\mathrm { C S T } } , \\hat { \\phi } _ { \\mathrm { C S T } } ) = 0 .\n$$", + "text_format": "latex", + "bbox": [ + 436, + 147, + 588, + 167 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5 Experiments ", + "text_level": 1, + "bbox": [ + 174, + 176, + 312, + 194 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We test the performance of the proposed method on both vision and language datasets. Cycle SelfTraining (CST) consistently outperforms state-of-the-art feature adaptation and self-training methods. Code is available at https://github.com/Liuhong99/CST. ", + "bbox": [ + 176, + 202, + 825, + 243 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.1 Setup", + "text_level": 1, + "bbox": [ + 174, + 253, + 253, + 267 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Datasets. We experiment on visual object recognition and linguistic sentiment classification tasks: Office-Home [64] has 65 classes from four kinds of environment with large domain gap: Artistic (Ar), Clip Art (Cl), Product $( \\mathbf { P r } )$ , and Real-World (Rw); VisDA-2017 [45] is a large-scale UDA dataset with two domains named Synthetic and Real. The datasets consist of over $2 0 0 \\mathrm { k }$ images from 12 categories of objects; Amazon Review [10] is a linguistic sentiment classification dataset of product reviews in four products: Books $\\mathbf { ( B ) }$ , DVDs (D), Electronics (E), and Kitchen $\\mathbf { \\eta } ( \\mathbf { K } )$ . ", + "bbox": [ + 174, + 272, + 825, + 356 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Implementation. We use ResNet-50 [26] (pretrained on ImageNet [53]) as feature extractors for vision tasks, and BERT [16] for linguistic tasks. On VisDA-2017, we also provide results of ResNet101 to include more baselines. We use cross-entropy loss for classification on the source domain. When training the target head $\\widehat { \\theta } _ { t }$ and updating the feature extractor with CST, we use squared loss to get the analytical solution of $\\widehat { \\theta } _ { t }$ directly and avoid calculating second order derivatives as metalearning [18]. Details on adapting squared loss to multi-class classification are deferred to Appendix B. We adopt SGD with initial learning rate $\\eta _ { 0 } = 2 e - 3$ for image classification and $\\eta _ { 0 } = 5 e - 4$ for sentiment classification. Following standard protocol in [26], we decay the learning rate by 0.1 each 50 epochs until 150 epochs. We run all the tasks 3 times and report mean and deviation in top-1 accuracy. For VisDA-2017, we report the mean class accuracy. Following Theorem 2, we also enhance CST with sharpness-aware regularization [19] $( \\mathbf { C S T + S A M } )$ , which help regularize the Lipschitzness of the function class. Due to space limit, we report mean accuracies in Tables 2 and 3 and defer standard deviation to Appendix C. ", + "bbox": [ + 173, + 361, + 826, + 546 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.2 Baselines ", + "text_level": 1, + "bbox": [ + 174, + 555, + 277, + 569 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We compare with two lines of works in domain adaptation: feature adaptation and self-training. We also compare with more complex state-of-the-arts and create stronger baselines by combining feature adaptation and self-training. ", + "bbox": [ + 178, + 578, + 821, + 621 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Feature Adaptation: DANN [22], MCD [54], CDAN [37] (which improves DANN with pseudolabel conditioning), MDD [73] (which improves previous domain adaptation with margin theory), Implicit Alignment (IA) [28] (which improves MDD to deal with label shift). ", + "bbox": [ + 173, + 626, + 826, + 669 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Self-Training. We include VAT [40], MixMatch [8] and FixMatch [57] in the semi-supervised learning literature as self-training methods. We also compare with self-training methods for UDA: CBST [77], which considers class imbalance in standard self-training, and KLD [78], which improves CBST with label regularization. However, these methods involve tricks specified for convolutional networks. Thus, in sentiment classification tasks where we use BERT backbones, we compare with other consistency regularization baselines: VAT [40], VAT $^ { \\cdot } +$ Entropy Minimization. ", + "bbox": [ + 173, + 674, + 825, + 758 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Feature Adaptation $^ +$ Self-Training. DIRT-T [56] combines DANN, VAT, and entropy minimization. We also create more powerful baselines: CDAN $^ +$ VAT $^ +$ Entropy and MDD $+$ Fixmatch. ", + "bbox": [ + 173, + 763, + 823, + 792 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Other SOTA. AFN [69] boosts transferability by large norm. STAR [38] aligns domains with stochastic classifiers. SENTRY [48] selects confident examples with a committee of random augmentations. ", + "bbox": [ + 173, + 797, + 823, + 827 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3 Results ", + "text_level": 1, + "bbox": [ + 173, + 837, + 264, + 851 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Results on 12 pairs of Office-Home tasks are shown in Table 2. When domain shift is large, standard self-training methods such as VAT and FixMatch suffer from the decay in pseudo-label quality. CST outperforms feature adaptation and self-training methods significantly in 9 out of 12 tasks. Note that CST does not involve manually setting confidence threshold or reweighting. ", + "bbox": [ + 176, + 856, + 825, + 911 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/eb42d296b2f1285d0c7b99e47a1d81c9ac4a636562d148c0779058e73bc8001b.jpg", + "table_caption": [ + "Table 2: Accuracy $( \\% )$ on Office-Home for unsupervised domain adaptation (ResNet-50). " + ], + "table_footnote": [], + "table_body": "
Method|Ar-Cl Ar-Pr Ar-Rw Cl-Ar Cl-Pr Cl-Rw Pr-Ar Pr-CIPr-Rw Rw-Ar Rw-Cl Rw-Pr|Avg.
DANN [22]45.659.370.147.058.560.946.143.768.563.251.876.857.6
CDAN [37]50.770.676.057.670.070.057.450.977.370.956.781.665.8
CDAN+VAT+Entropy52.271.576.461.170.367.859.554.478.673.259.082.767.3
FixMatch [57]51.874.280.163.573.861.364.751.480.073.356.881.767.7
MDD [73]54.973.777.860.071.471.861.253.678.172.560.282.368.1
MDD+IA [28]56.277.979.264.473.174.464.254.279.971.258.183.169.5
SENTRY [48]61.877.480.166.371.674.766.863.080.974.066.384.172.2
CST59.079.683.468.477.176.768.956.483.075.362.285.1|73.0
", + "bbox": [ + 174, + 104, + 825, + 239 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/064187228bcfd5fa0d44b25d3abd40425be164827f67f87214f6fccf6617bc69.jpg", + "table_caption": [ + "Table 3: Accuracy $( \\% )$ on Multi-Domain Sentiment Dataset for domain adaptation with BERT. " + ], + "table_footnote": [], + "table_body": "
MethodB-DB-EB-KD-BD-ED-KE-BE-DE-KK-BK-DK-EAvg.
Source-only89.788.490.990.188.590.286.988.591.587.687.391.289.2
DANN [22]90.289.590.991.090.690.287.187.592.887.887.693.289.9
VAT[40]90.691.091.790.890.892.087.286.992.686.987.792.990.1
VAT+Entropy90.491.391.591.091.192.487.586.392.486.587.593.190.1
MDD [73]90.490.491.890.290.991.087.586.392.589.087.992.190.0
CST91.592.992.691.992.693.590.289.493.887.988.393.591.5
", + "bbox": [ + 173, + 268, + 823, + 377 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Table 4 shows the results on VisDA-2017. CST surpasses state-of-the-arts with ResNet-50 and ResNet101 backbones. We also combine feature adaptation and self-training (DIRT-T, CDAN+VAT+entropy and MDD $^ { + }$ FixMatch) to test if feature adaptation alleviates the negative effect of domain shift in standard self-training. Results indicate that CST is a better solution than simple combination. ", + "bbox": [ + 174, + 411, + 825, + 467 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "While most traditional self-training methods include techniques specified for ConvNets such as Mixup [72], CST is a universal method and can directly work on sentiment classification by simply replacing the head and training objective of BERT [16]. In Table 3, most feature adaptation baselines improve over source only marginally, but CST outperforms all baselines on most tasks significantly. ", + "bbox": [ + 173, + 473, + 825, + 530 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5.4 Analysis ", + "text_level": 1, + "bbox": [ + 174, + 547, + 271, + 563 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Ablation Study. We study the role of each part of CST in self-training. CST w/o Tsallis removes the Tsallis entropy $L _ { \\mathrm { T s a l l i s } , \\alpha }$ . CST $+$ Entropy replaces the Tsallis entropy with standard entropy. FixMatch+Tsallis adds $L _ { \\mathrm { T s a l l i s } , \\alpha }$ to standard self-training. Observations are shown in Table 5. $\\mathrm { C S T + l }$ Entropy performs $3 . 7 \\%$ worse than CST, indicating that Tsallis entropy is a better regularization for pseudolabels than standard entropy. CST performs $5 . 4 \\%$ better than FixMatch, indicating that CST is better adapted to domain shift than standard self-training. While FixMatch+Tsallis outperforms FixMatch, it is still $3 . 6 \\%$ behind CST, with much larger total variation distance $d _ { \\mathrm { T V } }$ between pseudo-labels and ground-truths, indicating that CST makes pseudo-labels more reliable than standard self-training under domain shift. ", + "bbox": [ + 174, + 569, + 545, + 681 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/1f009038872b5ecebb92230a8969f0c1c81ac204407dd1ce16149601336c7a75.jpg", + "table_caption": [ + "Table 5: Ablation on VisDA-2017. " + ], + "table_footnote": [], + "table_body": "
MethodAccuracy ↑|drv↓
FixMatch [57]74.5 ± 0.20.22
Fixmatch+Tsallis76.3 ± 0.80.15
CST w/o Tsallis72.0 ± 0.40.16
CST+Entropy76.2 ± 0.60.20
CST79.9 ± 0.50.12
", + "bbox": [ + 557, + 580, + 823, + 678 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 681, + 823, + 736 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Quality of Pseudo-labels. We visualize the error of pseudo-labels during training on VisDA-2017 in Figure 5 (Left). The error of target classifier $\\theta _ { t }$ on the source domain decreases quickly in training, when both the error of pseudo-labels (error of $\\theta _ { s }$ on $Q$ ) and the total variation (TV) distance between pseudo-labels and ground-truths continue to decay, indicating that CST gradually refines pseudolabels. This forms a clear contrast to standard self-training as visualized in Figure 2 (Middle), where the distance $d _ { \\mathrm { T V } }$ remains nearly unchanged throughout training. ", + "bbox": [ + 173, + 741, + 825, + 825 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Comparison of Gibbs entropy and Tsallis entropy. We compare the pseudo-labels learned with standard Gibbs entropy and Tsallis entropy on $\\mathbf { A r { } C l }$ with ResNet-50 at epoch 40. We compute the difference between the largest and the second largest softmax scores of each target example and plot the histogram in Figure 5 (Right). Gibbs entropy makes the largest softmax output close to 1, indicating over-confidence. In this case, if the prediction is wrong, it can be hard to correct it using self-training. In contrast, Tsallis entropy allows the largest and the second largest scores to be similar. ", + "bbox": [ + 174, + 832, + 825, + 915 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/3398ef4904b4c447ef21ebadb24014f266b754a7009178d7c7d1a7ef77df12da.jpg", + "table_caption": [ + "Table 4: Mean Class Accuracy $( \\% )$ for unsupervised domain adaptation on VisDA-2017. " + ], + "table_footnote": [], + "table_body": "
MethodResNet-50ResNet-101MethodResNet-50ResNet-101
DANN [22]69.379.5CBST[77]176.4 ± 0.9
VAT [40]68.0±0.373.4 ± 0.5KLD [78]178.1 ± 0.2
DIRT-T [56]68.2 ± 0.377.2 ± 0.5MDD[73]74.681.6 ± 0.3
MCD [54]69.277.7AFN [69]176.1
CDAN [37]70.080.1MDD+IA [28]75.81
CDAN+VAT+Entropy76.5 ± 0.580.4± 0.7MDD+FixMatch77.8 ± 0.382.4 ± 0.4
MixMatch69.3 ± 0.477.0 ± 0.5STAR [38]182.7
FixMatch [57]74.5 ± 0.279.5 ± 0.3SENTRY [48]76.71
CST79.9 ± 0.584.8± 0.6CST+SAM80.6 ± 0.586.5 ± 0.7
", + "bbox": [ + 174, + 90, + 823, + 237 + ], + "page_idx": 9 + }, + { + "type": "image", + "img_path": "images/b438078399476e8bc688a6c6252f161f15cda1ea9f72241d501cd24f973a4fac.jpg", + "image_caption": [ + "Figure 5: Analysis. Left: Error of pseudo-labels and reverse pseudo-labels. The error of target classifier $\\theta _ { t }$ on the source domain decreases, indicating the quality of pseudo-labels is refined. Right: Histograms of the difference between the largest and the second largest softmax scores. Tsallis entropy avoids over-confidence. " + ], + "image_footnote": [], + "bbox": [ + 194, + 246, + 799, + 352 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "6 Related Work ", + "text_level": 1, + "bbox": [ + 174, + 404, + 321, + 421 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Self-Training. Self-training is a mainstream technique for semi-supervised learning [13]. In this work, we focus on pseudo-labeling [52, 31, 2], which uses unlabeled data by training on pseudo-labels generated by a source model. Other lines of work study consistency regularization [4, 51, 55, 40]. Recent works demonstrate the power of such methods [67, 57, 23]. Equipped with proper training techniques, these methods can achieve comparable results as standard training that uses much more labeled examples [17]. Zoph et al. [76] compare self-training to pre-training and joint training. Vu et al. [65], Mukherjee & Awadallah [42] show that task-level self-training works well in few-shot learning. These methods are tailored to semi-supervised learning or general representation learning and do not take domain shift into consideration explicitly. Wei et al. [66], Frei et al. [20] provide the first nice theoretical analysis of self-training based on the expansion assumption. ", + "bbox": [ + 173, + 429, + 825, + 568 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Domain Adaptation. Inspired by the generalization error bound of Ben-David et al. [7], Long et al. [34], Zellinger et al. [71] minimize distance measures between source and target distributions to learn domain-invariant features. Ganin et al. [22] (DANN) proposed to approximate the domain distance by adversarial learning. Follow-up works proposed various improvement upon DANN [63, 54, 37, 73, 28]. Popular as they are, failure cases exist in situation like label shift [74, 32], shift in support of domains [29], and large discrepancy between source and target [33]. Another line of works try to address domain adaptation with self-training. Shu et al. [56] improves DANN with VAT and entropy minimization. French et al. [21], Zou et al. [78], Li et al. [32] incorporated various semi-supervised learning techniques to boost domain adaptation performance. Kumar et al. [30], Chen et al. [15] and Cai et al. [11] showed self-training provably works in domain adaptation under certain assumptions. ", + "bbox": [ + 174, + 574, + 825, + 712 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "7 Conclusion ", + "text_level": 1, + "bbox": [ + 174, + 724, + 299, + 741 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "We propose cycle self-training in place of standard self-training to explicitly address the distribution shift in domain adaptation. We show that our method provably works under the expansion assumption and demonstrate hard cases for feature adaptation and standard self-training. Self-training (or pseudolabeling) is only one line of works in the semi-supervised learning literature. Future work can delve into the behaviors of other semi-supervised learning techniques including consistency regularization and data augmentation under distribution shift, and exploit them extensively for domain adaptation. ", + "bbox": [ + 174, + 750, + 825, + 833 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Acknowledgements ", + "text_level": 1, + "bbox": [ + 174, + 844, + 338, + 862 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "This work was supported by the National Natural Science Foundation of China under Grants 62022050 and 62021002, Beijing Nova Program under Grant Z201100006820041, China’s Ministry of Industry and Information Technology, the MOE Innovation Plan and the BNRist Innovation Fund. ", + "bbox": [ + 176, + 869, + 825, + 911 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "References ", + "text_level": 1, + "bbox": [ + 174, + 89, + 267, + 106 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "[1] Albadawy, E. A., Saha, A., and Mazurowski, M. A. Deep learning for segmentation of brain tumors: Impact of cross-institutional training and testing. Medical Physics, 45(3), 2018. \n[2] Arazo, E., Ortego, D., Albert, P., O’Connor, N. 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Despite", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 591, + 506, + 604 + ], + "spans": [ + { + "bbox": [ + 105, + 591, + 506, + 604 + ], + "score": 1.0, + "content": "their popularity, the impossibility theories [6] uncovered intrinsic limitations of learning invariant", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 601, + 478, + 615 + ], + "spans": [ + { + "bbox": [ + 105, + 601, + 478, + 615 + ], + "score": 1.0, + "content": "representations when it comes to label shift [74, 32] and shift in the support of domains [29].", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 40.5 + }, + { + "type": "text", + "bbox": [ + 107, + 618, + 505, + 696 + ], + "lines": [ + { + "bbox": [ + 106, + 618, + 506, + 632 + ], + "spans": [ + { + "bbox": [ + 106, + 618, + 506, + 632 + ], + "score": 1.0, + "content": "Recently, self-training (a.k.a. pseudo-labeling) [21, 78, 30, 32, 47, 68] has been gaining momentum", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 629, + 506, + 643 + ], + "spans": [ + { + "bbox": [ + 105, + 629, + 506, + 643 + ], + "score": 1.0, + "content": "as a promising alternative to feature adaptation. Originally tailored to semi-supervised learning,", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 641, + 505, + 653 + ], + "spans": [ + { + "bbox": [ + 105, + 641, + 505, + 653 + ], + "score": 1.0, + "content": "self-training generates pseudo-labels of unlabeled data, and jointly trains the model with source labels", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 650, + 506, + 665 + ], + "spans": [ + { + "bbox": [ + 105, + 650, + 506, + 665 + ], + "score": 1.0, + "content": "and target pseudo-labels [31, 39, 30]. However, the distributional shift in UDA makes pseudo-labeling", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 662, + 505, + 675 + ], + "spans": [ + { + "bbox": [ + 106, + 662, + 505, + 675 + ], + "score": 1.0, + "content": "more difficult. 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Thus previous works tailor self-training to UDA by selecting trustworthy pseudo-labels.", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 106, + 685, + 505, + 697 + ], + "spans": [ + { + "bbox": [ + 106, + 685, + 505, + 697 + ], + "score": 1.0, + "content": "Using confidence threshold or reweighting, recent works try to alleviate the negative effect of domain", + "type": "text" + } + ], + "index": 50 + } + ], + "index": 47 + } + ], + "page_idx": 0, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 118, + 703, + 396, + 714 + ], + "lines": [ + { + "bbox": [ + 118, + 701, + 397, + 716 + ], + "spans": [ + { + "bbox": [ + 118, + 701, + 397, + 716 + ], + "score": 1.0, + "content": "⇤Corresponding author: Mingsheng Long (mingsheng@tsinghua.edu.cn)", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 107, + 731, + 385, + 742 + ], + "lines": [ + { + "bbox": [ + 105, + 730, + 386, + 743 + ], + "spans": [ 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Since deep neural networks are known to be sensitive to subtle", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 509, + 505, + 522 + ], + "spans": [ + { + "bbox": [ + 105, + 509, + 505, + 522 + ], + "score": 1.0, + "content": "change in underlying distributions [70], models trained on one labeled dataset often fail to generalize", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 518, + 506, + 535 + ], + "spans": [ + { + "bbox": [ + 105, + 518, + 506, + 535 + ], + "score": 1.0, + "content": "to another unlabeled dataset [58, 1]. 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By reducing the", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 558, + 506, + 571 + ], + "spans": [ + { + "bbox": [ + 105, + 558, + 506, + 571 + ], + "score": 1.0, + "content": "distance of the source and target feature distributions, these methods learn invariant representations to", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 569, + 505, + 582 + ], + "spans": [ + { + "bbox": [ + 105, + 569, + 505, + 582 + ], + "score": 1.0, + "content": "facilitate knowledge transfer between domains [34, 22, 36, 54, 37, 73], with successful applications in", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 581, + 505, + 594 + ], + "spans": [ + { + "bbox": [ + 105, + 581, + 505, + 594 + ], + "score": 1.0, + "content": "various areas such as computer vision [63, 27, 77] and natural language processing [75, 49]. Despite", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 591, + 506, + 604 + ], + "spans": [ + { + "bbox": [ + 105, + 591, + 506, + 604 + ], + "score": 1.0, + "content": "their popularity, the impossibility theories [6] uncovered intrinsic limitations of learning invariant", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 601, + 478, + 615 + ], + "spans": [ + { + "bbox": [ + 105, + 601, + 478, + 615 + ], + "score": 1.0, + "content": "representations when it comes to label shift [74, 32] and shift in the support of domains [29].", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 40.5, + "bbox_fs": [ + 105, + 547, + 506, + 615 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 618, + 505, + 696 + ], + "lines": [ + { + "bbox": [ + 106, + 618, + 506, + 632 + ], + "spans": [ + { + "bbox": [ + 106, + 618, + 506, + 632 + ], + "score": 1.0, + "content": "Recently, self-training (a.k.a. pseudo-labeling) [21, 78, 30, 32, 47, 68] has been gaining momentum", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 629, + 506, + 643 + ], + "spans": [ + { + "bbox": [ + 105, + 629, + 506, + 643 + ], + "score": 1.0, + "content": "as a promising alternative to feature adaptation. Originally tailored to semi-supervised learning,", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 641, + 505, + 653 + ], + "spans": [ + { + "bbox": [ + 105, + 641, + 505, + 653 + ], + "score": 1.0, + "content": "self-training generates pseudo-labels of unlabeled data, and jointly trains the model with source labels", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 650, + 506, + 665 + ], + "spans": [ + { + "bbox": [ + 105, + 650, + 506, + 665 + ], + "score": 1.0, + "content": "and target pseudo-labels [31, 39, 30]. However, the distributional shift in UDA makes pseudo-labeling", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 662, + 505, + 675 + ], + "spans": [ + { + "bbox": [ + 106, + 662, + 505, + 675 + ], + "score": 1.0, + "content": "more difficult. Directly using all pseudo-labels is risky due to accumulated error and even trivial", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 106, + 673, + 506, + 685 + ], + "spans": [ + { + "bbox": [ + 106, + 673, + 506, + 685 + ], + "score": 1.0, + "content": "solution [14]. Thus previous works tailor self-training to UDA by selecting trustworthy pseudo-labels.", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 106, + 685, + 505, + 697 + ], + "spans": [ + { + "bbox": [ + 106, + 685, + 505, + 697 + ], + "score": 1.0, + "content": "Using confidence threshold or reweighting, recent works try to alleviate the negative effect of domain", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 106, + 223, + 505, + 236 + ], + "spans": [ + { + "bbox": [ + 106, + 223, + 505, + 236 + ], + "score": 1.0, + "content": "shift in standard self-training [78, 47], but they can be brittle and require expensive tweaking of the", + "type": "text", + "cross_page": true + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 235, + 451, + 246 + ], + "spans": [ + { + "bbox": [ + 106, + 235, + 451, + 246 + ], + "score": 1.0, + "content": "threshold or weight for different tasks, and their performance gain is still inconsistent.", + "type": "text", + "cross_page": true + } + ], + "index": 8 + } + ], + "index": 47, + "bbox_fs": [ + 105, + 618, + 506, + 697 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 128, + 69, + 483, + 165 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 128, + 69, + 483, + 165 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 128, + 69, + 483, + 165 + ], + "spans": [ + { + "bbox": [ + 128, + 69, + 483, + 165 + ], + "score": 0.968, + "type": "image", + "image_path": "a98d2d44c2b974a909fc041a6f8726476f59f9bdcb19e5febe93a6d25e86dd55.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 128, + 69, + 483, + 101.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 128, + 101.0, + 483, + 133.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 128, + 133.0, + 483, + 165.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 169, + 506, + 209 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 168, + 506, + 181 + ], + "spans": [ + { + "bbox": [ + 106, + 168, + 506, + 181 + ], + "score": 1.0, + "content": "Figure 1: Standard self-training vs. cycle self-training. In standard self-training, we generate target pseudo-", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 178, + 506, + 191 + ], + "spans": [ + { + "bbox": [ + 105, + 178, + 506, + 191 + ], + "score": 1.0, + "content": "labels with a source model, and then train the model with both source ground-truths and target pseudo-labels. In", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 188, + 506, + 201 + ], + "spans": [ + { + "bbox": [ + 106, + 188, + 506, + 201 + ], + "score": 1.0, + "content": "cycle self-training, we train a target classifier with target pseudo-labels in the inner loop, and make the target", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 197, + 475, + 212 + ], + "spans": [ + { + "bbox": [ + 105, + 197, + 475, + 212 + ], + "score": 1.0, + "content": "classifier perform well on the source domain by updating the shared representations in the outer loop.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 4.5 + } + ], + "index": 2.75 + }, + { + "type": "text", + "bbox": [ + 107, + 223, + 503, + 246 + ], + "lines": [ + { + "bbox": [ + 106, + 223, + 505, + 236 + ], + "spans": [ + { + "bbox": [ + 106, + 223, + 505, + 236 + ], + "score": 1.0, + "content": "shift in standard self-training [78, 47], but they can be brittle and require expensive tweaking of the", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 235, + 451, + 246 + ], + "spans": [ + { + "bbox": [ + 106, + 235, + 451, + 246 + ], + "score": 1.0, + "content": "threshold or weight for different tasks, and their performance gain is still inconsistent.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 7.5 + }, + { + "type": "text", + "bbox": [ + 106, + 250, + 505, + 339 + ], + "lines": [ + { + "bbox": [ + 106, + 251, + 505, + 263 + ], + "spans": [ + { + "bbox": [ + 106, + 251, + 505, + 263 + ], + "score": 1.0, + "content": "In this work, we first analyze the quality of pseudo-labels with or without domain shift to delve", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 262, + 505, + 274 + ], + "spans": [ + { + "bbox": [ + 106, + 262, + 505, + 274 + ], + "score": 1.0, + "content": "deeper into the difficulty of standard self-training in UDA. On popular benchmark datasets, when", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 272, + 506, + 285 + ], + "spans": [ + { + "bbox": [ + 105, + 272, + 506, + 285 + ], + "score": 1.0, + "content": "the source and target are the same, our analysis indicates that the pseudo-label distribution is almost", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 284, + 505, + 296 + ], + "spans": [ + { + "bbox": [ + 106, + 284, + 505, + 296 + ], + "score": 1.0, + "content": "identical to the ground-truth distribution. However, with distributional shift, their discrepancy can be", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 295, + 505, + 307 + ], + "spans": [ + { + "bbox": [ + 106, + 295, + 505, + 307 + ], + "score": 1.0, + "content": "very large with examples of several classes mostly misclassified into other classes. We also study", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 304, + 505, + 319 + ], + "spans": [ + { + "bbox": [ + 105, + 304, + 505, + 319 + ], + "score": 1.0, + "content": "the difficulty of selecting correct pseudo-labels with popular criteria under domain shift. Although", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 317, + 505, + 328 + ], + "spans": [ + { + "bbox": [ + 106, + 317, + 505, + 328 + ], + "score": 1.0, + "content": "entropy and confidence are reasonable selection criteria for correct pseudo-labels without domain", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 326, + 353, + 341 + ], + "spans": [ + { + "bbox": [ + 105, + 326, + 353, + 341 + ], + "score": 1.0, + "content": "shift, the domain shift makes their accuracy decrease sharply.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 12.5 + }, + { + "type": "text", + "bbox": [ + 107, + 343, + 505, + 475 + ], + "lines": [ + { + "bbox": [ + 106, + 344, + 506, + 356 + ], + "spans": [ + { + "bbox": [ + 106, + 344, + 506, + 356 + ], + "score": 1.0, + "content": "Our analysis shows that domain shift makes pseudo-labels unreliable and that self-training on selected", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 354, + 506, + 368 + ], + "spans": [ + { + "bbox": [ + 105, + 354, + 506, + 368 + ], + "score": 1.0, + "content": "target instances with accurate pseudo-labels is less successful. Thereby, more principled improvement", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 366, + 505, + 378 + ], + "spans": [ + { + "bbox": [ + 106, + 366, + 505, + 378 + ], + "score": 1.0, + "content": "of standard self-training should be tailored to UDA and address the domain shift explicitly. In this", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 377, + 505, + 389 + ], + "spans": [ + { + "bbox": [ + 106, + 377, + 505, + 389 + ], + "score": 1.0, + "content": "work, we propose Cycle Self-Training (CST), a principled self-training approach to UDA, which", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 388, + 505, + 400 + ], + "spans": [ + { + "bbox": [ + 106, + 388, + 505, + 400 + ], + "score": 1.0, + "content": "overcomes the limitations of standard self-training (see Figure 1). Different from previous works to", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 398, + 506, + 412 + ], + "spans": [ + { + "bbox": [ + 105, + 398, + 506, + 412 + ], + "score": 1.0, + "content": "select target pseudo-labels with hard-to-tweak protocols, CST learns to generalize the pseudo-labels", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 410, + 506, + 422 + ], + "spans": [ + { + "bbox": [ + 106, + 410, + 506, + 422 + ], + "score": 1.0, + "content": "across domains. Specifically, CST cycles between the use of target pseudo-labels to train a target", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 420, + 505, + 433 + ], + "spans": [ + { + "bbox": [ + 106, + 420, + 505, + 433 + ], + "score": 1.0, + "content": "classifier, and the update of shared representations to make the target classifier perform well on the", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 431, + 506, + 443 + ], + "spans": [ + { + "bbox": [ + 106, + 431, + 506, + 443 + ], + "score": 1.0, + "content": "source data. In contrast to the standard Gibbs entropy that makes the target predictions over-confident,", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 443, + 506, + 455 + ], + "spans": [ + { + "bbox": [ + 105, + 443, + 506, + 455 + ], + "score": 1.0, + "content": "we propose a confidence-friendly uncertainty measure based on the Tsallis entropy in information", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 453, + 506, + 465 + ], + "spans": [ + { + "bbox": [ + 105, + 453, + 506, + 465 + ], + "score": 1.0, + "content": "theory, which adaptively minimizes the uncertainty without manually tuning or setting thresholds.", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 463, + 506, + 477 + ], + "spans": [ + { + "bbox": [ + 106, + 463, + 506, + 477 + ], + "score": 1.0, + "content": "Our method is simple and generally applicable to vision and language tasks with various backbones.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 22.5 + }, + { + "type": "text", + "bbox": [ + 107, + 480, + 505, + 536 + ], + "lines": [ + { + "bbox": [ + 106, + 480, + 505, + 492 + ], + "spans": [ + { + "bbox": [ + 106, + 480, + 505, + 492 + ], + "score": 1.0, + "content": "We empirically evaluate our method on a series of standard UDA benchmarks. Results indicate that", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 491, + 505, + 503 + ], + "spans": [ + { + "bbox": [ + 106, + 491, + 505, + 503 + ], + "score": 1.0, + "content": "CST outperforms previous state-of-the-art methods in 21 out of 25 tasks for object recognition and", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 502, + 505, + 514 + ], + "spans": [ + { + "bbox": [ + 106, + 502, + 505, + 514 + ], + "score": 1.0, + "content": "sentiment classification. Theoretically, we prove that the minimizer of CST objective is endowed with", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 511, + 505, + 528 + ], + "spans": [ + { + "bbox": [ + 105, + 511, + 505, + 528 + ], + "score": 1.0, + "content": "general guarantees of target performance. We also study hard cases on specific distributions, showing", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 524, + 498, + 537 + ], + "spans": [ + { + "bbox": [ + 105, + 524, + 498, + 537 + ], + "score": 1.0, + "content": "that CST recovers target ground-truths while both feature adaptation and standard self-training fail.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 31 + }, + { + "type": "title", + "bbox": [ + 107, + 549, + 195, + 563 + ], + "lines": [ + { + "bbox": [ + 104, + 547, + 196, + 566 + ], + "spans": [ + { + "bbox": [ + 104, + 547, + 196, + 566 + ], + "score": 1.0, + "content": "2 Preliminaries", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 34 + }, + { + "type": "text", + "bbox": [ + 106, + 572, + 506, + 645 + ], + "lines": [ + { + "bbox": [ + 105, + 572, + 506, + 584 + ], + "spans": [ + { + "bbox": [ + 105, + 572, + 443, + 584 + ], + "score": 1.0, + "content": "We study unsupervised domain adaptation (UDA). 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In", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 188, + 506, + 201 + ], + "spans": [ + { + "bbox": [ + 106, + 188, + 506, + 201 + ], + "score": 1.0, + "content": "cycle self-training, we train a target classifier with target pseudo-labels in the inner loop, and make the target", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 197, + 475, + 212 + ], + "spans": [ + { + "bbox": [ + 105, + 197, + 475, + 212 + ], + "score": 1.0, + "content": "classifier perform well on the source domain by updating the shared representations in the outer loop.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 4.5 + } + ], + "index": 2.75 + }, + { + "type": "text", + "bbox": [ + 107, + 223, + 503, + 246 + ], + "lines": [], + "index": 7.5, + "bbox_fs": [ + 106, + 223, + 505, + 246 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 106, + 250, + 505, + 339 + ], + "lines": [ + { + "bbox": [ + 106, + 251, + 505, + 263 + ], + "spans": [ + { + "bbox": [ + 106, + 251, + 505, + 263 + ], + "score": 1.0, + "content": "In this work, we first analyze the quality of pseudo-labels with or without domain shift to delve", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 262, + 505, + 274 + ], + "spans": [ + { + "bbox": [ + 106, + 262, + 505, + 274 + ], + "score": 1.0, + "content": "deeper into the difficulty of standard self-training in UDA. On popular benchmark datasets, when", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 272, + 506, + 285 + ], + "spans": [ + { + "bbox": [ + 105, + 272, + 506, + 285 + ], + "score": 1.0, + "content": "the source and target are the same, our analysis indicates that the pseudo-label distribution is almost", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 284, + 505, + 296 + ], + "spans": [ + { + "bbox": [ + 106, + 284, + 505, + 296 + ], + "score": 1.0, + "content": "identical to the ground-truth distribution. However, with distributional shift, their discrepancy can be", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 295, + 505, + 307 + ], + "spans": [ + { + "bbox": [ + 106, + 295, + 505, + 307 + ], + "score": 1.0, + "content": "very large with examples of several classes mostly misclassified into other classes. We also study", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 304, + 505, + 319 + ], + "spans": [ + { + "bbox": [ + 105, + 304, + 505, + 319 + ], + "score": 1.0, + "content": "the difficulty of selecting correct pseudo-labels with popular criteria under domain shift. Although", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 317, + 505, + 328 + ], + "spans": [ + { + "bbox": [ + 106, + 317, + 505, + 328 + ], + "score": 1.0, + "content": "entropy and confidence are reasonable selection criteria for correct pseudo-labels without domain", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 326, + 353, + 341 + ], + "spans": [ + { + "bbox": [ + 105, + 326, + 353, + 341 + ], + "score": 1.0, + "content": "shift, the domain shift makes their accuracy decrease sharply.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 12.5, + "bbox_fs": [ + 105, + 251, + 506, + 341 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 343, + 505, + 475 + ], + "lines": [ + { + "bbox": [ + 106, + 344, + 506, + 356 + ], + "spans": [ + { + "bbox": [ + 106, + 344, + 506, + 356 + ], + "score": 1.0, + "content": "Our analysis shows that domain shift makes pseudo-labels unreliable and that self-training on selected", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 354, + 506, + 368 + ], + "spans": [ + { + "bbox": [ + 105, + 354, + 506, + 368 + ], + "score": 1.0, + "content": "target instances with accurate pseudo-labels is less successful. 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Different from previous works to", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 398, + 506, + 412 + ], + "spans": [ + { + "bbox": [ + 105, + 398, + 506, + 412 + ], + "score": 1.0, + "content": "select target pseudo-labels with hard-to-tweak protocols, CST learns to generalize the pseudo-labels", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 410, + 506, + 422 + ], + "spans": [ + { + "bbox": [ + 106, + 410, + 506, + 422 + ], + "score": 1.0, + "content": "across domains. 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In contrast to the standard Gibbs entropy that makes the target predictions over-confident,", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 443, + 506, + 455 + ], + "spans": [ + { + "bbox": [ + 105, + 443, + 506, + 455 + ], + "score": 1.0, + "content": "we propose a confidence-friendly uncertainty measure based on the Tsallis entropy in information", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 453, + 506, + 465 + ], + "spans": [ + { + "bbox": [ + 105, + 453, + 506, + 465 + ], + "score": 1.0, + "content": "theory, which adaptively minimizes the uncertainty without manually tuning or setting thresholds.", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 463, + 506, + 477 + ], + "spans": [ + { + "bbox": [ + 106, + 463, + 506, + 477 + ], + "score": 1.0, + "content": "Our method is simple and generally applicable to vision and language tasks with various backbones.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 22.5, + "bbox_fs": [ + 105, + 344, + 506, + 477 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 480, + 505, + 536 + ], + "lines": [ + { + "bbox": [ + 106, + 480, + 505, + 492 + ], + "spans": [ + { + "bbox": [ + 106, + 480, + 505, + 492 + ], + "score": 1.0, + "content": "We empirically evaluate our method on a series of standard UDA benchmarks. Results indicate that", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 491, + 505, + 503 + ], + "spans": [ + { + "bbox": [ + 106, + 491, + 505, + 503 + ], + "score": 1.0, + "content": "CST outperforms previous state-of-the-art methods in 21 out of 25 tasks for object recognition and", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 502, + 505, + 514 + ], + "spans": [ + { + "bbox": [ + 106, + 502, + 505, + 514 + ], + "score": 1.0, + "content": "sentiment classification. Theoretically, we prove that the minimizer of CST objective is endowed with", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 511, + 505, + 528 + ], + "spans": [ + { + "bbox": [ + 105, + 511, + 505, + 528 + ], + "score": 1.0, + "content": "general guarantees of target performance. We also study hard cases on specific distributions, showing", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 524, + 498, + 537 + ], + "spans": [ + { + "bbox": [ + 105, + 524, + 498, + 537 + ], + "score": 1.0, + "content": "that CST recovers target ground-truths while both feature adaptation and standard self-training fail.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 31, + "bbox_fs": [ + 105, + 480, + 505, + 537 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 549, + 195, + 563 + ], + "lines": [ + { + "bbox": [ + 104, + 547, + 196, + 566 + ], + "spans": [ + { + "bbox": [ + 104, + 547, + 196, + 566 + ], + "score": 1.0, + "content": "2 Preliminaries", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 34 + }, + { + "type": "text", + "bbox": [ + 106, + 572, + 506, + 645 + ], + "lines": [ + { + "bbox": [ + 105, + 572, + 506, + 584 + ], + "spans": [ + { + "bbox": [ + 105, + 572, + 443, + 584 + ], + "score": 1.0, + "content": "We study unsupervised domain adaptation (UDA). 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Left: Pseudo-label distributions", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 186, + 506, + 199 + ], + "spans": [ + { + "bbox": [ + 105, + 186, + 506, + 199 + ], + "score": 1.0, + "content": "with and without domain shift. Middle: Changes of pseudo-label distributions throughout training. 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For", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 227, + 506, + 241 + ], + "spans": [ + { + "bbox": [ + 105, + 227, + 339, + 241 + ], + "score": 1.0, + "content": "instance, Long et al. [34] used maximum mean discrepancy", + "type": "text" + }, + { + "bbox": [ + 339, + 229, + 363, + 240 + ], + "score": 0.88, + "content": "d _ { \\mathrm { M M D } }", + "type": "inline_equation" + }, + { + "bbox": [ + 363, + 227, + 506, + 241 + ], + "score": 1.0, + "content": ", and Ganin et al. 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Another popular variant", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 366, + 505, + 378 + ], + "spans": [ + { + "bbox": [ + 106, + 366, + 505, + 378 + ], + "score": 1.0, + "content": "of pseudo-labeling is the teacher-student model [4, 61], which iteratively improves the quality of", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 376, + 464, + 389 + ], + "spans": [ + { + "bbox": [ + 105, + 376, + 270, + 389 + ], + "score": 1.0, + "content": "pseudo-labels via alternatively replacing", + "type": "text" + }, + { + "bbox": [ + 270, + 377, + 280, + 387 + ], + "score": 0.88, + "content": "\\theta _ { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 280, + 376, + 298, + 389 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 298, + 377, + 309, + 388 + ], + "score": 0.89, + "content": "\\phi _ { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 310, + 376, + 331, + 389 + ], + "score": 1.0, + "content": "with", + "type": "text" + }, + { + "bbox": [ + 331, + 377, + 337, + 386 + ], + "score": 0.83, + "content": "\\theta", + "type": "inline_equation" + }, + { + "bbox": [ + 338, + 376, + 355, + 389 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 356, + 377, + 363, + 388 + ], + "score": 0.86, + "content": "\\phi", + "type": "inline_equation" + }, + { + "bbox": [ + 363, + 376, + 464, + 389 + ], + "score": 1.0, + "content": "of the previous iteration.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 17 + }, + { + "type": "title", + "bbox": [ + 107, + 395, + 292, + 407 + ], + "lines": [ + { + "bbox": [ + 105, + 393, + 294, + 410 + ], + "spans": [ + { + "bbox": [ + 105, + 393, + 294, + 410 + ], + "score": 1.0, + "content": "2.1 Limitations of Standard Self-Training", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 19 + }, + { + "type": "text", + "bbox": [ + 106, + 410, + 505, + 455 + ], + "lines": [ + { + "bbox": [ + 106, + 410, + 506, + 423 + ], + "spans": [ + { + "bbox": [ + 106, + 410, + 506, + 423 + ], + "score": 1.0, + "content": "Standard self-training with pseudo-labels uses unlabeled data efficiently for semi-supervised learn-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 420, + 506, + 435 + ], + "spans": [ + { + "bbox": [ + 105, + 420, + 506, + 435 + ], + "score": 1.0, + "content": "ing [31, 39, 57]. Here we carry out exploratory studies on the popular VisDA-2017 [45] dataset using", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 432, + 505, + 444 + ], + "spans": [ + { + "bbox": [ + 105, + 432, + 505, + 444 + ], + "score": 1.0, + "content": "ResNet-50 backbones. We find that domain shift makes the pseudo-labels biased towards several", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 443, + 500, + 455 + ], + "spans": [ + { + "bbox": [ + 106, + 443, + 500, + 455 + ], + "score": 1.0, + "content": "classes and thereby unreliable in UDA. See Appendix C.1 for details and results on more datasets.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 21.5 + }, + { + "type": "text", + "bbox": [ + 106, + 459, + 505, + 580 + ], + "lines": [ + { + "bbox": [ + 106, + 460, + 506, + 472 + ], + "spans": [ + { + "bbox": [ + 106, + 460, + 506, + 472 + ], + "score": 1.0, + "content": "Pseudo-label distributions with or without domain shift. We resample the original VisDA-2017", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 471, + 505, + 483 + ], + "spans": [ + { + "bbox": [ + 105, + 471, + 505, + 483 + ], + "score": 1.0, + "content": "to simulate different relationship between source and target domains: 1) i.i.d., 2) covariate shift, and", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 481, + 506, + 494 + ], + "spans": [ + { + "bbox": [ + 105, + 481, + 506, + 494 + ], + "score": 1.0, + "content": "3) label shift. We train the model on the three variants of source dataset and use it to generate target", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 104, + 492, + 506, + 505 + ], + "spans": [ + { + "bbox": [ + 104, + 492, + 506, + 505 + ], + "score": 1.0, + "content": "pseudo-labels. We show the distributions of target ground-truths and pseudo-labels in Figure 2 (Left).", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 503, + 506, + 516 + ], + "spans": [ + { + "bbox": [ + 106, + 503, + 506, + 516 + ], + "score": 1.0, + "content": "When the source and target distributions are identical, the distribution of pseudo-labels is almost", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 514, + 506, + 527 + ], + "spans": [ + { + "bbox": [ + 106, + 514, + 506, + 527 + ], + "score": 1.0, + "content": "the same as ground-truths, indicating the reliability of pseudo-labels. In contrast, when exposed to", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 524, + 506, + 538 + ], + "spans": [ + { + "bbox": [ + 105, + 524, + 506, + 538 + ], + "score": 1.0, + "content": "label shift or covariate shift, the distribution of pseudo-labels is significantly different from target", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 536, + 506, + 549 + ], + "spans": [ + { + "bbox": [ + 105, + 536, + 506, + 549 + ], + "score": 1.0, + "content": "ground-truths. Note that classes 2, 7, 8 and 12 appear rarely in the target pseudo-labels in the covariate", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 547, + 506, + 559 + ], + "spans": [ + { + "bbox": [ + 106, + 547, + 506, + 559 + ], + "score": 1.0, + "content": "shift setting, indicating that the pseudo-labels are biased towards several classes due to domain shift.", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 558, + 506, + 570 + ], + "spans": [ + { + "bbox": [ + 105, + 558, + 506, + 570 + ], + "score": 1.0, + "content": "Self-training with these pseudo-labels is risky since it may lead to misalignment of distributions and", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 569, + 318, + 581 + ], + "spans": [ + { + "bbox": [ + 105, + 569, + 318, + 581 + ], + "score": 1.0, + "content": "misclassify many examples of classes 2, 7, 8 and 12.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 29 + }, + { + "type": "text", + "bbox": [ + 106, + 585, + 505, + 673 + ], + "lines": [ + { + "bbox": [ + 106, + 584, + 506, + 598 + ], + "spans": [ + { + "bbox": [ + 106, + 584, + 506, + 598 + ], + "score": 1.0, + "content": "Change of pseudo-label distributions throughout training. To further study the change of pseudo-", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 596, + 506, + 609 + ], + "spans": [ + { + "bbox": [ + 105, + 596, + 506, + 609 + ], + "score": 1.0, + "content": "labels in standard self-training, we compute the total variation (TV) distance between target ground-", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 606, + 506, + 621 + ], + "spans": [ + { + "bbox": [ + 105, + 606, + 232, + 621 + ], + "score": 1.0, + "content": "truths and target pseudo-labels:", + "type": "text" + }, + { + "bbox": [ + 233, + 606, + 346, + 619 + ], + "score": 0.93, + "content": "\\begin{array} { r } { d _ { \\mathrm { T V } } ( c , \\dot { c ^ { \\prime } } ) = \\frac { 1 } { 2 } \\sum _ { i } \\| c _ { i } - c _ { i } ^ { \\prime } \\| } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 347, + 606, + 376, + 621 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 376, + 609, + 385, + 618 + ], + "score": 0.85, + "content": "c _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 386, + 606, + 462, + 621 + ], + "score": 1.0, + "content": "is the ratio of class", + "type": "text" + }, + { + "bbox": [ + 463, + 608, + 468, + 617 + ], + "score": 0.58, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 468, + 606, + 506, + 621 + ], + "score": 1.0, + "content": ". We plot", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 618, + 505, + 630 + ], + "spans": [ + { + "bbox": [ + 106, + 618, + 505, + 630 + ], + "score": 1.0, + "content": "its change during training in Figure 2 (Middle). Although the error rate of pseudo-labels continues", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 628, + 505, + 641 + ], + "spans": [ + { + "bbox": [ + 105, + 628, + 156, + 641 + ], + "score": 1.0, + "content": "to decrease,", + "type": "text" + }, + { + "bbox": [ + 157, + 629, + 173, + 640 + ], + "score": 0.87, + "content": "d _ { \\mathrm { T V } }", + "type": "inline_equation" + }, + { + "bbox": [ + 173, + 628, + 438, + 641 + ], + "score": 1.0, + "content": "remains almost unchanged at 0.26 throughout training. Note that", + "type": "text" + }, + { + "bbox": [ + 439, + 629, + 455, + 640 + ], + "score": 0.88, + "content": "d _ { \\mathrm { T V } }", + "type": "inline_equation" + }, + { + "bbox": [ + 455, + 628, + 505, + 641 + ], + "score": 1.0, + "content": "is the lower", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 640, + 505, + 652 + ], + "spans": [ + { + "bbox": [ + 106, + 640, + 393, + 652 + ], + "score": 1.0, + "content": "bound of the error rate of the pseudo-labels (shown in Appendix C.1). If", + "type": "text" + }, + { + "bbox": [ + 394, + 640, + 410, + 651 + ], + "score": 0.89, + "content": "d _ { \\mathrm { T V } }", + "type": "inline_equation" + }, + { + "bbox": [ + 410, + 640, + 505, + 652 + ], + "score": 1.0, + "content": "converges to 0.26, then", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 649, + 506, + 664 + ], + "spans": [ + { + "bbox": [ + 105, + 649, + 506, + 664 + ], + "score": 1.0, + "content": "the accuracy of pseudo-labels is upper-bounded by 0.74. This indicates that the important denoising", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 662, + 433, + 674 + ], + "spans": [ + { + "bbox": [ + 106, + 662, + 433, + 674 + ], + "score": 1.0, + "content": "ability [66] of pseudo-labels in standard self-training is hindered by domain shift.", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 38.5 + }, + { + "type": "text", + "bbox": [ + 107, + 678, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 105, + 677, + 506, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 506, + 690 + ], + "score": 1.0, + "content": "Difficulty of selecting reliable pseudo-labels under domain shift. To mitigate the negative effect", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 689, + 505, + 701 + ], + "spans": [ + { + "bbox": [ + 106, + 689, + 505, + 701 + ], + "score": 1.0, + "content": "of false pseudo-labels, recent works proposed to select correct pseudo-labels based on thresholding the", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 700, + 505, + 713 + ], + "spans": [ + { + "bbox": [ + 105, + 700, + 505, + 713 + ], + "score": 1.0, + "content": "entropy or confidence criteria [35, 21, 37, 57]. However, it remains unclear whether these strategies", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 710, + 505, + 724 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 505, + 724 + ], + "score": 1.0, + "content": "are still effective under domain shift. 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Left: Pseudo-label distributions", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 186, + 506, + 199 + ], + "spans": [ + { + "bbox": [ + 105, + 186, + 506, + 199 + ], + "score": 1.0, + "content": "with and without domain shift. Middle: Changes of pseudo-label distributions throughout training. Right:", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 198, + 364, + 208 + ], + "spans": [ + { + "bbox": [ + 106, + 198, + 364, + 208 + ], + "score": 1.0, + "content": "Quality of pseudo-labels under different pseudo-label selection criteria.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4 + } + ], + "index": 2.5 + }, + { + "type": "text", + "bbox": [ + 107, + 214, + 505, + 261 + ], + "lines": [ + { + "bbox": [ + 105, + 215, + 506, + 229 + ], + "spans": [ + { + "bbox": [ + 105, + 216, + 131, + 229 + ], + "score": 1.0, + "content": "Here,", + "type": "text" + }, + { + "bbox": [ + 131, + 215, + 150, + 229 + ], + "score": 0.93, + "content": "h _ { \\sharp } \\widehat { P }", + "type": "inline_equation" + }, + { + "bbox": [ + 150, + 216, + 312, + 229 + ], + "score": 1.0, + "content": "denotes the pushforward distribution of", + "type": "text" + }, + { + "bbox": [ + 313, + 215, + 322, + 227 + ], + "score": 0.86, + "content": "\\widehat { P }", + "type": "inline_equation" + }, + { + "bbox": [ + 322, + 216, + 342, + 229 + ], + "score": 1.0, + "content": ", and", + "type": "text" + }, + { + "bbox": [ + 343, + 217, + 367, + 229 + ], + "score": 0.9, + "content": "d ( \\cdot , \\cdot )", + "type": "inline_equation" + }, + { + "bbox": [ + 367, + 216, + 506, + 229 + ], + "score": 1.0, + "content": "is some distribution distance. For", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 227, + 506, + 241 + ], + "spans": [ + { + "bbox": [ + 105, + 227, + 339, + 241 + ], + "score": 1.0, + "content": "instance, Long et al. [34] used maximum mean discrepancy", + "type": "text" + }, + { + "bbox": [ + 339, + 229, + 363, + 240 + ], + "score": 0.88, + "content": "d _ { \\mathrm { M M D } }", + "type": "inline_equation" + }, + { + "bbox": [ + 363, + 227, + 506, + 241 + ], + "score": 1.0, + "content": ", and Ganin et al. [22] approximated", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 238, + 506, + 252 + ], + "spans": [ + { + "bbox": [ + 105, + 238, + 120, + 252 + ], + "score": 1.0, + "content": "the", + "type": "text" + }, + { + "bbox": [ + 121, + 239, + 147, + 250 + ], + "score": 0.81, + "content": "\\mathcal { H } \\Delta \\mathcal { H }", + "type": "inline_equation" + }, + { + "bbox": [ + 148, + 238, + 184, + 252 + ], + "score": 1.0, + "content": "-distance", + "type": "text" + }, + { + "bbox": [ + 184, + 240, + 211, + 250 + ], + "score": 0.91, + "content": "d _ { \\mathcal { H } \\Delta \\mathcal { H } }", + "type": "inline_equation" + }, + { + "bbox": [ + 212, + 238, + 506, + 252 + ], + "score": 1.0, + "content": "[7] with adversarial training. Despite its pervasiveness, recent works have", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 249, + 501, + 262 + ], + "spans": [ + { + "bbox": [ + 105, + 249, + 501, + 262 + ], + "score": 1.0, + "content": "shown the intrinsic limitations of feature adaptation under real-world situations [6, 74, 33, 32, 29].", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 7.5, + "bbox_fs": [ + 105, + 215, + 506, + 262 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 266, + 505, + 327 + ], + "lines": [ + { + "bbox": [ + 105, + 266, + 505, + 279 + ], + "spans": [ + { + "bbox": [ + 105, + 266, + 505, + 279 + ], + "score": 1.0, + "content": "Self-Training is considered a promising alternative to feature adaptation. In this work we mainly", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 276, + 506, + 290 + ], + "spans": [ + { + "bbox": [ + 105, + 276, + 506, + 290 + ], + "score": 1.0, + "content": "focus on pseudo-labeling [31, 30]. 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The target pseudo-labels are", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 302, + 505, + 317 + ], + "spans": [ + { + "bbox": [ + 105, + 303, + 178, + 317 + ], + "score": 1.0, + "content": "then generated by", + "type": "text" + }, + { + "bbox": [ + 178, + 304, + 189, + 316 + ], + "score": 0.88, + "content": "f _ { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 189, + 303, + 270, + 317 + ], + "score": 1.0, + "content": "on the target dataset", + "type": "text" + }, + { + "bbox": [ + 270, + 302, + 279, + 316 + ], + "score": 0.86, + "content": "\\widehat { Q }", + "type": "inline_equation" + }, + { + "bbox": [ + 279, + 303, + 505, + 317 + ], + "score": 1.0, + "content": ". To leverage unlabeled target data, self-training trains the", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 315, + 506, + 327 + ], + "spans": [ + { + "bbox": [ + 106, + 315, + 506, + 327 + ], + "score": 1.0, + "content": "model on the source and target datasets together with source ground-truths and target pseudo-labels:", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 12, + "bbox_fs": [ + 105, + 266, + 506, + 327 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 189, + 331, + 422, + 350 + ], + "lines": [ + { + "bbox": [ + 189, + 331, + 422, + 350 + ], + "spans": [ + { + "bbox": [ + 189, + 331, + 422, + 350 + ], + "score": 0.91, + "content": "\\operatorname* { m i n } _ { \\theta , \\phi } L _ { \\widehat { P } } ( \\theta , \\phi ) + \\mathbb { E } _ { x \\sim \\widehat { Q } } \\ell ( f _ { \\theta , \\phi } ( x ) , \\arg \\operatorname* { m a x } _ { i } \\{ f _ { \\theta , \\phi _ { s } } ( x ) _ { [ i ] } \\} ) .", + "type": "interline_equation", + "image_path": "7eb4ed6be74b99db248b902505b5c093a12694a3b85b7d17df4c597e37de3e0f.jpg" + } + ] + } + ], + "index": 15, + "virtual_lines": [ + { + "bbox": [ + 189, + 331, + 422, + 350 + ], + "spans": [], + "index": 15 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 354, + 505, + 388 + ], + "lines": [ + { + "bbox": [ + 105, + 353, + 506, + 367 + ], + "spans": [ + { + "bbox": [ + 105, + 353, + 506, + 367 + ], + "score": 1.0, + "content": "Self-training also uses label-sharpening as a standard protocol [31, 57]. Another popular variant", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 366, + 505, + 378 + ], + "spans": [ + { + "bbox": [ + 106, + 366, + 505, + 378 + ], + "score": 1.0, + "content": "of pseudo-labeling is the teacher-student model [4, 61], which iteratively improves the quality of", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 376, + 464, + 389 + ], + "spans": [ + { + "bbox": [ + 105, + 376, + 270, + 389 + ], + "score": 1.0, + "content": "pseudo-labels via alternatively replacing", + "type": "text" + }, + { + "bbox": [ + 270, + 377, + 280, + 387 + ], + "score": 0.88, + "content": "\\theta _ { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 280, + 376, + 298, + 389 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 298, + 377, + 309, + 388 + ], + "score": 0.89, + "content": "\\phi _ { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 310, + 376, + 331, + 389 + ], + "score": 1.0, + "content": "with", + "type": "text" + }, + { + "bbox": [ + 331, + 377, + 337, + 386 + ], + "score": 0.83, + "content": "\\theta", + "type": "inline_equation" + }, + { + "bbox": [ + 338, + 376, + 355, + 389 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 356, + 377, + 363, + 388 + ], + "score": 0.86, + "content": "\\phi", + "type": "inline_equation" + }, + { + "bbox": [ + 363, + 376, + 464, + 389 + ], + "score": 1.0, + "content": "of the previous iteration.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 17, + "bbox_fs": [ + 105, + 353, + 506, + 389 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 395, + 292, + 407 + ], + "lines": [ + { + "bbox": [ + 105, + 393, + 294, + 410 + ], + "spans": [ + { + "bbox": [ + 105, + 393, + 294, + 410 + ], + "score": 1.0, + "content": "2.1 Limitations of Standard Self-Training", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 19 + }, + { + "type": "text", + "bbox": [ + 106, + 410, + 505, + 455 + ], + "lines": [ + { + "bbox": [ + 106, + 410, + 506, + 423 + ], + "spans": [ + { + "bbox": [ + 106, + 410, + 506, + 423 + ], + "score": 1.0, + "content": "Standard self-training with pseudo-labels uses unlabeled data efficiently for semi-supervised learn-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 420, + 506, + 435 + ], + "spans": [ + { + "bbox": [ + 105, + 420, + 506, + 435 + ], + "score": 1.0, + "content": "ing [31, 39, 57]. Here we carry out exploratory studies on the popular VisDA-2017 [45] dataset using", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 432, + 505, + 444 + ], + "spans": [ + { + "bbox": [ + 105, + 432, + 505, + 444 + ], + "score": 1.0, + "content": "ResNet-50 backbones. We find that domain shift makes the pseudo-labels biased towards several", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 443, + 500, + 455 + ], + "spans": [ + { + "bbox": [ + 106, + 443, + 500, + 455 + ], + "score": 1.0, + "content": "classes and thereby unreliable in UDA. See Appendix C.1 for details and results on more datasets.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 21.5, + "bbox_fs": [ + 105, + 410, + 506, + 455 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 459, + 505, + 580 + ], + "lines": [ + { + "bbox": [ + 106, + 460, + 506, + 472 + ], + "spans": [ + { + "bbox": [ + 106, + 460, + 506, + 472 + ], + "score": 1.0, + "content": "Pseudo-label distributions with or without domain shift. We resample the original VisDA-2017", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 471, + 505, + 483 + ], + "spans": [ + { + "bbox": [ + 105, + 471, + 505, + 483 + ], + "score": 1.0, + "content": "to simulate different relationship between source and target domains: 1) i.i.d., 2) covariate shift, and", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 481, + 506, + 494 + ], + "spans": [ + { + "bbox": [ + 105, + 481, + 506, + 494 + ], + "score": 1.0, + "content": "3) label shift. We train the model on the three variants of source dataset and use it to generate target", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 104, + 492, + 506, + 505 + ], + "spans": [ + { + "bbox": [ + 104, + 492, + 506, + 505 + ], + "score": 1.0, + "content": "pseudo-labels. We show the distributions of target ground-truths and pseudo-labels in Figure 2 (Left).", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 503, + 506, + 516 + ], + "spans": [ + { + "bbox": [ + 106, + 503, + 506, + 516 + ], + "score": 1.0, + "content": "When the source and target distributions are identical, the distribution of pseudo-labels is almost", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 514, + 506, + 527 + ], + "spans": [ + { + "bbox": [ + 106, + 514, + 506, + 527 + ], + "score": 1.0, + "content": "the same as ground-truths, indicating the reliability of pseudo-labels. In contrast, when exposed to", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 524, + 506, + 538 + ], + "spans": [ + { + "bbox": [ + 105, + 524, + 506, + 538 + ], + "score": 1.0, + "content": "label shift or covariate shift, the distribution of pseudo-labels is significantly different from target", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 536, + 506, + 549 + ], + "spans": [ + { + "bbox": [ + 105, + 536, + 506, + 549 + ], + "score": 1.0, + "content": "ground-truths. Note that classes 2, 7, 8 and 12 appear rarely in the target pseudo-labels in the covariate", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 547, + 506, + 559 + ], + "spans": [ + { + "bbox": [ + 106, + 547, + 506, + 559 + ], + "score": 1.0, + "content": "shift setting, indicating that the pseudo-labels are biased towards several classes due to domain shift.", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 558, + 506, + 570 + ], + "spans": [ + { + "bbox": [ + 105, + 558, + 506, + 570 + ], + "score": 1.0, + "content": "Self-training with these pseudo-labels is risky since it may lead to misalignment of distributions and", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 569, + 318, + 581 + ], + "spans": [ + { + "bbox": [ + 105, + 569, + 318, + 581 + ], + "score": 1.0, + "content": "misclassify many examples of classes 2, 7, 8 and 12.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 29, + "bbox_fs": [ + 104, + 460, + 506, + 581 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 585, + 505, + 673 + ], + "lines": [ + { + "bbox": [ + 106, + 584, + 506, + 598 + ], + "spans": [ + { + "bbox": [ + 106, + 584, + 506, + 598 + ], + "score": 1.0, + "content": "Change of pseudo-label distributions throughout training. To further study the change of pseudo-", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 596, + 506, + 609 + ], + "spans": [ + { + "bbox": [ + 105, + 596, + 506, + 609 + ], + "score": 1.0, + "content": "labels in standard self-training, we compute the total variation (TV) distance between target ground-", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 606, + 506, + 621 + ], + "spans": [ + { + "bbox": [ + 105, + 606, + 232, + 621 + ], + "score": 1.0, + "content": "truths and target pseudo-labels:", + "type": "text" + }, + { + "bbox": [ + 233, + 606, + 346, + 619 + ], + "score": 0.93, + "content": "\\begin{array} { r } { d _ { \\mathrm { T V } } ( c , \\dot { c ^ { \\prime } } ) = \\frac { 1 } { 2 } \\sum _ { i } \\| c _ { i } - c _ { i } ^ { \\prime } \\| } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 347, + 606, + 376, + 621 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 376, + 609, + 385, + 618 + ], + "score": 0.85, + "content": "c _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 386, + 606, + 462, + 621 + ], + "score": 1.0, + "content": "is the ratio of class", + "type": "text" + }, + { + "bbox": [ + 463, + 608, + 468, + 617 + ], + "score": 0.58, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 468, + 606, + 506, + 621 + ], + "score": 1.0, + "content": ". We plot", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 618, + 505, + 630 + ], + "spans": [ + { + "bbox": [ + 106, + 618, + 505, + 630 + ], + "score": 1.0, + "content": "its change during training in Figure 2 (Middle). Although the error rate of pseudo-labels continues", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 628, + 505, + 641 + ], + "spans": [ + { + "bbox": [ + 105, + 628, + 156, + 641 + ], + "score": 1.0, + "content": "to decrease,", + "type": "text" + }, + { + "bbox": [ + 157, + 629, + 173, + 640 + ], + "score": 0.87, + "content": "d _ { \\mathrm { T V } }", + "type": "inline_equation" + }, + { + "bbox": [ + 173, + 628, + 438, + 641 + ], + "score": 1.0, + "content": "remains almost unchanged at 0.26 throughout training. Note that", + "type": "text" + }, + { + "bbox": [ + 439, + 629, + 455, + 640 + ], + "score": 0.88, + "content": "d _ { \\mathrm { T V } }", + "type": "inline_equation" + }, + { + "bbox": [ + 455, + 628, + 505, + 641 + ], + "score": 1.0, + "content": "is the lower", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 640, + 505, + 652 + ], + "spans": [ + { + "bbox": [ + 106, + 640, + 393, + 652 + ], + "score": 1.0, + "content": "bound of the error rate of the pseudo-labels (shown in Appendix C.1). If", + "type": "text" + }, + { + "bbox": [ + 394, + 640, + 410, + 651 + ], + "score": 0.89, + "content": "d _ { \\mathrm { T V } }", + "type": "inline_equation" + }, + { + "bbox": [ + 410, + 640, + 505, + 652 + ], + "score": 1.0, + "content": "converges to 0.26, then", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 649, + 506, + 664 + ], + "spans": [ + { + "bbox": [ + 105, + 649, + 506, + 664 + ], + "score": 1.0, + "content": "the accuracy of pseudo-labels is upper-bounded by 0.74. This indicates that the important denoising", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 662, + 433, + 674 + ], + "spans": [ + { + "bbox": [ + 106, + 662, + 433, + 674 + ], + "score": 1.0, + "content": "ability [66] of pseudo-labels in standard self-training is hindered by domain shift.", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 38.5, + "bbox_fs": [ + 105, + 584, + 506, + 674 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 678, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 105, + 677, + 506, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 506, + 690 + ], + "score": 1.0, + "content": "Difficulty of selecting reliable pseudo-labels under domain shift. To mitigate the negative effect", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 689, + 505, + 701 + ], + "spans": [ + { + "bbox": [ + 106, + 689, + 505, + 701 + ], + "score": 1.0, + "content": "of false pseudo-labels, recent works proposed to select correct pseudo-labels based on thresholding the", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 700, + 505, + 713 + ], + "spans": [ + { + "bbox": [ + 105, + 700, + 505, + 713 + ], + "score": 1.0, + "content": "entropy or confidence criteria [35, 21, 37, 57]. However, it remains unclear whether these strategies", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 710, + 505, + 724 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 505, + 724 + ], + "score": 1.0, + "content": "are still effective under domain shift. Here we compare the quality of pseudo-labels selected by", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 73, + 505, + 85 + ], + "spans": [ + { + "bbox": [ + 106, + 73, + 505, + 85 + ], + "score": 1.0, + "content": "different strategies with or without domain shift. For each strategy, we compute False Positive Rate", + "type": "text", + "cross_page": true + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 83, + 505, + 96 + ], + "spans": [ + { + "bbox": [ + 106, + 83, + 505, + 96 + ], + "score": 1.0, + "content": "and True Positive Rate for different thresholds and plot its ROC curve in Figure 2 (Right). When the", + "type": "text", + "cross_page": true + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 94, + 505, + 107 + ], + "spans": [ + { + "bbox": [ + 105, + 94, + 505, + 107 + ], + "score": 1.0, + "content": "source and target distributions are identical, both entropy and confidence are reasonable strategies for", + "type": "text", + "cross_page": true + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 105, + 506, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 105, + 234, + 118 + ], + "score": 1.0, + "content": "selecting correct pseudo-labels", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 234, + 105, + 281, + 117 + ], + "score": 0.55, + "content": "( \\mathrm { A U C } { = } 0 . 8 9 )", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 281, + 105, + 506, + 118 + ], + "score": 1.0, + "content": "). However, when the target pseudo-labels are generated", + "type": "text", + "cross_page": true + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 116, + 506, + 129 + ], + "spans": [ + { + "bbox": [ + 105, + 116, + 454, + 129 + ], + "score": 1.0, + "content": "by the source model, the quality of pseudo-labels decreases sharply under domain shift", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 455, + 117, + 500, + 127 + ], + "score": 0.51, + "content": "\\mathrm { \\Delta A U C { = } 0 . 7 8 }", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 501, + 116, + 506, + 129 + ], + "score": 1.0, + "content": ").", + "type": "text", + "cross_page": true + } + ], + "index": 4 + } + ], + "index": 44.5, + "bbox_fs": [ + 105, + 677, + 506, + 724 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 72, + 505, + 128 + ], + "lines": [ + { + "bbox": [ + 106, + 73, + 505, + 85 + ], + "spans": [ + { + "bbox": [ + 106, + 73, + 505, + 85 + ], + "score": 1.0, + "content": "different strategies with or without domain shift. For each strategy, we compute False Positive Rate", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 83, + 505, + 96 + ], + "spans": [ + { + "bbox": [ + 106, + 83, + 505, + 96 + ], + "score": 1.0, + "content": "and True Positive Rate for different thresholds and plot its ROC curve in Figure 2 (Right). When the", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 94, + 505, + 107 + ], + "spans": [ + { + "bbox": [ + 105, + 94, + 505, + 107 + ], + "score": 1.0, + "content": "source and target distributions are identical, both entropy and confidence are reasonable strategies for", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 105, + 506, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 105, + 234, + 118 + ], + "score": 1.0, + "content": "selecting correct pseudo-labels", + "type": "text" + }, + { + "bbox": [ + 234, + 105, + 281, + 117 + ], + "score": 0.55, + "content": "( \\mathrm { A U C } { = } 0 . 8 9 )", + "type": "inline_equation" + }, + { + "bbox": [ + 281, + 105, + 506, + 118 + ], + "score": 1.0, + "content": "). However, when the target pseudo-labels are generated", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 116, + 506, + 129 + ], + "spans": [ + { + "bbox": [ + 105, + 116, + 454, + 129 + ], + "score": 1.0, + "content": "by the source model, the quality of pseudo-labels decreases sharply under domain shift", + "type": "text" + }, + { + "bbox": [ + 455, + 117, + 500, + 127 + ], + "score": 0.51, + "content": "\\mathrm { \\Delta A U C { = } 0 . 7 8 }", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 116, + 506, + 129 + ], + "score": 1.0, + "content": ").", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 2 + }, + { + "type": "title", + "bbox": [ + 107, + 138, + 177, + 152 + ], + "lines": [ + { + "bbox": [ + 103, + 135, + 178, + 155 + ], + "spans": [ + { + "bbox": [ + 103, + 135, + 178, + 155 + ], + "score": 1.0, + "content": "3 Approach", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 5 + }, + { + "type": "text", + "bbox": [ + 107, + 157, + 505, + 191 + ], + "lines": [ + { + "bbox": [ + 105, + 157, + 506, + 170 + ], + "spans": [ + { + "bbox": [ + 105, + 157, + 506, + 170 + ], + "score": 1.0, + "content": "We present Cycle Self-Training (CST) to improve pseudo-labels under domain shift. An overview of", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 168, + 505, + 181 + ], + "spans": [ + { + "bbox": [ + 105, + 168, + 505, + 181 + ], + "score": 1.0, + "content": "our method is given in Figure 1. Cycle Self-Training iterates between a forward step and a reverse", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 179, + 454, + 192 + ], + "spans": [ + { + "bbox": [ + 105, + 179, + 454, + 192 + ], + "score": 1.0, + "content": "step to make self-trained classifiers generalize well on both target and source domains.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 7 + }, + { + "type": "title", + "bbox": [ + 107, + 195, + 214, + 207 + ], + "lines": [ + { + "bbox": [ + 104, + 192, + 215, + 210 + ], + "spans": [ + { + "bbox": [ + 104, + 192, + 215, + 210 + ], + "score": 1.0, + "content": "3.1 Cycle Self-Training", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 9 + }, + { + "type": "text", + "bbox": [ + 106, + 210, + 504, + 233 + ], + "lines": [ + { + "bbox": [ + 106, + 210, + 505, + 223 + ], + "spans": [ + { + "bbox": [ + 106, + 210, + 410, + 223 + ], + "score": 1.0, + "content": "Forward Step. Similar to standard self-training, we have a source classifier", + "type": "text" + }, + { + "bbox": [ + 411, + 211, + 421, + 222 + ], + "score": 0.88, + "content": "\\theta _ { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 421, + 210, + 505, + 223 + ], + "score": 1.0, + "content": "trained on top of the", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 221, + 505, + 234 + ], + "spans": [ + { + "bbox": [ + 106, + 221, + 197, + 234 + ], + "score": 1.0, + "content": "shared representations", + "type": "text" + }, + { + "bbox": [ + 197, + 222, + 204, + 233 + ], + "score": 0.85, + "content": "\\phi", + "type": "inline_equation" + }, + { + "bbox": [ + 205, + 221, + 505, + 234 + ], + "score": 1.0, + "content": "on the labeled source domain, and use it to generate target pseudo-labels as", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 10.5 + }, + { + "type": "interline_equation", + "bbox": [ + 249, + 237, + 361, + 257 + ], + "lines": [ + { + "bbox": [ + 249, + 237, + 361, + 257 + ], + "spans": [ + { + "bbox": [ + 249, + 237, + 361, + 257 + ], + "score": 0.94, + "content": "y ^ { \\prime } = \\arg \\operatorname* { m a x } _ { i } \\{ f _ { \\theta _ { s } , \\phi } ( x ) _ { [ i ] } \\} ,", + "type": "interline_equation", + "image_path": "f320bf246563b81f6d2648d2fdd1228bfad0d9c84e43d970ceea81de6211fd67.jpg" + } + ] + } + ], + "index": 12, + "virtual_lines": [ + { + "bbox": [ + 249, + 237, + 361, + 257 + ], + "spans": [], + "index": 12 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 262, + 505, + 375 + ], + "lines": [ + { + "bbox": [ + 105, + 263, + 506, + 277 + ], + "spans": [ + { + "bbox": [ + 105, + 263, + 141, + 277 + ], + "score": 1.0, + "content": "for each", + "type": "text" + }, + { + "bbox": [ + 142, + 267, + 149, + 275 + ], + "score": 0.74, + "content": "x", + "type": "inline_equation" + }, + { + "bbox": [ + 149, + 263, + 230, + 277 + ], + "score": 1.0, + "content": "in the target dataset", + "type": "text" + }, + { + "bbox": [ + 231, + 263, + 240, + 276 + ], + "score": 0.86, + "content": "\\widehat { Q }", + "type": "inline_equation" + }, + { + "bbox": [ + 240, + 263, + 506, + 277 + ], + "score": 1.0, + "content": ". Traditional self-training methods use confidence thresholding or", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 276, + 505, + 288 + ], + "spans": [ + { + "bbox": [ + 105, + 276, + 505, + 288 + ], + "score": 1.0, + "content": "reweighting to select reliable pseudo-labels. For example, Sohn et al. [57] select pseudo-labels with", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 286, + 505, + 299 + ], + "spans": [ + { + "bbox": [ + 106, + 286, + 505, + 299 + ], + "score": 1.0, + "content": "softmax value and Long et al. [37] add entropy reweighting to rely on examples with more confidence", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 298, + 505, + 310 + ], + "spans": [ + { + "bbox": [ + 105, + 298, + 505, + 310 + ], + "score": 1.0, + "content": "prediction. However, the output of deep networks is usually miscalibrated [25], and is not necessarily", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 309, + 505, + 320 + ], + "spans": [ + { + "bbox": [ + 106, + 309, + 505, + 320 + ], + "score": 1.0, + "content": "related to the ground-truth confidence even on the same distribution. In domain adaptation, as shown", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 320, + 506, + 333 + ], + "spans": [ + { + "bbox": [ + 105, + 320, + 506, + 333 + ], + "score": 1.0, + "content": "in Section 2.1, the discrepancy between the source and target domains makes pseudo-labels even", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 104, + 329, + 507, + 344 + ], + "spans": [ + { + "bbox": [ + 104, + 329, + 507, + 344 + ], + "score": 1.0, + "content": "more unreliable, and the performance of commonly used selection strategies is also unsatisfactory.", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 341, + 506, + 354 + ], + "spans": [ + { + "bbox": [ + 106, + 341, + 506, + 354 + ], + "score": 1.0, + "content": "Another drawback is the expensive tweaking in order to find the optimal confidence threshold for", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 353, + 504, + 364 + ], + "spans": [ + { + "bbox": [ + 106, + 353, + 504, + 364 + ], + "score": 1.0, + "content": "new tasks. To better apply self-training to domain adaptation, we expect that the model can gradually", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 104, + 362, + 443, + 377 + ], + "spans": [ + { + "bbox": [ + 104, + 362, + 443, + 377 + ], + "score": 1.0, + "content": "refine the pseudo-labels by itself without the cumbersome selection or thresholding.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 17.5 + }, + { + "type": "text", + "bbox": [ + 106, + 379, + 505, + 456 + ], + "lines": [ + { + "bbox": [ + 105, + 378, + 506, + 393 + ], + "spans": [ + { + "bbox": [ + 105, + 378, + 506, + 393 + ], + "score": 1.0, + "content": "Reverse Step. We design a complementary step with the following insights to improve self-training.", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 391, + 505, + 402 + ], + "spans": [ + { + "bbox": [ + 106, + 391, + 505, + 402 + ], + "score": 1.0, + "content": "Intuitively, the labels on the source domain contain both useful information that can transfer to the", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 401, + 505, + 413 + ], + "spans": [ + { + "bbox": [ + 105, + 401, + 505, + 413 + ], + "score": 1.0, + "content": "target domain and harmful information that can make pseudo-labels incorrect. Similarly, reliable", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 104, + 412, + 506, + 424 + ], + "spans": [ + { + "bbox": [ + 104, + 412, + 506, + 424 + ], + "score": 1.0, + "content": "pseudo-labels on the target domain can transfer to the source domain in turn, while models trained", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 423, + 506, + 436 + ], + "spans": [ + { + "bbox": [ + 105, + 423, + 506, + 436 + ], + "score": 1.0, + "content": "with incorrect pseudo-labels on the target domain cannot transfer to the source domain. In this sense,", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 434, + 506, + 446 + ], + "spans": [ + { + "bbox": [ + 105, + 434, + 506, + 446 + ], + "score": 1.0, + "content": "if we explicitly train the model to make target pseudo-labels informative of the source domain, we", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 444, + 495, + 457 + ], + "spans": [ + { + "bbox": [ + 105, + 444, + 495, + 457 + ], + "score": 1.0, + "content": "can gradually make the pseudo-labels more accurate and learn to generalize to the target domain.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 26 + }, + { + "type": "text", + "bbox": [ + 106, + 460, + 503, + 486 + ], + "lines": [ + { + "bbox": [ + 106, + 460, + 506, + 474 + ], + "spans": [ + { + "bbox": [ + 106, + 460, + 250, + 474 + ], + "score": 1.0, + "content": "Specifically, with the pseudo-labels", + "type": "text" + }, + { + "bbox": [ + 250, + 461, + 259, + 473 + ], + "score": 0.87, + "content": "y ^ { \\prime }", + "type": "inline_equation" + }, + { + "bbox": [ + 260, + 460, + 395, + 474 + ], + "score": 1.0, + "content": "generated by the source classifier", + "type": "text" + }, + { + "bbox": [ + 396, + 462, + 406, + 472 + ], + "score": 0.88, + "content": "\\theta _ { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 406, + 460, + 506, + 474 + ], + "score": 1.0, + "content": "at hand as in equation 3,", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 472, + 502, + 488 + ], + "spans": [ + { + "bbox": [ + 105, + 473, + 192, + 488 + ], + "score": 1.0, + "content": "we train a target head", + "type": "text" + }, + { + "bbox": [ + 192, + 472, + 215, + 486 + ], + "score": 0.93, + "content": "\\hat { \\theta } _ { t } ( \\phi )", + "type": "inline_equation" + }, + { + "bbox": [ + 216, + 473, + 326, + 488 + ], + "score": 1.0, + "content": "on top of the representation", + "type": "text" + }, + { + "bbox": [ + 327, + 475, + 334, + 486 + ], + "score": 0.86, + "content": "\\phi", + "type": "inline_equation" + }, + { + "bbox": [ + 334, + 473, + 494, + 488 + ], + "score": 1.0, + "content": "with pseudo-labels on the target domain", + "type": "text" + }, + { + "bbox": [ + 494, + 473, + 502, + 486 + ], + "score": 0.88, + "content": "\\widehat { Q }", + "type": "inline_equation" + } + ], + "index": 31 + } + ], + "index": 30.5 + }, + { + "type": "interline_equation", + "bbox": [ + 229, + 491, + 382, + 512 + ], + "lines": [ + { + "bbox": [ + 229, + 491, + 382, + 512 + ], + "spans": [ + { + "bbox": [ + 229, + 491, + 382, + 512 + ], + "score": 0.94, + "content": "\\hat { \\theta } _ { t } ( \\phi ) = \\underset { \\theta } { \\arg \\operatorname* { m i n } } \\mathbb { E } _ { \\boldsymbol { x } \\sim \\hat { \\boldsymbol { Q } } } \\ell ( f _ { \\theta , \\phi } ( \\boldsymbol { x } ) , y ^ { \\prime } ) .", + "type": "interline_equation", + "image_path": "03699fae3f7b59b86374fb91a0f3d780b856c7a8778a428e47452fb369f5cccb.jpg" + } + ] + } + ], + "index": 32, + "virtual_lines": [ + { + "bbox": [ + 229, + 491, + 382, + 512 + ], + "spans": [], + "index": 32 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 516, + 505, + 563 + ], + "lines": [ + { + "bbox": [ + 106, + 516, + 506, + 528 + ], + "spans": [ + { + "bbox": [ + 106, + 516, + 506, + 528 + ], + "score": 1.0, + "content": "We wish to make the target pseudo-labels informative of the source domain and gradually refine them.", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 527, + 505, + 539 + ], + "spans": [ + { + "bbox": [ + 105, + 527, + 308, + 539 + ], + "score": 1.0, + "content": "To this end, we update the shared feature extractor", + "type": "text" + }, + { + "bbox": [ + 309, + 528, + 316, + 539 + ], + "score": 0.86, + "content": "\\phi", + "type": "inline_equation" + }, + { + "bbox": [ + 316, + 527, + 505, + 539 + ], + "score": 1.0, + "content": "to predict accurately on the source domain and", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 104, + 538, + 505, + 553 + ], + "spans": [ + { + "bbox": [ + 104, + 539, + 245, + 553 + ], + "score": 1.0, + "content": "jointly enforce the target classifier", + "type": "text" + }, + { + "bbox": [ + 245, + 538, + 268, + 552 + ], + "score": 0.92, + "content": "\\hat { \\theta } _ { t } ( \\phi )", + "type": "inline_equation" + }, + { + "bbox": [ + 268, + 539, + 505, + 553 + ], + "score": 1.0, + "content": "to perform well on the source domain. This naturally leads", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 550, + 268, + 565 + ], + "spans": [ + { + "bbox": [ + 105, + 550, + 268, + 565 + ], + "score": 1.0, + "content": "to the objective of Cycle Self-Training:", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 34.5 + }, + { + "type": "interline_equation", + "bbox": [ + 196, + 567, + 414, + 588 + ], + "lines": [ + { + "bbox": [ + 196, + 567, + 414, + 588 + ], + "spans": [ + { + "bbox": [ + 196, + 567, + 414, + 588 + ], + "score": 0.91, + "content": "\\operatorname* { m i n i m i z e } _ { \\theta _ { s } , \\phi } L _ { \\mathrm { C y c l e } } ( \\theta _ { s } , \\phi ) : = L _ { \\hat { P } } ( \\theta _ { s } , \\phi ) + L _ { \\hat { P } } ( \\hat { \\theta } _ { t } ( \\phi ) , \\phi ) .", + "type": "interline_equation", + "image_path": "ed81524779eb8a44184f8a5fa701e5693bc66a771d5cf2175c8b352bbc8f7bc8.jpg" + } + ] + } + ], + "index": 37, + "virtual_lines": [ + { + "bbox": [ + 196, + 567, + 414, + 588 + ], + "spans": [], + "index": 37 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 590, + 506, + 728 + ], + "lines": [ + { + "bbox": [ + 106, + 590, + 505, + 604 + ], + "spans": [ + { + "bbox": [ + 106, + 591, + 405, + 604 + ], + "score": 1.0, + "content": "Bi-level Optimization. The objective in equation 5 relies on the solution", + "type": "text" + }, + { + "bbox": [ + 405, + 590, + 428, + 603 + ], + "score": 0.92, + "content": "\\hat { \\theta } _ { t } ( \\phi )", + "type": "inline_equation" + }, + { + "bbox": [ + 428, + 591, + 505, + 604 + ], + "score": 1.0, + "content": "to the objective in", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 602, + 506, + 615 + ], + "spans": [ + { + "bbox": [ + 106, + 602, + 506, + 615 + ], + "score": 1.0, + "content": "equation 4. Thus, CST formulates a bi-level optimization problem. In the inner loop we generate", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 612, + 506, + 626 + ], + "spans": [ + { + "bbox": [ + 105, + 612, + 506, + 626 + ], + "score": 1.0, + "content": "target pseudo-labels with the source classifier (equation 3), and train a target classifier with target", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 623, + 506, + 637 + ], + "spans": [ + { + "bbox": [ + 105, + 623, + 436, + 637 + ], + "score": 1.0, + "content": "pseudo-labels (equation 4). 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However, since the inner loop of the", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 646, + 506, + 658 + ], + "spans": [ + { + "bbox": [ + 106, + 646, + 381, + 658 + ], + "score": 1.0, + "content": "optimization in equation 4 only involves the light-weight linear head", + "type": "text" + }, + { + "bbox": [ + 381, + 646, + 390, + 657 + ], + "score": 0.87, + "content": "\\theta _ { t }", + "type": "inline_equation" + }, + { + "bbox": [ + 390, + 646, + 506, + 658 + ], + "score": 1.0, + "content": ", we propose to calculate the", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 657, + 505, + 671 + ], + "spans": [ + { + "bbox": [ + 105, + 658, + 180, + 671 + ], + "score": 1.0, + "content": "analytical form of", + "type": "text" + }, + { + "bbox": [ + 180, + 657, + 203, + 671 + ], + "score": 0.92, + "content": "\\hat { \\theta } _ { t } ( \\phi )", + "type": "inline_equation" + }, + { + "bbox": [ + 203, + 658, + 410, + 671 + ], + "score": 1.0, + "content": "and directly back-propagate to the feature extractor", + "type": "text" + }, + { + "bbox": [ + 410, + 659, + 417, + 670 + ], + "score": 0.85, + "content": "\\phi", + "type": "inline_equation" + }, + { + "bbox": [ + 417, + 658, + 505, + 671 + ], + "score": 1.0, + "content": "instead of calculating", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 668, + 506, + 682 + ], + "spans": [ + { + "bbox": [ + 105, + 668, + 506, + 682 + ], + "score": 1.0, + "content": "the second-order derivatives as in MAML [18]. The resulting framework is as fast as training two", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 682, + 505, + 694 + ], + "spans": [ + { + "bbox": [ + 105, + 682, + 277, + 694 + ], + "score": 1.0, + "content": "heads jointly. Also note that the solution", + "type": "text" + }, + { + "bbox": [ + 277, + 682, + 299, + 694 + ], + "score": 0.93, + "content": "\\hat { \\theta } _ { t } ( \\phi )", + "type": "inline_equation" + }, + { + "bbox": [ + 300, + 682, + 339, + 694 + ], + "score": 1.0, + "content": "relies on", + "type": "text" + }, + { + "bbox": [ + 340, + 683, + 349, + 693 + ], + "score": 0.86, + "content": "\\theta _ { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 349, + 682, + 428, + 694 + ], + "score": 1.0, + "content": "implicitly through", + "type": "text" + }, + { + "bbox": [ + 428, + 682, + 437, + 693 + ], + "score": 0.85, + "content": "y ^ { \\prime }", + "type": "inline_equation" + }, + { + "bbox": [ + 437, + 682, + 505, + 694 + ], + "score": 1.0, + "content": ". However, both", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 693, + 506, + 705 + ], + "spans": [ + { + "bbox": [ + 105, + 693, + 420, + 705 + ], + "score": 1.0, + "content": "standard self-training and our implementation use label sharpening, making", + "type": "text" + }, + { + "bbox": [ + 420, + 694, + 429, + 705 + ], + "score": 0.86, + "content": "y ^ { \\prime }", + "type": "inline_equation" + }, + { + "bbox": [ + 430, + 693, + 506, + 705 + ], + "score": 1.0, + "content": "not differentiable.", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 704, + 506, + 719 + ], + "spans": [ + { + "bbox": [ + 105, + 704, + 383, + 719 + ], + "score": 1.0, + "content": "Thus we follow vanilla self-training and do not consider the gradient of", + "type": "text" + }, + { + "bbox": [ + 384, + 705, + 406, + 718 + ], + "score": 0.93, + "content": "\\hat { \\theta } _ { t } ( \\phi )", + "type": "inline_equation" + }, + { + "bbox": [ + 406, + 704, + 429, + 719 + ], + "score": 1.0, + "content": "w.r.t.", + "type": "text" + }, + { + "bbox": [ + 429, + 705, + 438, + 717 + ], + "score": 0.87, + "content": "y ^ { \\prime }", + "type": "inline_equation" + }, + { + "bbox": [ + 439, + 704, + 506, + 719 + ], + "score": 1.0, + "content": "in the outer loop", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 716, + 506, + 729 + ], + "spans": [ + { + "bbox": [ + 105, + 716, + 506, + 729 + ], + "score": 1.0, + "content": "optimization. We defer the derivation and implementation of bi-level optimization to Appendix B.2.", + "type": "text" + } + ], + "index": 49 + } + ], + "index": 43.5 + } + ], + "page_idx": 3, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 302, + 742, + 308, + 750 + ], + "lines": [ + { + "bbox": [ + 301, + 741, + 310, + 752 + ], + "spans": [ + { + "bbox": [ + 301, + 741, + 310, + 752 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 11, + "width": 9 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 72, + 505, + 128 + ], + "lines": [], + "index": 2, + "bbox_fs": [ + 105, + 73, + 506, + 129 + ], + "lines_deleted": true + }, + { + "type": "title", + "bbox": [ + 107, + 138, + 177, + 152 + ], + "lines": [ + { + "bbox": [ + 103, + 135, + 178, + 155 + ], + "spans": [ + { + "bbox": [ + 103, + 135, + 178, + 155 + ], + "score": 1.0, + "content": "3 Approach", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 5 + }, + { + "type": "text", + "bbox": [ + 107, + 157, + 505, + 191 + ], + "lines": [ + { + "bbox": [ + 105, + 157, + 506, + 170 + ], + "spans": [ + { + "bbox": [ + 105, + 157, + 506, + 170 + ], + "score": 1.0, + "content": "We present Cycle Self-Training (CST) to improve pseudo-labels under domain shift. An overview of", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 168, + 505, + 181 + ], + "spans": [ + { + "bbox": [ + 105, + 168, + 505, + 181 + ], + "score": 1.0, + "content": "our method is given in Figure 1. Cycle Self-Training iterates between a forward step and a reverse", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 179, + 454, + 192 + ], + "spans": [ + { + "bbox": [ + 105, + 179, + 454, + 192 + ], + "score": 1.0, + "content": "step to make self-trained classifiers generalize well on both target and source domains.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 7, + "bbox_fs": [ + 105, + 157, + 506, + 192 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 195, + 214, + 207 + ], + "lines": [ + { + "bbox": [ + 104, + 192, + 215, + 210 + ], + "spans": [ + { + "bbox": [ + 104, + 192, + 215, + 210 + ], + "score": 1.0, + "content": "3.1 Cycle Self-Training", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 9 + }, + { + "type": "text", + "bbox": [ + 106, + 210, + 504, + 233 + ], + "lines": [ + { + "bbox": [ + 106, + 210, + 505, + 223 + ], + "spans": [ + { + "bbox": [ + 106, + 210, + 410, + 223 + ], + "score": 1.0, + "content": "Forward Step. Similar to standard self-training, we have a source classifier", + "type": "text" + }, + { + "bbox": [ + 411, + 211, + 421, + 222 + ], + "score": 0.88, + "content": "\\theta _ { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 421, + 210, + 505, + 223 + ], + "score": 1.0, + "content": "trained on top of the", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 221, + 505, + 234 + ], + "spans": [ + { + "bbox": [ + 106, + 221, + 197, + 234 + ], + "score": 1.0, + "content": "shared representations", + "type": "text" + }, + { + "bbox": [ + 197, + 222, + 204, + 233 + ], + "score": 0.85, + "content": "\\phi", + "type": "inline_equation" + }, + { + "bbox": [ + 205, + 221, + 505, + 234 + ], + "score": 1.0, + "content": "on the labeled source domain, and use it to generate target pseudo-labels as", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 10.5, + "bbox_fs": [ + 106, + 210, + 505, + 234 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 249, + 237, + 361, + 257 + ], + "lines": [ + { + "bbox": [ + 249, + 237, + 361, + 257 + ], + "spans": [ + { + "bbox": [ + 249, + 237, + 361, + 257 + ], + "score": 0.94, + "content": "y ^ { \\prime } = \\arg \\operatorname* { m a x } _ { i } \\{ f _ { \\theta _ { s } , \\phi } ( x ) _ { [ i ] } \\} ,", + "type": "interline_equation", + "image_path": "f320bf246563b81f6d2648d2fdd1228bfad0d9c84e43d970ceea81de6211fd67.jpg" + } + ] + } + ], + "index": 12, + "virtual_lines": [ + { + "bbox": [ + 249, + 237, + 361, + 257 + ], + "spans": [], + "index": 12 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 262, + 505, + 375 + ], + "lines": [ + { + "bbox": [ + 105, + 263, + 506, + 277 + ], + "spans": [ + { + "bbox": [ + 105, + 263, + 141, + 277 + ], + "score": 1.0, + "content": "for each", + "type": "text" + }, + { + "bbox": [ + 142, + 267, + 149, + 275 + ], + "score": 0.74, + "content": "x", + "type": "inline_equation" + }, + { + "bbox": [ + 149, + 263, + 230, + 277 + ], + "score": 1.0, + "content": "in the target dataset", + "type": "text" + }, + { + "bbox": [ + 231, + 263, + 240, + 276 + ], + "score": 0.86, + "content": "\\widehat { Q }", + "type": "inline_equation" + }, + { + "bbox": [ + 240, + 263, + 506, + 277 + ], + "score": 1.0, + "content": ". Traditional self-training methods use confidence thresholding or", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 276, + 505, + 288 + ], + "spans": [ + { + "bbox": [ + 105, + 276, + 505, + 288 + ], + "score": 1.0, + "content": "reweighting to select reliable pseudo-labels. For example, Sohn et al. [57] select pseudo-labels with", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 286, + 505, + 299 + ], + "spans": [ + { + "bbox": [ + 106, + 286, + 505, + 299 + ], + "score": 1.0, + "content": "softmax value and Long et al. [37] add entropy reweighting to rely on examples with more confidence", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 298, + 505, + 310 + ], + "spans": [ + { + "bbox": [ + 105, + 298, + 505, + 310 + ], + "score": 1.0, + "content": "prediction. However, the output of deep networks is usually miscalibrated [25], and is not necessarily", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 309, + 505, + 320 + ], + "spans": [ + { + "bbox": [ + 106, + 309, + 505, + 320 + ], + "score": 1.0, + "content": "related to the ground-truth confidence even on the same distribution. In domain adaptation, as shown", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 320, + 506, + 333 + ], + "spans": [ + { + "bbox": [ + 105, + 320, + 506, + 333 + ], + "score": 1.0, + "content": "in Section 2.1, the discrepancy between the source and target domains makes pseudo-labels even", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 104, + 329, + 507, + 344 + ], + "spans": [ + { + "bbox": [ + 104, + 329, + 507, + 344 + ], + "score": 1.0, + "content": "more unreliable, and the performance of commonly used selection strategies is also unsatisfactory.", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 341, + 506, + 354 + ], + "spans": [ + { + "bbox": [ + 106, + 341, + 506, + 354 + ], + "score": 1.0, + "content": "Another drawback is the expensive tweaking in order to find the optimal confidence threshold for", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 353, + 504, + 364 + ], + "spans": [ + { + "bbox": [ + 106, + 353, + 504, + 364 + ], + "score": 1.0, + "content": "new tasks. To better apply self-training to domain adaptation, we expect that the model can gradually", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 104, + 362, + 443, + 377 + ], + "spans": [ + { + "bbox": [ + 104, + 362, + 443, + 377 + ], + "score": 1.0, + "content": "refine the pseudo-labels by itself without the cumbersome selection or thresholding.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 17.5, + "bbox_fs": [ + 104, + 263, + 507, + 377 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 379, + 505, + 456 + ], + "lines": [ + { + "bbox": [ + 105, + 378, + 506, + 393 + ], + "spans": [ + { + "bbox": [ + 105, + 378, + 506, + 393 + ], + "score": 1.0, + "content": "Reverse Step. We design a complementary step with the following insights to improve self-training.", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 391, + 505, + 402 + ], + "spans": [ + { + "bbox": [ + 106, + 391, + 505, + 402 + ], + "score": 1.0, + "content": "Intuitively, the labels on the source domain contain both useful information that can transfer to the", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 401, + 505, + 413 + ], + "spans": [ + { + "bbox": [ + 105, + 401, + 505, + 413 + ], + "score": 1.0, + "content": "target domain and harmful information that can make pseudo-labels incorrect. Similarly, reliable", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 104, + 412, + 506, + 424 + ], + "spans": [ + { + "bbox": [ + 104, + 412, + 506, + 424 + ], + "score": 1.0, + "content": "pseudo-labels on the target domain can transfer to the source domain in turn, while models trained", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 423, + 506, + 436 + ], + "spans": [ + { + "bbox": [ + 105, + 423, + 506, + 436 + ], + "score": 1.0, + "content": "with incorrect pseudo-labels on the target domain cannot transfer to the source domain. In this sense,", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 434, + 506, + 446 + ], + "spans": [ + { + "bbox": [ + 105, + 434, + 506, + 446 + ], + "score": 1.0, + "content": "if we explicitly train the model to make target pseudo-labels informative of the source domain, we", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 444, + 495, + 457 + ], + "spans": [ + { + "bbox": [ + 105, + 444, + 495, + 457 + ], + "score": 1.0, + "content": "can gradually make the pseudo-labels more accurate and learn to generalize to the target domain.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 26, + "bbox_fs": [ + 104, + 378, + 506, + 457 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 460, + 503, + 486 + ], + "lines": [ + { + "bbox": [ + 106, + 460, + 506, + 474 + ], + "spans": [ + { + "bbox": [ + 106, + 460, + 250, + 474 + ], + "score": 1.0, + "content": "Specifically, with the pseudo-labels", + "type": "text" + }, + { + "bbox": [ + 250, + 461, + 259, + 473 + ], + "score": 0.87, + "content": "y ^ { \\prime }", + "type": "inline_equation" + }, + { + "bbox": [ + 260, + 460, + 395, + 474 + ], + "score": 1.0, + "content": "generated by the source classifier", + "type": "text" + }, + { + "bbox": [ + 396, + 462, + 406, + 472 + ], + "score": 0.88, + "content": "\\theta _ { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 406, + 460, + 506, + 474 + ], + "score": 1.0, + "content": "at hand as in equation 3,", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 472, + 502, + 488 + ], + "spans": [ + { + "bbox": [ + 105, + 473, + 192, + 488 + ], + "score": 1.0, + "content": "we train a target head", + "type": "text" + }, + { + "bbox": [ + 192, + 472, + 215, + 486 + ], + "score": 0.93, + "content": "\\hat { \\theta } _ { t } ( \\phi )", + "type": "inline_equation" + }, + { + "bbox": [ + 216, + 473, + 326, + 488 + ], + "score": 1.0, + "content": "on top of the representation", + "type": "text" + }, + { + "bbox": [ + 327, + 475, + 334, + 486 + ], + "score": 0.86, + "content": "\\phi", + "type": "inline_equation" + }, + { + "bbox": [ + 334, + 473, + 494, + 488 + ], + "score": 1.0, + "content": "with pseudo-labels on the target domain", + "type": "text" + }, + { + "bbox": [ + 494, + 473, + 502, + 486 + ], + "score": 0.88, + "content": "\\widehat { Q }", + "type": "inline_equation" + } + ], + "index": 31 + } + ], + "index": 30.5, + "bbox_fs": [ + 105, + 460, + 506, + 488 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 229, + 491, + 382, + 512 + ], + "lines": [ + { + "bbox": [ + 229, + 491, + 382, + 512 + ], + "spans": [ + { + "bbox": [ + 229, + 491, + 382, + 512 + ], + "score": 0.94, + "content": "\\hat { \\theta } _ { t } ( \\phi ) = \\underset { \\theta } { \\arg \\operatorname* { m i n } } \\mathbb { E } _ { \\boldsymbol { x } \\sim \\hat { \\boldsymbol { Q } } } \\ell ( f _ { \\theta , \\phi } ( \\boldsymbol { x } ) , y ^ { \\prime } ) .", + "type": "interline_equation", + "image_path": "03699fae3f7b59b86374fb91a0f3d780b856c7a8778a428e47452fb369f5cccb.jpg" + } + ] + } + ], + "index": 32, + "virtual_lines": [ + { + "bbox": [ + 229, + 491, + 382, + 512 + ], + "spans": [], + "index": 32 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 516, + 505, + 563 + ], + "lines": [ + { + "bbox": [ + 106, + 516, + 506, + 528 + ], + "spans": [ + { + "bbox": [ + 106, + 516, + 506, + 528 + ], + "score": 1.0, + "content": "We wish to make the target pseudo-labels informative of the source domain and gradually refine them.", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 527, + 505, + 539 + ], + "spans": [ + { + "bbox": [ + 105, + 527, + 308, + 539 + ], + "score": 1.0, + "content": "To this end, we update the shared feature extractor", + "type": "text" + }, + { + "bbox": [ + 309, + 528, + 316, + 539 + ], + "score": 0.86, + "content": "\\phi", + "type": "inline_equation" + }, + { + "bbox": [ + 316, + 527, + 505, + 539 + ], + "score": 1.0, + "content": "to predict accurately on the source domain and", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 104, + 538, + 505, + 553 + ], + "spans": [ + { + "bbox": [ + 104, + 539, + 245, + 553 + ], + "score": 1.0, + "content": "jointly enforce the target classifier", + "type": "text" + }, + { + "bbox": [ + 245, + 538, + 268, + 552 + ], + "score": 0.92, + "content": "\\hat { \\theta } _ { t } ( \\phi )", + "type": "inline_equation" + }, + { + "bbox": [ + 268, + 539, + 505, + 553 + ], + "score": 1.0, + "content": "to perform well on the source domain. This naturally leads", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 550, + 268, + 565 + ], + "spans": [ + { + "bbox": [ + 105, + 550, + 268, + 565 + ], + "score": 1.0, + "content": "to the objective of Cycle Self-Training:", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 34.5, + "bbox_fs": [ + 104, + 516, + 506, + 565 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 196, + 567, + 414, + 588 + ], + "lines": [ + { + "bbox": [ + 196, + 567, + 414, + 588 + ], + "spans": [ + { + "bbox": [ + 196, + 567, + 414, + 588 + ], + "score": 0.91, + "content": "\\operatorname* { m i n i m i z e } _ { \\theta _ { s } , \\phi } L _ { \\mathrm { C y c l e } } ( \\theta _ { s } , \\phi ) : = L _ { \\hat { P } } ( \\theta _ { s } , \\phi ) + L _ { \\hat { P } } ( \\hat { \\theta } _ { t } ( \\phi ) , \\phi ) .", + "type": "interline_equation", + "image_path": "ed81524779eb8a44184f8a5fa701e5693bc66a771d5cf2175c8b352bbc8f7bc8.jpg" + } + ] + } + ], + "index": 37, + "virtual_lines": [ + { + "bbox": [ + 196, + 567, + 414, + 588 + ], + "spans": [], + "index": 37 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 590, + 506, + 728 + ], + "lines": [ + { + "bbox": [ + 106, + 590, + 505, + 604 + ], + "spans": [ + { + "bbox": [ + 106, + 591, + 405, + 604 + ], + "score": 1.0, + "content": "Bi-level Optimization. The objective in equation 5 relies on the solution", + "type": "text" + }, + { + "bbox": [ + 405, + 590, + 428, + 603 + ], + "score": 0.92, + "content": "\\hat { \\theta } _ { t } ( \\phi )", + "type": "inline_equation" + }, + { + "bbox": [ + 428, + 591, + 505, + 604 + ], + "score": 1.0, + "content": "to the objective in", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 602, + 506, + 615 + ], + "spans": [ + { + "bbox": [ + 106, + 602, + 506, + 615 + ], + "score": 1.0, + "content": "equation 4. Thus, CST formulates a bi-level optimization problem. In the inner loop we generate", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 612, + 506, + 626 + ], + "spans": [ + { + "bbox": [ + 105, + 612, + 506, + 626 + ], + "score": 1.0, + "content": "target pseudo-labels with the source classifier (equation 3), and train a target classifier with target", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 623, + 506, + 637 + ], + "spans": [ + { + "bbox": [ + 105, + 623, + 436, + 637 + ], + "score": 1.0, + "content": "pseudo-labels (equation 4). After each inner loop, we update the feature extractor", + "type": "text" + }, + { + "bbox": [ + 437, + 624, + 444, + 636 + ], + "score": 0.86, + "content": "\\phi", + "type": "inline_equation" + }, + { + "bbox": [ + 444, + 623, + 506, + 637 + ], + "score": 1.0, + "content": "for one step in", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 635, + 506, + 647 + ], + "spans": [ + { + "bbox": [ + 106, + 635, + 506, + 647 + ], + "score": 1.0, + "content": "the outer loop (equation 5), and start a new inner loop again. However, since the inner loop of the", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 646, + 506, + 658 + ], + "spans": [ + { + "bbox": [ + 106, + 646, + 381, + 658 + ], + "score": 1.0, + "content": "optimization in equation 4 only involves the light-weight linear head", + "type": "text" + }, + { + "bbox": [ + 381, + 646, + 390, + 657 + ], + "score": 0.87, + "content": "\\theta _ { t }", + "type": "inline_equation" + }, + { + "bbox": [ + 390, + 646, + 506, + 658 + ], + "score": 1.0, + "content": ", we propose to calculate the", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 657, + 505, + 671 + ], + "spans": [ + { + "bbox": [ + 105, + 658, + 180, + 671 + ], + "score": 1.0, + "content": "analytical form of", + "type": "text" + }, + { + "bbox": [ + 180, + 657, + 203, + 671 + ], + "score": 0.92, + "content": "\\hat { \\theta } _ { t } ( \\phi )", + "type": "inline_equation" + }, + { + "bbox": [ + 203, + 658, + 410, + 671 + ], + "score": 1.0, + "content": "and directly back-propagate to the feature extractor", + "type": "text" + }, + { + "bbox": [ + 410, + 659, + 417, + 670 + ], + "score": 0.85, + "content": "\\phi", + "type": "inline_equation" + }, + { + "bbox": [ + 417, + 658, + 505, + 671 + ], + "score": 1.0, + "content": "instead of calculating", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 668, + 506, + 682 + ], + "spans": [ + { + "bbox": [ + 105, + 668, + 506, + 682 + ], + "score": 1.0, + "content": "the second-order derivatives as in MAML [18]. The resulting framework is as fast as training two", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 682, + 505, + 694 + ], + "spans": [ + { + "bbox": [ + 105, + 682, + 277, + 694 + ], + "score": 1.0, + "content": "heads jointly. Also note that the solution", + "type": "text" + }, + { + "bbox": [ + 277, + 682, + 299, + 694 + ], + "score": 0.93, + "content": "\\hat { \\theta } _ { t } ( \\phi )", + "type": "inline_equation" + }, + { + "bbox": [ + 300, + 682, + 339, + 694 + ], + "score": 1.0, + "content": "relies on", + "type": "text" + }, + { + "bbox": [ + 340, + 683, + 349, + 693 + ], + "score": 0.86, + "content": "\\theta _ { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 349, + 682, + 428, + 694 + ], + "score": 1.0, + "content": "implicitly through", + "type": "text" + }, + { + "bbox": [ + 428, + 682, + 437, + 693 + ], + "score": 0.85, + "content": "y ^ { \\prime }", + "type": "inline_equation" + }, + { + "bbox": [ + 437, + 682, + 505, + 694 + ], + "score": 1.0, + "content": ". However, both", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 693, + 506, + 705 + ], + "spans": [ + { + "bbox": [ + 105, + 693, + 420, + 705 + ], + "score": 1.0, + "content": "standard self-training and our implementation use label sharpening, making", + "type": "text" + }, + { + "bbox": [ + 420, + 694, + 429, + 705 + ], + "score": 0.86, + "content": "y ^ { \\prime }", + "type": "inline_equation" + }, + { + "bbox": [ + 430, + 693, + 506, + 705 + ], + "score": 1.0, + "content": "not differentiable.", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 704, + 506, + 719 + ], + "spans": [ + { + "bbox": [ + 105, + 704, + 383, + 719 + ], + "score": 1.0, + "content": "Thus we follow vanilla self-training and do not consider the gradient of", + "type": "text" + }, + { + "bbox": [ + 384, + 705, + 406, + 718 + ], + "score": 0.93, + "content": "\\hat { \\theta } _ { t } ( \\phi )", + "type": "inline_equation" + }, + { + "bbox": [ + 406, + 704, + 429, + 719 + ], + "score": 1.0, + "content": "w.r.t.", + "type": "text" + }, + { + "bbox": [ + 429, + 705, + 438, + 717 + ], + "score": 0.87, + "content": "y ^ { \\prime }", + "type": "inline_equation" + }, + { + "bbox": [ + 439, + 704, + 506, + 719 + ], + "score": 1.0, + "content": "in the outer loop", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 716, + 506, + 729 + ], + "spans": [ + { + "bbox": [ + 105, + 716, + 506, + 729 + ], + "score": 1.0, + "content": "optimization. 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Denote the expected error on the", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 300, + 318, + 317 + ], + "spans": [ + { + "bbox": [ + 105, + 300, + 176, + 317 + ], + "score": 1.0, + "content": "target domain by", + "type": "text" + }, + { + "bbox": [ + 177, + 302, + 313, + 315 + ], + "score": 0.91, + "content": "\\mathrm { E r r } _ { Q } ( f ) : = \\mathbb { E } _ { ( x , y ) \\sim Q } \\mathbb { I } ( \\tilde { f } ( x ) \\neq y )", + "type": "inline_equation" + }, + { + "bbox": [ + 313, + 300, + 318, + 317 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 13.5 + }, + { + "type": "text", + "bbox": [ + 107, + 318, + 504, + 352 + ], + "lines": [ + { + "bbox": [ + 105, + 318, + 506, + 331 + ], + "spans": [ + { + "bbox": [ + 105, + 318, + 506, + 331 + ], + "score": 1.0, + "content": "We study the CST algorithm under the expansion assumption of the mixture distribution [66, 11].", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 330, + 505, + 341 + ], + "spans": [ + { + "bbox": [ + 106, + 330, + 385, + 341 + ], + "score": 1.0, + "content": "Intuitively, this assumption indicates that the conditional distributions", + "type": "text" + }, + { + "bbox": [ + 386, + 330, + 397, + 340 + ], + "score": 0.88, + "content": "P _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 397, + 330, + 415, + 341 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 415, + 330, + 427, + 341 + ], + "score": 0.89, + "content": "Q _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 427, + 330, + 505, + 341 + ], + "score": 1.0, + "content": "are closely located", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 341, + 492, + 353 + ], + "spans": [ + { + "bbox": [ + 106, + 341, + 492, + 353 + ], + "score": 1.0, + "content": "and regularly shaped, enabling knowledge transfer from the source domain to the target domain.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 18 + }, + { + "type": "text", + "bbox": [ + 106, + 354, + 505, + 394 + ], + "lines": [ + { + "bbox": [ + 105, + 353, + 505, + 367 + ], + "spans": [ + { + "bbox": [ + 105, + 353, + 161, + 367 + ], + "score": 1.0, + "content": "Definition 1", + "type": "text" + }, + { + "bbox": [ + 162, + 354, + 183, + 367 + ], + "score": 0.85, + "content": "[ q , \\epsilon )", + "type": "inline_equation" + }, + { + "bbox": [ + 184, + 353, + 325, + 367 + ], + "score": 1.0, + "content": "-constant expansion [66]). We say", + "type": "text" + }, + { + "bbox": [ + 325, + 355, + 334, + 365 + ], + "score": 0.79, + "content": "P", + "type": "inline_equation" + }, + { + "bbox": [ + 335, + 353, + 352, + 367 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 352, + 355, + 361, + 366 + ], + "score": 0.82, + "content": "Q", + "type": "inline_equation" + }, + { + "bbox": [ + 362, + 353, + 390, + 367 + ], + "score": 1.0, + "content": "satisfy", + "type": "text" + }, + { + "bbox": [ + 390, + 355, + 412, + 367 + ], + "score": 0.89, + "content": "( q , \\epsilon )", + "type": "inline_equation" + }, + { + "bbox": [ + 412, + 353, + 505, + 367 + ], + "score": 1.0, + "content": "-constant expansion for", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 104, + 361, + 507, + 383 + ], + "spans": [ + { + "bbox": [ + 104, + 361, + 167, + 383 + ], + "score": 1.0, + "content": "some constant", + "type": "text" + }, + { + "bbox": [ + 167, + 366, + 215, + 378 + ], + "score": 0.91, + "content": "q , \\epsilon \\in ( 0 , 1 )", + "type": "inline_equation" + }, + { + "bbox": [ + 215, + 361, + 272, + 383 + ], + "score": 1.0, + "content": ", if for any set", + "type": "text" + }, + { + "bbox": [ + 273, + 366, + 302, + 376 + ], + "score": 0.9, + "content": "A \\in { \\mathcal { X } }", + "type": "inline_equation" + }, + { + "bbox": [ + 302, + 361, + 338, + 383 + ], + "score": 1.0, + "content": "and any", + "type": "text" + }, + { + "bbox": [ + 338, + 366, + 369, + 378 + ], + "score": 0.92, + "content": "i \\in [ K ]", + "type": "inline_equation" + }, + { + "bbox": [ + 369, + 361, + 391, + 383 + ], + "score": 1.0, + "content": "with", + "type": "text" + }, + { + "bbox": [ + 392, + 366, + 487, + 380 + ], + "score": 0.93, + "content": "{ \\textstyle \\frac { 1 } { 2 } } > P _ { \\frac { 1 } { 2 } ( P _ { i } + Q _ { i } ) } ( A ) > q", + "type": "inline_equation" + }, + { + "bbox": [ + 487, + 361, + 507, + 383 + ], + "score": 1.0, + "content": ", we", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 378, + 327, + 394 + ], + "spans": [ + { + "bbox": [ + 105, + 378, + 128, + 394 + ], + "score": 1.0, + "content": "have", + "type": "text" + }, + { + "bbox": [ + 128, + 379, + 324, + 394 + ], + "score": 0.89, + "content": "P _ { \\frac { 1 } { 2 } ( P _ { i } + Q _ { i } ) } ( { \\mathcal { N } } ( A ) \\backslash A ) > \\operatorname* { m i n } \\{ \\epsilon , P _ { \\frac { 1 } { 2 } ( P _ { i } + Q _ { i } ) } ( A ) \\} .", + "type": "inline_equation" + }, + { + "bbox": [ + 324, + 378, + 327, + 394 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 21 + }, + { + "type": "text", + "bbox": [ + 106, + 400, + 506, + 486 + ], + "lines": [ + { + "bbox": [ + 105, + 400, + 506, + 414 + ], + "spans": [ + { + "bbox": [ + 105, + 400, + 506, + 414 + ], + "score": 1.0, + "content": "Based on this expansion assumption, we consider a robustness-constrained version of CST. Later", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 411, + 505, + 425 + ], + "spans": [ + { + "bbox": [ + 105, + 411, + 447, + 425 + ], + "score": 1.0, + "content": "we will show that the robustness is closely related to the uncertainty. Denote by", + "type": "text" + }, + { + "bbox": [ + 448, + 412, + 458, + 423 + ], + "score": 0.87, + "content": "f _ { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 458, + 411, + 505, + 425 + ], + "score": 1.0, + "content": "the source", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 104, + 421, + 505, + 439 + ], + "spans": [ + { + "bbox": [ + 104, + 421, + 150, + 439 + ], + "score": 1.0, + "content": "model and", + "type": "text" + }, + { + "bbox": [ + 150, + 423, + 160, + 435 + ], + "score": 0.86, + "content": "f _ { t }", + "type": "inline_equation" + }, + { + "bbox": [ + 160, + 421, + 379, + 439 + ], + "score": 1.0, + "content": "the model trained on the target with pseudo-labels. Let", + "type": "text" + }, + { + "bbox": [ + 379, + 423, + 505, + 437 + ], + "score": 0.9, + "content": "R ( f _ { t } ) : = P _ { \\frac { 1 } { 2 } ( P + Q ) } ( \\{ x : \\exists x ^ { \\prime } \\in", + "type": "inline_equation" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 435, + 505, + 452 + ], + "spans": [ + { + "bbox": [ + 106, + 436, + 203, + 450 + ], + "score": 0.86, + "content": "\\mathcal { N } ( x ) , \\tilde { f } _ { t } ( x ) \\neq \\tilde { f } _ { t } ( x ^ { \\prime } ) \\} )", + "type": "inline_equation" + }, + { + "bbox": [ + 203, + 435, + 328, + 452 + ], + "score": 1.0, + "content": "represent the robustness [66] of", + "type": "text" + }, + { + "bbox": [ + 328, + 438, + 338, + 450 + ], + "score": 0.88, + "content": "f _ { t }", + "type": "inline_equation" + }, + { + "bbox": [ + 338, + 435, + 350, + 452 + ], + "score": 1.0, + "content": "on", + "type": "text" + }, + { + "bbox": [ + 351, + 439, + 360, + 448 + ], + "score": 0.82, + "content": "P", + "type": "inline_equation" + }, + { + "bbox": [ + 360, + 435, + 376, + 452 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 376, + 438, + 385, + 450 + ], + "score": 0.83, + "content": "Q", + "type": "inline_equation" + }, + { + "bbox": [ + 386, + 435, + 424, + 452 + ], + "score": 1.0, + "content": ". Suppose", + "type": "text" + }, + { + "bbox": [ + 425, + 437, + 505, + 451 + ], + "score": 0.91, + "content": "\\mathbb { E } _ { ( x , y ) \\sim Q } \\mathbb { I } ( \\tilde { f } _ { s } ( x ) \\neq", + "type": "inline_equation" + } + ], + "index": 26 + }, + { + "bbox": [ + 107, + 449, + 506, + 465 + ], + "spans": [ + { + "bbox": [ + 107, + 451, + 152, + 464 + ], + "score": 0.93, + "content": "\\tilde { f } _ { t } ( x ) ) \\leq c", + "type": "inline_equation" + }, + { + "bbox": [ + 152, + 449, + 170, + 465 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 171, + 452, + 214, + 464 + ], + "score": 0.92, + "content": "R ( f _ { t } ) \\leq \\rho", + "type": "inline_equation" + }, + { + "bbox": [ + 214, + 449, + 382, + 465 + ], + "score": 1.0, + "content": ". The following theorem states that when", + "type": "text" + }, + { + "bbox": [ + 383, + 452, + 393, + 464 + ], + "score": 0.88, + "content": "f _ { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 393, + 449, + 411, + 465 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 412, + 452, + 421, + 463 + ], + "score": 0.87, + "content": "f _ { t }", + "type": "inline_equation" + }, + { + "bbox": [ + 421, + 449, + 506, + 465 + ], + "score": 1.0, + "content": "behave similarly on", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 462, + 506, + 475 + ], + "spans": [ + { + "bbox": [ + 106, + 462, + 177, + 475 + ], + "score": 1.0, + "content": "the target domain", + "type": "text" + }, + { + "bbox": [ + 177, + 464, + 186, + 474 + ], + "score": 0.85, + "content": "Q", + "type": "inline_equation" + }, + { + "bbox": [ + 187, + 462, + 204, + 475 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 204, + 464, + 214, + 474 + ], + "score": 0.88, + "content": "f _ { t }", + "type": "inline_equation" + }, + { + "bbox": [ + 214, + 462, + 506, + 475 + ], + "score": 1.0, + "content": "is robust to local changes in input, the minimizer of the cycle source error", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 473, + 362, + 487 + ], + "spans": [ + { + "bbox": [ + 106, + 474, + 143, + 486 + ], + "score": 0.93, + "content": "\\mathrm { E r r } _ { P } ( f _ { t } )", + "type": "inline_equation" + }, + { + "bbox": [ + 144, + 473, + 253, + 487 + ], + "score": 1.0, + "content": "will guarantee low error of", + "type": "text" + }, + { + "bbox": [ + 254, + 474, + 264, + 486 + ], + "score": 0.89, + "content": "f _ { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 264, + 473, + 349, + 487 + ], + "score": 1.0, + "content": "on the target domain", + "type": "text" + }, + { + "bbox": [ + 350, + 474, + 358, + 485 + ], + "score": 0.85, + "content": "Q", + "type": "inline_equation" + }, + { + "bbox": [ + 359, + 473, + 362, + 487 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 26 + }, + { + "type": "text", + "bbox": [ + 106, + 489, + 506, + 516 + ], + "lines": [ + { + "bbox": [ + 105, + 488, + 506, + 505 + ], + "spans": [ + { + "bbox": [ + 105, + 488, + 284, + 505 + ], + "score": 1.0, + "content": "Theorem 1. Suppose Definition 1 holds for", + "type": "text" + }, + { + "bbox": [ + 284, + 491, + 294, + 500 + ], + "score": 0.81, + "content": "P", + "type": "inline_equation" + }, + { + "bbox": [ + 294, + 488, + 312, + 505 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 312, + 491, + 321, + 502 + ], + "score": 0.78, + "content": "Q", + "type": "inline_equation" + }, + { + "bbox": [ + 321, + 488, + 359, + 505 + ], + "score": 1.0, + "content": ". 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We then extend the margin loss:", + "type": "text" + }, + { + "bbox": [ + 465, + 576, + 505, + 587 + ], + "score": 0.88, + "content": "\\mathcal { M } ( v ) =", + "type": "inline_equation" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 587, + 506, + 601 + ], + "spans": [ + { + "bbox": [ + 106, + 588, + 220, + 601 + ], + "score": 0.89, + "content": "\\begin{array} { r } { \\operatorname* { m a x } _ { y } \\big ( v _ { [ y ] } - \\operatorname* { m a x } _ { y ^ { \\prime } \\neq y } v _ { [ y ^ { \\prime } ] } \\big ) } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 221, + 587, + 506, + 601 + ], + "score": 1.0, + "content": "(The difference between the largest and the second largest scores in", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 600, + 506, + 614 + ], + "spans": [ + { + "bbox": [ + 106, + 603, + 115, + 612 + ], + "score": 0.67, + "content": "v )", + "type": "inline_equation" + }, + { + "bbox": [ + 115, + 600, + 137, + 614 + ], + "score": 1.0, + "content": ", and", + "type": "text" + }, + { + "bbox": [ + 138, + 600, + 314, + 613 + ], + "score": 0.89, + "content": "\\dot { l } _ { \\gamma } ( f _ { t } ( x ) , f _ { s } ( x ) ) : = \\psi _ { \\gamma } ( - \\mathcal { M } ( f _ { t } ( x ) , \\tilde { f } _ { s } ( x ) ) )", + "type": "inline_equation" + }, + { + "bbox": [ + 315, + 600, + 387, + 614 + ], + "score": 1.0, + "content": ". 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Consider the following training objective for", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 104, + 621, + 508, + 642 + ], + "spans": [ + { + "bbox": [ + 104, + 621, + 178, + 642 + ], + "score": 1.0, + "content": "CST, denoted by", + "type": "text" + }, + { + "bbox": [ + 178, + 624, + 228, + 636 + ], + "score": 0.91, + "content": "L _ { \\mathrm { C S T } } ( f _ { s } , f _ { t } )", + "type": "inline_equation" + }, + { + "bbox": [ + 229, + 621, + 261, + 642 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 262, + 624, + 401, + 638 + ], + "score": 0.9, + "content": "\\mathcal { L } _ { \\widehat { P } , \\gamma } ( f _ { t } ) : = \\mathbb { E } _ { ( x , y ) \\sim \\widehat { P } } l _ { \\gamma } ( f _ { t } ( x ) , y )", + "type": "inline_equation" + }, + { + "bbox": [ + 401, + 621, + 508, + 642 + ], + "score": 1.0, + "content": "corresponds to the cycle", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 102, + 634, + 508, + 656 + ], + "spans": [ + { + "bbox": [ + 102, + 634, + 208, + 656 + ], + "score": 1.0, + "content": "source loss in equation 5,", + "type": "text" + }, + { + "bbox": [ + 208, + 638, + 376, + 653 + ], + "score": 0.9, + "content": "L _ { \\widehat { Q } , \\gamma } ( f _ { t } , f _ { s } ) : = \\mathbb { E } _ { ( x , y ) \\sim \\widehat { Q } } l _ { \\gamma } ( f _ { t } ( x ) , f _ { s } ( x ) )", + "type": "inline_equation" + }, + { + "bbox": [ + 377, + 634, + 508, + 656 + ], + "score": 1.0, + "content": "is consistent with the target loss", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 650, + 485, + 664 + ], + "spans": [ + { + "bbox": [ + 106, + 650, + 181, + 664 + ], + "score": 1.0, + "content": "in equation 4, and", + "type": "text" + }, + { + "bbox": [ + 181, + 651, + 223, + 663 + ], + "score": 0.93, + "content": "\\mathcal { M } ( f _ { t } ( x ) )", + "type": "inline_equation" + }, + { + "bbox": [ + 223, + 650, + 485, + 664 + ], + "score": 1.0, + "content": "is closely related to the uncertainty of predictions in equation 11.", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 37 + }, + { + "type": "interline_equation", + "bbox": [ + 143, + 667, + 467, + 695 + ], + "lines": [ + { + "bbox": [ + 143, + 667, + 467, + 695 + ], + "spans": [ + { + "bbox": [ + 143, + 667, + 467, + 695 + ], + "score": 0.91, + "content": "\\operatorname* { m i n } L _ { \\mathrm { C S T } } ( f _ { s } , f _ { t } ) : = L _ { \\widehat { P } , \\gamma } ( f _ { t } ) + L _ { \\widehat { Q } , \\gamma } ( f _ { t } , f _ { s } ) + \\frac { 1 - \\mathbb { E } _ { ( x , y ) \\sim \\frac { 1 } { 2 } ( \\widehat { P } + \\widehat { Q } ) } \\mathcal { M } ( f _ { t } ( x ) ) } { \\tau } .", + "type": "interline_equation", + "image_path": "c6d24ce0adbf8cbbf84bc22d55ac6324f6f73dadd0fed6d9251d5b91d46526cc.jpg" + } + ] + } + ], + "index": 42, + "virtual_lines": [ + { + "bbox": [ + 143, + 667, + 467, + 695 + ], + "spans": [], + "index": 42 + } + ] + }, + { + "type": "text", + "bbox": [ + 105, + 699, + 504, + 723 + ], + "lines": [ + { + "bbox": [ + 105, + 698, + 505, + 713 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 407, + 713 + ], + "score": 1.0, + "content": "The following theorem shows that the minimizer of the training objective", + "type": "text" + }, + { + "bbox": [ + 407, + 699, + 457, + 712 + ], + "score": 0.93, + "content": "L _ { \\mathrm { C S T } } ( f _ { s } , f _ { t } )", + "type": "inline_equation" + }, + { + "bbox": [ + 458, + 698, + 505, + 713 + ], + "score": 1.0, + "content": "guarantees", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 710, + 310, + 723 + ], + "spans": [ + { + "bbox": [ + 106, + 710, + 201, + 723 + ], + "score": 1.0, + "content": "low population error of", + "type": "text" + }, + { + "bbox": [ + 202, + 711, + 212, + 722 + ], + "score": 0.88, + "content": "f _ { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 212, + 710, + 298, + 723 + ], + "score": 1.0, + "content": "on the target domain", + "type": "text" + }, + { + "bbox": [ + 298, + 713, + 306, + 722 + ], + "score": 0.88, + "content": "Q", + "type": "inline_equation" + }, + { + "bbox": [ + 307, + 710, + 310, + 723 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 43.5 + } + ], + "page_idx": 5, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 302, + 741, + 309, + 750 + ], + "lines": [ + { + "bbox": [ + 302, + 741, + 310, + 752 + ], + "spans": [ + { + "bbox": [ + 302, + 741, + 310, + 752 + ], + "score": 1.0, + "content": "6", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 105, + 72, + 504, + 97 + ], + "lines": [ + { + "bbox": [ + 106, + 72, + 505, + 86 + ], + "spans": [ + { + "bbox": [ + 106, + 72, + 505, + 86 + ], + "score": 1.0, + "content": "update leads to no performance gain. 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Denote the expected error on the", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 300, + 318, + 317 + ], + "spans": [ + { + "bbox": [ + 105, + 300, + 176, + 317 + ], + "score": 1.0, + "content": "target domain by", + "type": "text" + }, + { + "bbox": [ + 177, + 302, + 313, + 315 + ], + "score": 0.91, + "content": "\\mathrm { E r r } _ { Q } ( f ) : = \\mathbb { E } _ { ( x , y ) \\sim Q } \\mathbb { I } ( \\tilde { f } ( x ) \\neq y )", + "type": "inline_equation" + }, + { + "bbox": [ + 313, + 300, + 318, + 317 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 13.5, + "bbox_fs": [ + 104, + 242, + 506, + 317 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 318, + 504, + 352 + ], + "lines": [ + { + "bbox": [ + 105, + 318, + 506, + 331 + ], + "spans": [ + { + "bbox": [ + 105, + 318, + 506, + 331 + ], + "score": 1.0, + "content": "We study the CST algorithm under the expansion assumption of the mixture distribution [66, 11].", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 330, + 505, + 341 + ], + "spans": [ + { + "bbox": [ + 106, + 330, + 385, + 341 + ], + "score": 1.0, + "content": "Intuitively, this assumption indicates that the conditional distributions", + "type": "text" + }, + { + "bbox": [ + 386, + 330, + 397, + 340 + ], + "score": 0.88, + "content": "P _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 397, + 330, + 415, + 341 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 415, + 330, + 427, + 341 + ], + "score": 0.89, + "content": "Q _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 427, + 330, + 505, + 341 + ], + "score": 1.0, + "content": "are closely located", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 341, + 492, + 353 + ], + "spans": [ + { + "bbox": [ + 106, + 341, + 492, + 353 + ], + "score": 1.0, + "content": "and regularly shaped, enabling knowledge transfer from the source domain to the target domain.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 18, + "bbox_fs": [ + 105, + 318, + 506, + 353 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 354, + 505, + 394 + ], + "lines": [ + { + "bbox": [ + 105, + 353, + 505, + 367 + ], + "spans": [ + { + "bbox": [ + 105, + 353, + 161, + 367 + ], + "score": 1.0, + "content": "Definition 1", + "type": "text" + }, + { + "bbox": [ + 162, + 354, + 183, + 367 + ], + "score": 0.85, + "content": "[ q , \\epsilon )", + "type": "inline_equation" + }, + { + "bbox": [ + 184, + 353, + 325, + 367 + ], + "score": 1.0, + "content": "-constant expansion [66]). We say", + "type": "text" + }, + { + "bbox": [ + 325, + 355, + 334, + 365 + ], + "score": 0.79, + "content": "P", + "type": "inline_equation" + }, + { + "bbox": [ + 335, + 353, + 352, + 367 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 352, + 355, + 361, + 366 + ], + "score": 0.82, + "content": "Q", + "type": "inline_equation" + }, + { + "bbox": [ + 362, + 353, + 390, + 367 + ], + "score": 1.0, + "content": "satisfy", + "type": "text" + }, + { + "bbox": [ + 390, + 355, + 412, + 367 + ], + "score": 0.89, + "content": "( q , \\epsilon )", + "type": "inline_equation" + }, + { + "bbox": [ + 412, + 353, + 505, + 367 + ], + "score": 1.0, + "content": "-constant expansion for", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 104, + 361, + 507, + 383 + ], + "spans": [ + { + "bbox": [ + 104, + 361, + 167, + 383 + ], + "score": 1.0, + "content": "some constant", + "type": "text" + }, + { + "bbox": [ + 167, + 366, + 215, + 378 + ], + "score": 0.91, + "content": "q , \\epsilon \\in ( 0 , 1 )", + "type": "inline_equation" + }, + { + "bbox": [ + 215, + 361, + 272, + 383 + ], + "score": 1.0, + "content": ", if for any set", + "type": "text" + }, + { + "bbox": [ + 273, + 366, + 302, + 376 + ], + "score": 0.9, + "content": "A \\in { \\mathcal { X } }", + "type": "inline_equation" + }, + { + "bbox": [ + 302, + 361, + 338, + 383 + ], + "score": 1.0, + "content": "and any", + "type": "text" + }, + { + "bbox": [ + 338, + 366, + 369, + 378 + ], + "score": 0.92, + "content": "i \\in [ K ]", + "type": "inline_equation" + }, + { + "bbox": [ + 369, + 361, + 391, + 383 + ], + "score": 1.0, + "content": "with", + "type": "text" + }, + { + "bbox": [ + 392, + 366, + 487, + 380 + ], + "score": 0.93, + "content": "{ \\textstyle \\frac { 1 } { 2 } } > P _ { \\frac { 1 } { 2 } ( P _ { i } + Q _ { i } ) } ( A ) > q", + "type": "inline_equation" + }, + { + "bbox": [ + 487, + 361, + 507, + 383 + ], + "score": 1.0, + "content": ", we", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 378, + 327, + 394 + ], + "spans": [ + { + "bbox": [ + 105, + 378, + 128, + 394 + ], + "score": 1.0, + "content": "have", + "type": "text" + }, + { + "bbox": [ + 128, + 379, + 324, + 394 + ], + "score": 0.89, + "content": "P _ { \\frac { 1 } { 2 } ( P _ { i } + Q _ { i } ) } ( { \\mathcal { N } } ( A ) \\backslash A ) > \\operatorname* { m i n } \\{ \\epsilon , P _ { \\frac { 1 } { 2 } ( P _ { i } + Q _ { i } ) } ( A ) \\} .", + "type": "inline_equation" + }, + { + "bbox": [ + 324, + 378, + 327, + 394 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 21, + "bbox_fs": [ + 104, + 353, + 507, + 394 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 400, + 506, + 486 + ], + "lines": [ + { + "bbox": [ + 105, + 400, + 506, + 414 + ], + "spans": [ + { + "bbox": [ + 105, + 400, + 506, + 414 + ], + "score": 1.0, + "content": "Based on this expansion assumption, we consider a robustness-constrained version of CST. Later", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 411, + 505, + 425 + ], + "spans": [ + { + "bbox": [ + 105, + 411, + 447, + 425 + ], + "score": 1.0, + "content": "we will show that the robustness is closely related to the uncertainty. Denote by", + "type": "text" + }, + { + "bbox": [ + 448, + 412, + 458, + 423 + ], + "score": 0.87, + "content": "f _ { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 458, + 411, + 505, + 425 + ], + "score": 1.0, + "content": "the source", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 104, + 421, + 505, + 439 + ], + "spans": [ + { + "bbox": [ + 104, + 421, + 150, + 439 + ], + "score": 1.0, + "content": "model and", + "type": "text" + }, + { + "bbox": [ + 150, + 423, + 160, + 435 + ], + "score": 0.86, + "content": "f _ { t }", + "type": "inline_equation" + }, + { + "bbox": [ + 160, + 421, + 379, + 439 + ], + "score": 1.0, + "content": "the model trained on the target with pseudo-labels. Let", + "type": "text" + }, + { + "bbox": [ + 379, + 423, + 505, + 437 + ], + "score": 0.9, + "content": "R ( f _ { t } ) : = P _ { \\frac { 1 } { 2 } ( P + Q ) } ( \\{ x : \\exists x ^ { \\prime } \\in", + "type": "inline_equation" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 435, + 505, + 452 + ], + "spans": [ + { + "bbox": [ + 106, + 436, + 203, + 450 + ], + "score": 0.86, + "content": "\\mathcal { N } ( x ) , \\tilde { f } _ { t } ( x ) \\neq \\tilde { f } _ { t } ( x ^ { \\prime } ) \\} )", + "type": "inline_equation" + }, + { + "bbox": [ + 203, + 435, + 328, + 452 + ], + "score": 1.0, + "content": "represent the robustness [66] of", + "type": "text" + }, + { + "bbox": [ + 328, + 438, + 338, + 450 + ], + "score": 0.88, + "content": "f _ { t }", + "type": "inline_equation" + }, + { + "bbox": [ + 338, + 435, + 350, + 452 + ], + "score": 1.0, + "content": "on", + "type": "text" + }, + { + "bbox": [ + 351, + 439, + 360, + 448 + ], + "score": 0.82, + "content": "P", + "type": "inline_equation" + }, + { + "bbox": [ + 360, + 435, + 376, + 452 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 376, + 438, + 385, + 450 + ], + "score": 0.83, + "content": "Q", + "type": "inline_equation" + }, + { + "bbox": [ + 386, + 435, + 424, + 452 + ], + "score": 1.0, + "content": ". Suppose", + "type": "text" + }, + { + "bbox": [ + 425, + 437, + 505, + 451 + ], + "score": 0.91, + "content": "\\mathbb { E } _ { ( x , y ) \\sim Q } \\mathbb { I } ( \\tilde { f } _ { s } ( x ) \\neq", + "type": "inline_equation" + } + ], + "index": 26 + }, + { + "bbox": [ + 107, + 449, + 506, + 465 + ], + "spans": [ + { + "bbox": [ + 107, + 451, + 152, + 464 + ], + "score": 0.93, + "content": "\\tilde { f } _ { t } ( x ) ) \\leq c", + "type": "inline_equation" + }, + { + "bbox": [ + 152, + 449, + 170, + 465 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 171, + 452, + 214, + 464 + ], + "score": 0.92, + "content": "R ( f _ { t } ) \\leq \\rho", + "type": "inline_equation" + }, + { + "bbox": [ + 214, + 449, + 382, + 465 + ], + "score": 1.0, + "content": ". 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Suppose Definition 1 holds for", + "type": "text" + }, + { + "bbox": [ + 284, + 491, + 294, + 500 + ], + "score": 0.81, + "content": "P", + "type": "inline_equation" + }, + { + "bbox": [ + 294, + 488, + 312, + 505 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 312, + 491, + 321, + 502 + ], + "score": 0.78, + "content": "Q", + "type": "inline_equation" + }, + { + "bbox": [ + 321, + 488, + 359, + 505 + ], + "score": 1.0, + "content": ". 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We then extend the margin loss:", + "type": "text" + }, + { + "bbox": [ + 465, + 576, + 505, + 587 + ], + "score": 0.88, + "content": "\\mathcal { M } ( v ) =", + "type": "inline_equation" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 587, + 506, + 601 + ], + "spans": [ + { + "bbox": [ + 106, + 588, + 220, + 601 + ], + "score": 0.89, + "content": "\\begin{array} { r } { \\operatorname* { m a x } _ { y } \\big ( v _ { [ y ] } - \\operatorname* { m a x } _ { y ^ { \\prime } \\neq y } v _ { [ y ^ { \\prime } ] } \\big ) } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 221, + 587, + 506, + 601 + ], + "score": 1.0, + "content": "(The difference between the largest and the second largest scores in", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 600, + 506, + 614 + ], + "spans": [ + { + "bbox": [ + 106, + 603, + 115, + 612 + ], + "score": 0.67, + "content": "v )", + "type": "inline_equation" + }, + { + "bbox": [ + 115, + 600, + 137, + 614 + ], + "score": 1.0, + "content": ", and", + "type": "text" + }, + { + "bbox": [ + 138, + 600, + 314, + 613 + ], + "score": 0.89, + "content": "\\dot { l } _ { \\gamma } ( f _ { t } ( x ) , f _ { s } ( x ) ) : = \\psi _ { \\gamma } ( - \\mathcal { M } ( f _ { t } ( x ) , \\tilde { f } _ { s } ( x ) ) )", + "type": "inline_equation" + }, + { + "bbox": [ + 315, + 600, + 387, + 614 + ], + "score": 1.0, + "content": ". 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Consider the following training objective for", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 104, + 621, + 508, + 642 + ], + "spans": [ + { + "bbox": [ + 104, + 621, + 178, + 642 + ], + "score": 1.0, + "content": "CST, denoted by", + "type": "text" + }, + { + "bbox": [ + 178, + 624, + 228, + 636 + ], + "score": 0.91, + "content": "L _ { \\mathrm { C S T } } ( f _ { s } , f _ { t } )", + "type": "inline_equation" + }, + { + "bbox": [ + 229, + 621, + 261, + 642 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 262, + 624, + 401, + 638 + ], + "score": 0.9, + "content": "\\mathcal { L } _ { \\widehat { P } , \\gamma } ( f _ { t } ) : = \\mathbb { E } _ { ( x , y ) \\sim \\widehat { P } } l _ { \\gamma } ( f _ { t } ( x ) , y )", + "type": "inline_equation" + }, + { + "bbox": [ + 401, + 621, + 508, + 642 + ], + "score": 1.0, + "content": "corresponds to the cycle", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 102, + 634, + 508, + 656 + ], + "spans": [ + { + "bbox": [ + 102, + 634, + 208, + 656 + ], + "score": 1.0, + "content": "source loss in equation 5,", + "type": "text" + }, + { + "bbox": [ + 208, + 638, + 376, + 653 + ], + "score": 0.9, + "content": "L _ { \\widehat { Q } , \\gamma } ( f _ { t } , f _ { s } ) : = \\mathbb { E } _ { ( x , y ) \\sim \\widehat { Q } } l _ { \\gamma } ( f _ { t } ( x ) , f _ { s } ( x ) )", + "type": "inline_equation" + }, + { + "bbox": [ + 377, + 634, + 508, + 656 + ], + "score": 1.0, + "content": "is consistent with the target loss", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 650, + 485, + 664 + ], + "spans": [ + { + "bbox": [ + 106, + 650, + 181, + 664 + ], + "score": 1.0, + "content": "in equation 4, and", + "type": "text" + }, + { + "bbox": [ + 181, + 651, + 223, + 663 + ], + "score": 0.93, + "content": "\\mathcal { M } ( f _ { t } ( x ) )", + "type": "inline_equation" + }, + { + "bbox": [ + 223, + 650, + 485, + 664 + ], + "score": 1.0, + "content": "is closely related to the uncertainty of predictions in equation 11.", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 37, + "bbox_fs": [ + 102, + 551, + 508, + 664 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 143, + 667, + 467, + 695 + ], + "lines": [ + { + "bbox": [ + 143, + 667, + 467, + 695 + ], + "spans": [ + { + "bbox": [ + 143, + 667, + 467, + 695 + ], + "score": 0.91, + "content": "\\operatorname* { m i n } L _ { \\mathrm { C S T } } ( f _ { s } , f _ { t } ) : = L _ { \\widehat { P } , \\gamma } ( f _ { t } ) + L _ { \\widehat { Q } , \\gamma } ( f _ { t } , f _ { s } ) + \\frac { 1 - 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For any solution of equation", + "type": "text" + }, + { + "bbox": [ + 236, + 87, + 247, + 97 + ], + "score": 0.29, + "content": "^ { 1 3 }", + "type": "inline_equation" + }, + { + "bbox": [ + 247, + 84, + 265, + 101 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 265, + 87, + 290, + 99 + ], + "score": 0.89, + "content": "\\gamma > 0", + "type": "inline_equation" + }, + { + "bbox": [ + 290, + 84, + 407, + 101 + ], + "score": 1.0, + "content": ", with probability larger than", + "type": "text" + }, + { + "bbox": [ + 407, + 87, + 430, + 97 + ], + "score": 0.83, + "content": "1 - \\delta", + "type": "inline_equation" + }, + { + "bbox": [ + 430, + 84, + 435, + 101 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "text", + "bbox": [ + 107, + 100, + 505, + 163 + ], + "lines": [ + { + "bbox": [ + 111, + 100, + 502, + 126 + ], + "spans": [ + { + "bbox": [ + 111, + 100, + 502, + 126 + ], + "score": 0.88, + "content": "\\mathrm { E r r } _ { Q } ( f _ { s } ) \\leq L _ { \\mathrm { C S T } } ( f _ { s } , f _ { t } ) + 2 q + \\frac { 4 K } { \\gamma } \\left[ \\widehat { R } ( \\mathcal { F } | _ { \\widehat { P } } ) + \\widehat { \\mathcal { R } } ( \\tilde { \\mathcal { F } } \\times \\mathcal { F } | _ { \\widehat { Q } } ) \\right] + \\frac { 2 } { \\tau } \\left[ \\widehat { R } ( \\mathcal { F } | _ { \\widehat { P } } ) + \\widehat { \\mathcal { R } } ( \\mathcal { F } | _ { \\widehat { Q } } ) \\right] + \\zeta ,", + "type": "inline_equation", + "image_path": "abf9e262a5e3b34a673b2e52b628f0724588d731fe9feb3ec08c87557ddb72ed.jpg" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 128, + 506, + 148 + ], + "spans": [ + { + "bbox": [ + 105, + 128, + 133, + 148 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 133, + 129, + 306, + 148 + ], + "score": 0.9, + "content": "\\zeta = O \\left( \\sqrt { \\log ( 1 / \\delta ) / n _ { s } } + \\sqrt { \\log ( 1 / \\delta ) / n _ { t } } \\right)", + "type": "inline_equation" + }, + { + "bbox": [ + 306, + 128, + 389, + 148 + ], + "score": 1.0, + "content": "is a low-order term.", + "type": "text" + }, + { + "bbox": [ + 389, + 131, + 419, + 144 + ], + "score": 0.91, + "content": "\\tilde { \\mathcal { F } } \\times \\mathcal { F }", + "type": "inline_equation" + }, + { + "bbox": [ + 420, + 128, + 506, + 148 + ], + "score": 1.0, + "content": "refers to the function", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 145, + 256, + 164 + ], + "spans": [ + { + "bbox": [ + 105, + 145, + 129, + 164 + ], + "score": 1.0, + "content": "class", + "type": "text" + }, + { + "bbox": [ + 129, + 147, + 251, + 162 + ], + "score": 0.86, + "content": "\\{ x f ( \\overleftarrow { x } ) _ { [ \\tilde { f } ^ { \\prime } ( x ) ] } : f , f ^ { \\prime } \\in \\mathcal { F } \\} _ { }", + "type": "inline_equation" + }, + { + "bbox": [ + 252, + 145, + 256, + 164 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 3 + }, + { + "type": "text", + "bbox": [ + 106, + 168, + 506, + 224 + ], + "lines": [ + { + "bbox": [ + 105, + 167, + 506, + 181 + ], + "spans": [ + { + "bbox": [ + 105, + 167, + 506, + 181 + ], + "score": 1.0, + "content": "Main insights. 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The generalization error", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 179, + 506, + 194 + ], + "spans": [ + { + "bbox": [ + 105, + 179, + 172, + 194 + ], + "score": 1.0, + "content": "of the classifier", + "type": "text" + }, + { + "bbox": [ + 172, + 180, + 182, + 191 + ], + "score": 0.89, + "content": "f _ { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 183, + 179, + 435, + 194 + ], + "score": 1.0, + "content": "on the target domain is bounded with the CST loss objective", + "type": "text" + }, + { + "bbox": [ + 435, + 180, + 486, + 192 + ], + "score": 0.93, + "content": "L _ { \\mathrm { C S T } } ( f _ { s } , f _ { t } )", + "type": "inline_equation" + }, + { + "bbox": [ + 486, + 179, + 506, + 194 + ], + "score": 1.0, + "content": ", the", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 191, + 506, + 203 + ], + "spans": [ + { + "bbox": [ + 106, + 191, + 280, + 203 + ], + "score": 1.0, + "content": "intrinsic property of the data distribution", + "type": "text" + }, + { + "bbox": [ + 280, + 193, + 286, + 202 + ], + "score": 0.73, + "content": "q", + "type": "inline_equation" + }, + { + "bbox": [ + 286, + 191, + 506, + 203 + ], + "score": 1.0, + "content": ", and the complexity of the function classes. In our", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 200, + 506, + 215 + ], + "spans": [ + { + "bbox": [ + 105, + 200, + 150, + 215 + ], + "score": 1.0, + "content": "algorithm,", + "type": "text" + }, + { + "bbox": [ + 151, + 201, + 201, + 213 + ], + "score": 0.93, + "content": "\\bar { L _ { \\mathrm { C S T } } } ( f _ { s } , f _ { t } )", + "type": "inline_equation" + }, + { + "bbox": [ + 201, + 200, + 367, + 215 + ], + "score": 1.0, + "content": "is minimized by the neural networks and", + "type": "text" + }, + { + "bbox": [ + 367, + 203, + 373, + 213 + ], + "score": 0.8, + "content": "q", + "type": "inline_equation" + }, + { + "bbox": [ + 374, + 200, + 506, + 215 + ], + "score": 1.0, + "content": "is a constant. 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Green dots for", + "type": "text" + }, + { + "bbox": [ + 311, + 450, + 334, + 459 + ], + "score": 0.91, + "content": "y = 1", + "type": "inline_equation" + }, + { + "bbox": [ + 334, + 448, + 382, + 460 + ], + "score": 1.0, + "content": ", red dots for", + "type": "text" + }, + { + "bbox": [ + 382, + 450, + 405, + 459 + ], + "score": 0.9, + "content": "y = 0", + "type": "inline_equation" + }, + { + "bbox": [ + 406, + 448, + 473, + 460 + ], + "score": 1.0, + "content": ", and blue dots for", + "type": "text" + }, + { + "bbox": [ + 473, + 450, + 503, + 459 + ], + "score": 0.91, + "content": "y = - 1", + "type": "inline_equation" + }, + { + "bbox": [ + 503, + 448, + 506, + 460 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 457, + 506, + 473 + ], + "spans": [ + { + "bbox": [ + 105, + 457, + 414, + 473 + ], + "score": 1.0, + "content": "The grey curve is the classification boundary of different features. The good feature", + "type": "text" + }, + { + "bbox": [ + 415, + 458, + 454, + 471 + ], + "score": 0.94, + "content": "x _ { [ 1 ] } ^ { 2 } - x _ { [ 2 ] } ^ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 455, + 457, + 506, + 473 + ], + "score": 1.0, + "content": "works on the", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 470, + 506, + 484 + ], + "spans": [ + { + "bbox": [ + 105, + 470, + 343, + 484 + ], + "score": 1.0, + "content": "target domain (shown in (a) and (c)), whereas the spurious feature", + "type": "text" + }, + { + "bbox": [ + 343, + 470, + 383, + 484 + ], + "score": 0.94, + "content": "x _ { [ 1 ] } ^ { 2 } - x _ { [ 3 ] } ^ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 383, + 470, + 506, + 484 + ], + "score": 1.0, + "content": "only works on the source domain", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 104, + 479, + 507, + 510 + ], + "spans": [ + { + "bbox": [ + 104, + 479, + 171, + 510 + ], + "score": 1.0, + "content": "(shown in (b) andwhile CST learns", + "type": "text" + }, + { + "bbox": [ + 210, + 479, + 464, + 510 + ], + "score": 1.0, + "content": "tion 4.2, we show that feature adaptation and standard self-training learn .", + "type": "text" + }, + { + "bbox": [ + 465, + 482, + 502, + 496 + ], + "score": 0.93, + "content": "x _ { [ 1 ] } ^ { 2 } - x _ { [ 3 ] } ^ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 503, + 479, + 507, + 510 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 171, + 495, + 210, + 508 + ], + "spans": [ + { + "bbox": [ + 171, + 495, + 210, + 508 + ], + "score": 0.93, + "content": "x _ { [ 1 ] } ^ { 2 } - x _ { [ 2 ] } ^ { 2 }", + "type": "inline_equation" + } + ], + "index": 29 + } + ], + "index": 27 + } + ], + "index": 25.0 + }, + { + "type": "text", + "bbox": [ + 106, + 515, + 506, + 608 + ], + "lines": [ + { + "bbox": [ + 106, + 515, + 505, + 527 + ], + "spans": [ + { + "bbox": [ + 106, + 515, + 505, + 527 + ], + "score": 1.0, + "content": "To make the features more tractable, we study the norm-constrained version of the algorithms (details", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 526, + 507, + 539 + ], + "spans": [ + { + "bbox": [ + 105, + 526, + 507, + 539 + ], + "score": 1.0, + "content": "are deferred to Section A.3.2). We compare the features learned by feature adaptation, standard self-", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 103, + 533, + 504, + 555 + ], + "spans": [ + { + "bbox": [ + 103, + 533, + 444, + 555 + ], + "score": 1.0, + "content": "training, and CST. Intuitively, feature adaptation fails because the ideal target solution", + "type": "text" + }, + { + "bbox": [ + 444, + 537, + 504, + 552 + ], + "score": 0.94, + "content": "y = x _ { [ 1 ] } ^ { 2 } - x _ { [ 2 ] } ^ { 2 }", + "type": "inline_equation" + } + ], + "index": 32 + }, + { + "bbox": [ + 104, + 546, + 510, + 568 + ], + "spans": [ + { + "bbox": [ + 104, + 549, + 421, + 567 + ], + "score": 1.0, + "content": "has larger distance in the feature space than other spurious solutions y = x2[1]", + "type": "text" + }, + { + "bbox": [ + 384, + 550, + 443, + 566 + ], + "score": 0.94, + "content": "y = x _ { [ 1 ] } ^ { 2 } - x _ { [ i ] } ^ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 422, + 546, + 510, + 568 + ], + "score": 1.0, + "content": "\u0000 x2[i] . 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This intuition is", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 597, + 309, + 609 + ], + "spans": [ + { + "bbox": [ + 106, + 597, + 309, + 609 + ], + "score": 1.0, + "content": "rigorously justified in the following two theorems.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 33.5 + }, + { + "type": "text", + "bbox": [ + 106, + 610, + 505, + 622 + ], + "lines": [ + { + "bbox": [ + 105, + 608, + 507, + 624 + ], + "spans": [ + { + "bbox": [ + 105, + 608, + 176, + 624 + ], + "score": 1.0, + "content": "Theorem 3. 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We experiment on visual object recognition and linguistic sentiment classification tasks:", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 226, + 506, + 240 + ], + "spans": [ + { + "bbox": [ + 105, + 226, + 506, + 240 + ], + "score": 1.0, + "content": "Office-Home [64] has 65 classes from four kinds of environment with large domain gap: Artistic (Ar),", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 237, + 506, + 250 + ], + "spans": [ + { + "bbox": [ + 106, + 237, + 199, + 250 + ], + "score": 1.0, + "content": "Clip Art (Cl), Product", + "type": "text" + }, + { + "bbox": [ + 200, + 238, + 217, + 249 + ], + "score": 0.66, + "content": "( \\mathbf { P r } )", + "type": "inline_equation" + }, + { + "bbox": [ + 218, + 237, + 506, + 250 + ], + "score": 1.0, + "content": ", and Real-World (Rw); VisDA-2017 [45] is a large-scale UDA dataset", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 248, + 505, + 261 + ], + "spans": [ + { + "bbox": [ + 105, + 248, + 415, + 261 + ], + "score": 1.0, + "content": "with two domains named Synthetic and Real. The datasets consist of over", + "type": "text" + }, + { + "bbox": [ + 415, + 249, + 437, + 259 + ], + "score": 0.47, + "content": "2 0 0 \\mathrm { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 437, + 248, + 505, + 261 + ], + "score": 1.0, + "content": "images from 12", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 260, + 506, + 272 + ], + "spans": [ + { + "bbox": [ + 105, + 260, + 506, + 272 + ], + "score": 1.0, + "content": "categories of objects; Amazon Review [10] is a linguistic sentiment classification dataset of product", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 271, + 434, + 282 + ], + "spans": [ + { + "bbox": [ + 106, + 271, + 236, + 282 + ], + "score": 1.0, + "content": "reviews in four products: Books", + "type": "text" + }, + { + "bbox": [ + 236, + 271, + 250, + 282 + ], + "score": 0.31, + "content": "\\mathbf { ( B ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 250, + 271, + 416, + 282 + ], + "score": 1.0, + "content": ", DVDs (D), Electronics (E), and Kitchen", + "type": "text" + }, + { + "bbox": [ + 416, + 271, + 430, + 281 + ], + "score": 0.31, + "content": "\\mathbf { \\eta } ( \\mathbf { K } )", + "type": "inline_equation" + }, + { + "bbox": [ + 431, + 271, + 434, + 282 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 10.5 + }, + { + "type": "text", + "bbox": [ + 106, + 286, + 506, + 433 + ], + "lines": [ + { + "bbox": [ + 106, + 287, + 506, + 299 + ], + "spans": [ + { + "bbox": [ + 106, + 287, + 506, + 299 + ], + "score": 1.0, + "content": "Implementation. We use ResNet-50 [26] (pretrained on ImageNet [53]) as feature extractors for", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 298, + 506, + 310 + ], + "spans": [ + { + "bbox": [ + 105, + 298, + 506, + 310 + ], + "score": 1.0, + "content": "vision tasks, and BERT [16] for linguistic tasks. On VisDA-2017, we also provide results of ResNet-", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 309, + 506, + 321 + ], + "spans": [ + { + "bbox": [ + 105, + 309, + 506, + 321 + ], + "score": 1.0, + "content": "101 to include more baselines. We use cross-entropy loss for classification on the source domain.", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 320, + 506, + 335 + ], + "spans": [ + { + "bbox": [ + 105, + 321, + 228, + 335 + ], + "score": 1.0, + "content": "When training the target head", + "type": "text" + }, + { + "bbox": [ + 229, + 320, + 238, + 332 + ], + "score": 0.88, + "content": "\\widehat { \\theta } _ { t }", + "type": "inline_equation" + }, + { + "bbox": [ + 239, + 321, + 506, + 335 + ], + "score": 1.0, + "content": "and updating the feature extractor with CST, we use squared loss", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 333, + 506, + 346 + ], + "spans": [ + { + "bbox": [ + 105, + 334, + 235, + 346 + ], + "score": 1.0, + "content": "to get the analytical solution of", + "type": "text" + }, + { + "bbox": [ + 235, + 333, + 245, + 345 + ], + "score": 0.88, + "content": "\\widehat { \\theta } _ { t }", + "type": "inline_equation" + }, + { + "bbox": [ + 245, + 334, + 506, + 346 + ], + "score": 1.0, + "content": "directly and avoid calculating second order derivatives as meta-", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 345, + 506, + 357 + ], + "spans": [ + { + "bbox": [ + 105, + 345, + 506, + 357 + ], + "score": 1.0, + "content": "learning [18]. Details on adapting squared loss to multi-class classification are deferred to Appendix B.", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 355, + 506, + 369 + ], + "spans": [ + { + "bbox": [ + 105, + 355, + 271, + 369 + ], + "score": 1.0, + "content": "We adopt SGD with initial learning rate", + "type": "text" + }, + { + "bbox": [ + 271, + 356, + 322, + 367 + ], + "score": 0.92, + "content": "\\eta _ { 0 } = 2 e - 3", + "type": "inline_equation" + }, + { + "bbox": [ + 323, + 355, + 438, + 369 + ], + "score": 1.0, + "content": "for image classification and", + "type": "text" + }, + { + "bbox": [ + 438, + 356, + 490, + 367 + ], + "score": 0.91, + "content": "\\eta _ { 0 } = 5 e - 4", + "type": "inline_equation" + }, + { + "bbox": [ + 490, + 355, + 506, + 369 + ], + "score": 1.0, + "content": "for", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 367, + 506, + 379 + ], + "spans": [ + { + "bbox": [ + 105, + 367, + 506, + 379 + ], + "score": 1.0, + "content": "sentiment classification. Following standard protocol in [26], we decay the learning rate by 0.1", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 377, + 506, + 390 + ], + "spans": [ + { + "bbox": [ + 105, + 377, + 506, + 390 + ], + "score": 1.0, + "content": "each 50 epochs until 150 epochs. We run all the tasks 3 times and report mean and deviation in", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 388, + 506, + 401 + ], + "spans": [ + { + "bbox": [ + 105, + 388, + 506, + 401 + ], + "score": 1.0, + "content": "top-1 accuracy. For VisDA-2017, we report the mean class accuracy. Following Theorem 2, we", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 399, + 505, + 412 + ], + "spans": [ + { + "bbox": [ + 105, + 399, + 347, + 412 + ], + "score": 1.0, + "content": "also enhance CST with sharpness-aware regularization [19]", + "type": "text" + }, + { + "bbox": [ + 347, + 400, + 397, + 411 + ], + "score": 0.63, + "content": "( \\mathbf { C S T + S A M } )", + "type": "inline_equation" + }, + { + "bbox": [ + 397, + 399, + 505, + 412 + ], + "score": 1.0, + "content": ", which help regularize the", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 410, + 506, + 422 + ], + "spans": [ + { + "bbox": [ + 105, + 410, + 506, + 422 + ], + "score": 1.0, + "content": "Lipschitzness of the function class. Due to space limit, we report mean accuracies in Tables 2 and 3", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 421, + 286, + 434 + ], + "spans": [ + { + "bbox": [ + 106, + 421, + 286, + 434 + ], + "score": 1.0, + "content": "and defer standard deviation to Appendix C.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 20 + }, + { + "type": "title", + "bbox": [ + 107, + 440, + 170, + 451 + ], + "lines": [ + { + "bbox": [ + 105, + 439, + 171, + 453 + ], + "spans": [ + { + "bbox": [ + 105, + 439, + 171, + 453 + ], + "score": 1.0, + "content": "5.2 Baselines", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 27 + }, + { + "type": "text", + "bbox": [ + 109, + 458, + 503, + 492 + ], + "lines": [ + { + "bbox": [ + 106, + 457, + 505, + 471 + ], + "spans": [ + { + "bbox": [ + 106, + 457, + 505, + 471 + ], + "score": 1.0, + "content": "We compare with two lines of works in domain adaptation: feature adaptation and self-training. We", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 107, + 469, + 504, + 482 + ], + "spans": [ + { + "bbox": [ + 107, + 469, + 504, + 482 + ], + "score": 1.0, + "content": "also compare with more complex state-of-the-arts and create stronger baselines by combining feature", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 479, + 222, + 494 + ], + "spans": [ + { + "bbox": [ + 106, + 479, + 222, + 494 + ], + "score": 1.0, + "content": "adaptation and self-training.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 29 + }, + { + "type": "text", + "bbox": [ + 106, + 496, + 506, + 530 + ], + "lines": [ + { + "bbox": [ + 105, + 496, + 506, + 509 + ], + "spans": [ + { + "bbox": [ + 105, + 496, + 506, + 509 + ], + "score": 1.0, + "content": "Feature Adaptation: DANN [22], MCD [54], CDAN [37] (which improves DANN with pseudo-", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 506, + 506, + 521 + ], + "spans": [ + { + "bbox": [ + 105, + 506, + 506, + 521 + ], + "score": 1.0, + "content": "label conditioning), MDD [73] (which improves previous domain adaptation with margin theory),", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 518, + 417, + 532 + ], + "spans": [ + { + "bbox": [ + 106, + 518, + 417, + 532 + ], + "score": 1.0, + "content": "Implicit Alignment (IA) [28] (which improves MDD to deal with label shift).", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 32 + }, + { + "type": "text", + "bbox": [ + 106, + 534, + 505, + 601 + ], + "lines": [ + { + "bbox": [ + 106, + 535, + 505, + 546 + ], + "spans": [ + { + "bbox": [ + 106, + 535, + 505, + 546 + ], + "score": 1.0, + "content": "Self-Training. We include VAT [40], MixMatch [8] and FixMatch [57] in the semi-supervised", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 546, + 506, + 558 + ], + "spans": [ + { + "bbox": [ + 106, + 546, + 506, + 558 + ], + "score": 1.0, + "content": "learning literature as self-training methods. We also compare with self-training methods for UDA:", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 556, + 506, + 569 + ], + "spans": [ + { + "bbox": [ + 105, + 556, + 506, + 569 + ], + "score": 1.0, + "content": "CBST [77], which considers class imbalance in standard self-training, and KLD [78], which improves", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 567, + 505, + 580 + ], + "spans": [ + { + "bbox": [ + 106, + 567, + 505, + 580 + ], + "score": 1.0, + "content": "CBST with label regularization. However, these methods involve tricks specified for convolutional", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 578, + 505, + 591 + ], + "spans": [ + { + "bbox": [ + 105, + 578, + 505, + 591 + ], + "score": 1.0, + "content": "networks. Thus, in sentiment classification tasks where we use BERT backbones, we compare with", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 590, + 437, + 601 + ], + "spans": [ + { + "bbox": [ + 106, + 590, + 338, + 601 + ], + "score": 1.0, + "content": "other consistency regularization baselines: VAT [40], VAT", + "type": "text" + }, + { + "bbox": [ + 339, + 591, + 345, + 599 + ], + "score": 0.26, + "content": "^ { \\cdot } +", + "type": "inline_equation" + }, + { + "bbox": [ + 345, + 590, + 437, + 601 + ], + "score": 1.0, + "content": "Entropy Minimization.", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 36.5 + }, + { + "type": "text", + "bbox": [ + 106, + 605, + 504, + 628 + ], + "lines": [ + { + "bbox": [ + 105, + 605, + 505, + 618 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 191, + 618 + ], + "score": 1.0, + "content": "Feature Adaptation", + "type": "text" + }, + { + "bbox": [ + 192, + 607, + 200, + 616 + ], + "score": 0.73, + "content": "^ +", + "type": "inline_equation" + }, + { + "bbox": [ + 201, + 605, + 505, + 618 + ], + "score": 1.0, + "content": "Self-Training. DIRT-T [56] combines DANN, VAT, and entropy minimiza-", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 617, + 471, + 628 + ], + "spans": [ + { + "bbox": [ + 106, + 617, + 319, + 628 + ], + "score": 1.0, + "content": "tion. We also create more powerful baselines: CDAN", + "type": "text" + }, + { + "bbox": [ + 320, + 618, + 326, + 626 + ], + "score": 0.41, + "content": "^ +", + "type": "inline_equation" + }, + { + "bbox": [ + 327, + 617, + 343, + 628 + ], + "score": 1.0, + "content": "VAT", + "type": "text" + }, + { + "bbox": [ + 344, + 618, + 350, + 626 + ], + "score": 0.26, + "content": "^ +", + "type": "inline_equation" + }, + { + "bbox": [ + 350, + 617, + 424, + 628 + ], + "score": 1.0, + "content": "Entropy and MDD", + "type": "text" + }, + { + "bbox": [ + 424, + 618, + 430, + 626 + ], + "score": 0.34, + "content": "+", + "type": "inline_equation" + }, + { + "bbox": [ + 430, + 617, + 471, + 628 + ], + "score": 1.0, + "content": "Fixmatch.", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 40.5 + }, + { + "type": "text", + "bbox": [ + 106, + 632, + 504, + 655 + ], + "lines": [ + { + "bbox": [ + 106, + 632, + 506, + 645 + ], + "spans": [ + { + "bbox": [ + 106, + 632, + 506, + 645 + ], + "score": 1.0, + "content": "Other SOTA. AFN [69] boosts transferability by large norm. STAR [38] aligns domains with stochas-", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 643, + 506, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 643, + 506, + 657 + ], + "score": 1.0, + "content": "tic classifiers. SENTRY [48] selects confident examples with a committee of random augmentations.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 42.5 + }, + { + "type": "title", + "bbox": [ + 106, + 663, + 162, + 674 + ], + "lines": [ + { + "bbox": [ + 106, + 662, + 162, + 675 + ], + "spans": [ + { + "bbox": [ + 106, + 662, + 162, + 675 + ], + "score": 1.0, + "content": "5.3 Results", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 44 + }, + { + "type": "text", + "bbox": [ + 108, + 678, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 106, + 678, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 678, + 505, + 689 + ], + "score": 1.0, + "content": "Results on 12 pairs of Office-Home tasks are shown in Table 2. When domain shift is large, standard", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 689, + 505, + 701 + ], + "spans": [ + { + "bbox": [ + 106, + 689, + 505, + 701 + ], + "score": 1.0, + "content": "self-training methods such as VAT and FixMatch suffer from the decay in pseudo-label quality. CST", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 700, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 700, + 506, + 712 + ], + "score": 1.0, + "content": "outperforms feature adaptation and self-training methods significantly in 9 out of 12 tasks. Note that", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 709, + 412, + 724 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 412, + 724 + ], + "score": 1.0, + "content": "CST does not involve manually setting confidence threshold or reweighting.", + "type": "text" + } + ], + "index": 48 + } + ], + "index": 46.5 + } + ], + "page_idx": 7, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 302, + 742, + 308, + 750 + ], + "lines": [ + { + "bbox": [ + 301, + 740, + 310, + 752 + ], + "spans": [ + { + "bbox": [ + 301, + 740, + 310, + 752 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 12, + "width": 9 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 105, + 72, + 505, + 100 + ], + "lines": [ + { + "bbox": [ + 105, + 71, + 506, + 87 + ], + "spans": [ + { + "bbox": [ + 105, + 71, + 223, + 87 + ], + "score": 1.0, + "content": "Theorem 4. For failure rate", + "type": "text" + }, + { + "bbox": [ + 223, + 73, + 248, + 84 + ], + "score": 0.9, + "content": "\\xi > 0", + "type": "inline_equation" + }, + { + "bbox": [ + 248, + 71, + 343, + 87 + ], + "score": 1.0, + "content": ", and target dataset size", + "type": "text" + }, + { + "bbox": [ + 343, + 72, + 403, + 87 + ], + "score": 0.93, + "content": "\\begin{array} { r } { n _ { t } > \\Theta ( \\log { \\frac { 1 } { \\xi } } ) } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 403, + 71, + 506, + 87 + ], + "score": 1.0, + "content": ", with probability at least", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 86, + 452, + 101 + ], + "spans": [ + { + "bbox": [ + 106, + 87, + 129, + 100 + ], + "score": 0.83, + "content": "1 - \\xi ,", + "type": "inline_equation" + }, + { + "bbox": [ + 130, + 87, + 192, + 101 + ], + "score": 1.0, + "content": ", the solution of", + "type": "text" + }, + { + "bbox": [ + 193, + 86, + 262, + 100 + ], + "score": 0.9, + "content": "C S T ( \\hat { \\phi } _ { \\mathrm { C S T } } , \\hat { \\theta } _ { \\mathrm { C S T } } )", + "type": "inline_equation" + }, + { + "bbox": [ + 262, + 87, + 452, + 101 + ], + "score": 1.0, + "content": "recovers the ground truth of the target dataset:", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5, + "bbox_fs": [ + 105, + 71, + 506, + 101 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 267, + 117, + 360, + 133 + ], + "lines": [ + { + "bbox": [ + 267, + 117, + 360, + 133 + ], + "spans": [ + { + "bbox": [ + 267, + 117, + 360, + 133 + ], + "score": 0.93, + "content": "\\mathrm { E r r } _ { Q } ( \\hat { \\theta } _ { \\mathrm { C S T } } , \\hat { \\phi } _ { \\mathrm { C S T } } ) = 0 .", + "type": "interline_equation", + "image_path": "a687f52493667af53742d40a8ef8dff8469302111c5c6a72746feb742d9f3911.jpg" + } + ] + } + ], + "index": 2, + "virtual_lines": [ + { + "bbox": [ + 267, + 117, + 360, + 133 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "title", + "bbox": [ + 107, + 140, + 191, + 154 + ], + "lines": [ + { + "bbox": [ + 104, + 139, + 193, + 157 + ], + "spans": [ + { + "bbox": [ + 104, + 139, + 193, + 157 + ], + "score": 1.0, + "content": "5 Experiments", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 3 + }, + { + "type": "text", + "bbox": [ + 108, + 160, + 505, + 193 + ], + "lines": [ + { + "bbox": [ + 105, + 159, + 506, + 173 + ], + "spans": [ + { + "bbox": [ + 105, + 159, + 506, + 173 + ], + "score": 1.0, + "content": "We test the performance of the proposed method on both vision and language datasets. Cycle Self-", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 171, + 506, + 183 + ], + "spans": [ + { + "bbox": [ + 106, + 171, + 506, + 183 + ], + "score": 1.0, + "content": "Training (CST) consistently outperforms state-of-the-art feature adaptation and self-training methods.", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 181, + 358, + 195 + ], + "spans": [ + { + "bbox": [ + 106, + 181, + 358, + 195 + ], + "score": 1.0, + "content": "Code is available at https://github.com/Liuhong99/CST.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 5, + "bbox_fs": [ + 105, + 159, + 506, + 195 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 201, + 155, + 212 + ], + "lines": [ + { + "bbox": [ + 105, + 198, + 156, + 216 + ], + "spans": [ + { + "bbox": [ + 105, + 198, + 156, + 216 + ], + "score": 1.0, + "content": "5.1 Setup", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 7 + }, + { + "type": "text", + "bbox": [ + 107, + 216, + 505, + 282 + ], + "lines": [ + { + "bbox": [ + 106, + 216, + 506, + 228 + ], + "spans": [ + { + "bbox": [ + 106, + 216, + 506, + 228 + ], + "score": 1.0, + "content": "Datasets. We experiment on visual object recognition and linguistic sentiment classification tasks:", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 226, + 506, + 240 + ], + "spans": [ + { + "bbox": [ + 105, + 226, + 506, + 240 + ], + "score": 1.0, + "content": "Office-Home [64] has 65 classes from four kinds of environment with large domain gap: Artistic (Ar),", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 237, + 506, + 250 + ], + "spans": [ + { + "bbox": [ + 106, + 237, + 199, + 250 + ], + "score": 1.0, + "content": "Clip Art (Cl), Product", + "type": "text" + }, + { + "bbox": [ + 200, + 238, + 217, + 249 + ], + "score": 0.66, + "content": "( \\mathbf { P r } )", + "type": "inline_equation" + }, + { + "bbox": [ + 218, + 237, + 506, + 250 + ], + "score": 1.0, + "content": ", and Real-World (Rw); VisDA-2017 [45] is a large-scale UDA dataset", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 248, + 505, + 261 + ], + "spans": [ + { + "bbox": [ + 105, + 248, + 415, + 261 + ], + "score": 1.0, + "content": "with two domains named Synthetic and Real. The datasets consist of over", + "type": "text" + }, + { + "bbox": [ + 415, + 249, + 437, + 259 + ], + "score": 0.47, + "content": "2 0 0 \\mathrm { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 437, + 248, + 505, + 261 + ], + "score": 1.0, + "content": "images from 12", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 260, + 506, + 272 + ], + "spans": [ + { + "bbox": [ + 105, + 260, + 506, + 272 + ], + "score": 1.0, + "content": "categories of objects; Amazon Review [10] is a linguistic sentiment classification dataset of product", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 271, + 434, + 282 + ], + "spans": [ + { + "bbox": [ + 106, + 271, + 236, + 282 + ], + "score": 1.0, + "content": "reviews in four products: Books", + "type": "text" + }, + { + "bbox": [ + 236, + 271, + 250, + 282 + ], + "score": 0.31, + "content": "\\mathbf { ( B ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 250, + 271, + 416, + 282 + ], + "score": 1.0, + "content": ", DVDs (D), Electronics (E), and Kitchen", + "type": "text" + }, + { + "bbox": [ + 416, + 271, + 430, + 281 + ], + "score": 0.31, + "content": "\\mathbf { \\eta } ( \\mathbf { K } )", + "type": "inline_equation" + }, + { + "bbox": [ + 431, + 271, + 434, + 282 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 10.5, + "bbox_fs": [ + 105, + 216, + 506, + 282 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 286, + 506, + 433 + ], + "lines": [ + { + "bbox": [ + 106, + 287, + 506, + 299 + ], + "spans": [ + { + "bbox": [ + 106, + 287, + 506, + 299 + ], + "score": 1.0, + "content": "Implementation. We use ResNet-50 [26] (pretrained on ImageNet [53]) as feature extractors for", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 298, + 506, + 310 + ], + "spans": [ + { + "bbox": [ + 105, + 298, + 506, + 310 + ], + "score": 1.0, + "content": "vision tasks, and BERT [16] for linguistic tasks. On VisDA-2017, we also provide results of ResNet-", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 309, + 506, + 321 + ], + "spans": [ + { + "bbox": [ + 105, + 309, + 506, + 321 + ], + "score": 1.0, + "content": "101 to include more baselines. We use cross-entropy loss for classification on the source domain.", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 320, + 506, + 335 + ], + "spans": [ + { + "bbox": [ + 105, + 321, + 228, + 335 + ], + "score": 1.0, + "content": "When training the target head", + "type": "text" + }, + { + "bbox": [ + 229, + 320, + 238, + 332 + ], + "score": 0.88, + "content": "\\widehat { \\theta } _ { t }", + "type": "inline_equation" + }, + { + "bbox": [ + 239, + 321, + 506, + 335 + ], + "score": 1.0, + "content": "and updating the feature extractor with CST, we use squared loss", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 333, + 506, + 346 + ], + "spans": [ + { + "bbox": [ + 105, + 334, + 235, + 346 + ], + "score": 1.0, + "content": "to get the analytical solution of", + "type": "text" + }, + { + "bbox": [ + 235, + 333, + 245, + 345 + ], + "score": 0.88, + "content": "\\widehat { \\theta } _ { t }", + "type": "inline_equation" + }, + { + "bbox": [ + 245, + 334, + 506, + 346 + ], + "score": 1.0, + "content": "directly and avoid calculating second order derivatives as meta-", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 345, + 506, + 357 + ], + "spans": [ + { + "bbox": [ + 105, + 345, + 506, + 357 + ], + "score": 1.0, + "content": "learning [18]. Details on adapting squared loss to multi-class classification are deferred to Appendix B.", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 355, + 506, + 369 + ], + "spans": [ + { + "bbox": [ + 105, + 355, + 271, + 369 + ], + "score": 1.0, + "content": "We adopt SGD with initial learning rate", + "type": "text" + }, + { + "bbox": [ + 271, + 356, + 322, + 367 + ], + "score": 0.92, + "content": "\\eta _ { 0 } = 2 e - 3", + "type": "inline_equation" + }, + { + "bbox": [ + 323, + 355, + 438, + 369 + ], + "score": 1.0, + "content": "for image classification and", + "type": "text" + }, + { + "bbox": [ + 438, + 356, + 490, + 367 + ], + "score": 0.91, + "content": "\\eta _ { 0 } = 5 e - 4", + "type": "inline_equation" + }, + { + "bbox": [ + 490, + 355, + 506, + 369 + ], + "score": 1.0, + "content": "for", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 367, + 506, + 379 + ], + "spans": [ + { + "bbox": [ + 105, + 367, + 506, + 379 + ], + "score": 1.0, + "content": "sentiment classification. Following standard protocol in [26], we decay the learning rate by 0.1", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 377, + 506, + 390 + ], + "spans": [ + { + "bbox": [ + 105, + 377, + 506, + 390 + ], + "score": 1.0, + "content": "each 50 epochs until 150 epochs. We run all the tasks 3 times and report mean and deviation in", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 388, + 506, + 401 + ], + "spans": [ + { + "bbox": [ + 105, + 388, + 506, + 401 + ], + "score": 1.0, + "content": "top-1 accuracy. For VisDA-2017, we report the mean class accuracy. Following Theorem 2, we", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 399, + 505, + 412 + ], + "spans": [ + { + "bbox": [ + 105, + 399, + 347, + 412 + ], + "score": 1.0, + "content": "also enhance CST with sharpness-aware regularization [19]", + "type": "text" + }, + { + "bbox": [ + 347, + 400, + 397, + 411 + ], + "score": 0.63, + "content": "( \\mathbf { C S T + S A M } )", + "type": "inline_equation" + }, + { + "bbox": [ + 397, + 399, + 505, + 412 + ], + "score": 1.0, + "content": ", which help regularize the", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 410, + 506, + 422 + ], + "spans": [ + { + "bbox": [ + 105, + 410, + 506, + 422 + ], + "score": 1.0, + "content": "Lipschitzness of the function class. Due to space limit, we report mean accuracies in Tables 2 and 3", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 421, + 286, + 434 + ], + "spans": [ + { + "bbox": [ + 106, + 421, + 286, + 434 + ], + "score": 1.0, + "content": "and defer standard deviation to Appendix C.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 20, + "bbox_fs": [ + 105, + 287, + 506, + 434 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 440, + 170, + 451 + ], + "lines": [ + { + "bbox": [ + 105, + 439, + 171, + 453 + ], + "spans": [ + { + "bbox": [ + 105, + 439, + 171, + 453 + ], + "score": 1.0, + "content": "5.2 Baselines", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 27 + }, + { + "type": "text", + "bbox": [ + 109, + 458, + 503, + 492 + ], + "lines": [ + { + "bbox": [ + 106, + 457, + 505, + 471 + ], + "spans": [ + { + "bbox": [ + 106, + 457, + 505, + 471 + ], + "score": 1.0, + "content": "We compare with two lines of works in domain adaptation: feature adaptation and self-training. We", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 107, + 469, + 504, + 482 + ], + "spans": [ + { + "bbox": [ + 107, + 469, + 504, + 482 + ], + "score": 1.0, + "content": "also compare with more complex state-of-the-arts and create stronger baselines by combining feature", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 479, + 222, + 494 + ], + "spans": [ + { + "bbox": [ + 106, + 479, + 222, + 494 + ], + "score": 1.0, + "content": "adaptation and self-training.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 29, + "bbox_fs": [ + 106, + 457, + 505, + 494 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 496, + 506, + 530 + ], + "lines": [ + { + "bbox": [ + 105, + 496, + 506, + 509 + ], + "spans": [ + { + "bbox": [ + 105, + 496, + 506, + 509 + ], + "score": 1.0, + "content": "Feature Adaptation: DANN [22], MCD [54], CDAN [37] (which improves DANN with pseudo-", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 506, + 506, + 521 + ], + "spans": [ + { + "bbox": [ + 105, + 506, + 506, + 521 + ], + "score": 1.0, + "content": "label conditioning), MDD [73] (which improves previous domain adaptation with margin theory),", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 518, + 417, + 532 + ], + "spans": [ + { + "bbox": [ + 106, + 518, + 417, + 532 + ], + "score": 1.0, + "content": "Implicit Alignment (IA) [28] (which improves MDD to deal with label shift).", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 32, + "bbox_fs": [ + 105, + 496, + 506, + 532 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 534, + 505, + 601 + ], + "lines": [ + { + "bbox": [ + 106, + 535, + 505, + 546 + ], + "spans": [ + { + "bbox": [ + 106, + 535, + 505, + 546 + ], + "score": 1.0, + "content": "Self-Training. We include VAT [40], MixMatch [8] and FixMatch [57] in the semi-supervised", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 546, + 506, + 558 + ], + "spans": [ + { + "bbox": [ + 106, + 546, + 506, + 558 + ], + "score": 1.0, + "content": "learning literature as self-training methods. We also compare with self-training methods for UDA:", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 556, + 506, + 569 + ], + "spans": [ + { + "bbox": [ + 105, + 556, + 506, + 569 + ], + "score": 1.0, + "content": "CBST [77], which considers class imbalance in standard self-training, and KLD [78], which improves", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 567, + 505, + 580 + ], + "spans": [ + { + "bbox": [ + 106, + 567, + 505, + 580 + ], + "score": 1.0, + "content": "CBST with label regularization. However, these methods involve tricks specified for convolutional", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 578, + 505, + 591 + ], + "spans": [ + { + "bbox": [ + 105, + 578, + 505, + 591 + ], + "score": 1.0, + "content": "networks. Thus, in sentiment classification tasks where we use BERT backbones, we compare with", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 590, + 437, + 601 + ], + "spans": [ + { + "bbox": [ + 106, + 590, + 338, + 601 + ], + "score": 1.0, + "content": "other consistency regularization baselines: VAT [40], VAT", + "type": "text" + }, + { + "bbox": [ + 339, + 591, + 345, + 599 + ], + "score": 0.26, + "content": "^ { \\cdot } +", + "type": "inline_equation" + }, + { + "bbox": [ + 345, + 590, + 437, + 601 + ], + "score": 1.0, + "content": "Entropy Minimization.", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 36.5, + "bbox_fs": [ + 105, + 535, + 506, + 601 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 605, + 504, + 628 + ], + "lines": [ + { + "bbox": [ + 105, + 605, + 505, + 618 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 191, + 618 + ], + "score": 1.0, + "content": "Feature Adaptation", + "type": "text" + }, + { + "bbox": [ + 192, + 607, + 200, + 616 + ], + "score": 0.73, + "content": "^ +", + "type": "inline_equation" + }, + { + "bbox": [ + 201, + 605, + 505, + 618 + ], + "score": 1.0, + "content": "Self-Training. DIRT-T [56] combines DANN, VAT, and entropy minimiza-", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 617, + 471, + 628 + ], + "spans": [ + { + "bbox": [ + 106, + 617, + 319, + 628 + ], + "score": 1.0, + "content": "tion. We also create more powerful baselines: CDAN", + "type": "text" + }, + { + "bbox": [ + 320, + 618, + 326, + 626 + ], + "score": 0.41, + "content": "^ +", + "type": "inline_equation" + }, + { + "bbox": [ + 327, + 617, + 343, + 628 + ], + "score": 1.0, + "content": "VAT", + "type": "text" + }, + { + "bbox": [ + 344, + 618, + 350, + 626 + ], + "score": 0.26, + "content": "^ +", + "type": "inline_equation" + }, + { + "bbox": [ + 350, + 617, + 424, + 628 + ], + "score": 1.0, + "content": "Entropy and MDD", + "type": "text" + }, + { + "bbox": [ + 424, + 618, + 430, + 626 + ], + "score": 0.34, + "content": "+", + "type": "inline_equation" + }, + { + "bbox": [ + 430, + 617, + 471, + 628 + ], + "score": 1.0, + "content": "Fixmatch.", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 40.5, + "bbox_fs": [ + 105, + 605, + 505, + 628 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 632, + 504, + 655 + ], + "lines": [ + { + "bbox": [ + 106, + 632, + 506, + 645 + ], + "spans": [ + { + "bbox": [ + 106, + 632, + 506, + 645 + ], + "score": 1.0, + "content": "Other SOTA. AFN [69] boosts transferability by large norm. STAR [38] aligns domains with stochas-", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 643, + 506, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 643, + 506, + 657 + ], + "score": 1.0, + "content": "tic classifiers. SENTRY [48] selects confident examples with a committee of random augmentations.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 42.5, + "bbox_fs": [ + 105, + 632, + 506, + 657 + ] + }, + { + "type": "title", + "bbox": [ + 106, + 663, + 162, + 674 + ], + "lines": [ + { + "bbox": [ + 106, + 662, + 162, + 675 + ], + "spans": [ + { + "bbox": [ + 106, + 662, + 162, + 675 + ], + "score": 1.0, + "content": "5.3 Results", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 44 + }, + { + "type": "text", + "bbox": [ + 108, + 678, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 106, + 678, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 678, + 505, + 689 + ], + "score": 1.0, + "content": "Results on 12 pairs of Office-Home tasks are shown in Table 2. When domain shift is large, standard", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 689, + 505, + 701 + ], + "spans": [ + { + "bbox": [ + 106, + 689, + 505, + 701 + ], + "score": 1.0, + "content": "self-training methods such as VAT and FixMatch suffer from the decay in pseudo-label quality. CST", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 700, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 700, + 506, + 712 + ], + "score": 1.0, + "content": "outperforms feature adaptation and self-training methods significantly in 9 out of 12 tasks. Note that", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 709, + 412, + 724 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 412, + 724 + ], + "score": 1.0, + "content": "CST does not involve manually setting confidence threshold or reweighting.", + "type": "text" + } + ], + "index": 48 + } + ], + "index": 46.5, + "bbox_fs": [ + 105, + 678, + 506, + 724 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 107, + 83, + 505, + 190 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 119, + 71, + 486, + 83 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 122, + 70, + 488, + 85 + ], + "spans": [ + { + "bbox": [ + 122, + 70, + 199, + 85 + ], + "score": 1.0, + "content": "Table 2: Accuracy", + "type": "text" + }, + { + "bbox": [ + 200, + 72, + 215, + 82 + ], + "score": 0.71, + "content": "( \\% )", + "type": "inline_equation" + }, + { + "bbox": [ + 216, + 70, + 488, + 85 + ], + "score": 1.0, + "content": "on Office-Home for unsupervised domain adaptation (ResNet-50).", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "table_body", + "bbox": [ + 107, + 83, + 505, + 190 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 107, + 83, + 505, + 190 + ], + "spans": [ + { + "bbox": [ + 107, + 83, + 505, + 190 + ], + "score": 0.978, + "html": "
Method|Ar-Cl Ar-Pr Ar-Rw Cl-Ar Cl-Pr Cl-Rw Pr-Ar Pr-CIPr-Rw Rw-Ar Rw-Cl Rw-Pr|Avg.
DANN [22]45.659.370.147.058.560.946.143.768.563.251.876.857.6
CDAN [37]50.770.676.057.670.070.057.450.977.370.956.781.665.8
CDAN+VAT+Entropy52.271.576.461.170.367.859.554.478.673.259.082.767.3
FixMatch [57]51.874.280.163.573.861.364.751.480.073.356.881.767.7
MDD [73]54.973.777.860.071.471.861.253.678.172.560.282.368.1
MDD+IA [28]56.277.979.264.473.174.464.254.279.971.258.183.169.5
SENTRY [48]61.877.480.166.371.674.766.863.080.974.066.384.172.2
CST59.079.683.468.477.176.768.956.483.075.362.285.1|73.0
", + "type": "table", + "image_path": "eb42d296b2f1285d0c7b99e47a1d81c9ac4a636562d148c0779058e73bc8001b.jpg" + } + ] + } + ], + "index": 2, + "virtual_lines": [ + { + "bbox": [ + 107, + 83, + 505, + 118.66666666666666 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 107, + 118.66666666666666, + 505, + 154.33333333333331 + ], + "spans": [], + "index": 2 + }, + { + "bbox": [ + 107, + 154.33333333333331, + 505, + 189.99999999999997 + ], + "spans": [], + "index": 3 + } + ] + } + ], + "index": 1.0 + }, + { + "type": "table", + "bbox": [ + 106, + 213, + 504, + 299 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 112, + 200, + 494, + 212 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 117, + 200, + 494, + 213 + ], + "spans": [ + { + "bbox": [ + 117, + 200, + 192, + 213 + ], + "score": 1.0, + "content": "Table 3: Accuracy", + "type": "text" + }, + { + "bbox": [ + 193, + 201, + 209, + 212 + ], + "score": 0.75, + "content": "( \\% )", + "type": "inline_equation" + }, + { + "bbox": [ + 209, + 200, + 494, + 213 + ], + "score": 1.0, + "content": "on Multi-Domain Sentiment Dataset for domain adaptation with BERT.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 4 + }, + { + "type": "table_body", + "bbox": [ + 106, + 213, + 504, + 299 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 106, + 213, + 504, + 299 + ], + "spans": [ + { + "bbox": [ + 106, + 213, + 504, + 299 + ], + "score": 0.974, + "html": "
MethodB-DB-EB-KD-BD-ED-KE-BE-DE-KK-BK-DK-EAvg.
Source-only89.788.490.990.188.590.286.988.591.587.687.391.289.2
DANN [22]90.289.590.991.090.690.287.187.592.887.887.693.289.9
VAT[40]90.691.091.790.890.892.087.286.992.686.987.792.990.1
VAT+Entropy90.491.391.591.091.192.487.586.392.486.587.593.190.1
MDD [73]90.490.491.890.290.991.087.586.392.589.087.992.190.0
CST91.592.992.691.992.693.590.289.493.887.988.393.591.5
", + "type": "table", + "image_path": "064187228bcfd5fa0d44b25d3abd40425be164827f67f87214f6fccf6617bc69.jpg" + } + ] + } + ], + "index": 6, + "virtual_lines": [ + { + "bbox": [ + 106, + 213, + 504, + 241.66666666666666 + ], + "spans": [], + "index": 5 + }, + { + "bbox": [ + 106, + 241.66666666666666, + 504, + 270.3333333333333 + ], + "spans": [], + "index": 6 + }, + { + "bbox": [ + 106, + 270.3333333333333, + 504, + 299.0 + ], + "spans": [], + "index": 7 + } + ] + } + ], + "index": 5.0 + }, + { + "type": "text", + "bbox": [ + 107, + 326, + 505, + 370 + ], + "lines": [ + { + "bbox": [ + 104, + 325, + 507, + 339 + ], + "spans": [ + { + "bbox": [ + 104, + 325, + 507, + 339 + ], + "score": 1.0, + "content": "Table 4 shows the results on VisDA-2017. CST surpasses state-of-the-arts with ResNet-50 and ResNet-", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 336, + 505, + 351 + ], + "spans": [ + { + "bbox": [ + 105, + 336, + 505, + 351 + ], + "score": 1.0, + "content": "101 backbones. We also combine feature adaptation and self-training (DIRT-T, CDAN+VAT+entropy", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 348, + 505, + 361 + ], + "spans": [ + { + "bbox": [ + 105, + 348, + 147, + 361 + ], + "score": 1.0, + "content": "and MDD", + "type": "text" + }, + { + "bbox": [ + 148, + 350, + 154, + 358 + ], + "score": 0.38, + "content": "^ { + }", + "type": "inline_equation" + }, + { + "bbox": [ + 155, + 348, + 505, + 361 + ], + "score": 1.0, + "content": "FixMatch) to test if feature adaptation alleviates the negative effect of domain shift in", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 359, + 480, + 371 + ], + "spans": [ + { + "bbox": [ + 106, + 359, + 480, + 371 + ], + "score": 1.0, + "content": "standard self-training. Results indicate that CST is a better solution than simple combination.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 9.5 + }, + { + "type": "text", + "bbox": [ + 106, + 375, + 505, + 420 + ], + "lines": [ + { + "bbox": [ + 105, + 375, + 505, + 388 + ], + "spans": [ + { + "bbox": [ + 105, + 375, + 505, + 388 + ], + "score": 1.0, + "content": "While most traditional self-training methods include techniques specified for ConvNets such as", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 386, + 505, + 398 + ], + "spans": [ + { + "bbox": [ + 105, + 386, + 505, + 398 + ], + "score": 1.0, + "content": "Mixup [72], CST is a universal method and can directly work on sentiment classification by simply", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 398, + 505, + 410 + ], + "spans": [ + { + "bbox": [ + 106, + 398, + 505, + 410 + ], + "score": 1.0, + "content": "replacing the head and training objective of BERT [16]. In Table 3, most feature adaptation baselines", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 408, + 507, + 421 + ], + "spans": [ + { + "bbox": [ + 105, + 408, + 507, + 421 + ], + "score": 1.0, + "content": "improve over source only marginally, but CST outperforms all baselines on most tasks significantly.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 13.5 + }, + { + "type": "title", + "bbox": [ + 107, + 434, + 166, + 446 + ], + "lines": [ + { + "bbox": [ + 105, + 433, + 168, + 447 + ], + "spans": [ + { + "bbox": [ + 105, + 433, + 168, + 447 + ], + "score": 1.0, + "content": "5.4 Analysis", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 16 + }, + { + "type": "text", + "bbox": [ + 107, + 451, + 334, + 540 + ], + "lines": [ + { + "bbox": [ + 106, + 451, + 334, + 463 + ], + "spans": [ + { + "bbox": [ + 106, + 451, + 334, + 463 + ], + "score": 1.0, + "content": "Ablation Study. We study the role of each part of CST", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 462, + 335, + 474 + ], + "spans": [ + { + "bbox": [ + 106, + 462, + 335, + 474 + ], + "score": 1.0, + "content": "in self-training. CST w/o Tsallis removes the Tsallis en-", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 473, + 334, + 487 + ], + "spans": [ + { + "bbox": [ + 106, + 473, + 129, + 487 + ], + "score": 1.0, + "content": "tropy", + "type": "text" + }, + { + "bbox": [ + 129, + 474, + 164, + 486 + ], + "score": 0.91, + "content": "L _ { \\mathrm { T s a l l i s } , \\alpha }", + "type": "inline_equation" + }, + { + "bbox": [ + 164, + 473, + 186, + 487 + ], + "score": 1.0, + "content": ". CST", + "type": "text" + }, + { + "bbox": [ + 187, + 475, + 193, + 483 + ], + "score": 0.27, + "content": "+", + "type": "inline_equation" + }, + { + "bbox": [ + 193, + 473, + 334, + 487 + ], + "score": 1.0, + "content": "Entropy replaces the Tsallis entropy", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 483, + 334, + 497 + ], + "spans": [ + { + "bbox": [ + 105, + 483, + 288, + 497 + ], + "score": 1.0, + "content": "with standard entropy. FixMatch+Tsallis adds", + "type": "text" + }, + { + "bbox": [ + 288, + 485, + 322, + 496 + ], + "score": 0.92, + "content": "L _ { \\mathrm { T s a l l i s } , \\alpha }", + "type": "inline_equation" + }, + { + "bbox": [ + 322, + 483, + 334, + 497 + ], + "score": 1.0, + "content": "to", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 495, + 335, + 507 + ], + "spans": [ + { + "bbox": [ + 106, + 495, + 335, + 507 + ], + "score": 1.0, + "content": "standard self-training. Observations are shown in Table 5.", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 505, + 334, + 519 + ], + "spans": [ + { + "bbox": [ + 106, + 506, + 132, + 517 + ], + "score": 0.48, + "content": "\\mathrm { C S T + l }", + "type": "inline_equation" + }, + { + "bbox": [ + 132, + 505, + 201, + 519 + ], + "score": 1.0, + "content": "Entropy performs", + "type": "text" + }, + { + "bbox": [ + 201, + 506, + 224, + 517 + ], + "score": 0.88, + "content": "3 . 7 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 224, + 505, + 334, + 519 + ], + "score": 1.0, + "content": "worse than CST, indicating", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 516, + 335, + 529 + ], + "spans": [ + { + "bbox": [ + 105, + 516, + 335, + 529 + ], + "score": 1.0, + "content": "that Tsallis entropy is a better regularization for pseudo-", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 528, + 334, + 540 + ], + "spans": [ + { + "bbox": [ + 106, + 528, + 284, + 540 + ], + "score": 1.0, + "content": "labels than standard entropy. CST performs", + "type": "text" + }, + { + "bbox": [ + 285, + 528, + 307, + 539 + ], + "score": 0.88, + "content": "5 . 4 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 307, + 528, + 334, + 540 + ], + "score": 1.0, + "content": "better", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 22.5 + }, + { + "type": "table", + "bbox": [ + 341, + 460, + 504, + 537 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 357, + 450, + 487, + 459 + ], + "group_id": 2, + "lines": [ + { + "bbox": [ + 357, + 449, + 488, + 461 + ], + "spans": [ + { + "bbox": [ + 357, + 449, + 488, + 461 + ], + "score": 1.0, + "content": "Table 5: Ablation on VisDA-2017.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 21 + }, + { + "type": "table_body", + "bbox": [ + 341, + 460, + 504, + 537 + ], + "group_id": 2, + "lines": [ + { + "bbox": [ + 341, + 460, + 504, + 537 + ], + "spans": [ + { + "bbox": [ + 341, + 460, + 504, + 537 + ], + "score": 0.971, + "html": "
MethodAccuracy ↑|drv↓
FixMatch [57]74.5 ± 0.20.22
Fixmatch+Tsallis76.3 ± 0.80.15
CST w/o Tsallis72.0 ± 0.40.16
CST+Entropy76.2 ± 0.60.20
CST79.9 ± 0.50.12
", + "type": "table", + "image_path": "1f009038872b5ecebb92230a8969f0c1c81ac204407dd1ce16149601336c7a75.jpg" + } + ] + } + ], + "index": 28, + "virtual_lines": [ + { + "bbox": [ + 341, + 460, + 504, + 475.4 + ], + "spans": [], + "index": 20 + }, + { + "bbox": [ + 341, + 475.4, + 504, + 490.79999999999995 + ], + "spans": [], + "index": 27 + }, + { + "bbox": [ + 341, + 490.79999999999995, + 504, + 506.19999999999993 + ], + "spans": [], + "index": 28 + }, + { + "bbox": [ + 341, + 506.19999999999993, + 504, + 521.5999999999999 + ], + "spans": [], + "index": 29 + }, + { + "bbox": [ + 341, + 521.5999999999999, + 504, + 536.9999999999999 + ], + "spans": [], + "index": 30 + } + ] + } + ], + "index": 24.5 + }, + { + "type": "text", + "bbox": [ + 107, + 540, + 504, + 583 + ], + "lines": [ + { + "bbox": [ + 106, + 539, + 506, + 551 + ], + "spans": [ + { + "bbox": [ + 106, + 539, + 506, + 551 + ], + "score": 1.0, + "content": "than FixMatch, indicating that CST is better adapted to domain shift than standard self-training. While", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 549, + 506, + 562 + ], + "spans": [ + { + "bbox": [ + 105, + 549, + 305, + 562 + ], + "score": 1.0, + "content": "FixMatch+Tsallis outperforms FixMatch, it is still", + "type": "text" + }, + { + "bbox": [ + 305, + 550, + 328, + 561 + ], + "score": 0.88, + "content": "3 . 6 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 328, + 549, + 506, + 562 + ], + "score": 1.0, + "content": "behind CST, with much larger total variation", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 561, + 505, + 573 + ], + "spans": [ + { + "bbox": [ + 106, + 561, + 142, + 573 + ], + "score": 1.0, + "content": "distance", + "type": "text" + }, + { + "bbox": [ + 143, + 561, + 159, + 572 + ], + "score": 0.88, + "content": "d _ { \\mathrm { T V } }", + "type": "inline_equation" + }, + { + "bbox": [ + 159, + 561, + 505, + 573 + ], + "score": 1.0, + "content": "between pseudo-labels and ground-truths, indicating that CST makes pseudo-labels", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 572, + 349, + 584 + ], + "spans": [ + { + "bbox": [ + 105, + 572, + 349, + 584 + ], + "score": 1.0, + "content": "more reliable than standard self-training under domain shift.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 32.5 + }, + { + "type": "text", + "bbox": [ + 106, + 587, + 505, + 654 + ], + "lines": [ + { + "bbox": [ + 106, + 587, + 505, + 600 + ], + "spans": [ + { + "bbox": [ + 106, + 587, + 505, + 600 + ], + "score": 1.0, + "content": "Quality of Pseudo-labels. We visualize the error of pseudo-labels during training on VisDA-2017 in", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 104, + 597, + 507, + 613 + ], + "spans": [ + { + "bbox": [ + 104, + 597, + 286, + 613 + ], + "score": 1.0, + "content": "Figure 5 (Left). The error of target classifier", + "type": "text" + }, + { + "bbox": [ + 286, + 599, + 296, + 610 + ], + "score": 0.86, + "content": "\\theta _ { t }", + "type": "inline_equation" + }, + { + "bbox": [ + 296, + 597, + 507, + 613 + ], + "score": 1.0, + "content": "on the source domain decreases quickly in training,", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 609, + 505, + 623 + ], + "spans": [ + { + "bbox": [ + 105, + 609, + 288, + 623 + ], + "score": 1.0, + "content": "when both the error of pseudo-labels (error of", + "type": "text" + }, + { + "bbox": [ + 288, + 610, + 298, + 621 + ], + "score": 0.87, + "content": "\\theta _ { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 299, + 609, + 311, + 623 + ], + "score": 1.0, + "content": "on", + "type": "text" + }, + { + "bbox": [ + 312, + 610, + 321, + 621 + ], + "score": 0.8, + "content": "Q", + "type": "inline_equation" + }, + { + "bbox": [ + 321, + 609, + 505, + 623 + ], + "score": 1.0, + "content": ") and the total variation (TV) distance between", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 621, + 506, + 633 + ], + "spans": [ + { + "bbox": [ + 105, + 621, + 506, + 633 + ], + "score": 1.0, + "content": "pseudo-labels and ground-truths continue to decay, indicating that CST gradually refines pseudo-", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 631, + 505, + 644 + ], + "spans": [ + { + "bbox": [ + 105, + 631, + 505, + 644 + ], + "score": 1.0, + "content": "labels. This forms a clear contrast to standard self-training as visualized in Figure 2 (Middle), where", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 641, + 363, + 656 + ], + "spans": [ + { + "bbox": [ + 105, + 641, + 156, + 656 + ], + "score": 1.0, + "content": "the distance", + "type": "text" + }, + { + "bbox": [ + 156, + 643, + 172, + 654 + ], + "score": 0.86, + "content": "d _ { \\mathrm { T V } }", + "type": "inline_equation" + }, + { + "bbox": [ + 173, + 641, + 363, + 656 + ], + "score": 1.0, + "content": "remains nearly unchanged throughout training.", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 37.5 + }, + { + "type": "text", + "bbox": [ + 107, + 659, + 505, + 725 + ], + "lines": [ + { + "bbox": [ + 106, + 658, + 505, + 671 + ], + "spans": [ + { + "bbox": [ + 106, + 658, + 505, + 671 + ], + "score": 1.0, + "content": "Comparison of Gibbs entropy and Tsallis entropy. We compare the pseudo-labels learned with", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 670, + 505, + 683 + ], + "spans": [ + { + "bbox": [ + 105, + 670, + 298, + 683 + ], + "score": 1.0, + "content": "standard Gibbs entropy and Tsallis entropy on", + "type": "text" + }, + { + "bbox": [ + 298, + 670, + 330, + 681 + ], + "score": 0.8, + "content": "\\mathbf { A r { } C l }", + "type": "inline_equation" + }, + { + "bbox": [ + 330, + 670, + 505, + 683 + ], + "score": 1.0, + "content": "with ResNet-50 at epoch 40. We compute", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 680, + 506, + 693 + ], + "spans": [ + { + "bbox": [ + 105, + 680, + 506, + 693 + ], + "score": 1.0, + "content": "the difference between the largest and the second largest softmax scores of each target example and", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 692, + 506, + 704 + ], + "spans": [ + { + "bbox": [ + 106, + 692, + 506, + 704 + ], + "score": 1.0, + "content": "plot the histogram in Figure 5 (Right). Gibbs entropy makes the largest softmax output close to 1,", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 701, + 506, + 717 + ], + "spans": [ + { + "bbox": [ + 105, + 701, + 506, + 717 + ], + "score": 1.0, + "content": "indicating over-confidence. In this case, if the prediction is wrong, it can be hard to correct it using", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 714, + 507, + 726 + ], + "spans": [ + { + "bbox": [ + 105, + 714, + 507, + 726 + ], + "score": 1.0, + "content": "self-training. In contrast, Tsallis entropy allows the largest and the second largest scores to be similar.", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 43.5 + } + ], + "page_idx": 8, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 302, + 741, + 309, + 750 + ], + "lines": [ + { + "bbox": [ + 302, + 741, + 309, + 752 + ], + "spans": [ + { + "bbox": [ + 302, + 741, + 309, + 752 + ], + "score": 1.0, + "content": "9", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "table", + "bbox": [ + 107, + 83, + 505, + 190 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 119, + 71, + 486, + 83 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 122, + 70, + 488, + 85 + ], + "spans": [ + { + "bbox": [ + 122, + 70, + 199, + 85 + ], + "score": 1.0, + "content": "Table 2: Accuracy", + "type": "text" + }, + { + "bbox": [ + 200, + 72, + 215, + 82 + ], + "score": 0.71, + "content": "( \\% )", + "type": "inline_equation" + }, + { + "bbox": [ + 216, + 70, + 488, + 85 + ], + "score": 1.0, + "content": "on Office-Home for unsupervised domain adaptation (ResNet-50).", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "table_body", + "bbox": [ + 107, + 83, + 505, + 190 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 107, + 83, + 505, + 190 + ], + "spans": [ + { + "bbox": [ + 107, + 83, + 505, + 190 + ], + "score": 0.978, + "html": "
Method|Ar-Cl Ar-Pr Ar-Rw Cl-Ar Cl-Pr Cl-Rw Pr-Ar Pr-CIPr-Rw Rw-Ar Rw-Cl Rw-Pr|Avg.
DANN [22]45.659.370.147.058.560.946.143.768.563.251.876.857.6
CDAN [37]50.770.676.057.670.070.057.450.977.370.956.781.665.8
CDAN+VAT+Entropy52.271.576.461.170.367.859.554.478.673.259.082.767.3
FixMatch [57]51.874.280.163.573.861.364.751.480.073.356.881.767.7
MDD [73]54.973.777.860.071.471.861.253.678.172.560.282.368.1
MDD+IA [28]56.277.979.264.473.174.464.254.279.971.258.183.169.5
SENTRY [48]61.877.480.166.371.674.766.863.080.974.066.384.172.2
CST59.079.683.468.477.176.768.956.483.075.362.285.1|73.0
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MethodB-DB-EB-KD-BD-ED-KE-BE-DE-KK-BK-DK-EAvg.
Source-only89.788.490.990.188.590.286.988.591.587.687.391.289.2
DANN [22]90.289.590.991.090.690.287.187.592.887.887.693.289.9
VAT[40]90.691.091.790.890.892.087.286.992.686.987.792.990.1
VAT+Entropy90.491.391.591.091.192.487.586.392.486.587.593.190.1
MDD [73]90.490.491.890.290.991.087.586.392.589.087.992.190.0
CST91.592.992.691.992.693.590.289.493.887.988.393.591.5
", + "type": "table", + "image_path": "064187228bcfd5fa0d44b25d3abd40425be164827f67f87214f6fccf6617bc69.jpg" + } + ] + } + ], + "index": 6, + "virtual_lines": [ + { + "bbox": [ + 106, + 213, + 504, + 241.66666666666666 + ], + "spans": [], + "index": 5 + }, + { + "bbox": [ + 106, + 241.66666666666666, + 504, + 270.3333333333333 + ], + "spans": [], + "index": 6 + }, + { + "bbox": [ + 106, + 270.3333333333333, + 504, + 299.0 + ], + "spans": [], + "index": 7 + } + ] + } + ], + "index": 5.0 + }, + { + "type": "text", + "bbox": [ + 107, + 326, + 505, + 370 + ], + "lines": [ + { + "bbox": [ + 104, + 325, + 507, + 339 + ], + "spans": [ + { + "bbox": [ + 104, + 325, + 507, + 339 + ], + "score": 1.0, + "content": "Table 4 shows the results on VisDA-2017. CST surpasses state-of-the-arts with ResNet-50 and ResNet-", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 336, + 505, + 351 + ], + "spans": [ + { + "bbox": [ + 105, + 336, + 505, + 351 + ], + "score": 1.0, + "content": "101 backbones. We also combine feature adaptation and self-training (DIRT-T, CDAN+VAT+entropy", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 348, + 505, + 361 + ], + "spans": [ + { + "bbox": [ + 105, + 348, + 147, + 361 + ], + "score": 1.0, + "content": "and MDD", + "type": "text" + }, + { + "bbox": [ + 148, + 350, + 154, + 358 + ], + "score": 0.38, + "content": "^ { + }", + "type": "inline_equation" + }, + { + "bbox": [ + 155, + 348, + 505, + 361 + ], + "score": 1.0, + "content": "FixMatch) to test if feature adaptation alleviates the negative effect of domain shift in", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 359, + 480, + 371 + ], + "spans": [ + { + "bbox": [ + 106, + 359, + 480, + 371 + ], + "score": 1.0, + "content": "standard self-training. Results indicate that CST is a better solution than simple combination.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 9.5, + "bbox_fs": [ + 104, + 325, + 507, + 371 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 375, + 505, + 420 + ], + "lines": [ + { + "bbox": [ + 105, + 375, + 505, + 388 + ], + "spans": [ + { + "bbox": [ + 105, + 375, + 505, + 388 + ], + "score": 1.0, + "content": "While most traditional self-training methods include techniques specified for ConvNets such as", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 386, + 505, + 398 + ], + "spans": [ + { + "bbox": [ + 105, + 386, + 505, + 398 + ], + "score": 1.0, + "content": "Mixup [72], CST is a universal method and can directly work on sentiment classification by simply", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 398, + 505, + 410 + ], + "spans": [ + { + "bbox": [ + 106, + 398, + 505, + 410 + ], + "score": 1.0, + "content": "replacing the head and training objective of BERT [16]. In Table 3, most feature adaptation baselines", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 408, + 507, + 421 + ], + "spans": [ + { + "bbox": [ + 105, + 408, + 507, + 421 + ], + "score": 1.0, + "content": "improve over source only marginally, but CST outperforms all baselines on most tasks significantly.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 13.5, + "bbox_fs": [ + 105, + 375, + 507, + 421 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 434, + 166, + 446 + ], + "lines": [ + { + "bbox": [ + 105, + 433, + 168, + 447 + ], + "spans": [ + { + "bbox": [ + 105, + 433, + 168, + 447 + ], + "score": 1.0, + "content": "5.4 Analysis", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 16 + }, + { + "type": "text", + "bbox": [ + 107, + 451, + 334, + 540 + ], + "lines": [ + { + "bbox": [ + 106, + 451, + 334, + 463 + ], + "spans": [ + { + "bbox": [ + 106, + 451, + 334, + 463 + ], + "score": 1.0, + "content": "Ablation Study. We study the role of each part of CST", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 462, + 335, + 474 + ], + "spans": [ + { + "bbox": [ + 106, + 462, + 335, + 474 + ], + "score": 1.0, + "content": "in self-training. CST w/o Tsallis removes the Tsallis en-", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 473, + 334, + 487 + ], + "spans": [ + { + "bbox": [ + 106, + 473, + 129, + 487 + ], + "score": 1.0, + "content": "tropy", + "type": "text" + }, + { + "bbox": [ + 129, + 474, + 164, + 486 + ], + "score": 0.91, + "content": "L _ { \\mathrm { T s a l l i s } , \\alpha }", + "type": "inline_equation" + }, + { + "bbox": [ + 164, + 473, + 186, + 487 + ], + "score": 1.0, + "content": ". CST", + "type": "text" + }, + { + "bbox": [ + 187, + 475, + 193, + 483 + ], + "score": 0.27, + "content": "+", + "type": "inline_equation" + }, + { + "bbox": [ + 193, + 473, + 334, + 487 + ], + "score": 1.0, + "content": "Entropy replaces the Tsallis entropy", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 483, + 334, + 497 + ], + "spans": [ + { + "bbox": [ + 105, + 483, + 288, + 497 + ], + "score": 1.0, + "content": "with standard entropy. FixMatch+Tsallis adds", + "type": "text" + }, + { + "bbox": [ + 288, + 485, + 322, + 496 + ], + "score": 0.92, + "content": "L _ { \\mathrm { T s a l l i s } , \\alpha }", + "type": "inline_equation" + }, + { + "bbox": [ + 322, + 483, + 334, + 497 + ], + "score": 1.0, + "content": "to", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 495, + 335, + 507 + ], + "spans": [ + { + "bbox": [ + 106, + 495, + 335, + 507 + ], + "score": 1.0, + "content": "standard self-training. Observations are shown in Table 5.", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 505, + 334, + 519 + ], + "spans": [ + { + "bbox": [ + 106, + 506, + 132, + 517 + ], + "score": 0.48, + "content": "\\mathrm { C S T + l }", + "type": "inline_equation" + }, + { + "bbox": [ + 132, + 505, + 201, + 519 + ], + "score": 1.0, + "content": "Entropy performs", + "type": "text" + }, + { + "bbox": [ + 201, + 506, + 224, + 517 + ], + "score": 0.88, + "content": "3 . 7 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 224, + 505, + 334, + 519 + ], + "score": 1.0, + "content": "worse than CST, indicating", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 516, + 335, + 529 + ], + "spans": [ + { + "bbox": [ + 105, + 516, + 335, + 529 + ], + "score": 1.0, + "content": "that Tsallis entropy is a better regularization for pseudo-", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 528, + 334, + 540 + ], + "spans": [ + { + "bbox": [ + 106, + 528, + 284, + 540 + ], + "score": 1.0, + "content": "labels than standard entropy. CST performs", + "type": "text" + }, + { + "bbox": [ + 285, + 528, + 307, + 539 + ], + "score": 0.88, + "content": "5 . 4 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 307, + 528, + 334, + 540 + ], + "score": 1.0, + "content": "better", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 539, + 506, + 551 + ], + "spans": [ + { + "bbox": [ + 106, + 539, + 506, + 551 + ], + "score": 1.0, + "content": "than FixMatch, indicating that CST is better adapted to domain shift than standard self-training. While", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 549, + 506, + 562 + ], + "spans": [ + { + "bbox": [ + 105, + 549, + 305, + 562 + ], + "score": 1.0, + "content": "FixMatch+Tsallis outperforms FixMatch, it is still", + "type": "text" + }, + { + "bbox": [ + 305, + 550, + 328, + 561 + ], + "score": 0.88, + "content": "3 . 6 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 328, + 549, + 506, + 562 + ], + "score": 1.0, + "content": "behind CST, with much larger total variation", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 561, + 505, + 573 + ], + "spans": [ + { + "bbox": [ + 106, + 561, + 142, + 573 + ], + "score": 1.0, + "content": "distance", + "type": "text" + }, + { + "bbox": [ + 143, + 561, + 159, + 572 + ], + "score": 0.88, + "content": "d _ { \\mathrm { T V } }", + "type": "inline_equation" + }, + { + "bbox": [ + 159, + 561, + 505, + 573 + ], + "score": 1.0, + "content": "between pseudo-labels and ground-truths, indicating that CST makes pseudo-labels", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 572, + 349, + 584 + ], + "spans": [ + { + "bbox": [ + 105, + 572, + 349, + 584 + ], + "score": 1.0, + "content": "more reliable than standard self-training under domain shift.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 22.5, + "bbox_fs": [ + 105, + 451, + 335, + 540 + ] + }, + { + "type": "table", + "bbox": [ + 341, + 460, + 504, + 537 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 357, + 450, + 487, + 459 + ], + "group_id": 2, + "lines": [ + { + "bbox": [ + 357, + 449, + 488, + 461 + ], + "spans": [ + { + "bbox": [ + 357, + 449, + 488, + 461 + ], + "score": 1.0, + "content": "Table 5: Ablation on VisDA-2017.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 21 + }, + { + "type": "table_body", + "bbox": [ + 341, + 460, + 504, + 537 + ], + "group_id": 2, + "lines": [ + { + "bbox": [ + 341, + 460, + 504, + 537 + ], + "spans": [ + { + "bbox": [ + 341, + 460, + 504, + 537 + ], + "score": 0.971, + "html": "
MethodAccuracy ↑|drv↓
FixMatch [57]74.5 ± 0.20.22
Fixmatch+Tsallis76.3 ± 0.80.15
CST w/o Tsallis72.0 ± 0.40.16
CST+Entropy76.2 ± 0.60.20
CST79.9 ± 0.50.12
", + "type": "table", + "image_path": "1f009038872b5ecebb92230a8969f0c1c81ac204407dd1ce16149601336c7a75.jpg" + } + ] + } + ], + "index": 28, + "virtual_lines": [ + { + "bbox": [ + 341, + 460, + 504, + 475.4 + ], + "spans": [], + "index": 20 + }, + { + "bbox": [ + 341, + 475.4, + 504, + 490.79999999999995 + ], + "spans": [], + "index": 27 + }, + { + "bbox": [ + 341, + 490.79999999999995, + 504, + 506.19999999999993 + ], + "spans": [], + "index": 28 + }, + { + "bbox": [ + 341, + 506.19999999999993, + 504, + 521.5999999999999 + ], + "spans": [], + "index": 29 + }, + { + "bbox": [ + 341, + 521.5999999999999, + 504, + 536.9999999999999 + ], + "spans": [], + "index": 30 + } + ] + } + ], + "index": 24.5 + }, + { + "type": "text", + "bbox": [ + 107, + 540, + 504, + 583 + ], + "lines": [], + "index": 32.5, + "bbox_fs": [ + 105, + 539, + 506, + 584 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 106, + 587, + 505, + 654 + ], + "lines": [ + { + "bbox": [ + 106, + 587, + 505, + 600 + ], + "spans": [ + { + "bbox": [ + 106, + 587, + 505, + 600 + ], + "score": 1.0, + "content": "Quality of Pseudo-labels. We visualize the error of pseudo-labels during training on VisDA-2017 in", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 104, + 597, + 507, + 613 + ], + "spans": [ + { + "bbox": [ + 104, + 597, + 286, + 613 + ], + "score": 1.0, + "content": "Figure 5 (Left). The error of target classifier", + "type": "text" + }, + { + "bbox": [ + 286, + 599, + 296, + 610 + ], + "score": 0.86, + "content": "\\theta _ { t }", + "type": "inline_equation" + }, + { + "bbox": [ + 296, + 597, + 507, + 613 + ], + "score": 1.0, + "content": "on the source domain decreases quickly in training,", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 609, + 505, + 623 + ], + "spans": [ + { + "bbox": [ + 105, + 609, + 288, + 623 + ], + "score": 1.0, + "content": "when both the error of pseudo-labels (error of", + "type": "text" + }, + { + "bbox": [ + 288, + 610, + 298, + 621 + ], + "score": 0.87, + "content": "\\theta _ { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 299, + 609, + 311, + 623 + ], + "score": 1.0, + "content": "on", + "type": "text" + }, + { + "bbox": [ + 312, + 610, + 321, + 621 + ], + "score": 0.8, + "content": "Q", + "type": "inline_equation" + }, + { + "bbox": [ + 321, + 609, + 505, + 623 + ], + "score": 1.0, + "content": ") and the total variation (TV) distance between", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 621, + 506, + 633 + ], + "spans": [ + { + "bbox": [ + 105, + 621, + 506, + 633 + ], + "score": 1.0, + "content": "pseudo-labels and ground-truths continue to decay, indicating that CST gradually refines pseudo-", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 631, + 505, + 644 + ], + "spans": [ + { + "bbox": [ + 105, + 631, + 505, + 644 + ], + "score": 1.0, + "content": "labels. This forms a clear contrast to standard self-training as visualized in Figure 2 (Middle), where", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 641, + 363, + 656 + ], + "spans": [ + { + "bbox": [ + 105, + 641, + 156, + 656 + ], + "score": 1.0, + "content": "the distance", + "type": "text" + }, + { + "bbox": [ + 156, + 643, + 172, + 654 + ], + "score": 0.86, + "content": "d _ { \\mathrm { T V } }", + "type": "inline_equation" + }, + { + "bbox": [ + 173, + 641, + 363, + 656 + ], + "score": 1.0, + "content": "remains nearly unchanged throughout training.", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 37.5, + "bbox_fs": [ + 104, + 587, + 507, + 656 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 659, + 505, + 725 + ], + "lines": [ + { + "bbox": [ + 106, + 658, + 505, + 671 + ], + "spans": [ + { + "bbox": [ + 106, + 658, + 505, + 671 + ], + "score": 1.0, + "content": "Comparison of Gibbs entropy and Tsallis entropy. We compare the pseudo-labels learned with", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 670, + 505, + 683 + ], + "spans": [ + { + "bbox": [ + 105, + 670, + 298, + 683 + ], + "score": 1.0, + "content": "standard Gibbs entropy and Tsallis entropy on", + "type": "text" + }, + { + "bbox": [ + 298, + 670, + 330, + 681 + ], + "score": 0.8, + "content": "\\mathbf { A r { } C l }", + "type": "inline_equation" + }, + { + "bbox": [ + 330, + 670, + 505, + 683 + ], + "score": 1.0, + "content": "with ResNet-50 at epoch 40. We compute", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 680, + 506, + 693 + ], + "spans": [ + { + "bbox": [ + 105, + 680, + 506, + 693 + ], + "score": 1.0, + "content": "the difference between the largest and the second largest softmax scores of each target example and", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 692, + 506, + 704 + ], + "spans": [ + { + "bbox": [ + 106, + 692, + 506, + 704 + ], + "score": 1.0, + "content": "plot the histogram in Figure 5 (Right). Gibbs entropy makes the largest softmax output close to 1,", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 701, + 506, + 717 + ], + "spans": [ + { + "bbox": [ + 105, + 701, + 506, + 717 + ], + "score": 1.0, + "content": "indicating over-confidence. In this case, if the prediction is wrong, it can be hard to correct it using", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 714, + 507, + 726 + ], + "spans": [ + { + "bbox": [ + 105, + 714, + 507, + 726 + ], + "score": 1.0, + "content": "self-training. In contrast, Tsallis entropy allows the largest and the second largest scores to be similar.", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 43.5, + "bbox_fs": [ + 105, + 658, + 507, + 726 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 107, + 72, + 504, + 188 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 124, + 59, + 483, + 70 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 127, + 58, + 484, + 72 + ], + "spans": [ + { + "bbox": [ + 127, + 58, + 253, + 72 + ], + "score": 1.0, + "content": "Table 4: Mean Class Accuracy", + "type": "text" + }, + { + "bbox": [ + 253, + 59, + 269, + 70 + ], + "score": 0.73, + "content": "( \\% )", + "type": "inline_equation" + }, + { + "bbox": [ + 269, + 58, + 484, + 72 + ], + "score": 1.0, + "content": "for unsupervised domain adaptation on VisDA-2017.", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "table_body", + "bbox": [ + 107, + 72, + 504, + 188 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 107, + 72, + 504, + 188 + ], + "spans": [ + { + "bbox": [ + 107, + 72, + 504, + 188 + ], + "score": 0.947, + "html": "
MethodResNet-50ResNet-101MethodResNet-50ResNet-101
DANN [22]69.379.5CBST[77]176.4 ± 0.9
VAT [40]68.0±0.373.4 ± 0.5KLD [78]178.1 ± 0.2
DIRT-T [56]68.2 ± 0.377.2 ± 0.5MDD[73]74.681.6 ± 0.3
MCD [54]69.277.7AFN [69]176.1
CDAN [37]70.080.1MDD+IA [28]75.81
CDAN+VAT+Entropy76.5 ± 0.580.4± 0.7MDD+FixMatch77.8 ± 0.382.4 ± 0.4
MixMatch69.3 ± 0.477.0 ± 0.5STAR [38]182.7
FixMatch [57]74.5 ± 0.279.5 ± 0.3SENTRY [48]76.71
CST79.9 ± 0.584.8± 0.6CST+SAM80.6 ± 0.586.5 ± 0.7
", + "type": "table", + "image_path": "3398ef4904b4c447ef21ebadb24014f266b754a7009178d7c7d1a7ef77df12da.jpg" + } + ] + } + ], + "index": 2, + "virtual_lines": [ + { + "bbox": [ + 107, + 72, + 504, + 110.66666666666666 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 107, + 110.66666666666666, + 504, + 149.33333333333331 + ], + "spans": [], + "index": 2 + }, + { + "bbox": [ + 107, + 149.33333333333331, + 504, + 187.99999999999997 + ], + "spans": [], + "index": 3 + } + ] + } + ], + "index": 1.0 + }, + { + "type": "image", + "bbox": [ + 119, + 195, + 489, + 279 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 119, + 195, + 489, + 279 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 119, + 195, + 489, + 279 + ], + "spans": [ + { + "bbox": [ + 119, + 195, + 489, + 279 + ], + "score": 0.935, + "type": "image", + "image_path": "b438078399476e8bc688a6c6252f161f15cda1ea9f72241d501cd24f973a4fac.jpg" + } + ] + } + ], + "index": 5, + "virtual_lines": [ + { + "bbox": [ + 119, + 195, + 489, + 223.0 + ], + "spans": [], + "index": 4 + }, + { + "bbox": [ + 119, + 223.0, + 489, + 251.0 + ], + "spans": [], + "index": 5 + }, + { + "bbox": [ + 119, + 251.0, + 489, + 279.0 + ], + "spans": [], + "index": 6 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 107, + 282, + 504, + 314 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 282, + 504, + 294 + ], + "spans": [ + { + "bbox": [ + 105, + 282, + 495, + 294 + ], + "score": 1.0, + "content": "Figure 5: Analysis. Left: Error of pseudo-labels and reverse pseudo-labels. The error of target classifier", + "type": "text" + }, + { + "bbox": [ + 495, + 283, + 504, + 293 + ], + "score": 0.83, + "content": "\\theta _ { t }", + "type": "inline_equation" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 293, + 505, + 304 + ], + "spans": [ + { + "bbox": [ + 105, + 293, + 505, + 304 + ], + "score": 1.0, + "content": "on the source domain decreases, indicating the quality of pseudo-labels is refined. Right: Histograms of the", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 303, + 499, + 315 + ], + "spans": [ + { + "bbox": [ + 105, + 303, + 499, + 315 + ], + "score": 1.0, + "content": "difference between the largest and the second largest softmax scores. 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[65], Mukherjee & Awadallah [42] show that task-level self-training works well in few-shot", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 415, + 506, + 430 + ], + "spans": [ + { + "bbox": [ + 105, + 415, + 506, + 430 + ], + "score": 1.0, + "content": "learning. These methods are tailored to semi-supervised learning or general representation learning", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 428, + 505, + 439 + ], + "spans": [ + { + "bbox": [ + 106, + 428, + 505, + 439 + ], + "score": 1.0, + "content": "and do not take domain shift into consideration explicitly. Wei et al. [66], Frei et al. [20] provide the", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 437, + 430, + 451 + ], + "spans": [ + { + "bbox": [ + 105, + 437, + 430, + 451 + ], + "score": 1.0, + "content": "first nice theoretical analysis of self-training based on the expansion assumption.", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 15.5 + }, + { + "type": "text", + "bbox": [ + 107, + 455, + 505, + 564 + ], + "lines": [ + { + "bbox": [ + 105, + 453, + 506, + 467 + ], + "spans": [ + { + "bbox": [ + 105, + 453, + 506, + 467 + ], + "score": 1.0, + "content": "Domain Adaptation. Inspired by the generalization error bound of Ben-David et al. [7], Long et al.", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 466, + 505, + 477 + ], + "spans": [ + { + "bbox": [ + 106, + 466, + 505, + 477 + ], + "score": 1.0, + "content": "[34], Zellinger et al. [71] minimize distance measures between source and target distributions to learn", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 477, + 505, + 488 + ], + "spans": [ + { + "bbox": [ + 106, + 477, + 505, + 488 + ], + "score": 1.0, + "content": "domain-invariant features. Ganin et al. [22] (DANN) proposed to approximate the domain distance", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 486, + 505, + 500 + ], + "spans": [ + { + "bbox": [ + 105, + 486, + 505, + 500 + ], + "score": 1.0, + "content": "by adversarial learning. Follow-up works proposed various improvement upon DANN [63, 54, 37,", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 497, + 506, + 510 + ], + "spans": [ + { + "bbox": [ + 105, + 497, + 506, + 510 + ], + "score": 1.0, + "content": "73, 28]. Popular as they are, failure cases exist in situation like label shift [74, 32], shift in support of", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 508, + 506, + 521 + ], + "spans": [ + { + "bbox": [ + 105, + 508, + 506, + 521 + ], + "score": 1.0, + "content": "domains [29], and large discrepancy between source and target [33]. Another line of works try to", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 518, + 506, + 533 + ], + "spans": [ + { + "bbox": [ + 105, + 518, + 506, + 533 + ], + "score": 1.0, + "content": "address domain adaptation with self-training. Shu et al. [56] improves DANN with VAT and entropy", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 531, + 506, + 543 + ], + "spans": [ + { + "bbox": [ + 105, + 531, + 506, + 543 + ], + "score": 1.0, + "content": "minimization. French et al. [21], Zou et al. [78], Li et al. [32] incorporated various semi-supervised", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 541, + 506, + 554 + ], + "spans": [ + { + "bbox": [ + 105, + 541, + 506, + 554 + ], + "score": 1.0, + "content": "learning techniques to boost domain adaptation performance. Kumar et al. [30], Chen et al. [15] and", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 552, + 507, + 565 + ], + "spans": [ + { + "bbox": [ + 105, + 552, + 507, + 565 + ], + "score": 1.0, + "content": "Cai et al. [11] showed self-training provably works in domain adaptation under certain assumptions.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 25.5 + }, + { + "type": "title", + "bbox": [ + 107, + 574, + 183, + 587 + ], + "lines": [ + { + "bbox": [ + 104, + 572, + 185, + 590 + ], + "spans": [ + { + "bbox": [ + 104, + 572, + 185, + 590 + ], + "score": 1.0, + "content": "7 Conclusion", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 31 + }, + { + "type": "text", + "bbox": [ + 107, + 594, + 505, + 660 + ], + "lines": [ + { + "bbox": [ + 106, + 593, + 505, + 606 + ], + "spans": [ + { + "bbox": [ + 106, + 593, + 505, + 606 + ], + "score": 1.0, + "content": "We propose cycle self-training in place of standard self-training to explicitly address the distribution", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 604, + 505, + 617 + ], + "spans": [ + { + "bbox": [ + 105, + 604, + 505, + 617 + ], + "score": 1.0, + "content": "shift in domain adaptation. We show that our method provably works under the expansion assumption", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 616, + 505, + 627 + ], + "spans": [ + { + "bbox": [ + 106, + 616, + 505, + 627 + ], + "score": 1.0, + "content": "and demonstrate hard cases for feature adaptation and standard self-training. Self-training (or pseudo-", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 625, + 506, + 639 + ], + "spans": [ + { + "bbox": [ + 105, + 625, + 506, + 639 + ], + "score": 1.0, + "content": "labeling) is only one line of works in the semi-supervised learning literature. Future work can delve", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 637, + 505, + 650 + ], + "spans": [ + { + "bbox": [ + 105, + 637, + 505, + 650 + ], + "score": 1.0, + "content": "into the behaviors of other semi-supervised learning techniques including consistency regularization", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 647, + 505, + 661 + ], + "spans": [ + { + "bbox": [ + 105, + 647, + 505, + 661 + ], + "score": 1.0, + "content": "and data augmentation under distribution shift, and exploit them extensively for domain adaptation.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 34.5 + }, + { + "type": "title", + "bbox": [ + 107, + 669, + 207, + 683 + ], + "lines": [ + { + "bbox": [ + 106, + 668, + 208, + 686 + ], + "spans": [ + { + "bbox": [ + 106, + 668, + 208, + 686 + ], + "score": 1.0, + "content": "Acknowledgements", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 38 + }, + { + "type": "text", + "bbox": [ + 108, + 689, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 106, + 688, + 505, + 701 + ], + "spans": [ + { + "bbox": [ + 106, + 688, + 505, + 701 + ], + "score": 1.0, + "content": "This work was supported by the National Natural Science Foundation of China under Grants 62022050", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 699, + 505, + 713 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 505, + 713 + ], + "score": 1.0, + "content": "and 62021002, Beijing Nova Program under Grant Z201100006820041, China’s Ministry of Industry", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 711, + 464, + 723 + ], + "spans": [ + { + "bbox": [ + 106, + 711, + 464, + 723 + ], + "score": 1.0, + "content": "and Information Technology, the MOE Innovation Plan and the BNRist Innovation Fund.", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 40 + } + ], + "page_idx": 9, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 301, + 742, + 311, + 750 + ], + "lines": [ + { + "bbox": [ + 299, + 740, + 313, + 754 + ], + "spans": [ + { + "bbox": [ + 299, + 740, + 313, + 754 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 14, + "width": 14 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "table", + "bbox": [ + 107, + 72, + 504, + 188 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 124, + 59, + 483, + 70 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 127, + 58, + 484, + 72 + ], + "spans": [ + { + "bbox": [ + 127, + 58, + 253, + 72 + ], + "score": 1.0, + "content": "Table 4: Mean Class Accuracy", + "type": "text" + }, + { + "bbox": [ + 253, + 59, + 269, + 70 + ], + "score": 0.73, + "content": "( \\% )", + "type": "inline_equation" + }, + { + "bbox": [ + 269, + 58, + 484, + 72 + ], + "score": 1.0, + "content": "for unsupervised domain adaptation on VisDA-2017.", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "table_body", + "bbox": [ + 107, + 72, + 504, + 188 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 107, + 72, + 504, + 188 + ], + "spans": [ + { + "bbox": [ + 107, + 72, + 504, + 188 + ], + "score": 0.947, + "html": "
MethodResNet-50ResNet-101MethodResNet-50ResNet-101
DANN [22]69.379.5CBST[77]176.4 ± 0.9
VAT [40]68.0±0.373.4 ± 0.5KLD [78]178.1 ± 0.2
DIRT-T [56]68.2 ± 0.377.2 ± 0.5MDD[73]74.681.6 ± 0.3
MCD [54]69.277.7AFN [69]176.1
CDAN [37]70.080.1MDD+IA [28]75.81
CDAN+VAT+Entropy76.5 ± 0.580.4± 0.7MDD+FixMatch77.8 ± 0.382.4 ± 0.4
MixMatch69.3 ± 0.477.0 ± 0.5STAR [38]182.7
FixMatch [57]74.5 ± 0.279.5 ± 0.3SENTRY [48]76.71
CST79.9 ± 0.584.8± 0.6CST+SAM80.6 ± 0.586.5 ± 0.7
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[20] provide the", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 437, + 430, + 451 + ], + "spans": [ + { + "bbox": [ + 105, + 437, + 430, + 451 + ], + "score": 1.0, + "content": "first nice theoretical analysis of self-training based on the expansion assumption.", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 15.5, + "bbox_fs": [ + 105, + 339, + 506, + 451 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 455, + 505, + 564 + ], + "lines": [ + { + "bbox": [ + 105, + 453, + 506, + 467 + ], + "spans": [ + { + "bbox": [ + 105, + 453, + 506, + 467 + ], + "score": 1.0, + "content": "Domain Adaptation. Inspired by the generalization error bound of Ben-David et al. [7], Long et al.", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 466, + 505, + 477 + ], + "spans": [ + { + "bbox": [ + 106, + 466, + 505, + 477 + ], + "score": 1.0, + "content": "[34], Zellinger et al. [71] minimize distance measures between source and target distributions to learn", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 477, + 505, + 488 + ], + "spans": [ + { + "bbox": [ + 106, + 477, + 505, + 488 + ], + "score": 1.0, + "content": "domain-invariant features. Ganin et al. [22] (DANN) proposed to approximate the domain distance", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 486, + 505, + 500 + ], + "spans": [ + { + "bbox": [ + 105, + 486, + 505, + 500 + ], + "score": 1.0, + "content": "by adversarial learning. Follow-up works proposed various improvement upon DANN [63, 54, 37,", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 497, + 506, + 510 + ], + "spans": [ + { + "bbox": [ + 105, + 497, + 506, + 510 + ], + "score": 1.0, + "content": "73, 28]. Popular as they are, failure cases exist in situation like label shift [74, 32], shift in support of", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 508, + 506, + 521 + ], + "spans": [ + { + "bbox": [ + 105, + 508, + 506, + 521 + ], + "score": 1.0, + "content": "domains [29], and large discrepancy between source and target [33]. Another line of works try to", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 518, + 506, + 533 + ], + "spans": [ + { + "bbox": [ + 105, + 518, + 506, + 533 + ], + "score": 1.0, + "content": "address domain adaptation with self-training. Shu et al. [56] improves DANN with VAT and entropy", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 531, + 506, + 543 + ], + "spans": [ + { + "bbox": [ + 105, + 531, + 506, + 543 + ], + "score": 1.0, + "content": "minimization. French et al. [21], Zou et al. [78], Li et al. 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We show that our method provably works under the expansion assumption", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 616, + 505, + 627 + ], + "spans": [ + { + "bbox": [ + 106, + 616, + 505, + 627 + ], + "score": 1.0, + "content": "and demonstrate hard cases for feature adaptation and standard self-training. Self-training (or pseudo-", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 625, + 506, + 639 + ], + "spans": [ + { + "bbox": [ + 105, + 625, + 506, + 639 + ], + "score": 1.0, + "content": "labeling) is only one line of works in the semi-supervised learning literature. 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Method|Ar-Cl Ar-Pr Ar-Rw Cl-Ar Cl-Pr Cl-Rw Pr-Ar Pr-CIPr-Rw Rw-Ar Rw-Cl Rw-Pr|Avg.
DANN [22]45.659.370.147.058.560.946.143.768.563.251.876.857.6
CDAN [37]50.770.676.057.670.070.057.450.977.370.956.781.665.8
CDAN+VAT+Entropy52.271.576.461.170.367.859.554.478.673.259.082.767.3
FixMatch [57]51.874.280.163.573.861.364.751.480.073.356.881.767.7
MDD [73]54.973.777.860.071.471.861.253.678.172.560.282.368.1
MDD+IA [28]56.277.979.264.473.174.464.254.279.971.258.183.169.5
SENTRY [48]61.877.480.166.371.674.766.863.080.974.066.384.172.2
CST59.079.683.468.477.176.768.956.483.075.362.285.1|73.0
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MethodB-DB-EB-KD-BD-ED-KE-BE-DE-KK-BK-DK-EAvg.
Source-only89.788.490.990.188.590.286.988.591.587.687.391.289.2
DANN [22]90.289.590.991.090.690.287.187.592.887.887.693.289.9
VAT[40]90.691.091.790.890.892.087.286.992.686.987.792.990.1
VAT+Entropy90.491.391.591.091.192.487.586.392.486.587.593.190.1
MDD [73]90.490.491.890.290.991.087.586.392.589.087.992.190.0
CST91.592.992.691.992.693.590.289.493.887.988.393.591.5
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MethodAccuracy ↑|drv↓
FixMatch [57]74.5 ± 0.20.22
Fixmatch+Tsallis76.3 ± 0.80.15
CST w/o Tsallis72.0 ± 0.40.16
CST+Entropy76.2 ± 0.60.20
CST79.9 ± 0.50.12
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MethodResNet-50ResNet-101MethodResNet-50ResNet-101
DANN [22]69.379.5CBST[77]176.4 ± 0.9
VAT [40]68.0±0.373.4 ± 0.5KLD [78]178.1 ± 0.2
DIRT-T [56]68.2 ± 0.377.2 ± 0.5MDD[73]74.681.6 ± 0.3
MCD [54]69.277.7AFN [69]176.1
CDAN [37]70.080.1MDD+IA [28]75.81
CDAN+VAT+Entropy76.5 ± 0.580.4± 0.7MDD+FixMatch77.8 ± 0.382.4 ± 0.4
MixMatch69.3 ± 0.477.0 ± 0.5STAR [38]182.7
FixMatch [57]74.5 ± 0.279.5 ± 0.3SENTRY [48]76.71
CST79.9 ± 0.584.8± 0.6CST+SAM80.6 ± 0.586.5 ± 0.7
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Yoshitaka Ushiku1, Tatsuya Harada1,2, and Kate Saenko3 + +1The University of Tokyo, 2RIKEN, 3Boston University {k-saito,ushiku,harada}@mi.t.u-tokyo.ac.jp, saenko@bu.edu + +# ABSTRACT + +We present a domain adaptation method for transferring neural representations from label-rich source domains to unlabeled target domains. Recent adversarial methods proposed for this task learn to align features across domains by “fooling” a special domain classifier network. However, a drawback of this approach is that the domain classifier simply labels the generated features as in-domain or not, without considering the boundaries between classes. This means that ambiguous target features can be generated near class boundaries, reducing target classification accuracy. We propose a novel approach, Adversarial Dropout Regularization (ADR), which encourages the generator to output more discriminative features for the target domain. Our key idea is to replace the traditional domain critic with a critic that detects non-discriminative features by using dropout on the classifier network. The generator then learns to avoid these areas of the feature space and thus creates better features. We apply our ADR approach to the problem of unsupervised domain adaptation for image classification and semantic segmentation tasks, and demonstrate significant improvements over the state of the art. + +# 1 INTRODUCTION + +Transferring knowledge learned by deep neural networks from label-rich domains to new target domains is a challenging problem, especially when the source and target input distributions have different characteristics. Such domain shifts occurs in many practical applications. For example, while simulated driving images rendered by games provide a rich source of labeled data for semantic segmentation Richter et al. (2016), deep models trained on such source data do not transfer well to real target domains (Fig. 1(a-d)). When target-domain labels are unavailable for fine-tuning, unsupervised domain adaptation must be applied to improve the source model. + +Recent methods for unsupervised domain adaptation attempt to reduce the discrepancy between the source and target features via adversarial learning (Tzeng et al. (2014); Ganin $\&$ Lempitsky (2014)). They divide the base network into a feature encoder $G$ and classifier $C$ , and add a separate domain classifier (critic) network $D$ . The critic takes the features generated by $G$ and labels them as either source- or target-domain. The encoder $G$ is then trained with an additional adversarial loss that maximizes $D$ ’s mistakes and thus aligns features across domains. + +However, a major drawback of this approach is that the critic simply predicts the domain label of the generated point and does not consider category information. Thus the generator may create features that look like they came from the right domain, but are not discriminative. In particular, it can generate points close to class boundaries, as shown in Fig. 1(e), which are likely to be misclassified by the source model. We argue that to achieve good performance on the target data, the adaptation model must take the decision boundaries between classes into account while aligning features across domains (Fig. 1(f)). Moreover, since our setting is unsupervised adaptation, this must be accomplished without labels on target data. + +In this paper, we propose a novel adversarial alignment technique that overcomes the above limitation and preserves class boundaries. We make the following observation: if the critic could detect points near the decision boundary, then the generator would have to avoid these areas of the feature space in order to fool the critic. Thus the critic would force the generator to create more discriminative features. How can we obtain such a critic? If we alter the boundary of the classifier $C$ slightly and measure the change in the posterior class probability $p ( y | x )$ , where $y$ and $x$ denote class and input respectively, then samples near the decision boundary are likely to have the largest change. In fact, this posterior discrepancy is inversely proportional to the distance from the class boundary. We thus propose to maximize this posterior discrepancy to turn $C$ into a critic sensitive to nondiscriminative points. We call this technique Adversarial Dropout Regularization. Here, dropout is not used in the standard way, which is to regularize the main classifier and make it insensitive to noise. Instead, we use dropout in an adversarial way, to transform the classifier into a critic sensitive to noise. Compared to previous adversarial feature alignment methods, where the distributions $p ( x )$ are aligned globally, our method aligns target features away from decision boundaries, as illustrated in Fig.1(f). + +![](images/b6f4ca41441b05f1a91aeb791d5664cfbced0e867e90f0899d66085405d66cc1.jpg) +Figure 1: (a-d) An illustration of a deep model trained on simulated source training data failing to segment a real target domain image: (a) shows the target image, (b) is the ground truth segmentation into semantic categories (car, road, etc), (c) is the output of the unadapted source model, (d) is the improved segmentation obtained by our proposed ADR method. (e) Previous distribution matching methods do not consider the source decision boundary when aligning source and target feature points. (f) We propose to use the boundary information to achieve low-density separation of aligned points. + +Our ADR approach has several benefits. First, we train the generator $G$ with feedback from the classifier $C$ , in contrast to existing methods, which use an unrelated critic $D$ . Second, our method is general and straightforward to apply to a variety of domain adaptation problems, such as classification and semantic segmentation. Finally, since ADR is trained to align distributions, it is also applicable to semi-supervised learning and training of generative models, such as Generative Adversarial Networks (GANs) (Goodfellow et al. (2014a)). Through extensive experiments, we demonstrate the benefit of ADR over existing domain adaptation approaches, achieving state-of-the-art results in difficult domain shifts. We also show an application to semi-supervised learning using GANs in appendix. + +# 2 RELATED WORK + +Domain Adaptation. Recent unsupervised domain adaptation (UDA) methods for visual data aim to align the feature distributions of the source and target domains (Sun et al. (2016); Sun & Saenko (2016); Tzeng et al. (2014); Ganin et al. (2016); Long et al. (2015b); Yan et al. (2017); Long et al. (2017)). Such methods are motivated by theoretical results stating that minimizing the divergence between domains will lower the upper bound of the error on target domain (Ben-David et al. (2010)). Many works in deep learning utilize the technique of distribution matching in hidden layers of a network such as a CNN (Tzeng et al. (2014); Ganin et al. (2016); Long et al. (2015b)). However, they measure the domain divergence based on the hidden features of the network without considering the relationship between its decision boundary and the target features, as we do in this paper. + +Low-density Separation. Many semi-supervised learning (SSL) methods utilize the relationship between the decision boundary and unlabeled samples, a technique called low-density separation (Chapelle & Zien (2005); Joachims (1999)). By placing the boundary in the area where the unlabeled samples are sparse, these models aim to obtain discriminative representations. Our method aims to achieve low-density separation for deep domain adaptation and is related to entropy minimization for semi-supervised learning (Grandvalet & Bengio (2005)). (Long et al. (2016)) used entropy minimization in their approach to directly measure how far samples are from a decision boundary by calculating entropy of the classifier’s output. On the other hand, our method tries to achieve low-density separation by slightly moving the boundary and detecting target samples sensitive to the movement. As long as target samples features are robust to the movement, they will be allowed to exist relatively nearby the boundary compared to source samples, as Fig. 1 shows. + +In (Long et al. (2016)) entropy minimization is only a part of the overall approach. To compare our ADR approach to entropy minimization more directly, we use a new baseline method. To our knowledge, though this method has not been proposed by any previous work, it is easily achieved by modifying a method proposed by (Springenberg (2015)). For this baseline, we train a model that generates features to minimize the entropy of the output probability for target samples. The details of the baseline are provided in appendix. In short, the generator tries to minimize the entropy of the target samples, whereas the critic tries to maximize it. The entropy is directly measured by the output of the classifier. This baseline is similar to our approach in that the goal of the method is to achieve low-density separation. + +Dropout. Dropout is a method that prevents deep networks from overfitting (Srivastava et al. (2014)) by randomly dropping units from the neural network during training. Effectively, dropout samples from an exponential number of different thinned networks at training time, which prevents units from co-adapting too much. At test time, predictions are obtained by using the outputs of all neurons. If the thinned networks are able to classify the samples accurately, the full network will as well. In other words, dropout encourages the network to be robust to noise. In our work, we use dropout to regularize the feature generation network $G$ , but in an adversarial way. We train the critic $C$ to be sensitive to the noise caused by dropout and use $C$ to regularize $G$ so that it generates noise-robust features. To our knowledge, this use of dropout is completely different from existing methods. + +# 3 METHOD + +We assume that we have access to a labeled source image $\mathbf { x _ { s } }$ and a corresponding label $y _ { s }$ drawn from a set of labeled source images $\{ X _ { s } , Y _ { s } \}$ , as well as an unlabeled target image $\mathbf { x _ { t } }$ drawn from unlabeled target images $X _ { t }$ . We train a feature generation network $G$ , which takes inputs $\mathbf { x _ { s } }$ or $\mathbf { x _ { t } }$ , and a network $C$ that acts as both the main classifier and the critic. When acting as the classifier, $C$ takes features from $G$ and classifies them into $K$ classes, predicting a $K$ -dimensional vector of logits $\{ l _ { 1 } , l _ { 2 } , l _ { 3 } . . . l _ { K } \}$ . The logits are then converted to class probabilities by applying the softmax function. Namely, the probability that $\mathbf { x }$ is classified into class $j$ is denoted by $\begin{array} { r } { p ( y = j | \mathbf { x } ) = \frac { e x p ( l _ { j } ) } { \sum _ { k = 1 } ^ { K } e x p ( l _ { k } ) } } \end{array}$ . We use the notation $p ( \mathbf { y } \vert \mathbf { x } )$ to denote the $K$ -dimensional probabilistic output for input $\mathbf { x }$ . + +When $C$ is acting as the critic, we want it to detect the feature encodings of target samples near the decision boundary. We propose to make $C$ sensitive to such samples by slightly perturbing its decision boundary and measuring the change in the posterior class probability $p ( \mathbf { y } \vert \mathbf { x } )$ . This change is likely to be largest for samples near the decision boundary. The network $C$ is then trained to increase this change, while the feature generation network $G$ is trained to decrease it. Through this adversarial training, $G$ learns to ‘fool’ the critic and generate target features far away from the decision boundary, thus avoiding ambiguous features. The weights of $G$ can be initialized either by pre-training on some auxiliary dataset (e.g., ImageNet), or with random weights, while $C$ uses random initialization. In the next section, we show how we utilize dropout to perturb the boundary in the critic and measure sensitivity. We then show the training procedure of our method. Finally, we give some intuition behind adversarial dropout and improve our method based on this insight. + +# 3.1 CLASSIFIER SELECTION VIA DROPOUT + +Consider the standard training of a neural network using dropout. For every sample within a minibatch, each node of the network is removed with some probability, effectively selecting a different classifier for every sample during training. We harness this idea in a very simple way. + +We forward input features $G ( \bf x _ { t } )$ to $C$ twice, dropping different nodes each time and obtaining two different output vectors denoted as $C _ { 1 } ( G ( \mathbf { x _ { t } } ) )$ , $\bar { C } _ { 2 } \bar { ( \cal G ( x _ { t } ) ) }$ . In other words, we are selecting two different classifiers $C _ { 1 }$ and $C _ { 2 }$ from $C$ by dropout as in Fig. 2. In the figure, the corresponding posterior probabilities are indicated as $p _ { 1 } ( \mathbf { y } | \mathbf { x _ { t } } )$ , $p _ { 2 } ( \mathbf { y } \vert \mathbf { x _ { t } } )$ , abbreviated as $p _ { 1 }$ and $p _ { 2 }$ in the following discussion. In order to detect the change of predictions near the boundary, the critic tries to increase the difference between the predictions of $C _ { 1 }$ and $C _ { 2 }$ . This difference corresponds to $C$ ’s sensitivity to the noise caused by dropout. + +To measure the sensitivity $d ( p _ { 1 } , p _ { 2 } )$ between the two obtained probabilistic outputs, we use the symmetric Kullback Leibler (KL) divergence. Formally, the divergence is calculated as + +$$ +d ( p _ { 1 } , p _ { 2 } ) = { \frac { 1 } { 2 } } ( D _ { k l } ( p _ { 1 } | p _ { 2 } ) + D _ { k l } ( p _ { 2 } | p _ { 1 } ) ) +$$ + +![](images/5b7992174e2f2c0d5a92732e1d6cc79162abd221b22a4267b1f8758b2b378f90.jpg) +Figure 2: Overview of ADR. Left: We train $G$ , $C$ with classification loss on source and sample a critic consisting of two classifiers using dropout. The critic’s sensitivity is measured as the divergence between the class predictions of $C _ { 1 }$ and $C _ { 2 }$ on the same input. Right: Adversarial training iterates two steps: the critic tries to maximize the sensitivity while the generator tries to minimize it. + +where KL divergence between $p$ and $q$ is denoted as $D _ { k l } ( p | q )$ . + +# 3.2 TRAINING PROCEDURE + +In our approach, $C$ works as both critic and classifier. The following three requirements are imposed by our method: 1) $C$ and $G$ must classify source samples correctly to obtain discriminative features; 2) $C$ should maximize the sensitivity for target samples to detect the samples near the boundary; 3) $G$ should learn to minimize the sensitivity to move target samples away from the boundary. + +The training within the same mini-batch consists of the following three steps. + +Step 1, in this step, $C$ is trained as a classifier. $C$ and $G$ have to classify source samples correctly to obtain discriminative features. Thus, we update both networks’ parameters based on the following standard classification loss. Given source labels $y _ { s }$ and samples $\mathbf { x _ { s } }$ , the objective in this step is + +$$ +\underset { G , C } { \operatorname* { m i n } } L ( X _ { s } , Y _ { s } ) = - \mathbb { E } _ { ( \mathbf { x } _ { s } , y _ { s } ) \sim ( X _ { s } , Y _ { s } ) } \sum _ { k = 1 } ^ { K } \mathbb { 1 } _ { [ k = y _ { s } ] } \log C ( G ( \mathbf { x } _ { \mathbf { s } } ) ) _ { k } +$$ + +$C ( G ( \mathbf { x _ { s } } ) ) _ { k }$ returns the probability that the sample $\mathbf { x _ { s } }$ is assigned to class $k$ + +Step 2, in this step, $C$ is trained as a critic to detect target samples near the boundary. Two classifiers are sampled from $C$ for each target sample using dropout twice to obtain $p _ { 1 }$ and $p _ { 2 }$ . Then, $C$ ’s parameters are updated to maximize the sensitivity as measured by Eq. 1. Since $C$ should learn discriminative features for source samples, in addition to the sensitivity term, we add Eq. 2. We experimentally confirmed that this term is essential to obtain good performance. + +$$ +\operatorname* { m i n } _ { C } L ( X _ { s } , Y _ { s } ) - L _ { a d v } ( X _ { t } ) +$$ + +$$ +L _ { a d v } ( X _ { t } ) = \mathbb { E } _ { \mathbf { x _ { t } } \sim X _ { t } } [ d ( C _ { 1 } ( G ( \mathbf { x _ { t } } ) ) , C _ { 2 } ( G ( \mathbf { x _ { t } } ) ) ) ] +$$ + +$C _ { 1 }$ and $C _ { 2 }$ are sampled from $C$ randomly. + +Step 3, in order to obtain representations where target samples are placed far from the decision boundary, $G$ is trained to minimize sensitivity. Here we do not add the categorical loss for source samples as in Step 2, as the generator is able to obtain discriminative features without it. + +$$ +\operatorname* { m i n } _ { G } L _ { a d v } ( X _ { t } ) +$$ + +We update the parameters of $C$ and $G$ in every step following the defined objectives. We experimentally found it beneficial to repeat Step 3 $n$ times for each mini-batch. + +![](images/e236a8f1f63678aa39e6008db6475416d17c9cf2b19a9b860caab2ab1b9a4cd9.jpg) +Figure 3: (Best viewed in color) Toy Experiment. Top row: Model trained without adaptation. Columns 1-5 show the decision boundary obtained by keeping one neuron in the last hidden layer and removing the rest. Red points are source samples of class one, green points are class two. Black points are target samples. The yellow region indicates where the samples are classified as class one, cyan region class two. We see that the neurons do not learn very diverse features. Column 6 shows the boundary obtained by keeping all 5 neurons. Bottom row: Boundaries learned by the model adapted by our adversarial dropout method. Unlike the top row, here neurons 3,4,5 learn diverse features which result in diverse boundaries. + +# 3.3 INSIGHT AND IMPROVEMENT + +Our ADR approach encourages different neurons of the classifier to learn different characteristics of the input (see Sec. 4.1.) The output is the combination of shared and unshared nodes, therefore, to maximize the sensitivity, the unshared nodes must learn different features of target samples. As learning proceeds, each neuron in $C$ will capture different characteristics. At the same time, to minimize the sensitivity, $G$ learns to extract pure categorical information. If $G$ outputs features which are not related to categorical information, such as texture, slight contrast or difference of color, $C$ will utilize them to maximize sensitivity. + +The trained classifier will be sensitive to the perturbation of targets caused by dropout. We note that our approach is contrary to methods called adversarial example training (Goodfellow et al. (2014b); Miyato et al. (2016)) which train the classifier to be robust to adversarial examples. They utilize input noise which can deceive or change the output of the classifier, and incorporate it to obtain a good classifier. Our ADR method encourages the feature generator to obtain noise-robust target features. However, with regard to the classifier, it is trained to be sensitive to noise. To improve the final accuracy, we learn another classifier $C ^ { \prime }$ that is not trained to be sensitive to the noise. $C ^ { \prime }$ takes features generated by $G$ and is trained with classification loss on source samples. The loss of $C ^ { \prime }$ is not used to update $G$ . We compare the accuracy of $C$ and $C ^ { \prime }$ in experiments on image classification. + +# 4 EXPERIMENTS + +# 4.1 EXPERIMENT ON TOY DATA + +Experimental Setting. In this experiment, we observe the decision boundary obtained by each neuron to demonstrate that ADR encourages the neurons to learn different input characteristics. We use synthetic “two moons” data for this problem. Two dimensional samples from two classes are generated as source samples. Target samples are obtained by rotating the source samples. In our setting, the rotation was set to 30 degrees and data was generated with scikit-learn (Pedregosa et al. (2011)). We train a six-layered fully-connected network; the lower 3 layers are used as feature generator, and upper 3 layers are used as classifier. We used Batch Normalization (Ioffe & Szegedy (2015)) and ReLU as activation function. The number of neurons are [2,5,5] for feature generator, [5,5,2] for classifier. We visualize the boundary obtained from each neuron in the last layer by removing the output of all other neurons. + +Results. We show the learned boundary in Fig. 3. In the baseline model trained only with source samples (top row), two of five neurons do not seem to learn an effective boundary, and three neurons learn a similar boundary. On the other hand, in our method (bottom row), although two neurons do not seem to learn any meaningful boundary, three neurons learn distinctive boundaries, demonstrating greater diversity. Each neuron is trained to be sensitive to the noise caused by target samples. The final decision boundary (rightmost column) classifies most target samples correctly. The accuracy of our proposed method is $96 \%$ whereas the accuracy of the non-adapted model was $84 \%$ . + +![](images/739f2d31aa495e5a9d6c4fd7b45d22559c2abb1868aa853612bc7403b34eaae2.jpg) +Figure 4: Relationship between sensitivity loss on target (blue line), on source (yellow line), and accuracy (red: accuracy of $C ^ { \prime }$ , green: accuracy of $C$ ) during training on digits. + +# 4.2 UNSUPERVISED DOMAIN ADAPTATION FOR CLASSIFICATION + +Experiments on Digits Classification. We evaluate our model on adaptation between digits datasets. We use MNIST (LeCun et al. (1998)), SVHN (Netzer et al. (2011)) and USPS datasets and follow the protocol of unsupervised domain adaptation used by (Tzeng et al. (2017)). To extensively compare our method with previous methods, in adaptation from MNIST to USPS, we applied our method to a different protocol used in Bousmalis et al. (2017). We assume no labeled target samples and use fixed hyper-parameters for all experiments, unlike other works that use a target validation set (Saito et al. (2017)). The number of iterations for Step 3 was fixed at $n = 4$ . We used the same network architecture as in (Tzeng et al. (2017)), but inserted a Batch Normalization layer before the activation layer to stabilize the training. We used Adam (Kingma & Ba (2014)) for optimizer and set the learning rate to $2 . 0 \times 1 0 ^ { - 4 }$ , a value commonly reported in the GAN literature. We compare our approach to several existing methods and to the entropy minimization baseline (ENT) obtained by modifying (Springenberg (2015)). As we mentioned in Section 2, this is a model that generates features to minimize the entropy of the output probability for target samples. Due to space limitations, we provide a detailed explanation of this baseline in the appendix. + +Results in Table 1 demonstrate that ADR obtains better performance than existing methods. In particular, on the challenging adaptation task from SVHN to MNIST, our method achieves much better accuracy than previously reported. Fig. 4 shows the learning curve of each experiment. As sensitivity loss increases, the target accuracy improves. This means that as critic $C$ learns to detect the non-discriminative samples, feature generator $G$ learns to fool it, resulting in improved accuracy. In addition, we can see that the sensitivity of source samples increases too. As mentioned in Sec 3.3, the critic network should learn to capture features which are not very important for classification, such as texture or slight edges, and it seems to also capture such information in source samples. The accuracy of the classifier $C ^ { \prime }$ (denoted by red), which is trained not to be sensitive to the noise, is almost always better than the accuracy of the critic network. In adaptation from SVHN to MNIST (Fig. 5(c)), the accuracy of the critic often suffers as it becomes too sensitive to the noise caused by dropout. On the other hand, the accuracy shown by the red line is stable. Our ENT baseline shows good performance compared to other existing methods. This result indicates the effectiveness of methods based on entropy minimization. In Fig. 5, we compare our proposed method and ENT in terms of entropy of target samples. Our method clearly decreases the entropy, because target samples are moved away from the decision boundary. Yet, its behavior is different from ENT. Interestingly, the entropy is made smaller than ENT in case of adaptation from USPS to MNIST (Fig. 4(a)) though ENT directly minimizes the entropy and our method does not. On the SVHN to MNIST task (Fig. 4(c)), the entropy of ADR is larger than ENT, which indicates that our method places the target samples closer to the decision boundary than ENT does. + +Experiments on Object Classification. We next evaluate our method on fine-tuning a pretrained CNN. We use a new domain adaptation benchmark called the VisDA Challenge (Peng et al. (2017)) which focuses on the challenging task of adapting from synthetic to real images. The source domain consists of 152,409 synthetic 2D images from 12 object classes rendered from 3D models. The validation and test target domains consists of real images, which belong to the same classes. We used the validation domain (55,400 images) as our target domain in an unsupervised domain adaptation setting. + +![](images/177e15de1ac8fd6d27b034896b5372cb923b428390b94b1a14d9cc289b6a1b4f.jpg) +Figure 5: Comparison of entropy of ours (blue line) with ENT (yellow line). The entropy is calculated on target samples by using the output of the classifier. + +Table 1: Results on digits datasets. Please note that $^ \dagger$ means the result obtained using a few labeled target samples for validation. The reported accuracy of our method is obtained from $C ^ { \prime }$ . ENT is our proposed entropy minimization baseline, described in the appendix. MNIST(P1) and MNIST(P2) indicate different experimental settings used in Tzeng et al. (2017) and Bousmalis et al. (2017) respectively. + +
METHODSVHN to MNISTUSPS to MNISTMNIST(P1) to USPSMNIST(P2) to USPS
Source Only67.168.177.078.9
LTN (Sener et al. (2016))78.8-1-
ATDA (Saito et al. (2017))86.2†=1-
DSN (Bousmalis et al. (2016))82.7†91.3†
PixelDA (Bousmalis et al. (2017)1=-95.9†
DANN (Ganin & Lempitsky (2014))73.973.0±2.077.1±1.885.1†
DoC (Tzeng et al. (2014))68.1±0.366.5±3.379.1±0.51
ADDA (Tzeng et al. (2017))76.0±1.890.1±0.889.4±0.2-
CoGAN (Liu & Tuzel (2016))did not converge89.1±0.891.2±0.8=
DTN (Taigman et al. (2016))84.71-
ENT (Our proposed baseline) Ours94.9±4.11 95.0±1.8791.2±1.92 93.1±1.2793.7±0.54 93.2±2.4696.7±1.27 96.1±0.29
+ +We evaluate our model on fine-tuning networks pretrained on ImageNet (Deng et al. (2009)): ResNet101 (He et al. (2016)) and ResNext (Xie et al. (2016)). For the feature generator, we use the pretrained CNN after removing the top fully connected layer. For the classification network, we use a three-layered fully connected network. + +Table 2 shows that our method outperformed other distribution matching methods and our new baseline (ENT) in finetuning both networks by a large margin. ENT did not achieve better performance than existing methods, though improvement over the source only model was observed. Although this method performed well on digits, it does not work as well here, possibly because of the larger shift between very different domains. In the experiment on ResNext, after training $G$ and $C$ , we retrained a classifier $C ^ { ' }$ just on the features generated by $G$ due to GPU memory limitations, and observed improvement in both networks. + +Fig. 6 visualizes the target features obtained by $G$ with the pretrained model, model fine-tuned on source, and our ADR method. While the embedding of the source only model does not separate classes well due to domain shift, we can see clearly improved separation with ADR. + +Image Segmentation experiments. Next, we apply our method to adaptation for semantic image segmentation. Image segmentation is different from classification in that we classify each pixel in the image. To evaluate the performance on segmentation, the synthetic GTA5 (Richter et al. (2016)) dataset is used as source, and real CityScape (Cordts et al. (2016)) dataset is used as target. Previous work tackled this problem by matching distributions of each pixel’s feature in a middle layer of the network (Hoffman et al. (2016)). In this work, we apply ADR by calculating sensitivity between all pixels. The training procedure is exactly the same as in classification experiments. + +We use the ResNet50 pretrained on ImageNet, and utilize an FCN (Long et al. (2015a)) based network architecture. Further, we utilize the more recent Dilated Residual Networks (DRN) 105 layered model (Yu et al. (2017)), which outperforms ResNet50 on a semantic segmentation task. + +Table 2: Results on Visda2017 classification datasets (Peng et al. (2017)). DANN and MMD are distribution alignment methods proposed by (Ganin & Lempitsky (2014)) and (Long et al. (2015b)) respectively. Ours (retrain classifier) means the classifier retrained for our proposed generator as we mentioned in Sec 3.3. Our proposed method shows much better performance than existing methods. + +
Methodgrrrdoraegpaleie 3ueoormorreiltuosiadsareraertrnaaa
Finetuning on ResNet101
Source Only55.153.3 61.959.180.617.979.731.281.026.573.58.552.4
MMD87.163.0 76.542.090.342.985.953.149.736.385.820.761.1
DANN81.977.7 82.844.381.229.565.128.651.954.682.87.857.4
ENT80.375.5 75.848.377.927.369.740.246.546.679.316.057.0
Ours94.151.3 83.272.288.768.892.870.277.263.682.930.372.9
Ours (retrained classifier)94.248.5 84.072.990.174.292.672.580.861.882.228.873.5
Finetuning on ResNeXt
Source Only74.3 37.6 61.8 68.2 59.510.7 81.412.8 61.6 26.070.05.647.4
MMD90.751.1 64.865.689.946.591.940.181.524.190.028.563.7
DANN86.066.3 60.8 56.079.853.782.325.258.231.089.326.159.6
ENT94.781.0 57.046.673.949.069.231.040.534.387.315.156.6
Ours86.3 71.987.678.193.084.894.578.991.858.977.726.777.5
Ours (retrained classifier)89.270.9 85.782.093.786.7 93.372.389.553.086.728.377.6
+ +![](images/f85e9efe625959ba93fdcfd4024851f548acbeebd038701c1fb299173a9f68e4.jpg) +Figure 6: Visualization of VisDA-classification (12 classes) target features using T-SNE (Maaten & Hinton (2008)): (a) features obtained by the Imagenet-pretrained ResNext model not finetuned on VisDA; (b) features from the ResNext model fine-tuned only on VisDA source samples without any adaptation; (c) features obtained by ResNext adapted by our ADR method. + +For the feature generator, we use the pretrained network without fully-connected layers. For the classifier, we use a fully-convolutional network with dropout layers. Due to limited memory, the batch size is set to 1. We include details of the network architecture in appendix. For comparison, we train a domain classifier based model for our network (DANN). We build a domain classifier network for the features of each pixel following (Hoffman et al. (2016)). + +In Table 3, we show the qualitative comparison with existing methods. ADR clearly improves mean IoU (Intersection-over-Union) compared to the source-only and competing models, beating state-ofthe-art by a large margin. When we apply ADR to DRN, the accuracy improves much more than for ResNet50, and is 12.4 points higher than the model trained only on GTA5 source samples. This is likely because ADR exploits the strong representation of the pretrained DRN network. Although we implemented ENT in this setting, the accuracy was much worse than the Source Only model with a mIoU of 15.0 in training ResNet50. The ENT method does not seem to work well on syntheticto-real shifts. Finally, we illustrate our method’s improvement on example input images, ground truth labels, images segmented by the Source Only model and our method in Fig. 7. While the Source Only model seems to suffer from domain shift, ADR generates a clean segmentation. These experiments demonstrate the effectiveness of ADR on semantic segmentation. + +# 5 CONCLUSION + +In this paper, we introduced a novel approach for aligning deep representation, Adversarial Dropout Regularization, which learns to generate discriminative features for the target domain. The method consists of a critic network that can detect samples near the task decision boundary and a feature generator that fools the critic. Our approach is general, applies to a variety of tasks, and does not require target domain labels. In extensive domain adaptation experiments, our method outperformed baseline methods, including entropy minimization, and achieved state-of-the-art results on three datasets. + +
NetworkMethodxeeepreBuiplng8irilen买uosradMur0mrrqeemIoU
VGG-16FCN Wild70.432.462.114.95.410.914.22.779.221.364.644.14.270.48.07.30.03.50.027.1
ResNet50Source OnlyDANNOurs64.572.487.824.919.115.673.714.83.920.62.59.39.718.017.319.015.913.119.90.05.57.774.916.472.042.30.039.58.612.117.513.49.927.70.00.01.80.05.89.70.00.00.025.326.433.3
73.077.471.082.020.131.562.274.332.643.55.29.068.477.8
DRN-105Source OnlyOurs25.986.210.910.150.578.83.320.112.27.425.428.613.015.078.384.57.338.963.952.17.966.35.229.67.832.70.90.213.719.20.78.324.937.3
21.226.581.154.613.680.8
+ +![](images/2a431aecdd2cbdb38788dec71565dbda6f38a671d3881b7e8cbaa1c5630bfb5c.jpg) +Table 3: Results on adaptation from $\mathrm { G T A } 5 $ Cityscapes. DANN and FCN Wild denote methods proposed by (Ganin & Lempitsky (2014)) and (Hoffman et al. (2016) respectively. +Figure 7: Comparison of results on two real images segmented by ResNet50. Clockwise from upper left: Original image; Ground truth; Segmented image before adaptation; Segmented image after adaptation by our method. + +We also show how to apply our method to train Generative Adversarial Networks for semisupervised learning in the appendix. + +# 6 ACKNOWLEDGEMENTS + +We would like to thank Trevor Darrell for his great advice on our paper. The first author’s stay at Boston University was partially supported by a scholarship from the University of Tokyo. The work was partially funded by the ImPACT Program of the Council for Science, Technology, and Innovation (Cabinet Office, Government of Japan), and was partially supported by CREST, JST. Saenko was supported by IARPA and NSF grants CCF-1723379 and IIS-1724237. + +# REFERENCES + +Shai Ben-David, John Blitzer, Koby Crammer, Alex Kulesza, Fernando Pereira, and Jennifer Wortman Vaughan. A theory of learning from different domains. Machine learning, 79(1-2):151–175, 2010. + +Konstantinos Bousmalis, George Trigeorgis, Nathan Silberman, Dilip Krishnan, and Dumitru Erhan. Domain separation networks. In NIPS, 2016. + +Konstantinos Bousmalis, Nathan Silberman, David Dohan, Dumitru Erhan, and Dilip Krishnan. Unsupervised pixel-level domain adaptation with generative adversarial networks. In CVPR, 2017. + +Olivier Chapelle and Alexander Zien. Semi-supervised classification by low density separation. In AISTATS, 2005. + +Marius Cordts, Mohamed Omran, Sebastian Ramos, Timo Rehfeld, Markus Enzweiler, Rodrigo Benenson, Uwe Franke, Stefan Roth, and Bernt Schiele. The cityscapes dataset for semantic urban scene understanding. In CVPR, 2016. + +Zihang Dai, Zhilin Yang, Fan Yang, William W Cohen, and Ruslan Salakhutdinov. Good semisupervised learning that requires a bad gan. arXiv preprint arXiv:1705.09783, 2017. + +Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scale hierarchical image database. In CVPR, 2009. + +Vincent Dumoulin, Ishmael Belghazi, Ben Poole, Alex Lamb, Martin Arjovsky, Olivier Mastropietro, and Aaron Courville. Adversarially learned inference. arXiv preprint arXiv:1606.00704, 2016. + +Yaroslav Ganin and Victor Lempitsky. Unsupervised domain adaptation by backpropagation. In ICML, 2014. + +Yaroslav Ganin, Evgeniya Ustinova, Hana Ajakan, Pascal Germain, Hugo Larochelle, Franc¸ois Laviolette, Mario Marchand, and Victor Lempitsky. Domain-adversarial training of neural networks. JMLR, 17(59):1–35, 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, 2014a. + +Ian J Goodfellow, Jonathon Shlens, and Christian Szegedy. Explaining and harnessing adversarial examples. In ICLR, 2014b. + +Yves Grandvalet and Yoshua Bengio. Semi-supervised learning by entropy minimization. In NIPS, 2005. + +Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In CVPR, 2016. + +Judy Hoffman, Dequan Wang, Fisher Yu, and Trevor Darrell. Fcns in the wild: Pixel-level adversarial and constraint-based adaptation. arXiv preprint arXiv:1612.02649, 2016. + +Sergey Ioffe and Christian Szegedy. Batch normalization: Accelerating deep network training by reducing internal covariate shift. In ICML, 2015. + +Thorsten Joachims. Transductive inference for text classification using support vector machines. In ICML, 1999. + +Diederik Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014. + +Yann LeCun, Leon Bottou, Yoshua Bengio, and Patrick Haffner. Gradient-based learning applied to ´ document recognition. Proceedings of the IEEE, 86(11):2278–2324, 1998. + +Ming-Yu Liu and Oncel Tuzel. Coupled generative adversarial networks. In NIPS, 2016. + +Jonathan Long, Evan Shelhamer, and Trevor Darrell. Fully convolutional networks for semantic segmentation. In CVPR, 2015a. + +Mingsheng Long, Yue Cao, Jianmin Wang, and Michael I Jordan. Learning transferable features with deep adaptation networks. In ICML, 2015b. + +Mingsheng Long, Han Zhu, Jianmin Wang, and Michael I Jordan. Unsupervised domain adaptation with residual transfer networks. In NIPS, 2016. + +Mingsheng Long, Jianmin Wang, and Michael I Jordan. Deep transfer learning with joint adaptation networks. In ICML, 2017. + +Lars Maaløe, Casper Kaae Sønderby, Søren Kaae Sønderby, and Ole Winther. Auxiliary deep generative models. arXiv preprint arXiv:1602.05473, 2016. + +Laurens van der Maaten and Geoffrey Hinton. Visualizing data using t-sne. JMLR, 9(Nov):2579– 2605, 2008. + +Takeru Miyato, Shin-ichi Maeda, Masanori Koyama, Ken Nakae, and Shin Ishii. Distributional smoothing with virtual adversarial training. 2016. + +Yuval Netzer, Tao Wang, Adam Coates, Alessandro Bissacco, Bo Wu, and Andrew Y Ng. Reading digits in natural images with unsupervised feature learning. In NIPS workshop on deep learning and unsupervised feature learning, 2011. + +Fabian Pedregosa, Ga”el Varoquaux, Alexandre Gramfort, Vincent Michel, Bertrand Thirion, Olivier Grisel, Mathieu Blondel, Peter Prettenhofer, Ron Weiss, Vincent Dubourg, et al. Scikitlearn: Machine learning in python. JMLR, 12(10):2825–2830, 2011. + +Xingchao Peng, Ben Usman, Neela Kaushik, Judy Hoffman, Dequan Wang, and Kate Saenko. Visda: The visual domain adaptation challenge. arXiv preprint arXiv:1710.06924, 2017. + +Stephan R Richter, Vibhav Vineet, Stefan Roth, and Vladlen Koltun. Playing for data: Ground truth from computer games. In ECCV, 2016. + +Kuniaki Saito, Yoshitaka Ushiku, and Tatsuya Harada. Asymmetric tri-training for unsupervised domain adaptation. In ICML, 2017. + +Tim Salimans, Ian Goodfellow, Wojciech Zaremba, Vicki Cheung, Alec Radford, and Xi Chen. Improved techniques for training gans. In NIPS, 2016. + +Ozan Sener, Hyun Oh Song, Ashutosh Saxena, and Silvio Savarese. Learning transferrable representations for unsupervised domain adaptation. In NIPS, 2016. + +Jost Tobias Springenberg. Unsupervised and semi-supervised learning with categorical generative adversarial networks. arXiv preprint arXiv:1511.06390, 2015. + +Nitish Srivastava, Geoffrey E Hinton, Alex Krizhevsky, Ilya Sutskever, and Ruslan Salakhutdinov. Dropout: a simple way to prevent neural networks from overfitting. JMLR, 15(1):1929–1958, 2014. + +Baochen Sun and Kate Saenko. Deep coral: Correlation alignment for deep domain adaptation. In ECCV 2016 Workshops, 2016. + +Baochen Sun, Jiashi Feng, and Kate Saenko. Return of frustratingly easy domain adaptation. In AAAI, 2016. + +Yaniv Taigman, Adam Polyak, and Lior Wolf. Unsupervised cross-domain image generation. In ICLR, 2016. + +Eric Tzeng, Judy Hoffman, Ning Zhang, Kate Saenko, and Trevor Darrell. Deep domain confusion: Maximizing for domain invariance. arXiv preprint arXiv:1412.3474, 2014. + +Eric Tzeng, Judy Hoffman, Kate Saenko, and Trevor Darrell. Adversarial discriminative domain adaptation. In CVPR, 2017. + +Saining Xie, Ross Girshick, Piotr Dollar, Zhuowen Tu, and Kaiming He. Aggregated residual trans- ´ formations for deep neural networks. arXiv preprint arXiv:1611.05431, 2016. + +Hongliang Yan, Yukang Ding, Peihua Li, Qilong Wang, Yong Xu, and Wangmeng Zuo. Mind the class weight bias: Weighted maximum mean discrepancy for unsupervised domain adaptation. In CVPR, 2017. + +Fisher Yu, Vladlen Koltun, and Thomas Funkhouser. Dilated residual networks. In CVPR, 2017. + +# APPENDIX + +# A ENTROPY BASED METHOD FOR DOMAIN ADAPTATION (ENT) + +Our method aims to move target samples away from the decision boundary. Some techniques used in training Generative Adversarial Networks can be applied to achieve our goal too. (Springenberg (2015); Salimans et al. (2016)) used small number of labeled samples to train critic. Critic is trained to classify real samples into $K$ classes. They also trained critic to move unlabeled real images away from the boundary by minimizing entropy of the critic’s output. Generated fake images are moved near the boundary by maximizing the entropy. On the other hand, generator is trained to generate fake images which should be placed away from the boundary. This kind of method can be easily applied to domain adaptation problem. We would like to describe the method along with our problem setting. + +Similar to our method, we have critic networks $C$ and generator $G$ . $C$ classifies samples into $K$ class. $C$ is trained to maximize the entropy of target samples, which encourages to move the target samples near the boundary. Then, $G$ is trained to minimize the entropy of them. Thus, $G$ tries to move target samples away from the boundary. + +The only difference from our method is that we used entropy term for adversarial training loss. That is, in this method, we replace our sensitivity term $d ( p _ { 1 } , p _ { 2 } )$ in Eq. 4 with entropy of the classifier output. The adversarial loss for this baseline method is a following one. + +$$ +\begin{array} { r c l } { { { \cal L } _ { a d v } ( X _ { t } ) } } & { { = } } & { { \displaystyle \mathbb { E } _ { { \mathbf { x _ { t } } } \sim X _ { t } } [ H [ p ( \mathbf { y } | { \mathbf { x _ { t } } } ) ] } } \\ { { { \cal H } [ p ( \mathbf { y } | { \mathbf { x _ { t } } } ) ] } } & { { = } } & { { \displaystyle - \sum _ { k = 1 } ^ { K } p ( y = k | { \mathbf { x _ { t } } } ) \log p ( y = k | { \mathbf { x _ { t } } } ) } } \end{array} +$$ + +$$ +H [ p ( y | x ) ] = - \sum _ { k = 1 } ^ { K } p ( y = k | x ) \log p ( y = k | x ) +$$ + +The hyper-parameter $n$ , how many times we update $G$ for adversarial loss in one mini-batch, is set as $n = 4$ . Experimentally, it worked well for all settings. + +# B DIGITS CLASSIFICATION TRAINING DETAIL + +We follow the protocol used in (Tzeng et al. (2017)). For adaptation from SVHN to MNIST, we used standard training splits of each datasets as training data. For evaluation, we used test splits of MNIST. For the adaptation between MNIST and USPS (P1), we sampled 2000 images from MNIST and 1800 images from USPS. For the adaptation between MNIST and USPS (P2), we used all training images of MNIST and USPS following Bousmalis et al. (2017). In these experiments, we composed the mini-batch half from source and half from target samples. The batch-size was set as 128 for both source and target. We report the score after repeating Step $1 { \sim } 3$ (please see Sec 3.2) 20000 times. For our baseline, ENT, we used the same network architecture and the same hyper-parameters as used in our proposed method. + +# C OBJECT CLASSIFICATION TRAINING DETAIL + +In this experiment, SGD with learning rate $1 . 0 \times 1 0 ^ { - 3 }$ is used to optimize the parameters. For the finetuning of ResNet101, we set batch-size as 32. Due to the limit of GPU memory, we set it as 24 in finetuning ResNext model. We report the score after 20 epochs training. In order to train MMD model, we use 5 RBF kernels with the following standard deviation parameters: + +$$ +\sigma = [ 0 . 1 , 0 . 0 5 , 0 . 0 1 , 0 . 0 0 0 1 , 0 . 0 0 0 0 1 ] +$$ + +We changed the number of the kernels and their parameters, but we could not observe significant performance difference. We report the performance after 5 epochs. We could not see any improvement after the epoch. + +To train a model (Ganin & Lempitsky (2014)), we used two-layered domain classification networks. Experimentally, we did not see any improvement when the network architecture is changed. According to the original method (Ganin $\&$ Lempitsky (2014)), learning rate is decreased every iteration. However, in our experiment, we could not see improvement, thus, we fixed learning rate $\mathrm { i . 0 \times 1 0 ^ { - 3 } }$ . We report the accuracy after 1 epoch. The accuracy dropped significantly after the first epoch. We assume this is due to the large domain difference between synthetic and real images. + +![](images/91334547d8f045bbc50bad32d13e84fbdd9717e2bd91e1f11d2951fede231eb5.jpg) +Figure 9: Example of results on segmentation experiments performed by DRN-105. From top to bottom, Original image; Ground truth; Segmented image before adaptation; Segmented image after adaptation by our method. + +For our new baseline, ENT, we used the same hyper-parameter as we used for our proposed method. Since the accuracy of ENT drops significantly after around 5 epochs, we report the accuracy after 5 epoch updates. + +# D SEGMENTATION EXPERIMENTS + +We modified FCN Long et al. (2015a) architecture suitable for ResNet structure. The features from ResBlock $2 { \sim } 4$ and the first convolution layer and maxpooling layer are used in our implementation. In Fig. 8, we show how we integrated the features of each layers. We regard the layers of ResNet50 as generator and rest of the networks, namely convolution and upsampling layers as a critic network. The input images were resized to $5 1 2 \mathrm { x } 1 0 2 4$ due to the limit of GPU memory. For the same reason, the batchsize was set to one. In Fig. 9, we show the example of segmented images by DRN-105. The images are cleanly segmented by our proposed method. + +![](images/239b4a962924dc544fc56d44223b3182af3fbba803795fe928439774dffc489c.jpg) +Figure 8: Overview of architecture for semantic segmentation + +# E SEMI-SUPERVISED LEARNING USING GANS + +In this section, we demonstrate how to apply our method in training a Generative Adversarial Network (GAN) applied to semi-supervised learning. We follow the method proposed by (Springenberg (2015); Salimans et al. (2016)), who use a $K$ -class classification network as a critic to train a GAN in the semi-supervised setting. + +Approach. In contrast to the domain adaptation setting, here $G$ tries to generate images which fool the critic $C$ . Also, in this setting, we are given labeled and unlabeled real images from the same domain. Then, we train the critic to classify labeled images correctly and to move unlabeled images far from the decision boundary. To achieve this, we propose to train the critic with the following objective: + +$$ +\operatorname* { m i n } _ { C } L _ { C } = L ( X _ { L } , Y _ { L } ) + L _ { a d v } ( X _ { u } ) - L _ { a d v } ( X _ { g } ) - H [ \frac { 1 } { M } \sum _ { i = 1 } ^ { M } p ( y | x _ { u } { } ^ { i } , C ) ] +$$ + +$$ +L _ { a d v } ( X _ { u } ) = \mathbb { E } _ { \mathbf { x _ { u } } \sim X _ { u } } [ d ( C _ { 1 } ( G ( \mathbf { x _ { u } } ) ) , C _ { 2 } ( G ( \mathbf { x _ { u } } ) ) ) ] +$$ + +![](images/63364abe673b063e24a800150d6aed5d16f2ac6fd54204e6ef2d434abc5d60e1.jpg) +Figure 10: Examples of generated images. + +
SVHN (% errors)CIFAR (% errors)
Labeled Only SDGM (Maalge et al. (2016)16.61 ± 0.24
CatGAN (Springenberg (2015))=19.58±0.46
ALI (Dumoulin et al. (2016))7.42±0.6517.99±1.62
ImpGAN (Salimans et al. (2016))8.11±1.318.63±2.32
Ours6.26±1.0519.63±0.37
+ +Table 4: Comparison with state-of-the-art methods on two benchmark datasets. Only methods without data augmentation are included. We used the same critic architecture as used in ImpGAN. + +$$ +L _ { a d v } ( X _ { g } ) = \mathbb { E } _ { { \mathbf { x } } _ { \mathbf { g } } \sim X _ { G } } [ d ( C _ { 1 } ( G ( { \mathbf { x } } _ { \mathbf { g } } ) ) , C _ { 2 } ( G ( { \mathbf { x } } _ { \mathbf { g } } ) ) ) ] +$$ + +where $X _ { L }$ denotes the subset of labeled samples, $X _ { u }$ denotes unlabeled ones and $X _ { g }$ denotes images generated by $G$ and $H$ denotes entropy as Eq.6 shows. The critic is trained to minimize the loss on labeled samples in the first term. Since unlabeled images should be far away from the decision boundary and should be distributed uniformly among the classes, we add the second and fourth term. The third term encourages the critic to detect fake images generated near the boundary. + +The objective of $G$ is as follows, + +$$ +\operatorname* { m i n } _ { G } L _ { a d v } ( X _ { g } ) + | | \mathbb { E } _ { x _ { g } \sim X _ { g } } f ( \mathbf { x _ { g } } ) - \mathbb { E } _ { \mathbf { x _ { u } } \sim X _ { u } } f ( \mathbf { x _ { u } } ) | | ^ { 2 } +$$ + +where the second term encourages generated images to be similar to real images, which is known to be effective to stabilize the training. The first term encourages the generator to create fake images which should be placed far away from the boundary. Such images should be similar to real images because they are likely to be assigned to some class with high probability. Here, we update $C$ and $G$ same number of times. + +Experiment. We evaluate our proposed GAN training method by using SVHN and CIFAR10 datasets, using the critic network architecture from (Salimans et al. (2016)). We set the batch size as 100 and used Adam with learning rate $2 . 0 \times 1 . 0 ^ { - 4 }$ for optimizer. After the conv6 layer of the critic, we constructed a classifier which was not concerned with adversarial learning process. + +In the experiment on SVHN, we replaced Weight Normalization with Batch Normalization for $C$ . Also, in the experiment on CIFAR10, we construct a classifier from a middle layer of the critic, which is not incorporated into the adversarial training step. This is motivated by the insight that the critic in our method is trained to be too sensitive to the dropout noise as we explained in Sec 3.3. + +Results. From Fig. 10(a), we can see that ADR seems to generate realistic SVHN images. Some images are significantly blurred, but most of the images are clear and diverse. As for generated CIFAR10 images, they do not seem as realistic, but some objects appear in most images. In Table 4, we can see that the accuracy of the critic trained by our method has better performance than other models for SVHN. For CIFAR10, the accuracy was slightly worse than other state-of-the-art methods. We conclude that, despite its clear advantage on the domain adaptation tasks, our method produces mixed results on the SSL tasks. It could still be useful for SSL, however, it needs further exploration to improve the accuracy. For example, in Eq. 6, we propose to maximize the entropy of the marginal class distribution of the unlabeled real images, as well as forcing them to be far from the boundary. However, these objectives may contradict each other, which may in turn degrade the performance. In late-breaking results, Dai et al. (2017) theoretically showed that just generating fake images that are far from decision boundaries does not help to improve accuracy in training GANs in the setting of SSL. Further improvement of our SSL approach based on these results is an interesting direction for future work. \ No newline at end of file diff --git a/parse/train/HJIoJWZCZ/HJIoJWZCZ_content_list.json b/parse/train/HJIoJWZCZ/HJIoJWZCZ_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..05e27c858077c6967429b3b32e08c83ff9d68c69 --- /dev/null +++ b/parse/train/HJIoJWZCZ/HJIoJWZCZ_content_list.json @@ -0,0 +1,1808 @@ +[ + { + "type": "text", + "text": "ADVERSARIAL DROPOUT REGULARIZATION ", + "text_level": 1, + "bbox": [ + 176, + 98, + 705, + 122 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Kuniaki Saito1, Yoshitaka Ushiku1, Tatsuya Harada1,2, and Kate Saenko3 ", + "bbox": [ + 258, + 150, + 736, + 166 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1The University of Tokyo, 2RIKEN, 3Boston University {k-saito,ushiku,harada}@mi.t.u-tokyo.ac.jp, saenko@bu.edu ", + "bbox": [ + 230, + 176, + 771, + 207 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ABSTRACT ", + "text_level": 1, + "bbox": [ + 454, + 241, + 544, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We present a domain adaptation method for transferring neural representations from label-rich source domains to unlabeled target domains. Recent adversarial methods proposed for this task learn to align features across domains by “fooling” a special domain classifier network. However, a drawback of this approach is that the domain classifier simply labels the generated features as in-domain or not, without considering the boundaries between classes. This means that ambiguous target features can be generated near class boundaries, reducing target classification accuracy. We propose a novel approach, Adversarial Dropout Regularization (ADR), which encourages the generator to output more discriminative features for the target domain. Our key idea is to replace the traditional domain critic with a critic that detects non-discriminative features by using dropout on the classifier network. The generator then learns to avoid these areas of the feature space and thus creates better features. We apply our ADR approach to the problem of unsupervised domain adaptation for image classification and semantic segmentation tasks, and demonstrate significant improvements over the state of the art. ", + "bbox": [ + 233, + 272, + 764, + 479 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 INTRODUCTION ", + "text_level": 1, + "bbox": [ + 176, + 506, + 336, + 522 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Transferring knowledge learned by deep neural networks from label-rich domains to new target domains is a challenging problem, especially when the source and target input distributions have different characteristics. Such domain shifts occurs in many practical applications. For example, while simulated driving images rendered by games provide a rich source of labeled data for semantic segmentation Richter et al. (2016), deep models trained on such source data do not transfer well to real target domains (Fig. 1(a-d)). When target-domain labels are unavailable for fine-tuning, unsupervised domain adaptation must be applied to improve the source model. ", + "bbox": [ + 174, + 526, + 825, + 625 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent methods for unsupervised domain adaptation attempt to reduce the discrepancy between the source and target features via adversarial learning (Tzeng et al. (2014); Ganin $\\&$ Lempitsky (2014)). They divide the base network into a feature encoder $G$ and classifier $C$ , and add a separate domain classifier (critic) network $D$ . The critic takes the features generated by $G$ and labels them as either source- or target-domain. The encoder $G$ is then trained with an additional adversarial loss that maximizes $D$ ’s mistakes and thus aligns features across domains. ", + "bbox": [ + 174, + 631, + 823, + 714 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, a major drawback of this approach is that the critic simply predicts the domain label of the generated point and does not consider category information. Thus the generator may create features that look like they came from the right domain, but are not discriminative. In particular, it can generate points close to class boundaries, as shown in Fig. 1(e), which are likely to be misclassified by the source model. We argue that to achieve good performance on the target data, the adaptation model must take the decision boundaries between classes into account while aligning features across domains (Fig. 1(f)). Moreover, since our setting is unsupervised adaptation, this must be accomplished without labels on target data. ", + "bbox": [ + 174, + 722, + 825, + 833 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we propose a novel adversarial alignment technique that overcomes the above limitation and preserves class boundaries. We make the following observation: if the critic could detect points near the decision boundary, then the generator would have to avoid these areas of the feature space in order to fool the critic. Thus the critic would force the generator to create more discriminative features. How can we obtain such a critic? If we alter the boundary of the classifier $C$ slightly and measure the change in the posterior class probability $p ( y | x )$ , where $y$ and $x$ denote class and input respectively, then samples near the decision boundary are likely to have the largest change. In fact, this posterior discrepancy is inversely proportional to the distance from the class boundary. We thus propose to maximize this posterior discrepancy to turn $C$ into a critic sensitive to nondiscriminative points. We call this technique Adversarial Dropout Regularization. Here, dropout is not used in the standard way, which is to regularize the main classifier and make it insensitive to noise. Instead, we use dropout in an adversarial way, to transform the classifier into a critic sensitive to noise. Compared to previous adversarial feature alignment methods, where the distributions $p ( x )$ are aligned globally, our method aligns target features away from decision boundaries, as illustrated in Fig.1(f). ", + "bbox": [ + 174, + 840, + 823, + 924 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b6f4ca41441b05f1a91aeb791d5664cfbced0e867e90f0899d66085405d66cc1.jpg", + "image_caption": [ + "Figure 1: (a-d) An illustration of a deep model trained on simulated source training data failing to segment a real target domain image: (a) shows the target image, (b) is the ground truth segmentation into semantic categories (car, road, etc), (c) is the output of the unadapted source model, (d) is the improved segmentation obtained by our proposed ADR method. (e) Previous distribution matching methods do not consider the source decision boundary when aligning source and target feature points. (f) We propose to use the boundary information to achieve low-density separation of aligned points. " + ], + "image_footnote": [], + "bbox": [ + 173, + 99, + 823, + 212 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 335, + 825, + 462 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our ADR approach has several benefits. First, we train the generator $G$ with feedback from the classifier $C$ , in contrast to existing methods, which use an unrelated critic $D$ . Second, our method is general and straightforward to apply to a variety of domain adaptation problems, such as classification and semantic segmentation. Finally, since ADR is trained to align distributions, it is also applicable to semi-supervised learning and training of generative models, such as Generative Adversarial Networks (GANs) (Goodfellow et al. (2014a)). Through extensive experiments, we demonstrate the benefit of ADR over existing domain adaptation approaches, achieving state-of-the-art results in difficult domain shifts. We also show an application to semi-supervised learning using GANs in appendix. ", + "bbox": [ + 173, + 468, + 825, + 593 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2 RELATED WORK ", + "text_level": 1, + "bbox": [ + 176, + 616, + 344, + 632 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Domain Adaptation. Recent unsupervised domain adaptation (UDA) methods for visual data aim to align the feature distributions of the source and target domains (Sun et al. (2016); Sun & Saenko (2016); Tzeng et al. (2014); Ganin et al. (2016); Long et al. (2015b); Yan et al. (2017); Long et al. (2017)). Such methods are motivated by theoretical results stating that minimizing the divergence between domains will lower the upper bound of the error on target domain (Ben-David et al. (2010)). Many works in deep learning utilize the technique of distribution matching in hidden layers of a network such as a CNN (Tzeng et al. (2014); Ganin et al. (2016); Long et al. (2015b)). However, they measure the domain divergence based on the hidden features of the network without considering the relationship between its decision boundary and the target features, as we do in this paper. ", + "bbox": [ + 173, + 638, + 825, + 763 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Low-density Separation. Many semi-supervised learning (SSL) methods utilize the relationship between the decision boundary and unlabeled samples, a technique called low-density separation (Chapelle & Zien (2005); Joachims (1999)). By placing the boundary in the area where the unlabeled samples are sparse, these models aim to obtain discriminative representations. Our method aims to achieve low-density separation for deep domain adaptation and is related to entropy minimization for semi-supervised learning (Grandvalet & Bengio (2005)). (Long et al. (2016)) used entropy minimization in their approach to directly measure how far samples are from a decision boundary by calculating entropy of the classifier’s output. On the other hand, our method tries to achieve low-density separation by slightly moving the boundary and detecting target samples sensitive to the movement. As long as target samples features are robust to the movement, they will be allowed to exist relatively nearby the boundary compared to source samples, as Fig. 1 shows. ", + "bbox": [ + 174, + 771, + 825, + 924 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In (Long et al. (2016)) entropy minimization is only a part of the overall approach. To compare our ADR approach to entropy minimization more directly, we use a new baseline method. To our knowledge, though this method has not been proposed by any previous work, it is easily achieved by modifying a method proposed by (Springenberg (2015)). For this baseline, we train a model that generates features to minimize the entropy of the output probability for target samples. The details of the baseline are provided in appendix. In short, the generator tries to minimize the entropy of the target samples, whereas the critic tries to maximize it. The entropy is directly measured by the output of the classifier. This baseline is similar to our approach in that the goal of the method is to achieve low-density separation. ", + "bbox": [ + 173, + 103, + 825, + 229 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Dropout. Dropout is a method that prevents deep networks from overfitting (Srivastava et al. (2014)) by randomly dropping units from the neural network during training. Effectively, dropout samples from an exponential number of different thinned networks at training time, which prevents units from co-adapting too much. At test time, predictions are obtained by using the outputs of all neurons. If the thinned networks are able to classify the samples accurately, the full network will as well. In other words, dropout encourages the network to be robust to noise. In our work, we use dropout to regularize the feature generation network $G$ , but in an adversarial way. We train the critic $C$ to be sensitive to the noise caused by dropout and use $C$ to regularize $G$ so that it generates noise-robust features. To our knowledge, this use of dropout is completely different from existing methods. ", + "bbox": [ + 174, + 236, + 825, + 361 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3 METHOD ", + "text_level": 1, + "bbox": [ + 174, + 381, + 282, + 396 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We assume that we have access to a labeled source image $\\mathbf { x _ { s } }$ and a corresponding label $y _ { s }$ drawn from a set of labeled source images $\\{ X _ { s } , Y _ { s } \\}$ , as well as an unlabeled target image $\\mathbf { x _ { t } }$ drawn from unlabeled target images $X _ { t }$ . We train a feature generation network $G$ , which takes inputs $\\mathbf { x _ { s } }$ or $\\mathbf { x _ { t } }$ , and a network $C$ that acts as both the main classifier and the critic. When acting as the classifier, $C$ takes features from $G$ and classifies them into $K$ classes, predicting a $K$ -dimensional vector of logits $\\{ l _ { 1 } , l _ { 2 } , l _ { 3 } . . . l _ { K } \\}$ . The logits are then converted to class probabilities by applying the softmax function. Namely, the probability that $\\mathbf { x }$ is classified into class $j$ is denoted by $\\begin{array} { r } { p ( y = j | \\mathbf { x } ) = \\frac { e x p ( l _ { j } ) } { \\sum _ { k = 1 } ^ { K } e x p ( l _ { k } ) } } \\end{array}$ . We use the notation $p ( \\mathbf { y } \\vert \\mathbf { x } )$ to denote the $K$ -dimensional probabilistic output for input $\\mathbf { x }$ . ", + "bbox": [ + 173, + 401, + 825, + 522 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "When $C$ is acting as the critic, we want it to detect the feature encodings of target samples near the decision boundary. We propose to make $C$ sensitive to such samples by slightly perturbing its decision boundary and measuring the change in the posterior class probability $p ( \\mathbf { y } \\vert \\mathbf { x } )$ . This change is likely to be largest for samples near the decision boundary. The network $C$ is then trained to increase this change, while the feature generation network $G$ is trained to decrease it. Through this adversarial training, $G$ learns to ‘fool’ the critic and generate target features far away from the decision boundary, thus avoiding ambiguous features. The weights of $G$ can be initialized either by pre-training on some auxiliary dataset (e.g., ImageNet), or with random weights, while $C$ uses random initialization. In the next section, we show how we utilize dropout to perturb the boundary in the critic and measure sensitivity. We then show the training procedure of our method. Finally, we give some intuition behind adversarial dropout and improve our method based on this insight. ", + "bbox": [ + 173, + 529, + 825, + 680 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1 CLASSIFIER SELECTION VIA DROPOUT ", + "text_level": 1, + "bbox": [ + 176, + 698, + 483, + 712 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Consider the standard training of a neural network using dropout. For every sample within a minibatch, each node of the network is removed with some probability, effectively selecting a different classifier for every sample during training. We harness this idea in a very simple way. ", + "bbox": [ + 176, + 713, + 823, + 755 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We forward input features $G ( \\bf x _ { t } )$ to $C$ twice, dropping different nodes each time and obtaining two different output vectors denoted as $C _ { 1 } ( G ( \\mathbf { x _ { t } } ) )$ , $\\bar { C } _ { 2 } \\bar { ( \\cal G ( x _ { t } ) ) }$ . In other words, we are selecting two different classifiers $C _ { 1 }$ and $C _ { 2 }$ from $C$ by dropout as in Fig. 2. In the figure, the corresponding posterior probabilities are indicated as $p _ { 1 } ( \\mathbf { y } | \\mathbf { x _ { t } } )$ , $p _ { 2 } ( \\mathbf { y } \\vert \\mathbf { x _ { t } } )$ , abbreviated as $p _ { 1 }$ and $p _ { 2 }$ in the following discussion. In order to detect the change of predictions near the boundary, the critic tries to increase the difference between the predictions of $C _ { 1 }$ and $C _ { 2 }$ . This difference corresponds to $C$ ’s sensitivity to the noise caused by dropout. ", + "bbox": [ + 174, + 761, + 825, + 859 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To measure the sensitivity $d ( p _ { 1 } , p _ { 2 } )$ between the two obtained probabilistic outputs, we use the symmetric Kullback Leibler (KL) divergence. Formally, the divergence is calculated as ", + "bbox": [ + 174, + 866, + 821, + 895 + ], + "page_idx": 2 + }, + { + "type": "equation", + "img_path": "images/1a8da715d2418ce484565bf6a1b5fd22b4e62eda43cef1ad4e37e44d98b65311.jpg", + "text": "$$\nd ( p _ { 1 } , p _ { 2 } ) = { \\frac { 1 } { 2 } } ( D _ { k l } ( p _ { 1 } | p _ { 2 } ) + D _ { k l } ( p _ { 2 } | p _ { 1 } ) )\n$$", + "text_format": "latex", + "bbox": [ + 359, + 898, + 637, + 928 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/5b7992174e2f2c0d5a92732e1d6cc79162abd221b22a4267b1f8758b2b378f90.jpg", + "image_caption": [ + "Figure 2: Overview of ADR. Left: We train $G$ , $C$ with classification loss on source and sample a critic consisting of two classifiers using dropout. The critic’s sensitivity is measured as the divergence between the class predictions of $C _ { 1 }$ and $C _ { 2 }$ on the same input. Right: Adversarial training iterates two steps: the critic tries to maximize the sensitivity while the generator tries to minimize it. " + ], + "image_footnote": [], + "bbox": [ + 189, + 103, + 810, + 291 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where KL divergence between $p$ and $q$ is denoted as $D _ { k l } ( p | q )$ . ", + "bbox": [ + 173, + 390, + 581, + 405 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2 TRAINING PROCEDURE ", + "text_level": 1, + "bbox": [ + 174, + 424, + 377, + 438 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In our approach, $C$ works as both critic and classifier. The following three requirements are imposed by our method: 1) $C$ and $G$ must classify source samples correctly to obtain discriminative features; 2) $C$ should maximize the sensitivity for target samples to detect the samples near the boundary; 3) $G$ should learn to minimize the sensitivity to move target samples away from the boundary. ", + "bbox": [ + 173, + 440, + 825, + 497 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The training within the same mini-batch consists of the following three steps. ", + "bbox": [ + 174, + 502, + 679, + 517 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Step 1, in this step, $C$ is trained as a classifier. $C$ and $G$ have to classify source samples correctly to obtain discriminative features. Thus, we update both networks’ parameters based on the following standard classification loss. Given source labels $y _ { s }$ and samples $\\mathbf { x _ { s } }$ , the objective in this step is ", + "bbox": [ + 173, + 523, + 826, + 568 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/4b1325385b386c0540bd566d7b46a2ca5e1ff4eb0613e4f0e4cf5ac068a57798.jpg", + "text": "$$\n\\underset { G , C } { \\operatorname* { m i n } } L ( X _ { s } , Y _ { s } ) = - \\mathbb { E } _ { ( \\mathbf { x } _ { s } , y _ { s } ) \\sim ( X _ { s } , Y _ { s } ) } \\sum _ { k = 1 } ^ { K } \\mathbb { 1 } _ { [ k = y _ { s } ] } \\log C ( G ( \\mathbf { x } _ { \\mathbf { s } } ) ) _ { k }\n$$", + "text_format": "latex", + "bbox": [ + 287, + 575, + 709, + 619 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$C ( G ( \\mathbf { x _ { s } } ) ) _ { k }$ returns the probability that the sample $\\mathbf { x _ { s } }$ is assigned to class $k$ ", + "bbox": [ + 176, + 627, + 666, + 642 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Step 2, in this step, $C$ is trained as a critic to detect target samples near the boundary. Two classifiers are sampled from $C$ for each target sample using dropout twice to obtain $p _ { 1 }$ and $p _ { 2 }$ . Then, $C$ ’s parameters are updated to maximize the sensitivity as measured by Eq. 1. Since $C$ should learn discriminative features for source samples, in addition to the sensitivity term, we add Eq. 2. We experimentally confirmed that this term is essential to obtain good performance. ", + "bbox": [ + 173, + 648, + 826, + 719 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/3bea588dbe0863badf61194488482a3385277235506fa8e3ede248f59902ba58.jpg", + "text": "$$\n\\operatorname* { m i n } _ { C } L ( X _ { s } , Y _ { s } ) - L _ { a d v } ( X _ { t } )\n$$", + "text_format": "latex", + "bbox": [ + 403, + 728, + 593, + 751 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/90c1c66e9efafa4cc0f95641a131aedd5cc5ac97e333de274aa5aca963fc4bd1.jpg", + "text": "$$\nL _ { a d v } ( X _ { t } ) = \\mathbb { E } _ { \\mathbf { x _ { t } } \\sim X _ { t } } [ d ( C _ { 1 } ( G ( \\mathbf { x _ { t } } ) ) , C _ { 2 } ( G ( \\mathbf { x _ { t } } ) ) ) ]\n$$", + "text_format": "latex", + "bbox": [ + 334, + 768, + 663, + 786 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$C _ { 1 }$ and $C _ { 2 }$ are sampled from $C$ randomly. ", + "bbox": [ + 174, + 791, + 450, + 806 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Step 3, in order to obtain representations where target samples are placed far from the decision boundary, $G$ is trained to minimize sensitivity. Here we do not add the categorical loss for source samples as in Step 2, as the generator is able to obtain discriminative features without it. ", + "bbox": [ + 174, + 813, + 825, + 856 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/63322fcba11ec7695b29e769454da8b5b4c792439b0879e7895c37150117c6a9.jpg", + "text": "$$\n\\operatorname* { m i n } _ { G } L _ { a d v } ( X _ { t } )\n$$", + "text_format": "latex", + "bbox": [ + 449, + 864, + 549, + 887 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We update the parameters of $C$ and $G$ in every step following the defined objectives. We experimentally found it beneficial to repeat Step 3 $n$ times for each mini-batch. ", + "bbox": [ + 173, + 895, + 825, + 924 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/e236a8f1f63678aa39e6008db6475416d17c9cf2b19a9b860caab2ab1b9a4cd9.jpg", + "image_caption": [ + "Figure 3: (Best viewed in color) Toy Experiment. Top row: Model trained without adaptation. Columns 1-5 show the decision boundary obtained by keeping one neuron in the last hidden layer and removing the rest. Red points are source samples of class one, green points are class two. Black points are target samples. The yellow region indicates where the samples are classified as class one, cyan region class two. We see that the neurons do not learn very diverse features. Column 6 shows the boundary obtained by keeping all 5 neurons. Bottom row: Boundaries learned by the model adapted by our adversarial dropout method. Unlike the top row, here neurons 3,4,5 learn diverse features which result in diverse boundaries. " + ], + "image_footnote": [], + "bbox": [ + 176, + 102, + 820, + 224 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3 INSIGHT AND IMPROVEMENT", + "text_level": 1, + "bbox": [ + 174, + 353, + 416, + 367 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our ADR approach encourages different neurons of the classifier to learn different characteristics of the input (see Sec. 4.1.) The output is the combination of shared and unshared nodes, therefore, to maximize the sensitivity, the unshared nodes must learn different features of target samples. As learning proceeds, each neuron in $C$ will capture different characteristics. At the same time, to minimize the sensitivity, $G$ learns to extract pure categorical information. If $G$ outputs features which are not related to categorical information, such as texture, slight contrast or difference of color, $C$ will utilize them to maximize sensitivity. ", + "bbox": [ + 174, + 371, + 825, + 468 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The trained classifier will be sensitive to the perturbation of targets caused by dropout. We note that our approach is contrary to methods called adversarial example training (Goodfellow et al. (2014b); Miyato et al. (2016)) which train the classifier to be robust to adversarial examples. They utilize input noise which can deceive or change the output of the classifier, and incorporate it to obtain a good classifier. Our ADR method encourages the feature generator to obtain noise-robust target features. However, with regard to the classifier, it is trained to be sensitive to noise. To improve the final accuracy, we learn another classifier $C ^ { \\prime }$ that is not trained to be sensitive to the noise. $C ^ { \\prime }$ takes features generated by $G$ and is trained with classification loss on source samples. The loss of $C ^ { \\prime }$ is not used to update $G$ . We compare the accuracy of $C$ and $C ^ { \\prime }$ in experiments on image classification. ", + "bbox": [ + 174, + 474, + 825, + 601 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4 EXPERIMENTS ", + "text_level": 1, + "bbox": [ + 176, + 627, + 326, + 642 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1 EXPERIMENT ON TOY DATA ", + "text_level": 1, + "bbox": [ + 176, + 662, + 405, + 676 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Experimental Setting. In this experiment, we observe the decision boundary obtained by each neuron to demonstrate that ADR encourages the neurons to learn different input characteristics. We use synthetic “two moons” data for this problem. Two dimensional samples from two classes are generated as source samples. Target samples are obtained by rotating the source samples. In our setting, the rotation was set to 30 degrees and data was generated with scikit-learn (Pedregosa et al. (2011)). We train a six-layered fully-connected network; the lower 3 layers are used as feature generator, and upper 3 layers are used as classifier. We used Batch Normalization (Ioffe & Szegedy (2015)) and ReLU as activation function. The number of neurons are [2,5,5] for feature generator, [5,5,2] for classifier. We visualize the boundary obtained from each neuron in the last layer by removing the output of all other neurons. ", + "bbox": [ + 173, + 680, + 825, + 819 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Results. We show the learned boundary in Fig. 3. In the baseline model trained only with source samples (top row), two of five neurons do not seem to learn an effective boundary, and three neurons learn a similar boundary. On the other hand, in our method (bottom row), although two neurons do not seem to learn any meaningful boundary, three neurons learn distinctive boundaries, demonstrating greater diversity. Each neuron is trained to be sensitive to the noise caused by target samples. The final decision boundary (rightmost column) classifies most target samples correctly. The accuracy of our proposed method is $96 \\%$ whereas the accuracy of the non-adapted model was $84 \\%$ . ", + "bbox": [ + 174, + 825, + 825, + 924 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/739f2d31aa495e5a9d6c4fd7b45d22559c2abb1868aa853612bc7403b34eaae2.jpg", + "image_caption": [ + "Figure 4: Relationship between sensitivity loss on target (blue line), on source (yellow line), and accuracy (red: accuracy of $C ^ { \\prime }$ , green: accuracy of $C$ ) during training on digits. " + ], + "image_footnote": [], + "bbox": [ + 178, + 99, + 821, + 242 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2 UNSUPERVISED DOMAIN ADAPTATION FOR CLASSIFICATION ", + "text_level": 1, + "bbox": [ + 174, + 306, + 635, + 320 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Experiments on Digits Classification. We evaluate our model on adaptation between digits datasets. We use MNIST (LeCun et al. (1998)), SVHN (Netzer et al. (2011)) and USPS datasets and follow the protocol of unsupervised domain adaptation used by (Tzeng et al. (2017)). To extensively compare our method with previous methods, in adaptation from MNIST to USPS, we applied our method to a different protocol used in Bousmalis et al. (2017). We assume no labeled target samples and use fixed hyper-parameters for all experiments, unlike other works that use a target validation set (Saito et al. (2017)). The number of iterations for Step 3 was fixed at $n = 4$ . We used the same network architecture as in (Tzeng et al. (2017)), but inserted a Batch Normalization layer before the activation layer to stabilize the training. We used Adam (Kingma & Ba (2014)) for optimizer and set the learning rate to $2 . 0 \\times 1 0 ^ { - 4 }$ , a value commonly reported in the GAN literature. We compare our approach to several existing methods and to the entropy minimization baseline (ENT) obtained by modifying (Springenberg (2015)). As we mentioned in Section 2, this is a model that generates features to minimize the entropy of the output probability for target samples. Due to space limitations, we provide a detailed explanation of this baseline in the appendix. ", + "bbox": [ + 173, + 340, + 825, + 535 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results in Table 1 demonstrate that ADR obtains better performance than existing methods. In particular, on the challenging adaptation task from SVHN to MNIST, our method achieves much better accuracy than previously reported. Fig. 4 shows the learning curve of each experiment. As sensitivity loss increases, the target accuracy improves. This means that as critic $C$ learns to detect the non-discriminative samples, feature generator $G$ learns to fool it, resulting in improved accuracy. In addition, we can see that the sensitivity of source samples increases too. As mentioned in Sec 3.3, the critic network should learn to capture features which are not very important for classification, such as texture or slight edges, and it seems to also capture such information in source samples. The accuracy of the classifier $C ^ { \\prime }$ (denoted by red), which is trained not to be sensitive to the noise, is almost always better than the accuracy of the critic network. In adaptation from SVHN to MNIST (Fig. 5(c)), the accuracy of the critic often suffers as it becomes too sensitive to the noise caused by dropout. On the other hand, the accuracy shown by the red line is stable. Our ENT baseline shows good performance compared to other existing methods. This result indicates the effectiveness of methods based on entropy minimization. In Fig. 5, we compare our proposed method and ENT in terms of entropy of target samples. Our method clearly decreases the entropy, because target samples are moved away from the decision boundary. Yet, its behavior is different from ENT. Interestingly, the entropy is made smaller than ENT in case of adaptation from USPS to MNIST (Fig. 4(a)) though ENT directly minimizes the entropy and our method does not. On the SVHN to MNIST task (Fig. 4(c)), the entropy of ADR is larger than ENT, which indicates that our method places the target samples closer to the decision boundary than ENT does. ", + "bbox": [ + 174, + 541, + 825, + 819 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Experiments on Object Classification. We next evaluate our method on fine-tuning a pretrained CNN. We use a new domain adaptation benchmark called the VisDA Challenge (Peng et al. (2017)) which focuses on the challenging task of adapting from synthetic to real images. The source domain consists of 152,409 synthetic 2D images from 12 object classes rendered from 3D models. The validation and test target domains consists of real images, which belong to the same classes. We used the validation domain (55,400 images) as our target domain in an unsupervised domain adaptation setting. ", + "bbox": [ + 174, + 827, + 825, + 924 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/177e15de1ac8fd6d27b034896b5372cb923b428390b94b1a14d9cc289b6a1b4f.jpg", + "image_caption": [ + "Figure 5: Comparison of entropy of ours (blue line) with ENT (yellow line). The entropy is calculated on target samples by using the output of the classifier. " + ], + "image_footnote": [], + "bbox": [ + 178, + 104, + 803, + 239 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/cebe388166950ef90d8cb324df11aaa66b6c377b12baa85b995f38fc178c531d.jpg", + "table_caption": [ + "Table 1: Results on digits datasets. Please note that $^ \\dagger$ means the result obtained using a few labeled target samples for validation. The reported accuracy of our method is obtained from $C ^ { \\prime }$ . ENT is our proposed entropy minimization baseline, described in the appendix. MNIST(P1) and MNIST(P2) indicate different experimental settings used in Tzeng et al. (2017) and Bousmalis et al. (2017) respectively. " + ], + "table_footnote": [], + "table_body": "
METHODSVHN to MNISTUSPS to MNISTMNIST(P1) to USPSMNIST(P2) to USPS
Source Only67.168.177.078.9
LTN (Sener et al. (2016))78.8-1-
ATDA (Saito et al. (2017))86.2†=1-
DSN (Bousmalis et al. (2016))82.7†91.3†
PixelDA (Bousmalis et al. (2017)1=-95.9†
DANN (Ganin & Lempitsky (2014))73.973.0±2.077.1±1.885.1†
DoC (Tzeng et al. (2014))68.1±0.366.5±3.379.1±0.51
ADDA (Tzeng et al. (2017))76.0±1.890.1±0.889.4±0.2-
CoGAN (Liu & Tuzel (2016))did not converge89.1±0.891.2±0.8=
DTN (Taigman et al. (2016))84.71-
ENT (Our proposed baseline) Ours94.9±4.11 95.0±1.8791.2±1.92 93.1±1.2793.7±0.54 93.2±2.4696.7±1.27 96.1±0.29
", + "bbox": [ + 187, + 275, + 807, + 469 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We evaluate our model on fine-tuning networks pretrained on ImageNet (Deng et al. (2009)): ResNet101 (He et al. (2016)) and ResNext (Xie et al. (2016)). For the feature generator, we use the pretrained CNN after removing the top fully connected layer. For the classification network, we use a three-layered fully connected network. ", + "bbox": [ + 174, + 559, + 825, + 614 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2 shows that our method outperformed other distribution matching methods and our new baseline (ENT) in finetuning both networks by a large margin. ENT did not achieve better performance than existing methods, though improvement over the source only model was observed. Although this method performed well on digits, it does not work as well here, possibly because of the larger shift between very different domains. In the experiment on ResNext, after training $G$ and $C$ , we retrained a classifier $C ^ { ' }$ just on the features generated by $G$ due to GPU memory limitations, and observed improvement in both networks. ", + "bbox": [ + 174, + 621, + 825, + 722 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Fig. 6 visualizes the target features obtained by $G$ with the pretrained model, model fine-tuned on source, and our ADR method. While the embedding of the source only model does not separate classes well due to domain shift, we can see clearly improved separation with ADR. ", + "bbox": [ + 174, + 728, + 821, + 770 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Image Segmentation experiments. Next, we apply our method to adaptation for semantic image segmentation. Image segmentation is different from classification in that we classify each pixel in the image. To evaluate the performance on segmentation, the synthetic GTA5 (Richter et al. (2016)) dataset is used as source, and real CityScape (Cordts et al. (2016)) dataset is used as target. Previous work tackled this problem by matching distributions of each pixel’s feature in a middle layer of the network (Hoffman et al. (2016)). In this work, we apply ADR by calculating sensitivity between all pixels. The training procedure is exactly the same as in classification experiments. ", + "bbox": [ + 174, + 777, + 825, + 875 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We use the ResNet50 pretrained on ImageNet, and utilize an FCN (Long et al. (2015a)) based network architecture. Further, we utilize the more recent Dilated Residual Networks (DRN) 105 layered model (Yu et al. (2017)), which outperforms ResNet50 on a semantic segmentation task. ", + "bbox": [ + 176, + 882, + 823, + 924 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f1424f829d13d5222f78094f2d533a494b462bd17dd04b218b7d8dfb038049e0.jpg", + "table_caption": [ + "Table 2: Results on Visda2017 classification datasets (Peng et al. (2017)). DANN and MMD are distribution alignment methods proposed by (Ganin & Lempitsky (2014)) and (Long et al. (2015b)) respectively. Ours (retrain classifier) means the classifier retrained for our proposed generator as we mentioned in Sec 3.3. Our proposed method shows much better performance than existing methods. " + ], + "table_footnote": [], + "table_body": "
Methodgrrrdoraegpaleie 3ueoormorreiltuosiadsareraertrnaaa
Finetuning on ResNet101
Source Only55.153.3 61.959.180.617.979.731.281.026.573.58.552.4
MMD87.163.0 76.542.090.342.985.953.149.736.385.820.761.1
DANN81.977.7 82.844.381.229.565.128.651.954.682.87.857.4
ENT80.375.5 75.848.377.927.369.740.246.546.679.316.057.0
Ours94.151.3 83.272.288.768.892.870.277.263.682.930.372.9
Ours (retrained classifier)94.248.5 84.072.990.174.292.672.580.861.882.228.873.5
Finetuning on ResNeXt
Source Only74.3 37.6 61.8 68.2 59.510.7 81.412.8 61.6 26.070.05.647.4
MMD90.751.1 64.865.689.946.591.940.181.524.190.028.563.7
DANN86.066.3 60.8 56.079.853.782.325.258.231.089.326.159.6
ENT94.781.0 57.046.673.949.069.231.040.534.387.315.156.6
Ours86.3 71.987.678.193.084.894.578.991.858.977.726.777.5
Ours (retrained classifier)89.270.9 85.782.093.786.7 93.372.389.553.086.728.377.6
", + "bbox": [ + 233, + 102, + 766, + 319 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f85e9efe625959ba93fdcfd4024851f548acbeebd038701c1fb299173a9f68e4.jpg", + "image_caption": [ + "Figure 6: Visualization of VisDA-classification (12 classes) target features using T-SNE (Maaten & Hinton (2008)): (a) features obtained by the Imagenet-pretrained ResNext model not finetuned on VisDA; (b) features from the ResNext model fine-tuned only on VisDA source samples without any adaptation; (c) features obtained by ResNext adapted by our ADR method. " + ], + "image_footnote": [], + "bbox": [ + 232, + 402, + 769, + 550 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "For the feature generator, we use the pretrained network without fully-connected layers. For the classifier, we use a fully-convolutional network with dropout layers. Due to limited memory, the batch size is set to 1. We include details of the network architecture in appendix. For comparison, we train a domain classifier based model for our network (DANN). We build a domain classifier network for the features of each pixel following (Hoffman et al. (2016)). ", + "bbox": [ + 174, + 623, + 825, + 694 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Table 3, we show the qualitative comparison with existing methods. ADR clearly improves mean IoU (Intersection-over-Union) compared to the source-only and competing models, beating state-ofthe-art by a large margin. When we apply ADR to DRN, the accuracy improves much more than for ResNet50, and is 12.4 points higher than the model trained only on GTA5 source samples. This is likely because ADR exploits the strong representation of the pretrained DRN network. Although we implemented ENT in this setting, the accuracy was much worse than the Source Only model with a mIoU of 15.0 in training ResNet50. The ENT method does not seem to work well on syntheticto-real shifts. Finally, we illustrate our method’s improvement on example input images, ground truth labels, images segmented by the Source Only model and our method in Fig. 7. While the Source Only model seems to suffer from domain shift, ADR generates a clean segmentation. These experiments demonstrate the effectiveness of ADR on semantic segmentation. ", + "bbox": [ + 174, + 700, + 825, + 853 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5 CONCLUSION ", + "text_level": 1, + "bbox": [ + 176, + 875, + 318, + 890 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we introduced a novel approach for aligning deep representation, Adversarial Dropout Regularization, which learns to generate discriminative features for the target domain. The method consists of a critic network that can detect samples near the task decision boundary and a feature generator that fools the critic. Our approach is general, applies to a variety of tasks, and does not require target domain labels. In extensive domain adaptation experiments, our method outperformed baseline methods, including entropy minimization, and achieved state-of-the-art results on three datasets. ", + "bbox": [ + 176, + 896, + 823, + 924 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/a5a27f174055b694ce32992a128d5d59e5363e7969657c64f7dd99c7d8377e4f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
NetworkMethodxeeepreBuiplng8irilen买uosradMur0mrrqeemIoU
VGG-16FCN Wild70.432.462.114.95.410.914.22.779.221.364.644.14.270.48.07.30.03.50.027.1
ResNet50Source OnlyDANNOurs64.572.487.824.919.115.673.714.83.920.62.59.39.718.017.319.015.913.119.90.05.57.774.916.472.042.30.039.58.612.117.513.49.927.70.00.01.80.05.89.70.00.00.025.326.433.3
73.077.471.082.020.131.562.274.332.643.55.29.068.477.8
DRN-105Source OnlyOurs25.986.210.910.150.578.83.320.112.27.425.428.613.015.078.384.57.338.963.952.17.966.35.229.67.832.70.90.213.719.20.78.324.937.3
21.226.581.154.613.680.8
", + "bbox": [ + 176, + 102, + 823, + 217 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/2a431aecdd2cbdb38788dec71565dbda6f38a671d3881b7e8cbaa1c5630bfb5c.jpg", + "image_caption": [ + "Table 3: Results on adaptation from $\\mathrm { G T A } 5 $ Cityscapes. DANN and FCN Wild denote methods proposed by (Ganin & Lempitsky (2014)) and (Hoffman et al. (2016) respectively. ", + "Figure 7: Comparison of results on two real images segmented by ResNet50. Clockwise from upper left: Original image; Ground truth; Segmented image before adaptation; Segmented image after adaptation by our method. " + ], + "image_footnote": [], + "bbox": [ + 174, + 258, + 815, + 383 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 439, + 825, + 508 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We also show how to apply our method to train Generative Adversarial Networks for semisupervised learning in the appendix. ", + "bbox": [ + 173, + 516, + 821, + 545 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6 ACKNOWLEDGEMENTS ", + "text_level": 1, + "bbox": [ + 176, + 565, + 397, + 580 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We would like to thank Trevor Darrell for his great advice on our paper. The first author’s stay at Boston University was partially supported by a scholarship from the University of Tokyo. The work was partially funded by the ImPACT Program of the Council for Science, Technology, and Innovation (Cabinet Office, Government of Japan), and was partially supported by CREST, JST. Saenko was supported by IARPA and NSF grants CCF-1723379 and IIS-1724237. 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", + "bbox": [ + 171, + 900, + 805, + 916 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "APPENDIX ", + "text_level": 1, + "bbox": [ + 176, + 103, + 264, + 117 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "A ENTROPY BASED METHOD FOR DOMAIN ADAPTATION (ENT) ", + "text_level": 1, + "bbox": [ + 176, + 123, + 725, + 140 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "Our method aims to move target samples away from the decision boundary. Some techniques used in training Generative Adversarial Networks can be applied to achieve our goal too. (Springenberg (2015); Salimans et al. (2016)) used small number of labeled samples to train critic. Critic is trained to classify real samples into $K$ classes. They also trained critic to move unlabeled real images away from the boundary by minimizing entropy of the critic’s output. Generated fake images are moved near the boundary by maximizing the entropy. On the other hand, generator is trained to generate fake images which should be placed away from the boundary. This kind of method can be easily applied to domain adaptation problem. We would like to describe the method along with our problem setting. ", + "bbox": [ + 173, + 145, + 825, + 270 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "Similar to our method, we have critic networks $C$ and generator $G$ . $C$ classifies samples into $K$ class. $C$ is trained to maximize the entropy of target samples, which encourages to move the target samples near the boundary. Then, $G$ is trained to minimize the entropy of them. Thus, $G$ tries to move target samples away from the boundary. ", + "bbox": [ + 173, + 276, + 825, + 333 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "The only difference from our method is that we used entropy term for adversarial training loss. That is, in this method, we replace our sensitivity term $d ( p _ { 1 } , p _ { 2 } )$ in Eq. 4 with entropy of the classifier output. The adversarial loss for this baseline method is a following one. ", + "bbox": [ + 174, + 340, + 823, + 382 + ], + "page_idx": 11 + }, + { + "type": "equation", + "img_path": "images/a2021b8ef809d13c1f4bdfe0b75167d5f46e6067ac40597da21cec262093e02a.jpg", + "text": "$$\n\\begin{array} { r c l } { { { \\cal L } _ { a d v } ( X _ { t } ) } } & { { = } } & { { \\displaystyle \\mathbb { E } _ { { \\mathbf { x _ { t } } } \\sim X _ { t } } [ H [ p ( \\mathbf { y } | { \\mathbf { x _ { t } } } ) ] } } \\\\ { { { \\cal H } [ p ( \\mathbf { y } | { \\mathbf { x _ { t } } } ) ] } } & { { = } } & { { \\displaystyle - \\sum _ { k = 1 } ^ { K } p ( y = k | { \\mathbf { x _ { t } } } ) \\log p ( y = k | { \\mathbf { x _ { t } } } ) } } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 320, + 385, + 676, + 449 + ], + "page_idx": 11 + }, + { + "type": "equation", + "img_path": "images/dbd5c4fe01e08cdcd9b9616b1e5c9d27f2275a6777f27ef7ac7f291a1cd848f9.jpg", + "text": "$$\nH [ p ( y | x ) ] = - \\sum _ { k = 1 } ^ { K } p ( y = k | x ) \\log p ( y = k | x )\n$$", + "text_format": "latex", + "bbox": [ + 343, + 453, + 653, + 496 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "The hyper-parameter $n$ , how many times we update $G$ for adversarial loss in one mini-batch, is set as $n = 4$ . Experimentally, it worked well for all settings. ", + "bbox": [ + 173, + 497, + 821, + 525 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "B DIGITS CLASSIFICATION TRAINING DETAIL ", + "text_level": 1, + "bbox": [ + 173, + 534, + 573, + 550 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "We follow the protocol used in (Tzeng et al. (2017)). For adaptation from SVHN to MNIST, we used standard training splits of each datasets as training data. For evaluation, we used test splits of MNIST. For the adaptation between MNIST and USPS (P1), we sampled 2000 images from MNIST and 1800 images from USPS. For the adaptation between MNIST and USPS (P2), we used all training images of MNIST and USPS following Bousmalis et al. (2017). In these experiments, we composed the mini-batch half from source and half from target samples. The batch-size was set as 128 for both source and target. We report the score after repeating Step $1 { \\sim } 3$ (please see Sec 3.2) 20000 times. For our baseline, ENT, we used the same network architecture and the same hyper-parameters as used in our proposed method. ", + "bbox": [ + 173, + 554, + 825, + 680 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "C OBJECT CLASSIFICATION TRAINING DETAIL ", + "text_level": 1, + "bbox": [ + 173, + 689, + 578, + 705 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "In this experiment, SGD with learning rate $1 . 0 \\times 1 0 ^ { - 3 }$ is used to optimize the parameters. For the finetuning of ResNet101, we set batch-size as 32. Due to the limit of GPU memory, we set it as 24 in finetuning ResNext model. We report the score after 20 epochs training. In order to train MMD model, we use 5 RBF kernels with the following standard deviation parameters: ", + "bbox": [ + 174, + 708, + 825, + 765 + ], + "page_idx": 11 + }, + { + "type": "equation", + "img_path": "images/5e5c787c3a5208e654ae34797e13f1eb8e10838a913d7366e482a0e916b2b935.jpg", + "text": "$$\n\\sigma = [ 0 . 1 , 0 . 0 5 , 0 . 0 1 , 0 . 0 0 0 1 , 0 . 0 0 0 0 1 ]\n$$", + "text_format": "latex", + "bbox": [ + 372, + 770, + 624, + 786 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "We changed the number of the kernels and their parameters, but we could not observe significant performance difference. We report the performance after 5 epochs. We could not see any improvement after the epoch. ", + "bbox": [ + 174, + 791, + 825, + 833 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "To train a model (Ganin & Lempitsky (2014)), we used two-layered domain classification networks. Experimentally, we did not see any improvement when the network architecture is changed. According to the original method (Ganin $\\&$ Lempitsky (2014)), learning rate is decreased every iteration. However, in our experiment, we could not see improvement, thus, we fixed learning rate $\\mathrm { i . 0 \\times 1 0 ^ { - 3 } }$ . We report the accuracy after 1 epoch. The accuracy dropped significantly after the first epoch. We assume this is due to the large domain difference between synthetic and real images. ", + "bbox": [ + 174, + 839, + 825, + 924 + ], + "page_idx": 11 + }, + { + "type": "image", + "img_path": "images/91334547d8f045bbc50bad32d13e84fbdd9717e2bd91e1f11d2951fede231eb5.jpg", + "image_caption": [ + "Figure 9: Example of results on segmentation experiments performed by DRN-105. From top to bottom, Original image; Ground truth; Segmented image before adaptation; Segmented image after adaptation by our method. " + ], + "image_footnote": [], + "bbox": [ + 174, + 101, + 823, + 353 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "For our new baseline, ENT, we used the same hyper-parameter as we used for our proposed method. Since the accuracy of ENT drops significantly after around 5 epochs, we report the accuracy after 5 epoch updates. ", + "bbox": [ + 174, + 431, + 825, + 473 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "D SEGMENTATION EXPERIMENTS ", + "text_level": 1, + "bbox": [ + 176, + 483, + 468, + 498 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "We modified FCN Long et al. (2015a) architecture suitable for ResNet structure. The features from ResBlock $2 { \\sim } 4$ and the first convolution layer and maxpooling layer are used in our implementation. In Fig. 8, we show how we integrated the features of each layers. We regard the layers of ResNet50 as generator and rest of the networks, namely convolution and upsampling layers as a critic network. The input images were resized to $5 1 2 \\mathrm { x } 1 0 2 4$ due to the limit of GPU memory. For the same reason, the batchsize was set to one. In Fig. 9, we show the example of segmented images by DRN-105. The images are cleanly segmented by our proposed method. ", + "bbox": [ + 174, + 503, + 552, + 670 + ], + "page_idx": 12 + }, + { + "type": "image", + "img_path": "images/239b4a962924dc544fc56d44223b3182af3fbba803795fe928439774dffc489c.jpg", + "image_caption": [ + "Figure 8: Overview of architecture for semantic segmentation " + ], + "image_footnote": [], + "bbox": [ + 588, + 473, + 825, + 631 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "E SEMI-SUPERVISED LEARNING USING GANS ", + "text_level": 1, + "bbox": [ + 173, + 690, + 573, + 705 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "In this section, we demonstrate how to apply our method in training a Generative Adversarial Network (GAN) applied to semi-supervised learning. We follow the method proposed by (Springenberg (2015); Salimans et al. (2016)), who use a $K$ -class classification network as a critic to train a GAN in the semi-supervised setting. ", + "bbox": [ + 173, + 720, + 825, + 777 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "Approach. In contrast to the domain adaptation setting, here $G$ tries to generate images which fool the critic $C$ . Also, in this setting, we are given labeled and unlabeled real images from the same domain. Then, we train the critic to classify labeled images correctly and to move unlabeled images far from the decision boundary. To achieve this, we propose to train the critic with the following objective: ", + "bbox": [ + 173, + 784, + 823, + 853 + ], + "page_idx": 12 + }, + { + "type": "equation", + "img_path": "images/b4e0bb62c8cc70e5af3a746f4ffc2fff759f31b06275f447fb8c07818b6c821a.jpg", + "text": "$$\n\\operatorname* { m i n } _ { C } L _ { C } = L ( X _ { L } , Y _ { L } ) + L _ { a d v } ( X _ { u } ) - L _ { a d v } ( X _ { g } ) - H [ \\frac { 1 } { M } \\sum _ { i = 1 } ^ { M } p ( y | x _ { u } { } ^ { i } , C ) ]\n$$", + "text_format": "latex", + "bbox": [ + 248, + 848, + 746, + 892 + ], + "page_idx": 12 + }, + { + "type": "equation", + "img_path": "images/4f3651718657720aa59752e868f8a29aa904e613e9650be8f9f4ef7a3210e164.jpg", + "text": "$$\nL _ { a d v } ( X _ { u } ) = \\mathbb { E } _ { \\mathbf { x _ { u } } \\sim X _ { u } } [ d ( C _ { 1 } ( G ( \\mathbf { x _ { u } } ) ) , C _ { 2 } ( G ( \\mathbf { x _ { u } } ) ) ) ]\n$$", + "text_format": "latex", + "bbox": [ + 328, + 907, + 668, + 925 + ], + "page_idx": 12 + }, + { + "type": "image", + "img_path": "images/63364abe673b063e24a800150d6aed5d16f2ac6fd54204e6ef2d434abc5d60e1.jpg", + "image_caption": [ + "Figure 10: Examples of generated images. " + ], + "image_footnote": [], + "bbox": [ + 174, + 101, + 815, + 242 + ], + "page_idx": 13 + }, + { + "type": "table", + "img_path": "images/c25d34b9848ce8a2264f46bff282c343fd96916cc65ef79946fd5a75454797ef.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
SVHN (% errors)CIFAR (% errors)
Labeled Only SDGM (Maalge et al. (2016)16.61 ± 0.24
CatGAN (Springenberg (2015))=19.58±0.46
ALI (Dumoulin et al. (2016))7.42±0.6517.99±1.62
ImpGAN (Salimans et al. (2016))8.11±1.318.63±2.32
Ours6.26±1.0519.63±0.37
", + "bbox": [ + 209, + 277, + 784, + 383 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "Table 4: Comparison with state-of-the-art methods on two benchmark datasets. Only methods without data augmentation are included. We used the same critic architecture as used in ImpGAN. ", + "bbox": [ + 171, + 393, + 825, + 421 + ], + "page_idx": 13 + }, + { + "type": "equation", + "img_path": "images/83537d900fab4ee7a3f1710393b244f2849254ece073bff6f7ec2ac627714516.jpg", + "text": "$$\nL _ { a d v } ( X _ { g } ) = \\mathbb { E } _ { { \\mathbf { x } } _ { \\mathbf { g } } \\sim X _ { G } } [ d ( C _ { 1 } ( G ( { \\mathbf { x } } _ { \\mathbf { g } } ) ) , C _ { 2 } ( G ( { \\mathbf { x } } _ { \\mathbf { g } } ) ) ) ]\n$$", + "text_format": "latex", + "bbox": [ + 330, + 465, + 668, + 483 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "where $X _ { L }$ denotes the subset of labeled samples, $X _ { u }$ denotes unlabeled ones and $X _ { g }$ denotes images generated by $G$ and $H$ denotes entropy as Eq.6 shows. The critic is trained to minimize the loss on labeled samples in the first term. Since unlabeled images should be far away from the decision boundary and should be distributed uniformly among the classes, we add the second and fourth term. The third term encourages the critic to detect fake images generated near the boundary. ", + "bbox": [ + 174, + 484, + 825, + 556 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "The objective of $G$ is as follows, ", + "bbox": [ + 174, + 561, + 388, + 575 + ], + "page_idx": 13 + }, + { + "type": "equation", + "img_path": "images/aa12383d6c54067bf716e7a8e1391d0066b156b3c026b96dcb40a20a36336bfa.jpg", + "text": "$$\n\\operatorname* { m i n } _ { G } L _ { a d v } ( X _ { g } ) + | | \\mathbb { E } _ { x _ { g } \\sim X _ { g } } f ( \\mathbf { x _ { g } } ) - \\mathbb { E } _ { \\mathbf { x _ { u } } \\sim X _ { u } } f ( \\mathbf { x _ { u } } ) | | ^ { 2 }\n$$", + "text_format": "latex", + "bbox": [ + 318, + 580, + 676, + 604 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "where the second term encourages generated images to be similar to real images, which is known to be effective to stabilize the training. The first term encourages the generator to create fake images which should be placed far away from the boundary. Such images should be similar to real images because they are likely to be assigned to some class with high probability. Here, we update $C$ and $G$ same number of times. ", + "bbox": [ + 174, + 609, + 825, + 680 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "Experiment. We evaluate our proposed GAN training method by using SVHN and CIFAR10 datasets, using the critic network architecture from (Salimans et al. (2016)). We set the batch size as 100 and used Adam with learning rate $2 . 0 \\times 1 . 0 ^ { - 4 }$ for optimizer. After the conv6 layer of the critic, we constructed a classifier which was not concerned with adversarial learning process. ", + "bbox": [ + 174, + 686, + 825, + 742 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "In the experiment on SVHN, we replaced Weight Normalization with Batch Normalization for $C$ . Also, in the experiment on CIFAR10, we construct a classifier from a middle layer of the critic, which is not incorporated into the adversarial training step. This is motivated by the insight that the critic in our method is trained to be too sensitive to the dropout noise as we explained in Sec 3.3. ", + "bbox": [ + 174, + 748, + 825, + 805 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "Results. From Fig. 10(a), we can see that ADR seems to generate realistic SVHN images. Some images are significantly blurred, but most of the images are clear and diverse. As for generated CIFAR10 images, they do not seem as realistic, but some objects appear in most images. In Table 4, we can see that the accuracy of the critic trained by our method has better performance than other models for SVHN. For CIFAR10, the accuracy was slightly worse than other state-of-the-art methods. We conclude that, despite its clear advantage on the domain adaptation tasks, our method produces mixed results on the SSL tasks. It could still be useful for SSL, however, it needs further exploration to improve the accuracy. For example, in Eq. 6, we propose to maximize the entropy of the marginal class distribution of the unlabeled real images, as well as forcing them to be far from the boundary. However, these objectives may contradict each other, which may in turn degrade the performance. In late-breaking results, Dai et al. (2017) theoretically showed that just generating fake images that are far from decision boundaries does not help to improve accuracy in training GANs in the setting of SSL. Further improvement of our SSL approach based on these results is an interesting direction for future work. 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Such domain shifts occurs in many practical applications. For example,", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 451, + 505, + 463 + ], + "spans": [ + { + "bbox": [ + 106, + 451, + 505, + 463 + ], + "score": 1.0, + "content": "while simulated driving images rendered by games provide a rich source of labeled data for semantic", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 462, + 505, + 474 + ], + "spans": [ + { + "bbox": [ + 105, + 462, + 505, + 474 + ], + "score": 1.0, + "content": "segmentation Richter et al. (2016), deep models trained on such source data do not transfer well", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 473, + 505, + 485 + ], + "spans": [ + { + "bbox": [ + 105, + 473, + 505, + 485 + ], + "score": 1.0, + "content": "to real target domains (Fig. 1(a-d)). When target-domain labels are unavailable for fine-tuning,", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 484, + 422, + 496 + ], + "spans": [ + { + "bbox": [ + 105, + 484, + 422, + 496 + ], + "score": 1.0, + "content": "unsupervised domain adaptation must be applied to improve the source model.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 24 + }, + { + "type": "text", + "bbox": [ + 107, + 500, + 504, + 566 + ], + "lines": [ + { + "bbox": [ + 106, + 501, + 505, + 512 + ], + "spans": [ + { + "bbox": [ + 106, + 501, + 505, + 512 + ], + "score": 1.0, + "content": "Recent methods for unsupervised domain adaptation attempt to reduce the discrepancy between the", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 511, + 504, + 524 + ], + "spans": [ + { + "bbox": [ + 105, + 511, + 415, + 524 + ], + "score": 1.0, + "content": "source and target features via adversarial learning (Tzeng et al. (2014); Ganin", + "type": "text" + }, + { + "bbox": [ + 415, + 512, + 425, + 522 + ], + "score": 0.3, + "content": "\\&", + "type": "inline_equation" + }, + { + "bbox": [ + 425, + 511, + 504, + 524 + ], + "score": 1.0, + "content": "Lempitsky (2014)).", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 522, + 506, + 535 + ], + "spans": [ + { + "bbox": [ + 105, + 522, + 317, + 535 + ], + "score": 1.0, + "content": "They divide the base network into a feature encoder", + "type": "text" + }, + { + "bbox": [ + 317, + 523, + 326, + 533 + ], + "score": 0.8, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 327, + 522, + 383, + 535 + ], + "score": 1.0, + "content": "and classifier", + "type": "text" + }, + { + "bbox": [ + 383, + 523, + 392, + 533 + ], + "score": 0.81, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 392, + 522, + 506, + 535 + ], + "score": 1.0, + "content": ", and add a separate domain", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 533, + 506, + 546 + ], + "spans": [ + { + "bbox": [ + 105, + 533, + 209, + 546 + ], + "score": 1.0, + "content": "classifier (critic) network", + "type": "text" + }, + { + "bbox": [ + 210, + 534, + 219, + 543 + ], + "score": 0.74, + "content": "D", + "type": "inline_equation" + }, + { + "bbox": [ + 219, + 533, + 392, + 546 + ], + "score": 1.0, + "content": ". The critic takes the features generated by", + "type": "text" + }, + { + "bbox": [ + 393, + 534, + 402, + 543 + ], + "score": 0.81, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 402, + 533, + 506, + 546 + ], + "score": 1.0, + "content": "and labels them as either", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 545, + 506, + 556 + ], + "spans": [ + { + "bbox": [ + 105, + 545, + 270, + 556 + ], + "score": 1.0, + "content": "source- or target-domain. The encoder", + "type": "text" + }, + { + "bbox": [ + 270, + 545, + 279, + 554 + ], + "score": 0.8, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 280, + 545, + 506, + 556 + ], + "score": 1.0, + "content": "is then trained with an additional adversarial loss that", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 555, + 369, + 567 + ], + "spans": [ + { + "bbox": [ + 105, + 555, + 152, + 567 + ], + "score": 1.0, + "content": "maximizes", + "type": "text" + }, + { + "bbox": [ + 152, + 556, + 162, + 565 + ], + "score": 0.76, + "content": "D", + "type": "inline_equation" + }, + { + "bbox": [ + 162, + 555, + 369, + 567 + ], + "score": 1.0, + "content": "’s mistakes and thus aligns features across domains.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 30.5 + }, + { + "type": "text", + "bbox": [ + 107, + 572, + 505, + 660 + ], + "lines": [ + { + "bbox": [ + 105, + 572, + 506, + 585 + ], + "spans": [ + { + "bbox": [ + 105, + 572, + 506, + 585 + ], + "score": 1.0, + "content": "However, a major drawback of this approach is that the critic simply predicts the domain label of", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 583, + 505, + 595 + ], + "spans": [ + { + "bbox": [ + 105, + 583, + 505, + 595 + ], + "score": 1.0, + "content": "the generated point and does not consider category information. Thus the generator may create", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 594, + 505, + 606 + ], + "spans": [ + { + "bbox": [ + 105, + 594, + 505, + 606 + ], + "score": 1.0, + "content": "features that look like they came from the right domain, but are not discriminative. In particular,", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 605, + 504, + 617 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 504, + 617 + ], + "score": 1.0, + "content": "it can generate points close to class boundaries, as shown in Fig. 1(e), which are likely to be mis-", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 615, + 506, + 629 + ], + "spans": [ + { + "bbox": [ + 105, + 615, + 506, + 629 + ], + "score": 1.0, + "content": "classified by the source model. We argue that to achieve good performance on the target data, the", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 626, + 505, + 641 + ], + "spans": [ + { + "bbox": [ + 105, + 626, + 505, + 641 + ], + "score": 1.0, + "content": "adaptation model must take the decision boundaries between classes into account while aligning", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 639, + 505, + 650 + ], + "spans": [ + { + "bbox": [ + 105, + 639, + 505, + 650 + ], + "score": 1.0, + "content": "features across domains (Fig. 1(f)). Moreover, since our setting is unsupervised adaptation, this", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 649, + 315, + 661 + ], + "spans": [ + { + "bbox": [ + 105, + 649, + 315, + 661 + ], + "score": 1.0, + "content": "must be accomplished without labels on target data.", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 37.5 + }, + { + "type": "text", + "bbox": [ + 107, + 666, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 666, + 505, + 677 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 505, + 677 + ], + "score": 1.0, + "content": "In this paper, we propose a novel adversarial alignment technique that overcomes the above limita-", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "score": 1.0, + "content": "tion and preserves class boundaries. We make the following observation: if the critic could detect", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 104, + 688, + 506, + 700 + ], + "spans": [ + { + "bbox": [ + 104, + 688, + 506, + 700 + ], + "score": 1.0, + "content": "points near the decision boundary, then the generator would have to avoid these areas of the feature", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "score": 1.0, + "content": "space in order to fool the critic. Thus the critic would force the generator to create more discrimina-", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 710, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 710, + 462, + 722 + ], + "score": 1.0, + "content": "tive features. How can we obtain such a critic? If we alter the boundary of the classifier", + "type": "text" + }, + { + "bbox": [ + 462, + 710, + 471, + 720 + ], + "score": 0.81, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 471, + 710, + 505, + 722 + ], + "score": 1.0, + "content": "slightly", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 721, + 506, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 721, + 341, + 734 + ], + "score": 1.0, + "content": "and measure the change in the posterior class probability", + "type": "text" + }, + { + "bbox": [ + 342, + 721, + 369, + 732 + ], + "score": 0.92, + "content": "p ( y | x )", + "type": "inline_equation" + }, + { + "bbox": [ + 369, + 721, + 401, + 734 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 401, + 722, + 408, + 732 + ], + "score": 0.8, + "content": "y", + "type": "inline_equation" + }, + { + "bbox": [ + 408, + 721, + 427, + 734 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 427, + 722, + 434, + 730 + ], + "score": 0.74, + "content": "x", + "type": "inline_equation" + }, + { + "bbox": [ + 434, + 721, + 506, + 734 + ], + "score": 1.0, + "content": "denote class and", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 44.5 + } + ], + "page_idx": 0, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 25, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 25, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2018", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 303, + 752, + 308, + 760 + ], + "lines": [ + { + "bbox": [ + 302, + 751, + 309, + 762 + ], + "spans": [ + { + "bbox": [ + 302, + 751, + 309, + 762 + ], + "score": 1.0, + "content": "1", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 108, + 78, + 432, + 97 + ], + "lines": [ + { + "bbox": [ + 106, + 78, + 433, + 98 + ], + "spans": [ + { + "bbox": [ + 106, + 78, + 433, + 98 + ], + "score": 1.0, + "content": "ADVERSARIAL DROPOUT REGULARIZATION", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 158, + 119, + 451, + 132 + ], + "lines": [ + { + "bbox": [ + 158, + 118, + 452, + 133 + ], + "spans": [ + { + "bbox": [ + 158, + 118, + 452, + 133 + ], + "score": 1.0, + "content": "Kuniaki Saito1, Yoshitaka Ushiku1, Tatsuya Harada1,2, and Kate Saenko3", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 1, + "bbox_fs": [ + 158, + 118, + 452, + 133 + ] + }, + { + "type": "text", + "bbox": [ + 141, + 140, + 472, + 164 + ], + "lines": [ + { + "bbox": [ + 191, + 138, + 419, + 155 + ], + "spans": [ + { + "bbox": [ + 191, + 138, + 419, + 155 + ], + "score": 1.0, + "content": "1The University of Tokyo, 2RIKEN, 3Boston University", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 139, + 151, + 473, + 165 + ], + "spans": [ + { + "bbox": [ + 139, + 151, + 473, + 165 + ], + "score": 1.0, + "content": "{k-saito,ushiku,harada}@mi.t.u-tokyo.ac.jp, saenko@bu.edu", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 2.5, + "bbox_fs": [ + 139, + 138, + 473, + 165 + ] + }, + { + "type": "title", + "bbox": [ + 278, + 191, + 333, + 203 + ], + "lines": [ + { + "bbox": [ + 276, + 190, + 335, + 204 + ], + "spans": [ + { + "bbox": [ + 276, + 190, + 335, + 204 + ], + "score": 1.0, + "content": "ABSTRACT", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 4 + }, + { + "type": "text", + "bbox": [ + 143, + 216, + 468, + 380 + ], + "lines": [ + { + "bbox": [ + 142, + 216, + 469, + 228 + ], + "spans": [ + { + "bbox": [ + 142, + 216, + 469, + 228 + ], + "score": 1.0, + "content": "We present a domain adaptation method for transferring neural representations", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 141, + 226, + 470, + 239 + ], + "spans": [ + { + "bbox": [ + 141, + 226, + 470, + 239 + ], + "score": 1.0, + "content": "from label-rich source domains to unlabeled target domains. Recent adversarial", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 141, + 237, + 470, + 250 + ], + "spans": [ + { + "bbox": [ + 141, + 237, + 470, + 250 + ], + "score": 1.0, + "content": "methods proposed for this task learn to align features across domains by “fool-", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 141, + 248, + 470, + 261 + ], + "spans": [ + { + "bbox": [ + 141, + 248, + 470, + 261 + ], + "score": 1.0, + "content": "ing” a special domain classifier network. However, a drawback of this approach is", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 141, + 259, + 469, + 271 + ], + "spans": [ + { + "bbox": [ + 141, + 259, + 469, + 271 + ], + "score": 1.0, + "content": "that the domain classifier simply labels the generated features as in-domain or not,", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 141, + 270, + 469, + 282 + ], + "spans": [ + { + "bbox": [ + 141, + 270, + 469, + 282 + ], + "score": 1.0, + "content": "without considering the boundaries between classes. This means that ambiguous", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 142, + 282, + 469, + 293 + ], + "spans": [ + { + "bbox": [ + 142, + 282, + 469, + 293 + ], + "score": 1.0, + "content": "target features can be generated near class boundaries, reducing target classifica-", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 141, + 293, + 469, + 304 + ], + "spans": [ + { + "bbox": [ + 141, + 293, + 469, + 304 + ], + "score": 1.0, + "content": "tion accuracy. We propose a novel approach, Adversarial Dropout Regularization", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 141, + 303, + 470, + 316 + ], + "spans": [ + { + "bbox": [ + 141, + 303, + 470, + 316 + ], + "score": 1.0, + "content": "(ADR), which encourages the generator to output more discriminative features for", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 142, + 315, + 470, + 326 + ], + "spans": [ + { + "bbox": [ + 142, + 315, + 470, + 326 + ], + "score": 1.0, + "content": "the target domain. Our key idea is to replace the traditional domain critic with a", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 142, + 326, + 470, + 337 + ], + "spans": [ + { + "bbox": [ + 142, + 326, + 470, + 337 + ], + "score": 1.0, + "content": "critic that detects non-discriminative features by using dropout on the classifier", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 142, + 336, + 469, + 348 + ], + "spans": [ + { + "bbox": [ + 142, + 336, + 469, + 348 + ], + "score": 1.0, + "content": "network. The generator then learns to avoid these areas of the feature space and", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 141, + 347, + 470, + 360 + ], + "spans": [ + { + "bbox": [ + 141, + 347, + 470, + 360 + ], + "score": 1.0, + "content": "thus creates better features. We apply our ADR approach to the problem of un-", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 141, + 358, + 469, + 370 + ], + "spans": [ + { + "bbox": [ + 141, + 358, + 469, + 370 + ], + "score": 1.0, + "content": "supervised domain adaptation for image classification and semantic segmentation", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 142, + 369, + 434, + 381 + ], + "spans": [ + { + "bbox": [ + 142, + 369, + 434, + 381 + ], + "score": 1.0, + "content": "tasks, and demonstrate significant improvements over the state of the art.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 12, + "bbox_fs": [ + 141, + 216, + 470, + 381 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 401, + 206, + 414 + ], + "lines": [ + { + "bbox": [ + 105, + 400, + 208, + 416 + ], + "spans": [ + { + "bbox": [ + 105, + 400, + 208, + 416 + ], + "score": 1.0, + "content": "1 INTRODUCTION", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 20 + }, + { + "type": "text", + "bbox": [ + 107, + 417, + 505, + 495 + ], + "lines": [ + { + "bbox": [ + 106, + 417, + 505, + 430 + ], + "spans": [ + { + "bbox": [ + 106, + 417, + 505, + 430 + ], + "score": 1.0, + "content": "Transferring knowledge learned by deep neural networks from label-rich domains to new target", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 429, + 505, + 441 + ], + "spans": [ + { + "bbox": [ + 105, + 429, + 505, + 441 + ], + "score": 1.0, + "content": "domains is a challenging problem, especially when the source and target input distributions have", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 439, + 505, + 452 + ], + "spans": [ + { + "bbox": [ + 105, + 439, + 505, + 452 + ], + "score": 1.0, + "content": "different characteristics. Such domain shifts occurs in many practical applications. For example,", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 451, + 505, + 463 + ], + "spans": [ + { + "bbox": [ + 106, + 451, + 505, + 463 + ], + "score": 1.0, + "content": "while simulated driving images rendered by games provide a rich source of labeled data for semantic", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 462, + 505, + 474 + ], + "spans": [ + { + "bbox": [ + 105, + 462, + 505, + 474 + ], + "score": 1.0, + "content": "segmentation Richter et al. (2016), deep models trained on such source data do not transfer well", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 473, + 505, + 485 + ], + "spans": [ + { + "bbox": [ + 105, + 473, + 505, + 485 + ], + "score": 1.0, + "content": "to real target domains (Fig. 1(a-d)). When target-domain labels are unavailable for fine-tuning,", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 484, + 422, + 496 + ], + "spans": [ + { + "bbox": [ + 105, + 484, + 422, + 496 + ], + "score": 1.0, + "content": "unsupervised domain adaptation must be applied to improve the source model.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 24, + "bbox_fs": [ + 105, + 417, + 505, + 496 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 500, + 504, + 566 + ], + "lines": [ + { + "bbox": [ + 106, + 501, + 505, + 512 + ], + "spans": [ + { + "bbox": [ + 106, + 501, + 505, + 512 + ], + "score": 1.0, + "content": "Recent methods for unsupervised domain adaptation attempt to reduce the discrepancy between the", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 511, + 504, + 524 + ], + "spans": [ + { + "bbox": [ + 105, + 511, + 415, + 524 + ], + "score": 1.0, + "content": "source and target features via adversarial learning (Tzeng et al. (2014); Ganin", + "type": "text" + }, + { + "bbox": [ + 415, + 512, + 425, + 522 + ], + "score": 0.3, + "content": "\\&", + "type": "inline_equation" + }, + { + "bbox": [ + 425, + 511, + 504, + 524 + ], + "score": 1.0, + "content": "Lempitsky (2014)).", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 522, + 506, + 535 + ], + "spans": [ + { + "bbox": [ + 105, + 522, + 317, + 535 + ], + "score": 1.0, + "content": "They divide the base network into a feature encoder", + "type": "text" + }, + { + "bbox": [ + 317, + 523, + 326, + 533 + ], + "score": 0.8, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 327, + 522, + 383, + 535 + ], + "score": 1.0, + "content": "and classifier", + "type": "text" + }, + { + "bbox": [ + 383, + 523, + 392, + 533 + ], + "score": 0.81, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 392, + 522, + 506, + 535 + ], + "score": 1.0, + "content": ", and add a separate domain", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 533, + 506, + 546 + ], + "spans": [ + { + "bbox": [ + 105, + 533, + 209, + 546 + ], + "score": 1.0, + "content": "classifier (critic) network", + "type": "text" + }, + { + "bbox": [ + 210, + 534, + 219, + 543 + ], + "score": 0.74, + "content": "D", + "type": "inline_equation" + }, + { + "bbox": [ + 219, + 533, + 392, + 546 + ], + "score": 1.0, + "content": ". The critic takes the features generated by", + "type": "text" + }, + { + "bbox": [ + 393, + 534, + 402, + 543 + ], + "score": 0.81, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 402, + 533, + 506, + 546 + ], + "score": 1.0, + "content": "and labels them as either", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 545, + 506, + 556 + ], + "spans": [ + { + "bbox": [ + 105, + 545, + 270, + 556 + ], + "score": 1.0, + "content": "source- or target-domain. The encoder", + "type": "text" + }, + { + "bbox": [ + 270, + 545, + 279, + 554 + ], + "score": 0.8, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 280, + 545, + 506, + 556 + ], + "score": 1.0, + "content": "is then trained with an additional adversarial loss that", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 555, + 369, + 567 + ], + "spans": [ + { + "bbox": [ + 105, + 555, + 152, + 567 + ], + "score": 1.0, + "content": "maximizes", + "type": "text" + }, + { + "bbox": [ + 152, + 556, + 162, + 565 + ], + "score": 0.76, + "content": "D", + "type": "inline_equation" + }, + { + "bbox": [ + 162, + 555, + 369, + 567 + ], + "score": 1.0, + "content": "’s mistakes and thus aligns features across domains.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 30.5, + "bbox_fs": [ + 105, + 501, + 506, + 567 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 572, + 505, + 660 + ], + "lines": [ + { + "bbox": [ + 105, + 572, + 506, + 585 + ], + "spans": [ + { + "bbox": [ + 105, + 572, + 506, + 585 + ], + "score": 1.0, + "content": "However, a major drawback of this approach is that the critic simply predicts the domain label of", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 583, + 505, + 595 + ], + "spans": [ + { + "bbox": [ + 105, + 583, + 505, + 595 + ], + "score": 1.0, + "content": "the generated point and does not consider category information. Thus the generator may create", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 594, + 505, + 606 + ], + "spans": [ + { + "bbox": [ + 105, + 594, + 505, + 606 + ], + "score": 1.0, + "content": "features that look like they came from the right domain, but are not discriminative. In particular,", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 605, + 504, + 617 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 504, + 617 + ], + "score": 1.0, + "content": "it can generate points close to class boundaries, as shown in Fig. 1(e), which are likely to be mis-", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 615, + 506, + 629 + ], + "spans": [ + { + "bbox": [ + 105, + 615, + 506, + 629 + ], + "score": 1.0, + "content": "classified by the source model. We argue that to achieve good performance on the target data, the", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 626, + 505, + 641 + ], + "spans": [ + { + "bbox": [ + 105, + 626, + 505, + 641 + ], + "score": 1.0, + "content": "adaptation model must take the decision boundaries between classes into account while aligning", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 639, + 505, + 650 + ], + "spans": [ + { + "bbox": [ + 105, + 639, + 505, + 650 + ], + "score": 1.0, + "content": "features across domains (Fig. 1(f)). Moreover, since our setting is unsupervised adaptation, this", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 649, + 315, + 661 + ], + "spans": [ + { + "bbox": [ + 105, + 649, + 315, + 661 + ], + "score": 1.0, + "content": "must be accomplished without labels on target data.", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 37.5, + "bbox_fs": [ + 105, + 572, + 506, + 661 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 666, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 666, + 505, + 677 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 505, + 677 + ], + "score": 1.0, + "content": "In this paper, we propose a novel adversarial alignment technique that overcomes the above limita-", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "score": 1.0, + "content": "tion and preserves class boundaries. We make the following observation: if the critic could detect", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 104, + 688, + 506, + 700 + ], + "spans": [ + { + "bbox": [ + 104, + 688, + 506, + 700 + ], + "score": 1.0, + "content": "points near the decision boundary, then the generator would have to avoid these areas of the feature", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "score": 1.0, + "content": "space in order to fool the critic. Thus the critic would force the generator to create more discrimina-", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 710, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 710, + 462, + 722 + ], + "score": 1.0, + "content": "tive features. How can we obtain such a critic? If we alter the boundary of the classifier", + "type": "text" + }, + { + "bbox": [ + 462, + 710, + 471, + 720 + ], + "score": 0.81, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 471, + 710, + 505, + 722 + ], + "score": 1.0, + "content": "slightly", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 721, + 506, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 721, + 341, + 734 + ], + "score": 1.0, + "content": "and measure the change in the posterior class probability", + "type": "text" + }, + { + "bbox": [ + 342, + 721, + 369, + 732 + ], + "score": 0.92, + "content": "p ( y | x )", + "type": "inline_equation" + }, + { + "bbox": [ + 369, + 721, + 401, + 734 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 401, + 722, + 408, + 732 + ], + "score": 0.8, + "content": "y", + "type": "inline_equation" + }, + { + "bbox": [ + 408, + 721, + 427, + 734 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 427, + 722, + 434, + 730 + ], + "score": 0.74, + "content": "x", + "type": "inline_equation" + }, + { + "bbox": [ + 434, + 721, + 506, + 734 + ], + "score": 1.0, + "content": "denote class and", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 266, + 504, + 279 + ], + "spans": [ + { + "bbox": [ + 105, + 266, + 504, + 279 + ], + "score": 1.0, + "content": "input respectively, then samples near the decision boundary are likely to have the largest change.", + "type": "text", + "cross_page": true + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 277, + 505, + 291 + ], + "spans": [ + { + "bbox": [ + 105, + 277, + 505, + 291 + ], + "score": 1.0, + "content": "In fact, this posterior discrepancy is inversely proportional to the distance from the class boundary.", + "type": "text", + "cross_page": true + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 289, + 505, + 302 + ], + "spans": [ + { + "bbox": [ + 106, + 289, + 372, + 302 + ], + "score": 1.0, + "content": "We thus propose to maximize this posterior discrepancy to turn", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 372, + 289, + 381, + 299 + ], + "score": 0.8, + "content": "C", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 381, + 289, + 505, + 302 + ], + "score": 1.0, + "content": "into a critic sensitive to non-", + "type": "text", + "cross_page": true + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 300, + 505, + 312 + ], + "spans": [ + { + "bbox": [ + 106, + 300, + 505, + 312 + ], + "score": 1.0, + "content": "discriminative points. We call this technique Adversarial Dropout Regularization. Here, dropout is", + "type": "text", + "cross_page": true + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 311, + 505, + 323 + ], + "spans": [ + { + "bbox": [ + 105, + 311, + 505, + 323 + ], + "score": 1.0, + "content": "not used in the standard way, which is to regularize the main classifier and make it insensitive to", + "type": "text", + "cross_page": true + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 322, + 505, + 334 + ], + "spans": [ + { + "bbox": [ + 106, + 322, + 505, + 334 + ], + "score": 1.0, + "content": "noise. Instead, we use dropout in an adversarial way, to transform the classifier into a critic sensitive", + "type": "text", + "cross_page": true + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 333, + 504, + 345 + ], + "spans": [ + { + "bbox": [ + 105, + 333, + 484, + 345 + ], + "score": 1.0, + "content": "to noise. Compared to previous adversarial feature alignment methods, where the distributions", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 484, + 333, + 504, + 345 + ], + "score": 0.9, + "content": "p ( x )", + "type": "inline_equation", + "cross_page": true + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 343, + 506, + 356 + ], + "spans": [ + { + "bbox": [ + 105, + 343, + 506, + 356 + ], + "score": 1.0, + "content": "are aligned globally, our method aligns target features away from decision boundaries, as illustrated", + "type": "text", + "cross_page": true + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 353, + 153, + 367 + ], + "spans": [ + { + "bbox": [ + 105, + 353, + 153, + 367 + ], + "score": 1.0, + "content": "in Fig.1(f).", + "type": "text", + "cross_page": true + } + ], + "index": 17 + } + ], + "index": 44.5, + "bbox_fs": [ + 104, + 666, + 506, + 734 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 106, + 79, + 504, + 168 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 106, + 79, + 504, + 168 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 79, + 504, + 168 + ], + "spans": [ + { + "bbox": [ + 106, + 79, + 504, + 168 + ], + "score": 0.968, + "type": "image", + "image_path": "b6f4ca41441b05f1a91aeb791d5664cfbced0e867e90f0899d66085405d66cc1.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 106, + 79, + 504, + 108.66666666666667 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 106, + 108.66666666666667, + 504, + 138.33333333333334 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 106, + 138.33333333333334, + 504, + 168.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 178, + 505, + 245 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 178, + 505, + 191 + ], + "spans": [ + { + "bbox": [ + 105, + 178, + 505, + 191 + ], + "score": 1.0, + "content": "Figure 1: (a-d) An illustration of a deep model trained on simulated source training data failing to segment", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 190, + 505, + 201 + ], + "spans": [ + { + "bbox": [ + 105, + 190, + 505, + 201 + ], + "score": 1.0, + "content": "a real target domain image: (a) shows the target image, (b) is the ground truth segmentation into semantic", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 200, + 505, + 213 + ], + "spans": [ + { + "bbox": [ + 105, + 200, + 505, + 213 + ], + "score": 1.0, + "content": "categories (car, road, etc), (c) is the output of the unadapted source model, (d) is the improved segmenta-", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 212, + 505, + 223 + ], + "spans": [ + { + "bbox": [ + 106, + 212, + 505, + 223 + ], + "score": 1.0, + "content": "tion obtained by our proposed ADR method. (e) Previous distribution matching methods do not consider the", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 223, + 505, + 235 + ], + "spans": [ + { + "bbox": [ + 105, + 223, + 505, + 235 + ], + "score": 1.0, + "content": "source decision boundary when aligning source and target feature points. (f) We propose to use the boundary", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 234, + 338, + 246 + ], + "spans": [ + { + "bbox": [ + 105, + 234, + 338, + 246 + ], + "score": 1.0, + "content": "information to achieve low-density separation of aligned points.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 5.5 + } + ], + "index": 3.25 + }, + { + "type": "text", + "bbox": [ + 107, + 266, + 505, + 366 + ], + "lines": [ + { + "bbox": [ + 105, + 266, + 504, + 279 + ], + "spans": [ + { + "bbox": [ + 105, + 266, + 504, + 279 + ], + "score": 1.0, + "content": "input respectively, then samples near the decision boundary are likely to have the largest change.", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 277, + 505, + 291 + ], + "spans": [ + { + "bbox": [ + 105, + 277, + 505, + 291 + ], + "score": 1.0, + "content": "In fact, this posterior discrepancy is inversely proportional to the distance from the class boundary.", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 289, + 505, + 302 + ], + "spans": [ + { + "bbox": [ + 106, + 289, + 372, + 302 + ], + "score": 1.0, + "content": "We thus propose to maximize this posterior discrepancy to turn", + "type": "text" + }, + { + "bbox": [ + 372, + 289, + 381, + 299 + ], + "score": 0.8, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 381, + 289, + 505, + 302 + ], + "score": 1.0, + "content": "into a critic sensitive to non-", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 300, + 505, + 312 + ], + "spans": [ + { + "bbox": [ + 106, + 300, + 505, + 312 + ], + "score": 1.0, + "content": "discriminative points. We call this technique Adversarial Dropout Regularization. Here, dropout is", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 311, + 505, + 323 + ], + "spans": [ + { + "bbox": [ + 105, + 311, + 505, + 323 + ], + "score": 1.0, + "content": "not used in the standard way, which is to regularize the main classifier and make it insensitive to", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 322, + 505, + 334 + ], + "spans": [ + { + "bbox": [ + 106, + 322, + 505, + 334 + ], + "score": 1.0, + "content": "noise. Instead, we use dropout in an adversarial way, to transform the classifier into a critic sensitive", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 333, + 504, + 345 + ], + "spans": [ + { + "bbox": [ + 105, + 333, + 484, + 345 + ], + "score": 1.0, + "content": "to noise. Compared to previous adversarial feature alignment methods, where the distributions", + "type": "text" + }, + { + "bbox": [ + 484, + 333, + 504, + 345 + ], + "score": 0.9, + "content": "p ( x )", + "type": "inline_equation" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 343, + 506, + 356 + ], + "spans": [ + { + "bbox": [ + 105, + 343, + 506, + 356 + ], + "score": 1.0, + "content": "are aligned globally, our method aligns target features away from decision boundaries, as illustrated", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 353, + 153, + 367 + ], + "spans": [ + { + "bbox": [ + 105, + 353, + 153, + 367 + ], + "score": 1.0, + "content": "in Fig.1(f).", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 13 + }, + { + "type": "text", + "bbox": [ + 106, + 371, + 505, + 470 + ], + "lines": [ + { + "bbox": [ + 106, + 372, + 505, + 384 + ], + "spans": [ + { + "bbox": [ + 106, + 372, + 395, + 384 + ], + "score": 1.0, + "content": "Our ADR approach has several benefits. First, we train the generator", + "type": "text" + }, + { + "bbox": [ + 396, + 372, + 405, + 381 + ], + "score": 0.81, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 405, + 372, + 505, + 384 + ], + "score": 1.0, + "content": "with feedback from the", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 382, + 506, + 395 + ], + "spans": [ + { + "bbox": [ + 106, + 382, + 144, + 395 + ], + "score": 1.0, + "content": "classifier", + "type": "text" + }, + { + "bbox": [ + 144, + 383, + 153, + 393 + ], + "score": 0.77, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 154, + 382, + 399, + 395 + ], + "score": 1.0, + "content": ", in contrast to existing methods, which use an unrelated critic", + "type": "text" + }, + { + "bbox": [ + 400, + 383, + 409, + 392 + ], + "score": 0.72, + "content": "D", + "type": "inline_equation" + }, + { + "bbox": [ + 410, + 382, + 506, + 395 + ], + "score": 1.0, + "content": ". Second, our method is", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 393, + 505, + 406 + ], + "spans": [ + { + "bbox": [ + 105, + 393, + 505, + 406 + ], + "score": 1.0, + "content": "general and straightforward to apply to a variety of domain adaptation problems, such as classifica-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 404, + 505, + 417 + ], + "spans": [ + { + "bbox": [ + 106, + 404, + 505, + 417 + ], + "score": 1.0, + "content": "tion and semantic segmentation. Finally, since ADR is trained to align distributions, it is also appli-", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 415, + 505, + 428 + ], + "spans": [ + { + "bbox": [ + 105, + 415, + 505, + 428 + ], + "score": 1.0, + "content": "cable to semi-supervised learning and training of generative models, such as Generative Adversarial", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 425, + 505, + 439 + ], + "spans": [ + { + "bbox": [ + 105, + 425, + 505, + 439 + ], + "score": 1.0, + "content": "Networks (GANs) (Goodfellow et al. (2014a)). Through extensive experiments, we demonstrate", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 436, + 505, + 450 + ], + "spans": [ + { + "bbox": [ + 105, + 436, + 505, + 450 + ], + "score": 1.0, + "content": "the benefit of ADR over existing domain adaptation approaches, achieving state-of-the-art results", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 447, + 505, + 461 + ], + "spans": [ + { + "bbox": [ + 105, + 447, + 505, + 461 + ], + "score": 1.0, + "content": "in difficult domain shifts. We also show an application to semi-supervised learning using GANs in", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 459, + 149, + 471 + ], + "spans": [ + { + "bbox": [ + 105, + 459, + 149, + 471 + ], + "score": 1.0, + "content": "appendix.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 22 + }, + { + "type": "title", + "bbox": [ + 108, + 488, + 211, + 501 + ], + "lines": [ + { + "bbox": [ + 104, + 487, + 213, + 504 + ], + "spans": [ + { + "bbox": [ + 104, + 487, + 213, + 504 + ], + "score": 1.0, + "content": "2 RELATED WORK", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 27 + }, + { + "type": "text", + "bbox": [ + 106, + 506, + 505, + 605 + ], + "lines": [ + { + "bbox": [ + 106, + 506, + 505, + 518 + ], + "spans": [ + { + "bbox": [ + 106, + 506, + 505, + 518 + ], + "score": 1.0, + "content": "Domain Adaptation. Recent unsupervised domain adaptation (UDA) methods for visual data aim", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 518, + 505, + 530 + ], + "spans": [ + { + "bbox": [ + 106, + 518, + 505, + 530 + ], + "score": 1.0, + "content": "to align the feature distributions of the source and target domains (Sun et al. (2016); Sun & Saenko", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 528, + 505, + 541 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 505, + 541 + ], + "score": 1.0, + "content": "(2016); Tzeng et al. (2014); Ganin et al. (2016); Long et al. (2015b); Yan et al. (2017); Long et al.", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 538, + 505, + 552 + ], + "spans": [ + { + "bbox": [ + 105, + 538, + 505, + 552 + ], + "score": 1.0, + "content": "(2017)). 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However,", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 581, + 505, + 597 + ], + "spans": [ + { + "bbox": [ + 105, + 581, + 505, + 597 + ], + "score": 1.0, + "content": "they measure the domain divergence based on the hidden features of the network without considering", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 593, + 478, + 608 + ], + "spans": [ + { + "bbox": [ + 105, + 593, + 478, + 608 + ], + "score": 1.0, + "content": "the relationship between its decision boundary and the target features, as we do in this paper.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 32 + }, + { + "type": "text", + "bbox": [ + 107, + 611, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 611, + 505, + 623 + ], + "spans": [ + { + "bbox": [ + 105, + 611, + 505, + 623 + ], + "score": 1.0, + "content": "Low-density Separation. Many semi-supervised learning (SSL) methods utilize the relationship", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 621, + 505, + 635 + ], + "spans": [ + { + "bbox": [ + 105, + 621, + 505, + 635 + ], + "score": 1.0, + "content": "between the decision boundary and unlabeled samples, a technique called low-density separa-", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 633, + 505, + 645 + ], + "spans": [ + { + "bbox": [ + 105, + 633, + 505, + 645 + ], + "score": 1.0, + "content": "tion (Chapelle & Zien (2005); Joachims (1999)). By placing the boundary in the area where the", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 645, + 505, + 656 + ], + "spans": [ + { + "bbox": [ + 106, + 645, + 505, + 656 + ], + "score": 1.0, + "content": "unlabeled samples are sparse, these models aim to obtain discriminative representations. 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Finally, since ADR is trained to align distributions, it is also appli-", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 415, + 505, + 428 + ], + "spans": [ + { + "bbox": [ + 105, + 415, + 505, + 428 + ], + "score": 1.0, + "content": "cable to semi-supervised learning and training of generative models, such as Generative Adversarial", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 425, + 505, + 439 + ], + "spans": [ + { + "bbox": [ + 105, + 425, + 505, + 439 + ], + "score": 1.0, + "content": "Networks (GANs) (Goodfellow et al. (2014a)). 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We also show an application to semi-supervised learning using GANs in", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 459, + 149, + 471 + ], + "spans": [ + { + "bbox": [ + 105, + 459, + 149, + 471 + ], + "score": 1.0, + "content": "appendix.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 22, + "bbox_fs": [ + 105, + 372, + 506, + 471 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 488, + 211, + 501 + ], + "lines": [ + { + "bbox": [ + 104, + 487, + 213, + 504 + ], + "spans": [ + { + "bbox": [ + 104, + 487, + 213, + 504 + ], + "score": 1.0, + "content": "2 RELATED WORK", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 27 + }, + { + "type": "text", + "bbox": [ + 106, + 506, + 505, + 605 + ], + "lines": [ + { + "bbox": [ + 106, + 506, + 505, + 518 + ], + "spans": [ + { + "bbox": [ + 106, + 506, + 505, + 518 + ], + "score": 1.0, + "content": "Domain Adaptation. Recent unsupervised domain adaptation (UDA) methods for visual data aim", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 518, + 505, + 530 + ], + "spans": [ + { + "bbox": [ + 106, + 518, + 505, + 530 + ], + "score": 1.0, + "content": "to align the feature distributions of the source and target domains (Sun et al. (2016); Sun & Saenko", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 528, + 505, + 541 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 505, + 541 + ], + "score": 1.0, + "content": "(2016); Tzeng et al. (2014); Ganin et al. (2016); Long et al. (2015b); Yan et al. (2017); Long et al.", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 538, + 505, + 552 + ], + "spans": [ + { + "bbox": [ + 105, + 538, + 505, + 552 + ], + "score": 1.0, + "content": "(2017)). 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Our method", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 655, + 504, + 666 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 504, + 666 + ], + "score": 1.0, + "content": "aims to achieve low-density separation for deep domain adaptation and is related to entropy min-", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "score": 1.0, + "content": "imization for semi-supervised learning (Grandvalet & Bengio (2005)). (Long et al. (2016)) used", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 677, + 505, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 505, + 690 + ], + "score": 1.0, + "content": "entropy minimization in their approach to directly measure how far samples are from a decision", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 688, + 506, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 688, + 506, + 700 + ], + "score": 1.0, + "content": "boundary by calculating entropy of the classifier’s output. 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As long as target samples features are robust to the movement, they will be", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 720, + 479, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 479, + 733 + ], + "score": 1.0, + "content": "allowed to exist relatively nearby the boundary compared to source samples, as Fig. 1 shows.", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 42, + "bbox_fs": [ + 105, + 611, + 506, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 82, + 505, + 182 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 505, + 94 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 505, + 94 + ], + "score": 1.0, + "content": "In (Long et al. (2016)) entropy minimization is only a part of the overall approach. To compare", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 93, + 505, + 105 + ], + "spans": [ + { + "bbox": [ + 106, + 93, + 505, + 105 + ], + "score": 1.0, + "content": "our ADR approach to entropy minimization more directly, we use a new baseline method. To our", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 104, + 506, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 104, + 506, + 118 + ], + "score": 1.0, + "content": "knowledge, though this method has not been proposed by any previous work, it is easily achieved", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 115, + 506, + 128 + ], + "spans": [ + { + "bbox": [ + 106, + 115, + 506, + 128 + ], + "score": 1.0, + "content": "by modifying a method proposed by (Springenberg (2015)). For this baseline, we train a model that", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 127, + 506, + 139 + ], + "spans": [ + { + "bbox": [ + 105, + 127, + 506, + 139 + ], + "score": 1.0, + "content": "generates features to minimize the entropy of the output probability for target samples. The details", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 136, + 506, + 150 + ], + "spans": [ + { + "bbox": [ + 105, + 136, + 506, + 150 + ], + "score": 1.0, + "content": "of the baseline are provided in appendix. In short, the generator tries to minimize the entropy of", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 148, + 505, + 160 + ], + "spans": [ + { + "bbox": [ + 106, + 148, + 505, + 160 + ], + "score": 1.0, + "content": "the target samples, whereas the critic tries to maximize it. The entropy is directly measured by the", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 158, + 506, + 173 + ], + "spans": [ + { + "bbox": [ + 105, + 158, + 506, + 173 + ], + "score": 1.0, + "content": "output of the classifier. This baseline is similar to our approach in that the goal of the method is to", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 170, + 234, + 183 + ], + "spans": [ + { + "bbox": [ + 106, + 170, + 234, + 183 + ], + "score": 1.0, + "content": "achieve low-density separation.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 4 + }, + { + "type": "text", + "bbox": [ + 107, + 187, + 505, + 286 + ], + "lines": [ + { + "bbox": [ + 105, + 187, + 505, + 200 + ], + "spans": [ + { + "bbox": [ + 105, + 187, + 505, + 200 + ], + "score": 1.0, + "content": "Dropout. Dropout is a method that prevents deep networks from overfitting (Srivastava et al. (2014))", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 198, + 505, + 211 + ], + "spans": [ + { + "bbox": [ + 106, + 198, + 505, + 211 + ], + "score": 1.0, + "content": "by randomly dropping units from the neural network during training. Effectively, dropout samples", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 208, + 505, + 222 + ], + "spans": [ + { + "bbox": [ + 106, + 208, + 505, + 222 + ], + "score": 1.0, + "content": "from an exponential number of different thinned networks at training time, which prevents units from", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 221, + 506, + 232 + ], + "spans": [ + { + "bbox": [ + 106, + 221, + 506, + 232 + ], + "score": 1.0, + "content": "co-adapting too much. At test time, predictions are obtained by using the outputs of all neurons. If", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 230, + 506, + 245 + ], + "spans": [ + { + "bbox": [ + 105, + 230, + 506, + 245 + ], + "score": 1.0, + "content": "the thinned networks are able to classify the samples accurately, the full network will as well. In", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 242, + 505, + 255 + ], + "spans": [ + { + "bbox": [ + 106, + 242, + 505, + 255 + ], + "score": 1.0, + "content": "other words, dropout encourages the network to be robust to noise. 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To our knowledge, this use of dropout is completely different from existing methods.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 13 + }, + { + "type": "title", + "bbox": [ + 107, + 302, + 173, + 314 + ], + "lines": [ + { + "bbox": [ + 104, + 299, + 175, + 317 + ], + "spans": [ + { + "bbox": [ + 104, + 299, + 175, + 317 + ], + "score": 1.0, + "content": "3 METHOD", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 18 + }, + { + "type": "text", + "bbox": [ + 106, + 318, + 505, + 414 + ], + "lines": [ + { + "bbox": [ + 106, + 317, + 505, + 331 + ], + "spans": [ + { + "bbox": [ + 106, + 317, + 344, + 331 + ], + "score": 1.0, + "content": "We assume that we have access to a labeled source image", + "type": "text" + }, + { + "bbox": [ + 344, + 320, + 356, + 329 + ], + "score": 0.86, + "content": "\\mathbf { x _ { s } }", + "type": "inline_equation" + }, + { + "bbox": [ + 356, + 317, + 465, + 331 + ], + "score": 1.0, + "content": "and a corresponding label", + "type": "text" + }, + { + "bbox": [ + 465, + 320, + 476, + 330 + ], + "score": 0.84, + "content": "y _ { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 476, + 317, + 505, + 331 + ], + "score": 1.0, + "content": "drawn", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 328, + 505, + 342 + ], + "spans": [ + { + "bbox": [ + 105, + 328, + 252, + 342 + ], + "score": 1.0, + "content": "from a set of labeled source images", + "type": "text" + }, + { + "bbox": [ + 253, + 329, + 290, + 341 + ], + "score": 0.93, + "content": "\\{ X _ { s } , Y _ { s } \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 290, + 328, + 442, + 342 + ], + "score": 1.0, + "content": ", as well as an unlabeled target image", + "type": "text" + }, + { + "bbox": [ + 443, + 331, + 454, + 340 + ], + "score": 0.82, + "content": "\\mathbf { x _ { t } }", + "type": "inline_equation" + }, + { + "bbox": [ + 454, + 328, + 505, + 342 + ], + "score": 1.0, + "content": "drawn from", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 104, + 337, + 506, + 355 + ], + "spans": [ + { + "bbox": [ + 104, + 337, + 204, + 355 + ], + "score": 1.0, + "content": "unlabeled target images", + "type": "text" + }, + { + "bbox": [ + 204, + 340, + 217, + 351 + ], + "score": 0.88, + "content": "X _ { t }", + "type": "inline_equation" + }, + { + "bbox": [ + 217, + 337, + 376, + 355 + ], + "score": 1.0, + "content": ". 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The logits are then converted to class probabilities by applying the softmax function.", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 383, + 506, + 406 + ], + "spans": [ + { + "bbox": [ + 105, + 383, + 222, + 406 + ], + "score": 1.0, + "content": "Namely, the probability that", + "type": "text" + }, + { + "bbox": [ + 223, + 388, + 231, + 397 + ], + "score": 0.64, + "content": "\\mathbf { x }", + "type": "inline_equation" + }, + { + "bbox": [ + 231, + 383, + 322, + 406 + ], + "score": 1.0, + "content": "is classified into class", + "type": "text" + }, + { + "bbox": [ + 322, + 387, + 329, + 398 + ], + "score": 0.81, + "content": "j", + "type": "inline_equation" + }, + { + "bbox": [ + 329, + 383, + 387, + 406 + ], + "score": 1.0, + "content": "is denoted by", + "type": "text" + }, + { + "bbox": [ + 388, + 384, + 501, + 403 + ], + "score": 0.92, + "content": "\\begin{array} { r } { p ( y = j | \\mathbf { x } ) = \\frac { e x p ( l _ { j } ) } { \\sum _ { k = 1 } ^ { K } e x p ( l _ { k } ) } } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 383, + 506, + 406 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 401, + 464, + 415 + ], + "spans": [ + { + "bbox": [ + 106, + 401, + 187, + 415 + ], + "score": 1.0, + "content": "We use the notation", + "type": "text" + }, + { + "bbox": [ + 188, + 401, + 216, + 414 + ], + "score": 0.92, + "content": "p ( \\mathbf { y } \\vert \\mathbf { x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 217, + 401, + 272, + 415 + ], + "score": 1.0, + "content": "to denote the", + "type": "text" + }, + { + "bbox": [ + 272, + 402, + 282, + 412 + ], + "score": 0.82, + "content": "K", + "type": "inline_equation" + }, + { + "bbox": [ + 282, + 401, + 453, + 415 + ], + "score": 1.0, + "content": "-dimensional probabilistic output for input", + "type": "text" + }, + { + "bbox": [ + 453, + 405, + 460, + 411 + ], + "score": 0.49, + "content": "\\mathbf { x }", + "type": "inline_equation" + }, + { + "bbox": [ + 460, + 401, + 464, + 415 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 22.5 + }, + { + "type": "text", + "bbox": [ + 106, + 419, + 505, + 539 + ], + "lines": [ + { + "bbox": [ + 105, + 418, + 505, + 431 + ], + "spans": [ + { + "bbox": [ + 105, + 418, + 133, + 431 + ], + "score": 1.0, + "content": "When", + "type": "text" + }, + { + "bbox": [ + 134, + 419, + 143, + 429 + ], + "score": 0.8, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 144, + 418, + 505, + 431 + ], + "score": 1.0, + "content": "is acting as the critic, we want it to detect the feature encodings of target samples near", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 430, + 505, + 442 + ], + "spans": [ + { + "bbox": [ + 106, + 430, + 287, + 442 + ], + "score": 1.0, + "content": "the decision boundary. We propose to make", + "type": "text" + }, + { + "bbox": [ + 288, + 430, + 297, + 439 + ], + "score": 0.8, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 297, + 430, + 505, + 442 + ], + "score": 1.0, + "content": "sensitive to such samples by slightly perturbing its", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 439, + 505, + 454 + ], + "spans": [ + { + "bbox": [ + 105, + 439, + 420, + 454 + ], + "score": 1.0, + "content": "decision boundary and measuring the change in the posterior class probability", + "type": "text" + }, + { + "bbox": [ + 420, + 441, + 449, + 452 + ], + "score": 0.93, + "content": "p ( \\mathbf { y } \\vert \\mathbf { x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 450, + 439, + 505, + 454 + ], + "score": 1.0, + "content": ". This change", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 451, + 506, + 464 + ], + "spans": [ + { + "bbox": [ + 105, + 451, + 421, + 464 + ], + "score": 1.0, + "content": "is likely to be largest for samples near the decision boundary. The network", + "type": "text" + }, + { + "bbox": [ + 421, + 452, + 430, + 461 + ], + "score": 0.8, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 431, + 451, + 506, + 464 + ], + "score": 1.0, + "content": "is then trained to", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 461, + 505, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 461, + 351, + 475 + ], + "score": 1.0, + "content": "increase this change, while the feature generation network", + "type": "text" + }, + { + "bbox": [ + 351, + 463, + 360, + 472 + ], + "score": 0.8, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 361, + 461, + 505, + 475 + ], + "score": 1.0, + "content": "is trained to decrease it. Through", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 474, + 505, + 486 + ], + "spans": [ + { + "bbox": [ + 106, + 474, + 206, + 486 + ], + "score": 1.0, + "content": "this adversarial training,", + "type": "text" + }, + { + "bbox": [ + 207, + 474, + 216, + 484 + ], + "score": 0.78, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 216, + 474, + 505, + 486 + ], + "score": 1.0, + "content": "learns to ‘fool’ the critic and generate target features far away from the", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 484, + 506, + 497 + ], + "spans": [ + { + "bbox": [ + 106, + 484, + 395, + 497 + ], + "score": 1.0, + "content": "decision boundary, thus avoiding ambiguous features. The weights of", + "type": "text" + }, + { + "bbox": [ + 396, + 485, + 405, + 494 + ], + "score": 0.81, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 405, + 484, + 506, + 497 + ], + "score": 1.0, + "content": "can be initialized either", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 495, + 506, + 508 + ], + "spans": [ + { + "bbox": [ + 105, + 495, + 474, + 508 + ], + "score": 1.0, + "content": "by pre-training on some auxiliary dataset (e.g., ImageNet), or with random weights, while", + "type": "text" + }, + { + "bbox": [ + 475, + 496, + 484, + 506 + ], + "score": 0.79, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 484, + 495, + 506, + 508 + ], + "score": 1.0, + "content": "uses", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 104, + 506, + 505, + 519 + ], + "spans": [ + { + "bbox": [ + 104, + 506, + 505, + 519 + ], + "score": 1.0, + "content": "random initialization. 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Finally,", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 529, + 495, + 541 + ], + "spans": [ + { + "bbox": [ + 106, + 529, + 495, + 541 + ], + "score": 1.0, + "content": "we give some intuition behind adversarial dropout and improve our method based on this insight.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 32 + }, + { + "type": "title", + "bbox": [ + 108, + 553, + 296, + 564 + ], + "lines": [ + { + "bbox": [ + 106, + 552, + 298, + 565 + ], + "spans": [ + { + "bbox": [ + 106, + 552, + 298, + 565 + ], + "score": 1.0, + "content": "3.1 CLASSIFIER SELECTION VIA DROPOUT", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 38 + }, + { + "type": "text", + "bbox": [ + 108, + 565, + 504, + 598 + ], + "lines": [ + { + "bbox": [ + 106, + 564, + 505, + 578 + ], + "spans": [ + { + "bbox": [ + 106, + 564, + 505, + 578 + ], + "score": 1.0, + "content": "Consider the standard training of a neural network using dropout. For every sample within a mini-", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 576, + 505, + 588 + ], + "spans": [ + { + "bbox": [ + 106, + 576, + 505, + 588 + ], + "score": 1.0, + "content": "batch, each node of the network is removed with some probability, effectively selecting a different", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 586, + 450, + 601 + ], + "spans": [ + { + "bbox": [ + 106, + 586, + 450, + 601 + ], + "score": 1.0, + "content": "classifier for every sample during training. We harness this idea in a very simple way.", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 40 + }, + { + "type": "text", + "bbox": [ + 107, + 603, + 505, + 681 + ], + "lines": [ + { + "bbox": [ + 105, + 602, + 506, + 617 + ], + "spans": [ + { + "bbox": [ + 105, + 602, + 218, + 617 + ], + "score": 1.0, + "content": "We forward input features", + "type": "text" + }, + { + "bbox": [ + 218, + 604, + 245, + 615 + ], + "score": 0.93, + "content": "G ( \\bf x _ { t } )", + "type": "inline_equation" + }, + { + "bbox": [ + 245, + 602, + 259, + 617 + ], + "score": 1.0, + "content": "to", + "type": "text" + }, + { + "bbox": [ + 259, + 604, + 268, + 614 + ], + "score": 0.82, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 268, + 602, + 506, + 617 + ], + "score": 1.0, + "content": "twice, dropping different nodes each time and obtaining", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 614, + 505, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 614, + 268, + 628 + ], + "score": 1.0, + "content": "two different output vectors denoted as", + "type": "text" + }, + { + "bbox": [ + 268, + 614, + 314, + 627 + ], + "score": 0.86, + "content": "C _ { 1 } ( G ( \\mathbf { x _ { t } } ) )", + "type": "inline_equation" + }, + { + "bbox": [ + 314, + 614, + 319, + 628 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 320, + 614, + 365, + 627 + ], + "score": 0.84, + "content": "\\bar { C } _ { 2 } \\bar { ( \\cal G ( x _ { t } ) ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 365, + 614, + 505, + 628 + ], + "score": 1.0, + "content": ". In other words, we are selecting", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 624, + 505, + 639 + ], + "spans": [ + { + "bbox": [ + 105, + 624, + 202, + 639 + ], + "score": 1.0, + "content": "two different classifiers", + "type": "text" + }, + { + "bbox": [ + 203, + 626, + 215, + 637 + ], + "score": 0.89, + "content": "C _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 216, + 624, + 234, + 639 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 234, + 626, + 246, + 637 + ], + "score": 0.88, + "content": "C _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 246, + 624, + 270, + 639 + ], + "score": 1.0, + "content": "from", + "type": "text" + }, + { + "bbox": [ + 270, + 627, + 279, + 636 + ], + "score": 0.8, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 279, + 624, + 505, + 639 + ], + "score": 1.0, + "content": "by dropout as in Fig. 2. In the figure, the corresponding", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 636, + 505, + 650 + ], + "spans": [ + { + "bbox": [ + 105, + 636, + 259, + 650 + ], + "score": 1.0, + "content": "posterior probabilities are indicated as", + "type": "text" + }, + { + "bbox": [ + 259, + 637, + 297, + 649 + ], + "score": 0.75, + "content": "p _ { 1 } ( \\mathbf { y } | \\mathbf { x _ { t } } )", + "type": "inline_equation" + }, + { + "bbox": [ + 297, + 636, + 300, + 650 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 300, + 636, + 338, + 649 + ], + "score": 0.66, + "content": "p _ { 2 } ( \\mathbf { y } \\vert \\mathbf { x _ { t } } )", + "type": "inline_equation" + }, + { + "bbox": [ + 338, + 636, + 399, + 650 + ], + "score": 1.0, + "content": ", abbreviated as", + "type": "text" + }, + { + "bbox": [ + 400, + 638, + 411, + 648 + ], + "score": 0.86, + "content": "p _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 411, + 636, + 428, + 650 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 428, + 638, + 439, + 648 + ], + "score": 0.85, + "content": "p _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 439, + 636, + 505, + 650 + ], + "score": 1.0, + "content": "in the following", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 647, + 505, + 660 + ], + "spans": [ + { + "bbox": [ + 105, + 647, + 505, + 660 + ], + "score": 1.0, + "content": "discussion. In order to detect the change of predictions near the boundary, the critic tries to increase", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 658, + 505, + 672 + ], + "spans": [ + { + "bbox": [ + 105, + 658, + 272, + 672 + ], + "score": 1.0, + "content": "the difference between the predictions of", + "type": "text" + }, + { + "bbox": [ + 272, + 659, + 285, + 669 + ], + "score": 0.9, + "content": "C _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 285, + 658, + 303, + 672 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 303, + 659, + 316, + 669 + ], + "score": 0.89, + "content": "C _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 316, + 658, + 444, + 672 + ], + "score": 1.0, + "content": ". 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(2016)) entropy minimization is only a part of the overall approach. To compare", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 93, + 505, + 105 + ], + "spans": [ + { + "bbox": [ + 106, + 93, + 505, + 105 + ], + "score": 1.0, + "content": "our ADR approach to entropy minimization more directly, we use a new baseline method. To our", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 104, + 506, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 104, + 506, + 118 + ], + "score": 1.0, + "content": "knowledge, though this method has not been proposed by any previous work, it is easily achieved", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 115, + 506, + 128 + ], + "spans": [ + { + "bbox": [ + 106, + 115, + 506, + 128 + ], + "score": 1.0, + "content": "by modifying a method proposed by (Springenberg (2015)). For this baseline, we train a model that", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 127, + 506, + 139 + ], + "spans": [ + { + "bbox": [ + 105, + 127, + 506, + 139 + ], + "score": 1.0, + "content": "generates features to minimize the entropy of the output probability for target samples. The details", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 136, + 506, + 150 + ], + "spans": [ + { + "bbox": [ + 105, + 136, + 506, + 150 + ], + "score": 1.0, + "content": "of the baseline are provided in appendix. In short, the generator tries to minimize the entropy of", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 148, + 505, + 160 + ], + "spans": [ + { + "bbox": [ + 106, + 148, + 505, + 160 + ], + "score": 1.0, + "content": "the target samples, whereas the critic tries to maximize it. 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(2014))", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 198, + 505, + 211 + ], + "spans": [ + { + "bbox": [ + 106, + 198, + 505, + 211 + ], + "score": 1.0, + "content": "by randomly dropping units from the neural network during training. Effectively, dropout samples", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 208, + 505, + 222 + ], + "spans": [ + { + "bbox": [ + 106, + 208, + 505, + 222 + ], + "score": 1.0, + "content": "from an exponential number of different thinned networks at training time, which prevents units from", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 221, + 506, + 232 + ], + "spans": [ + { + "bbox": [ + 106, + 221, + 506, + 232 + ], + "score": 1.0, + "content": "co-adapting too much. At test time, predictions are obtained by using the outputs of all neurons. If", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 230, + 506, + 245 + ], + "spans": [ + { + "bbox": [ + 105, + 230, + 506, + 245 + ], + "score": 1.0, + "content": "the thinned networks are able to classify the samples accurately, the full network will as well. In", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 242, + 505, + 255 + ], + "spans": [ + { + "bbox": [ + 106, + 242, + 505, + 255 + ], + "score": 1.0, + "content": "other words, dropout encourages the network to be robust to noise. 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To our knowledge, this use of dropout is completely different from existing methods.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 13, + "bbox_fs": [ + 105, + 187, + 506, + 287 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 302, + 173, + 314 + ], + "lines": [ + { + "bbox": [ + 104, + 299, + 175, + 317 + ], + "spans": [ + { + "bbox": [ + 104, + 299, + 175, + 317 + ], + "score": 1.0, + "content": "3 METHOD", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 18 + }, + { + "type": "text", + "bbox": [ + 106, + 318, + 505, + 414 + ], + "lines": [ + { + "bbox": [ + 106, + 317, + 505, + 331 + ], + "spans": [ + { + "bbox": [ + 106, + 317, + 344, + 331 + ], + "score": 1.0, + "content": "We assume that we have access to a labeled source image", + "type": "text" + }, + { + "bbox": [ + 344, + 320, + 356, + 329 + ], + "score": 0.86, + "content": "\\mathbf { x _ { s } }", + "type": "inline_equation" + }, + { + "bbox": [ + 356, + 317, + 465, + 331 + ], + "score": 1.0, + "content": "and a corresponding label", + "type": "text" + }, + { + "bbox": [ + 465, + 320, + 476, + 330 + ], + "score": 0.84, + "content": "y _ { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 476, + 317, + 505, + 331 + ], + "score": 1.0, + "content": "drawn", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 328, + 505, + 342 + ], + "spans": [ + { + "bbox": [ + 105, + 328, + 252, + 342 + ], + "score": 1.0, + "content": "from a set of labeled source images", + "type": "text" + }, + { + "bbox": [ + 253, + 329, + 290, + 341 + ], + "score": 0.93, + "content": "\\{ X _ { s } , Y _ { s } \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 290, + 328, + 442, + 342 + ], + "score": 1.0, + "content": ", as well as an unlabeled target image", + "type": "text" + }, + { + "bbox": [ + 443, + 331, + 454, + 340 + ], + "score": 0.82, + "content": "\\mathbf { x _ { t } }", + "type": "inline_equation" + }, + { + "bbox": [ + 454, + 328, + 505, + 342 + ], + "score": 1.0, + "content": "drawn from", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 104, + 337, + 506, + 355 + ], + "spans": [ + { + "bbox": [ + 104, + 337, + 204, + 355 + ], + "score": 1.0, + "content": "unlabeled target images", + "type": "text" + }, + { + "bbox": [ + 204, + 340, + 217, + 351 + ], + "score": 0.88, + "content": "X _ { t }", + "type": "inline_equation" + }, + { + "bbox": [ + 217, + 337, + 376, + 355 + ], + "score": 1.0, + "content": ". 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The logits are then converted to class probabilities by applying the softmax function.", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 383, + 506, + 406 + ], + "spans": [ + { + "bbox": [ + 105, + 383, + 222, + 406 + ], + "score": 1.0, + "content": "Namely, the probability that", + "type": "text" + }, + { + "bbox": [ + 223, + 388, + 231, + 397 + ], + "score": 0.64, + "content": "\\mathbf { x }", + "type": "inline_equation" + }, + { + "bbox": [ + 231, + 383, + 322, + 406 + ], + "score": 1.0, + "content": "is classified into class", + "type": "text" + }, + { + "bbox": [ + 322, + 387, + 329, + 398 + ], + "score": 0.81, + "content": "j", + "type": "inline_equation" + }, + { + "bbox": [ + 329, + 383, + 387, + 406 + ], + "score": 1.0, + "content": "is denoted by", + "type": "text" + }, + { + "bbox": [ + 388, + 384, + 501, + 403 + ], + "score": 0.92, + "content": "\\begin{array} { r } { p ( y = j | \\mathbf { x } ) = \\frac { e x p ( l _ { j } ) } { \\sum _ { k = 1 } ^ { K } e x p ( l _ { k } ) } } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 383, + 506, + 406 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 401, + 464, + 415 + ], + "spans": [ + { + "bbox": [ + 106, + 401, + 187, + 415 + ], + "score": 1.0, + "content": "We use the notation", + "type": "text" + }, + { + "bbox": [ + 188, + 401, + 216, + 414 + ], + "score": 0.92, + "content": "p ( \\mathbf { y } \\vert \\mathbf { x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 217, + 401, + 272, + 415 + ], + "score": 1.0, + "content": "to denote the", + "type": "text" + }, + { + "bbox": [ + 272, + 402, + 282, + 412 + ], + "score": 0.82, + "content": "K", + "type": "inline_equation" + }, + { + "bbox": [ + 282, + 401, + 453, + 415 + ], + "score": 1.0, + "content": "-dimensional probabilistic output for input", + "type": "text" + }, + { + "bbox": [ + 453, + 405, + 460, + 411 + ], + "score": 0.49, + "content": "\\mathbf { x }", + "type": "inline_equation" + }, + { + "bbox": [ + 460, + 401, + 464, + 415 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 22.5, + "bbox_fs": [ + 104, + 317, + 506, + 415 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 419, + 505, + 539 + ], + "lines": [ + { + "bbox": [ + 105, + 418, + 505, + 431 + ], + "spans": [ + { + "bbox": [ + 105, + 418, + 133, + 431 + ], + "score": 1.0, + "content": "When", + "type": "text" + }, + { + "bbox": [ + 134, + 419, + 143, + 429 + ], + "score": 0.8, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 144, + 418, + 505, + 431 + ], + "score": 1.0, + "content": "is acting as the critic, we want it to detect the feature encodings of target samples near", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 430, + 505, + 442 + ], + "spans": [ + { + "bbox": [ + 106, + 430, + 287, + 442 + ], + "score": 1.0, + "content": "the decision boundary. 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This change", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 451, + 506, + 464 + ], + "spans": [ + { + "bbox": [ + 105, + 451, + 421, + 464 + ], + "score": 1.0, + "content": "is likely to be largest for samples near the decision boundary. The network", + "type": "text" + }, + { + "bbox": [ + 421, + 452, + 430, + 461 + ], + "score": 0.8, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 431, + 451, + 506, + 464 + ], + "score": 1.0, + "content": "is then trained to", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 461, + 505, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 461, + 351, + 475 + ], + "score": 1.0, + "content": "increase this change, while the feature generation network", + "type": "text" + }, + { + "bbox": [ + 351, + 463, + 360, + 472 + ], + "score": 0.8, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 361, + 461, + 505, + 475 + ], + "score": 1.0, + "content": "is trained to decrease it. Through", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 474, + 505, + 486 + ], + "spans": [ + { + "bbox": [ + 106, + 474, + 206, + 486 + ], + "score": 1.0, + "content": "this adversarial training,", + "type": "text" + }, + { + "bbox": [ + 207, + 474, + 216, + 484 + ], + "score": 0.78, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 216, + 474, + 505, + 486 + ], + "score": 1.0, + "content": "learns to ‘fool’ the critic and generate target features far away from the", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 484, + 506, + 497 + ], + "spans": [ + { + "bbox": [ + 106, + 484, + 395, + 497 + ], + "score": 1.0, + "content": "decision boundary, thus avoiding ambiguous features. The weights of", + "type": "text" + }, + { + "bbox": [ + 396, + 485, + 405, + 494 + ], + "score": 0.81, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 405, + 484, + 506, + 497 + ], + "score": 1.0, + "content": "can be initialized either", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 495, + 506, + 508 + ], + "spans": [ + { + "bbox": [ + 105, + 495, + 474, + 508 + ], + "score": 1.0, + "content": "by pre-training on some auxiliary dataset (e.g., ImageNet), or with random weights, while", + "type": "text" + }, + { + "bbox": [ + 475, + 496, + 484, + 506 + ], + "score": 0.79, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 484, + 495, + 506, + 508 + ], + "score": 1.0, + "content": "uses", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 104, + 506, + 505, + 519 + ], + "spans": [ + { + "bbox": [ + 104, + 506, + 505, + 519 + ], + "score": 1.0, + "content": "random initialization. In the next section, we show how we utilize dropout to perturb the boundary", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 518, + 505, + 530 + ], + "spans": [ + { + "bbox": [ + 105, + 518, + 505, + 530 + ], + "score": 1.0, + "content": "in the critic and measure sensitivity. We then show the training procedure of our method. Finally,", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 529, + 495, + 541 + ], + "spans": [ + { + "bbox": [ + 106, + 529, + 495, + 541 + ], + "score": 1.0, + "content": "we give some intuition behind adversarial dropout and improve our method based on this insight.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 32, + "bbox_fs": [ + 104, + 418, + 506, + 541 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 553, + 296, + 564 + ], + "lines": [ + { + "bbox": [ + 106, + 552, + 298, + 565 + ], + "spans": [ + { + "bbox": [ + 106, + 552, + 298, + 565 + ], + "score": 1.0, + "content": "3.1 CLASSIFIER SELECTION VIA DROPOUT", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 38 + }, + { + "type": "text", + "bbox": [ + 108, + 565, + 504, + 598 + ], + "lines": [ + { + "bbox": [ + 106, + 564, + 505, + 578 + ], + "spans": [ + { + "bbox": [ + 106, + 564, + 505, + 578 + ], + "score": 1.0, + "content": "Consider the standard training of a neural network using dropout. For every sample within a mini-", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 576, + 505, + 588 + ], + "spans": [ + { + "bbox": [ + 106, + 576, + 505, + 588 + ], + "score": 1.0, + "content": "batch, each node of the network is removed with some probability, effectively selecting a different", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 586, + 450, + 601 + ], + "spans": [ + { + "bbox": [ + 106, + 586, + 450, + 601 + ], + "score": 1.0, + "content": "classifier for every sample during training. We harness this idea in a very simple way.", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 40, + "bbox_fs": [ + 106, + 564, + 505, + 601 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 603, + 505, + 681 + ], + "lines": [ + { + "bbox": [ + 105, + 602, + 506, + 617 + ], + "spans": [ + { + "bbox": [ + 105, + 602, + 218, + 617 + ], + "score": 1.0, + "content": "We forward input features", + "type": "text" + }, + { + "bbox": [ + 218, + 604, + 245, + 615 + ], + "score": 0.93, + "content": "G ( \\bf x _ { t } )", + "type": "inline_equation" + }, + { + "bbox": [ + 245, + 602, + 259, + 617 + ], + "score": 1.0, + "content": "to", + "type": "text" + }, + { + "bbox": [ + 259, + 604, + 268, + 614 + ], + "score": 0.82, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 268, + 602, + 506, + 617 + ], + "score": 1.0, + "content": "twice, dropping different nodes each time and obtaining", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 614, + 505, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 614, + 268, + 628 + ], + "score": 1.0, + "content": "two different output vectors denoted as", + "type": "text" + }, + { + "bbox": [ + 268, + 614, + 314, + 627 + ], + "score": 0.86, + "content": "C _ { 1 } ( G ( \\mathbf { x _ { t } } ) )", + "type": "inline_equation" + }, + { + "bbox": [ + 314, + 614, + 319, + 628 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 320, + 614, + 365, + 627 + ], + "score": 0.84, + "content": "\\bar { C } _ { 2 } \\bar { ( \\cal G ( x _ { t } ) ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 365, + 614, + 505, + 628 + ], + "score": 1.0, + "content": ". 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In the figure, the corresponding", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 636, + 505, + 650 + ], + "spans": [ + { + "bbox": [ + 105, + 636, + 259, + 650 + ], + "score": 1.0, + "content": "posterior probabilities are indicated as", + "type": "text" + }, + { + "bbox": [ + 259, + 637, + 297, + 649 + ], + "score": 0.75, + "content": "p _ { 1 } ( \\mathbf { y } | \\mathbf { x _ { t } } )", + "type": "inline_equation" + }, + { + "bbox": [ + 297, + 636, + 300, + 650 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 300, + 636, + 338, + 649 + ], + "score": 0.66, + "content": "p _ { 2 } ( \\mathbf { y } \\vert \\mathbf { x _ { t } } )", + "type": "inline_equation" + }, + { + "bbox": [ + 338, + 636, + 399, + 650 + ], + "score": 1.0, + "content": ", abbreviated as", + "type": "text" + }, + { + "bbox": [ + 400, + 638, + 411, + 648 + ], + "score": 0.86, + "content": "p _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 411, + 636, + 428, + 650 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 428, + 638, + 439, + 648 + ], + "score": 0.85, + "content": "p _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 439, + 636, + 505, + 650 + ], + "score": 1.0, + "content": "in the following", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 647, + 505, + 660 + ], + "spans": [ + { + "bbox": [ + 105, + 647, + 505, + 660 + ], + "score": 1.0, + "content": "discussion. 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Since", + "type": "text" + }, + { + "bbox": [ + 441, + 537, + 451, + 547 + ], + "score": 0.82, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 451, + 536, + 506, + 549 + ], + "score": 1.0, + "content": "should learn", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 547, + 505, + 559 + ], + "spans": [ + { + "bbox": [ + 106, + 547, + 505, + 559 + ], + "score": 1.0, + "content": "discriminative features for source samples, in addition to the sensitivity term, we add Eq. 2. 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Since", + "type": "text" + }, + { + "bbox": [ + 441, + 537, + 451, + 547 + ], + "score": 0.82, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 451, + 536, + 506, + 549 + ], + "score": 1.0, + "content": "should learn", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 547, + 505, + 559 + ], + "spans": [ + { + "bbox": [ + 106, + 547, + 505, + 559 + ], + "score": 1.0, + "content": "discriminative features for source samples, in addition to the sensitivity term, we add Eq. 2. We", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 558, + 428, + 572 + ], + "spans": [ + { + "bbox": [ + 106, + 558, + 428, + 572 + ], + "score": 1.0, + "content": "experimentally confirmed that this term is essential to obtain good performance.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 23, + "bbox_fs": [ + 104, + 514, + 506, + 572 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 247, + 577, + 363, + 595 + ], + "lines": [ + { + "bbox": [ + 247, + 577, + 363, + 595 + ], + "spans": [ + { + "bbox": [ + 247, + 577, + 363, + 595 + ], + "score": 0.92, + "content": "\\operatorname* { m i n } _ { C } L ( X _ { s } , Y _ { s } ) - L _ { a d v } ( X _ { t } )", + "type": "interline_equation", + "image_path": "3bea588dbe0863badf61194488482a3385277235506fa8e3ede248f59902ba58.jpg" + } + ] + } + ], + "index": 26, + "virtual_lines": [ + { + "bbox": [ + 247, + 577, + 363, + 595 + ], + "spans": [], + "index": 26 + } + ] + }, + { + "type": "interline_equation", + "bbox": [ + 205, + 609, + 406, + 623 + ], + "lines": [ + { + "bbox": [ + 205, + 609, + 406, + 623 + ], + "spans": [ + { + "bbox": [ + 205, + 609, + 406, + 623 + ], + "score": 0.87, + "content": "L _ { a d v } ( X _ { t } ) = \\mathbb { E } _ { \\mathbf { x _ { t } } \\sim X _ { t } } [ d ( C _ { 1 } ( G ( \\mathbf { x _ { t } } ) ) , C _ { 2 } ( G ( \\mathbf { x _ { t } } ) ) ) ]", + "type": "interline_equation", + "image_path": "90c1c66e9efafa4cc0f95641a131aedd5cc5ac97e333de274aa5aca963fc4bd1.jpg" + } + ] + } + ], + "index": 27, + "virtual_lines": [ + { + "bbox": [ + 205, + 609, + 406, + 623 + ], + "spans": [], + "index": 27 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 627, + 276, + 639 + ], + "lines": [ + { + "bbox": [ + 107, + 625, + 276, + 642 + ], + "spans": [ + { + "bbox": [ + 107, + 628, + 119, + 639 + ], + "score": 0.87, + "content": "C _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 119, + 625, + 137, + 642 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 138, + 628, + 150, + 639 + ], + "score": 0.88, + "content": "C _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 151, + 625, + 224, + 642 + ], + "score": 1.0, + "content": "are sampled from", + "type": "text" + }, + { + "bbox": [ + 224, + 628, + 233, + 637 + ], + "score": 0.82, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 233, + 625, + 276, + 642 + ], + "score": 1.0, + "content": "randomly.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 28, + "bbox_fs": [ + 107, + 625, + 276, + 642 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 644, + 505, + 678 + ], + "lines": [ + { + "bbox": [ + 105, + 644, + 506, + 658 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 506, + 658 + ], + "score": 1.0, + "content": "Step 3, in order to obtain representations where target samples are placed far from the decision", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 656, + 505, + 668 + ], + "spans": [ + { + "bbox": [ + 105, + 656, + 149, + 668 + ], + "score": 1.0, + "content": "boundary,", + "type": "text" + }, + { + "bbox": [ + 149, + 656, + 158, + 666 + ], + "score": 0.82, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 159, + 656, + 505, + 668 + ], + "score": 1.0, + "content": "is trained to minimize sensitivity. 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We experi-", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 720, + 399, + 732 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 284, + 732 + ], + "score": 1.0, + "content": "mentally found it beneficial to repeat Step 3", + "type": "text" + }, + { + "bbox": [ + 284, + 725, + 291, + 730 + ], + "score": 0.62, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 291, + 720, + 399, + 732 + ], + "score": 1.0, + "content": "times for each mini-batch.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 33.5, + "bbox_fs": [ + 105, + 709, + 504, + 732 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 108, + 81, + 502, + 178 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 108, + 81, + 502, + 178 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 108, + 81, + 502, + 178 + ], + "spans": [ + { + "bbox": [ + 108, + 81, + 502, + 178 + ], + "score": 0.973, + "type": "image", + "image_path": "e236a8f1f63678aa39e6008db6475416d17c9cf2b19a9b860caab2ab1b9a4cd9.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 108, + 81, + 502, + 113.33333333333334 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 108, + 113.33333333333334, + 502, + 145.66666666666669 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 108, + 145.66666666666669, + 502, + 178.00000000000003 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 187, + 506, + 264 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 187, + 506, + 199 + ], + "spans": [ + { + "bbox": [ + 105, + 187, + 506, + 199 + ], + "score": 1.0, + "content": "Figure 3: (Best viewed in color) Toy Experiment. Top row: Model trained without adaptation. Columns 1-5", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 198, + 506, + 211 + ], + "spans": [ + { + "bbox": [ + 105, + 198, + 506, + 211 + ], + "score": 1.0, + "content": "show the decision boundary obtained by keeping one neuron in the last hidden layer and removing the rest.", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 209, + 506, + 222 + ], + "spans": [ + { + "bbox": [ + 105, + 209, + 506, + 222 + ], + "score": 1.0, + "content": "Red points are source samples of class one, green points are class two. Black points are target samples. The", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 221, + 505, + 232 + ], + "spans": [ + { + "bbox": [ + 106, + 221, + 505, + 232 + ], + "score": 1.0, + "content": "yellow region indicates where the samples are classified as class one, cyan region class two. We see that the", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 231, + 505, + 243 + ], + "spans": [ + { + "bbox": [ + 105, + 231, + 505, + 243 + ], + "score": 1.0, + "content": "neurons do not learn very diverse features. Column 6 shows the boundary obtained by keeping all 5 neurons.", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 242, + 506, + 255 + ], + "spans": [ + { + "bbox": [ + 105, + 242, + 506, + 255 + ], + "score": 1.0, + "content": "Bottom row: Boundaries learned by the model adapted by our adversarial dropout method. Unlike the top row,", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 254, + 380, + 264 + ], + "spans": [ + { + "bbox": [ + 106, + 254, + 380, + 264 + ], + "score": 1.0, + "content": "here neurons 3,4,5 learn diverse features which result in diverse boundaries.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 6 + } + ], + "index": 3.5 + }, + { + "type": "title", + "bbox": [ + 107, + 280, + 255, + 291 + ], + "lines": [ + { + "bbox": [ + 106, + 280, + 256, + 292 + ], + "spans": [ + { + "bbox": [ + 106, + 280, + 256, + 292 + ], + "score": 1.0, + "content": "3.3 INSIGHT AND IMPROVEMENT", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 10 + }, + { + "type": "text", + "bbox": [ + 107, + 294, + 505, + 371 + ], + "lines": [ + { + "bbox": [ + 106, + 294, + 505, + 307 + ], + "spans": [ + { + "bbox": [ + 106, + 294, + 505, + 307 + ], + "score": 1.0, + "content": "Our ADR approach encourages different neurons of the classifier to learn different characteristics", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 305, + 505, + 317 + ], + "spans": [ + { + "bbox": [ + 106, + 305, + 505, + 317 + ], + "score": 1.0, + "content": "of the input (see Sec. 4.1.) The output is the combination of shared and unshared nodes, therefore,", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 316, + 505, + 329 + ], + "spans": [ + { + "bbox": [ + 105, + 316, + 505, + 329 + ], + "score": 1.0, + "content": "to maximize the sensitivity, the unshared nodes must learn different features of target samples. As", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 327, + 505, + 340 + ], + "spans": [ + { + "bbox": [ + 106, + 327, + 249, + 340 + ], + "score": 1.0, + "content": "learning proceeds, each neuron in", + "type": "text" + }, + { + "bbox": [ + 249, + 327, + 259, + 337 + ], + "score": 0.78, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 259, + 327, + 505, + 340 + ], + "score": 1.0, + "content": "will capture different characteristics. At the same time, to", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 338, + 505, + 350 + ], + "spans": [ + { + "bbox": [ + 105, + 338, + 210, + 350 + ], + "score": 1.0, + "content": "minimize the sensitivity,", + "type": "text" + }, + { + "bbox": [ + 210, + 338, + 219, + 348 + ], + "score": 0.78, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 220, + 338, + 426, + 350 + ], + "score": 1.0, + "content": "learns to extract pure categorical information. If", + "type": "text" + }, + { + "bbox": [ + 426, + 338, + 436, + 348 + ], + "score": 0.81, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 436, + 338, + 505, + 350 + ], + "score": 1.0, + "content": "outputs features", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 349, + 506, + 361 + ], + "spans": [ + { + "bbox": [ + 106, + 349, + 506, + 361 + ], + "score": 1.0, + "content": "which are not related to categorical information, such as texture, slight contrast or difference of", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 360, + 306, + 372 + ], + "spans": [ + { + "bbox": [ + 106, + 360, + 131, + 372 + ], + "score": 1.0, + "content": "color,", + "type": "text" + }, + { + "bbox": [ + 132, + 360, + 141, + 370 + ], + "score": 0.79, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 141, + 360, + 306, + 372 + ], + "score": 1.0, + "content": "will utilize them to maximize sensitivity.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 14 + }, + { + "type": "text", + "bbox": [ + 107, + 376, + 505, + 476 + ], + "lines": [ + { + "bbox": [ + 106, + 376, + 506, + 389 + ], + "spans": [ + { + "bbox": [ + 106, + 376, + 506, + 389 + ], + "score": 1.0, + "content": "The trained classifier will be sensitive to the perturbation of targets caused by dropout. We note that", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 388, + 505, + 401 + ], + "spans": [ + { + "bbox": [ + 105, + 388, + 505, + 401 + ], + "score": 1.0, + "content": "our approach is contrary to methods called adversarial example training (Goodfellow et al. (2014b);", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 398, + 506, + 412 + ], + "spans": [ + { + "bbox": [ + 105, + 398, + 506, + 412 + ], + "score": 1.0, + "content": "Miyato et al. (2016)) which train the classifier to be robust to adversarial examples. They utilize", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 409, + 505, + 423 + ], + "spans": [ + { + "bbox": [ + 105, + 409, + 505, + 423 + ], + "score": 1.0, + "content": "input noise which can deceive or change the output of the classifier, and incorporate it to obtain", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 420, + 506, + 434 + ], + "spans": [ + { + "bbox": [ + 105, + 420, + 506, + 434 + ], + "score": 1.0, + "content": "a good classifier. Our ADR method encourages the feature generator to obtain noise-robust target", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 432, + 505, + 444 + ], + "spans": [ + { + "bbox": [ + 106, + 432, + 505, + 444 + ], + "score": 1.0, + "content": "features. However, with regard to the classifier, it is trained to be sensitive to noise. To improve the", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 442, + 506, + 455 + ], + "spans": [ + { + "bbox": [ + 105, + 442, + 273, + 455 + ], + "score": 1.0, + "content": "final accuracy, we learn another classifier", + "type": "text" + }, + { + "bbox": [ + 273, + 443, + 285, + 453 + ], + "score": 0.86, + "content": "C ^ { \\prime }", + "type": "inline_equation" + }, + { + "bbox": [ + 285, + 442, + 469, + 455 + ], + "score": 1.0, + "content": "that is not trained to be sensitive to the noise.", + "type": "text" + }, + { + "bbox": [ + 469, + 443, + 481, + 453 + ], + "score": 0.85, + "content": "C ^ { \\prime }", + "type": "inline_equation" + }, + { + "bbox": [ + 481, + 442, + 506, + 455 + ], + "score": 1.0, + "content": "takes", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 453, + 506, + 466 + ], + "spans": [ + { + "bbox": [ + 105, + 453, + 195, + 466 + ], + "score": 1.0, + "content": "features generated by", + "type": "text" + }, + { + "bbox": [ + 195, + 454, + 204, + 464 + ], + "score": 0.81, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 204, + 453, + 482, + 466 + ], + "score": 1.0, + "content": "and is trained with classification loss on source samples. The loss of", + "type": "text" + }, + { + "bbox": [ + 483, + 453, + 494, + 464 + ], + "score": 0.88, + "content": "C ^ { \\prime }", + "type": "inline_equation" + }, + { + "bbox": [ + 495, + 453, + 506, + 466 + ], + "score": 1.0, + "content": "is", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 464, + 505, + 477 + ], + "spans": [ + { + "bbox": [ + 105, + 464, + 181, + 477 + ], + "score": 1.0, + "content": "not used to update", + "type": "text" + }, + { + "bbox": [ + 181, + 465, + 190, + 474 + ], + "score": 0.8, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 190, + 464, + 309, + 477 + ], + "score": 1.0, + "content": ". We compare the accuracy of", + "type": "text" + }, + { + "bbox": [ + 309, + 465, + 318, + 474 + ], + "score": 0.85, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 318, + 464, + 335, + 477 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 336, + 465, + 347, + 474 + ], + "score": 0.88, + "content": "C ^ { \\prime }", + "type": "inline_equation" + }, + { + "bbox": [ + 347, + 464, + 505, + 477 + ], + "score": 1.0, + "content": "in experiments on image classification.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 22 + }, + { + "type": "title", + "bbox": [ + 108, + 497, + 200, + 509 + ], + "lines": [ + { + "bbox": [ + 105, + 496, + 201, + 511 + ], + "spans": [ + { + "bbox": [ + 105, + 496, + 201, + 511 + ], + "score": 1.0, + "content": "4 EXPERIMENTS", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 27 + }, + { + "type": "title", + "bbox": [ + 108, + 525, + 248, + 536 + ], + "lines": [ + { + "bbox": [ + 105, + 524, + 250, + 537 + ], + "spans": [ + { + "bbox": [ + 105, + 524, + 250, + 537 + ], + "score": 1.0, + "content": "4.1 EXPERIMENT ON TOY DATA", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 28 + }, + { + "type": "text", + "bbox": [ + 106, + 539, + 505, + 649 + ], + "lines": [ + { + "bbox": [ + 106, + 539, + 505, + 552 + ], + "spans": [ + { + "bbox": [ + 106, + 539, + 505, + 552 + ], + "score": 1.0, + "content": "Experimental Setting. In this experiment, we observe the decision boundary obtained by each", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 550, + 505, + 562 + ], + "spans": [ + { + "bbox": [ + 106, + 550, + 505, + 562 + ], + "score": 1.0, + "content": "neuron to demonstrate that ADR encourages the neurons to learn different input characteristics. We", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 561, + 506, + 574 + ], + "spans": [ + { + "bbox": [ + 106, + 561, + 506, + 574 + ], + "score": 1.0, + "content": "use synthetic “two moons” data for this problem. Two dimensional samples from two classes are", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 572, + 506, + 585 + ], + "spans": [ + { + "bbox": [ + 105, + 572, + 506, + 585 + ], + "score": 1.0, + "content": "generated as source samples. Target samples are obtained by rotating the source samples. In our", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 583, + 506, + 596 + ], + "spans": [ + { + "bbox": [ + 105, + 583, + 506, + 596 + ], + "score": 1.0, + "content": "setting, the rotation was set to 30 degrees and data was generated with scikit-learn (Pedregosa et al.", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 594, + 506, + 607 + ], + "spans": [ + { + "bbox": [ + 106, + 594, + 506, + 607 + ], + "score": 1.0, + "content": "(2011)). We train a six-layered fully-connected network; the lower 3 layers are used as feature", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 104, + 604, + 505, + 618 + ], + "spans": [ + { + "bbox": [ + 104, + 604, + 505, + 618 + ], + "score": 1.0, + "content": "generator, and upper 3 layers are used as classifier. We used Batch Normalization (Ioffe & Szegedy", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 615, + 505, + 629 + ], + "spans": [ + { + "bbox": [ + 105, + 615, + 505, + 629 + ], + "score": 1.0, + "content": "(2015)) and ReLU as activation function. The number of neurons are [2,5,5] for feature generator,", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 626, + 505, + 640 + ], + "spans": [ + { + "bbox": [ + 105, + 626, + 505, + 640 + ], + "score": 1.0, + "content": "[5,5,2] for classifier. We visualize the boundary obtained from each neuron in the last layer by", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 638, + 273, + 650 + ], + "spans": [ + { + "bbox": [ + 105, + 638, + 273, + 650 + ], + "score": 1.0, + "content": "removing the output of all other neurons.", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 33.5 + }, + { + "type": "text", + "bbox": [ + 107, + 654, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 655, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 505, + 667 + ], + "score": 1.0, + "content": "Results. We show the learned boundary in Fig. 3. In the baseline model trained only with source", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "score": 1.0, + "content": "samples (top row), two of five neurons do not seem to learn an effective boundary, and three neurons", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "score": 1.0, + "content": "learn a similar boundary. On the other hand, in our method (bottom row), although two neurons do", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 689, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 689, + 505, + 700 + ], + "score": 1.0, + "content": "not seem to learn any meaningful boundary, three neurons learn distinctive boundaries, demonstrat-", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "score": 1.0, + "content": "ing greater diversity. Each neuron is trained to be sensitive to the noise caused by target samples. The", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 709, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 505, + 723 + ], + "score": 1.0, + "content": "final decision boundary (rightmost column) classifies most target samples correctly. The accuracy", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 721, + 468, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 721, + 213, + 733 + ], + "score": 1.0, + "content": "of our proposed method is", + "type": "text" + }, + { + "bbox": [ + 213, + 721, + 233, + 731 + ], + "score": 0.85, + "content": "96 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 234, + 721, + 444, + 733 + ], + "score": 1.0, + "content": "whereas the accuracy of the non-adapted model was", + "type": "text" + }, + { + "bbox": [ + 444, + 721, + 464, + 731 + ], + "score": 0.87, + "content": "84 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 464, + 721, + 468, + 733 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 42 + } + ], + "page_idx": 4, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2018", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 308, + 760 + ], + "lines": [ + { + "bbox": [ + 302, + 750, + 309, + 763 + ], + "spans": [ + { + "bbox": [ + 302, + 750, + 309, + 763 + ], + "score": 1.0, + "content": "5", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "image", + "bbox": [ + 108, + 81, + 502, + 178 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 108, + 81, + 502, + 178 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 108, + 81, + 502, + 178 + ], + "spans": [ + { + "bbox": [ + 108, + 81, + 502, + 178 + ], + "score": 0.973, + "type": "image", + "image_path": "e236a8f1f63678aa39e6008db6475416d17c9cf2b19a9b860caab2ab1b9a4cd9.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 108, + 81, + 502, + 113.33333333333334 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 108, + 113.33333333333334, + 502, + 145.66666666666669 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 108, + 145.66666666666669, + 502, + 178.00000000000003 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 187, + 506, + 264 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 187, + 506, + 199 + ], + "spans": [ + { + "bbox": [ + 105, + 187, + 506, + 199 + ], + "score": 1.0, + "content": "Figure 3: (Best viewed in color) Toy Experiment. Top row: Model trained without adaptation. Columns 1-5", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 198, + 506, + 211 + ], + "spans": [ + { + "bbox": [ + 105, + 198, + 506, + 211 + ], + "score": 1.0, + "content": "show the decision boundary obtained by keeping one neuron in the last hidden layer and removing the rest.", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 209, + 506, + 222 + ], + "spans": [ + { + "bbox": [ + 105, + 209, + 506, + 222 + ], + "score": 1.0, + "content": "Red points are source samples of class one, green points are class two. Black points are target samples. The", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 221, + 505, + 232 + ], + "spans": [ + { + "bbox": [ + 106, + 221, + 505, + 232 + ], + "score": 1.0, + "content": "yellow region indicates where the samples are classified as class one, cyan region class two. We see that the", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 231, + 505, + 243 + ], + "spans": [ + { + "bbox": [ + 105, + 231, + 505, + 243 + ], + "score": 1.0, + "content": "neurons do not learn very diverse features. Column 6 shows the boundary obtained by keeping all 5 neurons.", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 242, + 506, + 255 + ], + "spans": [ + { + "bbox": [ + 105, + 242, + 506, + 255 + ], + "score": 1.0, + "content": "Bottom row: Boundaries learned by the model adapted by our adversarial dropout method. Unlike the top row,", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 254, + 380, + 264 + ], + "spans": [ + { + "bbox": [ + 106, + 254, + 380, + 264 + ], + "score": 1.0, + "content": "here neurons 3,4,5 learn diverse features which result in diverse boundaries.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 6 + } + ], + "index": 3.5 + }, + { + "type": "title", + "bbox": [ + 107, + 280, + 255, + 291 + ], + "lines": [ + { + "bbox": [ + 106, + 280, + 256, + 292 + ], + "spans": [ + { + "bbox": [ + 106, + 280, + 256, + 292 + ], + "score": 1.0, + "content": "3.3 INSIGHT AND IMPROVEMENT", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 10 + }, + { + "type": "text", + "bbox": [ + 107, + 294, + 505, + 371 + ], + "lines": [ + { + "bbox": [ + 106, + 294, + 505, + 307 + ], + "spans": [ + { + "bbox": [ + 106, + 294, + 505, + 307 + ], + "score": 1.0, + "content": "Our ADR approach encourages different neurons of the classifier to learn different characteristics", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 305, + 505, + 317 + ], + "spans": [ + { + "bbox": [ + 106, + 305, + 505, + 317 + ], + "score": 1.0, + "content": "of the input (see Sec. 4.1.) The output is the combination of shared and unshared nodes, therefore,", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 316, + 505, + 329 + ], + "spans": [ + { + "bbox": [ + 105, + 316, + 505, + 329 + ], + "score": 1.0, + "content": "to maximize the sensitivity, the unshared nodes must learn different features of target samples. As", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 327, + 505, + 340 + ], + "spans": [ + { + "bbox": [ + 106, + 327, + 249, + 340 + ], + "score": 1.0, + "content": "learning proceeds, each neuron in", + "type": "text" + }, + { + "bbox": [ + 249, + 327, + 259, + 337 + ], + "score": 0.78, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 259, + 327, + 505, + 340 + ], + "score": 1.0, + "content": "will capture different characteristics. At the same time, to", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 338, + 505, + 350 + ], + "spans": [ + { + "bbox": [ + 105, + 338, + 210, + 350 + ], + "score": 1.0, + "content": "minimize the sensitivity,", + "type": "text" + }, + { + "bbox": [ + 210, + 338, + 219, + 348 + ], + "score": 0.78, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 220, + 338, + 426, + 350 + ], + "score": 1.0, + "content": "learns to extract pure categorical information. If", + "type": "text" + }, + { + "bbox": [ + 426, + 338, + 436, + 348 + ], + "score": 0.81, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 436, + 338, + 505, + 350 + ], + "score": 1.0, + "content": "outputs features", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 349, + 506, + 361 + ], + "spans": [ + { + "bbox": [ + 106, + 349, + 506, + 361 + ], + "score": 1.0, + "content": "which are not related to categorical information, such as texture, slight contrast or difference of", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 360, + 306, + 372 + ], + "spans": [ + { + "bbox": [ + 106, + 360, + 131, + 372 + ], + "score": 1.0, + "content": "color,", + "type": "text" + }, + { + "bbox": [ + 132, + 360, + 141, + 370 + ], + "score": 0.79, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 141, + 360, + 306, + 372 + ], + "score": 1.0, + "content": "will utilize them to maximize sensitivity.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 14, + "bbox_fs": [ + 105, + 294, + 506, + 372 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 376, + 505, + 476 + ], + "lines": [ + { + "bbox": [ + 106, + 376, + 506, + 389 + ], + "spans": [ + { + "bbox": [ + 106, + 376, + 506, + 389 + ], + "score": 1.0, + "content": "The trained classifier will be sensitive to the perturbation of targets caused by dropout. We note that", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 388, + 505, + 401 + ], + "spans": [ + { + "bbox": [ + 105, + 388, + 505, + 401 + ], + "score": 1.0, + "content": "our approach is contrary to methods called adversarial example training (Goodfellow et al. (2014b);", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 398, + 506, + 412 + ], + "spans": [ + { + "bbox": [ + 105, + 398, + 506, + 412 + ], + "score": 1.0, + "content": "Miyato et al. (2016)) which train the classifier to be robust to adversarial examples. They utilize", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 409, + 505, + 423 + ], + "spans": [ + { + "bbox": [ + 105, + 409, + 505, + 423 + ], + "score": 1.0, + "content": "input noise which can deceive or change the output of the classifier, and incorporate it to obtain", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 420, + 506, + 434 + ], + "spans": [ + { + "bbox": [ + 105, + 420, + 506, + 434 + ], + "score": 1.0, + "content": "a good classifier. Our ADR method encourages the feature generator to obtain noise-robust target", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 432, + 505, + 444 + ], + "spans": [ + { + "bbox": [ + 106, + 432, + 505, + 444 + ], + "score": 1.0, + "content": "features. However, with regard to the classifier, it is trained to be sensitive to noise. To improve the", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 442, + 506, + 455 + ], + "spans": [ + { + "bbox": [ + 105, + 442, + 273, + 455 + ], + "score": 1.0, + "content": "final accuracy, we learn another classifier", + "type": "text" + }, + { + "bbox": [ + 273, + 443, + 285, + 453 + ], + "score": 0.86, + "content": "C ^ { \\prime }", + "type": "inline_equation" + }, + { + "bbox": [ + 285, + 442, + 469, + 455 + ], + "score": 1.0, + "content": "that is not trained to be sensitive to the noise.", + "type": "text" + }, + { + "bbox": [ + 469, + 443, + 481, + 453 + ], + "score": 0.85, + "content": "C ^ { \\prime }", + "type": "inline_equation" + }, + { + "bbox": [ + 481, + 442, + 506, + 455 + ], + "score": 1.0, + "content": "takes", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 453, + 506, + 466 + ], + "spans": [ + { + "bbox": [ + 105, + 453, + 195, + 466 + ], + "score": 1.0, + "content": "features generated by", + "type": "text" + }, + { + "bbox": [ + 195, + 454, + 204, + 464 + ], + "score": 0.81, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 204, + 453, + 482, + 466 + ], + "score": 1.0, + "content": "and is trained with classification loss on source samples. The loss of", + "type": "text" + }, + { + "bbox": [ + 483, + 453, + 494, + 464 + ], + "score": 0.88, + "content": "C ^ { \\prime }", + "type": "inline_equation" + }, + { + "bbox": [ + 495, + 453, + 506, + 466 + ], + "score": 1.0, + "content": "is", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 464, + 505, + 477 + ], + "spans": [ + { + "bbox": [ + 105, + 464, + 181, + 477 + ], + "score": 1.0, + "content": "not used to update", + "type": "text" + }, + { + "bbox": [ + 181, + 465, + 190, + 474 + ], + "score": 0.8, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 190, + 464, + 309, + 477 + ], + "score": 1.0, + "content": ". We compare the accuracy of", + "type": "text" + }, + { + "bbox": [ + 309, + 465, + 318, + 474 + ], + "score": 0.85, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 318, + 464, + 335, + 477 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 336, + 465, + 347, + 474 + ], + "score": 0.88, + "content": "C ^ { \\prime }", + "type": "inline_equation" + }, + { + "bbox": [ + 347, + 464, + 505, + 477 + ], + "score": 1.0, + "content": "in experiments on image classification.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 22, + "bbox_fs": [ + 105, + 376, + 506, + 477 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 497, + 200, + 509 + ], + "lines": [ + { + "bbox": [ + 105, + 496, + 201, + 511 + ], + "spans": [ + { + "bbox": [ + 105, + 496, + 201, + 511 + ], + "score": 1.0, + "content": "4 EXPERIMENTS", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 27 + }, + { + "type": "title", + "bbox": [ + 108, + 525, + 248, + 536 + ], + "lines": [ + { + "bbox": [ + 105, + 524, + 250, + 537 + ], + "spans": [ + { + "bbox": [ + 105, + 524, + 250, + 537 + ], + "score": 1.0, + "content": "4.1 EXPERIMENT ON TOY DATA", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 28 + }, + { + "type": "text", + "bbox": [ + 106, + 539, + 505, + 649 + ], + "lines": [ + { + "bbox": [ + 106, + 539, + 505, + 552 + ], + "spans": [ + { + "bbox": [ + 106, + 539, + 505, + 552 + ], + "score": 1.0, + "content": "Experimental Setting. In this experiment, we observe the decision boundary obtained by each", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 550, + 505, + 562 + ], + "spans": [ + { + "bbox": [ + 106, + 550, + 505, + 562 + ], + "score": 1.0, + "content": "neuron to demonstrate that ADR encourages the neurons to learn different input characteristics. We", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 561, + 506, + 574 + ], + "spans": [ + { + "bbox": [ + 106, + 561, + 506, + 574 + ], + "score": 1.0, + "content": "use synthetic “two moons” data for this problem. Two dimensional samples from two classes are", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 572, + 506, + 585 + ], + "spans": [ + { + "bbox": [ + 105, + 572, + 506, + 585 + ], + "score": 1.0, + "content": "generated as source samples. Target samples are obtained by rotating the source samples. In our", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 583, + 506, + 596 + ], + "spans": [ + { + "bbox": [ + 105, + 583, + 506, + 596 + ], + "score": 1.0, + "content": "setting, the rotation was set to 30 degrees and data was generated with scikit-learn (Pedregosa et al.", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 594, + 506, + 607 + ], + "spans": [ + { + "bbox": [ + 106, + 594, + 506, + 607 + ], + "score": 1.0, + "content": "(2011)). We train a six-layered fully-connected network; the lower 3 layers are used as feature", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 104, + 604, + 505, + 618 + ], + "spans": [ + { + "bbox": [ + 104, + 604, + 505, + 618 + ], + "score": 1.0, + "content": "generator, and upper 3 layers are used as classifier. We used Batch Normalization (Ioffe & Szegedy", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 615, + 505, + 629 + ], + "spans": [ + { + "bbox": [ + 105, + 615, + 505, + 629 + ], + "score": 1.0, + "content": "(2015)) and ReLU as activation function. The number of neurons are [2,5,5] for feature generator,", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 626, + 505, + 640 + ], + "spans": [ + { + "bbox": [ + 105, + 626, + 505, + 640 + ], + "score": 1.0, + "content": "[5,5,2] for classifier. We visualize the boundary obtained from each neuron in the last layer by", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 638, + 273, + 650 + ], + "spans": [ + { + "bbox": [ + 105, + 638, + 273, + 650 + ], + "score": 1.0, + "content": "removing the output of all other neurons.", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 33.5, + "bbox_fs": [ + 104, + 539, + 506, + 650 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 654, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 655, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 505, + 667 + ], + "score": 1.0, + "content": "Results. We show the learned boundary in Fig. 3. In the baseline model trained only with source", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "score": 1.0, + "content": "samples (top row), two of five neurons do not seem to learn an effective boundary, and three neurons", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "score": 1.0, + "content": "learn a similar boundary. On the other hand, in our method (bottom row), although two neurons do", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 689, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 689, + 505, + 700 + ], + "score": 1.0, + "content": "not seem to learn any meaningful boundary, three neurons learn distinctive boundaries, demonstrat-", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "score": 1.0, + "content": "ing greater diversity. Each neuron is trained to be sensitive to the noise caused by target samples. The", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 709, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 505, + 723 + ], + "score": 1.0, + "content": "final decision boundary (rightmost column) classifies most target samples correctly. The accuracy", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 721, + 468, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 721, + 213, + 733 + ], + "score": 1.0, + "content": "of our proposed method is", + "type": "text" + }, + { + "bbox": [ + 213, + 721, + 233, + 731 + ], + "score": 0.85, + "content": "96 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 234, + 721, + 444, + 733 + ], + "score": 1.0, + "content": "whereas the accuracy of the non-adapted model was", + "type": "text" + }, + { + "bbox": [ + 444, + 721, + 464, + 731 + ], + "score": 0.87, + "content": "84 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 464, + 721, + 468, + 733 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 42, + "bbox_fs": [ + 105, + 655, + 506, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 109, + 79, + 503, + 192 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 109, + 79, + 503, + 192 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 109, + 79, + 503, + 192 + ], + "spans": [ + { + "bbox": [ + 109, + 79, + 503, + 192 + ], + "score": 0.964, + "type": "image", + "image_path": "739f2d31aa495e5a9d6c4fd7b45d22559c2abb1868aa853612bc7403b34eaae2.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 109, + 79, + 503, + 116.66666666666666 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 109, + 116.66666666666666, + 503, + 154.33333333333331 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 109, + 154.33333333333331, + 503, + 191.99999999999997 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 196, + 504, + 218 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 194, + 505, + 210 + ], + "spans": [ + { + "bbox": [ + 105, + 194, + 505, + 210 + ], + "score": 1.0, + "content": "Figure 4: Relationship between sensitivity loss on target (blue line), on source (yellow line), and accuracy", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 207, + 360, + 219 + ], + "spans": [ + { + "bbox": [ + 105, + 207, + 171, + 219 + ], + "score": 1.0, + "content": "(red: accuracy of", + "type": "text" + }, + { + "bbox": [ + 172, + 207, + 182, + 217 + ], + "score": 0.85, + "content": "C ^ { \\prime }", + "type": "inline_equation" + }, + { + "bbox": [ + 182, + 207, + 256, + 219 + ], + "score": 1.0, + "content": ", green: accuracy of", + "type": "text" + }, + { + "bbox": [ + 256, + 208, + 264, + 217 + ], + "score": 0.73, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 265, + 207, + 360, + 219 + ], + "score": 1.0, + "content": ") during training on digits.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 3.5 + } + ], + "index": 2.25 + }, + { + "type": "title", + "bbox": [ + 107, + 243, + 389, + 254 + ], + "lines": [ + { + "bbox": [ + 105, + 241, + 391, + 255 + ], + "spans": [ + { + "bbox": [ + 105, + 241, + 391, + 255 + ], + "score": 1.0, + "content": "4.2 UNSUPERVISED DOMAIN ADAPTATION FOR CLASSIFICATION", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 5 + }, + { + "type": "text", + "bbox": [ + 106, + 270, + 505, + 424 + ], + "lines": [ + { + "bbox": [ + 106, + 270, + 504, + 282 + ], + "spans": [ + { + "bbox": [ + 106, + 270, + 504, + 282 + ], + "score": 1.0, + "content": "Experiments on Digits Classification. We evaluate our model on adaptation between digits", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 281, + 505, + 294 + ], + "spans": [ + { + "bbox": [ + 105, + 281, + 505, + 294 + ], + "score": 1.0, + "content": "datasets. We use MNIST (LeCun et al. (1998)), SVHN (Netzer et al. (2011)) and USPS datasets", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 291, + 504, + 304 + ], + "spans": [ + { + "bbox": [ + 106, + 291, + 504, + 304 + ], + "score": 1.0, + "content": "and follow the protocol of unsupervised domain adaptation used by (Tzeng et al. (2017)). To exten-", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 303, + 505, + 316 + ], + "spans": [ + { + "bbox": [ + 105, + 303, + 505, + 316 + ], + "score": 1.0, + "content": "sively compare our method with previous methods, in adaptation from MNIST to USPS, we applied", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 314, + 506, + 327 + ], + "spans": [ + { + "bbox": [ + 105, + 314, + 506, + 327 + ], + "score": 1.0, + "content": "our method to a different protocol used in Bousmalis et al. (2017). We assume no labeled target", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 326, + 505, + 337 + ], + "spans": [ + { + "bbox": [ + 106, + 326, + 505, + 337 + ], + "score": 1.0, + "content": "samples and use fixed hyper-parameters for all experiments, unlike other works that use a target", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 336, + 505, + 348 + ], + "spans": [ + { + "bbox": [ + 106, + 336, + 439, + 348 + ], + "score": 1.0, + "content": "validation set (Saito et al. (2017)). The number of iterations for Step 3 was fixed at", + "type": "text" + }, + { + "bbox": [ + 439, + 336, + 464, + 346 + ], + "score": 0.89, + "content": "n = 4", + "type": "inline_equation" + }, + { + "bbox": [ + 465, + 336, + 505, + 348 + ], + "score": 1.0, + "content": ". We used", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 347, + 506, + 360 + ], + "spans": [ + { + "bbox": [ + 106, + 347, + 506, + 360 + ], + "score": 1.0, + "content": "the same network architecture as in (Tzeng et al. (2017)), but inserted a Batch Normalization layer", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 358, + 505, + 371 + ], + "spans": [ + { + "bbox": [ + 105, + 358, + 505, + 371 + ], + "score": 1.0, + "content": "before the activation layer to stabilize the training. We used Adam (Kingma & Ba (2014)) for opti-", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 368, + 507, + 383 + ], + "spans": [ + { + "bbox": [ + 105, + 368, + 239, + 383 + ], + "score": 1.0, + "content": "mizer and set the learning rate to", + "type": "text" + }, + { + "bbox": [ + 239, + 369, + 284, + 380 + ], + "score": 0.93, + "content": "2 . 0 \\times 1 0 ^ { - 4 }", + "type": "inline_equation" + }, + { + "bbox": [ + 285, + 368, + 507, + 383 + ], + "score": 1.0, + "content": ", a value commonly reported in the GAN literature. We", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 380, + 505, + 392 + ], + "spans": [ + { + "bbox": [ + 105, + 380, + 505, + 392 + ], + "score": 1.0, + "content": "compare our approach to several existing methods and to the entropy minimization baseline (ENT)", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 390, + 506, + 403 + ], + "spans": [ + { + "bbox": [ + 106, + 390, + 506, + 403 + ], + "score": 1.0, + "content": "obtained by modifying (Springenberg (2015)). As we mentioned in Section 2, this is a model that", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 402, + 506, + 415 + ], + "spans": [ + { + "bbox": [ + 105, + 402, + 506, + 415 + ], + "score": 1.0, + "content": "generates features to minimize the entropy of the output probability for target samples. Due to space", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 412, + 420, + 425 + ], + "spans": [ + { + "bbox": [ + 106, + 412, + 420, + 425 + ], + "score": 1.0, + "content": "limitations, we provide a detailed explanation of this baseline in the appendix.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 12.5 + }, + { + "type": "text", + "bbox": [ + 107, + 429, + 505, + 649 + ], + "lines": [ + { + "bbox": [ + 106, + 429, + 505, + 442 + ], + "spans": [ + { + "bbox": [ + 106, + 429, + 505, + 442 + ], + "score": 1.0, + "content": "Results in Table 1 demonstrate that ADR obtains better performance than existing methods. In", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 441, + 505, + 452 + ], + "spans": [ + { + "bbox": [ + 105, + 441, + 505, + 452 + ], + "score": 1.0, + "content": "particular, on the challenging adaptation task from SVHN to MNIST, our method achieves much", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 452, + 506, + 464 + ], + "spans": [ + { + "bbox": [ + 106, + 452, + 506, + 464 + ], + "score": 1.0, + "content": "better accuracy than previously reported. Fig. 4 shows the learning curve of each experiment. As", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 463, + 506, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 463, + 431, + 475 + ], + "score": 1.0, + "content": "sensitivity loss increases, the target accuracy improves. This means that as critic", + "type": "text" + }, + { + "bbox": [ + 431, + 463, + 441, + 473 + ], + "score": 0.79, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 441, + 463, + 506, + 475 + ], + "score": 1.0, + "content": "learns to detect", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 471, + 506, + 487 + ], + "spans": [ + { + "bbox": [ + 105, + 471, + 304, + 487 + ], + "score": 1.0, + "content": "the non-discriminative samples, feature generator", + "type": "text" + }, + { + "bbox": [ + 304, + 474, + 313, + 484 + ], + "score": 0.81, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 314, + 471, + 506, + 487 + ], + "score": 1.0, + "content": "learns to fool it, resulting in improved accuracy.", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 484, + 505, + 497 + ], + "spans": [ + { + "bbox": [ + 105, + 484, + 505, + 497 + ], + "score": 1.0, + "content": "In addition, we can see that the sensitivity of source samples increases too. As mentioned in Sec 3.3,", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 495, + 505, + 508 + ], + "spans": [ + { + "bbox": [ + 105, + 495, + 505, + 508 + ], + "score": 1.0, + "content": "the critic network should learn to capture features which are not very important for classification,", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 506, + 505, + 519 + ], + "spans": [ + { + "bbox": [ + 106, + 506, + 505, + 519 + ], + "score": 1.0, + "content": "such as texture or slight edges, and it seems to also capture such information in source samples. The", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 518, + 506, + 529 + ], + "spans": [ + { + "bbox": [ + 105, + 518, + 210, + 529 + ], + "score": 1.0, + "content": "accuracy of the classifier", + "type": "text" + }, + { + "bbox": [ + 210, + 518, + 222, + 528 + ], + "score": 0.86, + "content": "C ^ { \\prime }", + "type": "inline_equation" + }, + { + "bbox": [ + 223, + 518, + 506, + 529 + ], + "score": 1.0, + "content": "(denoted by red), which is trained not to be sensitive to the noise, is", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 528, + 506, + 541 + ], + "spans": [ + { + "bbox": [ + 106, + 528, + 506, + 541 + ], + "score": 1.0, + "content": "almost always better than the accuracy of the critic network. In adaptation from SVHN to MNIST", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 540, + 505, + 552 + ], + "spans": [ + { + "bbox": [ + 106, + 540, + 505, + 552 + ], + "score": 1.0, + "content": "(Fig. 5(c)), the accuracy of the critic often suffers as it becomes too sensitive to the noise caused by", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 550, + 505, + 562 + ], + "spans": [ + { + "bbox": [ + 105, + 550, + 505, + 562 + ], + "score": 1.0, + "content": "dropout. On the other hand, the accuracy shown by the red line is stable. Our ENT baseline shows", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 561, + 506, + 573 + ], + "spans": [ + { + "bbox": [ + 105, + 561, + 506, + 573 + ], + "score": 1.0, + "content": "good performance compared to other existing methods. This result indicates the effectiveness of", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 572, + 505, + 585 + ], + "spans": [ + { + "bbox": [ + 106, + 572, + 505, + 585 + ], + "score": 1.0, + "content": "methods based on entropy minimization. In Fig. 5, we compare our proposed method and ENT in", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 584, + 504, + 595 + ], + "spans": [ + { + "bbox": [ + 106, + 584, + 504, + 595 + ], + "score": 1.0, + "content": "terms of entropy of target samples. Our method clearly decreases the entropy, because target samples", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 104, + 593, + 505, + 607 + ], + "spans": [ + { + "bbox": [ + 104, + 593, + 505, + 607 + ], + "score": 1.0, + "content": "are moved away from the decision boundary. Yet, its behavior is different from ENT. Interestingly,", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 604, + 505, + 618 + ], + "spans": [ + { + "bbox": [ + 105, + 604, + 505, + 618 + ], + "score": 1.0, + "content": "the entropy is made smaller than ENT in case of adaptation from USPS to MNIST (Fig. 4(a)) though", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 104, + 614, + 505, + 630 + ], + "spans": [ + { + "bbox": [ + 104, + 614, + 505, + 630 + ], + "score": 1.0, + "content": "ENT directly minimizes the entropy and our method does not. On the SVHN to MNIST task (Fig.", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 626, + 506, + 640 + ], + "spans": [ + { + "bbox": [ + 105, + 626, + 506, + 640 + ], + "score": 1.0, + "content": "4(c)), the entropy of ADR is larger than ENT, which indicates that our method places the target", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 638, + 333, + 650 + ], + "spans": [ + { + "bbox": [ + 105, + 638, + 333, + 650 + ], + "score": 1.0, + "content": "samples closer to the decision boundary than ENT does.", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 29.5 + }, + { + "type": "text", + "bbox": [ + 107, + 655, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "score": 1.0, + "content": "Experiments on Object Classification. We next evaluate our method on fine-tuning a pretrained", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "score": 1.0, + "content": "CNN. We use a new domain adaptation benchmark called the VisDA Challenge (Peng et al. (2017))", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 676, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 676, + 505, + 689 + ], + "score": 1.0, + "content": "which focuses on the challenging task of adapting from synthetic to real images. The source domain", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 688, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 688, + 505, + 700 + ], + "score": 1.0, + "content": "consists of 152,409 synthetic 2D images from 12 object classes rendered from 3D models. The", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 699, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 505, + 711 + ], + "score": 1.0, + "content": "validation and test target domains consists of real images, which belong to the same classes. 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We evaluate our model on adaptation between digits", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 281, + 505, + 294 + ], + "spans": [ + { + "bbox": [ + 105, + 281, + 505, + 294 + ], + "score": 1.0, + "content": "datasets. We use MNIST (LeCun et al. (1998)), SVHN (Netzer et al. (2011)) and USPS datasets", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 291, + 504, + 304 + ], + "spans": [ + { + "bbox": [ + 106, + 291, + 504, + 304 + ], + "score": 1.0, + "content": "and follow the protocol of unsupervised domain adaptation used by (Tzeng et al. (2017)). To exten-", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 303, + 505, + 316 + ], + "spans": [ + { + "bbox": [ + 105, + 303, + 505, + 316 + ], + "score": 1.0, + "content": "sively compare our method with previous methods, in adaptation from MNIST to USPS, we applied", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 314, + 506, + 327 + ], + "spans": [ + { + "bbox": [ + 105, + 314, + 506, + 327 + ], + "score": 1.0, + "content": "our method to a different protocol used in Bousmalis et al. (2017). We assume no labeled target", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 326, + 505, + 337 + ], + "spans": [ + { + "bbox": [ + 106, + 326, + 505, + 337 + ], + "score": 1.0, + "content": "samples and use fixed hyper-parameters for all experiments, unlike other works that use a target", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 336, + 505, + 348 + ], + "spans": [ + { + "bbox": [ + 106, + 336, + 439, + 348 + ], + "score": 1.0, + "content": "validation set (Saito et al. (2017)). The number of iterations for Step 3 was fixed at", + "type": "text" + }, + { + "bbox": [ + 439, + 336, + 464, + 346 + ], + "score": 0.89, + "content": "n = 4", + "type": "inline_equation" + }, + { + "bbox": [ + 465, + 336, + 505, + 348 + ], + "score": 1.0, + "content": ". 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We used Adam (Kingma & Ba (2014)) for opti-", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 368, + 507, + 383 + ], + "spans": [ + { + "bbox": [ + 105, + 368, + 239, + 383 + ], + "score": 1.0, + "content": "mizer and set the learning rate to", + "type": "text" + }, + { + "bbox": [ + 239, + 369, + 284, + 380 + ], + "score": 0.93, + "content": "2 . 0 \\times 1 0 ^ { - 4 }", + "type": "inline_equation" + }, + { + "bbox": [ + 285, + 368, + 507, + 383 + ], + "score": 1.0, + "content": ", a value commonly reported in the GAN literature. We", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 380, + 505, + 392 + ], + "spans": [ + { + "bbox": [ + 105, + 380, + 505, + 392 + ], + "score": 1.0, + "content": "compare our approach to several existing methods and to the entropy minimization baseline (ENT)", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 390, + 506, + 403 + ], + "spans": [ + { + "bbox": [ + 106, + 390, + 506, + 403 + ], + "score": 1.0, + "content": "obtained by modifying (Springenberg (2015)). As we mentioned in Section 2, this is a model that", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 402, + 506, + 415 + ], + "spans": [ + { + "bbox": [ + 105, + 402, + 506, + 415 + ], + "score": 1.0, + "content": "generates features to minimize the entropy of the output probability for target samples. Due to space", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 412, + 420, + 425 + ], + "spans": [ + { + "bbox": [ + 106, + 412, + 420, + 425 + ], + "score": 1.0, + "content": "limitations, we provide a detailed explanation of this baseline in the appendix.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 12.5, + "bbox_fs": [ + 105, + 270, + 507, + 425 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 429, + 505, + 649 + ], + "lines": [ + { + "bbox": [ + 106, + 429, + 505, + 442 + ], + "spans": [ + { + "bbox": [ + 106, + 429, + 505, + 442 + ], + "score": 1.0, + "content": "Results in Table 1 demonstrate that ADR obtains better performance than existing methods. In", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 441, + 505, + 452 + ], + "spans": [ + { + "bbox": [ + 105, + 441, + 505, + 452 + ], + "score": 1.0, + "content": "particular, on the challenging adaptation task from SVHN to MNIST, our method achieves much", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 452, + 506, + 464 + ], + "spans": [ + { + "bbox": [ + 106, + 452, + 506, + 464 + ], + "score": 1.0, + "content": "better accuracy than previously reported. Fig. 4 shows the learning curve of each experiment. As", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 463, + 506, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 463, + 431, + 475 + ], + "score": 1.0, + "content": "sensitivity loss increases, the target accuracy improves. This means that as critic", + "type": "text" + }, + { + "bbox": [ + 431, + 463, + 441, + 473 + ], + "score": 0.79, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 441, + 463, + 506, + 475 + ], + "score": 1.0, + "content": "learns to detect", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 471, + 506, + 487 + ], + "spans": [ + { + "bbox": [ + 105, + 471, + 304, + 487 + ], + "score": 1.0, + "content": "the non-discriminative samples, feature generator", + "type": "text" + }, + { + "bbox": [ + 304, + 474, + 313, + 484 + ], + "score": 0.81, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 314, + 471, + 506, + 487 + ], + "score": 1.0, + "content": "learns to fool it, resulting in improved accuracy.", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 484, + 505, + 497 + ], + "spans": [ + { + "bbox": [ + 105, + 484, + 505, + 497 + ], + "score": 1.0, + "content": "In addition, we can see that the sensitivity of source samples increases too. As mentioned in Sec 3.3,", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 495, + 505, + 508 + ], + "spans": [ + { + "bbox": [ + 105, + 495, + 505, + 508 + ], + "score": 1.0, + "content": "the critic network should learn to capture features which are not very important for classification,", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 506, + 505, + 519 + ], + "spans": [ + { + "bbox": [ + 106, + 506, + 505, + 519 + ], + "score": 1.0, + "content": "such as texture or slight edges, and it seems to also capture such information in source samples. 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This result indicates the effectiveness of", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 572, + 505, + 585 + ], + "spans": [ + { + "bbox": [ + 106, + 572, + 505, + 585 + ], + "score": 1.0, + "content": "methods based on entropy minimization. In Fig. 5, we compare our proposed method and ENT in", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 584, + 504, + 595 + ], + "spans": [ + { + "bbox": [ + 106, + 584, + 504, + 595 + ], + "score": 1.0, + "content": "terms of entropy of target samples. Our method clearly decreases the entropy, because target samples", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 104, + 593, + 505, + 607 + ], + "spans": [ + { + "bbox": [ + 104, + 593, + 505, + 607 + ], + "score": 1.0, + "content": "are moved away from the decision boundary. Yet, its behavior is different from ENT. Interestingly,", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 604, + 505, + 618 + ], + "spans": [ + { + "bbox": [ + 105, + 604, + 505, + 618 + ], + "score": 1.0, + "content": "the entropy is made smaller than ENT in case of adaptation from USPS to MNIST (Fig. 4(a)) though", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 104, + 614, + 505, + 630 + ], + "spans": [ + { + "bbox": [ + 104, + 614, + 505, + 630 + ], + "score": 1.0, + "content": "ENT directly minimizes the entropy and our method does not. 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The entropy is calculated on", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 203, + 291, + 215 + ], + "spans": [ + { + "bbox": [ + 105, + 203, + 291, + 215 + ], + "score": 1.0, + "content": "target samples by using the output of the classifier.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 3.5 + } + ], + "index": 2.25 + }, + { + "type": "table", + "bbox": [ + 115, + 218, + 494, + 372 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 115, + 218, + 494, + 372 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 115, + 218, + 494, + 372 + ], + "spans": [ + { + "bbox": [ + 115, + 218, + 494, + 372 + ], + "score": 0.977, + "html": "
METHODSVHN to MNISTUSPS to MNISTMNIST(P1) to USPSMNIST(P2) to USPS
Source Only67.168.177.078.9
LTN (Sener et al. (2016))78.8-1-
ATDA (Saito et al. (2017))86.2†=1-
DSN (Bousmalis et al. (2016))82.7†91.3†
PixelDA (Bousmalis et al. (2017)1=-95.9†
DANN (Ganin & Lempitsky (2014))73.973.0±2.077.1±1.885.1†
DoC (Tzeng et al. (2014))68.1±0.366.5±3.379.1±0.51
ADDA (Tzeng et al. (2017))76.0±1.890.1±0.889.4±0.2-
CoGAN (Liu & Tuzel (2016))did not converge89.1±0.891.2±0.8=
DTN (Taigman et al. (2016))84.71-
ENT (Our proposed baseline) Ours94.9±4.11 95.0±1.8791.2±1.92 93.1±1.2793.7±0.54 93.2±2.4696.7±1.27 96.1±0.29
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Please note that", + "type": "text" + }, + { + "bbox": [ + 304, + 381, + 310, + 392 + ], + "score": 0.81, + "content": "^ \\dagger", + "type": "inline_equation" + }, + { + "bbox": [ + 311, + 380, + 505, + 393 + ], + "score": 1.0, + "content": "means the result obtained using a few labeled target", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 390, + 505, + 405 + ], + "spans": [ + { + "bbox": [ + 105, + 390, + 384, + 405 + ], + "score": 1.0, + "content": "samples for validation. The reported accuracy of our method is obtained from", + "type": "text" + }, + { + "bbox": [ + 384, + 391, + 395, + 401 + ], + "score": 0.85, + "content": "C ^ { \\prime }", + "type": "inline_equation" + }, + { + "bbox": [ + 396, + 390, + 505, + 405 + ], + "score": 1.0, + "content": ". 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METHODSVHN to MNISTUSPS to MNISTMNIST(P1) to USPSMNIST(P2) to USPS
Source Only67.168.177.078.9
LTN (Sener et al. (2016))78.8-1-
ATDA (Saito et al. (2017))86.2†=1-
DSN (Bousmalis et al. (2016))82.7†91.3†
PixelDA (Bousmalis et al. (2017)1=-95.9†
DANN (Ganin & Lempitsky (2014))73.973.0±2.077.1±1.885.1†
DoC (Tzeng et al. (2014))68.1±0.366.5±3.379.1±0.51
ADDA (Tzeng et al. (2017))76.0±1.890.1±0.889.4±0.2-
CoGAN (Liu & Tuzel (2016))did not converge89.1±0.891.2±0.8=
DTN (Taigman et al. (2016))84.71-
ENT (Our proposed baseline) Ours94.9±4.11 95.0±1.8791.2±1.92 93.1±1.2793.7±0.54 93.2±2.4696.7±1.27 96.1±0.29
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While the embedding of the source only model does not separate", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 599, + 443, + 612 + ], + "spans": [ + { + "bbox": [ + 105, + 599, + 443, + 612 + ], + "score": 1.0, + "content": "classes well due to domain shift, we can see clearly improved separation with ADR.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 24, + "bbox_fs": [ + 105, + 577, + 504, + 612 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 616, + 505, + 693 + ], + "lines": [ + { + "bbox": [ + 105, + 615, + 505, + 630 + ], + "spans": [ + { + "bbox": [ + 105, + 615, + 505, + 630 + ], + "score": 1.0, + "content": "Image Segmentation experiments. Next, we apply our method to adaptation for semantic image", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 627, + 505, + 639 + ], + "spans": [ + { + "bbox": [ + 105, + 627, + 505, + 639 + ], + "score": 1.0, + "content": "segmentation. Image segmentation is different from classification in that we classify each pixel in", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 638, + 505, + 650 + ], + "spans": [ + { + "bbox": [ + 105, + 638, + 505, + 650 + ], + "score": 1.0, + "content": "the image. To evaluate the performance on segmentation, the synthetic GTA5 (Richter et al. (2016))", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 648, + 505, + 662 + ], + "spans": [ + { + "bbox": [ + 105, + 648, + 505, + 662 + ], + "score": 1.0, + "content": "dataset is used as source, and real CityScape (Cordts et al. (2016)) dataset is used as target. Previous", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 659, + 505, + 672 + ], + "spans": [ + { + "bbox": [ + 106, + 659, + 505, + 672 + ], + "score": 1.0, + "content": "work tackled this problem by matching distributions of each pixel’s feature in a middle layer of the", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 670, + 506, + 684 + ], + "spans": [ + { + "bbox": [ + 105, + 670, + 506, + 684 + ], + "score": 1.0, + "content": "network (Hoffman et al. (2016)). In this work, we apply ADR by calculating sensitivity between all", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 682, + 437, + 695 + ], + "spans": [ + { + "bbox": [ + 106, + 682, + 437, + 695 + ], + "score": 1.0, + "content": "pixels. The training procedure is exactly the same as in classification experiments.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 29, + "bbox_fs": [ + 105, + 615, + 506, + 695 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 699, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 699, + 506, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 506, + 711 + ], + "score": 1.0, + "content": "We use the ResNet50 pretrained on ImageNet, and utilize an FCN (Long et al. (2015a)) based", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "network architecture. Further, we utilize the more recent Dilated Residual Networks (DRN) 105", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 721, + 504, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 504, + 733 + ], + "score": 1.0, + "content": "layered model (Yu et al. (2017)), which outperforms ResNet50 on a semantic segmentation task.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 34, + "bbox_fs": [ + 106, + 699, + 506, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 143, + 81, + 469, + 253 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 143, + 81, + 469, + 253 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 143, + 81, + 469, + 253 + ], + "spans": [ + { + "bbox": [ + 143, + 81, + 469, + 253 + ], + "score": 0.98, + "html": "
Methodgrrrdoraegpaleie 3ueoormorreiltuosiadsareraertrnaaa
Finetuning on ResNet101
Source Only55.153.3 61.959.180.617.979.731.281.026.573.58.552.4
MMD87.163.0 76.542.090.342.985.953.149.736.385.820.761.1
DANN81.977.7 82.844.381.229.565.128.651.954.682.87.857.4
ENT80.375.5 75.848.377.927.369.740.246.546.679.316.057.0
Ours94.151.3 83.272.288.768.892.870.277.263.682.930.372.9
Ours (retrained classifier)94.248.5 84.072.990.174.292.672.580.861.882.228.873.5
Finetuning on ResNeXt
Source Only74.3 37.6 61.8 68.2 59.510.7 81.412.8 61.6 26.070.05.647.4
MMD90.751.1 64.865.689.946.591.940.181.524.190.028.563.7
DANN86.066.3 60.8 56.079.853.782.325.258.231.089.326.159.6
ENT94.781.0 57.046.673.949.069.231.040.534.387.315.156.6
Ours86.3 71.987.678.193.084.894.578.991.858.977.726.777.5
Ours (retrained classifier)89.270.9 85.782.093.786.7 93.372.389.553.086.728.377.6
", + "type": "table", + "image_path": "f1424f829d13d5222f78094f2d533a494b462bd17dd04b218b7d8dfb038049e0.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 143, + 81, + 469, + 138.33333333333334 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 143, + 138.33333333333334, + 469, + 195.66666666666669 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 143, + 195.66666666666669, + 469, + 253.00000000000003 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "table_caption", + "bbox": [ + 106, + 257, + 506, + 300 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 256, + 505, + 268 + ], + "spans": [ + { + "bbox": [ + 105, + 256, + 505, + 268 + ], + "score": 1.0, + "content": "Table 2: Results on Visda2017 classification datasets (Peng et al. (2017)). DANN and MMD are distribution", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 268, + 505, + 279 + ], + "spans": [ + { + "bbox": [ + 106, + 268, + 505, + 279 + ], + "score": 1.0, + "content": "alignment methods proposed by (Ganin & Lempitsky (2014)) and (Long et al. (2015b)) respectively. Ours", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 279, + 506, + 291 + ], + "spans": [ + { + "bbox": [ + 106, + 279, + 506, + 291 + ], + "score": 1.0, + "content": "(retrain classifier) means the classifier retrained for our proposed generator as we mentioned in Sec 3.3. Our", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 290, + 370, + 302 + ], + "spans": [ + { + "bbox": [ + 105, + 290, + 370, + 302 + ], + "score": 1.0, + "content": "proposed method shows much better performance than existing methods.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 4.5 + } + ], + "index": 2.75 + }, + { + "type": "image", + "bbox": [ + 142, + 319, + 471, + 436 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 142, + 319, + 471, + 436 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 142, + 319, + 471, + 436 + ], + "spans": [ + { + "bbox": [ + 142, + 319, + 471, + 436 + ], + "score": 0.971, + "type": "image", + "image_path": "f85e9efe625959ba93fdcfd4024851f548acbeebd038701c1fb299173a9f68e4.jpg" + } + ] + } + ], + "index": 8, + "virtual_lines": [ + { + "bbox": [ + 142, + 319, + 471, + 358.0 + ], + "spans": [], + "index": 7 + }, + { + "bbox": [ + 142, + 358.0, + 471, + 397.0 + ], + "spans": [], + "index": 8 + }, + { + "bbox": [ + 142, + 397.0, + 471, + 436.0 + ], + "spans": [], + "index": 9 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 107, + 444, + 504, + 484 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 443, + 505, + 456 + ], + "spans": [ + { + "bbox": [ + 105, + 443, + 505, + 456 + ], + "score": 1.0, + "content": "Figure 6: Visualization of VisDA-classification (12 classes) target features using T-SNE (Maaten & Hinton", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 454, + 505, + 466 + ], + "spans": [ + { + "bbox": [ + 106, + 454, + 505, + 466 + ], + "score": 1.0, + "content": "(2008)): (a) features obtained by the Imagenet-pretrained ResNext model not finetuned on VisDA; (b) features", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 463, + 505, + 476 + ], + "spans": [ + { + "bbox": [ + 105, + 463, + 505, + 476 + ], + "score": 1.0, + "content": "from the ResNext model fine-tuned only on VisDA source samples without any adaptation; (c) features obtained", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 474, + 259, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 474, + 259, + 486 + ], + "score": 1.0, + "content": "by ResNext adapted by our ADR method.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 11.5 + } + ], + "index": 9.75 + }, + { + "type": "text", + "bbox": [ + 107, + 494, + 505, + 550 + ], + "lines": [ + { + "bbox": [ + 105, + 493, + 505, + 507 + ], + "spans": [ + { + "bbox": [ + 105, + 493, + 505, + 507 + ], + "score": 1.0, + "content": "For the feature generator, we use the pretrained network without fully-connected layers. For the", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 504, + 505, + 519 + ], + "spans": [ + { + "bbox": [ + 105, + 504, + 505, + 519 + ], + "score": 1.0, + "content": "classifier, we use a fully-convolutional network with dropout layers. Due to limited memory, the", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 515, + 505, + 529 + ], + "spans": [ + { + "bbox": [ + 105, + 515, + 505, + 529 + ], + "score": 1.0, + "content": "batch size is set to 1. We include details of the network architecture in appendix. For comparison,", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 527, + 506, + 540 + ], + "spans": [ + { + "bbox": [ + 105, + 527, + 506, + 540 + ], + "score": 1.0, + "content": "we train a domain classifier based model for our network (DANN). We build a domain classifier", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 538, + 397, + 551 + ], + "spans": [ + { + "bbox": [ + 105, + 538, + 397, + 551 + ], + "score": 1.0, + "content": "network for the features of each pixel following (Hoffman et al. (2016)).", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 16 + }, + { + "type": "text", + "bbox": [ + 107, + 555, + 505, + 676 + ], + "lines": [ + { + "bbox": [ + 105, + 555, + 505, + 568 + ], + "spans": [ + { + "bbox": [ + 105, + 555, + 505, + 568 + ], + "score": 1.0, + "content": "In Table 3, we show the qualitative comparison with existing methods. ADR clearly improves mean", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 565, + 505, + 579 + ], + "spans": [ + { + "bbox": [ + 105, + 565, + 505, + 579 + ], + "score": 1.0, + "content": "IoU (Intersection-over-Union) compared to the source-only and competing models, beating state-of-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 577, + 506, + 591 + ], + "spans": [ + { + "bbox": [ + 105, + 577, + 506, + 591 + ], + "score": 1.0, + "content": "the-art by a large margin. When we apply ADR to DRN, the accuracy improves much more than for", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 588, + 506, + 600 + ], + "spans": [ + { + "bbox": [ + 105, + 588, + 506, + 600 + ], + "score": 1.0, + "content": "ResNet50, and is 12.4 points higher than the model trained only on GTA5 source samples. This is", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 598, + 506, + 613 + ], + "spans": [ + { + "bbox": [ + 105, + 598, + 506, + 613 + ], + "score": 1.0, + "content": "likely because ADR exploits the strong representation of the pretrained DRN network. Although we", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 610, + 505, + 622 + ], + "spans": [ + { + "bbox": [ + 105, + 610, + 505, + 622 + ], + "score": 1.0, + "content": "implemented ENT in this setting, the accuracy was much worse than the Source Only model with", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 621, + 505, + 633 + ], + "spans": [ + { + "bbox": [ + 105, + 621, + 505, + 633 + ], + "score": 1.0, + "content": "a mIoU of 15.0 in training ResNet50. The ENT method does not seem to work well on synthetic-", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 632, + 505, + 645 + ], + "spans": [ + { + "bbox": [ + 105, + 632, + 505, + 645 + ], + "score": 1.0, + "content": "to-real shifts. Finally, we illustrate our method’s improvement on example input images, ground", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 642, + 505, + 656 + ], + "spans": [ + { + "bbox": [ + 105, + 642, + 505, + 656 + ], + "score": 1.0, + "content": "truth labels, images segmented by the Source Only model and our method in Fig. 7. While the", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 654, + 505, + 666 + ], + "spans": [ + { + "bbox": [ + 106, + 654, + 505, + 666 + ], + "score": 1.0, + "content": "Source Only model seems to suffer from domain shift, ADR generates a clean segmentation. These", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 664, + 420, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 664, + 420, + 678 + ], + "score": 1.0, + "content": "experiments demonstrate the effectiveness of ADR on semantic segmentation.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 24 + }, + { + "type": "title", + "bbox": [ + 108, + 693, + 195, + 705 + ], + "lines": [ + { + "bbox": [ + 104, + 691, + 197, + 708 + ], + "spans": [ + { + "bbox": [ + 104, + 691, + 197, + 708 + ], + "score": 1.0, + "content": "5 CONCLUSION", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 30 + }, + { + "type": "text", + "bbox": [ + 108, + 710, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "In this paper, we introduced a novel approach for aligning deep representation, Adversarial Dropout", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 720, + 505, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 720, + 505, + 733 + ], + "score": 1.0, + "content": "Regularization, which learns to generate discriminative features for the target domain. 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Methodgrrrdoraegpaleie 3ueoormorreiltuosiadsareraertrnaaa
Finetuning on ResNet101
Source Only55.153.3 61.959.180.617.979.731.281.026.573.58.552.4
MMD87.163.0 76.542.090.342.985.953.149.736.385.820.761.1
DANN81.977.7 82.844.381.229.565.128.651.954.682.87.857.4
ENT80.375.5 75.848.377.927.369.740.246.546.679.316.057.0
Ours94.151.3 83.272.288.768.892.870.277.263.682.930.372.9
Ours (retrained classifier)94.248.5 84.072.990.174.292.672.580.861.882.228.873.5
Finetuning on ResNeXt
Source Only74.3 37.6 61.8 68.2 59.510.7 81.412.8 61.6 26.070.05.647.4
MMD90.751.1 64.865.689.946.591.940.181.524.190.028.563.7
DANN86.066.3 60.8 56.079.853.782.325.258.231.089.326.159.6
ENT94.781.0 57.046.673.949.069.231.040.534.387.315.156.6
Ours86.3 71.987.678.193.084.894.578.991.858.977.726.777.5
Ours (retrained classifier)89.270.9 85.782.093.786.7 93.372.389.553.086.728.377.6
", + "type": "table", + "image_path": "f1424f829d13d5222f78094f2d533a494b462bd17dd04b218b7d8dfb038049e0.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 143, + 81, + 469, + 138.33333333333334 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 143, + 138.33333333333334, + 469, + 195.66666666666669 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 143, + 195.66666666666669, + 469, + 253.00000000000003 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "table_caption", + "bbox": [ + 106, + 257, + 506, + 300 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 256, + 505, + 268 + ], + "spans": [ + { + "bbox": [ + 105, + 256, + 505, + 268 + ], + "score": 1.0, + "content": "Table 2: Results on Visda2017 classification datasets (Peng et al. (2017)). 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Our", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 290, + 370, + 302 + ], + "spans": [ + { + "bbox": [ + 105, + 290, + 370, + 302 + ], + "score": 1.0, + "content": "proposed method shows much better performance than existing methods.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 4.5 + } + ], + "index": 2.75 + }, + { + "type": "image", + "bbox": [ + 142, + 319, + 471, + 436 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 142, + 319, + 471, + 436 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 142, + 319, + 471, + 436 + ], + "spans": [ + { + "bbox": [ + 142, + 319, + 471, + 436 + ], + "score": 0.971, + "type": "image", + "image_path": "f85e9efe625959ba93fdcfd4024851f548acbeebd038701c1fb299173a9f68e4.jpg" + } + ] + } + ], + "index": 8, + "virtual_lines": [ + { + "bbox": [ + 142, + 319, + 471, + 358.0 + ], + "spans": [], + "index": 7 + }, + { + "bbox": [ + 142, + 358.0, + 471, + 397.0 + ], + "spans": [], + "index": 8 + }, + { + "bbox": [ + 142, + 397.0, + 471, + 436.0 + ], + "spans": [], + "index": 9 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 107, + 444, + 504, + 484 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 443, + 505, + 456 + ], + "spans": [ + { + "bbox": [ + 105, + 443, + 505, + 456 + ], + "score": 1.0, + "content": "Figure 6: Visualization of VisDA-classification (12 classes) target features using T-SNE (Maaten & Hinton", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 454, + 505, + 466 + ], + "spans": [ + { + "bbox": [ + 106, + 454, + 505, + 466 + ], + "score": 1.0, + "content": "(2008)): (a) features obtained by the Imagenet-pretrained ResNext model not finetuned on VisDA; (b) features", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 463, + 505, + 476 + ], + "spans": [ + { + "bbox": [ + 105, + 463, + 505, + 476 + ], + "score": 1.0, + "content": "from the ResNext model fine-tuned only on VisDA source samples without any adaptation; (c) features obtained", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 474, + 259, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 474, + 259, + 486 + ], + "score": 1.0, + "content": "by ResNext adapted by our ADR method.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 11.5 + } + ], + "index": 9.75 + }, + { + "type": "text", + "bbox": [ + 107, + 494, + 505, + 550 + ], + "lines": [ + { + "bbox": [ + 105, + 493, + 505, + 507 + ], + "spans": [ + { + "bbox": [ + 105, + 493, + 505, + 507 + ], + "score": 1.0, + "content": "For the feature generator, we use the pretrained network without fully-connected layers. For the", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 504, + 505, + 519 + ], + "spans": [ + { + "bbox": [ + 105, + 504, + 505, + 519 + ], + "score": 1.0, + "content": "classifier, we use a fully-convolutional network with dropout layers. Due to limited memory, the", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 515, + 505, + 529 + ], + "spans": [ + { + "bbox": [ + 105, + 515, + 505, + 529 + ], + "score": 1.0, + "content": "batch size is set to 1. We include details of the network architecture in appendix. For comparison,", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 527, + 506, + 540 + ], + "spans": [ + { + "bbox": [ + 105, + 527, + 506, + 540 + ], + "score": 1.0, + "content": "we train a domain classifier based model for our network (DANN). 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ADR clearly improves mean", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 565, + 505, + 579 + ], + "spans": [ + { + "bbox": [ + 105, + 565, + 505, + 579 + ], + "score": 1.0, + "content": "IoU (Intersection-over-Union) compared to the source-only and competing models, beating state-of-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 577, + 506, + 591 + ], + "spans": [ + { + "bbox": [ + 105, + 577, + 506, + 591 + ], + "score": 1.0, + "content": "the-art by a large margin. When we apply ADR to DRN, the accuracy improves much more than for", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 588, + 506, + 600 + ], + "spans": [ + { + "bbox": [ + 105, + 588, + 506, + 600 + ], + "score": 1.0, + "content": "ResNet50, and is 12.4 points higher than the model trained only on GTA5 source samples. This is", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 598, + 506, + 613 + ], + "spans": [ + { + "bbox": [ + 105, + 598, + 506, + 613 + ], + "score": 1.0, + "content": "likely because ADR exploits the strong representation of the pretrained DRN network. Although we", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 610, + 505, + 622 + ], + "spans": [ + { + "bbox": [ + 105, + 610, + 505, + 622 + ], + "score": 1.0, + "content": "implemented ENT in this setting, the accuracy was much worse than the Source Only model with", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 621, + 505, + 633 + ], + "spans": [ + { + "bbox": [ + 105, + 621, + 505, + 633 + ], + "score": 1.0, + "content": "a mIoU of 15.0 in training ResNet50. 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These", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 664, + 420, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 664, + 420, + 678 + ], + "score": 1.0, + "content": "experiments demonstrate the effectiveness of ADR on semantic segmentation.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 24, + "bbox_fs": [ + 105, + 555, + 506, + 678 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 693, + 195, + 705 + ], + "lines": [ + { + "bbox": [ + 104, + 691, + 197, + 708 + ], + "spans": [ + { + "bbox": [ + 104, + 691, + 197, + 708 + ], + "score": 1.0, + "content": "5 CONCLUSION", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 30 + }, + { + "type": "text", + "bbox": [ + 108, + 710, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "In this paper, we introduced a novel approach for aligning deep representation, Adversarial Dropout", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 720, + 505, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 720, + 505, + 733 + ], + "score": 1.0, + "content": "Regularization, which learns to generate discriminative features for the target domain. 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NetworkMethodxeeepreBuiplng8irilen买uosradMur0mrrqeemIoU
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In extensive domain adaptation experiments, our method outperformed", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 104, + 379, + 506, + 395 + ], + "spans": [ + { + "bbox": [ + 104, + 379, + 506, + 395 + ], + "score": 1.0, + "content": "baseline methods, including entropy minimization, and achieved state-of-the-art results on three", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 391, + 144, + 405 + ], + "spans": [ + { + "bbox": [ + 105, + 391, + 144, + 405 + ], + "score": 1.0, + "content": "datasets.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 13 + }, + { + "type": "text", + "bbox": [ + 106, + 409, + 503, + 432 + ], + "lines": [ + { + "bbox": [ + 106, + 408, + 505, + 421 + ], + "spans": [ + { + "bbox": [ + 106, + 408, + 505, + 421 + ], + "score": 1.0, + "content": "We also show how to apply our method to train Generative Adversarial Networks for semi-", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 420, + 253, + 432 + ], + "spans": [ + { + "bbox": [ + 105, + 420, + 253, + 432 + ], + "score": 1.0, + "content": "supervised learning in the appendix.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 16.5 + }, + { + "type": "title", + "bbox": [ + 108, + 448, + 243, + 460 + ], + "lines": [ + { + "bbox": [ + 105, + 447, + 245, + 462 + ], + "spans": [ + { + "bbox": [ + 105, + 447, + 245, + 462 + ], + "score": 1.0, + "content": "6 ACKNOWLEDGEMENTS", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 18 + }, + { + "type": "text", + "bbox": [ + 107, + 473, + 505, + 528 + ], + "lines": [ + { + "bbox": [ + 106, + 471, + 505, + 487 + ], + "spans": [ + { + "bbox": [ + 106, + 471, + 505, + 487 + ], + "score": 1.0, + "content": "We would like to thank Trevor Darrell for his great advice on our paper. The first author’s stay", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 484, + 505, + 498 + ], + "spans": [ + { + "bbox": [ + 105, + 484, + 505, + 498 + ], + "score": 1.0, + "content": "at Boston University was partially supported by a scholarship from the University of Tokyo. 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The first author’s stay", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 484, + 505, + 498 + ], + "spans": [ + { + "bbox": [ + 105, + 484, + 505, + 498 + ], + "score": 1.0, + "content": "at Boston University was partially supported by a scholarship from the University of Tokyo. 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Some techniques used", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 125, + 505, + 139 + ], + "spans": [ + { + "bbox": [ + 105, + 125, + 505, + 139 + ], + "score": 1.0, + "content": "in training Generative Adversarial Networks can be applied to achieve our goal too. (Springenberg", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 137, + 505, + 149 + ], + "spans": [ + { + "bbox": [ + 106, + 137, + 505, + 149 + ], + "score": 1.0, + "content": "(2015); Salimans et al. (2016)) used small number of labeled samples to train critic. 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Thus,", + "type": "text" + }, + { + "bbox": [ + 464, + 242, + 473, + 252 + ], + "score": 0.8, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 473, + 241, + 506, + 255 + ], + "score": 1.0, + "content": "tries to", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 253, + 293, + 266 + ], + "spans": [ + { + "bbox": [ + 106, + 253, + 293, + 266 + ], + "score": 1.0, + "content": "move target samples away from the boundary.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 12.5 + }, + { + "type": "text", + "bbox": [ + 107, + 270, + 504, + 303 + ], + "lines": [ + { + "bbox": [ + 105, + 268, + 506, + 282 + ], + "spans": [ + { + "bbox": [ + 105, + 268, + 506, + 282 + ], + "score": 1.0, + "content": "The only difference from our method is that we used entropy term for adversarial training loss. That", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 281, + 505, + 293 + ], + "spans": [ + { + "bbox": [ + 106, + 281, + 310, + 293 + ], + "score": 1.0, + "content": "is, in this method, we replace our sensitivity term", + "type": "text" + }, + { + "bbox": [ + 311, + 281, + 347, + 292 + ], + "score": 0.93, + "content": "d ( p _ { 1 } , p _ { 2 } )", + "type": "inline_equation" + }, + { + "bbox": [ + 348, + 281, + 505, + 293 + ], + "score": 1.0, + "content": "in Eq. 4 with entropy of the classifier", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 291, + 395, + 304 + ], + "spans": [ + { + "bbox": [ + 105, + 291, + 395, + 304 + ], + "score": 1.0, + "content": "output. The adversarial loss for this baseline method is a following one.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 16 + }, + { + "type": "interline_equation", + "bbox": [ + 196, + 305, + 414, + 356 + ], + "lines": [ + { + "bbox": [ + 196, + 305, + 414, + 356 + ], + "spans": [ + { + "bbox": [ + 196, + 305, + 414, + 356 + ], + "score": 0.93, + "content": "\\begin{array} { r c l } { { { \\cal L } _ { a d v } ( X _ { t } ) } } & { { = } } & { { \\displaystyle \\mathbb { E } _ { { \\mathbf { x _ { t } } } \\sim X _ { t } } [ H [ p ( \\mathbf { y } | { \\mathbf { x _ { t } } } ) ] } } \\\\ { { { \\cal H } [ p ( \\mathbf { y } | { \\mathbf { x _ { t } } } ) ] } } & { { = } } & { { \\displaystyle - \\sum _ { k = 1 } ^ { K } p ( y = k | { \\mathbf { x _ { t } } } ) \\log p ( y = k | { \\mathbf { x _ { t } } } ) } } \\end{array}", + "type": "interline_equation", + "image_path": "a2021b8ef809d13c1f4bdfe0b75167d5f46e6067ac40597da21cec262093e02a.jpg" + } + ] + } + ], + "index": 19, + "virtual_lines": [ + { + "bbox": [ + 196, + 305, + 414, + 322.0 + ], + "spans": [], + "index": 18 + }, + { + "bbox": [ + 196, + 322.0, + 414, + 339.0 + ], + "spans": [], + "index": 19 + }, + { + "bbox": [ + 196, + 339.0, + 414, + 356.0 + ], + "spans": [], + "index": 20 + } + ] + }, + { + "type": "interline_equation", + "bbox": [ + 210, + 359, + 400, + 393 + ], + "lines": [ + { + "bbox": [ + 210, + 359, + 400, + 393 + ], + "spans": [ + { + "bbox": [ + 210, + 359, + 400, + 393 + ], + "score": 0.94, + "content": "H [ p ( y | x ) ] = - \\sum _ { k = 1 } ^ { K } p ( y = k | x ) \\log p ( y = k | x )", + "type": "interline_equation", + "image_path": "dbd5c4fe01e08cdcd9b9616b1e5c9d27f2275a6777f27ef7ac7f291a1cd848f9.jpg" + } + ] + } + ], + "index": 21.5, + "virtual_lines": [ + { + "bbox": [ + 210, + 359, + 400, + 376.0 + ], + "spans": [], + "index": 21 + }, + { + "bbox": [ + 210, + 376.0, + 400, + 393.0 + ], + "spans": [], + "index": 22 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 394, + 503, + 416 + ], + "lines": [ + { + "bbox": [ + 106, + 393, + 505, + 406 + ], + "spans": [ + { + "bbox": [ + 106, + 393, + 193, + 406 + ], + "score": 1.0, + "content": "The hyper-parameter", + "type": "text" + }, + { + "bbox": [ + 193, + 397, + 200, + 404 + ], + "score": 0.76, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 200, + 393, + 316, + 406 + ], + "score": 1.0, + "content": ", how many times we update", + "type": "text" + }, + { + "bbox": [ + 317, + 395, + 326, + 404 + ], + "score": 0.82, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 326, + 393, + 505, + 406 + ], + "score": 1.0, + "content": "for adversarial loss in one mini-batch, is set", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 403, + 335, + 417 + ], + "spans": [ + { + "bbox": [ + 105, + 403, + 117, + 417 + ], + "score": 1.0, + "content": "as", + "type": "text" + }, + { + "bbox": [ + 117, + 405, + 143, + 415 + ], + "score": 0.88, + "content": "n = 4", + "type": "inline_equation" + }, + { + "bbox": [ + 143, + 403, + 335, + 417 + ], + "score": 1.0, + "content": ". Experimentally, it worked well for all settings.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 23.5 + }, + { + "type": "title", + "bbox": [ + 106, + 423, + 351, + 436 + ], + "lines": [ + { + "bbox": [ + 105, + 422, + 352, + 438 + ], + "spans": [ + { + "bbox": [ + 105, + 422, + 352, + 438 + ], + "score": 1.0, + "content": "B DIGITS CLASSIFICATION TRAINING DETAIL", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 25 + }, + { + "type": "text", + "bbox": [ + 106, + 439, + 505, + 539 + ], + "lines": [ + { + "bbox": [ + 106, + 439, + 506, + 452 + ], + "spans": [ + { + "bbox": [ + 106, + 439, + 506, + 452 + ], + "score": 1.0, + "content": "We follow the protocol used in (Tzeng et al. (2017)). For adaptation from SVHN to MNIST, we", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 450, + 504, + 462 + ], + "spans": [ + { + "bbox": [ + 106, + 450, + 504, + 462 + ], + "score": 1.0, + "content": "used standard training splits of each datasets as training data. For evaluation, we used test splits", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 462, + 505, + 474 + ], + "spans": [ + { + "bbox": [ + 106, + 462, + 505, + 474 + ], + "score": 1.0, + "content": "of MNIST. For the adaptation between MNIST and USPS (P1), we sampled 2000 images from", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 471, + 506, + 485 + ], + "spans": [ + { + "bbox": [ + 105, + 471, + 506, + 485 + ], + "score": 1.0, + "content": "MNIST and 1800 images from USPS. For the adaptation between MNIST and USPS (P2), we used", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 483, + 506, + 497 + ], + "spans": [ + { + "bbox": [ + 105, + 483, + 506, + 497 + ], + "score": 1.0, + "content": "all training images of MNIST and USPS following Bousmalis et al. (2017). In these experiments,", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 493, + 506, + 508 + ], + "spans": [ + { + "bbox": [ + 105, + 493, + 506, + 508 + ], + "score": 1.0, + "content": "we composed the mini-batch half from source and half from target samples. The batch-size was", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 505, + 505, + 518 + ], + "spans": [ + { + "bbox": [ + 105, + 505, + 436, + 518 + ], + "score": 1.0, + "content": "set as 128 for both source and target. We report the score after repeating Step", + "type": "text" + }, + { + "bbox": [ + 437, + 506, + 456, + 516 + ], + "score": 0.45, + "content": "1 { \\sim } 3", + "type": "inline_equation" + }, + { + "bbox": [ + 456, + 505, + 505, + 518 + ], + "score": 1.0, + "content": "(please see", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 515, + 505, + 529 + ], + "spans": [ + { + "bbox": [ + 105, + 515, + 505, + 529 + ], + "score": 1.0, + "content": "Sec 3.2) 20000 times. For our baseline, ENT, we used the same network architecture and the same", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 528, + 310, + 540 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 310, + 540 + ], + "score": 1.0, + "content": "hyper-parameters as used in our proposed method.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 30 + }, + { + "type": "title", + "bbox": [ + 106, + 546, + 354, + 559 + ], + "lines": [ + { + "bbox": [ + 106, + 544, + 356, + 560 + ], + "spans": [ + { + "bbox": [ + 106, + 544, + 356, + 560 + ], + "score": 1.0, + "content": "C OBJECT CLASSIFICATION TRAINING DETAIL", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 35 + }, + { + "type": "text", + "bbox": [ + 107, + 561, + 505, + 606 + ], + "lines": [ + { + "bbox": [ + 105, + 561, + 505, + 574 + ], + "spans": [ + { + "bbox": [ + 105, + 561, + 281, + 574 + ], + "score": 1.0, + "content": "In this experiment, SGD with learning rate", + "type": "text" + }, + { + "bbox": [ + 281, + 561, + 328, + 573 + ], + "score": 0.92, + "content": "1 . 0 \\times 1 0 ^ { - 3 }", + "type": "inline_equation" + }, + { + "bbox": [ + 329, + 561, + 505, + 574 + ], + "score": 1.0, + "content": "is used to optimize the parameters. For the", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 573, + 505, + 585 + ], + "spans": [ + { + "bbox": [ + 105, + 573, + 505, + 585 + ], + "score": 1.0, + "content": "finetuning of ResNet101, we set batch-size as 32. Due to the limit of GPU memory, we set it as 24", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 584, + 506, + 597 + ], + "spans": [ + { + "bbox": [ + 105, + 584, + 506, + 597 + ], + "score": 1.0, + "content": "in finetuning ResNext model. We report the score after 20 epochs training. In order to train MMD", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 595, + 426, + 607 + ], + "spans": [ + { + "bbox": [ + 105, + 595, + 426, + 607 + ], + "score": 1.0, + "content": "model, we use 5 RBF kernels with the following standard deviation parameters:", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 37.5 + }, + { + "type": "interline_equation", + "bbox": [ + 228, + 610, + 382, + 623 + ], + "lines": [ + { + "bbox": [ + 228, + 610, + 382, + 623 + ], + "spans": [ + { + "bbox": [ + 228, + 610, + 382, + 623 + ], + "score": 0.9, + "content": "\\sigma = [ 0 . 1 , 0 . 0 5 , 0 . 0 1 , 0 . 0 0 0 1 , 0 . 0 0 0 0 1 ]", + "type": "interline_equation", + "image_path": "5e5c787c3a5208e654ae34797e13f1eb8e10838a913d7366e482a0e916b2b935.jpg" + } + ] + } + ], + "index": 40, + "virtual_lines": [ + { + "bbox": [ + 228, + 610, + 382, + 623 + ], + "spans": [], + "index": 40 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 627, + 505, + 660 + ], + "lines": [ + { + "bbox": [ + 105, + 626, + 505, + 640 + ], + "spans": [ + { + "bbox": [ + 105, + 626, + 505, + 640 + ], + "score": 1.0, + "content": "We changed the number of the kernels and their parameters, but we could not observe significant per-", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 637, + 505, + 651 + ], + "spans": [ + { + "bbox": [ + 105, + 637, + 505, + 651 + ], + "score": 1.0, + "content": "formance difference. We report the performance after 5 epochs. We could not see any improvement", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 648, + 170, + 662 + ], + "spans": [ + { + "bbox": [ + 106, + 648, + 170, + 662 + ], + "score": 1.0, + "content": "after the epoch.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 42 + }, + { + "type": "text", + "bbox": [ + 107, + 665, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 666, + 504, + 677 + ], + "spans": [ + { + "bbox": [ + 106, + 666, + 504, + 677 + ], + "score": 1.0, + "content": "To train a model (Ganin & Lempitsky (2014)), we used two-layered domain classification networks.", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 677, + 504, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 504, + 689 + ], + "score": 1.0, + "content": "Experimentally, we did not see any improvement when the network architecture is changed. Accord-", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 245, + 700 + ], + "score": 1.0, + "content": "ing to the original method (Ganin", + "type": "text" + }, + { + "bbox": [ + 246, + 689, + 254, + 698 + ], + "score": 0.26, + "content": "\\&", + "type": "inline_equation" + }, + { + "bbox": [ + 255, + 687, + 505, + 700 + ], + "score": 1.0, + "content": "Lempitsky (2014)), learning rate is decreased every iteration.", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 104, + 698, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 104, + 698, + 456, + 711 + ], + "score": 1.0, + "content": "However, in our experiment, we could not see improvement, thus, we fixed learning rate", + "type": "text" + }, + { + "bbox": [ + 457, + 698, + 501, + 709 + ], + "score": 0.91, + "content": "\\mathrm { i . 0 \\times 1 0 ^ { - 3 } }", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 698, + 505, + 711 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "We report the accuracy after 1 epoch. The accuracy dropped significantly after the first epoch. We", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 720, + 444, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 444, + 734 + ], + "score": 1.0, + "content": "assume this is due to the large domain difference between synthetic and real images.", + "type": "text" + } + ], + "index": 49 + } + ], + "index": 46.5 + } + ], + "page_idx": 11, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2018", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 751, + 311, + 760 + ], + "lines": [ + { + "bbox": [ + 299, + 750, + 313, + 764 + ], + "spans": [ + { + "bbox": [ + 299, + 750, + 313, + 764 + ], + "score": 1.0, + "content": "12", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 108, + 82, + 162, + 93 + ], + "lines": [ + { + "bbox": [ + 106, + 79, + 163, + 97 + ], + "spans": [ + { + "bbox": [ + 106, + 79, + 163, + 97 + ], + "score": 1.0, + "content": "APPENDIX", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "title", + "bbox": [ + 108, + 98, + 444, + 111 + ], + "lines": [ + { + "bbox": [ + 105, + 97, + 446, + 114 + ], + "spans": [ + { + "bbox": [ + 105, + 97, + 446, + 114 + ], + "score": 1.0, + "content": "A ENTROPY BASED METHOD FOR DOMAIN ADAPTATION (ENT)", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 1 + }, + { + "type": "text", + "bbox": [ + 106, + 115, + 505, + 214 + ], + "lines": [ + { + "bbox": [ + 105, + 114, + 505, + 128 + ], + "spans": [ + { + "bbox": [ + 105, + 114, + 505, + 128 + ], + "score": 1.0, + "content": "Our method aims to move target samples away from the decision boundary. Some techniques used", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 125, + 505, + 139 + ], + "spans": [ + { + "bbox": [ + 105, + 125, + 505, + 139 + ], + "score": 1.0, + "content": "in training Generative Adversarial Networks can be applied to achieve our goal too. (Springenberg", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 137, + 505, + 149 + ], + "spans": [ + { + "bbox": [ + 106, + 137, + 505, + 149 + ], + "score": 1.0, + "content": "(2015); Salimans et al. (2016)) used small number of labeled samples to train critic. Critic is trained", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 147, + 505, + 161 + ], + "spans": [ + { + "bbox": [ + 105, + 147, + 226, + 161 + ], + "score": 1.0, + "content": "to classify real samples into", + "type": "text" + }, + { + "bbox": [ + 226, + 149, + 237, + 158 + ], + "score": 0.81, + "content": "K", + "type": "inline_equation" + }, + { + "bbox": [ + 237, + 147, + 505, + 161 + ], + "score": 1.0, + "content": "classes. They also trained critic to move unlabeled real images", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 159, + 506, + 172 + ], + "spans": [ + { + "bbox": [ + 106, + 159, + 506, + 172 + ], + "score": 1.0, + "content": "away from the boundary by minimizing entropy of the critic’s output. Generated fake images are", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 169, + 505, + 182 + ], + "spans": [ + { + "bbox": [ + 105, + 169, + 505, + 182 + ], + "score": 1.0, + "content": "moved near the boundary by maximizing the entropy. On the other hand, generator is trained to", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 181, + 505, + 193 + ], + "spans": [ + { + "bbox": [ + 105, + 181, + 505, + 193 + ], + "score": 1.0, + "content": "generate fake images which should be placed away from the boundary. This kind of method can be", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 192, + 505, + 204 + ], + "spans": [ + { + "bbox": [ + 106, + 192, + 505, + 204 + ], + "score": 1.0, + "content": "easily applied to domain adaptation problem. We would like to describe the method along with our", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 202, + 174, + 217 + ], + "spans": [ + { + "bbox": [ + 105, + 202, + 174, + 217 + ], + "score": 1.0, + "content": "problem setting.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 6, + "bbox_fs": [ + 105, + 114, + 506, + 217 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 219, + 505, + 264 + ], + "lines": [ + { + "bbox": [ + 106, + 219, + 504, + 231 + ], + "spans": [ + { + "bbox": [ + 106, + 219, + 303, + 231 + ], + "score": 1.0, + "content": "Similar to our method, we have critic networks", + "type": "text" + }, + { + "bbox": [ + 303, + 220, + 312, + 230 + ], + "score": 0.81, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 313, + 219, + 372, + 231 + ], + "score": 1.0, + "content": "and generator", + "type": "text" + }, + { + "bbox": [ + 373, + 220, + 382, + 230 + ], + "score": 0.72, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 382, + 219, + 388, + 231 + ], + "score": 1.0, + "content": ".", + "type": "text" + }, + { + "bbox": [ + 389, + 220, + 398, + 230 + ], + "score": 0.7, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 398, + 219, + 493, + 231 + ], + "score": 1.0, + "content": "classifies samples into", + "type": "text" + }, + { + "bbox": [ + 493, + 220, + 504, + 230 + ], + "score": 0.76, + "content": "K", + "type": "inline_equation" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 230, + 506, + 243 + ], + "spans": [ + { + "bbox": [ + 106, + 230, + 132, + 243 + ], + "score": 1.0, + "content": "class.", + "type": "text" + }, + { + "bbox": [ + 132, + 231, + 141, + 241 + ], + "score": 0.79, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 141, + 230, + 506, + 243 + ], + "score": 1.0, + "content": "is trained to maximize the entropy of target samples, which encourages to move the target", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 241, + 506, + 255 + ], + "spans": [ + { + "bbox": [ + 106, + 241, + 248, + 255 + ], + "score": 1.0, + "content": "samples near the boundary. Then,", + "type": "text" + }, + { + "bbox": [ + 248, + 242, + 257, + 252 + ], + "score": 0.81, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 257, + 241, + 464, + 255 + ], + "score": 1.0, + "content": "is trained to minimize the entropy of them. Thus,", + "type": "text" + }, + { + "bbox": [ + 464, + 242, + 473, + 252 + ], + "score": 0.8, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 473, + 241, + 506, + 255 + ], + "score": 1.0, + "content": "tries to", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 253, + 293, + 266 + ], + "spans": [ + { + "bbox": [ + 106, + 253, + 293, + 266 + ], + "score": 1.0, + "content": "move target samples away from the boundary.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 12.5, + "bbox_fs": [ + 106, + 219, + 506, + 266 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 270, + 504, + 303 + ], + "lines": [ + { + "bbox": [ + 105, + 268, + 506, + 282 + ], + "spans": [ + { + "bbox": [ + 105, + 268, + 506, + 282 + ], + "score": 1.0, + "content": "The only difference from our method is that we used entropy term for adversarial training loss. That", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 281, + 505, + 293 + ], + "spans": [ + { + "bbox": [ + 106, + 281, + 310, + 293 + ], + "score": 1.0, + "content": "is, in this method, we replace our sensitivity term", + "type": "text" + }, + { + "bbox": [ + 311, + 281, + 347, + 292 + ], + "score": 0.93, + "content": "d ( p _ { 1 } , p _ { 2 } )", + "type": "inline_equation" + }, + { + "bbox": [ + 348, + 281, + 505, + 293 + ], + "score": 1.0, + "content": "in Eq. 4 with entropy of the classifier", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 291, + 395, + 304 + ], + "spans": [ + { + "bbox": [ + 105, + 291, + 395, + 304 + ], + "score": 1.0, + "content": "output. The adversarial loss for this baseline method is a following one.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 16, + "bbox_fs": [ + 105, + 268, + 506, + 304 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 196, + 305, + 414, + 356 + ], + "lines": [ + { + "bbox": [ + 196, + 305, + 414, + 356 + ], + "spans": [ + { + "bbox": [ + 196, + 305, + 414, + 356 + ], + "score": 0.93, + "content": "\\begin{array} { r c l } { { { \\cal L } _ { a d v } ( X _ { t } ) } } & { { = } } & { { \\displaystyle \\mathbb { E } _ { { \\mathbf { x _ { t } } } \\sim X _ { t } } [ H [ p ( \\mathbf { y } | { \\mathbf { x _ { t } } } ) ] } } \\\\ { { { \\cal H } [ p ( \\mathbf { y } | { \\mathbf { x _ { t } } } ) ] } } & { { = } } & { { \\displaystyle - \\sum _ { k = 1 } ^ { K } p ( y = k | { \\mathbf { x _ { t } } } ) \\log p ( y = k | { \\mathbf { x _ { t } } } ) } } \\end{array}", + "type": "interline_equation", + "image_path": "a2021b8ef809d13c1f4bdfe0b75167d5f46e6067ac40597da21cec262093e02a.jpg" + } + ] + } + ], + "index": 19, + "virtual_lines": [ + { + "bbox": [ + 196, + 305, + 414, + 322.0 + ], + "spans": [], + "index": 18 + }, + { + "bbox": [ + 196, + 322.0, + 414, + 339.0 + ], + "spans": [], + "index": 19 + }, + { + "bbox": [ + 196, + 339.0, + 414, + 356.0 + ], + "spans": [], + "index": 20 + } + ] + }, + { + "type": "interline_equation", + "bbox": [ + 210, + 359, + 400, + 393 + ], + "lines": [ + { + "bbox": [ + 210, + 359, + 400, + 393 + ], + "spans": [ + { + "bbox": [ + 210, + 359, + 400, + 393 + ], + "score": 0.94, + "content": "H [ p ( y | x ) ] = - \\sum _ { k = 1 } ^ { K } p ( y = k | x ) \\log p ( y = k | x )", + "type": "interline_equation", + "image_path": "dbd5c4fe01e08cdcd9b9616b1e5c9d27f2275a6777f27ef7ac7f291a1cd848f9.jpg" + } + ] + } + ], + "index": 21.5, + "virtual_lines": [ + { + "bbox": [ + 210, + 359, + 400, + 376.0 + ], + "spans": [], + "index": 21 + }, + { + "bbox": [ + 210, + 376.0, + 400, + 393.0 + ], + "spans": [], + "index": 22 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 394, + 503, + 416 + ], + "lines": [ + { + "bbox": [ + 106, + 393, + 505, + 406 + ], + "spans": [ + { + "bbox": [ + 106, + 393, + 193, + 406 + ], + "score": 1.0, + "content": "The hyper-parameter", + "type": "text" + }, + { + "bbox": [ + 193, + 397, + 200, + 404 + ], + "score": 0.76, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 200, + 393, + 316, + 406 + ], + "score": 1.0, + "content": ", how many times we update", + "type": "text" + }, + { + "bbox": [ + 317, + 395, + 326, + 404 + ], + "score": 0.82, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 326, + 393, + 505, + 406 + ], + "score": 1.0, + "content": "for adversarial loss in one mini-batch, is set", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 403, + 335, + 417 + ], + "spans": [ + { + "bbox": [ + 105, + 403, + 117, + 417 + ], + "score": 1.0, + "content": "as", + "type": "text" + }, + { + "bbox": [ + 117, + 405, + 143, + 415 + ], + "score": 0.88, + "content": "n = 4", + "type": "inline_equation" + }, + { + "bbox": [ + 143, + 403, + 335, + 417 + ], + "score": 1.0, + "content": ". Experimentally, it worked well for all settings.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 23.5, + "bbox_fs": [ + 105, + 393, + 505, + 417 + ] + }, + { + "type": "title", + "bbox": [ + 106, + 423, + 351, + 436 + ], + "lines": [ + { + "bbox": [ + 105, + 422, + 352, + 438 + ], + "spans": [ + { + "bbox": [ + 105, + 422, + 352, + 438 + ], + "score": 1.0, + "content": "B DIGITS CLASSIFICATION TRAINING DETAIL", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 25 + }, + { + "type": "text", + "bbox": [ + 106, + 439, + 505, + 539 + ], + "lines": [ + { + "bbox": [ + 106, + 439, + 506, + 452 + ], + "spans": [ + { + "bbox": [ + 106, + 439, + 506, + 452 + ], + "score": 1.0, + "content": "We follow the protocol used in (Tzeng et al. (2017)). For adaptation from SVHN to MNIST, we", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 450, + 504, + 462 + ], + "spans": [ + { + "bbox": [ + 106, + 450, + 504, + 462 + ], + "score": 1.0, + "content": "used standard training splits of each datasets as training data. For evaluation, we used test splits", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 462, + 505, + 474 + ], + "spans": [ + { + "bbox": [ + 106, + 462, + 505, + 474 + ], + "score": 1.0, + "content": "of MNIST. For the adaptation between MNIST and USPS (P1), we sampled 2000 images from", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 471, + 506, + 485 + ], + "spans": [ + { + "bbox": [ + 105, + 471, + 506, + 485 + ], + "score": 1.0, + "content": "MNIST and 1800 images from USPS. For the adaptation between MNIST and USPS (P2), we used", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 483, + 506, + 497 + ], + "spans": [ + { + "bbox": [ + 105, + 483, + 506, + 497 + ], + "score": 1.0, + "content": "all training images of MNIST and USPS following Bousmalis et al. (2017). In these experiments,", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 493, + 506, + 508 + ], + "spans": [ + { + "bbox": [ + 105, + 493, + 506, + 508 + ], + "score": 1.0, + "content": "we composed the mini-batch half from source and half from target samples. The batch-size was", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 505, + 505, + 518 + ], + "spans": [ + { + "bbox": [ + 105, + 505, + 436, + 518 + ], + "score": 1.0, + "content": "set as 128 for both source and target. We report the score after repeating Step", + "type": "text" + }, + { + "bbox": [ + 437, + 506, + 456, + 516 + ], + "score": 0.45, + "content": "1 { \\sim } 3", + "type": "inline_equation" + }, + { + "bbox": [ + 456, + 505, + 505, + 518 + ], + "score": 1.0, + "content": "(please see", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 515, + 505, + 529 + ], + "spans": [ + { + "bbox": [ + 105, + 515, + 505, + 529 + ], + "score": 1.0, + "content": "Sec 3.2) 20000 times. For our baseline, ENT, we used the same network architecture and the same", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 528, + 310, + 540 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 310, + 540 + ], + "score": 1.0, + "content": "hyper-parameters as used in our proposed method.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 30, + "bbox_fs": [ + 105, + 439, + 506, + 540 + ] + }, + { + "type": "title", + "bbox": [ + 106, + 546, + 354, + 559 + ], + "lines": [ + { + "bbox": [ + 106, + 544, + 356, + 560 + ], + "spans": [ + { + "bbox": [ + 106, + 544, + 356, + 560 + ], + "score": 1.0, + "content": "C OBJECT CLASSIFICATION TRAINING DETAIL", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 35 + }, + { + "type": "text", + "bbox": [ + 107, + 561, + 505, + 606 + ], + "lines": [ + { + "bbox": [ + 105, + 561, + 505, + 574 + ], + "spans": [ + { + "bbox": [ + 105, + 561, + 281, + 574 + ], + "score": 1.0, + "content": "In this experiment, SGD with learning rate", + "type": "text" + }, + { + "bbox": [ + 281, + 561, + 328, + 573 + ], + "score": 0.92, + "content": "1 . 0 \\times 1 0 ^ { - 3 }", + "type": "inline_equation" + }, + { + "bbox": [ + 329, + 561, + 505, + 574 + ], + "score": 1.0, + "content": "is used to optimize the parameters. For the", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 573, + 505, + 585 + ], + "spans": [ + { + "bbox": [ + 105, + 573, + 505, + 585 + ], + "score": 1.0, + "content": "finetuning of ResNet101, we set batch-size as 32. Due to the limit of GPU memory, we set it as 24", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 584, + 506, + 597 + ], + "spans": [ + { + "bbox": [ + 105, + 584, + 506, + 597 + ], + "score": 1.0, + "content": "in finetuning ResNext model. We report the score after 20 epochs training. In order to train MMD", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 595, + 426, + 607 + ], + "spans": [ + { + "bbox": [ + 105, + 595, + 426, + 607 + ], + "score": 1.0, + "content": "model, we use 5 RBF kernels with the following standard deviation parameters:", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 37.5, + "bbox_fs": [ + 105, + 561, + 506, + 607 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 228, + 610, + 382, + 623 + ], + "lines": [ + { + "bbox": [ + 228, + 610, + 382, + 623 + ], + "spans": [ + { + "bbox": [ + 228, + 610, + 382, + 623 + ], + "score": 0.9, + "content": "\\sigma = [ 0 . 1 , 0 . 0 5 , 0 . 0 1 , 0 . 0 0 0 1 , 0 . 0 0 0 0 1 ]", + "type": "interline_equation", + "image_path": "5e5c787c3a5208e654ae34797e13f1eb8e10838a913d7366e482a0e916b2b935.jpg" + } + ] + } + ], + "index": 40, + "virtual_lines": [ + { + "bbox": [ + 228, + 610, + 382, + 623 + ], + "spans": [], + "index": 40 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 627, + 505, + 660 + ], + "lines": [ + { + "bbox": [ + 105, + 626, + 505, + 640 + ], + "spans": [ + { + "bbox": [ + 105, + 626, + 505, + 640 + ], + "score": 1.0, + "content": "We changed the number of the kernels and their parameters, but we could not observe significant per-", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 637, + 505, + 651 + ], + "spans": [ + { + "bbox": [ + 105, + 637, + 505, + 651 + ], + "score": 1.0, + "content": "formance difference. We report the performance after 5 epochs. We could not see any improvement", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 648, + 170, + 662 + ], + "spans": [ + { + "bbox": [ + 106, + 648, + 170, + 662 + ], + "score": 1.0, + "content": "after the epoch.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 42, + "bbox_fs": [ + 105, + 626, + 505, + 662 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 665, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 666, + 504, + 677 + ], + "spans": [ + { + "bbox": [ + 106, + 666, + 504, + 677 + ], + "score": 1.0, + "content": "To train a model (Ganin & Lempitsky (2014)), we used two-layered domain classification networks.", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 677, + 504, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 504, + 689 + ], + "score": 1.0, + "content": "Experimentally, we did not see any improvement when the network architecture is changed. Accord-", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 245, + 700 + ], + "score": 1.0, + "content": "ing to the original method (Ganin", + "type": "text" + }, + { + "bbox": [ + 246, + 689, + 254, + 698 + ], + "score": 0.26, + "content": "\\&", + "type": "inline_equation" + }, + { + "bbox": [ + 255, + 687, + 505, + 700 + ], + "score": 1.0, + "content": "Lempitsky (2014)), learning rate is decreased every iteration.", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 104, + 698, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 104, + 698, + 456, + 711 + ], + "score": 1.0, + "content": "However, in our experiment, we could not see improvement, thus, we fixed learning rate", + "type": "text" + }, + { + "bbox": [ + 457, + 698, + 501, + 709 + ], + "score": 0.91, + "content": "\\mathrm { i . 0 \\times 1 0 ^ { - 3 } }", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 698, + 505, + 711 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "We report the accuracy after 1 epoch. The accuracy dropped significantly after the first epoch. We", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 720, + 444, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 444, + 734 + ], + "score": 1.0, + "content": "assume this is due to the large domain difference between synthetic and real images.", + "type": "text" + } + ], + "index": 49 + } + ], + "index": 46.5, + "bbox_fs": [ + 104, + 666, + 505, + 734 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 107, + 80, + 504, + 280 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 107, + 80, + 504, + 280 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 107, + 80, + 504, + 280 + ], + "spans": [ + { + "bbox": [ + 107, + 80, + 504, + 280 + ], + "score": 0.976, + "type": "image", + "image_path": "91334547d8f045bbc50bad32d13e84fbdd9717e2bd91e1f11d2951fede231eb5.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 107, + 80, + 504, + 146.66666666666669 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 107, + 146.66666666666669, + 504, + 213.33333333333337 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 107, + 213.33333333333337, + 504, + 280.00000000000006 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 107, + 291, + 505, + 324 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 290, + 505, + 304 + ], + "spans": [ + { + "bbox": [ + 105, + 290, + 505, + 304 + ], + "score": 1.0, + "content": "Figure 9: Example of results on segmentation experiments performed by DRN-105. From top to bottom,", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 302, + 505, + 315 + ], + "spans": [ + { + "bbox": [ + 105, + 302, + 505, + 315 + ], + "score": 1.0, + "content": "Original image; Ground truth; Segmented image before adaptation; Segmented image after adaptation by our", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 313, + 138, + 324 + ], + "spans": [ + { + "bbox": [ + 105, + 313, + 138, + 324 + ], + "score": 1.0, + "content": "method.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4 + } + ], + "index": 2.5 + }, + { + "type": "text", + "bbox": [ + 107, + 342, + 505, + 375 + ], + "lines": [ + { + "bbox": [ + 105, + 341, + 505, + 355 + ], + "spans": [ + { + "bbox": [ + 105, + 341, + 505, + 355 + ], + "score": 1.0, + "content": "For our new baseline, ENT, we used the same hyper-parameter as we used for our proposed method.", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 352, + 506, + 366 + ], + "spans": [ + { + "bbox": [ + 105, + 352, + 506, + 366 + ], + "score": 1.0, + "content": "Since the accuracy of ENT drops significantly after around 5 epochs, we report the accuracy after 5", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 364, + 169, + 377 + ], + "spans": [ + { + "bbox": [ + 105, + 364, + 169, + 377 + ], + "score": 1.0, + "content": "epoch updates.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 7 + }, + { + "type": "title", + "bbox": [ + 108, + 383, + 287, + 395 + ], + "lines": [ + { + "bbox": [ + 105, + 381, + 289, + 397 + ], + "spans": [ + { + "bbox": [ + 105, + 381, + 289, + 397 + ], + "score": 1.0, + "content": "D SEGMENTATION EXPERIMENTS", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 9 + }, + { + "type": "text", + "bbox": [ + 107, + 399, + 338, + 531 + ], + "lines": [ + { + "bbox": [ + 106, + 398, + 339, + 411 + ], + "spans": [ + { + "bbox": [ + 106, + 398, + 339, + 411 + ], + "score": 1.0, + "content": "We modified FCN Long et al. (2015a) architecture suit-", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 410, + 339, + 421 + ], + "spans": [ + { + "bbox": [ + 106, + 410, + 339, + 421 + ], + "score": 1.0, + "content": "able for ResNet structure. The features from ResBlock", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 420, + 340, + 433 + ], + "spans": [ + { + "bbox": [ + 106, + 421, + 126, + 432 + ], + "score": 0.62, + "content": "2 { \\sim } 4", + "type": "inline_equation" + }, + { + "bbox": [ + 126, + 420, + 340, + 433 + ], + "score": 1.0, + "content": "and the first convolution layer and maxpooling layer", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 432, + 339, + 443 + ], + "spans": [ + { + "bbox": [ + 105, + 432, + 339, + 443 + ], + "score": 1.0, + "content": "are used in our implementation. 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To achieve this, we propose to train the critic with the following", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 663, + 149, + 679 + ], + "spans": [ + { + "bbox": [ + 105, + 663, + 149, + 679 + ], + "score": 1.0, + "content": "objective:", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 33, + "bbox_fs": [ + 105, + 621, + 506, + 679 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 152, + 672, + 457, + 707 + ], + "lines": [ + { + "bbox": [ + 152, + 672, + 457, + 707 + ], + "spans": [ + { + "bbox": [ + 152, + 672, + 457, + 707 + ], + "score": 0.92, + "content": "\\operatorname* { m i n } _ { C } L _ { C } = L ( X _ { L } , Y _ { L } ) + L _ { a d v } ( X _ { u } ) - L _ { a d v } ( X _ { g } ) - H [ \\frac { 1 } { M } \\sum _ { i = 1 } ^ { M } p ( y | x _ { u } { } ^ { i } , C ) ]", + "type": "interline_equation", + "image_path": "b4e0bb62c8cc70e5af3a746f4ffc2fff759f31b06275f447fb8c07818b6c821a.jpg" + } + ] + } + ], + "index": 37, + "virtual_lines": [ + { + "bbox": [ + 152, + 672, + 457, + 683.6666666666666 + ], + "spans": [], + "index": 36 + }, + { + "bbox": [ + 152, + 683.6666666666666, + 457, + 695.3333333333333 + ], + "spans": [], + "index": 37 + }, + { + "bbox": [ + 152, + 695.3333333333333, + 457, + 706.9999999999999 + ], + "spans": [], + "index": 38 + } + ] + }, + { + "type": "interline_equation", + "bbox": [ + 201, + 719, + 409, + 733 + ], + "lines": [ + { + "bbox": [ + 201, + 719, + 409, + 733 + ], + "spans": [ + { + "bbox": [ + 201, + 719, + 409, + 733 + ], + "score": 0.85, + "content": "L _ { a d v } ( X _ { u } ) = \\mathbb { E } _ { \\mathbf { x _ { u } } \\sim X _ { u } } [ d ( C _ { 1 } ( G ( \\mathbf { x _ { u } } ) ) , C _ { 2 } ( G ( \\mathbf { x _ { u } } ) ) ) ]", + "type": "interline_equation", + "image_path": "4f3651718657720aa59752e868f8a29aa904e613e9650be8f9f4ef7a3210e164.jpg" + } + ] + } + ], + "index": 39, + "virtual_lines": [ + { + "bbox": [ + 201, + 719, + 409, + 733 + ], + "spans": [], + "index": 39 + } + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 107, + 80, + 499, + 192 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 107, + 80, + 499, + 192 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 107, + 80, + 499, + 192 + ], + "spans": [ + { + "bbox": [ + 107, + 80, + 499, + 192 + ], + "score": 0.968, + "type": "image", + "image_path": "63364abe673b063e24a800150d6aed5d16f2ac6fd54204e6ef2d434abc5d60e1.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 107, + 80, + 499, + 117.33333333333334 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 107, + 117.33333333333334, + 499, + 154.66666666666669 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 107, + 154.66666666666669, + 499, + 192.00000000000003 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 221, + 199, + 389, + 211 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 218, + 198, + 389, + 213 + ], + "spans": [ + { + "bbox": [ + 218, + 198, + 389, + 213 + ], + "score": 1.0, + "content": "Figure 10: Examples of generated images.", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 3 + } + ], + "index": 2.0 + }, + { + "type": "table", + "bbox": [ + 128, + 220, + 480, + 304 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 128, + 220, + 480, + 304 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 128, + 220, + 480, + 304 + ], + "spans": [ + { + "bbox": [ + 128, + 220, + 480, + 304 + ], + "score": 0.969, + "html": "
SVHN (% errors)CIFAR (% errors)
Labeled Only SDGM (Maalge et al. (2016)16.61 ± 0.24
CatGAN (Springenberg (2015))=19.58±0.46
ALI (Dumoulin et al. (2016))7.42±0.6517.99±1.62
ImpGAN (Salimans et al. (2016))8.11±1.318.63±2.32
Ours6.26±1.0519.63±0.37
", + "type": "table", + "image_path": "c25d34b9848ce8a2264f46bff282c343fd96916cc65ef79946fd5a75454797ef.jpg" + } + ] + } + ], + "index": 5, + "virtual_lines": [ + { + "bbox": [ + 128, + 220, + 480, + 248.0 + ], + "spans": [], + "index": 4 + }, + { + "bbox": [ + 128, + 248.0, + 480, + 276.0 + ], + "spans": [], + "index": 5 + }, + { + "bbox": [ + 128, + 276.0, + 480, + 304.0 + ], + "spans": [], + "index": 6 + } + ] + } + ], + "index": 5 + }, + { + "type": "text", + "bbox": [ + 105, + 312, + 505, + 334 + ], + "lines": [ + { + "bbox": [ + 106, + 312, + 504, + 324 + ], + "spans": [ + { + "bbox": [ + 106, + 312, + 504, + 324 + ], + "score": 1.0, + "content": "Table 4: Comparison with state-of-the-art methods on two benchmark datasets. Only methods with-", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 323, + 483, + 335 + ], + "spans": [ + { + "bbox": [ + 106, + 323, + 483, + 335 + ], + "score": 1.0, + "content": "out data augmentation are included. We used the same critic architecture as used in ImpGAN.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 7.5 + }, + { + "type": "interline_equation", + "bbox": [ + 202, + 369, + 409, + 383 + ], + "lines": [ + { + "bbox": [ + 202, + 369, + 409, + 383 + ], + "spans": [ + { + "bbox": [ + 202, + 369, + 409, + 383 + ], + "score": 0.9, + "content": "L _ { a d v } ( X _ { g } ) = \\mathbb { E } _ { { \\mathbf { x } } _ { \\mathbf { g } } \\sim X _ { G } } [ d ( C _ { 1 } ( G ( { \\mathbf { x } } _ { \\mathbf { g } } ) ) , C _ { 2 } ( G ( { \\mathbf { x } } _ { \\mathbf { g } } ) ) ) ]", + "type": "interline_equation", + "image_path": "83537d900fab4ee7a3f1710393b244f2849254ece073bff6f7ec2ac627714516.jpg" + } + ] + } + ], + "index": 9, + "virtual_lines": [ + { + "bbox": [ + 202, + 369, + 409, + 383 + ], + "spans": [], + "index": 9 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 384, + 505, + 441 + ], + "lines": [ + { + "bbox": [ + 106, + 385, + 505, + 397 + ], + "spans": [ + { + "bbox": [ + 106, + 385, + 133, + 397 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 133, + 385, + 148, + 396 + ], + "score": 0.89, + "content": "X _ { L }", + "type": "inline_equation" + }, + { + "bbox": [ + 149, + 385, + 301, + 397 + ], + "score": 1.0, + "content": "denotes the subset of labeled samples,", + "type": "text" + }, + { + "bbox": [ + 301, + 385, + 316, + 396 + ], + "score": 0.88, + "content": "X _ { u }", + "type": "inline_equation" + }, + { + "bbox": [ + 316, + 385, + 426, + 397 + ], + "score": 1.0, + "content": "denotes unlabeled ones and", + "type": "text" + }, + { + "bbox": [ + 427, + 385, + 441, + 397 + ], + "score": 0.89, + "content": "X _ { g }", + "type": "inline_equation" + }, + { + "bbox": [ + 441, + 385, + 505, + 397 + ], + "score": 1.0, + "content": "denotes images", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 395, + 505, + 408 + ], + "spans": [ + { + "bbox": [ + 105, + 395, + 160, + 408 + ], + "score": 1.0, + "content": "generated by", + "type": "text" + }, + { + "bbox": [ + 160, + 396, + 170, + 406 + ], + "score": 0.82, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 170, + 395, + 188, + 408 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 188, + 396, + 198, + 406 + ], + "score": 0.82, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 199, + 395, + 505, + 408 + ], + "score": 1.0, + "content": "denotes entropy as Eq.6 shows. The critic is trained to minimize the loss on", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 406, + 505, + 418 + ], + "spans": [ + { + "bbox": [ + 106, + 406, + 505, + 418 + ], + "score": 1.0, + "content": "labeled samples in the first term. Since unlabeled images should be far away from the decision", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 418, + 505, + 430 + ], + "spans": [ + { + "bbox": [ + 106, + 418, + 505, + 430 + ], + "score": 1.0, + "content": "boundary and should be distributed uniformly among the classes, we add the second and fourth", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 428, + 480, + 442 + ], + "spans": [ + { + "bbox": [ + 105, + 428, + 480, + 442 + ], + "score": 1.0, + "content": "term. The third term encourages the critic to detect fake images generated near the boundary.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 12 + }, + { + "type": "text", + "bbox": [ + 107, + 445, + 238, + 456 + ], + "lines": [ + { + "bbox": [ + 106, + 443, + 240, + 459 + ], + "spans": [ + { + "bbox": [ + 106, + 443, + 174, + 459 + ], + "score": 1.0, + "content": "The objective of", + "type": "text" + }, + { + "bbox": [ + 174, + 446, + 183, + 455 + ], + "score": 0.84, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 183, + 443, + 240, + 459 + ], + "score": 1.0, + "content": "is as follows,", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 15 + }, + { + "type": "interline_equation", + "bbox": [ + 195, + 460, + 414, + 479 + ], + "lines": [ + { + "bbox": [ + 195, + 460, + 414, + 479 + ], + "spans": [ + { + "bbox": [ + 195, + 460, + 414, + 479 + ], + "score": 0.9, + "content": "\\operatorname* { m i n } _ { G } L _ { a d v } ( X _ { g } ) + | | \\mathbb { E } _ { x _ { g } \\sim X _ { g } } f ( \\mathbf { x _ { g } } ) - \\mathbb { E } _ { \\mathbf { x _ { u } } \\sim X _ { u } } f ( \\mathbf { x _ { u } } ) | | ^ { 2 }", + "type": "interline_equation", + "image_path": "aa12383d6c54067bf716e7a8e1391d0066b156b3c026b96dcb40a20a36336bfa.jpg" + } + ] + } + ], + "index": 16, + "virtual_lines": [ + { + "bbox": [ + 195, + 460, + 414, + 479 + ], + "spans": [], + "index": 16 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 483, + 505, + 539 + ], + "lines": [ + { + "bbox": [ + 106, + 484, + 505, + 496 + ], + "spans": [ + { + "bbox": [ + 106, + 484, + 505, + 496 + ], + "score": 1.0, + "content": "where the second term encourages generated images to be similar to real images, which is known to", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 494, + 505, + 507 + ], + "spans": [ + { + "bbox": [ + 105, + 494, + 505, + 507 + ], + "score": 1.0, + "content": "be effective to stabilize the training. The first term encourages the generator to create fake images", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 504, + 505, + 519 + ], + "spans": [ + { + "bbox": [ + 105, + 504, + 505, + 519 + ], + "score": 1.0, + "content": "which should be placed far away from the boundary. Such images should be similar to real images", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 516, + 505, + 529 + ], + "spans": [ + { + "bbox": [ + 105, + 516, + 477, + 529 + ], + "score": 1.0, + "content": "because they are likely to be assigned to some class with high probability. Here, we update", + "type": "text" + }, + { + "bbox": [ + 478, + 517, + 487, + 526 + ], + "score": 0.82, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 487, + 516, + 505, + 529 + ], + "score": 1.0, + "content": "and", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 107, + 527, + 210, + 540 + ], + "spans": [ + { + "bbox": [ + 107, + 528, + 115, + 537 + ], + "score": 0.79, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 116, + 527, + 210, + 540 + ], + "score": 1.0, + "content": "same number of times.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 19 + }, + { + "type": "text", + "bbox": [ + 107, + 544, + 505, + 588 + ], + "lines": [ + { + "bbox": [ + 105, + 543, + 506, + 557 + ], + "spans": [ + { + "bbox": [ + 105, + 543, + 506, + 557 + ], + "score": 1.0, + "content": "Experiment. We evaluate our proposed GAN training method by using SVHN and CIFAR10", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 555, + 506, + 568 + ], + "spans": [ + { + "bbox": [ + 105, + 555, + 506, + 568 + ], + "score": 1.0, + "content": "datasets, using the critic network architecture from (Salimans et al. (2016)). We set the batch size as", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 565, + 506, + 579 + ], + "spans": [ + { + "bbox": [ + 105, + 565, + 261, + 579 + ], + "score": 1.0, + "content": "100 and used Adam with learning rate", + "type": "text" + }, + { + "bbox": [ + 261, + 565, + 309, + 577 + ], + "score": 0.92, + "content": "2 . 0 \\times 1 . 0 ^ { - 4 }", + "type": "inline_equation" + }, + { + "bbox": [ + 309, + 565, + 506, + 579 + ], + "score": 1.0, + "content": "for optimizer. After the conv6 layer of the critic,", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 577, + 453, + 590 + ], + "spans": [ + { + "bbox": [ + 105, + 577, + 453, + 590 + ], + "score": 1.0, + "content": "we constructed a classifier which was not concerned with adversarial learning process.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 23.5 + }, + { + "type": "text", + "bbox": [ + 107, + 593, + 505, + 638 + ], + "lines": [ + { + "bbox": [ + 105, + 594, + 505, + 605 + ], + "spans": [ + { + "bbox": [ + 105, + 594, + 492, + 605 + ], + "score": 1.0, + "content": "In the experiment on SVHN, we replaced Weight Normalization with Batch Normalization for", + "type": "text" + }, + { + "bbox": [ + 492, + 594, + 501, + 604 + ], + "score": 0.76, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 502, + 594, + 505, + 605 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 605, + 505, + 617 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 505, + 617 + ], + "score": 1.0, + "content": "Also, in the experiment on CIFAR10, we construct a classifier from a middle layer of the critic,", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 617, + 505, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 617, + 505, + 628 + ], + "score": 1.0, + "content": "which is not incorporated into the adversarial training step. This is motivated by the insight that the", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 627, + 493, + 639 + ], + "spans": [ + { + "bbox": [ + 105, + 627, + 493, + 639 + ], + "score": 1.0, + "content": "critic in our method is trained to be too sensitive to the dropout noise as we explained in Sec 3.3.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 27.5 + }, + { + "type": "text", + "bbox": [ + 106, + 643, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 643, + 505, + 656 + ], + "spans": [ + { + "bbox": [ + 105, + 643, + 505, + 656 + ], + "score": 1.0, + "content": "Results. From Fig. 10(a), we can see that ADR seems to generate realistic SVHN images. Some", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 655, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 655, + 505, + 667 + ], + "score": 1.0, + "content": "images are significantly blurred, but most of the images are clear and diverse. As for generated", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "score": 1.0, + "content": "CIFAR10 images, they do not seem as realistic, but some objects appear in most images. In Ta-", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 677, + 505, + 688 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 505, + 688 + ], + "score": 1.0, + "content": "ble 4, we can see that the accuracy of the critic trained by our method has better performance than", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 687, + 506, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 506, + 700 + ], + "score": 1.0, + "content": "other models for SVHN. For CIFAR10, the accuracy was slightly worse than other state-of-the-art", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 699, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 505, + 711 + ], + "score": 1.0, + "content": "methods. We conclude that, despite its clear advantage on the domain adaptation tasks, our method", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 710, + 506, + 721 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 506, + 721 + ], + "score": 1.0, + "content": "produces mixed results on the SSL tasks. It could still be useful for SSL, however, it needs further", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 720, + 506, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 506, + 733 + ], + "score": 1.0, + "content": "exploration to improve the accuracy. For example, in Eq. 6, we propose to maximize the entropy of", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 33.5 + } + ], + "page_idx": 13, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 25, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 25, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2018", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 751, + 311, + 760 + ], + "lines": [ + { + "bbox": [ + 299, + 750, + 313, + 764 + ], + "spans": [ + { + "bbox": [ + 299, + 750, + 313, + 764 + ], + "score": 1.0, + "content": "14", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "image", + "bbox": [ + 107, + 80, + 499, + 192 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 107, + 80, + 499, + 192 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 107, + 80, + 499, + 192 + ], + "spans": [ + { + "bbox": [ + 107, + 80, + 499, + 192 + ], + "score": 0.968, + "type": "image", + "image_path": "63364abe673b063e24a800150d6aed5d16f2ac6fd54204e6ef2d434abc5d60e1.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 107, + 80, + 499, + 117.33333333333334 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 107, + 117.33333333333334, + 499, + 154.66666666666669 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 107, + 154.66666666666669, + 499, + 192.00000000000003 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 221, + 199, + 389, + 211 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 218, + 198, + 389, + 213 + ], + "spans": [ + { + "bbox": [ + 218, + 198, + 389, + 213 + ], + "score": 1.0, + "content": "Figure 10: Examples of generated images.", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 3 + } + ], + "index": 2.0 + }, + { + "type": "table", + "bbox": [ + 128, + 220, + 480, + 304 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 128, + 220, + 480, + 304 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 128, + 220, + 480, + 304 + ], + "spans": [ + { + "bbox": [ + 128, + 220, + 480, + 304 + ], + "score": 0.969, + "html": "
SVHN (% errors)CIFAR (% errors)
Labeled Only SDGM (Maalge et al. (2016)16.61 ± 0.24
CatGAN (Springenberg (2015))=19.58±0.46
ALI (Dumoulin et al. (2016))7.42±0.6517.99±1.62
ImpGAN (Salimans et al. (2016))8.11±1.318.63±2.32
Ours6.26±1.0519.63±0.37
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We used the same critic architecture as used in ImpGAN.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 7.5, + "bbox_fs": [ + 106, + 312, + 504, + 335 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 202, + 369, + 409, + 383 + ], + "lines": [ + { + "bbox": [ + 202, + 369, + 409, + 383 + ], + "spans": [ + { + "bbox": [ + 202, + 369, + 409, + 383 + ], + "score": 0.9, + "content": "L _ { a d v } ( X _ { g } ) = \\mathbb { E } _ { { \\mathbf { x } } _ { \\mathbf { g } } \\sim X _ { G } } [ d ( C _ { 1 } ( G ( { \\mathbf { x } } _ { \\mathbf { g } } ) ) , C _ { 2 } ( G ( { \\mathbf { x } } _ { \\mathbf { g } } ) ) ) ]", + "type": "interline_equation", + "image_path": "83537d900fab4ee7a3f1710393b244f2849254ece073bff6f7ec2ac627714516.jpg" + } + ] + } + ], + "index": 9, + "virtual_lines": [ + { + "bbox": [ + 202, + 369, + 409, + 383 + ], + "spans": [], + "index": 9 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 384, + 505, + 441 + ], + "lines": [ + { + "bbox": [ + 106, + 385, + 505, + 397 + ], + "spans": [ + { + "bbox": [ + 106, + 385, + 133, + 397 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 133, + 385, + 148, + 396 + ], + "score": 0.89, + "content": "X _ { L }", + "type": "inline_equation" + }, + { + "bbox": [ + 149, + 385, + 301, + 397 + ], + "score": 1.0, + "content": "denotes the subset of labeled samples,", + "type": "text" + }, + { + "bbox": [ + 301, + 385, + 316, + 396 + ], + "score": 0.88, + "content": "X _ { u }", + "type": "inline_equation" + }, + { + "bbox": [ + 316, + 385, + 426, + 397 + ], + "score": 1.0, + "content": "denotes unlabeled ones and", + "type": "text" + }, + { + "bbox": [ + 427, + 385, + 441, + 397 + ], + "score": 0.89, + "content": "X _ { g }", + "type": "inline_equation" + }, + { + "bbox": [ + 441, + 385, + 505, + 397 + ], + "score": 1.0, + "content": "denotes images", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 395, + 505, + 408 + ], + "spans": [ + { + "bbox": [ + 105, + 395, + 160, + 408 + ], + "score": 1.0, + "content": "generated by", + "type": "text" + }, + { + "bbox": [ + 160, + 396, + 170, + 406 + ], + "score": 0.82, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 170, + 395, + 188, + 408 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 188, + 396, + 198, + 406 + ], + "score": 0.82, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 199, + 395, + 505, + 408 + ], + "score": 1.0, + "content": "denotes entropy as Eq.6 shows. The critic is trained to minimize the loss on", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 406, + 505, + 418 + ], + "spans": [ + { + "bbox": [ + 106, + 406, + 505, + 418 + ], + "score": 1.0, + "content": "labeled samples in the first term. Since unlabeled images should be far away from the decision", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 418, + 505, + 430 + ], + "spans": [ + { + "bbox": [ + 106, + 418, + 505, + 430 + ], + "score": 1.0, + "content": "boundary and should be distributed uniformly among the classes, we add the second and fourth", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 428, + 480, + 442 + ], + "spans": [ + { + "bbox": [ + 105, + 428, + 480, + 442 + ], + "score": 1.0, + "content": "term. The third term encourages the critic to detect fake images generated near the boundary.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 12, + "bbox_fs": [ + 105, + 385, + 505, + 442 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 445, + 238, + 456 + ], + "lines": [ + { + "bbox": [ + 106, + 443, + 240, + 459 + ], + "spans": [ + { + "bbox": [ + 106, + 443, + 174, + 459 + ], + "score": 1.0, + "content": "The objective of", + "type": "text" + }, + { + "bbox": [ + 174, + 446, + 183, + 455 + ], + "score": 0.84, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 183, + 443, + 240, + 459 + ], + "score": 1.0, + "content": "is as follows,", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 15, + "bbox_fs": [ + 106, + 443, + 240, + 459 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 195, + 460, + 414, + 479 + ], + "lines": [ + { + "bbox": [ + 195, + 460, + 414, + 479 + ], + "spans": [ + { + "bbox": [ + 195, + 460, + 414, + 479 + ], + "score": 0.9, + "content": "\\operatorname* { m i n } _ { G } L _ { a d v } ( X _ { g } ) + | | \\mathbb { E } _ { x _ { g } \\sim X _ { g } } f ( \\mathbf { x _ { g } } ) - \\mathbb { E } _ { \\mathbf { x _ { u } } \\sim X _ { u } } f ( \\mathbf { x _ { u } } ) | | ^ { 2 }", + "type": "interline_equation", + "image_path": "aa12383d6c54067bf716e7a8e1391d0066b156b3c026b96dcb40a20a36336bfa.jpg" + } + ] + } + ], + "index": 16, + "virtual_lines": [ + { + "bbox": [ + 195, + 460, + 414, + 479 + ], + "spans": [], + "index": 16 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 483, + 505, + 539 + ], + "lines": [ + { + "bbox": [ + 106, + 484, + 505, + 496 + ], + "spans": [ + { + "bbox": [ + 106, + 484, + 505, + 496 + ], + "score": 1.0, + "content": "where the second term encourages generated images to be similar to real images, which is known to", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 494, + 505, + 507 + ], + "spans": [ + { + "bbox": [ + 105, + 494, + 505, + 507 + ], + "score": 1.0, + "content": "be effective to stabilize the training. The first term encourages the generator to create fake images", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 504, + 505, + 519 + ], + "spans": [ + { + "bbox": [ + 105, + 504, + 505, + 519 + ], + "score": 1.0, + "content": "which should be placed far away from the boundary. Such images should be similar to real images", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 516, + 505, + 529 + ], + "spans": [ + { + "bbox": [ + 105, + 516, + 477, + 529 + ], + "score": 1.0, + "content": "because they are likely to be assigned to some class with high probability. Here, we update", + "type": "text" + }, + { + "bbox": [ + 478, + 517, + 487, + 526 + ], + "score": 0.82, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 487, + 516, + 505, + 529 + ], + "score": 1.0, + "content": "and", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 107, + 527, + 210, + 540 + ], + "spans": [ + { + "bbox": [ + 107, + 528, + 115, + 537 + ], + "score": 0.79, + "content": "G", + "type": "inline_equation" + }, + { + "bbox": [ + 116, + 527, + 210, + 540 + ], + "score": 1.0, + "content": "same number of times.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 19, + "bbox_fs": [ + 105, + 484, + 505, + 540 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 544, + 505, + 588 + ], + "lines": [ + { + "bbox": [ + 105, + 543, + 506, + 557 + ], + "spans": [ + { + "bbox": [ + 105, + 543, + 506, + 557 + ], + "score": 1.0, + "content": "Experiment. We evaluate our proposed GAN training method by using SVHN and CIFAR10", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 555, + 506, + 568 + ], + "spans": [ + { + "bbox": [ + 105, + 555, + 506, + 568 + ], + "score": 1.0, + "content": "datasets, using the critic network architecture from (Salimans et al. (2016)). We set the batch size as", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 565, + 506, + 579 + ], + "spans": [ + { + "bbox": [ + 105, + 565, + 261, + 579 + ], + "score": 1.0, + "content": "100 and used Adam with learning rate", + "type": "text" + }, + { + "bbox": [ + 261, + 565, + 309, + 577 + ], + "score": 0.92, + "content": "2 . 0 \\times 1 . 0 ^ { - 4 }", + "type": "inline_equation" + }, + { + "bbox": [ + 309, + 565, + 506, + 579 + ], + "score": 1.0, + "content": "for optimizer. After the conv6 layer of the critic,", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 577, + 453, + 590 + ], + "spans": [ + { + "bbox": [ + 105, + 577, + 453, + 590 + ], + "score": 1.0, + "content": "we constructed a classifier which was not concerned with adversarial learning process.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 23.5, + "bbox_fs": [ + 105, + 543, + 506, + 590 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 593, + 505, + 638 + ], + "lines": [ + { + "bbox": [ + 105, + 594, + 505, + 605 + ], + "spans": [ + { + "bbox": [ + 105, + 594, + 492, + 605 + ], + "score": 1.0, + "content": "In the experiment on SVHN, we replaced Weight Normalization with Batch Normalization for", + "type": "text" + }, + { + "bbox": [ + 492, + 594, + 501, + 604 + ], + "score": 0.76, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 502, + 594, + 505, + 605 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 605, + 505, + 617 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 505, + 617 + ], + "score": 1.0, + "content": "Also, in the experiment on CIFAR10, we construct a classifier from a middle layer of the critic,", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 617, + 505, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 617, + 505, + 628 + ], + "score": 1.0, + "content": "which is not incorporated into the adversarial training step. This is motivated by the insight that the", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 627, + 493, + 639 + ], + "spans": [ + { + "bbox": [ + 105, + 627, + 493, + 639 + ], + "score": 1.0, + "content": "critic in our method is trained to be too sensitive to the dropout noise as we explained in Sec 3.3.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 27.5, + "bbox_fs": [ + 105, + 594, + 505, + 639 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 643, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 643, + 505, + 656 + ], + "spans": [ + { + "bbox": [ + 105, + 643, + 505, + 656 + ], + "score": 1.0, + "content": "Results. From Fig. 10(a), we can see that ADR seems to generate realistic SVHN images. Some", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 655, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 655, + 505, + 667 + ], + "score": 1.0, + "content": "images are significantly blurred, but most of the images are clear and diverse. As for generated", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "score": 1.0, + "content": "CIFAR10 images, they do not seem as realistic, but some objects appear in most images. In Ta-", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 677, + 505, + 688 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 505, + 688 + ], + "score": 1.0, + "content": "ble 4, we can see that the accuracy of the critic trained by our method has better performance than", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 687, + 506, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 506, + 700 + ], + "score": 1.0, + "content": "other models for SVHN. For CIFAR10, the accuracy was slightly worse than other state-of-the-art", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 699, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 505, + 711 + ], + "score": 1.0, + "content": "methods. We conclude that, despite its clear advantage on the domain adaptation tasks, our method", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 710, + 506, + 721 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 506, + 721 + ], + "score": 1.0, + "content": "produces mixed results on the SSL tasks. It could still be useful for SSL, however, it needs further", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 720, + 506, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 506, + 733 + ], + "score": 1.0, + "content": "exploration to improve the accuracy. For example, in Eq. 6, we propose to maximize the entropy of", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "the marginal class distribution of the unlabeled real images, as well as forcing them to be far from", + "type": "text", + "cross_page": true + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 94, + 505, + 105 + ], + "spans": [ + { + "bbox": [ + 106, + 94, + 505, + 105 + ], + "score": 1.0, + "content": "the boundary. However, these objectives may contradict each other, which may in turn degrade the", + "type": "text", + "cross_page": true + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 104, + 506, + 117 + ], + "spans": [ + { + "bbox": [ + 105, + 104, + 506, + 117 + ], + "score": 1.0, + "content": "performance. In late-breaking results, Dai et al. (2017) theoretically showed that just generating fake", + "type": "text", + "cross_page": true + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 506, + 128 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 506, + 128 + ], + "score": 1.0, + "content": "images that are far from decision boundaries does not help to improve accuracy in training GANs in", + "type": "text", + "cross_page": true + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 125, + 506, + 140 + ], + "spans": [ + { + "bbox": [ + 105, + 125, + 506, + 140 + ], + "score": 1.0, + "content": "the setting of SSL. Further improvement of our SSL approach based on these results is an interesting", + "type": "text", + "cross_page": true + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 137, + 210, + 149 + ], + "spans": [ + { + "bbox": [ + 106, + 137, + 210, + 149 + ], + "score": 1.0, + "content": "direction for future work.", + "type": "text", + "cross_page": true + } + ], + "index": 5 + } + ], + "index": 33.5, + "bbox_fs": [ + 105, + 643, + 506, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 505, + 148 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "the marginal class distribution of the unlabeled real images, as well as forcing them to be far from", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 94, + 505, + 105 + ], + "spans": [ + { + "bbox": [ + 106, + 94, + 505, + 105 + ], + "score": 1.0, + "content": "the boundary. 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METHODSVHN to MNISTUSPS to MNISTMNIST(P1) to USPSMNIST(P2) to USPS
Source Only67.168.177.078.9
LTN (Sener et al. (2016))78.8-1-
ATDA (Saito et al. (2017))86.2†=1-
DSN (Bousmalis et al. (2016))82.7†91.3†
PixelDA (Bousmalis et al. (2017)1=-95.9†
DANN (Ganin & Lempitsky (2014))73.973.0±2.077.1±1.885.1†
DoC (Tzeng et al. (2014))68.1±0.366.5±3.379.1±0.51
ADDA (Tzeng et al. (2017))76.0±1.890.1±0.889.4±0.2-
CoGAN (Liu & Tuzel (2016))did not converge89.1±0.891.2±0.8=
DTN (Taigman et al. (2016))84.71-
ENT (Our proposed baseline) Ours94.9±4.11 95.0±1.8791.2±1.92 93.1±1.2793.7±0.54 93.2±2.4696.7±1.27 96.1±0.29
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Methodgrrrdoraegpaleie 3ueoormorreiltuosiadsareraertrnaaa
Finetuning on ResNet101
Source Only55.153.3 61.959.180.617.979.731.281.026.573.58.552.4
MMD87.163.0 76.542.090.342.985.953.149.736.385.820.761.1
DANN81.977.7 82.844.381.229.565.128.651.954.682.87.857.4
ENT80.375.5 75.848.377.927.369.740.246.546.679.316.057.0
Ours94.151.3 83.272.288.768.892.870.277.263.682.930.372.9
Ours (retrained classifier)94.248.5 84.072.990.174.292.672.580.861.882.228.873.5
Finetuning on ResNeXt
Source Only74.3 37.6 61.8 68.2 59.510.7 81.412.8 61.6 26.070.05.647.4
MMD90.751.1 64.865.689.946.591.940.181.524.190.028.563.7
DANN86.066.3 60.8 56.079.853.782.325.258.231.089.326.159.6
ENT94.781.0 57.046.673.949.069.231.040.534.387.315.156.6
Ours86.3 71.987.678.193.084.894.578.991.858.977.726.777.5
Ours (retrained classifier)89.270.9 85.782.093.786.7 93.372.389.553.086.728.377.6
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NetworkMethodxeeepreBuiplng8irilen买uosradMur0mrrqeemIoU
VGG-16FCN Wild70.432.462.114.95.410.914.22.779.221.364.644.14.270.48.07.30.03.50.027.1
ResNet50Source OnlyDANNOurs64.572.487.824.919.115.673.714.83.920.62.59.39.718.017.319.015.913.119.90.05.57.774.916.472.042.30.039.58.612.117.513.49.927.70.00.01.80.05.89.70.00.00.025.326.433.3
73.077.471.082.020.131.562.274.332.643.55.29.068.477.8
DRN-105Source OnlyOurs25.986.210.910.150.578.83.320.112.27.425.428.613.015.078.384.57.338.963.952.17.966.35.229.67.832.70.90.213.719.20.78.324.937.3
21.226.581.154.613.680.8
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SVHN (% errors)CIFAR (% errors)
Labeled Only SDGM (Maalge et al. (2016)16.61 ± 0.24
CatGAN (Springenberg (2015))=19.58±0.46
ALI (Dumoulin et al. (2016))7.42±0.6517.99±1.62
ImpGAN (Salimans et al. (2016))8.11±1.318.63±2.32
Ours6.26±1.0519.63±0.37
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sha256:1e0608a49dda76b8158372e126a52144809b4af0d962f5b4889a8eb9c34f5d51 +size 19759 diff --git a/parse/train/J4gRj6d5Qm/J4gRj6d5Qm_content_list.json b/parse/train/J4gRj6d5Qm/J4gRj6d5Qm_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..247541a3d60c115bb725e4d558f87999202a546e --- /dev/null +++ b/parse/train/J4gRj6d5Qm/J4gRj6d5Qm_content_list.json @@ -0,0 +1,1041 @@ +[ + { + "type": "text", + "text": "Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting ", + "text_level": 1, + "bbox": [ + 189, + 122, + 810, + 172 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Haixu Wu, Jiehui Xu, Jianmin Wang, Mingsheng Long $( \\boxtimes )$ School of Software, BNRist, Tsinghua University, China {whx20,xjh20}@mails.tsinghua.edu.cn, {jimwang,mingsheng}@tsinghua.edu.cn ", + "bbox": [ + 191, + 224, + 805, + 268 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract ", + "text_level": 1, + "bbox": [ + 462, + 303, + 535, + 320 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Extending the forecasting time is a critical demand for real applications, such as extreme weather early warning and long-term energy consumption planning. This paper studies the long-term forecasting problem of time series. Prior Transformerbased models adopt various self-attention mechanisms to discover the long-range dependencies. However, intricate temporal patterns of the long-term future prohibit the model from finding reliable dependencies. Also, Transformers have to adopt the sparse versions of point-wise self-attentions for long series efficiency, resulting in the information utilization bottleneck. Going beyond Transformers, we design Autoformer as a novel decomposition architecture with an Auto-Correlation mechanism. We break with the pre-processing convention of series decomposition and renovate it as a basic inner block of deep models. This design empowers Autoformer with progressive decomposition capacities for complex time series. Further, inspired by the stochastic process theory, we design the Auto-Correlation mechanism based on the series periodicity, which conducts the dependencies discovery and representation aggregation at the sub-series level. Auto-Correlation outperforms self-attention in both efficiency and accuracy. In long-term forecasting, Autoformer yields stateof-the-art accuracy, with a $38 \\%$ relative improvement on six benchmarks, covering five practical applications: energy, traffic, economics, weather and disease. Code is available at this repository: https://github.com/thuml/Autoformer. ", + "bbox": [ + 232, + 335, + 766, + 599 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 Introduction ", + "text_level": 1, + "bbox": [ + 174, + 626, + 310, + 643 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Time series forecasting has been widely used in energy consumption, traffic and economics planning, weather and disease propagation forecasting. In these real-world applications, one pressing demand is to extend the forecast time into the far future, which is quite meaningful for the long-term planning and early warning. Thus, in this paper, we study the long-term forecasting problem of time series, characterizing itself by the large length of predicted time series. Recent deep forecasting models [41, 17, 20, 28, 23, 29, 19, 35] have achieved great progress, especially the Transformer-based models. Benefiting from the self-attention mechanism, Transformers obtain great advantage in modeling long-term dependencies for sequential data, which enables more powerful big models [7, 11]. ", + "bbox": [ + 174, + 657, + 825, + 768 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, the forecasting task is extremely challenging under the long-term setting. First, it is unreliable to discover the temporal dependencies directly from the long-term time series because the dependencies can be obscured by entangled temporal patterns. Second, canonical Transformers with self-attention mechanisms are computationally prohibitive for long-term forecasting because of the quadratic complexity of sequence length. Previous Transformer-based forecasting models [41, 17, 20] mainly focus on improving self-attention to a sparse version. While performance is significantly improved, these models still utilize the point-wise representation aggregation. Thus, in the process of efficiency improvement, they will sacrifice the information utilization because of the sparse point-wise connections, resulting in a bottleneck for long-term forecasting of time series. ", + "bbox": [ + 174, + 775, + 825, + 900 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To reason about the intricate temporal patterns, we try to take the idea of decomposition, which is a standard method in time series analysis [1, 27]. It can be used to process the complex time series and extract more predictable components. However, under the forecasting context, it can only be used as the pre-processing of past series because the future is unknown [15]. This common usage limits the capabilities of decomposition and overlooks the potential future interactions among decomposed components. Thus, we attempt to go beyond pre-processing usage of decomposition and propose a generic architecture to empower the deep forecasting models with immanent capacity of progressive decomposition. Further, decomposition can ravel out the entangled temporal patterns and highlight the inherent properties of time series [15]. Benefiting from this, we try to take advantage of the series periodicity to renovate the point-wise connection in self-attention. We observe that the sub-series at the same phase position among periods often present similar temporal processes. Thus, we try to construct a series-level connection based on the process similarity derived by series periodicity. ", + "bbox": [ + 174, + 92, + 825, + 257 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Based on the above motivations, we propose an original Autoformer in place of the Transformers for long-term time series forecasting. Autoformer still follows residual and encoder-decoder structure but renovates Transformer into a decomposition forecasting architecture. By embedding our proposed decomposition blocks as the inner operators, Autoformer can progressively separate the long-term trend information from predicted hidden variables. This design allows our model to alternately decompose and refine the intermediate results during the forecasting procedure. Inspired by the stochastic process theory [8, 24], Autoformer introduces an Auto-Correlation mechanism in place of self-attention, which discovers the sub-series similarity based on the series periodicity and aggregates similar sub-series from underlying periods. This series-wise mechanism achieves $\\mathcal { O } ( L \\log L )$ complexity for length- $L$ series and breaks the information utilization bottleneck by expanding the point-wise representation aggregation to sub-series level. Autoformer achieves the state-of-the-art accuracy on six benchmarks. The contributions are summarized as follows: ", + "bbox": [ + 174, + 263, + 825, + 429 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "• To tackle the intricate temporal patterns of the long-term future, we present Autoformer as a decomposition architecture and design the inner decomposition block to empower the deep forecasting model with immanent progressive decomposition capacity. • We propose an Auto-Correlation mechanism with dependencies discovery and information aggregation at the series level. Our mechanism is beyond previous self-attention family and can simultaneously benefit the computation efficiency and information utilization. • Autoformer achieves a $38 \\%$ relative improvement under the long-term setting on six benchmarks, covering five real-world applications: energy, traffic, economics, weather and disease. ", + "bbox": [ + 217, + 440, + 825, + 561 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2 Related Work ", + "text_level": 1, + "bbox": [ + 174, + 578, + 323, + 594 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1 Models for Time Series Forecasting ", + "text_level": 1, + "bbox": [ + 176, + 603, + 459, + 618 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Due to the immense importance of time series forecasting, various models have been well developed. Many time series forecasting methods start from the classic tools [32, 9]. ARIMA [6, 5] tackles the forecasting problem by transforming the non-stationary process to stationary through differencing. The filtering method is also introduced for series forecasting [18, 10]. Besides, recurrent neural networks (RNNs) models are used to model the temporal dependencies for time series [36, 26, 40, 22]. DeepAR [28] combines autoregressive methods and RNNs to model the probabilistic distribution of future series. LSTNet [19] introduces convolutional neural networks (CNNs) with recurrent-skip connections to capture the short-term and long-term temporal patterns. Attention-based RNNs [39, 30, 31] introduce the temporal attention to explore the long-range dependencies for prediction. Also, many works based on temporal convolution networks (TCN) [34, 4, 3, 29] attempt to model the temporal causality with the causal convolution. These deep forecasting models mainly focus on the temporal relation modeling by recurrent connections, temporal attention or causal convolution. ", + "bbox": [ + 173, + 628, + 826, + 794 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, Transformers [35, 38] based on the self-attention mechanism shows great power in sequential data, such as natural language processing [11, 7], audio processing [14] and even computer vision [12, 21]. However, applying self-attention to long-term time series forecasting is computationally prohibitive because of the quadratic complexity of sequence length $L$ in both memory and time. LogTrans [20] introduces the local convolution to Transformer and proposes the LogSparse attention to select time steps following the exponentially increasing intervals, which reduces the complexity to $\\mathcal { O } ( L ( \\log L ) ^ { 2 } )$ . Reformer [17] presents the local-sensitive hashing (LSH) attention and reduces the complexity to $\\mathcal { O } ( L \\log L )$ . Informer [41] extends Transformer with KL-divergence based ProbSparse attention and also achieves $\\mathcal { O } ( L \\log L )$ complexity. Note that these methods are based on the vanilla Transformer and try to improve the self-attention mechanism to a sparse version, which still follows the point-wise dependency and aggregation. In this paper, our proposed Auto-Correlation mechanism is based on the inherent periodicity of time series and can provide series-wise connections. ", + "bbox": [ + 174, + 800, + 825, + 911 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 90, + 825, + 147 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2 Decomposition of Time Series ", + "text_level": 1, + "bbox": [ + 176, + 162, + 418, + 178 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As a standard method in time series analysis, time series decomposition [1, 27] deconstructs a time series into several components, each representing one of the underlying categories of patterns that are more predictable. It is primarily useful for exploring historical changes over time. For the forecasting tasks, decomposition is always used as the pre-processing of historical series before predicting future series [15, 2], such as Prophet [33] with trend-seasonality decomposition and N-BEATS [23] with basis expansion and DeepGLO [29] with matrix decomposition. However, such pre-processing is limited by the plain decomposition effect of historical series and overlooks the hierarchical interaction between the underlying patterns of series in the long-term future. This paper takes the decomposition idea from a new progressive dimension. Our Autoformer harnesses the decomposition as an inner block of deep models, which can progressively decompose the hidden series throughout the whole forecasting process, including both the past series and the predicted intermediate results. ", + "bbox": [ + 174, + 188, + 825, + 340 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3 Autoformer ", + "text_level": 1, + "bbox": [ + 174, + 358, + 303, + 376 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The time series forecasting problem is to predict the most probable length- $O$ series in the future given the past length- ${ \\mathbf { \\nabla } } \\cdot { I }$ series, denoting as input-I-predict- $O$ . The long-term forecasting setting is to predict the long-term future, i.e. larger $O$ . As aforementioned, we have highlighted the difficulties of long-term series forecasting: handling intricate temporal patterns and breaking the bottleneck of computation efficiency and information utilization. To tackle these two challenges, we introduce the decomposition as a builtin block to the deep forecasting model and propose Autoformer as a decomposition architecture. Besides, we design the Auto-Correlation mechanism to discover the period-based dependencies and aggregate similar sub-series from underlying periods. ", + "bbox": [ + 174, + 388, + 825, + 501 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1 Decomposition Architecture ", + "text_level": 1, + "bbox": [ + 176, + 516, + 408, + 531 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We renovate Transformer [35] to a deep decomposition architecture (Figure 1), including the inner series decomposition block, Auto-Correlation mechanism, and corresponding Encoder and Decoder. ", + "bbox": [ + 174, + 541, + 825, + 570 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Series decomposition block To learn with the complex temporal patterns in long-term forecasting context, we take the idea of decomposition [1, 27], which can separate the series into trend-cyclical and seasonal parts. These two parts reflect the long-term progression and the seasonality of the series respectively. However, directly decomposing is unrealizable for future series because the future is just unknown. To tackle this dilemma, we present a series decomposition block as an inner operation of Autoformer (Figure 1), which can extract the long-term stationary trend from predicted intermediate hidden variables progressively. Concretely, we adapt the moving average to smooth out periodic fluctuations and highlight the long-term trends. For length- $L$ input series $\\breve { \\mathcal { X } } \\in \\mathbb { R } ^ { L \\times d }$ , the process is: ", + "bbox": [ + 173, + 577, + 825, + 689 + ], + "page_idx": 2 + }, + { + "type": "equation", + "img_path": "images/282df0854e95928f14b62ed4e853f369b7025077bb7d2e1cc6605fe5b7efcf53.jpg", + "text": "$$\n\\begin{array} { r l } & { \\mathcal { X } _ { \\mathrm { t } } = \\mathrm { A v g P o o l } ( \\mathrm { P a d d i n g } ( \\mathcal { X } ) ) } \\\\ & { \\mathcal { X } _ { \\mathrm { s } } = \\mathcal { X } - \\mathcal { X } _ { \\mathrm { t } } , } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 397, + 691, + 599, + 728 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\boldsymbol { \\mathcal { X } } _ { \\mathrm { s } } , \\boldsymbol { \\mathcal { X } } _ { \\mathrm { t } } \\in \\mathbb { R } ^ { L \\times d }$ denote the seasonal and the extracted trend-cyclical part respectively. We adopt the $\\operatorname { A v g P o o l } ( \\cdot )$ for moving average with the padding operation to keep the series length unchanged. We use $\\mathcal { X } _ { \\mathrm { s } } , \\mathcal { X } _ { \\mathrm { t } } = \\mathrm { S e r i e s D e c o m p } ( \\mathcal { X } )$ to summarize above equations, which is a model inner block. ", + "bbox": [ + 174, + 732, + 825, + 775 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Model inputs The inputs of encoder part are the past $I$ time steps $\\mathcal { X } _ { \\mathrm { e n } } \\in \\mathbb { R } ^ { I \\times d }$ . As a decomposition architecture (Figure 1), the input of Autoformer decoder contains both the seasonal part $\\chi _ { \\mathrm { d e s } } \\in$ $\\mathbb { R } ^ { ( \\frac { I } { 2 } + O ) \\times d }$ and trend-cyclical part $\\chi _ { \\mathrm { d e t } } \\in \\mathbb { R } ^ { ( \\frac { I } { 2 } + O ) \\times d }$ to be refined. Each initialization consists of two parts: the component decomposed from the latter half of encoder’s input $\\mathcal { X } _ { \\mathrm { e n } }$ with length $\\frac { I } { 2 }$ to provide recent information, placeholders with length $O$ filled by scalars. It’s formulized as follows: ", + "bbox": [ + 173, + 784, + 825, + 856 + ], + "page_idx": 2 + }, + { + "type": "equation", + "img_path": "images/2ca468ee556859c90f1fc9a7b942f1134137418316e28b4815e04a5396ca9b82.jpg", + "text": "$$\n\\begin{array} { r l } & { \\mathcal { X } _ { \\mathrm { e n s } } , \\mathcal { X } _ { \\mathrm { e n t } } = \\mathrm { S e r i e s D e c o m p } ( \\mathcal { X } _ { \\mathrm { e n } \\frac { I } { 2 } : I } ) } \\\\ & { \\qquad \\mathcal { X } _ { \\mathrm { d e s } } = \\mathrm { C o n c a t } ( \\mathcal { X } _ { \\mathrm { e n s } } , \\mathcal { X } _ { 0 } ) } \\\\ & { \\qquad \\mathcal { X } _ { \\mathrm { d e t } } = \\mathrm { C o n c a t } ( \\mathcal { X } _ { \\mathrm { e n t } } , \\mathcal { X } _ { \\mathrm { M e a n } } ) , } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 372, + 858, + 624, + 916 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/1ebb1575216e8696f19f85fe903bb441210d41e8973469f64d31b9ac1d64fa43.jpg", + "image_caption": [ + "Figure 1: Autoformer architecture. The encoder eliminates the long-term trend-cyclical part by series decomposition blocks (blue blocks) and focuses on seasonal patterns modeling. The decoder accumulates the trend part extracted from hidden variables progressively. The past seasonal information from encoder is utilized by the encoder-decoder Auto-Correlation (center green block in decoder). " + ], + "image_footnote": [], + "bbox": [ + 174, + 88, + 825, + 286 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\chi _ { \\mathrm { e n s } } , \\chi _ { \\mathrm { e n t } } \\in \\mathbb { R } ^ { \\frac { I } { 2 } \\times d }$ denote the seasonal and trend-cyclical parts of $\\mathcal { X } _ { \\mathrm { e n } }$ respectively, and $\\mathcal { X } _ { 0 } , \\mathcal { X } _ { \\mathrm { M e a n } } \\in \\mathbb { R } ^ { O \\times d }$ denote the placeholders filled with zero and the mean of $\\mathcal { X } _ { \\mathrm { e n } }$ respectively. ", + "bbox": [ + 174, + 368, + 823, + 400 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Encoder As shown in Figure 1, the encoder focuses on the seasonal part modeling. The output of the encoder contains the past seasonal information and will be used as the cross information to help the decoder refine prediction results. Suppose we have $N$ encoder layers. The overall equations for $l$ -th encoder layer are summarized as $\\mathcal { X } _ { \\mathrm { e n } } ^ { \\hat { l } ^ { \\mathrm { ~ \\tiny ~ \\cdot ~ } } } = \\mathrm { E n c o d e r } ( \\mathcal { X } _ { \\mathrm { e n } } ^ { l - 1 } )$ . Details are shown as follows: ", + "bbox": [ + 173, + 412, + 826, + 469 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/cf5b96dae4c206d1e884f885670db030d85b3cb046d302cbd50a4dac521f6449.jpg", + "text": "$$\n\\begin{array} { r l } & { S _ { \\mathrm { e n } } ^ { l , 1 } , \\ l _ { - } = \\mathrm { S e r i e s D e c o m p } \\Big ( \\mathrm { A u t o - C o r r e l a t i o n } ( \\mathcal { X } _ { \\mathrm { e n } } ^ { l - 1 } ) + \\mathcal { X } _ { \\mathrm { e n } } ^ { l - 1 } \\Big ) } \\\\ & { S _ { \\mathrm { e n } } ^ { l , 2 } , \\ l _ { - } = \\mathrm { S e r i e s D e c o m p } \\Big ( \\mathrm { F e e d F o r w a r d } ( S _ { \\mathrm { e n } } ^ { l , 1 } ) + S _ { \\mathrm { e n } } ^ { l , 1 } \\Big ) , } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 292, + 474, + 704, + 529 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\underline { { { \\bf \\Pi } } } ^ { 6 6 } \\underline { { { \\bf \\Pi } } } ^ { 5 9 }$ is the eliminated trend part. $\\mathcal { X } _ { \\mathrm { e n } } ^ { l } = S _ { \\mathrm { e n } } ^ { l , 2 } , l \\in \\{ 1 , \\cdots , N \\}$ denotes the output of $l$ -th encoder layer and $\\mathcal { X } _ { \\mathrm { e n } } ^ { 0 }$ is the embedded $\\mathcal { X } _ { \\mathrm { e n } }$ . $S _ { \\mathrm { e n } } ^ { l , i }$ , $i \\in \\{ 1 , 2 \\}$ represents the seasonal component after the -th series decomposition block in the $l$ -th layer respectively. We will give detailed description of Auto-Correlation $( \\cdot )$ in the next section, which can seamlessly replace the self-attention. ", + "bbox": [ + 173, + 532, + 825, + 592 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Decoder The decoder contains two parts: the accumulation structure for trend-cyclical components and the stacked Auto-Correlation mechanism for seasonal components (Figure 1). Each decoder layer contains the inner Auto-Correlation and encoder-decoder Auto-Correlation, which can refine the prediction and utilize the past seasonal information respectively. Note that the model extracts the potential trend from the intermediate hidden variables during the decoder, allowing Autoformer to progressively refine the trend prediction and eliminate interference information for period-based dependencies discovery in Auto-Correlation. Suppose there are $M$ decoder layers. With the latent variable $\\chi _ { \\mathrm { e n } } ^ { N }$ from the encoder, the equations of $l$ -th decoder layer can be summarized as $\\mathcal { X } _ { \\mathrm { d e } } ^ { l } =$ $\\mathrm { D e c o d e r } ( \\mathcal { X } _ { \\mathrm { d e } } ^ { l - 1 } , \\mathcal { X } _ { \\mathrm { e n } } ^ { N } )$ . The decoder can be formalized as follows: ", + "bbox": [ + 173, + 604, + 826, + 734 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/61949f61e35543e7ee1153307307222fd6b2e0d60dadeae1cc3fce06995e170c.jpg", + "text": "$$\n\\begin{array} { r l } & { S _ { \\mathrm { d e } } ^ { l , 1 } , \\mathcal { T } _ { \\mathrm { d e } } ^ { l , 1 } = \\mathrm { S e r i e s D e c o m p } \\left( \\mathrm { A u t o - C o r r e l a t i o n } ( \\mathcal { X } _ { \\mathrm { d e } } ^ { l - 1 } ) + \\mathcal { X } _ { \\mathrm { d e } } ^ { l - 1 } \\right) } \\\\ & { S _ { \\mathrm { d e } } ^ { l , 2 } , \\mathcal { T } _ { \\mathrm { d e } } ^ { l , 2 } = \\mathrm { S e r i e s D e c o m p } \\left( \\mathrm { A u t o - C o r r e l a t i o n } ( S _ { \\mathrm { d e } } ^ { l , 1 } , \\mathcal { X } _ { \\mathrm { e n } } ^ { N } ) + S _ { \\mathrm { d e } } ^ { l , 1 } \\right) } \\\\ & { S _ { \\mathrm { d e } } ^ { l , 3 } , \\mathcal { T } _ { \\mathrm { d e } } ^ { l , 3 } = \\mathrm { S e r i e s D e c o m p } \\left( \\mathrm { F e e d F o r w a r d } ( S _ { \\mathrm { d e } } ^ { l , 2 } ) + S _ { \\mathrm { d e } } ^ { l , 2 } \\right) } \\\\ & { \\qquad \\mathcal { T } _ { \\mathrm { d e } } ^ { l } = \\mathcal { T } _ { \\mathrm { d e } } ^ { l - 1 } + \\mathcal { W } _ { l , 1 } \\ast \\mathcal { T } _ { \\mathrm { d e } } ^ { l , 1 } + \\mathcal { W } _ { l , 2 } \\ast \\mathcal { T } _ { \\mathrm { d e } } ^ { l , 2 } + \\mathcal { W } _ { l , 3 } \\ast \\mathcal { T } _ { \\mathrm { d e } } ^ { l , 3 } , } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 274, + 738, + 723, + 844 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal { X } _ { \\mathrm { d e } } ^ { l } = { S } _ { \\mathrm { d e } } ^ { l , 3 } , l \\in \\{ 1 , \\cdots , M \\}$ denotes the output of $l$ -th decoder layer. $\\mathcal { X } _ { \\mathrm { d e } } ^ { 0 }$ is embedded from $\\mathcal { X } _ { \\mathrm { d e s } }$ de de for deep transform and $\\mathcal { T } _ { \\mathrm { d e } } ^ { 0 } = \\mathcal { X } _ { \\mathrm { d e t } }$ is for accumulatio . $S _ { \\mathrm { d e } } ^ { l , i } , T _ { \\mathrm { d e } } ^ { l , i } , i \\in \\{ 1 , 2 , 3 \\}$ represent the $i$ $l$ -th layer respectively. $\\mathcal { W } _ { l , i } , i \\in \\{ 1 , 2 , 3 \\}$ represents the projector for the $i$ -th extracted trend $\\mathcal { T } _ { \\mathrm { d e } } ^ { l , i }$ . ", + "bbox": [ + 173, + 848, + 825, + 912 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/611e264868072bea6977edb6f802f5f63a12c602deabbfe382df58f997963cca.jpg", + "image_caption": [ + "Figure 2: Auto-Correlation (left) and Time Delay Aggregation (right). We utilize the Fast Fourier Transform to calculate the autocorrelation $\\mathcal { R } ( \\tau )$ , which reflects the time-delay similarities. Then the similar sub-processes are rolled to the same index based on selected delay $\\tau$ and aggregated by $\\mathcal { R } ( \\tau )$ . " + ], + "image_footnote": [], + "bbox": [ + 173, + 90, + 826, + 272 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The final prediction is the sum of the two refined decomposed components, as $\\mathcal { W } _ { S } \\ast \\mathcal { X } _ { \\mathrm { d e } } ^ { M } + \\mathcal { T } _ { \\mathrm { d e } } ^ { M }$ where is to project the deep transformed seasonal component to the target dimension. ", + "bbox": [ + 174, + 339, + 825, + 371 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2 Auto-Correlation Mechanism ", + "text_level": 1, + "bbox": [ + 174, + 381, + 418, + 395 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As shown in Figure 2, we propose the Auto-Correlation mechanism with series-wise connections to expand the information utilization. Auto-Correlation discovers the period-based dependencies by calculating the series autocorrelation and aggregates similar sub-series by time delay aggregation. ", + "bbox": [ + 173, + 400, + 826, + 443 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Period-based dependencies It is observed that the same phase position among periods naturally provides similar sub-processes. Inspired by the stochastic process theory [8, 24], for a real discretetime process $\\{ \\mathcal { X } _ { t } \\}$ , we can obtain the autocorrelation $\\mathcal { R } _ { \\mathcal { X } \\mathcal { X } } ( \\tau )$ by the following equations: ", + "bbox": [ + 173, + 457, + 825, + 501 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/fb64cef2f5829fd289fb477f5c815edeb42f5543fa2e2009089f66659843dcdb.jpg", + "text": "$$\n\\mathcal { R } _ { \\mathcal { X } \\mathcal { X } } ( \\tau ) = \\operatorname* { l i m } _ { L \\infty } \\frac { 1 } { L } \\sum _ { t = 1 } ^ { L } \\mathcal { X } _ { t } \\mathcal { X } _ { t - \\tau } .\n$$", + "text_format": "latex", + "bbox": [ + 387, + 507, + 611, + 551 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\mathcal { R } _ { \\mathcal { X } \\mathcal { X } } ( \\tau )$ reflects the time-delay similarity between $\\{ \\mathcal { X } _ { t } \\}$ and its $\\tau$ lag series $\\{ \\mathcal { X } _ { t - \\tau } \\}$ . As shown in Figure 2, we use the autocorrelation $\\mathcal { R } ( \\tau )$ as the unnormalized confidence of estimated period length $\\tau$ . Then, we choose the most possible $k$ period lengths $\\tau _ { 1 } , \\cdots , \\tau _ { k }$ . The period-based dependencies are derived by the above estimated periods and can be weighted by the corresponding autocorrelation. ", + "bbox": [ + 173, + 556, + 825, + 614 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "1Time delay aggregation The period-based dependencies connect the sub-series among estimated 1periods. Thus, we present the time delay aggregation block (Figure 2), which can roll the series based on selected time delay $\\tau _ { 1 } , \\cdots , \\tau _ { k }$ . This operation can align similar sub-series that are at the same phase position of estimated periods, which is different from the point-wise dot-product aggregation in self-attention family. Finally, we aggregate the sub-series by softmax normalized confidences. ", + "bbox": [ + 173, + 627, + 826, + 699 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the single head situation and time series $\\mathcal { X }$ with length- $L$ , after the projector, we get query $\\mathcal { Q }$ , key $\\kappa$ and value $\\nu$ . Thus, it can replace self-attention seamlessly. The Auto-Correlation mechanism is: ", + "bbox": [ + 171, + 704, + 823, + 733 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/6e1702fd112f4259c360baac62f3388d05edd202271aca6d8571fd7c14922488.jpg", + "text": "$$\n\\begin{array} { r l } & { \\qquad \\tau _ { 1 } , \\cdots , \\tau _ { k } = \\underset { \\tau \\in \\{ 1 , \\cdots , L \\} } { \\mathrm { a r g } \\mathrm { T o p k } } ( \\mathcal { R } _ { \\mathcal { Q } , \\mathcal { K } } ( \\tau ) ) } \\\\ & { \\qquad \\widehat { \\mathcal { R } } _ { \\mathcal { Q } , \\mathcal { K } } ( \\tau _ { 1 } ) , \\cdots , \\widehat { \\mathcal { R } } _ { \\mathcal { Q } , \\mathcal { K } } ( \\tau _ { k } ) = \\mathrm { S o f t M a x } ( \\mathcal { R } _ { \\mathcal { Q } , \\mathcal { K } } ( \\tau _ { 1 } ) , \\cdots , \\mathcal { R } _ { \\mathcal { Q } , \\mathcal { K } } ( \\tau _ { k } ) ) } \\\\ & { \\mathrm { A u t o - C o r r e l a t i o n } ( \\mathcal { Q } , \\mathcal { K } , \\mathcal { V } ) = \\underset { i = 1 } { \\overset { k } { \\sum } } \\mathrm { R o l l } ( \\mathcal { V } , \\tau _ { i } ) \\widehat { \\mathcal { R } } _ { \\mathcal { Q } , \\mathcal { K } } ( \\tau _ { i } ) , } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 267, + 738, + 730, + 835 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where ar $\\boldsymbol { \\mathrm { \\xi ^ { 2 } } } \\mathrm { T o p k } ( \\cdot )$ is to get the arguments of the Topk autocorrelations and let $k = \\lfloor c \\times \\log L \\rfloor$ , $c$ is a hyper-parameter. $\\mathcal { R } _ { \\mathcal { Q } , \\kappa }$ is autocorrelation between series $\\mathcal { Q }$ and $\\kappa$ . $\\mathrm { R o l l } ( \\mathcal { X } , \\tau )$ represents the operation to $\\mathcal { X }$ with time delay $\\tau$ , during which elements that are shifted beyond the first position are re-introduced at the last position. For the encoder-decoder Auto-Correlation (Figure 1), $\\kappa , \\nu$ are from the encoder $\\chi _ { \\mathrm { e n } } ^ { N }$ and will be resized to length- $O$ , $\\mathcal { Q }$ is from the previous block of the decoder. ", + "bbox": [ + 173, + 840, + 826, + 912 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b3a1dd188e9913684d89e9998ab12a2c0b4d1275bd0f7f003ea51f10541c2ec2.jpg", + "image_caption": [ + "Figure 3: Auto-Correlation vs. self-attention family. Full Attention [35] (a) adapts the fully connection among all time points. Sparse Attention [17, 41] (b) selects points based on the proposed similarity metrics. LogSparse Attention [20] (c) chooses points following the exponentially increasing intervals. Auto-Correlation (d) focuses on the connections of sub-series among underlying periods. " + ], + "image_footnote": [], + "bbox": [ + 176, + 88, + 823, + 292 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For the multi-head version used in Autoformer, with hidden variables of $d _ { \\mathrm { m o d e l } }$ channels, $h$ heads, the query, key and value for $i$ -th head are $\\mathcal { Q } _ { i } , \\mathcal { K } _ { i } , \\mathcal { V } _ { i } \\in \\mathbb { R } ^ { L \\times \\frac { d _ { \\mathrm { m o d e l } } } { h } }$ , $i \\in \\{ 1 , \\cdots , h \\}$ . The process is: ", + "bbox": [ + 171, + 364, + 825, + 398 + ], + "page_idx": 5 + }, + { + "type": "equation", + "img_path": "images/62c004a35e71d95d2adf122bec64c3548f70fa05424bd3536c4b4e3582ae4569.jpg", + "text": "$$\n\\begin{array} { r l } & { \\mathrm { M u l t i H e a d } ( \\mathcal { Q } , K , \\mathcal { V } ) = \\mathcal { W } _ { \\mathrm { o u t p u t } } * \\mathrm { C o n c a t } ( \\mathrm { h e a d } _ { 1 } , \\cdot \\cdot \\cdot , \\mathrm { h e a d } _ { h } ) } \\\\ & { \\quad \\quad \\quad \\mathrm { w h e r e ~ h e a d } _ { i } = \\mathrm { A u t o - C o r r e l a t i o n } ( \\mathcal { Q } _ { i } , K _ { i } , \\mathcal { V } _ { i } ) . } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 285, + 401, + 714, + 438 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Efficient computation For period-based dependencies, these dependencies point to sub-processes at the same phase position of underlying periods and are inherently sparse. Here, we select the most possible delays to avoid picking the opposite phases. Because we aggregate ${ \\mathcal { O } } ( \\log L )$ series whose length is $L$ , the complexity of Equations 6 and 7 is $\\mathcal { O } ( L \\log L )$ . For the autocorrelation computation (Equation 5), given time series $\\{ \\mathcal { X } _ { t } \\}$ , $\\mathcal { R } _ { \\mathcal { X } \\mathcal { X } } ( \\tau )$ can be calculated by Fast Fourier Transforms (FFT) based on the Wiener–Khinchin theorem [37]: ", + "bbox": [ + 173, + 445, + 826, + 530 + ], + "page_idx": 5 + }, + { + "type": "equation", + "img_path": "images/2d3d564e0485f3fffbb3432f06a689f28d47f204dc0cc229606fec48019eb783.jpg", + "text": "$$\n\\begin{array} { r l } & { \\displaystyle \\mathcal { S } _ { \\mathcal { X } \\mathcal { X } } ( f ) = \\mathcal { F } \\left( \\mathcal { X } _ { t } \\right) \\mathcal { F } ^ { * } \\left( \\mathcal { X } _ { t } \\right) = \\int _ { - \\infty } ^ { \\infty } \\mathcal { X } _ { t } e ^ { - i 2 \\pi t f } \\mathrm { d } t \\overline { { \\int _ { - \\infty } ^ { \\infty } \\mathcal { X } _ { t } e ^ { - i 2 \\pi t f } \\mathrm { d } t } } } \\\\ & { \\displaystyle \\mathcal { R } _ { \\mathcal { X } \\mathcal { X } } ( \\tau ) = \\mathcal { F } ^ { - 1 } \\left( S _ { \\mathcal { X } \\mathcal { X } } ( f ) \\right) = \\int _ { - \\infty } ^ { \\infty } S _ { \\mathcal { X } \\mathcal { X } } ( f ) e ^ { i 2 \\pi f \\tau } \\mathrm { d } f , } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 276, + 534, + 722, + 606 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\tau \\in \\{ 1 , \\cdots , L \\}$ , $\\mathcal { F }$ denotes the FFT and ${ \\mathcal { F } } ^ { - 1 }$ is its inverse. $^ *$ denotes the conjugate operation and $\\mathcal { S } _ { \\mathcal { X X } } ( f )$ is in the frequency domain. Note that the series autocorrelation of all lags in $\\{ 1 , \\cdots , L \\}$ can be calculated at once by FFT. Thus, Auto-Correlation achieves the $\\mathcal { O } ( L \\log L )$ complexity. ", + "bbox": [ + 176, + 609, + 820, + 652 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Auto-Correlation vs. self-attention family Different from the point-wise self-attention family, Auto-Correlation presents the series-wise connections (Figure 3). Concretely, for the temporal dependencies, we find the dependencies among sub-series based on the periodicity. In contrast, the self-attention family only calculates the relation between scattered points. Though some selfattentions [20, 41] consider the local information, they only utilize this to help point-wise dependencies discovery. For the information aggregation, we adopt the time delay block to aggregate the similar sub-series from underlying periods. In contrast, self-attentions aggregate the selected points by dot-product. Benefiting from the inherent sparsity and sub-series-level representation aggregation, Auto-Correlation can simultaneously benefit the computation efficiency and information utilization. ", + "bbox": [ + 173, + 665, + 826, + 791 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4 Experiments ", + "text_level": 1, + "bbox": [ + 174, + 809, + 312, + 827 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We extensively evaluate the proposed Autoformer on six real-world benchmarks, covering five mainstream time series forecasting applications: energy, traffic, economics, weather and disease. ", + "bbox": [ + 173, + 840, + 823, + 869 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets Here is a description of the six experiment datasets: (1) ETT [41] dataset contains the data collected from electricity transformers, including load and oil temperature that are recorded every ", + "bbox": [ + 173, + 882, + 821, + 911 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/52266c9dbd8161d0a8bdaa7f10b0a3b498678a2fbad400c2e8c8e72446796d73.jpg", + "table_caption": [ + "Table 1: Multivariate results with different prediction lengths $O \\in \\{ 9 6 , 1 9 2 , 3 3 6 , 7 2 0 \\}$ . We set the input length $I$ as 36 for ILI and 96 for the others. A lower MSE or MAE indicates a better prediction. " + ], + "table_footnote": [ + "\\* ETT means the ETTm2. See supplementary materials for the full benchmark of ETTh1, ETTh2, ETTm1. " + ], + "table_body": "
Models AutoformerInformer[41]LogTrans[20]Reformer[17]LSTNet[19]LSTM[13]TCN[3]
MetricMSEMAEMSEMAEMSEMAEMSEMAEMSE MAEMSE MAEMSEMAE
T96 192 3360.255 0.281 0.3390.339 0.3400.365 0.5330.453 0.5630.768 0.9890.642 0.7570.6580.6193.142 3.1541.365 1.3692.041 2.2491.073 1.1123.041 3.0721.330 1.339
1.078 0.827 1.549
720 960.422 0.2010.372 0.4191.363 3.3790.887 1.3883.0481.3340.872 1.3282.6310.972 1.2423.160 3.1711.369 1.368 2.7202.5681.238 1.2873.105 3.1351.348 1.354
erneera192 3360.2220.317 0.3340.274 0.2960.368 0.3860.258 0.2660.357 0.3680.312 0.3480.402 0.4330.680 0.645 0.7250.6760.375 0.4420.437 0.4730.985 0.9960.813 0.821
7200.231 0.2540.338 0.3610.300 0.3730.394 0.4390.280 0.2830.380 0.3760.350 0.3400.433 0.4200.828 0.9570.727 0.8110.439 0.9800.473 0.8141.000 1.4380.824 0.784
uepeg96 1920.1970.3230.8470.7520.9680.8121.0650.8291.5511.058 1.4531.049 3.0041.432
3360.300 0.5090.369 0.5241.2040.8951.0400.8511.1880.9061.4771.0281.8461.1793.0481.444
7201.4470.9411.672 2.4781.036 1.3101.659 1.9411.081 1.1271.357 1.5100.976 1.0161.507 2.2851.031 1.2432.136 2.9841.2313.1131.459
960.6130.3880.7190.3910.6840.3840.7320.4231.4273.1501.458
[Tjeee1920.6160.3820.6960.3790.6850.3900.7330.4201.107 1.1570.685 0.7060.843 0.8470.453 0.4531.438 1.4630.784 0.794
336 7200.6220.3370.7770.4200.7330.4080.7420.4201.2160.7300.8530.4551.4790.799
0.6600.4080.8640.4720.7170.3960.7550.4231.4810.8051.5000.8051.4990.804
waaeee960.2660.3360.3000.3840.4580.4900.6890.5960.5940.5870.3690.4060.6150.589
192 3360.3070.3670.5980.5440.6580.5890.7520.6380.5600.5650.4160.4350.6290.600
7200.3590.3950.5780.5230.7970.6520.6390.5960.5970.5870.4550.4540.6390.608
0.4190.4281.0590.7410.8690.6751.1300.7920.6180.5990.5350.5200.6390.610
243.4835.764
361.2871.6774.4801.4444.4001.3826.0261.7705.9141.7346.6241.830
Ⅱ483.1031.1484.7551.4674.7991.4674.7831.4485.3401.6686.6311.8456.8581.879
2.6691.0854.7631.4694.8001.4684.8321.4656.0801.7876.7361.8576.968
601.1255.2641.5645.2781.5604.8821.4835.5481.720 6.8701.8797.1271.892 1.918
2.770
", + "bbox": [ + 173, + 126, + 825, + 506 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "15 minutes between July 2016 and July 2018. (2) Electricity1 dataset contains the hourly electricity consumption of 321 customers from 2012 to 2014. (3) Exchange [19] records the daily exchange rates of eight different countries ranging from 1990 to 2016. (4) Traffic2 is a collection of hourly data from California Department of Transportation, which describes the road occupancy rates measured by different sensors on San Francisco Bay area freeways. (5) Weather3 is recorded every 10 minutes for 2020 whole year, which contains 21 meteorological indicators, such as air temperature, humidity, etc. (6) $I L I ^ { 4 }$ includes the weekly recorded influenza-like illness (ILI) patients data from Centers for Disease Control and Prevention of the United States between 2002 and 2021, which describes the ratio of patients seen with ILI and the total number of the patients. We follow standard protocol and split all datasets into training, validation and test set in chronological order by the ratio of 6:2:2 for the ETT dataset and 7:1:2 for the other datasets. ", + "bbox": [ + 173, + 531, + 825, + 684 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Implementation details Our method is trained with L2 loss, using the ADAM [16] optimizer with an initial learning rate of $1 0 ^ { - 4 }$ . Batch size is set to 32. The training process is early stopped within 10 epochs. All experiments are repeated three times, implemented in PyTorch [25] and conducted on a single NVIDIA TITAN RTX 24GB GPUs. The hyper-parameter $c$ of Auto-Correlation is in the range of 1 to 3 to trade off performance and efficiency. See supplementary materials for standard deviations and sensitivity analysis. Autoformer contains 2 encoder layers and 1 decoder layer. ", + "bbox": [ + 173, + 694, + 825, + 777 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Baselines We include 10 baseline methods. For the multivariate setting, we select three latest stateof-the-art transformer-based models: Informer [41], Reformer [17], LogTrans [20], two RNN-based models: LSTNet [19], LSTM [13] and CNN-based TCN [3] as baselines. For the univariate setting, we include more competitive baselines: N-BEATS[23], DeepAR [28], Prophet [33] and ARMIA [1]. ", + "bbox": [ + 174, + 787, + 825, + 843 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0b627e1d44ceb110476fbbd79f418eefb3c5de77241146900a5c22035547c876.jpg", + "table_caption": [ + "Table 2: Univariate results with different prediction lengths $O \\in \\{ 9 6 , 1 9 2 , 3 3 6 , 7 2 0 \\}$ on typical datasets. We set the input length $I$ as 96. A lower MSE or MAE indicates a better prediction. " + ], + "table_footnote": [], + "table_body": "
Models Autoformer N-BEATS[23] Informer[41] LogTrans[20] Reformer[17] DeepAR[28] Prophet[33] ARIMA[1]
Metric1MSE MAE MSEMAEMSE MAEMSEMAEMSEMAEMSE MAEMSE MAE MSE MAE
960.065 0.1890.0820.2190.088 0.2250.0820.2170.1310.2880.0990.2370.287 0.456 0.211 0.362
1920.118 0.256 0.1200.2680.132 0.2830.1330.2840.1860.3540.1540.3100.312 0.483 0.261 0.406
3360.1540.305 0.2260.3700.1800.336 0.2010.3610.2200.3810.2770.4280.331 0.474 0.317 0.448
7200.182 0.335 0.1880.338 0.3000.435 0.2680.4070.2670.4300.332 0.468 0.5340.593 0.366 0.487
aepeg960.241 0.387 0.1560.2990.591（0.615 0.2790.4411.3270.9440.417 0.515 0.828 0.762 0.112 0.245
1920.273 0.403 0.6690.6651.1830.912 1.9501.0481.2580.9240.813 0.735 0.909 0.974 0.304 0.404
3360.508 0.539 0.6110.6051.367 0.984 2.4381.2622.1791.2961.331 0.962 1.304 0.988 0.736 0.598
7200.991 0.768 1.1110.8601.8721.072 2.0101.2471.2800.9531.894 1.181 3.238 1.566 1.871 0.935
", + "bbox": [ + 173, + 125, + 830, + 279 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.1 Main Results ", + "text_level": 1, + "bbox": [ + 173, + 299, + 305, + 314 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To compare performances under different future horizons, we fix the input length and evaluate models with a wide range of prediction lengths: 96, 192, 336, 720. This setting precisely meets the definition of long-term forecasting. Here are results on both the multivariate and univariate settings. ", + "bbox": [ + 174, + 324, + 825, + 366 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Multivariate results As for the multivariate setting, Autoformer achieves the consistent state-ofthe-art performance in all benchmarks and all prediction length settings (Table 1). Especially, under the input-96-predict-336 setting, compared to previous state-of-the-art results, Autoformer gives $74 \\%$ $1 . 3 3 4 { } 0 . 3 3 9 _ { . }$ ) MSE reduction in ETT, $18 \\%$ $0 . 2 8 0 { } 0 . 2 3 1$ ) in Electricity, $61 \\%$ ( $1 . 3 5 7 { } 0 . 5 0 9 \\rangle$ in Exchange, $15 \\%$ $( 0 . 7 3 3 { } 0 . 6 2 2 )$ in Traffic and $21 \\%$ $( 0 . 4 5 5 { } 0 . 3 5 9 )$ ) in Weather. For the input36-predict-60 setting of ILI, Autoformer makes $43 \\%$ $4 . 8 8 2 { } 2 . 7 7 0$ ) MSE reduction. Overall, Autoformer yields a $38 \\%$ averaged MSE reduction among above settings. Note that Autoformer still provides remarkable improvements in the Exchange dataset that is without obvious periodicity. See supplementary materials for detailed showcases. Besides, we can also find that the performance of Autoformer changes quite steadily as the prediction length $O$ increases. It means that Autoformer retains better long-term robustness, which is meaningful for real-world practical applications, such as weather early warning and long-term energy consumption planning. ", + "bbox": [ + 173, + 375, + 826, + 542 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Univariate results We list the univariate results of two typical datasets in Table 2. Under the comparison with extensive baselines, our Autoformer still achieves state-of-the-art performance for the long-term forecasting tasks. In particular, for the input-96-predict-336 setting, our model achieves $14 \\%$ $0 . 1 8 0 { } 0 . 1 4 5$ MSE reduction on the ETT dataset with obvious periodicity. For the Exchange dataset without obvious periodicity, Autoformer surpasses other baselines by $17 \\%$ $( 0 . 6 1 1 { } 0 . 5 0 8 )$ and shows greater long-term forecasting capacity. Also, we find that ARIMA [1] performs best in the input-96-predict-96 setting of the Exchange dataset but fails in the long-term setting. This situation of ARIMA can be benefited from its inherent capacity for non-stationary economic data but is limited by the intricate temporal patterns of real-world series. ", + "bbox": [ + 173, + 551, + 825, + 676 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.2 Ablation studies ", + "text_level": 1, + "bbox": [ + 174, + 693, + 326, + 707 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/f3267c9ffb0709b04d20d44b69cea4a5d6f80e9e1ad7cf53d50e148f69ec1a8b.jpg", + "table_caption": [ + "Table 3: Ablation of decomposition in multivariate ETT with MSE metric. Ours adopts our progressive architecture into other models. Sep employs two models to forecast pre-decomposed seasonal and trend-cyclical components separately. Promotion is the MSE reduction compared to Origin. " + ], + "table_footnote": [], + "table_body": "
Input-96Transformer[35]Informer[41]LogTrans[17]Reformer[20]Promotion
Predict-O| OriginSepOursOriginSepOursOriginSepOursOrigin SepOursSepOurs
960.6040.3110.2040.3650.4900.3540.7680.8620.2310.6580.4450.2180.0690.347
1921.060 0.760（0.2660.5330.6580.4320.9890.5330.3781.0780.510 0.3360.300 0.562
3361.4130.6650.3751.3631.4690.4811.3340.7620.3621.5491.0280.3660.4341.019
7202.6723.2000.5373.3792.7660.8223.0482.6010.5392.6312.8450.5020.079 2.332
", + "bbox": [ + 173, + 771, + 825, + 868 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Decomposition architecture With our proposed progressive decomposition architecture, other models can gain consistent promotion, especially as the prediction length $O$ increases (Table 3). This verifies that our method can generalize to other models and release the capacity of other dependencies learning mechanisms, alleviate the distraction caused by intricate patterns. Besides, our architecture outperforms the pre-processing, although the latter employs a bigger model and more parameters. Especially, pre-decomposing may even bring negative effect because it neglects the interaction of components during long-term future, such as Transformer [35] predict-720, Informer [41] predict-336. ", + "bbox": [ + 173, + 883, + 823, + 911 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 92, + 825, + 161 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Auto-Correlation vs. self-attention family As shown in Table 4, our proposed Auto-Correlation achieves the best performance under various input- ${ \\mathbf { \\nabla } } J$ -predict- $O$ settings, which verifies the effectiveness of series-wise connections comparing to point-wise self-attentions (Figure 3). Furthermore, we can also observe that Auto-Correlation is memory efficiency from the last column of Table 4, which can be used in long sequence forecasting, such as input-336-predict-1440. ", + "bbox": [ + 174, + 174, + 825, + 244 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/8a1c7a7b0f3818ccf9690fa4d7b20f84d23baf3a2cad4a8205686e2fe885f2ed.jpg", + "table_caption": [ + "Table 4: Comparison of Auto-Correlation and self-attention in the multivariate ETT. We replace the Auto-Correlation in Autoformer with different self-attentions. The “-” indicates the out-of-memory. " + ], + "table_footnote": [], + "table_body": "
Input Length I Prediction Length O96192336
336720144033672014403367201440
Auto- CorrelationMSE MAE0.339 0.3720.422 0.4190.555 0.4960.355 0.3920.429 0.4300.503 0.4840.361 0.4060.425 0.4400.574 0.534
Full Attention[35]MSE MAE0.375 0.4250.537 0.5020.667 0.5890.450 0.4700.554 0.533- -0.501 0.4850.647 0.4911 =
LogSparse Attention[20]MSE MAE0.362 0.4130.539 0.5220.582 0.5290.420 0.4500.552 0.5130.958 0.7360.474 0.4740.601 0.524- =
LSH Attention[17]MSE MAE0.366 0.4040.502 0.4750.663 0.5670.407 0.4210.636 0.5711.069 0.7560.442 0.4760.615 0.5321 -
ProbSparse Attention[41]MSE MAE0.481 0.4720.822 0.5590.715 0.5860.404 0.4251.148 0.6540.732 0.6020.417 0.4340.631 0.5281.133 0.691
", + "bbox": [ + 173, + 290, + 825, + 489 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "4.3 Model Analysis ", + "text_level": 1, + "bbox": [ + 174, + 506, + 320, + 521 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Time series decomposition As shown in Figure 4, without our series decomposition block, the forecasting model cannot capture the increasing trend and peaks of the seasonal part. By adding the series decomposition blocks, Autoformer can aggregate and refine the trend-cyclical part from series progressively. This design also facilitates the learning of the seasonal part, especially the peaks and troughs. This verifies the necessity of our proposed progressive decomposition architecture. ", + "bbox": [ + 173, + 531, + 825, + 602 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/226af42008cf294d2ad17509100d9847b1a2e1adc1ae3b98a6fc44cc7d5195f9.jpg", + "image_caption": [ + "Figure 4: Visualization of learned seasonal gradually add the decomposition blocks in $\\mathcal { X } _ { \\mathrm { d e } } ^ { M }$ and trend-cyclical der from left to rig $\\mathcal { T } _ { \\mathrm { d e } } ^ { M }$ of the last decoder layer. Wehis case is from ETT dataset under input-96-predict-720 setting. For clearness, we add the linear growth to raw data additionally. " + ], + "image_footnote": [], + "bbox": [ + 176, + 611, + 821, + 733 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Dependencies learning The marked time delay sizes in Figure 5(a) indicate the most likely periods. Our learned periodicity can guide the model to aggregate the sub-series from the same or neighbor phase of periods by $\\mathrm { R o l l } ( \\mathcal { X } , \\tau _ { i } )$ , $i \\in \\{ 1 , \\cdots , 6 \\}$ . For the last time step (declining stage), AutoCorrelation fully utilizes all similar sub-series without omissions or errors compared to self-attentions. This verifies that Autoformer can discover the relevant information more sufficiently and precisely. ", + "bbox": [ + 174, + 799, + 826, + 869 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Complex seasonality modeling As shown in Figure 6, the lags that Autoformer learns from deep representations can indicate the real seasonality of raw series. For example, the learned lags of the daily recorded Exchange dataset present the monthly, quarterly and yearly periods (Figure 6 (b)). For the hourly recorded Traffic dataset (Figure 6 (c)), the learned lags show the intervals as 24-hours and 168-hours, which match the daily and weekly periods of real-world scenarios. These results show that Autoformer can capture the complex seasonalities of real-world series from deep representations and further provide a human-interpretable prediction. ", + "bbox": [ + 173, + 882, + 821, + 911 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/1f8ff11071d73f33cde0d525eb867796c34772cd0e34d9f2c2266d99a710dd8f.jpg", + "image_caption": [ + "Figure 5: Visualization of learned dependencies. For clearness, we select the top-6 time delay sizes $\\tau _ { 1 } , \\cdots , \\tau _ { 6 }$ of Auto-Correlation and mark them in raw series (red lines). For self-attentions, top-6 similar points with respect to the last time step (red stars) are also marked by orange points. " + ], + "image_footnote": [], + "bbox": [ + 173, + 88, + 821, + 203 + ], + "page_idx": 9 + }, + { + "type": "image", + "img_path": "images/487dd7c7362dd1bad3b32de704db93d0e84eac245cf0c6717299a42cde5d4a6b.jpg", + "image_caption": [ + "Figure 6: Statistics of learned lags. For each time series in the test set, we count the top 10 lags learned by decoder for the input-96-predict-336 task. Figure (a)-(d) are the density histograms. " + ], + "image_footnote": [], + "bbox": [ + 174, + 261, + 821, + 368 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "", + "bbox": [ + 173, + 419, + 825, + 489 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Efficiency analysis We compare the running memory and time among Auto-Correlation-based and self-attention-based models (Figure 7) during the training phase. The proposed Autoformer shows $\\mathcal { O } ( L \\log L )$ complexity in both memory and time and achieves better long-term sequences efficiency. ", + "bbox": [ + 174, + 503, + 825, + 546 + ], + "page_idx": 9 + }, + { + "type": "image", + "img_path": "images/9945f941aa3e41c082433f9479d4023d07440ec79228f1bcc87357764c332377.jpg", + "image_caption": [ + "Figure 7: Efficiency Analysis. For memory, we replace Auto-Correlation with self-attention family in Autoformer and record the memory with input 96. For running time, we run the Auto-Correlation or self-attentions $1 0 ^ { 3 }$ times to get the execution time per step. The output length increases exponentially. " + ], + "image_footnote": [], + "bbox": [ + 173, + 559, + 825, + 704 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "5 Conclusions ", + "text_level": 1, + "bbox": [ + 174, + 768, + 307, + 786 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "This paper studies the long-term forecasting problem of time series, which is a pressing demand for real-world applications. However, the intricate temporal patterns prevent the model from learning reliable dependencies. We propose the Autoformer as a decomposition architecture by embedding the series decomposition block as an inner operator, which can progressively aggregate the longterm trend part from intermediate prediction. Besides, we design an efficient Auto-Correlation mechanism to conduct dependencies discovery and information aggregation at the series level, which contrasts clearly from the previous self-attention family. Autoformer can naturally achieve $\\mathcal { O } ( L \\log L )$ complexity and yield consistent state-of-the-art performance in extensive real-world datasets. ", + "bbox": [ + 173, + 800, + 826, + 911 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Acknowledgments and Disclosure of Funding ", + "text_level": 1, + "bbox": [ + 174, + 88, + 553, + 107 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "This work was supported by the National Natural Science Foundation of China under Grants 62022050 and 62021002, Beijing Nova Program under Grant Z201100006820041, China’s Ministry of Industry and Information Technology, the MOE Innovation Plan and the BNRist Innovation Fund. ", + "bbox": [ + 174, + 119, + 826, + 162 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "References ", + "text_level": 1, + "bbox": [ + 174, + 180, + 267, + 196 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "[1] O. Anderson and M. Kendall. Time-series. 2nd edn. J. R. Stat. Soc. (Series D), 1976. [2] Reza Asadi and Amelia C Regan. A spatio-temporal decomposition based deep neural network for time series forecasting. Appl. 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0000000000000000000000000000000000000000..8592a95271e36fbdb3326ac71f5fd73f946d07b8 --- /dev/null +++ b/parse/train/Sk9yuql0Z/Sk9yuql0Z.md @@ -0,0 +1,329 @@ +# MITIGATING ADVERSARIAL EFFECTS THROUGH RAN-DOMIZATION + +Cihang Xie, Zhishuai Zhang & Alan L. Yuille + +Department of Computer Science +The Johns Hopkins University +Baltimore, MD 21218 USA +{cihangxie306, zhshuai.zhang, alan.l.yuille}@gmail.com + +Jianyu Wang Baidu Research USA Sunnyvale, CA 94089 USA wjyouch@gmail.com + +Zhou Ren +Snap Inc. +Venice, CA 90291 USA +zhou.ren@snapchat.com + +# ABSTRACT + +Convolutional neural networks have demonstrated high accuracy on various tasks in recent years. However, they are extremely vulnerable to adversarial examples. For example, imperceptible perturbations added to clean images can cause convolutional neural networks to fail. In this paper, we propose to utilize randomization at inference time to mitigate adversarial effects. Specifically, we use two randomization operations: random resizing, which resizes the input images to a random size, and random padding, which pads zeros around the input images in a random manner. Extensive experiments demonstrate that the proposed randomization method is very effective at defending against both single-step and iterative attacks. Our method provides the following advantages: 1) no additional training or fine-tuning, 2) very few additional computations, 3) compatible with other adversarial defense methods. By combining the proposed randomization method with an adversarially trained model, it achieves a normalized score of 0.924 (ranked No.2 among 107 defense teams) in the NIPS 2017 adversarial examples defense challenge, which is far better than using adversarial training alone with a normalized score of 0.773 (ranked No.56). The code is public available at https: //github.com/cihangxie/NIPS2017_adv_challenge_defense. + +# 1 INTRODUCTION + +Convolutional Neural Networks (CNNs) have been successfully applied to a wide range of vision tasks, including image classification (Krizhevsky et al., 2012; Simonyan & Zisserman, 2015; He et al., 2016a), object detection (Girshick, 2015; Ren et al., 2015; Zhang et al., 2017), semantic segmentation (Long et al., 2015; Chen et al., 2017), visual concept discovery (Wang et al., 2017) etc. However, recent works show that CNNs are extremely vulnerable to small perturbations to the input image. For example, adding visually imperceptible perturbations to the original image can result in failures for image classification (Szegedy et al., 2014; Goodfellow et al., 2015), object detection (Xie et al., 2017) and semantic segmentation (Xie et al., 2017; Fischer et al., 2017; Cisse et al., 2017). These perturbed images are called adversarial examples and Figure 1 gives an example. Adversarial examples pose a great security danger to the deployment of commercial machine learning systems. Thus, making CNNs more robust to adversarial examples is a very important yet challenging problem. Recent works (Papernot et al., 2016b; Kurakin et al., 2017; Tramer et al., 2017; Cao & Gong, \` + +![](images/48b3009e8ed26fd44338fb7b72d9eaf8e2ea6476d67d321696065b4e396f4087.jpg) +Figure 1: This is an adversarial example crafted for VGG (Simonyan & Zisserman, 2015). The left image is classified correctly as king penguin, the center image is the adversarial perturbation (magnified by 10 and enlarged by 128 for better visualization), and the right image is the adversarial example misclassfied as chihuahua. + +2017; Metzen et al., 2017; Feinman et al., 2017; Meng & Chen, 2017) are making progress on this line of research. + +Adversarial attacks can be divided into two categories: single-step attacks, which perform only one step of gradient computation, and iterative attacks, which perform multiple steps. Intuitively, the perturbation generated by iterative methods may easily get over-fitted to the specific network parameters, and thus be less transferable. On the other hand, single-step methods may not be strong enough to fool the network. For examples, it has been demonstrated that single-step attacks, like Fast Gradient Sign Method (FGSM) (Goodfellow et al., 2015), have better transferability but weaker attack rate than iterative attacks, like DeepFool (Moosavi-Dezfooli et al., 2016). + +Due to the weak generalization of iterative attacks, low-level image transformations, e.g., resizing, padding, compression, etc, may probably destroy the specific structure of adversarial perturbations, thus making it a good defense. It can even defend against white-box iterative attacks if random transformations are applied. This is because each test image goes through random transformations and the attacker does not know the specific transformation when generating adversarial noise. Recently, adversarial training (Kurakin et al., 2017; Tramer et al., 2017) was developed to defend against \` single-step attacks. Thus by adding the proposed random transformations as additional layers to an adversarially trained model (Tramer et al., 2017), it is expected that the method is able to effec- \` tively defend against both single-step and iterative attacks, including both black-box and white-box settings. + +Based on the above reasoning, in this paper, we propose a defense method by randomization at inference time, i.e., random resizing and random padding, to mitigate adversarial effects. To the best of our knowledge, this is the first work that demonstrates the effectiveness of randomization at inference time on mitigating adversarial effects on large-scale dataset, e.g., ImageNet (Deng et al., 2009). The proposed method provides the following advantages: + +• Randomization at inference time makes the network much more robust to adversarial images, especially for iterative attacks (both white-box and black box), but hardly hurts the performance on clean (non-adversarial) images. Experiments on section 4.2 support this argument. +• There is no additional training or fine-tuning required which is easy for implementation. +• Very few computations are required by adding the two randomization layers, thus there is nearly no run time increase. +• Randomization layers are compatible to different network structures and adversarial defense methods, which can serve as a basic network module for adversarial defense. + +We conduct comprehensive experiments to test the effectiveness of our defense method, using different network structures, against different attack methods, and under different attack scenarios. The results in Section 4 demonstrate that the proposed randomization layers can significantly mitigate adversarial effects, especially for iterative attack methods. Moreover, we submitted the model, which combines the proposed randomization layers and an adversarially trained model (Tramer\` et al., 2017), to the NIPS 2017 adversarial examples defense challenge. It reaches a normalized score of 0.924 (ranked No.2 among 107 defense teams), which is far better than just using adversarial training (Tramer et al., 2017) alone with a normalized score of \` 0.773 (ranked No.56). + +# 2 RELATED WORK + +# 2.1 GENERATING ADVERSARIAL EXAMPLES + +Generating adversarial examples has been extensively studied recently. (Szegedy et al., 2014) first showed that adversarial examples, computed by adding visually imperceptible perturbations to the original images, make CNNs predict wrong labels with high confidence. (Goodfellow et al., 2015) proposed the fast gradient sign method to generate adversarial examples based on the linear nature of CNNs, and also proposed adversarial training for defense. (Moosavi-Dezfooli et al., 2016) generated adversarial examples by assuming that the loss function can be linearized around the current data point at each iteration. (Carlini & Wagner, 2017) developed a stronger attack to find adversarial perturbations by introducing auxiliary variables which incooperate the pixel value constrain, e.g., pixel intensity must be within the range [0,255], naturally into the loss function and make the optimization process easier. (Liu et al., 2017) proposed an ensemble-based approaches to generate adversarial examples with stronger transferability. Unlike the works above, (Biggio & Laskov, 2012; Koh & Liang, 2017) showed that manipulating only a small fraction of the training data can significantly increase the number of misclassified samples at test time for learning algorithms, and such attacks are called poisoning attacks. + +# 2.2 DEFENDING AGAINST ADVERSARIAL EXAMPLES + +Opposite to generating adversarial examples, there is also progress on reducing the effects of adversarial examples. (Papernot et al., 2016b) showed networks trained using defensive distillation can effectively defend against adversarial examples. (Kurakin et al., 2017) proposed to replace the original clean images with a mixture of clean images and corresponding adversarial images in each training batch to improve the network robustness. (Tramer et al., 2017) improved the robustness \` further by training the network on an ensemble of adversarial images generated from the trained model itself and from a number of other pre-trained models. Cao & Gong (2017) proposed a regionbased classification to let models be robust to adversarial examples. (Metzen et al., 2017) trained a detector on the inner layer of the classifier to detect adversarial examples. (Feinman et al., 2017) detected adversarial examples by looking at the Bayesian uncertainty estimates of the input images in dropout neural networks and by performing density estimation in the subspace of deep features learned by the model. MagNet (Meng & Chen, 2017) detected adversarial examples with large perturbation using detector networks, and pushed adversarial examples with small perturbation towards the manifold of clean images. + +# 3 APPROACH + +# 3.1 AN OVERVIEW OF GENERATING ADVERSARIAL EXAMPLES + +Before introducing the proposed adversarial defense method, we give an overview of generating adversarial examples. Let $X _ { n }$ denote the $n$ -th image in a dataset containing $N$ images, and let $y _ { n } ^ { \mathrm { t r u e } }$ denote the corresponding ground-truth label. We use $\theta$ to denote the network parameters, and $L ( X _ { n } , y _ { n } ^ { \mathrm { t r u e } } ; \theta )$ to denote the loss. For the adversarial example generation, the goal is to maximize the loss $L ( X _ { n } + r _ { n } , y _ { n } ^ { \mathrm { t r u e } } ; \theta )$ for each image $X _ { n }$ , under the constraint that the generated adversarial example $X _ { n } ^ { \mathrm { a d v } } = X _ { n } + r _ { n }$ should look visually similar to the original image $X _ { n }$ , i.e., $| | r _ { n } | | \leq \epsilon$ , and the corresponding predicted label $y _ { n } ^ { \mathrm { a d v } } \neq y _ { n } ^ { \mathrm { t r u e } }$ . + +In our experiment, we consider three different attack methods, including one single-step attack method and two iterative attack methods. We use the cleverhans library (Papernot et al., 2016a) to generate adversarial examples, where all these attacks have been implemented via TensorFlow. + +• Fast Gradient Sign Method (FGSM): FGSM (Goodfellow et al., 2015) is a single-step attack method. It finds the adversarial perturbation that yields the highest increase of the linear cost function under $l _ { \infty }$ -norm. The update equation is + +$$ +X _ { n } ^ { \mathrm { a d v } } = X _ { n } + \epsilon \cdot s i g n \big ( \nabla _ { X _ { n } } L ( X _ { n } , y _ { n } ^ { \mathrm { t r u e } } ; \theta ) \big ) , +$$ + +where $\epsilon$ controls the magnitude of adversarial perturbation. In the experiment, we choose $\epsilon = \{ 2 , 5 , 1 0 \}$ , which corresponds to small, medium and high magnitude of adversarial perturbations, respectively. + +• DeepFool: DeepFool (Moosavi-Dezfooli et al., 2016) is an iterative attack method which finds the minimal perturbation to cross the decision boundary based on the linearization of the classifier at each iteration. Any $l _ { p }$ -norm can be used with DeepFool, and we choose $l _ { 2 }$ -norm for the study in this paper. + +• Carlini $\&$ Wagner (C&W): C&W (Carlini & Wagner, 2017) is a stronger iterative attack method proposed recently. It finds the adversarial perturbation $r _ { n }$ by using an auxiliary variable $\omega _ { n }$ as + +$$ +r _ { n } = { \frac { 1 } { 2 } } ( t a n h ( \omega _ { n } + 1 ) ) - X _ { n } . +$$ + +Then the loss function optimizes the auxiliary variable $\omega _ { n }$ + +$$ +\operatorname* { m i n } _ { \omega _ { n } } | | \frac { 1 } { 2 } ( t a n h ( \omega _ { n } ) + 1 ) - X _ { n } | | + c \cdot f ( \frac { 1 } { 2 } ( t a n h ( \omega _ { n } ) + 1 ) ) . +$$ + +The function $f ( \cdot )$ is defined as + +$$ +f ( x ) = \operatorname* { m a x } ( Z ( x ) _ { y ^ { \mathrm { t u e } } } - \operatorname* { m a x } \{ Z ( x ) _ { i } : i \neq y ^ { \mathrm { t r u e } } \} , - k ) , +$$ + +where $Z ( x ) _ { i }$ is the logits output for class $i$ , and $k$ controls the confidence gap between the adversarial class and true class. C&W can also work with various $l _ { p }$ -norm, and we choose $l _ { 2 }$ -norm in the experiments. + +# 3.2 DEFENDING AGAINST ADVERSARIAL EXAMPLES + +The goal of defense is to build a network that is robust to adversarial examples, i.e., it can classify adversarial images correctly with little performance loss on non-adversarial (clean) images. Towards this goal, we propose a randomization-based method, as shown in Figure 2, which adds a random resizing layer and a random padding layer to the beginning of the classification networks. There is no re-training or fine-tuning needed which makes the proposed method very easy to implement. + +# 3.2.1 RANDOMIZATION LAYERS + +The first randomization layer is a random resizing layer, which resizes the original image $X _ { n }$ with the size $W \times H \times 3$ to a new image $X _ { n } ^ { \prime }$ with random size $W ^ { \prime } \times H ^ { \prime } \times 3$ . Note that, $| W ^ { \prime } - W |$ and $| H ^ { \prime } - H |$ should be within a reasonablely small range, otherwise the network performance on non-adversarial images would significantly drop. Taking Inception-ResNet network (Szegedy et al., 2017) as an example, the original data input size is $2 9 9 \times 2 9 9 \times 3$ . Empirically we found that the network performance hardly drops if we control the height and width of the resized image $X _ { n } ^ { \prime }$ to be within the range [299, 331). + +The second randomization layer is the random padding layer, which pads zeros around the resized image in a random manner. Specifically, by padding the resized image $X _ { n } ^ { \prime }$ into a new image $X _ { n } ^ { \prime \prime }$ with the size $W ^ { \prime \prime } \times H ^ { \prime \prime } \times 3$ , we can choose to pad $w$ zero pixels on the left, $W ^ { \prime \prime } - W ^ { \prime } - w$ zero pixels on the right, $h$ zero pixels on the top and $H ^ { \prime \prime } - H ^ { \prime } - h$ zero pixels on the bottom. This results in a total number of $\left( W ^ { \prime \prime } - W ^ { \prime } + 1 \right) \times \left( H ^ { \prime \prime } - H ^ { \prime } + 1 \right)$ different possible padding patterns. + +During implementation, the original image first goes through two randomization layers, and then we pass the transformed image to the original CNN for classification. The pipeline is illustrated in Figure 2. + +# 3.2.2 RANDOMIZATION LAYERS $^ +$ ADVERSARIAL TRAINING + +Note that our randomization-based method is good at defending against iterative attacks, and adversarial training (Kurakin et al., 2017; Tramer et al., 2017) can effectively increase the robustness of \` neural networks to single-step attacks. Thus, to make the best of both worlds, we can combine the proposed randomization layers and an adversarially trained model (Tramer et al., 2017) together to \` defend against both single-step and iterative attacks. + +![](images/b391dc2283db9234f0f293be29409bb96e04b1cf038128ded1f2d00537f1f162.jpg) +Figure 2: The pipeline of our randomization-based defense mechanism. The input image $X _ { n }$ first goes through the random resizing layer with a random scale applied. Then the random padding layer pads the resized image $X _ { n } ^ { \prime }$ in a random manner. The resulting padded image $X _ { n } ^ { \prime \prime }$ is used for classification. + +# 4 EXPERIMENTS + +# 4.1 EXPERIMENT SETUP + +Dataset: It is less meaningful to attack the images that are already classified wrongly. Therefore, we randomly choose 5000 images from the ImageNet validation set that are classified correctly by all the considered networks to form our test dataset. All these images are of the size $2 9 9 \times 2 9 9 \times 3$ . + +Networks: We test with four publicly available networks1,2, including Inception- $\nu 3$ (Szegedy et al., 2016), ResNet- $\cdot \nu 2$ (He et al., 2016b) of 101 layers, Inception-ResNet- $\cdot \nu 2$ (Szegedy et al., 2017), and ens-adv-Inception-ResNet- $\nu 2$ which applies the ensemble adversarial training (Tramer et al., 2017) \` on Inception-ResNet- $\nu 2$ . These networks have been trained on ImageNet, and we do not perform any re-training or fine-tuning on them for the whole experiments. + +Defense Models: The defense models consist of the original networks (i.e., four above-mentioned networks) and two additional randomization layers. For the random resizing layer, it changes the input shape from $2 9 9 \times 2 9 9 \times 3$ to $r n d \times r n d \times 3$ , where rnd is a integer randomly sampled from the range [299, 331). For the random padding layer, it pads the resized image to the shape of $3 3 1 \times 3 3 1 \times 3$ in a random manner. By applying these two randomization layers, we can create 330 +$\sum _ { r n d = 2 9 9 } ( 3 3 1 - r n d + 1 ) ^ { 2 } = 1 2 5 2 8$ different patterns for a single image. Since there exists small variance on model performance w.r.t. different random patterns, we run the defense model three times independently and report the average accuracy. + +Target Models under Different Attack Scenarios: The strongest attack would be that the attackers consider ALL possible patterns of the defense models when generating the adversarial examples. However, this is computationally impossible, because failing a large number of patterns (e.g., 12528 here) at the same time takes extremely long time, and may not even converge. Thus, we let attackers use the target models to generate adversarial examples instead, and consider the following three different attack scenarios. + +• Vanilla Attack: The attackers do not know the existence of the randomization layers and the target model is just the original network. + +Table 1: Top-1 classification accuracy on the clean images. We see that adding random resizing and random padding cause very little accuracy drop on clean (non-adversarial) images. + +
ModelsInception-v3ResNet-v2-101Inception-ResNet-v2ens-adv-Inception-ResNet-v2
w/o randomization layers100%100%100%100%
wrandomization layers97.3%98.3%99.3%99.2%
+ +• Single-Pattern Attack: The attackers know the existence of the randomization layers. In order to mimic the structures of defense models, the target model is chosen as the original network $^ +$ randomization layers with only one predefined pattern. + +• Ensemble-Pattern Attack: The attackers know the existence of the randomization layers. In order to mimic the structures of defense models in a more representative way, the target model is chosen as the original network $^ +$ randomization layers with an ensemble of predefined patterns. + +Target Models and Defense Models: The target models and the defense models are exactly the same except for the parameter settings of the randomization layers, i.e., the randomization parameters at the target models are predefined while randomization parameters at the defense models are randomly generated at test time. The original networks (e.g., Inception- $\nu 3$ ) utilized by the target models and the defense models are the same. The attackers first generate adversarial examples using the target models, and then evaluate the classification accuracy of these generated adversarial examples on both the target and defense models. A low accuracy of the target model indicates that the attack is successful, and a high accuracy of the defense model indicates that the defense is effective. + +# 4.2 CLEAN IMAGES + +Table 1 shows the top-1 accuracy of networks with and without randomization layers on the clean images. We can see that randomization layers introduce negligible performance degradation on clean images. Specifically, we can observe that: (1) models with more advanced architectures tend to have less performance degradation, e.g., Inception-ResNet- $\cdot \nu 2$ only has $0 . 7 \%$ degradation while Inception-v3 has $2 . 7 \%$ degradation; (2) ensemble adversarial training brings nearly no performance degradation to the models, e.g., Inception-ResNet-v2 and ens-adv-Inception-ResNet-v2 have nearly the same performance degradation. + +# 4.3 VANILLA ATTACK SCENARIO + +For the vanilla attack scenario, the attackers are not aware of randomization layers, and directly use the original networks as the target model to generate adversarial examples. The attack ability on the defense models mostly rely on the transferability of adversarial examples to different resizing and padding. From the top-1 accuracy presented in Table 2, we observe that randomization layers can mitigate the adversarial effects for both single-step and iterative attacks significantly. As for singlestep attacks FGSM-, larger $\epsilon$ indicates stronger transferability, thus making it harder to defend. However, we can still get satisfactory accuracy of the defense model on single-step attacks (even with large $\epsilon$ ) using ens-adv-Inception-ResNet- $\cdot \nu 2$ $9 4 . 3 \%$ top-1 accuracy). As for iterative attacks, attackers always reach a very high attack rate on target model, but have almost no impact on models after randomization layers are applied. This is because iterative attack methods are over-fitted to the target models thus have weak transferability. + +# 4.4 SINGLE-PATTERN ATTACK SCENARIO + +For the single-pattern attack scenario, the attackers are aware of the existence of randomization layers and also the parameters of the random resizing and random padding (i.e., from $2 9 9 \times 2 9 9$ to $3 3 1 \times 3 3 1$ ), but they do not know the specific randomization patterns utilized by the defense models (even the defense models themselves do not know these specific randomization patterns since they are randomly instantiated at test time). In order to generate adversarial examples, the attackers choose the target models as the original networks $^ +$ randomization layers but with only one specific pattern to compute the gradient. In this experiment, the specific pattern that we use is to place the original input $X _ { n }$ at the center of the padded image $X _ { n } ^ { \prime \prime }$ , i.e., no resizing is applied, and 16 zeros pixels are padded on the left, right, top and bottom on the input images, respectively. Table 3 shows the top-1 accuracy of both target models and defense models, and similar results to vanilla attack scenario are observed: (1) for single-step attacks, randomization layers are less effective on mitigating adversarial effects for a larger $\epsilon$ , while the adversarially trained models are able to defend against such attacks; (2) for iterative attacks, they reach high attack rates on target models, while have nearly no impact on defense models. + +Table 2: Top-1 classification accuracy under the vanilla attack scenario. We see that randomization layers effectively mitigate adversarial effects for all attacks and all networks. Particularly, combining randomization layers with ensemble adversarial training (ens-adv-Inception-ResNet-v2) performs very well on all attacks. + +
ModelsInception-v3ResNet-v2-101Inception-ResNet-v2ens-adv-Inception-ResNet-v2
targetmodeldefensemodeltargetmodeldefensemodeltargetmodeldefensemodeltargetmodeldefensemodel
FGSM-233.2%65.1%26.3%71.8%65.3%81.0%84.4%95.7%
FGSM-531.1%54.5%20.4%54.3%61.7%74.1%87.4%94.5%
FGSM-1033.0%52.4%20.4%46.1%61.2%71.3%90.2%94.3%
DeepFool0%98.3%0%97.7%0%98.2%0.2%99.1%
C&W0%96.9%0%97.1%0.3%97.7%0.9%98.8%
+ +Table 3: Top-1 classification accuracy under the single-pattern attack scenario. We see that randomization layers effectively mitigate adversarial effects for all attacks and all networks. Particularly, combining randomization layers with ensemble adversarial training (ens-adv-Inception-ResNet- $\cdot \nu 2$ ) performs very well on all attacks. + +
ModelsInception-v3ResNet-v2-101Inception-ResNet-v2ens-adv-Inception-ResNet-v2
targetmodeldefensemodeltargetmodeldefensemodeltargetmodeldefensemodeltargetmodeldefensemodel
FGSM-235.1%63.8%29.5%70.1%71.6%83.4%86.3%96.4%
FGSM-532.4%53.9%23.2%52.3%68.3%78.2%88.4%95.4%
FGSM-1034.7%51.8%22.4%43.8%66.8%75.6%90.7%95.2%
DeepFool1.1%98.2%1.7%97.8%0.6%98.4%1.0%99.2%
C&W1.1%97.4%1.7%97.0%0.8%97.9%1.6%99.1%
+ +# 4.5 ENSEMBLE-PATTERN ATTACK SCENARIO + +For the ensemble-pattern attack scenario, similar to single-pattern attack scenario, the attackers are aware of the randomization layers and the parameters of the random resizing and random padding (i.e., starting from $2 9 9 \times 2 9 9$ to $3 3 1 \times 3 3 1$ ), but they do not know the specific patterns utilized by the defense models at test time. The target models thus are constructed in a more representative way: let randomization layers choose an ensemble of predefined patterns, and the goal of the attackers is to let all chosen patterns fail on classification. In this experiment, the specific ensemble patterns that we choose are: (1) first resize the input image to five different scales $\{ 2 9 9 , 3 0 7 , 3 1 5 , 3 2 3 , 3 3 1 \}$ ; (2) then pad each resized image to five different patterns, where the resized image is placed at the top left, top right, bottom left, bottom right, and center of the padded image, respectively. Since there is only one padding pattern for the resized image with size 331, we can obtain $4 * 5 + 1 = 2 1$ patterns in total. Due to the large computation amounts introduced by the ensemble-pattern attack scenario, we randomly choose 500 images out of the entire test dataset for this experiment. The top-1 accuracy for the target model here is calculated by summing up the number of correctly classified patterns of each image over the entire pattern number of all images. For the results presented in Table 4, we can see that the adversarial examples generated under ensemble-pattern attack scenario are much stronger. For single-step attacks, the generated adversarial examples can let the performance of the defense model with an adversarially trained network drop around $8 \%$ compared to the performance under vanilla attack and single-pattern attack scenarios, and drop much more on other defense models. For iterative attacks, we observe that the adversarial examples generated by C&W are stronger than those generated by DeepFool, e.g., the defense model with Inception- $\nu 3$ has an accuracy of $8 1 . 3 \%$ on DeepFool, while only has an accuracy of $6 2 . 9 \%$ on C&W. We argue that this is due to the more advanced loss function (i.e., introduction of auxiliary variable for pixel value control) utilized by C&W than DeepFool. Additionally, the accuracy of defense model on C&W can be improved by utilizing more advanced architecture (e.g., ResNet-v2-101 has higher accuracy than Inception-v3) and applying ensemble adversarial training (e.g., ens-adv-Inception-ResNet- $\nu 2$ has higher accuracy than Inception-ResNet-v2). For the best defense model that we have, ens-adv-Inception-ResNet- $\nu 2$ $^ +$ randomization layers reaches the top-1 accuracy of $9 3 . 5 \%$ on DeepFool and $8 6 . 1 \%$ on C&W, respectively. + +Table 4: Top-1 classification accuracy under the ensemble-pattern attack scenario. Similar to vanilla attack and single-pattern attack scenarios, we see that randomization layers increase the accuracy under all attacks and networks. This clearly demonstrates the effectiveness of the proposed randomization method on defending against adversarial examples, even under this very strong attack scenario. + +
ModelsInception-v3ResNet-v2-101Inception-ResNet-v2ens-adv-Inception-ResNet-v2
targetmodeldefensemodeltargetmodeldefensemodeltargetmodeldefensemodeltargetmodeldefensemodel
FGSM-237.3%41.2%39.2%44.9%71.5%74.3%86.2%88.9%
FGSM-531.7%34.0%24.6%29.7%65.2%67.3%85.8%87.5%
FGSM-1030.4%32.8%18.6%21.7%62.9%64.5%86.6%87.9%
DeepFool0.6%81.3%0.9%80.5%0.9%69.4%1.6%93.5%
C&W0.6%62.9%1.0%74.3%1.6%68.3%5.8%86.1%
+ +# 4.6 DIAGNOSTIC EXPERIMENT + +Due to the large amount of possible patterns introduced by randomization layers, it is hard to analyze the effectiveness of random resizing and random padding precisely. In this section, we limit the freedom of randomization to be a small number (i.e., 4 in random padding and 1 in random resizing) and analyze the effectiveness of these two operations separately. The same 500 images in section 4.5 are used in this experiment. In addition, the input images for target models and defense models are resized to the shape $3 3 0 \times 3 3 0 \times 3$ beforehand. + +# 4.6.1 ONE PIXEL PADDING + +For the random padding, there are only 4 patterns when padding the input images from $3 3 0 \times 3 3 0 \times 3$ to $3 3 1 \times 3 3 1 \times 3$ . In order to construct a stronger attack, we follow the experiment setup in section 4.5 where 3 chosen patterns are ensembled. Specifically, the target model takes an ensemble of patterns where the original images are at the top left, top right and bottom left (3 patterns) of the padded images, and the defense model takes the last pattern where the original images are at the bottom right of the padded images. Note that, since there is no randomization in the defense model, we only run the defense model once. Table 5 summaries the results, and we can see that: (1) adversarial examples generated by single-step attacks have strong transferability, but still cannot attack the defense model with an adversarially trained model successfully (i.e., the defense model with ensadv-Inception-ResNet- $\nu 2$ ); (2) adversarial examples generated by iterative attacks are much less transferable between different padding patterns even when only 4 different patterns exist. The results demonstrate that creating different padding patterns can effectively mitigate adversarial effects. + +Table 5: Top-1 classification accuracy under one pixel padding scenario. This table shows that creating different padding patterns (even 1-pixel padding) can effectively mitigate adversarial effects. + +
ModelsInception-v3ResNet-v2-101Inception-ResNet-v2ens-adv-Inception-ResNet-v2
targetmodeldefensemodeltargetmodeldefensemodeltargetmodeldefensemodeltargetmodeldefensemodel
FGSM-236.4%39.6%29.8%34.4%71.3%74.0%88.2%94.8%
FGSM-533.5%36.2%22.2%26.2%68.4%71.0%92.1%94.4%
FGSM-1034.5%38.8%21.3%23.6%67.4%70.4%93.7%94.0%
DeepFool0.9%97.2%0.9%95.2%0.9%87.6%1.5%99.2%
C&W0.8%70.2%0.9%76.8%1.0%79.4%2.4%98.2%
+ +Table 6: Top-1 classification accuracy under one pixel resizing scenario. This table shows that resizing image to a different scale (even 1-pixel scale) can effectively mitigate adversarial effects. + +
ModelsInception-v3ResNet-v2-101Inception-ResNet-v2ens-adv-Inception-ResNet-v2
targetmodeldefensemodeltargetmodeldefensemodeltargetmodeldefensemodeltargetmodeldefensemodel
FGSM-230.8%56.2%31.6%44.6%66.2%75.0%87.6%97.2%
FGSM-531.2%48.8%25.6%35.8%61.4%70.2%91.2%96.6%
FGSM-1036.4%51.0%23.8%32.6%62.8%68.2%94.8%95.2%
DeepFool2.6%99.4%1.0%98.6%1.2%97.4%1.2%99.4%
C&W2.6%97.8%1.0%94.8%2.0%94.8%1.8%99.6%
+ +# 4.6.2 ONE-PIXEL RESIZING + +For the random resizing, there is only 1 pattern that exists when the input images are resized from $3 3 0 \times 3 3 0 \times 3$ to $3 3 1 \times 3 3 1 \times 3$ . The results in Table 6 indicate that resizing the images by only 1 pixel can effectively destroy the transferability of adversarial examples by both single-step and iterative attacks. + +# 5 NIPS 2017 ADVERSARIAL EXAMPLES DEFENSE CHALLENGE + +We submitted our model to the NIPS 2017 adversarial examples defense challenge3 for a more comprehensive performance evaluation. The test dataset contains 5000 images which are all of the size $2 9 9 \times 2 9 9 \times 3$ , and their corresponding labels are the same as the ImageNet 1000-class labels. Each defense method are run on all 5000 adversarial images generated against all adversarial attacks. For each correctly classified image, the defense method gets one point. The normalized score for each defense method is computed using the following formula: + +$$ +\mathrm { s c o r e } = \frac { 1 } { M } \sum _ { \mathrm { a t t a c k } \in A } \sum _ { n = 1 } ^ { 5 0 0 0 } \left[ \mathrm { d e f e n s e } ( \mathrm { a t t a c k } ( X _ { n } ) ) = y _ { n } ^ { \mathrm { t r u e } } \right] , +$$ + +where $A$ is the set of all attacks, $M$ is the total number of generated adversarial examples by all attacks, and the function $[ \cdot ]$ is the indicator function which equals to 1 when the prediction is true. + +# 5.1 CHALLENGE RESULTS + +The best defense model in our experiments, i.e., randomization layers $^ +$ ens-adv-Inception-Resnet$\nu 2$ , was submitted to the challenge. To increase the classification accuracy, we (1) changed the resizing range from [299, 331) to [310, 331); (2) averaged the prediction results over 30 randomization patterns for each image; (3) flipped the input image with probability 0.5 for each randomization pattern. + +By evaluating our model against 156 different attacks, it reaches a normalized score of 0.924 (ranked No.2 among 107 defense models), which is far better than using ensemble adversarial training (Tramer et al., 2017) alone with a normalized score of \` 0.773 (ranked No.56). This result further demonstrates that the proposed randomization method effectively make deep networks much more robust to adversarial attacks. + +# 6 CONCLUSION + +In this paper, we propose a randomization-based mechanism to mitigate adversarial effects. We conduct comprehensive experiments to validate the effectiveness of our defense method, using different network structures, against different attack methods, and under different attack scenarios. The experimental results show that adversarial examples rarely transfer between different randomization patterns, especially for iterative attacks. In addition, the proposed randomization layers are compatible to different network structures and adversarial defense methods, which can serve as a basic module for defense against adversarial examples. By adding the proposed randomization layers to an adversarially trained model (Tramer et al., 2017), it achieves a normalized score of \` 0.924 (ranked No.2 among 107 defense models) in the NIPS 2017 adversarial examples defense challenge, which is far better than using adversarial training alone with a normalized score of 0.773 (ranked No.56). The code is public available at https://github.com/cihangxie/NIPS2017_ adv_challenge_defense. + +# ACKNOWLEDGEMENTS + +This work is supported by a gift grant from SNAP Research, ONR–N00014-15-1-2356 and NSF Visual Cortex on Silicon CCF-1317560. + +# REFERENCES + +Battista Biggio and Pavel Laskov. Poisoning attacks against support vector machines. In International Conference on Machine Learning, 2012. + +Xiaoyu Cao and Neil Zhenqiang Gong. Mitigating evasion attacks to deep neural networks via region-based classification. In Proceedings of the 33rd Annual Computer Security Applications Conference. ACM, 2017. + +Nicholas Carlini and David Wagner. Towards evaluating the robustness of neural networks. In IEEE Symposium on Security and Privacy. IEEE, 2017. + +Liang-Chieh Chen, George Papandreou, Iasonas Kokkinos, Kevin Murphy, and Alan L Yuille. Deeplab: Semantic image segmentation with deep convolutional nets, atrous convolution, and fully connected crfs. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2017. + +Moustapha Cisse, Yossi Adi, Natalia Neverova, and Joseph Keshet. Houdini: Fooling deep structured prediction models. arXiv preprint arXiv:1707.05373, 2017. + +Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scale hierarchical image database. In Computer Vision and Pattern Recognition. IEEE, 2009. + +Reuben Feinman, Ryan R Curtin, Saurabh Shintre, and Andrew B Gardner. Detecting adversarial samples from artifacts. arXiv preprint arXiv:1703.00410, 2017. + +Volker Fischer, Mummadi Chaithanya Kumar, Jan Hendrik Metzen, and Thomas Brox. Adversarial examples for semantic image segmentation. arXiv preprint arXiv:1703.01101, 2017. + +Ross Girshick. Fast r-cnn. In International Conference on Computer Vision. IEEE, 2015. + +Ian J Goodfellow, Jonathon Shlens, and Christian Szegedy. Explaining and harnessing adversarial examples. In International Conference on Learning Representations, 2015. + +Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Computer Vision and Pattern Recognition. IEEE, 2016a. + +Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Identity mappings in deep residual networks. In European Conference on Computer Vision. Springer, 2016b. + +Pang Wei Koh and Percy Liang. Understanding black-box predictions via influence functions. arXiv preprint arXiv:1703.04730, 2017. + +Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. Imagenet classification with deep convolutional neural networks. In Advances in Neural Information Processing Systems, 2012. + +Alexey Kurakin, Ian Goodfellow, and Samy Bengio. Adversarial machine learning at scale. In International Conference on Learning Representations, 2017. + +Yanpei Liu, Xinyun Chen, Chang Liu, and Dawn Song. Delving into transferable adversarial examples and black-box attacks. In International Conference on Learning Representations, 2017. + +Jonathan Long, Evan Shelhamer, and Trevor Darrell. Fully convolutional networks for semantic segmentation. In Computer Vision and Pattern Recognition. IEEE, 2015. + +Dongyu Meng and Hao Chen. Magnet: a two-pronged defense against adversarial examples. arXiv preprint arXiv:1705.09064, 2017. + +Jan Hendrik Metzen, Tim Genewein, Volker Fischer, and Bastian Bischoff. On detecting adversarial perturbations. In International Conference on Learning Representations, 2017. + +Seyed-Mohsen Moosavi-Dezfooli, Alhussein Fawzi, and Pascal Frossard. Deepfool: a simple and accurate method to fool deep neural networks. In Computer Vision and Pattern Recognition. IEEE, 2016. + +Nicolas Papernot, Ian Goodfellow, Ryan Sheatsley, Reuben Feinman, and Patrick McDaniel. cleverhans v1.0.0: an adversarial machine learning library. arXiv preprint arXiv:1610.00768, 2016a. + +Nicolas Papernot, Patrick McDaniel, Xi Wu, Somesh Jha, and Ananthram Swami. Distillation as a defense to adversarial perturbations against deep neural networks. In IEEE Symposium on Security and Privacy. IEEE, 2016b. + +Shaoqing Ren, Kaiming He, Ross Girshick, and Jian Sun. Faster r-cnn: Towards real-time object detection with region proposal networks. In Advances in Neural Information Processing Systems, 2015. + +Karen Simonyan and Andrew Zisserman. Very deep convolutional networks for large-scale image recognition. In International Conference on Learning Representations, 2015. + +Christian Szegedy, Wojciech Zaremba, Ilya Sutskever, Joan Bruna, Dumitru Erhan, Ian Goodfellow, and Rob Fergus. Intriguing properties of neural networks. In International Conference on Learning Representations, 2014. + +Christian Szegedy, Vincent Vanhoucke, Sergey Ioffe, Jon Shlens, and Zbigniew Wojna. Rethinking the inception architecture for computer vision. In Computer Vision and Pattern Recognition. IEEE, 2016. + +Christian Szegedy, Sergey Ioffe, Vincent Vanhoucke, and Alexander A Alemi. Inception-v4, inception-resnet and the impact of residual connections on learning. In AAAI, 2017. + +Florian Tramer, Alexey Kurakin, Nicolas Papernot, Dan Boneh, and Patrick McDaniel. Ensemble \` adversarial training: Attacks and defenses. arXiv preprint arXiv:1705.07204, 2017. + +Jianyu Wang, Zhishuai Zhang, Cihang Xie, Yuyin Zhou, Vittal Premachandran, Jun Zhu, Lingxi Xie, and Alan Yuille. Visual concepts and compositional voting. arXiv preprint arXiv:1711.04451, 2017. + +Cihang Xie, Jianyu Wang, Zhishuai Zhang, Yuyin Zhou, Lingxi Xie, and Alan Yuille. Adversarial Examples for Semantic Segmentation and Object Detection. In International Conference on Computer Vision. IEEE, 2017. + +Zhishuai Zhang, Siyuan Qiao, Cihang Xie, Wei Shen, Bo Wang, and Alan L Yuille. Single-shot object detection with enriched semantics. arXiv preprint arXiv:1712.00433, 2017. + +# APPENDIX A OTHER RANDOMIZATION METHODS + +Besides random resizing and random padding, we further evaluate the effectiveness of four other randomization methods against adversarial examples. All these four methods are used as dataaugmentation during the standard network training. + +• Random Brightness: a brightness factor $\delta$ is randomly picked in the interval $[ - \delta _ { \mathrm { m a x } } , \delta _ { \mathrm { m a x } } ]$ to adjust the brightness of the normalized image $\hat { X _ { n } }$ . We choose $\begin{array} { r } { \delta _ { \mathrm { m a x } } = \frac { 3 2 } { 2 5 5 } } \end{array}$ . +• Random Saturation: a saturation factor $\alpha$ is randomly picked in the interval $[ \alpha _ { l o w e r } , \alpha _ { u p p e r } ]$ to adjust the saturation of the normalized image $\hat { X _ { n } }$ . We choose $\alpha _ { l o w e r } =$ 0.5 and $\alpha _ { u p p e r } = 1 . 5$ . +• Random Hue: a hue factor $\theta$ is randomly picked in the interval $[ - \theta _ { \mathrm { m a x } } , \theta _ { \mathrm { m a x } } ]$ to adjust the hue of the normalized image ${ \hat { X _ { n } } }$ . We choose $\theta _ { \mathrm { m a x } } = 0 . 2$ . +• Random Contrast: a contrast factor $\beta$ is randomly picked in the interval $[ \beta _ { l o w e r } , \beta _ { u p p e r } ]$ to adjust the contrast of the normalized image $\hat { X _ { n } }$ . We choose $\beta _ { l o w e r } = 0 . 5$ and $\beta _ { u p p e r } = 1 . 5$ . + +Note that, (1) the parameters chosen above are the same as the ones used during network training process4; (2) the pixel value of the normalized image $\hat { X _ { n } }$ are all within the interval $[ 0 , 1 ]$ , and we also use this range to clip the pixel value of the image after pre-processing. + +Following the experiment setup in section 4, we first evaluate the effectiveness of each of these randomization methods on the 5000 clean images. The results are shown in the Table 7. We can see that these methods hardly hurt the performance on clean images. We further combine the proposed randomization layers, i.e., random resizing layer and random padding layer, with each of these randomization methods (denoted as $^ { 6 6 } + + ^ { 7 }$ ). We see that the combined randomization modules only cause very little accuracy drop on clean images. + +Table 7: Top-1 classification accuracy on clean images. We see that these four randomization methods hardly hurt the performance on clean images. We use $^ { 6 6 } { + + ^ { 9 9 } }$ to denote the addition of the proposed randomization layers, i.e., random resizing and random padding, and the results indicate that combined models still performs pretty good on clean images. + +
ModelsInception-v3ResNet-v2-101Inception-ResNet-v2ens-adv-Inception-ResNet-v2
random brightness99.6%99.7%99.8%99.8%
random brightness ++98.6%98.1%99.1%99.2%
random saturation99.6%99.7%99.9%99.9%
random saturation ++98.6%98.3%99.3%99.3%
random hue99.4%99.6%99.7%99.4%
random hue ++98.6%98.3%99.2%99.1%
random contrast99.5%99.6%99.7%99.6%
random contrast ++98.6%98.2%99.3%99.1%
+ +We then evaluate the effectiveness of these randomization methods against the adversarial examples generated under the vanilla attack scenario. The results are shown in the Tables 8 - 11. Compared to the results in Table 2, all these four methods are much less effective than the proposed randomization layers. By combining the proposed randomization layers with each of these four randomization methods (denoted as $^ { 6 6 } { + } { + } ^ { , 9 } )$ , the performance can be slightly improved than using the proposed randomization layers alone. + +Since each of these four randomization methods alone are not as effective as our proposed randomization methods against adversarial examples generated under the vanilla attack scenario, we do not further investigate their effectiveness under single-pattern attack and ensemble-pattern attack scenarios. However, combining these randomization methods with our proposed randomization layers together provides a way to build a slightly stronger defense mechanism. + +Table 8: Top-1 classification accuracy by using random brightness under the vanilla attack scenario. Compared to the results in Table 2, random brightness is much less effective than the proposed randomization layers. By combing random brightness and the proposed randomization layers (denoted as random brightness $^ { + + }$ ), it reaches slightly better performance than using the proposed randomization layers alone. + +
ModelsInception-v3ResNet-v2-101Inception-ResNet-v2ens-adv-Inception-ResNet-v2
randombright-nessrandombright-ness++randombright-nessrandombright-ness++randombright-nessrandombright-ness++randombright-nessrandombright-ness++
FGSM-234.9%67.0%28.5%73.5%66.4%81.3%85.0%95.8%
FGSM-531.9%55.5%21.6%55.7%62.4%74.7%87.6%95.0%
FGSM-1033.2%52.9%20.9%47.2%61.8%71.5%90.4%94.5%
DeepFool79.4%98.1%82.3%97.5%62.8%98.3%79.0%99.1%
C&W34.5%96.9%47.7%97.2%51.3%98.0%42.3%98.6%
+ +Table 9: Top-1 classification accuracy by using random saturation under the vanilla attack scenario. Compared to the results in Table 2, random saturation is much less effective than the proposed randomization layers. By combing random saturation and the proposed randomization layers (denoted as random saturation $^ { + + }$ ), it reaches slightly better performance than using the proposed randomization layers alone. + +
ModelsInception-v3ResNet-v2-101Inception-ResNet-v2ens-adv-Inception-ResNet-v2
randomsatura-tionrandomsatura-tion++randomrandomrandomrandom satura-tion++randomsatura-tionrandom satura-tion++
satura-tionsatura-tion++satura-tion
FGSM-234.2%66.5%27.9%73.6%66.3%81.5%85.2%95.7%
FGSM-531.8%55.2%21.1%55.7%62.1%74.6%87.0%95.0%
FGSM-1033.5%52.2%20.7%46.5%61.7%71.4%90.1%93.9%
DeepFool82.6%98.1%79.6%97.6%64.7%98.2%78.5%99.0%
C&W39.2%97.2%47.5%96.9%51.7%97.7%50.9%99.1%
+ +Table 10: Top-1 classification accuracy by using random hue under the vanilla attack scenario. Compared to the results in Table 2, random hue is much less effective than the proposed randomization layers. By combing random hue and the proposed randomization layers (denoted as random $\mathbf { h u e + + }$ ), it reaches slightly better performance than using the proposed randomization layers alone. + +
ModelsInception-v3ResNet-v2-101Inception-ResNet-v2ens-adv-Inception-ResNet-v2
randomhuerandomhue++randomhuerandomhue++randomhuerandomhue++randomhuerandomhue++
FGSM-238.1%69.0%32.0%74.9%68.6%83.0%87.4%95.8%
FGSM-533.9%57.2%23.0%57.6%64.0%76.1%86.7%93.9%
FGSM-1036.4%54.2%22.1%48.4%63.0%72.5%88.0%91.3%
DeepFool95.0%97.9%91.2%97.6%86.5%98.4%96.8%99.1%
C&W72.1%97.3%74.0%97.0%77.4%98.2%81.1%98.8%
+ +Table 11: Top-1 classification accuracy by using random contrast under the vanilla attack scenario. Compared to the results in Table 2, random contrast is much less effective than the proposed randomization layers. By combing random contrast and the proposed randomization layers (denoted as random contrast $^ { + + }$ ), it reaches slightly better performance than using the proposed randomization layers alone. + +
ModelsInception-v3ResNet-v2-101Inception-ResNet-v2ens-adv-Inception-ResNet-v2
randomcon-trastrandomcon-trast++randomcon-trastrandomcon-trast++randomcon-trastrandomcon-trast++randomcon-trastrandomcon-trast++
FGSM-237.0%68.0%29.4%74.1%67.2%82.5%85.9%96.0%
FGSM-532.7%56.3%22.7%57.0%63.1%74.9%88.1%94.9%
FGSM-1034.4%53.5%21.2%47.0%62.1%72.0%90.6%94.3%
DeepFool90.4%98.1%87.5%97.5%73.8%98.1%90.8%99.0%
C&W56.8%97.0%57.1%96.7%63.7%97.9%67.6%98.8%
+ +# APPENDIX B RANDOMIZATION LAYERS WITH SMALLER SIZE + +Instead of resizing the input image to a larger size, we here resize the input image to a smaller size, i.e., the resizing parameter is randomly sampled from the range [267, 299). The random padding layer then pads the resized image to the shape of $2 9 9 \times 2 9 9 \times 3$ in a random manner. Note that, the random resizing layer and the random padding layer here have the same freedom as the ones used in the paper, i.e., they create the same number, 12528, of different patterns for a single image. We evaluate the effectiveness of this parameter setting on both the 5000 clean images and the adversarial examples generated under the vanilla attack scenario. The results are shown in the Table 12. We see that randomization layers still work well with smaller size images, but is slightly worse than using larger size images as in the paper. This is because resizing to a smaller size loses certain information of the original image. + +Table 12: Top-1 classification accuracy on the clean images and the adversarial examples generated under the vanilla attack scenario. Compared to the results in Tables 1 and 2, randomization parameters applied here (i.e., resize between [267, 299), and pad to $2 9 9 \times 2 9 9 \times 3 )$ ) is slightly worse than the randomization parameters applied in the paper (i.e., resize between [299, 331), and pad to $3 3 1 \times 3 3 1 \times 3 )$ . + +
ModelsInception-v3ResNet-v2-101Inception-ResNet-v2ens-adv-Inception-ResNet-v2
clean images98.2%97.5%99.1%98.7%
FGSM-263.1%65.0%79.9%95.0%
FGSM-553.4%48.3%73.3%94.0%
FGSM-1050.8%40.5%70.6%93.4%
DeepFool97.2%96.5%96.0%98.6%
C&W95.2%95.2%97.2%97.8%
+ +# APPENDIX C RANDOMIZATION LAYERS WITH MULTIPLE ITERATIONS + +In this section, we show the relationship between the top-1 accuracy of the defense model and the iteration number performed on each image. Specifically, we choose ens-adv-Inception-ResNet- $\nu 2 +$ randomization layers as the defense model for the experiment. The same trend can be observed for other defense models. + +For the defense model, the iteration number is chosen to be $\{ 1 , 5 , 1 0 , 2 0 , 3 0 \}$ , and it is evaluated on the 5000 clean test images and the adversarial examples generated under all three attack scenarios. The results are shown in the Figures 3 - 5. We can observe that (1) increasing the number of iteration can slightly improve the top-1 classification accuracy of the defense model on clean images and adversarial examples generated under both the vanilla attack and the single-pattern attack scenarios; (2) increasing the number of iteration has nearly no improvement for the top-1 classification accuracy of the defense model on adversarial examples generated by single-step attacks under the ensemble-pattern attack scenario; (3) increasing the number of iteration can improve the top-1 classification accuracy of the defense model on adversarial examples generated by iterative attacks under the ensemble-pattern attack scenario. + +![](images/a25aa63356ef141cc900583f46c838547d3cb72eeae8c3fce9b665da139db3ec.jpg) +Figure 3: Top-1 classification accuracy on the clean images and the adversarial examples generated under the vanilla attack scenrio. + +![](images/0cf83e4d60ebaeaa48670a3eae350647157c26303fc23d006fea2afbff49f186.jpg) +Figure 4: Top-1 classification accuracy on the adversarial examples generated under the single-pattern attack scenrio. + +![](images/49c765887d9ca814549732caf7e88c202b46e49cbcf0f3ce57891fd62a33e450.jpg) +Figure 5: Top-1 classification accuracy on the adversarial examples generated under the ensemble-pattern attack scenrio. \ No newline at end of file diff --git a/parse/train/Sk9yuql0Z/Sk9yuql0Z_content_list.json b/parse/train/Sk9yuql0Z/Sk9yuql0Z_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..2b3a01fe82a7286738c09ba2445827c5e9ed7b99 --- /dev/null +++ b/parse/train/Sk9yuql0Z/Sk9yuql0Z_content_list.json @@ -0,0 +1,1715 @@ +[ + { + "type": "text", + "text": "MITIGATING ADVERSARIAL EFFECTS THROUGH RAN-DOMIZATION", + "text_level": 1, + "bbox": [ + 174, + 99, + 820, + 145 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Cihang Xie, Zhishuai Zhang & Alan L. Yuille ", + "bbox": [ + 186, + 170, + 501, + 185 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Department of Computer Science \nThe Johns Hopkins University \nBaltimore, MD 21218 USA \n{cihangxie306, zhshuai.zhang, alan.l.yuille}@gmail.com ", + "bbox": [ + 184, + 186, + 710, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jianyu Wang Baidu Research USA Sunnyvale, CA 94089 USA wjyouch@gmail.com ", + "bbox": [ + 184, + 261, + 367, + 316 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zhou Ren \nSnap Inc. \nVenice, CA 90291 USA \nzhou.ren@snapchat.com ", + "bbox": [ + 183, + 338, + 392, + 393 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ABSTRACT ", + "text_level": 1, + "bbox": [ + 454, + 431, + 544, + 445 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Convolutional neural networks have demonstrated high accuracy on various tasks in recent years. However, they are extremely vulnerable to adversarial examples. For example, imperceptible perturbations added to clean images can cause convolutional neural networks to fail. In this paper, we propose to utilize randomization at inference time to mitigate adversarial effects. Specifically, we use two randomization operations: random resizing, which resizes the input images to a random size, and random padding, which pads zeros around the input images in a random manner. Extensive experiments demonstrate that the proposed randomization method is very effective at defending against both single-step and iterative attacks. Our method provides the following advantages: 1) no additional training or fine-tuning, 2) very few additional computations, 3) compatible with other adversarial defense methods. By combining the proposed randomization method with an adversarially trained model, it achieves a normalized score of 0.924 (ranked No.2 among 107 defense teams) in the NIPS 2017 adversarial examples defense challenge, which is far better than using adversarial training alone with a normalized score of 0.773 (ranked No.56). The code is public available at https: //github.com/cihangxie/NIPS2017_adv_challenge_defense. ", + "bbox": [ + 233, + 463, + 764, + 699 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 INTRODUCTION ", + "text_level": 1, + "bbox": [ + 176, + 726, + 336, + 741 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Convolutional Neural Networks (CNNs) have been successfully applied to a wide range of vision tasks, including image classification (Krizhevsky et al., 2012; Simonyan & Zisserman, 2015; He et al., 2016a), object detection (Girshick, 2015; Ren et al., 2015; Zhang et al., 2017), semantic segmentation (Long et al., 2015; Chen et al., 2017), visual concept discovery (Wang et al., 2017) etc. However, recent works show that CNNs are extremely vulnerable to small perturbations to the input image. For example, adding visually imperceptible perturbations to the original image can result in failures for image classification (Szegedy et al., 2014; Goodfellow et al., 2015), object detection (Xie et al., 2017) and semantic segmentation (Xie et al., 2017; Fischer et al., 2017; Cisse et al., 2017). These perturbed images are called adversarial examples and Figure 1 gives an example. Adversarial examples pose a great security danger to the deployment of commercial machine learning systems. Thus, making CNNs more robust to adversarial examples is a very important yet challenging problem. Recent works (Papernot et al., 2016b; Kurakin et al., 2017; Tramer et al., 2017; Cao & Gong, \\` ", + "bbox": [ + 173, + 757, + 825, + 922 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/48b3009e8ed26fd44338fb7b72d9eaf8e2ea6476d67d321696065b4e396f4087.jpg", + "image_caption": [ + "Figure 1: This is an adversarial example crafted for VGG (Simonyan & Zisserman, 2015). The left image is classified correctly as king penguin, the center image is the adversarial perturbation (magnified by 10 and enlarged by 128 for better visualization), and the right image is the adversarial example misclassfied as chihuahua. " + ], + "image_footnote": [], + "bbox": [ + 207, + 99, + 792, + 224 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2017; Metzen et al., 2017; Feinman et al., 2017; Meng & Chen, 2017) are making progress on this line of research. ", + "bbox": [ + 176, + 311, + 821, + 340 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Adversarial attacks can be divided into two categories: single-step attacks, which perform only one step of gradient computation, and iterative attacks, which perform multiple steps. Intuitively, the perturbation generated by iterative methods may easily get over-fitted to the specific network parameters, and thus be less transferable. On the other hand, single-step methods may not be strong enough to fool the network. For examples, it has been demonstrated that single-step attacks, like Fast Gradient Sign Method (FGSM) (Goodfellow et al., 2015), have better transferability but weaker attack rate than iterative attacks, like DeepFool (Moosavi-Dezfooli et al., 2016). ", + "bbox": [ + 174, + 347, + 825, + 445 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Due to the weak generalization of iterative attacks, low-level image transformations, e.g., resizing, padding, compression, etc, may probably destroy the specific structure of adversarial perturbations, thus making it a good defense. It can even defend against white-box iterative attacks if random transformations are applied. This is because each test image goes through random transformations and the attacker does not know the specific transformation when generating adversarial noise. Recently, adversarial training (Kurakin et al., 2017; Tramer et al., 2017) was developed to defend against \\` single-step attacks. Thus by adding the proposed random transformations as additional layers to an adversarially trained model (Tramer et al., 2017), it is expected that the method is able to effec- \\` tively defend against both single-step and iterative attacks, including both black-box and white-box settings. ", + "bbox": [ + 174, + 452, + 825, + 590 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Based on the above reasoning, in this paper, we propose a defense method by randomization at inference time, i.e., random resizing and random padding, to mitigate adversarial effects. To the best of our knowledge, this is the first work that demonstrates the effectiveness of randomization at inference time on mitigating adversarial effects on large-scale dataset, e.g., ImageNet (Deng et al., 2009). The proposed method provides the following advantages: ", + "bbox": [ + 174, + 598, + 825, + 667 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "• Randomization at inference time makes the network much more robust to adversarial images, especially for iterative attacks (both white-box and black box), but hardly hurts the performance on clean (non-adversarial) images. Experiments on section 4.2 support this argument. \n• There is no additional training or fine-tuning required which is easy for implementation. \n• Very few computations are required by adding the two randomization layers, thus there is nearly no run time increase. \n• Randomization layers are compatible to different network structures and adversarial defense methods, which can serve as a basic network module for adversarial defense. ", + "bbox": [ + 215, + 680, + 825, + 827 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We conduct comprehensive experiments to test the effectiveness of our defense method, using different network structures, against different attack methods, and under different attack scenarios. The results in Section 4 demonstrate that the proposed randomization layers can significantly mitigate adversarial effects, especially for iterative attack methods. Moreover, we submitted the model, which combines the proposed randomization layers and an adversarially trained model (Tramer\\` et al., 2017), to the NIPS 2017 adversarial examples defense challenge. It reaches a normalized score of 0.924 (ranked No.2 among 107 defense teams), which is far better than just using adversarial training (Tramer et al., 2017) alone with a normalized score of \\` 0.773 (ranked No.56). ", + "bbox": [ + 174, + 840, + 825, + 924 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "", + "bbox": [ + 173, + 103, + 821, + 132 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2 RELATED WORK ", + "text_level": 1, + "bbox": [ + 176, + 155, + 344, + 171 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.1 GENERATING ADVERSARIAL EXAMPLES ", + "text_level": 1, + "bbox": [ + 176, + 189, + 495, + 202 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Generating adversarial examples has been extensively studied recently. (Szegedy et al., 2014) first showed that adversarial examples, computed by adding visually imperceptible perturbations to the original images, make CNNs predict wrong labels with high confidence. (Goodfellow et al., 2015) proposed the fast gradient sign method to generate adversarial examples based on the linear nature of CNNs, and also proposed adversarial training for defense. (Moosavi-Dezfooli et al., 2016) generated adversarial examples by assuming that the loss function can be linearized around the current data point at each iteration. (Carlini & Wagner, 2017) developed a stronger attack to find adversarial perturbations by introducing auxiliary variables which incooperate the pixel value constrain, e.g., pixel intensity must be within the range [0,255], naturally into the loss function and make the optimization process easier. (Liu et al., 2017) proposed an ensemble-based approaches to generate adversarial examples with stronger transferability. Unlike the works above, (Biggio & Laskov, 2012; Koh & Liang, 2017) showed that manipulating only a small fraction of the training data can significantly increase the number of misclassified samples at test time for learning algorithms, and such attacks are called poisoning attacks. ", + "bbox": [ + 174, + 215, + 825, + 410 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2 DEFENDING AGAINST ADVERSARIAL EXAMPLES", + "text_level": 1, + "bbox": [ + 174, + 430, + 555, + 444 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Opposite to generating adversarial examples, there is also progress on reducing the effects of adversarial examples. (Papernot et al., 2016b) showed networks trained using defensive distillation can effectively defend against adversarial examples. (Kurakin et al., 2017) proposed to replace the original clean images with a mixture of clean images and corresponding adversarial images in each training batch to improve the network robustness. (Tramer et al., 2017) improved the robustness \\` further by training the network on an ensemble of adversarial images generated from the trained model itself and from a number of other pre-trained models. Cao & Gong (2017) proposed a regionbased classification to let models be robust to adversarial examples. (Metzen et al., 2017) trained a detector on the inner layer of the classifier to detect adversarial examples. (Feinman et al., 2017) detected adversarial examples by looking at the Bayesian uncertainty estimates of the input images in dropout neural networks and by performing density estimation in the subspace of deep features learned by the model. MagNet (Meng & Chen, 2017) detected adversarial examples with large perturbation using detector networks, and pushed adversarial examples with small perturbation towards the manifold of clean images. ", + "bbox": [ + 174, + 458, + 825, + 651 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3 APPROACH", + "text_level": 1, + "bbox": [ + 176, + 675, + 297, + 690 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1 AN OVERVIEW OF GENERATING ADVERSARIAL EXAMPLES", + "text_level": 1, + "bbox": [ + 176, + 708, + 625, + 723 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Before introducing the proposed adversarial defense method, we give an overview of generating adversarial examples. Let $X _ { n }$ denote the $n$ -th image in a dataset containing $N$ images, and let $y _ { n } ^ { \\mathrm { t r u e } }$ denote the corresponding ground-truth label. We use $\\theta$ to denote the network parameters, and $L ( X _ { n } , y _ { n } ^ { \\mathrm { t r u e } } ; \\theta )$ to denote the loss. For the adversarial example generation, the goal is to maximize the loss $L ( X _ { n } + r _ { n } , y _ { n } ^ { \\mathrm { t r u e } } ; \\theta )$ for each image $X _ { n }$ , under the constraint that the generated adversarial example $X _ { n } ^ { \\mathrm { a d v } } = X _ { n } + r _ { n }$ should look visually similar to the original image $X _ { n }$ , i.e., $| | r _ { n } | | \\leq \\epsilon$ , and the corresponding predicted label $y _ { n } ^ { \\mathrm { a d v } } \\neq y _ { n } ^ { \\mathrm { t r u e } }$ . ", + "bbox": [ + 174, + 734, + 825, + 834 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In our experiment, we consider three different attack methods, including one single-step attack method and two iterative attack methods. We use the cleverhans library (Papernot et al., 2016a) to generate adversarial examples, where all these attacks have been implemented via TensorFlow. ", + "bbox": [ + 174, + 840, + 823, + 882 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "• Fast Gradient Sign Method (FGSM): FGSM (Goodfellow et al., 2015) is a single-step attack method. It finds the adversarial perturbation that yields the highest increase of the linear cost function under $l _ { \\infty }$ -norm. The update equation is ", + "bbox": [ + 215, + 895, + 823, + 924 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "", + "bbox": [ + 232, + 103, + 622, + 117 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/256d0580ab719538c36dbc65ddaa18b6508c027919ce8cd831ad834e72a8a2b4.jpg", + "text": "$$\nX _ { n } ^ { \\mathrm { a d v } } = X _ { n } + \\epsilon \\cdot s i g n \\big ( \\nabla _ { X _ { n } } L ( X _ { n } , y _ { n } ^ { \\mathrm { t r u e } } ; \\theta ) \\big ) ,\n$$", + "text_format": "latex", + "bbox": [ + 380, + 121, + 673, + 138 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\epsilon$ controls the magnitude of adversarial perturbation. In the experiment, we choose $\\epsilon = \\{ 2 , 5 , 1 0 \\}$ , which corresponds to small, medium and high magnitude of adversarial perturbations, respectively. ", + "bbox": [ + 230, + 140, + 823, + 181 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "• DeepFool: DeepFool (Moosavi-Dezfooli et al., 2016) is an iterative attack method which finds the minimal perturbation to cross the decision boundary based on the linearization of the classifier at each iteration. Any $l _ { p }$ -norm can be used with DeepFool, and we choose $l _ { 2 }$ -norm for the study in this paper. ", + "bbox": [ + 218, + 184, + 825, + 241 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "• Carlini $\\&$ Wagner (C&W): C&W (Carlini & Wagner, 2017) is a stronger iterative attack method proposed recently. It finds the adversarial perturbation $r _ { n }$ by using an auxiliary variable $\\omega _ { n }$ as ", + "bbox": [ + 215, + 244, + 823, + 285 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/6ac2e21a49ac9a59dcee26a8cc88dbc8ae952e60add70940c62a298ad305ebe3.jpg", + "text": "$$\nr _ { n } = { \\frac { 1 } { 2 } } ( t a n h ( \\omega _ { n } + 1 ) ) - X _ { n } .\n$$", + "text_format": "latex", + "bbox": [ + 424, + 284, + 632, + 313 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Then the loss function optimizes the auxiliary variable $\\omega _ { n }$ ", + "bbox": [ + 233, + 314, + 612, + 329 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/9a4c56ddb6d5a120595154f56ce8c6cdd23b4680a466e4b911993433976f94cb.jpg", + "text": "$$\n\\operatorname* { m i n } _ { \\omega _ { n } } | | \\frac { 1 } { 2 } ( t a n h ( \\omega _ { n } ) + 1 ) - X _ { n } | | + c \\cdot f ( \\frac { 1 } { 2 } ( t a n h ( \\omega _ { n } ) + 1 ) ) .\n$$", + "text_format": "latex", + "bbox": [ + 328, + 330, + 725, + 359 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The function $f ( \\cdot )$ is defined as ", + "bbox": [ + 233, + 364, + 436, + 378 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/471d0561206caf18e7dae8a27a418ea0baf79b3fc6adce078bd4d7d503c07252.jpg", + "text": "$$\nf ( x ) = \\operatorname* { m a x } ( Z ( x ) _ { y ^ { \\mathrm { t u e } } } - \\operatorname* { m a x } \\{ Z ( x ) _ { i } : i \\neq y ^ { \\mathrm { t r u e } } \\} , - k ) ,\n$$", + "text_format": "latex", + "bbox": [ + 346, + 381, + 707, + 397 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $Z ( x ) _ { i }$ is the logits output for class $i$ , and $k$ controls the confidence gap between the adversarial class and true class. C&W can also work with various $l _ { p }$ -norm, and we choose $l _ { 2 }$ -norm in the experiments. ", + "bbox": [ + 235, + 400, + 823, + 441 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2 DEFENDING AGAINST ADVERSARIAL EXAMPLES", + "text_level": 1, + "bbox": [ + 174, + 458, + 557, + 472 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The goal of defense is to build a network that is robust to adversarial examples, i.e., it can classify adversarial images correctly with little performance loss on non-adversarial (clean) images. Towards this goal, we propose a randomization-based method, as shown in Figure 2, which adds a random resizing layer and a random padding layer to the beginning of the classification networks. There is no re-training or fine-tuning needed which makes the proposed method very easy to implement. ", + "bbox": [ + 174, + 483, + 825, + 553 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.1 RANDOMIZATION LAYERS ", + "text_level": 1, + "bbox": [ + 176, + 568, + 411, + 582 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The first randomization layer is a random resizing layer, which resizes the original image $X _ { n }$ with the size $W \\times H \\times 3$ to a new image $X _ { n } ^ { \\prime }$ with random size $W ^ { \\prime } \\times H ^ { \\prime } \\times 3$ . Note that, $| W ^ { \\prime } - W |$ and $| H ^ { \\prime } - H |$ should be within a reasonablely small range, otherwise the network performance on non-adversarial images would significantly drop. Taking Inception-ResNet network (Szegedy et al., 2017) as an example, the original data input size is $2 9 9 \\times 2 9 9 \\times 3$ . Empirically we found that the network performance hardly drops if we control the height and width of the resized image $X _ { n } ^ { \\prime }$ to be within the range [299, 331). ", + "bbox": [ + 173, + 592, + 825, + 690 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The second randomization layer is the random padding layer, which pads zeros around the resized image in a random manner. Specifically, by padding the resized image $X _ { n } ^ { \\prime }$ into a new image $X _ { n } ^ { \\prime \\prime }$ with the size $W ^ { \\prime \\prime } \\times H ^ { \\prime \\prime } \\times 3$ , we can choose to pad $w$ zero pixels on the left, $W ^ { \\prime \\prime } - W ^ { \\prime } - w$ zero pixels on the right, $h$ zero pixels on the top and $H ^ { \\prime \\prime } - H ^ { \\prime } - h$ zero pixels on the bottom. This results in a total number of $\\left( W ^ { \\prime \\prime } - W ^ { \\prime } + 1 \\right) \\times \\left( H ^ { \\prime \\prime } - H ^ { \\prime } + 1 \\right)$ different possible padding patterns. ", + "bbox": [ + 174, + 695, + 825, + 767 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "During implementation, the original image first goes through two randomization layers, and then we pass the transformed image to the original CNN for classification. The pipeline is illustrated in Figure 2. ", + "bbox": [ + 174, + 773, + 825, + 815 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.2 RANDOMIZATION LAYERS $^ +$ ADVERSARIAL TRAINING ", + "text_level": 1, + "bbox": [ + 174, + 829, + 607, + 844 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Note that our randomization-based method is good at defending against iterative attacks, and adversarial training (Kurakin et al., 2017; Tramer et al., 2017) can effectively increase the robustness of \\` neural networks to single-step attacks. Thus, to make the best of both worlds, we can combine the proposed randomization layers and an adversarially trained model (Tramer et al., 2017) together to \\` defend against both single-step and iterative attacks. ", + "bbox": [ + 174, + 853, + 825, + 924 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/b391dc2283db9234f0f293be29409bb96e04b1cf038128ded1f2d00537f1f162.jpg", + "image_caption": [ + "Figure 2: The pipeline of our randomization-based defense mechanism. The input image $X _ { n }$ first goes through the random resizing layer with a random scale applied. Then the random padding layer pads the resized image $X _ { n } ^ { \\prime }$ in a random manner. The resulting padded image $X _ { n } ^ { \\prime \\prime }$ is used for classification. " + ], + "image_footnote": [], + "bbox": [ + 183, + 106, + 826, + 338 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4 EXPERIMENTS ", + "text_level": 1, + "bbox": [ + 176, + 434, + 326, + 449 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1 EXPERIMENT SETUP ", + "text_level": 1, + "bbox": [ + 176, + 467, + 356, + 481 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dataset: It is less meaningful to attack the images that are already classified wrongly. Therefore, we randomly choose 5000 images from the ImageNet validation set that are classified correctly by all the considered networks to form our test dataset. All these images are of the size $2 9 9 \\times 2 9 9 \\times 3$ . ", + "bbox": [ + 174, + 494, + 825, + 536 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Networks: We test with four publicly available networks1,2, including Inception- $\\nu 3$ (Szegedy et al., 2016), ResNet- $\\cdot \\nu 2$ (He et al., 2016b) of 101 layers, Inception-ResNet- $\\cdot \\nu 2$ (Szegedy et al., 2017), and ens-adv-Inception-ResNet- $\\nu 2$ which applies the ensemble adversarial training (Tramer et al., 2017) \\` on Inception-ResNet- $\\nu 2$ . These networks have been trained on ImageNet, and we do not perform any re-training or fine-tuning on them for the whole experiments. ", + "bbox": [ + 173, + 542, + 825, + 613 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Defense Models: The defense models consist of the original networks (i.e., four above-mentioned networks) and two additional randomization layers. For the random resizing layer, it changes the input shape from $2 9 9 \\times 2 9 9 \\times 3$ to $r n d \\times r n d \\times 3$ , where rnd is a integer randomly sampled from the range [299, 331). For the random padding layer, it pads the resized image to the shape of $3 3 1 \\times 3 3 1 \\times 3$ in a random manner. By applying these two randomization layers, we can create 330 \n$\\sum _ { r n d = 2 9 9 } ( 3 3 1 - r n d + 1 ) ^ { 2 } = 1 2 5 2 8$ different patterns for a single image. Since there exists small variance on model performance w.r.t. different random patterns, we run the defense model three times independently and report the average accuracy. ", + "bbox": [ + 173, + 619, + 825, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Target Models under Different Attack Scenarios: The strongest attack would be that the attackers consider ALL possible patterns of the defense models when generating the adversarial examples. However, this is computationally impossible, because failing a large number of patterns (e.g., 12528 here) at the same time takes extremely long time, and may not even converge. Thus, we let attackers use the target models to generate adversarial examples instead, and consider the following three different attack scenarios. ", + "bbox": [ + 174, + 756, + 825, + 839 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "• Vanilla Attack: The attackers do not know the existence of the randomization layers and the target model is just the original network. ", + "bbox": [ + 207, + 852, + 823, + 881 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/f7a87e7b923a88f8e0adc99a1b2c5c1e87d84b1e032095c951694d1d5697a82d.jpg", + "table_caption": [ + "Table 1: Top-1 classification accuracy on the clean images. We see that adding random resizing and random padding cause very little accuracy drop on clean (non-adversarial) images. " + ], + "table_footnote": [], + "table_body": "
ModelsInception-v3ResNet-v2-101Inception-ResNet-v2ens-adv-Inception-ResNet-v2
w/o randomization layers100%100%100%100%
wrandomization layers97.3%98.3%99.3%99.2%
", + "bbox": [ + 178, + 141, + 821, + 214 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "• Single-Pattern Attack: The attackers know the existence of the randomization layers. In order to mimic the structures of defense models, the target model is chosen as the original network $^ +$ randomization layers with only one predefined pattern. ", + "bbox": [ + 217, + 241, + 825, + 284 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "• Ensemble-Pattern Attack: The attackers know the existence of the randomization layers. In order to mimic the structures of defense models in a more representative way, the target model is chosen as the original network $^ +$ randomization layers with an ensemble of predefined patterns. ", + "bbox": [ + 217, + 287, + 825, + 344 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Target Models and Defense Models: The target models and the defense models are exactly the same except for the parameter settings of the randomization layers, i.e., the randomization parameters at the target models are predefined while randomization parameters at the defense models are randomly generated at test time. The original networks (e.g., Inception- $\\nu 3$ ) utilized by the target models and the defense models are the same. The attackers first generate adversarial examples using the target models, and then evaluate the classification accuracy of these generated adversarial examples on both the target and defense models. A low accuracy of the target model indicates that the attack is successful, and a high accuracy of the defense model indicates that the defense is effective. ", + "bbox": [ + 174, + 357, + 825, + 468 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2 CLEAN IMAGES ", + "text_level": 1, + "bbox": [ + 174, + 487, + 323, + 501 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1 shows the top-1 accuracy of networks with and without randomization layers on the clean images. We can see that randomization layers introduce negligible performance degradation on clean images. Specifically, we can observe that: (1) models with more advanced architectures tend to have less performance degradation, e.g., Inception-ResNet- $\\cdot \\nu 2$ only has $0 . 7 \\%$ degradation while Inception-v3 has $2 . 7 \\%$ degradation; (2) ensemble adversarial training brings nearly no performance degradation to the models, e.g., Inception-ResNet-v2 and ens-adv-Inception-ResNet-v2 have nearly the same performance degradation. ", + "bbox": [ + 174, + 513, + 825, + 611 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3 VANILLA ATTACK SCENARIO ", + "text_level": 1, + "bbox": [ + 176, + 628, + 416, + 643 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For the vanilla attack scenario, the attackers are not aware of randomization layers, and directly use the original networks as the target model to generate adversarial examples. The attack ability on the defense models mostly rely on the transferability of adversarial examples to different resizing and padding. From the top-1 accuracy presented in Table 2, we observe that randomization layers can mitigate the adversarial effects for both single-step and iterative attacks significantly. As for singlestep attacks FGSM-\u000f, larger $\\epsilon$ indicates stronger transferability, thus making it harder to defend. However, we can still get satisfactory accuracy of the defense model on single-step attacks (even with large $\\epsilon$ ) using ens-adv-Inception-ResNet- $\\cdot \\nu 2$ $9 4 . 3 \\%$ top-1 accuracy). As for iterative attacks, attackers always reach a very high attack rate on target model, but have almost no impact on models after randomization layers are applied. This is because iterative attack methods are over-fitted to the target models thus have weak transferability. ", + "bbox": [ + 174, + 656, + 825, + 809 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4 SINGLE-PATTERN ATTACK SCENARIO", + "text_level": 1, + "bbox": [ + 176, + 827, + 475, + 842 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For the single-pattern attack scenario, the attackers are aware of the existence of randomization layers and also the parameters of the random resizing and random padding (i.e., from $2 9 9 \\times 2 9 9$ to $3 3 1 \\times 3 3 1$ ), but they do not know the specific randomization patterns utilized by the defense models (even the defense models themselves do not know these specific randomization patterns since they are randomly instantiated at test time). In order to generate adversarial examples, the attackers choose the target models as the original networks $^ +$ randomization layers but with only one specific pattern to compute the gradient. In this experiment, the specific pattern that we use is to place the original input $X _ { n }$ at the center of the padded image $X _ { n } ^ { \\prime \\prime }$ , i.e., no resizing is applied, and 16 zeros pixels are padded on the left, right, top and bottom on the input images, respectively. Table 3 shows the top-1 accuracy of both target models and defense models, and similar results to vanilla attack scenario are observed: (1) for single-step attacks, randomization layers are less effective on mitigating adversarial effects for a larger $\\epsilon$ , while the adversarially trained models are able to defend against such attacks; (2) for iterative attacks, they reach high attack rates on target models, while have nearly no impact on defense models. ", + "bbox": [ + 174, + 854, + 823, + 924 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/1850526665cf95de722fac8eb55948dd851b7674e5ed589cdafa394a060b212b.jpg", + "table_caption": [ + "Table 2: Top-1 classification accuracy under the vanilla attack scenario. We see that randomization layers effectively mitigate adversarial effects for all attacks and all networks. Particularly, combining randomization layers with ensemble adversarial training (ens-adv-Inception-ResNet-v2) performs very well on all attacks. " + ], + "table_footnote": [], + "table_body": "
ModelsInception-v3ResNet-v2-101Inception-ResNet-v2ens-adv-Inception-ResNet-v2
targetmodeldefensemodeltargetmodeldefensemodeltargetmodeldefensemodeltargetmodeldefensemodel
FGSM-233.2%65.1%26.3%71.8%65.3%81.0%84.4%95.7%
FGSM-531.1%54.5%20.4%54.3%61.7%74.1%87.4%94.5%
FGSM-1033.0%52.4%20.4%46.1%61.2%71.3%90.2%94.3%
DeepFool0%98.3%0%97.7%0%98.2%0.2%99.1%
C&W0%96.9%0%97.1%0.3%97.7%0.9%98.8%
", + "bbox": [ + 173, + 167, + 825, + 314 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/2d308f4aca054eed2b4b010547f1a317397847f183c5cd9f607fd3bdbab1d6af.jpg", + "table_caption": [ + "Table 3: Top-1 classification accuracy under the single-pattern attack scenario. We see that randomization layers effectively mitigate adversarial effects for all attacks and all networks. Particularly, combining randomization layers with ensemble adversarial training (ens-adv-Inception-ResNet- $\\cdot \\nu 2$ ) performs very well on all attacks. " + ], + "table_footnote": [], + "table_body": "
ModelsInception-v3ResNet-v2-101Inception-ResNet-v2ens-adv-Inception-ResNet-v2
targetmodeldefensemodeltargetmodeldefensemodeltargetmodeldefensemodeltargetmodeldefensemodel
FGSM-235.1%63.8%29.5%70.1%71.6%83.4%86.3%96.4%
FGSM-532.4%53.9%23.2%52.3%68.3%78.2%88.4%95.4%
FGSM-1034.7%51.8%22.4%43.8%66.8%75.6%90.7%95.2%
DeepFool1.1%98.2%1.7%97.8%0.6%98.4%1.0%99.2%
C&W1.1%97.4%1.7%97.0%0.8%97.9%1.6%99.1%
", + "bbox": [ + 173, + 397, + 826, + 542 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "", + "bbox": [ + 173, + 570, + 825, + 696 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5 ENSEMBLE-PATTERN ATTACK SCENARIO ", + "text_level": 1, + "bbox": [ + 176, + 717, + 500, + 731 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For the ensemble-pattern attack scenario, similar to single-pattern attack scenario, the attackers are aware of the randomization layers and the parameters of the random resizing and random padding (i.e., starting from $2 9 9 \\times 2 9 9$ to $3 3 1 \\times 3 3 1$ ), but they do not know the specific patterns utilized by the defense models at test time. The target models thus are constructed in a more representative way: let randomization layers choose an ensemble of predefined patterns, and the goal of the attackers is to let all chosen patterns fail on classification. In this experiment, the specific ensemble patterns that we choose are: (1) first resize the input image to five different scales $\\{ 2 9 9 , 3 0 7 , 3 1 5 , 3 2 3 , 3 3 1 \\}$ ; (2) then pad each resized image to five different patterns, where the resized image is placed at the top left, top right, bottom left, bottom right, and center of the padded image, respectively. Since there is only one padding pattern for the resized image with size 331, we can obtain $4 * 5 + 1 = 2 1$ patterns in total. Due to the large computation amounts introduced by the ensemble-pattern attack scenario, we randomly choose 500 images out of the entire test dataset for this experiment. The top-1 accuracy for the target model here is calculated by summing up the number of correctly classified patterns of each image over the entire pattern number of all images. For the results presented in Table 4, we can see that the adversarial examples generated under ensemble-pattern attack scenario are much stronger. For single-step attacks, the generated adversarial examples can let the performance of the defense model with an adversarially trained network drop around $8 \\%$ compared to the performance under vanilla attack and single-pattern attack scenarios, and drop much more on other defense models. For iterative attacks, we observe that the adversarial examples generated by C&W are stronger than those generated by DeepFool, e.g., the defense model with Inception- $\\nu 3$ has an accuracy of $8 1 . 3 \\%$ on DeepFool, while only has an accuracy of $6 2 . 9 \\%$ on C&W. We argue that this is due to the more advanced loss function (i.e., introduction of auxiliary variable for pixel value control) utilized by C&W than DeepFool. Additionally, the accuracy of defense model on C&W can be improved by utilizing more advanced architecture (e.g., ResNet-v2-101 has higher accuracy than Inception-v3) and applying ensemble adversarial training (e.g., ens-adv-Inception-ResNet- $\\nu 2$ has higher accuracy than Inception-ResNet-v2). For the best defense model that we have, ens-adv-Inception-ResNet- $\\nu 2$ $^ +$ randomization layers reaches the top-1 accuracy of $9 3 . 5 \\%$ on DeepFool and $8 6 . 1 \\%$ on C&W, respectively. ", + "bbox": [ + 173, + 743, + 825, + 924 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a5f5f049a290593d5c99320c3903b6b4ea7a50d09c509f730261fde2a47ca05a.jpg", + "table_caption": [ + "Table 4: Top-1 classification accuracy under the ensemble-pattern attack scenario. Similar to vanilla attack and single-pattern attack scenarios, we see that randomization layers increase the accuracy under all attacks and networks. This clearly demonstrates the effectiveness of the proposed randomization method on defending against adversarial examples, even under this very strong attack scenario. " + ], + "table_footnote": [], + "table_body": "
ModelsInception-v3ResNet-v2-101Inception-ResNet-v2ens-adv-Inception-ResNet-v2
targetmodeldefensemodeltargetmodeldefensemodeltargetmodeldefensemodeltargetmodeldefensemodel
FGSM-237.3%41.2%39.2%44.9%71.5%74.3%86.2%88.9%
FGSM-531.7%34.0%24.6%29.7%65.2%67.3%85.8%87.5%
FGSM-1030.4%32.8%18.6%21.7%62.9%64.5%86.6%87.9%
DeepFool0.6%81.3%0.9%80.5%0.9%69.4%1.6%93.5%
C&W0.6%62.9%1.0%74.3%1.6%68.3%5.8%86.1%
", + "bbox": [ + 173, + 180, + 825, + 325 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "", + "bbox": [ + 173, + 358, + 825, + 566 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6 DIAGNOSTIC EXPERIMENT ", + "text_level": 1, + "bbox": [ + 176, + 592, + 400, + 606 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Due to the large amount of possible patterns introduced by randomization layers, it is hard to analyze the effectiveness of random resizing and random padding precisely. In this section, we limit the freedom of randomization to be a small number (i.e., 4 in random padding and 1 in random resizing) and analyze the effectiveness of these two operations separately. The same 500 images in section 4.5 are used in this experiment. In addition, the input images for target models and defense models are resized to the shape $3 3 0 \\times 3 3 0 \\times 3$ beforehand. ", + "bbox": [ + 174, + 621, + 825, + 705 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6.1 ONE PIXEL PADDING ", + "text_level": 1, + "bbox": [ + 176, + 729, + 375, + 744 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "For the random padding, there are only 4 patterns when padding the input images from $3 3 0 \\times 3 3 0 \\times 3$ to $3 3 1 \\times 3 3 1 \\times 3$ . In order to construct a stronger attack, we follow the experiment setup in section 4.5 where 3 chosen patterns are ensembled. Specifically, the target model takes an ensemble of patterns where the original images are at the top left, top right and bottom left (3 patterns) of the padded images, and the defense model takes the last pattern where the original images are at the bottom right of the padded images. Note that, since there is no randomization in the defense model, we only run the defense model once. Table 5 summaries the results, and we can see that: (1) adversarial examples generated by single-step attacks have strong transferability, but still cannot attack the defense model with an adversarially trained model successfully (i.e., the defense model with ensadv-Inception-ResNet- $\\nu 2$ ); (2) adversarial examples generated by iterative attacks are much less transferable between different padding patterns even when only 4 different patterns exist. The results demonstrate that creating different padding patterns can effectively mitigate adversarial effects. ", + "bbox": [ + 174, + 757, + 825, + 924 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/ddbf82dab98d11b4ec804e9536e64fc830a6f8fc88e592a97f1d5f2ea68f8304.jpg", + "table_caption": [ + "Table 5: Top-1 classification accuracy under one pixel padding scenario. This table shows that creating different padding patterns (even 1-pixel padding) can effectively mitigate adversarial effects. " + ], + "table_footnote": [], + "table_body": "
ModelsInception-v3ResNet-v2-101Inception-ResNet-v2ens-adv-Inception-ResNet-v2
targetmodeldefensemodeltargetmodeldefensemodeltargetmodeldefensemodeltargetmodeldefensemodel
FGSM-236.4%39.6%29.8%34.4%71.3%74.0%88.2%94.8%
FGSM-533.5%36.2%22.2%26.2%68.4%71.0%92.1%94.4%
FGSM-1034.5%38.8%21.3%23.6%67.4%70.4%93.7%94.0%
DeepFool0.9%97.2%0.9%95.2%0.9%87.6%1.5%99.2%
C&W0.8%70.2%0.9%76.8%1.0%79.4%2.4%98.2%
", + "bbox": [ + 173, + 141, + 825, + 286 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/db4fc58373e021e6bbc56ab326d0e43d13af8c9ff40303a58ff718a293bda7bd.jpg", + "table_caption": [ + "Table 6: Top-1 classification accuracy under one pixel resizing scenario. This table shows that resizing image to a different scale (even 1-pixel scale) can effectively mitigate adversarial effects. " + ], + "table_footnote": [], + "table_body": "
ModelsInception-v3ResNet-v2-101Inception-ResNet-v2ens-adv-Inception-ResNet-v2
targetmodeldefensemodeltargetmodeldefensemodeltargetmodeldefensemodeltargetmodeldefensemodel
FGSM-230.8%56.2%31.6%44.6%66.2%75.0%87.6%97.2%
FGSM-531.2%48.8%25.6%35.8%61.4%70.2%91.2%96.6%
FGSM-1036.4%51.0%23.8%32.6%62.8%68.2%94.8%95.2%
DeepFool2.6%99.4%1.0%98.6%1.2%97.4%1.2%99.4%
C&W2.6%97.8%1.0%94.8%2.0%94.8%1.8%99.6%
", + "bbox": [ + 173, + 342, + 825, + 487 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "4.6.2 ONE-PIXEL RESIZING ", + "text_level": 1, + "bbox": [ + 174, + 513, + 382, + 529 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "For the random resizing, there is only 1 pattern that exists when the input images are resized from $3 3 0 \\times 3 3 0 \\times 3$ to $3 3 1 \\times 3 3 1 \\times 3$ . The results in Table 6 indicate that resizing the images by only 1 pixel can effectively destroy the transferability of adversarial examples by both single-step and iterative attacks. ", + "bbox": [ + 173, + 539, + 825, + 594 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5 NIPS 2017 ADVERSARIAL EXAMPLES DEFENSE CHALLENGE ", + "text_level": 1, + "bbox": [ + 174, + 616, + 714, + 633 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We submitted our model to the NIPS 2017 adversarial examples defense challenge3 for a more comprehensive performance evaluation. The test dataset contains 5000 images which are all of the size $2 9 9 \\times 2 9 9 \\times 3$ , and their corresponding labels are the same as the ImageNet 1000-class labels. Each defense method are run on all 5000 adversarial images generated against all adversarial attacks. For each correctly classified image, the defense method gets one point. The normalized score for each defense method is computed using the following formula: ", + "bbox": [ + 173, + 648, + 825, + 734 + ], + "page_idx": 8 + }, + { + "type": "equation", + "img_path": "images/bb66dddbf90ac17217662fd9866c1a815b58375accf48ddf4f55b248371231ed.jpg", + "text": "$$\n\\mathrm { s c o r e } = \\frac { 1 } { M } \\sum _ { \\mathrm { a t t a c k } \\in A } \\sum _ { n = 1 } ^ { 5 0 0 0 } \\left[ \\mathrm { d e f e n s e } ( \\mathrm { a t t a c k } ( X _ { n } ) ) = y _ { n } ^ { \\mathrm { t r u e } } \\right] ,\n$$", + "text_format": "latex", + "bbox": [ + 312, + 742, + 681, + 786 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "where $A$ is the set of all attacks, $M$ is the total number of generated adversarial examples by all attacks, and the function $[ \\cdot ]$ is the indicator function which equals to 1 when the prediction is true. ", + "bbox": [ + 174, + 792, + 825, + 823 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5.1 CHALLENGE RESULTS ", + "text_level": 1, + "bbox": [ + 174, + 840, + 370, + 856 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "The best defense model in our experiments, i.e., randomization layers $^ +$ ens-adv-Inception-Resnet$\\nu 2$ , was submitted to the challenge. To increase the classification accuracy, we (1) changed the resizing range from [299, 331) to [310, 331); (2) averaged the prediction results over 30 randomization patterns for each image; (3) flipped the input image with probability 0.5 for each randomization pattern. ", + "bbox": [ + 176, + 867, + 823, + 897 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 103, + 821, + 146 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "By evaluating our model against 156 different attacks, it reaches a normalized score of 0.924 (ranked No.2 among 107 defense models), which is far better than using ensemble adversarial training (Tramer et al., 2017) alone with a normalized score of \\` 0.773 (ranked No.56). This result further demonstrates that the proposed randomization method effectively make deep networks much more robust to adversarial attacks. ", + "bbox": [ + 174, + 152, + 825, + 222 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "6 CONCLUSION ", + "text_level": 1, + "bbox": [ + 174, + 243, + 318, + 260 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "In this paper, we propose a randomization-based mechanism to mitigate adversarial effects. We conduct comprehensive experiments to validate the effectiveness of our defense method, using different network structures, against different attack methods, and under different attack scenarios. The experimental results show that adversarial examples rarely transfer between different randomization patterns, especially for iterative attacks. In addition, the proposed randomization layers are compatible to different network structures and adversarial defense methods, which can serve as a basic module for defense against adversarial examples. By adding the proposed randomization layers to an adversarially trained model (Tramer et al., 2017), it achieves a normalized score of \\` 0.924 (ranked No.2 among 107 defense models) in the NIPS 2017 adversarial examples defense challenge, which is far better than using adversarial training alone with a normalized score of 0.773 (ranked No.56). The code is public available at https://github.com/cihangxie/NIPS2017_ adv_challenge_defense. ", + "bbox": [ + 174, + 275, + 825, + 441 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "ACKNOWLEDGEMENTS ", + "text_level": 1, + "bbox": [ + 176, + 464, + 367, + 479 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "This work is supported by a gift grant from SNAP Research, ONR–N00014-15-1-2356 and NSF Visual Cortex on Silicon CCF-1317560. ", + "bbox": [ + 174, + 494, + 821, + 522 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "REFERENCES ", + "text_level": 1, + "bbox": [ + 176, + 545, + 285, + 560 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Battista Biggio and Pavel Laskov. Poisoning attacks against support vector machines. In International Conference on Machine Learning, 2012. ", + "bbox": [ + 173, + 569, + 821, + 598 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Xiaoyu Cao and Neil Zhenqiang Gong. Mitigating evasion attacks to deep neural networks via region-based classification. 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", + "bbox": [ + 174, + 881, + 825, + 922 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Cihang Xie, Jianyu Wang, Zhishuai Zhang, Yuyin Zhou, Lingxi Xie, and Alan Yuille. Adversarial Examples for Semantic Segmentation and Object Detection. In International Conference on Computer Vision. IEEE, 2017. ", + "bbox": [ + 176, + 103, + 821, + 145 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "Zhishuai Zhang, Siyuan Qiao, Cihang Xie, Wei Shen, Bo Wang, and Alan L Yuille. Single-shot object detection with enriched semantics. arXiv preprint arXiv:1712.00433, 2017. ", + "bbox": [ + 174, + 155, + 823, + 184 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "APPENDIX A OTHER RANDOMIZATION METHODS ", + "text_level": 1, + "bbox": [ + 174, + 102, + 604, + 118 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "Besides random resizing and random padding, we further evaluate the effectiveness of four other randomization methods against adversarial examples. All these four methods are used as dataaugmentation during the standard network training. ", + "bbox": [ + 176, + 132, + 825, + 175 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "• Random Brightness: a brightness factor $\\delta$ is randomly picked in the interval $[ - \\delta _ { \\mathrm { m a x } } , \\delta _ { \\mathrm { m a x } } ]$ to adjust the brightness of the normalized image $\\hat { X _ { n } }$ . We choose $\\begin{array} { r } { \\delta _ { \\mathrm { m a x } } = \\frac { 3 2 } { 2 5 5 } } \\end{array}$ . \n• Random Saturation: a saturation factor $\\alpha$ is randomly picked in the interval $[ \\alpha _ { l o w e r } , \\alpha _ { u p p e r } ]$ to adjust the saturation of the normalized image $\\hat { X _ { n } }$ . We choose $\\alpha _ { l o w e r } =$ 0.5 and $\\alpha _ { u p p e r } = 1 . 5$ . \n• Random Hue: a hue factor $\\theta$ is randomly picked in the interval $[ - \\theta _ { \\mathrm { m a x } } , \\theta _ { \\mathrm { m a x } } ]$ to adjust the hue of the normalized image ${ \\hat { X _ { n } } }$ . We choose $\\theta _ { \\mathrm { m a x } } = 0 . 2$ . \n• Random Contrast: a contrast factor $\\beta$ is randomly picked in the interval $[ \\beta _ { l o w e r } , \\beta _ { u p p e r } ]$ to adjust the contrast of the normalized image $\\hat { X _ { n } }$ . We choose $\\beta _ { l o w e r } = 0 . 5$ and $\\beta _ { u p p e r } = 1 . 5$ . ", + "bbox": [ + 215, + 185, + 825, + 335 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "Note that, (1) the parameters chosen above are the same as the ones used during network training process4; (2) the pixel value of the normalized image $\\hat { X _ { n } }$ are all within the interval $[ 0 , 1 ]$ , and we also use this range to clip the pixel value of the image after pre-processing. ", + "bbox": [ + 176, + 345, + 825, + 390 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "Following the experiment setup in section 4, we first evaluate the effectiveness of each of these randomization methods on the 5000 clean images. The results are shown in the Table 7. We can see that these methods hardly hurt the performance on clean images. We further combine the proposed randomization layers, i.e., random resizing layer and random padding layer, with each of these randomization methods (denoted as $^ { 6 6 } + + ^ { 7 }$ ). We see that the combined randomization modules only cause very little accuracy drop on clean images. ", + "bbox": [ + 174, + 396, + 825, + 479 + ], + "page_idx": 12 + }, + { + "type": "table", + "img_path": "images/ee1124c3f76bde054f599243676b17e54b17d22111dd0bac1b90566e8bc3c191.jpg", + "table_caption": [ + "Table 7: Top-1 classification accuracy on clean images. We see that these four randomization methods hardly hurt the performance on clean images. We use $^ { 6 6 } { + + ^ { 9 9 } }$ to denote the addition of the proposed randomization layers, i.e., random resizing and random padding, and the results indicate that combined models still performs pretty good on clean images. " + ], + "table_footnote": [], + "table_body": "
ModelsInception-v3ResNet-v2-101Inception-ResNet-v2ens-adv-Inception-ResNet-v2
random brightness99.6%99.7%99.8%99.8%
random brightness ++98.6%98.1%99.1%99.2%
random saturation99.6%99.7%99.9%99.9%
random saturation ++98.6%98.3%99.3%99.3%
random hue99.4%99.6%99.7%99.4%
random hue ++98.6%98.3%99.2%99.1%
random contrast99.5%99.6%99.7%99.6%
random contrast ++98.6%98.2%99.3%99.1%
", + "bbox": [ + 176, + 559, + 820, + 720 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "We then evaluate the effectiveness of these randomization methods against the adversarial examples generated under the vanilla attack scenario. The results are shown in the Tables 8 - 11. Compared to the results in Table 2, all these four methods are much less effective than the proposed randomization layers. By combining the proposed randomization layers with each of these four randomization methods (denoted as $^ { 6 6 } { + } { + } ^ { , 9 } )$ , the performance can be slightly improved than using the proposed randomization layers alone. ", + "bbox": [ + 173, + 741, + 825, + 824 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "Since each of these four randomization methods alone are not as effective as our proposed randomization methods against adversarial examples generated under the vanilla attack scenario, we do not further investigate their effectiveness under single-pattern attack and ensemble-pattern attack scenarios. However, combining these randomization methods with our proposed randomization layers together provides a way to build a slightly stronger defense mechanism. ", + "bbox": [ + 174, + 830, + 825, + 901 + ], + "page_idx": 12 + }, + { + "type": "table", + "img_path": "images/241df516881557f904257b857685708c093f5a5bcd788734712e22bdd8aa507d.jpg", + "table_caption": [ + "Table 8: Top-1 classification accuracy by using random brightness under the vanilla attack scenario. Compared to the results in Table 2, random brightness is much less effective than the proposed randomization layers. By combing random brightness and the proposed randomization layers (denoted as random brightness $^ { + + }$ ), it reaches slightly better performance than using the proposed randomization layers alone. " + ], + "table_footnote": [], + "table_body": "
ModelsInception-v3ResNet-v2-101Inception-ResNet-v2ens-adv-Inception-ResNet-v2
randombright-nessrandombright-ness++randombright-nessrandombright-ness++randombright-nessrandombright-ness++randombright-nessrandombright-ness++
FGSM-234.9%67.0%28.5%73.5%66.4%81.3%85.0%95.8%
FGSM-531.9%55.5%21.6%55.7%62.4%74.7%87.6%95.0%
FGSM-1033.2%52.9%20.9%47.2%61.8%71.5%90.4%94.5%
DeepFool79.4%98.1%82.3%97.5%62.8%98.3%79.0%99.1%
C&W34.5%96.9%47.7%97.2%51.3%98.0%42.3%98.6%
", + "bbox": [ + 173, + 200, + 825, + 361 + ], + "page_idx": 13 + }, + { + "type": "table", + "img_path": "images/a77bd7ea9d65edad3499f047bba7c530008b294dd86121fa2def44e3afd05811.jpg", + "table_caption": [ + "Table 9: Top-1 classification accuracy by using random saturation under the vanilla attack scenario. Compared to the results in Table 2, random saturation is much less effective than the proposed randomization layers. By combing random saturation and the proposed randomization layers (denoted as random saturation $^ { + + }$ ), it reaches slightly better performance than using the proposed randomization layers alone. " + ], + "table_footnote": [], + "table_body": "
ModelsInception-v3ResNet-v2-101Inception-ResNet-v2ens-adv-Inception-ResNet-v2
randomsatura-tionrandomsatura-tion++randomrandomrandomrandom satura-tion++randomsatura-tionrandom satura-tion++
satura-tionsatura-tion++satura-tion
FGSM-234.2%66.5%27.9%73.6%66.3%81.5%85.2%95.7%
FGSM-531.8%55.2%21.1%55.7%62.1%74.6%87.0%95.0%
FGSM-1033.5%52.2%20.7%46.5%61.7%71.4%90.1%93.9%
DeepFool82.6%98.1%79.6%97.6%64.7%98.2%78.5%99.0%
C&W39.2%97.2%47.5%96.9%51.7%97.7%50.9%99.1%
", + "bbox": [ + 173, + 486, + 825, + 645 + ], + "page_idx": 13 + }, + { + "type": "table", + "img_path": "images/159990e9477e81f3b8b7168e7a5a656d363edfa0315ec3fe5ab3ce9c887e700d.jpg", + "table_caption": [ + "Table 10: Top-1 classification accuracy by using random hue under the vanilla attack scenario. Compared to the results in Table 2, random hue is much less effective than the proposed randomization layers. By combing random hue and the proposed randomization layers (denoted as random $\\mathbf { h u e + + }$ ), it reaches slightly better performance than using the proposed randomization layers alone. " + ], + "table_footnote": [], + "table_body": "
ModelsInception-v3ResNet-v2-101Inception-ResNet-v2ens-adv-Inception-ResNet-v2
randomhuerandomhue++randomhuerandomhue++randomhuerandomhue++randomhuerandomhue++
FGSM-238.1%69.0%32.0%74.9%68.6%83.0%87.4%95.8%
FGSM-533.9%57.2%23.0%57.6%64.0%76.1%86.7%93.9%
FGSM-1036.4%54.2%22.1%48.4%63.0%72.5%88.0%91.3%
DeepFool95.0%97.9%91.2%97.6%86.5%98.4%96.8%99.1%
C&W72.1%97.3%74.0%97.0%77.4%98.2%81.1%98.8%
", + "bbox": [ + 173, + 757, + 825, + 904 + ], + "page_idx": 13 + }, + { + "type": "table", + "img_path": "images/6f3b024c88dd017504069a106ef4000d10bd683f52dadbc7e9bf4c4674b24fb9.jpg", + "table_caption": [ + "Table 11: Top-1 classification accuracy by using random contrast under the vanilla attack scenario. Compared to the results in Table 2, random contrast is much less effective than the proposed randomization layers. By combing random contrast and the proposed randomization layers (denoted as random contrast $^ { + + }$ ), it reaches slightly better performance than using the proposed randomization layers alone. " + ], + "table_footnote": [], + "table_body": "
ModelsInception-v3ResNet-v2-101Inception-ResNet-v2ens-adv-Inception-ResNet-v2
randomcon-trastrandomcon-trast++randomcon-trastrandomcon-trast++randomcon-trastrandomcon-trast++randomcon-trastrandomcon-trast++
FGSM-237.0%68.0%29.4%74.1%67.2%82.5%85.9%96.0%
FGSM-532.7%56.3%22.7%57.0%63.1%74.9%88.1%94.9%
FGSM-1034.4%53.5%21.2%47.0%62.1%72.0%90.6%94.3%
DeepFool90.4%98.1%87.5%97.5%73.8%98.1%90.8%99.0%
C&W56.8%97.0%57.1%96.7%63.7%97.9%67.6%98.8%
", + "bbox": [ + 173, + 181, + 826, + 342 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "APPENDIX B RANDOMIZATION LAYERS WITH SMALLER SIZE ", + "text_level": 1, + "bbox": [ + 176, + 364, + 700, + 381 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "Instead of resizing the input image to a larger size, we here resize the input image to a smaller size, i.e., the resizing parameter is randomly sampled from the range [267, 299). The random padding layer then pads the resized image to the shape of $2 9 9 \\times 2 9 9 \\times 3$ in a random manner. Note that, the random resizing layer and the random padding layer here have the same freedom as the ones used in the paper, i.e., they create the same number, 12528, of different patterns for a single image. We evaluate the effectiveness of this parameter setting on both the 5000 clean images and the adversarial examples generated under the vanilla attack scenario. The results are shown in the Table 12. We see that randomization layers still work well with smaller size images, but is slightly worse than using larger size images as in the paper. This is because resizing to a smaller size loses certain information of the original image. ", + "bbox": [ + 173, + 395, + 825, + 535 + ], + "page_idx": 14 + }, + { + "type": "table", + "img_path": "images/b63d8a7250398b8bd06b39e706ab64735a9a5b36a087184c416f91f69b0751b1.jpg", + "table_caption": [ + "Table 12: Top-1 classification accuracy on the clean images and the adversarial examples generated under the vanilla attack scenario. Compared to the results in Tables 1 and 2, randomization parameters applied here (i.e., resize between [267, 299), and pad to $2 9 9 \\times 2 9 9 \\times 3 )$ ) is slightly worse than the randomization parameters applied in the paper (i.e., resize between [299, 331), and pad to $3 3 1 \\times 3 3 1 \\times 3 )$ . " + ], + "table_footnote": [], + "table_body": "
ModelsInception-v3ResNet-v2-101Inception-ResNet-v2ens-adv-Inception-ResNet-v2
clean images98.2%97.5%99.1%98.7%
FGSM-263.1%65.0%79.9%95.0%
FGSM-553.4%48.3%73.3%94.0%
FGSM-1050.8%40.5%70.6%93.4%
DeepFool97.2%96.5%96.0%98.6%
C&W95.2%95.2%97.2%97.8%
", + "bbox": [ + 176, + 628, + 821, + 761 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "APPENDIX C RANDOMIZATION LAYERS WITH MULTIPLE ITERATIONS ", + "text_level": 1, + "bbox": [ + 173, + 786, + 769, + 804 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "In this section, we show the relationship between the top-1 accuracy of the defense model and the iteration number performed on each image. Specifically, we choose ens-adv-Inception-ResNet- $\\nu 2 +$ randomization layers as the defense model for the experiment. The same trend can be observed for other defense models. ", + "bbox": [ + 174, + 818, + 825, + 875 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "For the defense model, the iteration number is chosen to be $\\{ 1 , 5 , 1 0 , 2 0 , 3 0 \\}$ , and it is evaluated on the 5000 clean test images and the adversarial examples generated under all three attack scenarios. The results are shown in the Figures 3 - 5. We can observe that (1) increasing the number of iteration can slightly improve the top-1 classification accuracy of the defense model on clean images and adversarial examples generated under both the vanilla attack and the single-pattern attack scenarios; (2) increasing the number of iteration has nearly no improvement for the top-1 classification accuracy of the defense model on adversarial examples generated by single-step attacks under the ensemble-pattern attack scenario; (3) increasing the number of iteration can improve the top-1 classification accuracy of the defense model on adversarial examples generated by iterative attacks under the ensemble-pattern attack scenario. ", + "bbox": [ + 174, + 881, + 825, + 924 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "", + "bbox": [ + 173, + 103, + 825, + 202 + ], + "page_idx": 15 + }, + { + "type": "image", + "img_path": "images/a25aa63356ef141cc900583f46c838547d3cb72eeae8c3fce9b665da139db3ec.jpg", + "image_caption": [ + "Figure 3: Top-1 classification accuracy on the clean images and the adversarial examples generated under the vanilla attack scenrio. " + ], + "image_footnote": [], + "bbox": [ + 184, + 224, + 364, + 378 + ], + "page_idx": 15 + }, + { + "type": "image", + "img_path": "images/0cf83e4d60ebaeaa48670a3eae350647157c26303fc23d006fea2afbff49f186.jpg", + "image_caption": [ + "Figure 4: Top-1 classification accuracy on the adversarial examples generated under the single-pattern attack scenrio. " + ], + "image_footnote": [], + "bbox": [ + 405, + 224, + 588, + 378 + ], + "page_idx": 15 + }, + { + "type": "image", + "img_path": "images/49c765887d9ca814549732caf7e88c202b46e49cbcf0f3ce57891fd62a33e450.jpg", + "image_caption": [ + "Figure 5: Top-1 classification accuracy on the adversarial examples generated under the ensemble-pattern attack scenrio. " + ], + "image_footnote": [], + "bbox": [ + 629, + 224, + 810, + 378 + ], + "page_idx": 15 + } +] \ No newline at end of file diff --git a/parse/train/Sk9yuql0Z/Sk9yuql0Z_model.json b/parse/train/Sk9yuql0Z/Sk9yuql0Z_model.json new file mode 100644 index 0000000000000000000000000000000000000000..d38495a69fd22db5c8ac4b17ba244e699d35cbb1 --- /dev/null +++ b/parse/train/Sk9yuql0Z/Sk9yuql0Z_model.json @@ -0,0 +1,24248 @@ +[ + { + "layout_dets": [ + { + "category_id": 1, + "poly": [ + 398, + 1020, + 1301, + 1020, + 1301, + 1540, + 398, + 1540 + ], + "score": 0.984 + }, + { + "category_id": 1, + "poly": [ + 297, + 1668, + 1404, + 1668, + 1404, + 2033, + 297, + 2033 + ], + "score": 0.983 + }, + { + "category_id": 1, + "poly": [ + 314, + 577, + 625, + 577, + 625, + 699, + 314, + 699 + ], + "score": 0.96 + }, + { + "category_id": 0, + "poly": [ + 299, + 220, + 1396, + 220, + 1396, + 322, + 299, + 322 + ], + "score": 0.955 + }, + { + "category_id": 0, + "poly": [ + 302, + 1598, + 573, + 1598, + 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MULTI-AGENT COMPETITION + +Trapit Bansal∗ UMass Amherst + +Jakub Pachocki OpenAI + +Szymon Sidor OpenAI + +Ilya Sutskever OpenAI + +Igor Mordatch OpenAI + +# ABSTRACT + +Reinforcement learning algorithms can train agents that solve problems in complex, interesting environments. Normally, the complexity of the trained agent is closely related to the complexity of the environment. This suggests that a highly capable agent requires a complex environment for training. In this paper, we point out that a competitive multi-agent environment trained with self-play can produce behaviors that are far more complex than the environment itself. We also point out that such environments come with a natural curriculum, because for any skill level, an environment full of agents of this level will have the right level of difficulty. + +This work introduces several competitive multi-agent environments where agents compete in a 3D world with simulated physics. The trained agents learn a wide variety of complex and interesting skills, even though the environment themselves are relatively simple. The skills include behaviors such as running, blocking, ducking, tackling, fooling opponents, kicking, and defending using both arms and legs. A highlight of the learned behaviors can be found here: https://goo.gl/eR7fbX. + +# 1 INTRODUCTION + +Reinforcement Learning (RL) is exciting because good reinforcement learning algorithms exist (Mnih et al., 2015; Silver et al., 2016; Schulman et al., 2015a; Mnih et al., 2016; Schulman et al., 2015b; Lillicrap et al., 2015; Schulman et al., 2017), allowing us to train agents that accomplish a great variety of interesting tasks. We can train an agent to play Atari games from pixels (Mnih et al., 2015) or get humanoids to walk (Schulman et al., 2017). RL is exciting partly because it is easy to envision an RL algorithm producing a broadly competent agent when trained on an appropriate curriculum of environments. + +In general, training an agent to perform a highly complex task requires a highly complex environment, and these can be difficult to create. However, there exists a class of environments where the behavior produced by the agents can be far more complex than the environments; this is the class of the competitive multi-agent environments trained with self-play. Such environments have two very attractive properties: (1) Even very simple competitive multi-agent environments can produce extremely complex behaviors. For example, the game of Go has very simple rules, but the strategies needed to win are extremely complex. This is because the complexity of these environments is produced by the competing agents that act in it. Thus, as the other agents become more competent, the environment effectively becomes more complex. (2) When trained with self-play, the competitive multi-agent environment provides the agents with a perfect curriculum. This happens because no matter how weak or strong an agent is, an environment populated with other agents of comparable strength provides the right challenge to the agent, facilitating maximally rapid learning and avoiding getting stuck. + +Self-play in competitive multi-agent environments is not a new idea – it has already been explored in TD-gammon (Tesauro, 1995) and refined in AlphaGo (Silver et al., 2016) and Dota 2 (OpenAI). In both cases, the resulting behavior was far more complex than the environment itself, and the self-play approach provided the agents with a perfectly tuned curriculum for each task. In this paper, we investigate whether the idea of competitive multi-agent environments can yield fruit in other domains: specifically, in the domain of continuous control, where balance, dexterity, and manipulation are the key skills. + +In more detail, we introduce several multi-agent tasks with competing goals in a 3D world with simulated physics, using the MuJoCo framework (Todorov et al., 2012), where the agents would need to learn highly developed motor skills in order to succeed in the competitive environment. We train the agents using a distributed implementation of a recent policy gradient algorithm, Proximal Policy Optimization (Schulman et al., 2017). By adding a simple exploration curriculum to aid exploration in the environment we find that agents learn a high level of dexterity in order to achieve their goals, in particular we find numerous emergent skills for which it may be difficult to engineer a reward. Specifically, the agents learned a wide variety of skills and behaviors that include running, blocking, ducking, tackling, fooling opponents, kicking, and defending using arms and legs. Highlight of the learned behaviors on the various tasks can be found here: https://goo.gl/eR7fbX + +# 2 PRELIMINARIES + +In this section, we review some background on policy gradient methods, Proximal Policy Optimization and related work in the multi-agent reinforcement learning domain. + +Notation: We consider multi-agent Markov games (Littman, 1994). A Markov game for $N$ agents is a partially observable Markov decision process (MDP) defined by: a set of states $s$ describing the state of the world and the possible joint configuration of all the agents, a set of observations $\mathcal { O } ^ { 1 } , \ldots , \mathcal { O } ^ { N }$ of each agent, a set of actions of each agent $\mathcal { A } ^ { 1 } , \ldots , \mathcal { A } ^ { \tilde { N } }$ , a transition function $\tau :$ $\mathcal { S } \times \mathcal { A } ^ { 1 } \cdot \cdot \cdot \mathcal { A } ^ { N } \to \mathcal { S }$ determining distribution over next states, and a reward for each agent $i$ which is a function of the state and the agent’s action $r ^ { i } : \mathcal { S } \times \mathcal { A } ^ { i } \to \mathbb { R }$ . Agents choose their actions according to a stochastic policy $\pi _ { \theta ^ { i } } : \mathcal { O } ^ { i } \times \mathcal { A } ^ { i } [ 0 , 1 ]$ , where $\theta ^ { i }$ are the parameters of the policy. For continuous control problems considered here, $\pi _ { \theta }$ is Gaussian where the mean and variance are deep neural networks with parameter $\theta$ . Each agent $i$ aims to maximize its own total expected return $\begin{array} { r } { R ^ { i } = \sum _ { t = 0 } ^ { T } \gamma ^ { t } r _ { t } ^ { i } } \end{array}$ , where $\gamma$ is a discount factor and $T$ is the time horizon + +Policy Gradient: Policy gradient methods work by directly computing an estimate of the gradient of policy parameters in order to maximize the expected return using stochastic gradient descent. These methods are behind much of the recent success in using deep neural networks for control (Schulman et al., 2015b; Heess et al., 2017; Lillicrap et al., 2015; Silver et al., 2016). Such methods are also attractive because they don’t require an explicit model of the world. There are several different expressions for the policy gradient estimator which have the form $g : = \mathbb { E } \left[ A _ { t } \nabla _ { \theta } \log \pi _ { \theta } \right]$ . Different choices of $A _ { t }$ lead to different algorithms, for example taking the sample return of a trajectory $\boldsymbol { A } _ { t } = \sum _ { t } \boldsymbol { r } _ { t }$ leads to the REINFORCE algorithm (Williams, 1992). However, such algorithms suffer from high variance in the gradient estimates and it’s typical to use a baseline, such as a value function baseline, to ameliorate the high variance. Generalized advantage estimation (Schulman et al., 2015b) takes this approach of using a learned value function to reduce variance at the cost of some bias and using an exponentially weighted estimator of the advantage function. + +Proximal Policy Optimization (PPO): Achieving good results with policy gradient algorithms requires carefully tuning the step-size (Schulman et al., 2015a). Moreover, most policy gradient methods perform one gradient update per sampled trajectory and have high sample complexity. Recently, Schulman et al. (2017) proposed the PPO algorithm which addresses both these problems. This uses a surrogate objective which is maximized while penalizing large changes to the policy. Let $\begin{array} { r } { l _ { t } ( \theta ) ~ = ~ \frac { \pi _ { \theta } ^ { - } \left( a _ { t } | s _ { t } \right) ^ { - } } { \pi _ { \theta _ { o l d } } \left( a _ { t } | s _ { t } \right) } } \end{array}$ denote the likelihood ratio. Then PPO optimizes the objective: $L = \mathbb { E } \left[ \operatorname* { m i n } ( l _ { t } ( \theta ) \hat { A } _ { t } , \operatorname { c l i p } ( l _ { t } ( \theta ) , 1 - \epsilon , 1 + \epsilon ) \hat { A } _ { t } ) \right]$ , where $\hat { A } _ { t }$ is the generalized advantage estimate and $\mathrm { c l i p } ( l _ { t } ( \theta ) , 1 - \epsilon , 1 + \epsilon )$ clips $l _ { t } ( \theta )$ in the interval $[ 1 - \epsilon , 1 + \epsilon ]$ . The algorithm alternates between sampling multiple trajectories from the policy and performing several epochs of SGD on the sampled dataset to optimize this surrogate objective. Since the state value function is also simultaneously approximated, the error for the value function approximation is also added to the surrogate objective to compute the complete objective function (Schulman et al., 2017). + +Related Work: Tan (1993) explored the multi-agent setting with independently learning agents using Q-learning, in particular exploring advantages of cooperative agents over independent agents in a 2D grid world. This was further explored by Matignon et al. (2012) again in the cooperative setting. A lot of the work on multi-agent RL is focused on cooperative settings, see Busoniu et al. (2008) for a review of multi-agent RL and Panait & Luke (2005) for a review focused on cooperative settings. Stanley & Miikkulainen (2004) trained agents in a competitive 2D world, using evolutionary strategies to evolve both weights and structure of policies with competition as a fitness measure. Tampuu et al. (2017) studied the application of deep Q-learning to train Pong agents with competitive and collaborative rewarding schemes. He et al. (2016) used deep Q-learning to model competitive games where only one agent is learning and the Q network implicitly models the opponent. Silver et al. (2016) used self-play with deep reinforcement learning techniques to master the game of Go. Sukhbaatar et al. (2017) introduced a self-play method for generating an automatic training curriculum in single-agent environments. From a game-theoretic perspective, Heinrich & Silver (2016) studied fictitious self-play for achieving approximate Nash equilibrium in zero-sum games like Poker. Recently, Foerster et al. (2017a) introduced an algorithm which explicitly accounts for the fact that the opponent is also learning and showed that it can achieve cooperation in iterated prisoner’s dilemma, however the algorithm requires access to the opponent’s parameters. Recently, Lowe et al. (2017) and Foerster et al. (2017b) proposed methods for centralized learning in multi-agent domains, where the idea is to use an actor-critic method with a central critic which can observe the joint state and actions of all agents in order to reduce variance, evaluating on 2D games and StarCraft. In this work, we do not rely on centralized training and address the variance problem by using very large batchsize through a distributed implementation of the PPO algorithm. Moreover, we study fully competitive settings in a 3D world with simulated physics whereas prior applications have focused on toy 2D worlds or game-theoretic problems. Recent work on learning dexterous locomotion skills in 3D environments by adding complexity in the agent’s environment (Heess et al., 2017) is also related. However, whereas Heess et al. (2017) learn complex behaviours by engineering complexity into the environment design and by engineering dense reward functions for these environments, the resultant complexity in our work is due to the presence of other learning agents in a simple environment. Our work is also related to early work in the graphics community (Sims, 1994) on evolving creature morphology in varying environments using genetic algorithm and work in animation (Wampler et al., 2010) for adversarial games. The competitive multi-agent learning framework is also related to generative adversarial networks (Goodfellow et al., 2014) and work on learning robust grasping policies through an adversary (Pinto et al., 2017). + +# 3 COMPETITIVE ENVIRONMENTS + +![](images/0bc53a965370e58dc6fba3823a2d9d3f433c6c327fbd86c872932af6f33f371e.jpg) +Figure 1: Illustrations of competitive environments we consider in our work: Run to Goal, You Shall Not Pass, Sumo, and Kick and Defend. + +We introduce four competitive environments and experiment with two types of agents. In this paper we focus on two agent worlds, that is 1-vs-1 games, though these environments can be extended to include multiple agents for a mixed competitive and co-operative setup. We will now describe the four environments and the competitive rewards in each environment. Figure 1 shows a rendering of the environments. We consider two three-dimensional agent bodies: ant and humanoid. The ant is a quadrupedal body with $1 2 \mathrm { D o F }$ and 8 actuated joints. Humanoid has 23 DoF and 17 actuated joints. + +Run to Goal: The agents start by facing each other in a 3D world and they each have goals on the opposite side of the word (see Fig.1a). The agent that reaches its goal first wins. Reaching the goal before the opponent gives a reward of $+ 1 0 0 0$ to the agent and -1000 to the opponent. If no agent reaches its goal then they both get -1000. + +You Shall Not Pass: This is the same world as the previous task, but one agent (the blocker) now has the objective of blocking the other agent from reaching it’s goal while not falling down. If the blocker is successful in preventing the opponent from reaching the goal and is standing at the end of episode then it gets $+ 1 0 0 0$ reward, if it is not standing then it gets 0 reward, and the opponent gets -1000 reward. If the opponent is successful in reaching it’s goal then it gets $+ 1 0 0 0$ reward and the blocker gets -1000 reward. + +Sumo: The agents compete on a round arena (see Fig.1c) and the goal of each agent is to either knock the other agent to the ground or to push them out of the ring. The winner gets $+ 1 0 0 0$ and the other agent gets -1000. If there is a draw then both agents get -1000. + +Kick and Defend: This a standard penalty shootout (see Fig.1d). One agent has to kick a ball through the goal, which has a fixed width of 6 units, while the other agent defends. Successful kick or defend gives the agent $+ 1 0 0 0$ reward and the opponent -1000 reward. The defender cannot go beyond the goal-keeping area which is a distance 3 units from the goal, doing so terminates the game with a penalty of -1000 for the defender. We give two additional rewards for defender: if defender is successful and it made contact with the ball then it gets additional $+ 5 0 0$ reward, and if the defender is successful and still standing at the end of the game then it gets another additional reward of $+ 5 0 0$ . We found the latter two rewards to yield more realistic looking defending behaviors. + +# 4 TRAINING COMPETITIVE AGENTS + +In this section we describe the multi-agent training framework. We use a policy gradient algorithm, Proximal Policy Optimization (PPO) (Schulman et al., 2017), described previously. We adopt a decentralized training approach and use a distributed implementation of PPO for very large scale multi-agent training. This allows us to use really large batch-sizes during training ameliorating the variance problem to some extent while also aiding in exploration. Our distributed PPO implementation is similar to the implementation of Heess et al. (2017), where instead of the KL penalty we used the clipped objective as proposed in PPO (Schulman et al., 2017). We do multiple rollouts in parallel for each agent and have separate optimizers for each agent. We collect a large amount of rollouts from the parallel workers and for each agent optimize the objective with the collected batch on 4 GPUs. The approach is same as synchronous actor critic of Mnih et al. (2016). Instead of estimating a truncated generalized advantage estimate (GAE) from a small number of steps per rollout, as in Schulman et al. (2017); Heess et al. (2017), we estimate GAE from the full rollouts. This is important as the competition reward is a sparse reward given at the termination of the episode. + +There are further challenges in applying distributed PPO to train multiple competitive agents. One is the problem of exploration with sparse reward and second is the choice of opponent during training which effects the stability of training. We now turn our attention to these issues. + +# 4.1 EXPLORATION CURRICULUM + +The success of agents in the competitive games requires the agents to occasionally solve the task (i.e. win the competition) by random actions. The probability of this happening in most games is minuscule as they require as a prerequisite some fundamental motor skills like the ability to walk. For example, the only way a kicker in the kick-and-defend task would achieve any positive reward is if it moves towards the ball and causes sufficient displacement to it so as to make it go past the goal boundaries which is also obstructed by a defender. This is a problem of training from sparse reward which is an active area of current research (Andrychowicz et al., 2017). To overcome this problem, we can use simple dense rewards at each step to allow the agents to learn basic motor skills initially. Such rewards have been previously researched for tasks like walking forward and standing up, see for e.g. Schulman et al. (2015b) and Duan et al. (2016). However, engineering such dense rewards for the competitive tasks is not straight forward. Moreover, such engineered rewards defeat the purpose of the competitive multi-agent training as we would like the agents to benefit from the natural curriculum arising from the multi-agent training. To overcome this chicken-and-egg problem, we instead propose to use a simple curriculum for training. + +We use a dense reward at every step in the beginning phase of the training to allow agents to learn basic motor skills, like walking forward or being able to stand, which would increase the probability of random actions from the agent yielding a positive reward. We refer to this reward as the exploration reward. The exploration reward is gradually annealed to zero, in favor of the competition reward, to allow the agents to train for the majority of the training using the sparse competition reward. This is achieved using a linear annealing factor $\alpha$ . So, at time-step $t$ , if the exploration reward is $s _ { t }$ , the competition reward is $R$ and $T$ is the termination time-step, then the reward is: + +![](images/611e1d088992578d7def0edfa3a82e9cac54d0c160389f20d84a21b79c6c4f59.jpg) +Figure 2: Opponent Sampling: Training rewards for two opponent sampling strategies. + +$$ +r _ { t } = \alpha _ { t } s _ { t } + ( 1 - \alpha _ { t } ) \mathbb { I } [ t = = T ] R +$$ + +This ameliorates the problem of exploration with the sparse reward, which is particularly tough in a 3D world with simulated physics and complex agents like humanoid, while still benefiting from training for the sparse competition reward for the majority of the training. During a typical training run, the agents would train on the dense reward for only about $10 \mathrm { - } 1 5 \%$ of the training epochs. The dense rewards used are described in the Appendix A and are generally composed of the following terms: distance to goal, velocity in $\mathbf { X }$ -direction, control cost, impact cost, standing reward. These rewards are adopted from existing work and we did not tune weights on the various reward terms. In particular, it is important to note that there is no dense reward term for many of the complex emergent behaviors and we also show in the experiment section how the learned behaviors are affected if we do not anneal the dense reward to benefit from optimizing the sparse competition reward. + +# 4.2 OPPONENT SAMPLING + +In the competitive multi-agent framework, all agents are simultaneously training in opponent pairs. Thus, the skill of opponents encountered during training could have significant impact on the learning of the agents. We found that training agents against the most recent opponent leads to imbalance in training where one agent becomes more skilled than the other agent early in training and the other agent is unable to recover. Fig. 2a shows the rewards during training with this naive approach (for the “run to goal” task with ant). Instead, we found that training against random old versions of the opponent to work much better. Thus, during training, for each rollout for an agent we sample old parameters for the opponent. Fig. 2b shows the rewards for agents trained using this strategy. This leads to more stable training and more robust policies. We further analyze the effect of this opponent sampling in the experiments section. Note that for self-play this means that the policy at any time should be able to defeat random older versions of itself, thus ensuring continual learning. + +# 5 EXPERIMENTS + +We train agents for the four competitive tasks using the training methods described previously. Our aim is to show that competitive multi-agent training provides a natural curriculum during learning which allows agents to learn complex behaviors. We provide additional training details and analyze various aspects of the competitive multi-agent training in this section. A highlight of the learned behaviors can be seen in the videos. Code for the environments as well as learned policy parameters for agents on all the environments are available: https://github.com/openai/multiagent-competition. + +# 5.1 EXPERIMENTAL DETAILS + +Policies and Value Functions: We compare both MLP and LSTM for the policies and the value functions. MLP had 2 hidden layers with 128 units each. For LSTM networks, the input was first projected to a 128 dimensional embedding using a fully connected layer with ReLU activation which is then fed into a single-layer LSTM with 128 hidden state dimension and the output is projected to the action dimension using another fully connected layer. We used Gaussian policies with mean given by the output of the networks and a diagonal covariance matrix whose entries are also treated as trianable parameters. The policy outputs are clipped to lie within the control range. We used + +MLP policy and value functions for the run-to-goal and you-shall-not-pass environments, and LSTM policy and value function for sumo and kick-and-defend. This is because earlier experiments did not yield good results with MLP policy on these tasks. For LSTM policy we used truncated BPTT with a truncation of 10 timesteps. The policy and the value functions have separate parameters. For the asymmetric games, you-shall-not-pass and kick-and-defend, we use separate policies for the two agents in a game. + +Observations: For the Ant body we use all the joint angles of the agent, its velocity of all its joints, the contact forces acting on the body and the relative position and all the joint angles for the opponent. For the Humanoid body, in addition to the above we also give the centre-of-mass based inertia tensor, velocity vector and the actuator forces for the body. In addition to these, there are other environment specific observations. For the Sumo environment, we give the torso’s orientation vector as the input, the radial distance from the edge of the ring of all the agents and the time remaining in the game. For kick-and-defend, we give the relative position of the ball from the agent, the relative distance of the ball from goal and the relative position of the ball from the two goal posts. Note that none of the agents observe the complete global state of the multi-agent world and only observe relevant sub-parts of the state vector to keep observations as close to real-world scenarios as possible. + +Algorithm Parameters: We use Adam (Kingma & Ba, 2014) with learning rate 0.001. The clipping parameter in PPO $\epsilon = 0 . 2$ , discounting factor $\gamma = 0 . 9 9 5$ and generalized advantage estimate parameter $\lambda = 0 . 9 5$ . Each iteration, we collect 409600 samples from the parallel rollouts and perform multiple epochs of PPO training in mini-batches consisting of 5120 samples. For MLP policies we did 6 epochs of SGD per iteration and for LSTM policies we did 3 epochs. We don’t use any entropy bonus. We found $l _ { 2 }$ regularization of the policy and value network parameters to be useful. The co-efficient $\alpha _ { t }$ in eq. 1 for the exploration reward is annealed to 0 in 500 iterations for all the environments except for kick-and-defend in which it is annealed in 1000 iterations. + +# 5.2 LEARNED BEHAVIORS + +We observe numerous interesting learned behaviors demonstrated by the agents as a result of the complexity arising out of the competitive multi-agent training. Different random seeds often lead to somewhat different behaviors. Refer to the videos for highlights of the learned policies on all the tasks. On Run-to-Goal, we observe the quadruped Ants demonstrate behaviors like blocking, standing robustly, using legs to topple the opponent and running towards the goal. Humanoids try to avoid each other and run towards their goal really fast, occasionally they will bump into each other with force and try to recover from the impact. On You-Shall-Not-Pass, we observe the blocking humanoid learn to block by raising its hand while the other humanoid eventually learned to duck in order to cross. On Sumo, we observe multiple different strategies used by the Ant and Humanoid. Humanoids, for example, demonstrate a stable fighting stance and learned to knock the opponent using their heads. In a different run, we observe that one agent learned to charge towards the opponent whereas the opponent tried to fool it by stepping out of the opponents way at the edge of the ring. On kick-and-defend, we observe that the kicker learned a good kicking policy where it can go towards random ball positions, uses its feet to kick the ball high and tries to avoid the defender. We also see a fooling behavior in the kicker’s motions where it moves left and right quickly once close to the ball to fool the defender. The defender learned to defend by moving in response to the motion of the kicker and using its hands and legs to obstruct the ball. + +These movement strategies are not just useful in competition, for example the skills learned in the Sumo can transfer to other situations even without other agents. In one case, we took the agent trained on the multi-agent Sumo task and faced it with the task of standing while being perturbed by wind forces. The agent receives the zero vector for parts of the opponent observation. We found that the agent managed to stay upright despite never seeing the windy environment or observing wind forces. Please see Appendix B.1 for details of the experiment and quantitative results. Refer to the video for a demonstration. + +# 5.3 EFFECT OF EXPLORATION CURRICULUM + +In section 4.1 we introduced an exploration curriculum to help agents explore in a 3D world. One question that arises is the extent to which the outcome of learning is affected by this exploration reward and to explore the benefit of this exploration reward. As already argued, we found the exploration reward to be crucial for learning as otherwise the agents are unable to explore the sparse competition reward. However, the learned behaviors are mostly a result of the natural curriculum arising out of the multi-agent competition and not due to the dense exploration reward. To see this, first note that we do not give any reward for many of the complex learned behaviours described previously. We further test this by not annealing the exploration reward and always having a dense reward which is a sum of the exploration reward and the competition reward. We take these agents trained without curriculum and pit them against agents trained with exploration curriculum. We plot the average win-rates over 800 games at various intervals during training in Fig. 3, for the sumo and kick-and-defend environments. For kick-and-defend there are two plots, one where kicker is trained with curriculum while keeper without it and vice versa. Observe that the agents trained with curriculum beat the non-curriculum agents by a margin. We found agents trained without curriculum exhibit either non-optimal behaviors for the competition or end up optimizing for a particular component of the dense reward. For example, for Sumo, the agents just learn to stand and move towards center of the arena, and for kick-and-defend, the defender optimizes for being able to stand up but doesn’t learn to defend while the kicker learns a non-optimal strategy of carrying the ball with itself to the goal (rather than kicking) – a policy which is easily defeated by a defender trained with curriculum. Moreover, training without curriculum also takes more samples to learn. We also show these behaviours qualitatively in the videos. These results echo some recent findings (albeit in the single agent case), like Andrychowicz et al. (2017) who found that optimizing for the sparse reward yields better return than optimizing for hand crafted dense rewards. For the competitive multi-agent case, these results shed further light on the importance of the natural curriculum. + +![](images/b945f11d066fc08722a430402c33d364604cc71ecf37dc98786df3ca4e0addcf.jpg) +Figure 3: Effect for exploration curriculum: win-rate of agents trained by annealing the exploration reward against agents which constantly receive the dense exploration reward. The agents which optimized for the sparse competition reward benefit from the natural curriculum of multi-agent training and defeat the other agent by a margin. + +
8 1.0 0.8 0.51.0 - 0.36 0.360.8 0.37 1 0.390.5 0.35 0.38 10.0 0.29 0.33 0.33E[Win] 0.34 0.36 0.36
0.0 E[Loss]0.51 0.410.49 0.420.49 0.41- 0.320.50 1
+ +Table 1: The effect of opponent sampling. $\mathbb { E } [ \mathrm { L o s s } ]$ and $\mathbb { E } [ \mathrm { W i n } ]$ are the expected loss and win-rates for agents trained with a particular $\delta$ as described in 5.4. For humanoid $\delta \ : = \ : 0 . 5$ gives highest win-rate and lowest loss, whereas for Ant $\delta = 0$ was best. + +
81.00.80.50.0E[Win]
1.010.260.130.370.25
0.80.50.4610.220.520.400.630.35
0.590.5810.73
0.00.550.360.16-
E[Loss]0.530.400.170.541
+ +# 5.4 EFFECT OF OPPONENT SAMPLING + +In section 4.2, we introduced the past opponent sampling method for training competitive agents simultaneously. This choice of opponent could be important as it affects the natural curriculum for the agents. We test different opponent sampling strategies by considering a threshold on the oldest opponent for each agent. That is, instead of uniform random over the entire history, we can consider sampling opponent from $\mathrm { U n i f o r m } ( \delta v , v )$ where $v$ is the iteration number for the latest available parameters of the opponent and $\delta \in [ 0 , 1 ]$ is a threshold. Thus, $\delta = 1 . 0$ corresponds to the latest available opponent and $\delta = 0 . 0$ corresponds to uniform sampling over the entire history. We train agents on the Sumo task via self-play, using a $\delta \in \{ 1 . 0 , 0 . 8 , \bar { 0 . 5 } , \bar { 0 . 0 } \}$ and pit the four agents against each other to understand which sampling strategy leads to more robust policies. Since the agents have different skills and strengths at various points during training, we compute a Monte Carlo estimate of the expected win-rate for two agents that have seen the same number of samples taken at a random point during training. This is done by taking average of the win-rates of 30 agents at intervals of 100 iterations after a burn-in of 3000 iterations, where each win-rate is computed from an average over 800 episodes. Table 1a reports the results for Humanoid and Table 1b reports the results for Ant. First note that training against the latest opponent leads to worst performance, as argued earlier. Surprisingly, we found that uniform random $\delta = 0 . 0$ ) over the entire history to have the highest win-rate for Ant and $\delta = 0 . 5$ to have the highest win-rate for Humanoid. This could be because Ant with random policy on a small arena is still a good opponent while a Humanoid with random policy is unable to stand and thus always looses in a few steps. The differences in these win-rates for different sampling strategies show that the choice of the opponent during sampling is important and care must be taken while designing training algorithms for such competitive environments. + +# 5.5 LEARNING ROBUST POLICIES + +Over-fitting to a particular dataset is often a problem in supervised learning. Similar problems can arise in reinforcement learning setups when there is no or little variation in the environment. We discovered two such problems in our competitive multi-agent training framework and we analyze and propose solutions to address these issues. + +# 5.5.1 RANDOMIZATION IN WORLD + +In order to learn robust policies which generalize better we can introduce randomness in the environment, for example the arena radius for the sumo environment can be randomized, the ball position for the kick-and-defend environment can be randomized, agent start positions can be randomized. However, we found that while randomization is crucial to learn policies which generalize better, it might hinder learning early on as there might be too many things for the agents to explore. Indeed, we observe that in kick-and-defend the agents are unable to learn to kick with a lot of randomization in both the ball and agent positions, whereas when trained with no randomization the learned policies are overfit to the particular position of the ball (see Fig. 4). Thus, in order to learn policies that generalize well, we introduce a simple curriculum in the randomization where we start with a small amount of randomization which is easier to solve and then gradually increase the randomization during training. We found this curriculum to work well for all the environments. + +# 5.5.2 COMPETING AGAINST ENSEMBLE OF POLICIES + +Another related problem that we observed is over-fitting to the behavior of the opponent when trained for very long. This results in policies which are good against particular types of opponents but do not generalize to other opponents (say opponents trained with a different random seed). This overfitting can also be observed in win-rates against opponent during training, where one would see oscillations as agents try to adapt to their particular opponent and changes in their strategies. To overcome this we propose learning multiple policies simultaneously. Thus, there is a pool of policies and in each rollout for a particular policy one of the other policies is selected at random as the opponent (in symmetric games, the same policy can also be an opponent). This is similar to multi-task learning (Caruana, 1998) where the same network is used to model multiple related tasks which allows sharing of statistical strength among tasks and reduces overfitting. In this case, the pool of all policies as opponents – current and throughout the history of training – creates a natural distribution over related tasks for multi-task learning. We found random policy initialization to provide enough diversity between agent policies, however techniques that explicitly encourage diversity (Liu & Wang, 2016) can potentially be incorporated in the future. + +In order to test the robustness of training policies in an ensemble, we experiment on the Sumo environment with Ant and Humanoid bodies. We train a pool of three policies in an ensemble and take the policy with the highest average training reward in the last 500 iterations as the best ensemble policy. We also train three independent policies via self-play, that is just a single policy is trained in a run, and again take the policy with the highest average training reward in last 500 iterations as the best self-play policy. Then we pit the best ensemble policy against the best self-play policy and record average win-rates over 800 games. Fig. 5 shows the win-rates over training iterations (after 1000 iterations of training). We find that training in ensemble performs significantly better for the humanoid body, whereas for ant the performance is similar to training a single policy. Again we suspect this is because there is not enough variability in the behavior of ant across different runs. While training single policies might occasionally get stuck in a local minima and learn suboptimal behaviors, we found that when training in an ensemble to be more robust to such minima. Qualitatively, we see more robust behavior of the humanoid trained in ensemble (see video). + +![](images/152bfacb47e873bf346837e201498b80a5c6447de979e7d7bfc9455e1f8b8c6a.jpg) +Figure 4: Win-rate of kicker vs iterations with full randomization + +![](images/f5e400e02f6c6d1d2a0808d79e102f4c6f33d5a9225e9a4aafd4f4d34c22885b.jpg) +Figure 5: $\%$ Win-rate of agents trained in ensemble vs agents trained with just a single policy. Humanoid Sumo (left) and Ant Sumo (right). + +# 6 CONCLUSION + +We have presented several new competitive multi-agent 3D physically simulated environments. We demonstrate the development of highly complex skills in simple environments with simple rewards. In future work, it would be interesting to conduct larger scale experiments in more complex environments that encourage agents to both compete and cooperate with each other. Incorporation of additional skills, such as reasoning about other agents, potentially via techniques from Foerster et al. (2017a), may also be important in our setting. + +# REFERENCES + +Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, and Wojciech Zaremba. Hindsight experience replay. arXiv preprint arXiv:1707.01495, 2017. +Lucian Busoniu, Robert Babuska, and Bart De Schutter. A comprehensive survey of multiagent reinforcement learning. IEEE Transactions on Systems, Man, And Cybernetics-Part C: Applications and Reviews, 38 (2), 2008, 2008. +Rich Caruana. Multitask learning. In Learning to learn, pp. 95–133. Springer, 1998. +Yan Duan, Xi Chen, Rein Houthooft, John Schulman, and Pieter Abbeel. 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In Intelligent Robots and Systems (IROS), 2012 IEEE/RSJ International Conference on, pp. 5026– 5033. IEEE, 2012. + +Kevin Wampler, Erik Andersen, Evan Herbst, Yongjoon Lee, and Zoran Popovic. Character anima- ´ tion in two-player adversarial games. ACM Transactions on Graphics (TOG), 29(3):26, 2010. + +Ronald J Williams. Simple statistical gradient-following algorithms for connectionist reinforcement learning. Machine learning, 8(3-4):229–256, 1992. + +# A EXPLORATION REWARDS + +We define the dense exploration rewards used for the tasks in this section. Our exploration reward terms are based on adapting the rewards defined previously for the training humanoids and quadrupeds to walk (Duan et al., 2016; Schulman et al., 2015b). We first review this locomotion reward and then define the task-specific dense rewards. These rewards take the form $r _ { t } ( s , a ) = v _ { f w d } + c _ { t } ( s , a ) + C _ { a l i v e }$ where $v _ { f w d }$ is the velocity in the forward direction, a bonus for standing $C _ { a l i v e }$ and costs for impact and action $c _ { t } ( s , a )$ . We considered the following locomotion reward defined for Humanoid-v1 environment in OpenAI Gym package: + +$$ +r _ { t } ^ { h } ( s , a ) = v _ { f w d } + c ^ { h } ( s , a ) + C _ { a l i v e } = v _ { f w d } - 0 . 1 | a | | ^ { 2 } - 5 \cdot 1 0 ^ { - 7 } | | F _ { i m p a c t } | | ^ { 2 } + C _ { a l i v e } +$$ + +where $F _ { i m p a c t }$ is the contact force vector clipped to values between 1 and 1, and $C _ { a l i v e }$ is a bonus for the center of the body being at a certain height, defined as $C _ { a l i v e } = + 5$ if $2 . 0 \geq z _ { b o d y } \geq 1 . 0$ , else 0. + +Similarly, the following is the reward for quadruped locomotion: + +$$ +r _ { t } ^ { q } ( s , a ) = v _ { f w d } + c ^ { q } ( s , a ) = v _ { f w d } - 0 . 5 | a | | ^ { 2 } - 5 \cdot 1 0 ^ { - 4 } | | F _ { i m p a c t } | | ^ { 2 } + C _ { a l i v e } +$$ + +where $C _ { a l i v e } = + 1$ if $1 . 0 \geq z _ { b o d y } \geq 0 . 2$ , else 0. + +In the following, superscript $h$ refers to humanoid agents and superscript $q$ refers to quadruped. We redefine $C _ { a l i v e }$ to be $+ 5$ if $z _ { b o d y } \ge 1 . 0$ , else $- 5$ for humanoid, and $C _ { a l i v e } = + 1$ if $z _ { b o d y } \ge 0 . 2 8$ else $- 1$ for quadruped. + +Run to Goal For humanoids, reward is $r ^ { h } ( s , a ) - | x - g |$ where $x - g$ is the $l _ { 1 }$ distance of the agent from the goal $g$ along the $x$ -axis. For ant, reward is similar $r ^ { q } ( s , a ) - | x - g |$ . + +You Shall not Pass For the agent whose goal is to reach the other side, the reward is same as for run-to-goal. For the blocking agent, the reward for humanoid is $c ^ { h } ( s , a ) + C _ { a l i v e } + | x ^ { \prime } - g |$ where $| x ^ { \prime } - g |$ is the distance of opponent to the goal. + +Sumo For humanoids, reward is $c ^ { h } ( s , a ) + C _ { a l i v e } - ( x ^ { 2 } + y ^ { 2 } ) ^ { 0 . 5 }$ , where the last term is distance from the center of the ring. Similarly for ant: $c ^ { q } ( s , a ) + C _ { a l i v e } - ( x ^ { 2 } + y ^ { 2 } ) ^ { 0 . 5 }$ + +Kick and Defend: For kicker, reward is $r ^ { h } ( s , a ) - | | x - b | | - | b _ { x } - g |$ , where $b$ is the $( x , y )$ position of the ball, $b _ { x }$ is the $x$ -coordinate of the ball and $g$ is the $x$ -coordinate of the goal-post. For defender, reward is $c ^ { h } ( s , a ) + C _ { a l i v e } + | b _ { x } - g |$ where for $C _ { a l i v e }$ we only gave positive reward if the defender was in front of the goal area. + +Table 2: Average number of steps before agent falls. Sumo Agent refers to the agent trained in Sumo environment whereas Walker Agent refers to the agent trained to walk in a single agent environment. + +
Force Magnitude
200300400500600
Sumo Agent372 ± 146327±150247± 143181 ± 114123 ± 57
Walker Agent179± 54139± 42116± 32103±2395 ± 20
+ +# B ADDITIONAL RESULTS + +# B.1 TRANSFER RESULTS + +We took the agent trained on the multi-agent Sumo task and faced it with the task of standing while being perturbed by wind forces. The agent receives a zero vector for parts of the observation space which correspond to the opponent. We calculate the number of steps before the agent falls down (i.e. when $z _ { b o d y } \le 0 . 5$ ) or the agent is pushed out of the arena and report the average steps over 200 episodes. Episodes last a maximum of 500 time steps. In half the episodes the wind force is applied in a radially outwards direction and in the remaining half it is applied in the radially inwards direction. We allow 50 steps for the agent to stabilize and apply the force at intervals of 50 steps where in between the intervals the force magnitude is decayed at a constant rate: + +$$ +F _ { t } = { \left\{ \begin{array} { l l } { \qquad F } & { { \mathrm { i f ~ } } t \equiv 0 { \pmod { 5 0 } } } \\ { 0 . 9 * F _ { t - 1 } } & { { \mathrm { o t h e r w i s e } } } \end{array} \right. } +$$ + +where $F \in \{ 2 0 0 , 3 0 0 , 4 0 0 , 5 0 0 , 6 0 0 \}$ . + +We compare with a humanoid agent trained in a single agent environment for the task of walking. We used same LSTM policy architecture as used for the Sumo agent and trained the humanoid in the publicly available OpenAI Gym Humanoid-v1 environment using PPO. We then apply force on this agent using the same method as above where the direction of the force is in the direction the agent is walking in half the episodes and opposite to it in the remaining half. We record average number of steps to fall using the same condition as for the Sumo agent. + +Table 2 shows the average number of steps over 200 episodes along with the standard deviation. We see that the humanoid trained in Sumo is more robust to adversarial forces and able to withstand large magnitude of force for many steps. \ No newline at end of file diff --git a/parse/train/Sy0GnUxCb/Sy0GnUxCb_content_list.json b/parse/train/Sy0GnUxCb/Sy0GnUxCb_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..f3948f4b369c121bcf8fd0a27993cefa6449bba5 --- /dev/null +++ b/parse/train/Sy0GnUxCb/Sy0GnUxCb_content_list.json @@ -0,0 +1,1384 @@ +[ + { + "type": "text", + "text": "EMERGENT COMPLEXITY VIA MULTI-AGENT COMPETITION ", + "text_level": 1, + "bbox": [ + 174, + 99, + 720, + 145 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Trapit Bansal∗ UMass Amherst ", + "bbox": [ + 184, + 170, + 292, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jakub Pachocki OpenAI ", + "bbox": [ + 316, + 170, + 429, + 199 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Szymon Sidor OpenAI ", + "bbox": [ + 452, + 171, + 552, + 199 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Ilya Sutskever OpenAI ", + "bbox": [ + 575, + 171, + 678, + 199 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Igor Mordatch OpenAI ", + "bbox": [ + 699, + 171, + 807, + 199 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ABSTRACT ", + "text_level": 1, + "bbox": [ + 454, + 236, + 544, + 251 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Reinforcement learning algorithms can train agents that solve problems in complex, interesting environments. Normally, the complexity of the trained agent is closely related to the complexity of the environment. This suggests that a highly capable agent requires a complex environment for training. In this paper, we point out that a competitive multi-agent environment trained with self-play can produce behaviors that are far more complex than the environment itself. We also point out that such environments come with a natural curriculum, because for any skill level, an environment full of agents of this level will have the right level of difficulty. ", + "bbox": [ + 233, + 267, + 764, + 378 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This work introduces several competitive multi-agent environments where agents compete in a 3D world with simulated physics. The trained agents learn a wide variety of complex and interesting skills, even though the environment themselves are relatively simple. The skills include behaviors such as running, blocking, ducking, tackling, fooling opponents, kicking, and defending using both arms and legs. A highlight of the learned behaviors can be found here: https://goo.gl/eR7fbX. ", + "bbox": [ + 233, + 381, + 764, + 478 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 INTRODUCTION ", + "text_level": 1, + "bbox": [ + 176, + 506, + 336, + 522 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Reinforcement Learning (RL) is exciting because good reinforcement learning algorithms exist (Mnih et al., 2015; Silver et al., 2016; Schulman et al., 2015a; Mnih et al., 2016; Schulman et al., 2015b; Lillicrap et al., 2015; Schulman et al., 2017), allowing us to train agents that accomplish a great variety of interesting tasks. We can train an agent to play Atari games from pixels (Mnih et al., 2015) or get humanoids to walk (Schulman et al., 2017). RL is exciting partly because it is easy to envision an RL algorithm producing a broadly competent agent when trained on an appropriate curriculum of environments. ", + "bbox": [ + 174, + 537, + 825, + 635 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In general, training an agent to perform a highly complex task requires a highly complex environment, and these can be difficult to create. However, there exists a class of environments where the behavior produced by the agents can be far more complex than the environments; this is the class of the competitive multi-agent environments trained with self-play. Such environments have two very attractive properties: (1) Even very simple competitive multi-agent environments can produce extremely complex behaviors. For example, the game of Go has very simple rules, but the strategies needed to win are extremely complex. This is because the complexity of these environments is produced by the competing agents that act in it. Thus, as the other agents become more competent, the environment effectively becomes more complex. (2) When trained with self-play, the competitive multi-agent environment provides the agents with a perfect curriculum. This happens because no matter how weak or strong an agent is, an environment populated with other agents of comparable strength provides the right challenge to the agent, facilitating maximally rapid learning and avoiding getting stuck. ", + "bbox": [ + 174, + 643, + 825, + 823 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Self-play in competitive multi-agent environments is not a new idea – it has already been explored in TD-gammon (Tesauro, 1995) and refined in AlphaGo (Silver et al., 2016) and Dota 2 (OpenAI). In both cases, the resulting behavior was far more complex than the environment itself, and the self-play approach provided the agents with a perfectly tuned curriculum for each task. In this paper, we investigate whether the idea of competitive multi-agent environments can yield fruit in other domains: specifically, in the domain of continuous control, where balance, dexterity, and manipulation are the key skills. ", + "bbox": [ + 174, + 830, + 823, + 900 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "", + "bbox": [ + 173, + 103, + 823, + 132 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In more detail, we introduce several multi-agent tasks with competing goals in a 3D world with simulated physics, using the MuJoCo framework (Todorov et al., 2012), where the agents would need to learn highly developed motor skills in order to succeed in the competitive environment. We train the agents using a distributed implementation of a recent policy gradient algorithm, Proximal Policy Optimization (Schulman et al., 2017). By adding a simple exploration curriculum to aid exploration in the environment we find that agents learn a high level of dexterity in order to achieve their goals, in particular we find numerous emergent skills for which it may be difficult to engineer a reward. Specifically, the agents learned a wide variety of skills and behaviors that include running, blocking, ducking, tackling, fooling opponents, kicking, and defending using arms and legs. Highlight of the learned behaviors on the various tasks can be found here: https://goo.gl/eR7fbX ", + "bbox": [ + 173, + 138, + 825, + 279 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2 PRELIMINARIES ", + "text_level": 1, + "bbox": [ + 176, + 300, + 339, + 315 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this section, we review some background on policy gradient methods, Proximal Policy Optimization and related work in the multi-agent reinforcement learning domain. ", + "bbox": [ + 174, + 333, + 820, + 361 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Notation: We consider multi-agent Markov games (Littman, 1994). A Markov game for $N$ agents is a partially observable Markov decision process (MDP) defined by: a set of states $s$ describing the state of the world and the possible joint configuration of all the agents, a set of observations $\\mathcal { O } ^ { 1 } , \\ldots , \\mathcal { O } ^ { N }$ of each agent, a set of actions of each agent $\\mathcal { A } ^ { 1 } , \\ldots , \\mathcal { A } ^ { \\tilde { N } }$ , a transition function $\\tau :$ $\\mathcal { S } \\times \\mathcal { A } ^ { 1 } \\cdot \\cdot \\cdot \\mathcal { A } ^ { N } \\to \\mathcal { S }$ determining distribution over next states, and a reward for each agent $i$ which is a function of the state and the agent’s action $r ^ { i } : \\mathcal { S } \\times \\mathcal { A } ^ { i } \\to \\mathbb { R }$ . Agents choose their actions according to a stochastic policy $\\pi _ { \\theta ^ { i } } : \\mathcal { O } ^ { i } \\times \\mathcal { A } ^ { i } [ 0 , 1 ]$ , where $\\theta ^ { i }$ are the parameters of the policy. For continuous control problems considered here, $\\pi _ { \\theta }$ is Gaussian where the mean and variance are deep neural networks with parameter $\\theta$ . Each agent $i$ aims to maximize its own total expected return $\\begin{array} { r } { R ^ { i } = \\sum _ { t = 0 } ^ { T } \\gamma ^ { t } r _ { t } ^ { i } } \\end{array}$ , where $\\gamma$ is a discount factor and $T$ is the time horizon ", + "bbox": [ + 173, + 367, + 825, + 511 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Policy Gradient: Policy gradient methods work by directly computing an estimate of the gradient of policy parameters in order to maximize the expected return using stochastic gradient descent. These methods are behind much of the recent success in using deep neural networks for control (Schulman et al., 2015b; Heess et al., 2017; Lillicrap et al., 2015; Silver et al., 2016). Such methods are also attractive because they don’t require an explicit model of the world. There are several different expressions for the policy gradient estimator which have the form $g : = \\mathbb { E } \\left[ A _ { t } \\nabla _ { \\theta } \\log \\pi _ { \\theta } \\right]$ . Different choices of $A _ { t }$ lead to different algorithms, for example taking the sample return of a trajectory $\\boldsymbol { A } _ { t } = \\sum _ { t } \\boldsymbol { r } _ { t }$ leads to the REINFORCE algorithm (Williams, 1992). However, such algorithms suffer from high variance in the gradient estimates and it’s typical to use a baseline, such as a value function baseline, to ameliorate the high variance. Generalized advantage estimation (Schulman et al., 2015b) takes this approach of using a learned value function to reduce variance at the cost of some bias and using an exponentially weighted estimator of the advantage function. ", + "bbox": [ + 173, + 517, + 825, + 684 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Proximal Policy Optimization (PPO): Achieving good results with policy gradient algorithms requires carefully tuning the step-size (Schulman et al., 2015a). Moreover, most policy gradient methods perform one gradient update per sampled trajectory and have high sample complexity. Recently, Schulman et al. (2017) proposed the PPO algorithm which addresses both these problems. This uses a surrogate objective which is maximized while penalizing large changes to the policy. Let $\\begin{array} { r } { l _ { t } ( \\theta ) ~ = ~ \\frac { \\pi _ { \\theta } ^ { - } \\left( a _ { t } | s _ { t } \\right) ^ { - } } { \\pi _ { \\theta _ { o l d } } \\left( a _ { t } | s _ { t } \\right) } } \\end{array}$ denote the likelihood ratio. Then PPO optimizes the objective: $L = \\mathbb { E } \\left[ \\operatorname* { m i n } ( l _ { t } ( \\theta ) \\hat { A } _ { t } , \\operatorname { c l i p } ( l _ { t } ( \\theta ) , 1 - \\epsilon , 1 + \\epsilon ) \\hat { A } _ { t } ) \\right]$ , where $\\hat { A } _ { t }$ is the generalized advantage estimate and $\\mathrm { c l i p } ( l _ { t } ( \\theta ) , 1 - \\epsilon , 1 + \\epsilon )$ clips $l _ { t } ( \\theta )$ in the interval $[ 1 - \\epsilon , 1 + \\epsilon ]$ . The algorithm alternates between sampling multiple trajectories from the policy and performing several epochs of SGD on the sampled dataset to optimize this surrogate objective. Since the state value function is also simultaneously approximated, the error for the value function approximation is also added to the surrogate objective to compute the complete objective function (Schulman et al., 2017). ", + "bbox": [ + 173, + 690, + 825, + 875 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Related Work: Tan (1993) explored the multi-agent setting with independently learning agents using Q-learning, in particular exploring advantages of cooperative agents over independent agents in a 2D grid world. This was further explored by Matignon et al. (2012) again in the cooperative setting. A lot of the work on multi-agent RL is focused on cooperative settings, see Busoniu et al. (2008) for a review of multi-agent RL and Panait & Luke (2005) for a review focused on cooperative settings. Stanley & Miikkulainen (2004) trained agents in a competitive 2D world, using evolutionary strategies to evolve both weights and structure of policies with competition as a fitness measure. Tampuu et al. (2017) studied the application of deep Q-learning to train Pong agents with competitive and collaborative rewarding schemes. He et al. (2016) used deep Q-learning to model competitive games where only one agent is learning and the Q network implicitly models the opponent. Silver et al. (2016) used self-play with deep reinforcement learning techniques to master the game of Go. Sukhbaatar et al. (2017) introduced a self-play method for generating an automatic training curriculum in single-agent environments. From a game-theoretic perspective, Heinrich & Silver (2016) studied fictitious self-play for achieving approximate Nash equilibrium in zero-sum games like Poker. Recently, Foerster et al. (2017a) introduced an algorithm which explicitly accounts for the fact that the opponent is also learning and showed that it can achieve cooperation in iterated prisoner’s dilemma, however the algorithm requires access to the opponent’s parameters. Recently, Lowe et al. (2017) and Foerster et al. (2017b) proposed methods for centralized learning in multi-agent domains, where the idea is to use an actor-critic method with a central critic which can observe the joint state and actions of all agents in order to reduce variance, evaluating on 2D games and StarCraft. In this work, we do not rely on centralized training and address the variance problem by using very large batchsize through a distributed implementation of the PPO algorithm. Moreover, we study fully competitive settings in a 3D world with simulated physics whereas prior applications have focused on toy 2D worlds or game-theoretic problems. Recent work on learning dexterous locomotion skills in 3D environments by adding complexity in the agent’s environment (Heess et al., 2017) is also related. However, whereas Heess et al. (2017) learn complex behaviours by engineering complexity into the environment design and by engineering dense reward functions for these environments, the resultant complexity in our work is due to the presence of other learning agents in a simple environment. Our work is also related to early work in the graphics community (Sims, 1994) on evolving creature morphology in varying environments using genetic algorithm and work in animation (Wampler et al., 2010) for adversarial games. The competitive multi-agent learning framework is also related to generative adversarial networks (Goodfellow et al., 2014) and work on learning robust grasping policies through an adversary (Pinto et al., 2017). ", + "bbox": [ + 176, + 882, + 823, + 924 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 103, + 825, + 518 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3 COMPETITIVE ENVIRONMENTS ", + "text_level": 1, + "bbox": [ + 176, + 541, + 465, + 556 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/0bc53a965370e58dc6fba3823a2d9d3f433c6c327fbd86c872932af6f33f371e.jpg", + "image_caption": [ + "Figure 1: Illustrations of competitive environments we consider in our work: Run to Goal, You Shall Not Pass, Sumo, and Kick and Defend. " + ], + "image_footnote": [], + "bbox": [ + 174, + 577, + 823, + 670 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We introduce four competitive environments and experiment with two types of agents. In this paper we focus on two agent worlds, that is 1-vs-1 games, though these environments can be extended to include multiple agents for a mixed competitive and co-operative setup. We will now describe the four environments and the competitive rewards in each environment. Figure 1 shows a rendering of the environments. We consider two three-dimensional agent bodies: ant and humanoid. The ant is a quadrupedal body with $1 2 \\mathrm { D o F }$ and 8 actuated joints. Humanoid has 23 DoF and 17 actuated joints. ", + "bbox": [ + 174, + 728, + 825, + 811 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Run to Goal: The agents start by facing each other in a 3D world and they each have goals on the opposite side of the word (see Fig.1a). The agent that reaches its goal first wins. Reaching the goal before the opponent gives a reward of $+ 1 0 0 0$ to the agent and -1000 to the opponent. If no agent reaches its goal then they both get -1000. ", + "bbox": [ + 174, + 819, + 823, + 875 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "You Shall Not Pass: This is the same world as the previous task, but one agent (the blocker) now has the objective of blocking the other agent from reaching it’s goal while not falling down. If the blocker is successful in preventing the opponent from reaching the goal and is standing at the end of episode then it gets $+ 1 0 0 0$ reward, if it is not standing then it gets 0 reward, and the opponent gets -1000 reward. If the opponent is successful in reaching it’s goal then it gets $+ 1 0 0 0$ reward and the blocker gets -1000 reward. ", + "bbox": [ + 174, + 882, + 823, + 924 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "", + "bbox": [ + 176, + 103, + 821, + 145 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Sumo: The agents compete on a round arena (see Fig.1c) and the goal of each agent is to either knock the other agent to the ground or to push them out of the ring. The winner gets $+ 1 0 0 0$ and the other agent gets -1000. If there is a draw then both agents get -1000. ", + "bbox": [ + 174, + 152, + 823, + 195 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Kick and Defend: This a standard penalty shootout (see Fig.1d). One agent has to kick a ball through the goal, which has a fixed width of 6 units, while the other agent defends. Successful kick or defend gives the agent $+ 1 0 0 0$ reward and the opponent -1000 reward. The defender cannot go beyond the goal-keeping area which is a distance 3 units from the goal, doing so terminates the game with a penalty of -1000 for the defender. We give two additional rewards for defender: if defender is successful and it made contact with the ball then it gets additional $+ 5 0 0$ reward, and if the defender is successful and still standing at the end of the game then it gets another additional reward of $+ 5 0 0$ . We found the latter two rewards to yield more realistic looking defending behaviors. ", + "bbox": [ + 174, + 202, + 825, + 313 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4 TRAINING COMPETITIVE AGENTS ", + "text_level": 1, + "bbox": [ + 176, + 333, + 488, + 349 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section we describe the multi-agent training framework. We use a policy gradient algorithm, Proximal Policy Optimization (PPO) (Schulman et al., 2017), described previously. We adopt a decentralized training approach and use a distributed implementation of PPO for very large scale multi-agent training. This allows us to use really large batch-sizes during training ameliorating the variance problem to some extent while also aiding in exploration. Our distributed PPO implementation is similar to the implementation of Heess et al. (2017), where instead of the KL penalty we used the clipped objective as proposed in PPO (Schulman et al., 2017). We do multiple rollouts in parallel for each agent and have separate optimizers for each agent. We collect a large amount of rollouts from the parallel workers and for each agent optimize the objective with the collected batch on 4 GPUs. The approach is same as synchronous actor critic of Mnih et al. (2016). Instead of estimating a truncated generalized advantage estimate (GAE) from a small number of steps per rollout, as in Schulman et al. (2017); Heess et al. (2017), we estimate GAE from the full rollouts. This is important as the competition reward is a sparse reward given at the termination of the episode. ", + "bbox": [ + 174, + 366, + 825, + 546 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "There are further challenges in applying distributed PPO to train multiple competitive agents. One is the problem of exploration with sparse reward and second is the choice of opponent during training which effects the stability of training. We now turn our attention to these issues. ", + "bbox": [ + 176, + 553, + 820, + 595 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1 EXPLORATION CURRICULUM", + "text_level": 1, + "bbox": [ + 176, + 613, + 416, + 626 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The success of agents in the competitive games requires the agents to occasionally solve the task (i.e. win the competition) by random actions. The probability of this happening in most games is minuscule as they require as a prerequisite some fundamental motor skills like the ability to walk. For example, the only way a kicker in the kick-and-defend task would achieve any positive reward is if it moves towards the ball and causes sufficient displacement to it so as to make it go past the goal boundaries which is also obstructed by a defender. This is a problem of training from sparse reward which is an active area of current research (Andrychowicz et al., 2017). To overcome this problem, we can use simple dense rewards at each step to allow the agents to learn basic motor skills initially. Such rewards have been previously researched for tasks like walking forward and standing up, see for e.g. Schulman et al. (2015b) and Duan et al. (2016). However, engineering such dense rewards for the competitive tasks is not straight forward. Moreover, such engineered rewards defeat the purpose of the competitive multi-agent training as we would like the agents to benefit from the natural curriculum arising from the multi-agent training. To overcome this chicken-and-egg problem, we instead propose to use a simple curriculum for training. ", + "bbox": [ + 174, + 638, + 825, + 833 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We use a dense reward at every step in the beginning phase of the training to allow agents to learn basic motor skills, like walking forward or being able to stand, which would increase the probability of random actions from the agent yielding a positive reward. We refer to this reward as the exploration reward. The exploration reward is gradually annealed to zero, in favor of the competition reward, to allow the agents to train for the majority of the training using the sparse competition reward. This is achieved using a linear annealing factor $\\alpha$ . So, at time-step $t$ , if the exploration reward is $s _ { t }$ , the competition reward is $R$ and $T$ is the termination time-step, then the reward is: ", + "bbox": [ + 174, + 840, + 823, + 924 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/611e1d088992578d7def0edfa3a82e9cac54d0c160389f20d84a21b79c6c4f59.jpg", + "image_caption": [ + "Figure 2: Opponent Sampling: Training rewards for two opponent sampling strategies. " + ], + "image_footnote": [], + "bbox": [ + 183, + 101, + 818, + 213 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "", + "bbox": [ + 173, + 266, + 687, + 281 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/f545273695d1fea526ce9d5faa51fb178d327fa4a5bccb1363ff43021ef47541.jpg", + "text": "$$\nr _ { t } = \\alpha _ { t } s _ { t } + ( 1 - \\alpha _ { t } ) \\mathbb { I } [ t = = T ] R\n$$", + "text_format": "latex", + "bbox": [ + 385, + 287, + 612, + 305 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This ameliorates the problem of exploration with the sparse reward, which is particularly tough in a 3D world with simulated physics and complex agents like humanoid, while still benefiting from training for the sparse competition reward for the majority of the training. During a typical training run, the agents would train on the dense reward for only about $10 \\mathrm { - } 1 5 \\%$ of the training epochs. The dense rewards used are described in the Appendix A and are generally composed of the following terms: distance to goal, velocity in $\\mathbf { X }$ -direction, control cost, impact cost, standing reward. These rewards are adopted from existing work and we did not tune weights on the various reward terms. In particular, it is important to note that there is no dense reward term for many of the complex emergent behaviors and we also show in the experiment section how the learned behaviors are affected if we do not anneal the dense reward to benefit from optimizing the sparse competition reward. ", + "bbox": [ + 173, + 311, + 825, + 450 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2 OPPONENT SAMPLING ", + "text_level": 1, + "bbox": [ + 176, + 468, + 370, + 482 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the competitive multi-agent framework, all agents are simultaneously training in opponent pairs. Thus, the skill of opponents encountered during training could have significant impact on the learning of the agents. We found that training agents against the most recent opponent leads to imbalance in training where one agent becomes more skilled than the other agent early in training and the other agent is unable to recover. Fig. 2a shows the rewards during training with this naive approach (for the “run to goal” task with ant). Instead, we found that training against random old versions of the opponent to work much better. Thus, during training, for each rollout for an agent we sample old parameters for the opponent. Fig. 2b shows the rewards for agents trained using this strategy. This leads to more stable training and more robust policies. We further analyze the effect of this opponent sampling in the experiments section. Note that for self-play this means that the policy at any time should be able to defeat random older versions of itself, thus ensuring continual learning. ", + "bbox": [ + 174, + 494, + 825, + 647 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5 EXPERIMENTS ", + "text_level": 1, + "bbox": [ + 176, + 667, + 326, + 684 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We train agents for the four competitive tasks using the training methods described previously. Our aim is to show that competitive multi-agent training provides a natural curriculum during learning which allows agents to learn complex behaviors. We provide additional training details and analyze various aspects of the competitive multi-agent training in this section. A highlight of the learned behaviors can be seen in the videos. Code for the environments as well as learned policy parameters for agents on all the environments are available: https://github.com/openai/multiagent-competition. ", + "bbox": [ + 174, + 699, + 825, + 784 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1 EXPERIMENTAL DETAILS ", + "text_level": 1, + "bbox": [ + 176, + 800, + 390, + 814 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Policies and Value Functions: We compare both MLP and LSTM for the policies and the value functions. MLP had 2 hidden layers with 128 units each. For LSTM networks, the input was first projected to a 128 dimensional embedding using a fully connected layer with ReLU activation which is then fed into a single-layer LSTM with 128 hidden state dimension and the output is projected to the action dimension using another fully connected layer. We used Gaussian policies with mean given by the output of the networks and a diagonal covariance matrix whose entries are also treated as trianable parameters. The policy outputs are clipped to lie within the control range. We used ", + "bbox": [ + 174, + 825, + 825, + 924 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "MLP policy and value functions for the run-to-goal and you-shall-not-pass environments, and LSTM policy and value function for sumo and kick-and-defend. This is because earlier experiments did not yield good results with MLP policy on these tasks. For LSTM policy we used truncated BPTT with a truncation of 10 timesteps. The policy and the value functions have separate parameters. For the asymmetric games, you-shall-not-pass and kick-and-defend, we use separate policies for the two agents in a game. ", + "bbox": [ + 174, + 103, + 825, + 188 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Observations: For the Ant body we use all the joint angles of the agent, its velocity of all its joints, the contact forces acting on the body and the relative position and all the joint angles for the opponent. For the Humanoid body, in addition to the above we also give the centre-of-mass based inertia tensor, velocity vector and the actuator forces for the body. In addition to these, there are other environment specific observations. For the Sumo environment, we give the torso’s orientation vector as the input, the radial distance from the edge of the ring of all the agents and the time remaining in the game. For kick-and-defend, we give the relative position of the ball from the agent, the relative distance of the ball from goal and the relative position of the ball from the two goal posts. Note that none of the agents observe the complete global state of the multi-agent world and only observe relevant sub-parts of the state vector to keep observations as close to real-world scenarios as possible. ", + "bbox": [ + 174, + 194, + 825, + 333 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Algorithm Parameters: We use Adam (Kingma & Ba, 2014) with learning rate 0.001. The clipping parameter in PPO $\\epsilon = 0 . 2$ , discounting factor $\\gamma = 0 . 9 9 5$ and generalized advantage estimate parameter $\\lambda = 0 . 9 5$ . Each iteration, we collect 409600 samples from the parallel rollouts and perform multiple epochs of PPO training in mini-batches consisting of 5120 samples. For MLP policies we did 6 epochs of SGD per iteration and for LSTM policies we did 3 epochs. We don’t use any entropy bonus. We found $l _ { 2 }$ regularization of the policy and value network parameters to be useful. The co-efficient $\\alpha _ { t }$ in eq. 1 for the exploration reward is annealed to 0 in 500 iterations for all the environments except for kick-and-defend in which it is annealed in 1000 iterations. ", + "bbox": [ + 174, + 340, + 825, + 450 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2 LEARNED BEHAVIORS ", + "text_level": 1, + "bbox": [ + 176, + 469, + 369, + 483 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We observe numerous interesting learned behaviors demonstrated by the agents as a result of the complexity arising out of the competitive multi-agent training. Different random seeds often lead to somewhat different behaviors. Refer to the videos for highlights of the learned policies on all the tasks. On Run-to-Goal, we observe the quadruped Ants demonstrate behaviors like blocking, standing robustly, using legs to topple the opponent and running towards the goal. Humanoids try to avoid each other and run towards their goal really fast, occasionally they will bump into each other with force and try to recover from the impact. On You-Shall-Not-Pass, we observe the blocking humanoid learn to block by raising its hand while the other humanoid eventually learned to duck in order to cross. On Sumo, we observe multiple different strategies used by the Ant and Humanoid. Humanoids, for example, demonstrate a stable fighting stance and learned to knock the opponent using their heads. In a different run, we observe that one agent learned to charge towards the opponent whereas the opponent tried to fool it by stepping out of the opponents way at the edge of the ring. On kick-and-defend, we observe that the kicker learned a good kicking policy where it can go towards random ball positions, uses its feet to kick the ball high and tries to avoid the defender. We also see a fooling behavior in the kicker’s motions where it moves left and right quickly once close to the ball to fool the defender. The defender learned to defend by moving in response to the motion of the kicker and using its hands and legs to obstruct the ball. ", + "bbox": [ + 174, + 496, + 825, + 732 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "These movement strategies are not just useful in competition, for example the skills learned in the Sumo can transfer to other situations even without other agents. In one case, we took the agent trained on the multi-agent Sumo task and faced it with the task of standing while being perturbed by wind forces. The agent receives the zero vector for parts of the opponent observation. We found that the agent managed to stay upright despite never seeing the windy environment or observing wind forces. Please see Appendix B.1 for details of the experiment and quantitative results. Refer to the video for a demonstration. ", + "bbox": [ + 174, + 739, + 823, + 837 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3 EFFECT OF EXPLORATION CURRICULUM", + "text_level": 1, + "bbox": [ + 174, + 854, + 495, + 869 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In section 4.1 we introduced an exploration curriculum to help agents explore in a 3D world. One question that arises is the extent to which the outcome of learning is affected by this exploration reward and to explore the benefit of this exploration reward. As already argued, we found the exploration reward to be crucial for learning as otherwise the agents are unable to explore the sparse competition reward. However, the learned behaviors are mostly a result of the natural curriculum arising out of the multi-agent competition and not due to the dense exploration reward. To see this, first note that we do not give any reward for many of the complex learned behaviours described previously. We further test this by not annealing the exploration reward and always having a dense reward which is a sum of the exploration reward and the competition reward. We take these agents trained without curriculum and pit them against agents trained with exploration curriculum. We plot the average win-rates over 800 games at various intervals during training in Fig. 3, for the sumo and kick-and-defend environments. For kick-and-defend there are two plots, one where kicker is trained with curriculum while keeper without it and vice versa. Observe that the agents trained with curriculum beat the non-curriculum agents by a margin. We found agents trained without curriculum exhibit either non-optimal behaviors for the competition or end up optimizing for a particular component of the dense reward. For example, for Sumo, the agents just learn to stand and move towards center of the arena, and for kick-and-defend, the defender optimizes for being able to stand up but doesn’t learn to defend while the kicker learns a non-optimal strategy of carrying the ball with itself to the goal (rather than kicking) – a policy which is easily defeated by a defender trained with curriculum. Moreover, training without curriculum also takes more samples to learn. We also show these behaviours qualitatively in the videos. These results echo some recent findings (albeit in the single agent case), like Andrychowicz et al. (2017) who found that optimizing for the sparse reward yields better return than optimizing for hand crafted dense rewards. For the competitive multi-agent case, these results shed further light on the importance of the natural curriculum. ", + "bbox": [ + 176, + 882, + 823, + 924 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b945f11d066fc08722a430402c33d364604cc71ecf37dc98786df3ca4e0addcf.jpg", + "image_caption": [ + "Figure 3: Effect for exploration curriculum: win-rate of agents trained by annealing the exploration reward against agents which constantly receive the dense exploration reward. The agents which optimized for the sparse competition reward benefit from the natural curriculum of multi-agent training and defeat the other agent by a margin. " + ], + "image_footnote": [], + "bbox": [ + 179, + 101, + 812, + 222 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/069c1227b382b2ce30262126022418f6704cfd94e0ce61369066d86c4670c2a2.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
8 1.0 0.8 0.51.0 - 0.36 0.360.8 0.37 1 0.390.5 0.35 0.38 10.0 0.29 0.33 0.33E[Win] 0.34 0.36 0.36
0.0 E[Loss]0.51 0.410.49 0.420.49 0.41- 0.320.50 1
", + "bbox": [ + 534, + 303, + 820, + 378 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/feb7f23a62523fe691a6ec555233a99c1dae552f0e8ed0d3a946c4e8fadbd1ee.jpg", + "table_caption": [ + "Table 1: The effect of opponent sampling. $\\mathbb { E } [ \\mathrm { L o s s } ]$ and $\\mathbb { E } [ \\mathrm { W i n } ]$ are the expected loss and win-rates for agents trained with a particular $\\delta$ as described in 5.4. For humanoid $\\delta \\ : = \\ : 0 . 5$ gives highest win-rate and lowest loss, whereas for Ant $\\delta = 0$ was best. " + ], + "table_footnote": [], + "table_body": "
81.00.80.50.0E[Win]
1.010.260.130.370.25
0.80.50.4610.220.520.400.630.35
0.590.5810.73
0.00.550.360.16-
E[Loss]0.530.400.170.541
", + "bbox": [ + 179, + 303, + 465, + 378 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "", + "bbox": [ + 173, + 478, + 825, + 768 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4 EFFECT OF OPPONENT SAMPLING ", + "text_level": 1, + "bbox": [ + 176, + 786, + 449, + 800 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In section 4.2, we introduced the past opponent sampling method for training competitive agents simultaneously. This choice of opponent could be important as it affects the natural curriculum for the agents. We test different opponent sampling strategies by considering a threshold on the oldest opponent for each agent. That is, instead of uniform random over the entire history, we can consider sampling opponent from $\\mathrm { U n i f o r m } ( \\delta v , v )$ where $v$ is the iteration number for the latest available parameters of the opponent and $\\delta \\in [ 0 , 1 ]$ is a threshold. Thus, $\\delta = 1 . 0$ corresponds to the latest available opponent and $\\delta = 0 . 0$ corresponds to uniform sampling over the entire history. We train agents on the Sumo task via self-play, using a $\\delta \\in \\{ 1 . 0 , 0 . 8 , \\bar { 0 . 5 } , \\bar { 0 . 0 } \\}$ and pit the four agents against each other to understand which sampling strategy leads to more robust policies. Since the agents have different skills and strengths at various points during training, we compute a Monte Carlo estimate of the expected win-rate for two agents that have seen the same number of samples taken at a random point during training. This is done by taking average of the win-rates of 30 agents at intervals of 100 iterations after a burn-in of 3000 iterations, where each win-rate is computed from an average over 800 episodes. Table 1a reports the results for Humanoid and Table 1b reports the results for Ant. First note that training against the latest opponent leads to worst performance, as argued earlier. Surprisingly, we found that uniform random $\\delta = 0 . 0$ ) over the entire history to have the highest win-rate for Ant and $\\delta = 0 . 5$ to have the highest win-rate for Humanoid. This could be because Ant with random policy on a small arena is still a good opponent while a Humanoid with random policy is unable to stand and thus always looses in a few steps. The differences in these win-rates for different sampling strategies show that the choice of the opponent during sampling is important and care must be taken while designing training algorithms for such competitive environments. ", + "bbox": [ + 174, + 813, + 825, + 924 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 104, + 825, + 284 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.5 LEARNING ROBUST POLICIES ", + "text_level": 1, + "bbox": [ + 176, + 304, + 419, + 318 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Over-fitting to a particular dataset is often a problem in supervised learning. Similar problems can arise in reinforcement learning setups when there is no or little variation in the environment. We discovered two such problems in our competitive multi-agent training framework and we analyze and propose solutions to address these issues. ", + "bbox": [ + 174, + 330, + 823, + 386 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.5.1 RANDOMIZATION IN WORLD ", + "text_level": 1, + "bbox": [ + 176, + 404, + 428, + 417 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In order to learn robust policies which generalize better we can introduce randomness in the environment, for example the arena radius for the sumo environment can be randomized, the ball position for the kick-and-defend environment can be randomized, agent start positions can be randomized. However, we found that while randomization is crucial to learn policies which generalize better, it might hinder learning early on as there might be too many things for the agents to explore. Indeed, we observe that in kick-and-defend the agents are unable to learn to kick with a lot of randomization in both the ball and agent positions, whereas when trained with no randomization the learned policies are overfit to the particular position of the ball (see Fig. 4). Thus, in order to learn policies that generalize well, we introduce a simple curriculum in the randomization where we start with a small amount of randomization which is easier to solve and then gradually increase the randomization during training. We found this curriculum to work well for all the environments. ", + "bbox": [ + 174, + 429, + 825, + 582 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.5.2 COMPETING AGAINST ENSEMBLE OF POLICIES ", + "text_level": 1, + "bbox": [ + 174, + 601, + 549, + 614 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Another related problem that we observed is over-fitting to the behavior of the opponent when trained for very long. This results in policies which are good against particular types of opponents but do not generalize to other opponents (say opponents trained with a different random seed). This overfitting can also be observed in win-rates against opponent during training, where one would see oscillations as agents try to adapt to their particular opponent and changes in their strategies. To overcome this we propose learning multiple policies simultaneously. Thus, there is a pool of policies and in each rollout for a particular policy one of the other policies is selected at random as the opponent (in symmetric games, the same policy can also be an opponent). This is similar to multi-task learning (Caruana, 1998) where the same network is used to model multiple related tasks which allows sharing of statistical strength among tasks and reduces overfitting. In this case, the pool of all policies as opponents – current and throughout the history of training – creates a natural distribution over related tasks for multi-task learning. We found random policy initialization to provide enough diversity between agent policies, however techniques that explicitly encourage diversity (Liu & Wang, 2016) can potentially be incorporated in the future. ", + "bbox": [ + 174, + 625, + 825, + 819 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In order to test the robustness of training policies in an ensemble, we experiment on the Sumo environment with Ant and Humanoid bodies. We train a pool of three policies in an ensemble and take the policy with the highest average training reward in the last 500 iterations as the best ensemble policy. We also train three independent policies via self-play, that is just a single policy is trained in a run, and again take the policy with the highest average training reward in last 500 iterations as the best self-play policy. Then we pit the best ensemble policy against the best self-play policy and record average win-rates over 800 games. Fig. 5 shows the win-rates over training iterations (after 1000 iterations of training). We find that training in ensemble performs significantly better for the humanoid body, whereas for ant the performance is similar to training a single policy. Again we suspect this is because there is not enough variability in the behavior of ant across different runs. While training single policies might occasionally get stuck in a local minima and learn suboptimal behaviors, we found that when training in an ensemble to be more robust to such minima. Qualitatively, we see more robust behavior of the humanoid trained in ensemble (see video). ", + "bbox": [ + 174, + 827, + 823, + 924 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/152bfacb47e873bf346837e201498b80a5c6447de979e7d7bfc9455e1f8b8c6a.jpg", + "image_caption": [ + "Figure 4: Win-rate of kicker vs iterations with full randomization " + ], + "image_footnote": [], + "bbox": [ + 176, + 113, + 346, + 207 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/f5e400e02f6c6d1d2a0808d79e102f4c6f33d5a9225e9a4aafd4f4d34c22885b.jpg", + "image_caption": [ + "Figure 5: $\\%$ Win-rate of agents trained in ensemble vs agents trained with just a single policy. Humanoid Sumo (left) and Ant Sumo (right). " + ], + "image_footnote": [], + "bbox": [ + 370, + 114, + 820, + 207 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 285, + 825, + 369 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6 CONCLUSION ", + "text_level": 1, + "bbox": [ + 176, + 388, + 318, + 405 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We have presented several new competitive multi-agent 3D physically simulated environments. We demonstrate the development of highly complex skills in simple environments with simple rewards. In future work, it would be interesting to conduct larger scale experiments in more complex environments that encourage agents to both compete and cooperate with each other. Incorporation of additional skills, such as reasoning about other agents, potentially via techniques from Foerster et al. (2017a), may also be important in our setting. 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", + "bbox": [ + 173, + 325, + 823, + 354 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "A EXPLORATION REWARDS ", + "text_level": 1, + "bbox": [ + 176, + 382, + 419, + 398 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "We define the dense exploration rewards used for the tasks in this section. Our exploration reward terms are based on adapting the rewards defined previously for the training humanoids and quadrupeds to walk (Duan et al., 2016; Schulman et al., 2015b). We first review this locomotion reward and then define the task-specific dense rewards. These rewards take the form $r _ { t } ( s , a ) = v _ { f w d } + c _ { t } ( s , a ) + C _ { a l i v e }$ where $v _ { f w d }$ is the velocity in the forward direction, a bonus for standing $C _ { a l i v e }$ and costs for impact and action $c _ { t } ( s , a )$ . We considered the following locomotion reward defined for Humanoid-v1 environment in OpenAI Gym package: ", + "bbox": [ + 173, + 414, + 825, + 512 + ], + "page_idx": 10 + }, + { + "type": "equation", + "img_path": "images/8271a92c7b2da20ed5c446c3f4511d88f0a02cb7e4fd2df531900c1362e14023.jpg", + "text": "$$\nr _ { t } ^ { h } ( s , a ) = v _ { f w d } + c ^ { h } ( s , a ) + C _ { a l i v e } = v _ { f w d } - 0 . 1 | a | | ^ { 2 } - 5 \\cdot 1 0 ^ { - 7 } | | F _ { i m p a c t } | | ^ { 2 } + C _ { a l i v e }\n$$", + "text_format": "latex", + "bbox": [ + 196, + 518, + 782, + 539 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "where $F _ { i m p a c t }$ is the contact force vector clipped to values between 1 and 1, and $C _ { a l i v e }$ is a bonus for the center of the body being at a certain height, defined as $C _ { a l i v e } = + 5$ if $2 . 0 \\geq z _ { b o d y } \\geq 1 . 0$ , else 0. ", + "bbox": [ + 174, + 545, + 825, + 588 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Similarly, the following is the reward for quadruped locomotion: ", + "bbox": [ + 174, + 594, + 598, + 609 + ], + "page_idx": 10 + }, + { + "type": "equation", + "img_path": "images/8f49cdb2b1d236de7d32e669a52e207c0a44f7e3f0cfb5c86d994125b69059ba.jpg", + "text": "$$\nr _ { t } ^ { q } ( s , a ) = v _ { f w d } + c ^ { q } ( s , a ) = v _ { f w d } - 0 . 5 | a | | ^ { 2 } - 5 \\cdot 1 0 ^ { - 4 } | | F _ { i m p a c t } | | ^ { 2 } + C _ { a l i v e }\n$$", + "text_format": "latex", + "bbox": [ + 238, + 614, + 759, + 633 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "where $C _ { a l i v e } = + 1$ if $1 . 0 \\geq z _ { b o d y } \\geq 0 . 2$ , else 0. ", + "bbox": [ + 174, + 640, + 491, + 656 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "In the following, superscript $h$ refers to humanoid agents and superscript $q$ refers to quadruped. We redefine $C _ { a l i v e }$ to be $+ 5$ if $z _ { b o d y } \\ge 1 . 0$ , else $- 5$ for humanoid, and $C _ { a l i v e } = + 1$ if $z _ { b o d y } \\ge 0 . 2 8$ else $- 1$ for quadruped. ", + "bbox": [ + 174, + 662, + 823, + 705 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Run to Goal For humanoids, reward is $r ^ { h } ( s , a ) - | x - g |$ where $x - g$ is the $l _ { 1 }$ distance of the agent from the goal $g$ along the $x$ -axis. For ant, reward is similar $r ^ { q } ( s , a ) - | x - g |$ . ", + "bbox": [ + 173, + 719, + 823, + 750 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "You Shall not Pass For the agent whose goal is to reach the other side, the reward is same as for run-to-goal. For the blocking agent, the reward for humanoid is $c ^ { h } ( s , a ) + C _ { a l i v e } + | x ^ { \\prime } - g |$ where $| x ^ { \\prime } - g |$ is the distance of opponent to the goal. ", + "bbox": [ + 174, + 765, + 823, + 808 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Sumo For humanoids, reward is $c ^ { h } ( s , a ) + C _ { a l i v e } - ( x ^ { 2 } + y ^ { 2 } ) ^ { 0 . 5 }$ , where the last term is distance from the center of the ring. Similarly for ant: $c ^ { q } ( s , a ) + C _ { a l i v e } - ( x ^ { 2 } + y ^ { 2 } ) ^ { 0 . 5 }$ ", + "bbox": [ + 173, + 821, + 821, + 853 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Kick and Defend: For kicker, reward is $r ^ { h } ( s , a ) - | | x - b | | - | b _ { x } - g |$ , where $b$ is the $( x , y )$ position of the ball, $b _ { x }$ is the $x$ -coordinate of the ball and $g$ is the $x$ -coordinate of the goal-post. For defender, reward is $c ^ { h } ( s , a ) + C _ { a l i v e } + | b _ { x } - g |$ where for $C _ { a l i v e }$ we only gave positive reward if the defender was in front of the goal area. ", + "bbox": [ + 174, + 867, + 823, + 924 + ], + "page_idx": 10 + }, + { + "type": "table", + "img_path": "images/f75253e2221d8b44fb99c2bd37b6851dec021ae2e228de525188c17d3b7ff086.jpg", + "table_caption": [ + "Table 2: Average number of steps before agent falls. Sumo Agent refers to the agent trained in Sumo environment whereas Walker Agent refers to the agent trained to walk in a single agent environment. " + ], + "table_footnote": [], + "table_body": "
Force Magnitude
200300400500600
Sumo Agent372 ± 146327±150247± 143181 ± 114123 ± 57
Walker Agent179± 54139± 42116± 32103±2395 ± 20
", + "bbox": [ + 222, + 101, + 774, + 160 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "B ADDITIONAL RESULTS ", + "text_level": 1, + "bbox": [ + 174, + 224, + 398, + 241 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "B.1 TRANSFER RESULTS ", + "text_level": 1, + "bbox": [ + 174, + 256, + 357, + 270 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "We took the agent trained on the multi-agent Sumo task and faced it with the task of standing while being perturbed by wind forces. The agent receives a zero vector for parts of the observation space which correspond to the opponent. We calculate the number of steps before the agent falls down (i.e. when $z _ { b o d y } \\le 0 . 5$ ) or the agent is pushed out of the arena and report the average steps over 200 episodes. Episodes last a maximum of 500 time steps. In half the episodes the wind force is applied in a radially outwards direction and in the remaining half it is applied in the radially inwards direction. We allow 50 steps for the agent to stabilize and apply the force at intervals of 50 steps where in between the intervals the force magnitude is decayed at a constant rate: ", + "bbox": [ + 173, + 281, + 825, + 393 + ], + "page_idx": 11 + }, + { + "type": "equation", + "img_path": "images/28957d3b59adcd66bdd352d2787ef82f430257231afb79ed6d116c37acc9b288.jpg", + "text": "$$\nF _ { t } = { \\left\\{ \\begin{array} { l l } { \\qquad F } & { { \\mathrm { i f ~ } } t \\equiv 0 { \\pmod { 5 0 } } } \\\\ { 0 . 9 * F _ { t - 1 } } & { { \\mathrm { o t h e r w i s e } } } \\end{array} \\right. }\n$$", + "text_format": "latex", + "bbox": [ + 351, + 398, + 635, + 434 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "where $F \\in \\{ 2 0 0 , 3 0 0 , 4 0 0 , 5 0 0 , 6 0 0 \\}$ . ", + "bbox": [ + 176, + 440, + 424, + 455 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "We compare with a humanoid agent trained in a single agent environment for the task of walking. We used same LSTM policy architecture as used for the Sumo agent and trained the humanoid in the publicly available OpenAI Gym Humanoid-v1 environment using PPO. We then apply force on this agent using the same method as above where the direction of the force is in the direction the agent is walking in half the episodes and opposite to it in the remaining half. We record average number of steps to fall using the same condition as for the Sumo agent. ", + "bbox": [ + 173, + 455, + 825, + 539 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "Table 2 shows the average number of steps over 200 episodes along with the standard deviation. We see that the humanoid trained in Sumo is more robust to adversarial forces and able to withstand large magnitude of force for many steps. 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Normally, the complexity of the trained agent is", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 141, + 234, + 469, + 247 + ], + "spans": [ + { + "bbox": [ + 141, + 234, + 469, + 247 + ], + "score": 1.0, + "content": "closely related to the complexity of the environment. This suggests that a highly", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 141, + 245, + 470, + 258 + ], + "spans": [ + { + "bbox": [ + 141, + 245, + 470, + 258 + ], + "score": 1.0, + "content": "capable agent requires a complex environment for training. In this paper, we point", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 141, + 257, + 470, + 268 + ], + "spans": [ + { + "bbox": [ + 141, + 257, + 470, + 268 + ], + "score": 1.0, + "content": "out that a competitive multi-agent environment trained with self-play can produce", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 141, + 266, + 470, + 280 + ], + "spans": [ + { + "bbox": [ + 141, + 266, + 470, + 280 + ], + "score": 1.0, + "content": "behaviors that are far more complex than the environment itself. We also point out", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 141, + 278, + 469, + 290 + ], + "spans": [ + { + "bbox": [ + 141, + 278, + 469, + 290 + ], + "score": 1.0, + "content": "that such environments come with a natural curriculum, because for any skill level,", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 141, + 288, + 459, + 302 + ], + "spans": [ + { + "bbox": [ + 141, + 288, + 459, + 302 + ], + "score": 1.0, + "content": "an environment full of agents of this level will have the right level of difficulty.", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 16.5 + }, + { + "type": "text", + "bbox": [ + 143, + 302, + 468, + 379 + ], + "lines": [ + { + "bbox": [ + 142, + 302, + 469, + 315 + ], + "spans": [ + { + "bbox": [ + 142, + 302, + 469, + 315 + ], + "score": 1.0, + "content": "This work introduces several competitive multi-agent environments where agents", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 141, + 312, + 470, + 326 + ], + "spans": [ + { + "bbox": [ + 141, + 312, + 470, + 326 + ], + "score": 1.0, + "content": "compete in a 3D world with simulated physics. The trained agents learn a", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 141, + 324, + 470, + 336 + ], + "spans": [ + { + "bbox": [ + 141, + 324, + 470, + 336 + ], + "score": 1.0, + "content": "wide variety of complex and interesting skills, even though the environment", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 141, + 334, + 470, + 348 + ], + "spans": [ + { + "bbox": [ + 141, + 334, + 470, + 348 + ], + "score": 1.0, + "content": "themselves are relatively simple. The skills include behaviors such as running,", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 141, + 345, + 470, + 359 + ], + "spans": [ + { + "bbox": [ + 141, + 345, + 470, + 359 + ], + "score": 1.0, + "content": "blocking, ducking, tackling, fooling opponents, kicking, and defending using", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 141, + 356, + 469, + 369 + ], + "spans": [ + { + "bbox": [ + 141, + 356, + 469, + 369 + ], + "score": 1.0, + "content": "both arms and legs. A highlight of the learned behaviors can be found here:", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 141, + 367, + 234, + 380 + ], + "spans": [ + { + "bbox": [ + 141, + 367, + 234, + 380 + ], + "score": 1.0, + "content": "https://goo.gl/eR7fbX.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 24 + }, + { + "type": "title", + "bbox": [ + 108, + 401, + 206, + 414 + ], + "lines": [ + { + "bbox": [ + 105, + 400, + 208, + 416 + ], + "spans": [ + { + "bbox": [ + 105, + 400, + 208, + 416 + ], + "score": 1.0, + "content": "1 INTRODUCTION", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 28 + }, + { + "type": "text", + "bbox": [ + 107, + 426, + 505, + 503 + ], + "lines": [ + { + "bbox": [ + 105, + 426, + 505, + 438 + ], + "spans": [ + { + "bbox": [ + 105, + 426, + 505, + 438 + ], + "score": 1.0, + "content": "Reinforcement Learning (RL) is exciting because good reinforcement learning algorithms exist", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 437, + 505, + 450 + ], + "spans": [ + { + "bbox": [ + 106, + 437, + 505, + 450 + ], + "score": 1.0, + "content": "(Mnih et al., 2015; Silver et al., 2016; Schulman et al., 2015a; Mnih et al., 2016; Schulman et al.,", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 448, + 505, + 460 + ], + "spans": [ + { + "bbox": [ + 106, + 448, + 505, + 460 + ], + "score": 1.0, + "content": "2015b; Lillicrap et al., 2015; Schulman et al., 2017), allowing us to train agents that accomplish a", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 459, + 505, + 472 + ], + "spans": [ + { + "bbox": [ + 105, + 459, + 505, + 472 + ], + "score": 1.0, + "content": "great variety of interesting tasks. We can train an agent to play Atari games from pixels (Mnih et al.,", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 470, + 505, + 483 + ], + "spans": [ + { + "bbox": [ + 105, + 470, + 505, + 483 + ], + "score": 1.0, + "content": "2015) or get humanoids to walk (Schulman et al., 2017). RL is exciting partly because it is easy", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 481, + 505, + 494 + ], + "spans": [ + { + "bbox": [ + 105, + 481, + 505, + 494 + ], + "score": 1.0, + "content": "to envision an RL algorithm producing a broadly competent agent when trained on an appropriate", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 493, + 222, + 504 + ], + "spans": [ + { + "bbox": [ + 106, + 493, + 222, + 504 + ], + "score": 1.0, + "content": "curriculum of environments.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 32 + }, + { + "type": "text", + "bbox": [ + 107, + 510, + 505, + 652 + ], + "lines": [ + { + "bbox": [ + 106, + 510, + 504, + 522 + ], + "spans": [ + { + "bbox": [ + 106, + 510, + 504, + 522 + ], + "score": 1.0, + "content": "In general, training an agent to perform a highly complex task requires a highly complex environ-", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 520, + 505, + 532 + ], + "spans": [ + { + "bbox": [ + 105, + 520, + 505, + 532 + ], + "score": 1.0, + "content": "ment, and these can be difficult to create. 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Such environments have two", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 554, + 505, + 566 + ], + "spans": [ + { + "bbox": [ + 106, + 554, + 505, + 566 + ], + "score": 1.0, + "content": "very attractive properties: (1) Even very simple competitive multi-agent environments can produce", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 564, + 505, + 577 + ], + "spans": [ + { + "bbox": [ + 105, + 564, + 505, + 577 + ], + "score": 1.0, + "content": "extremely complex behaviors. For example, the game of Go has very simple rules, but the strategies", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 576, + 505, + 588 + ], + "spans": [ + { + "bbox": [ + 105, + 576, + 505, + 588 + ], + "score": 1.0, + "content": "needed to win are extremely complex. This is because the complexity of these environments is pro-", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 585, + 505, + 599 + ], + "spans": [ + { + "bbox": [ + 105, + 585, + 505, + 599 + ], + "score": 1.0, + "content": "duced by the competing agents that act in it. Thus, as the other agents become more competent, the", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 596, + 506, + 611 + ], + "spans": [ + { + "bbox": [ + 105, + 596, + 506, + 611 + ], + "score": 1.0, + "content": "environment effectively becomes more complex. (2) When trained with self-play, the competitive", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 607, + 506, + 622 + ], + "spans": [ + { + "bbox": [ + 105, + 607, + 506, + 622 + ], + "score": 1.0, + "content": "multi-agent environment provides the agents with a perfect curriculum. This happens because no", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 619, + 505, + 632 + ], + "spans": [ + { + "bbox": [ + 105, + 619, + 505, + 632 + ], + "score": 1.0, + "content": "matter how weak or strong an agent is, an environment populated with other agents of comparable", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 104, + 628, + 505, + 645 + ], + "spans": [ + { + "bbox": [ + 104, + 628, + 505, + 645 + ], + "score": 1.0, + "content": "strength provides the right challenge to the agent, facilitating maximally rapid learning and avoiding", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 641, + 162, + 654 + ], + "spans": [ + { + "bbox": [ + 105, + 641, + 162, + 654 + ], + "score": 1.0, + "content": "getting stuck.", + "type": "text" + } + ], + "index": 48 + } + ], + "index": 42 + }, + { + "type": "text", + "bbox": [ + 107, + 658, + 504, + 713 + ], + "lines": [ + { + "bbox": [ + 106, + 658, + 505, + 669 + ], + "spans": [ + { + "bbox": [ + 106, + 658, + 505, + 669 + ], + "score": 1.0, + "content": "Self-play in competitive multi-agent environments is not a new idea – it has already been explored", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 106, + 669, + 504, + 681 + ], + "spans": [ + { + "bbox": [ + 106, + 669, + 504, + 681 + ], + "score": 1.0, + "content": "in TD-gammon (Tesauro, 1995) and refined in AlphaGo (Silver et al., 2016) and Dota 2 (OpenAI).", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 105, + 679, + 505, + 692 + ], + "spans": [ + { + "bbox": [ + 105, + 679, + 505, + 692 + ], + "score": 1.0, + "content": "In both cases, the resulting behavior was far more complex than the environment itself, and the", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 105, + 691, + 506, + 704 + ], + "spans": [ + { + "bbox": [ + 105, + 691, + 506, + 704 + ], + "score": 1.0, + "content": "self-play approach provided the agents with a perfectly tuned curriculum for each task. In this", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 105, + 701, + 506, + 715 + ], + "spans": [ + { + "bbox": [ + 105, + 701, + 506, + 715 + ], + "score": 1.0, + "content": "paper, we investigate whether the idea of competitive multi-agent environments can yield fruit in", + "type": "text" + } + ], + "index": 53 + } + ], + "index": 51 + } + ], + "page_idx": 0, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 116, + 722, + 429, + 731 + ], + "lines": [ + { + "bbox": [ + 118, + 720, + 430, + 733 + ], + "spans": [ + { + "bbox": [ + 118, + 720, + 430, + 733 + ], + "score": 1.0, + "content": "∗Work done as an intern at OpenAI. Correspondence to tbansal@cs.umass.edu", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 107, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2018", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 752, + 308, + 760 + ], + "lines": [ + { + "bbox": [ + 302, + 751, + 309, + 762 + ], + "spans": [ + { + "bbox": [ + 302, + 751, + 309, + 762 + ], + "score": 1.0, + "content": "1", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 107, + 79, + 441, + 115 + ], + "lines": [ + { + "bbox": [ + 105, + 77, + 442, + 97 + ], + "spans": [ + { + "bbox": [ + 105, + 77, + 442, + 97 + ], + "score": 1.0, + "content": "EMERGENT COMPLEXITY VIA MULTI-AGENT", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 98, + 215, + 118 + ], + "spans": [ + { + "bbox": [ + 106, + 98, + 215, + 118 + ], + "score": 1.0, + "content": "COMPETITION", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "text", + "bbox": [ + 113, + 135, + 179, + 157 + ], + "lines": [ + { + "bbox": [ + 111, + 135, + 177, + 147 + ], + "spans": [ + { + "bbox": [ + 111, + 135, + 177, + 147 + ], + "score": 1.0, + "content": "Trapit Bansal∗", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 112, + 146, + 181, + 158 + ], + "spans": [ + { + "bbox": [ + 112, + 146, + 181, + 158 + ], + "score": 1.0, + "content": "UMass Amherst", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 2.5, + "bbox_fs": [ + 111, + 135, + 181, + 158 + ] + }, + { + "type": "text", + "bbox": [ + 194, + 135, + 263, + 158 + ], + "lines": [ + { + "bbox": [ + 192, + 135, + 264, + 147 + ], + "spans": [ + { + "bbox": [ + 192, + 135, + 264, + 147 + ], + "score": 1.0, + "content": "Jakub Pachocki", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 191, + 145, + 229, + 159 + ], + "spans": [ + { + "bbox": [ + 191, + 145, + 229, + 159 + ], + "score": 1.0, + "content": "OpenAI", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4.5, + "bbox_fs": [ + 191, + 135, + 264, + 159 + ] + }, + { + "type": "text", + "bbox": [ + 277, + 136, + 338, + 158 + ], + "lines": [ + { + "bbox": [ + 276, + 135, + 339, + 148 + ], + "spans": [ + { + "bbox": [ + 276, + 135, + 339, + 148 + ], + "score": 1.0, + "content": "Szymon Sidor", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 275, + 145, + 313, + 159 + ], + "spans": [ + { + "bbox": [ + 275, + 145, + 313, + 159 + ], + "score": 1.0, + "content": "OpenAI", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 6.5, + "bbox_fs": [ + 275, + 135, + 339, + 159 + ] + }, + { + "type": "text", + "bbox": [ + 352, + 136, + 415, + 158 + ], + "lines": [ + { + "bbox": [ + 352, + 134, + 417, + 148 + ], + "spans": [ + { + "bbox": [ + 352, + 134, + 417, + 148 + ], + "score": 1.0, + "content": "Ilya Sutskever", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 351, + 145, + 388, + 159 + ], + "spans": [ + { + "bbox": [ + 351, + 145, + 388, + 159 + ], + "score": 1.0, + "content": "OpenAI", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 8.5, + "bbox_fs": [ + 351, + 134, + 417, + 159 + ] + }, + { + "type": "text", + "bbox": [ + 428, + 136, + 494, + 158 + ], + "lines": [ + { + "bbox": [ + 428, + 134, + 495, + 147 + ], + "spans": [ + { + "bbox": [ + 428, + 134, + 495, + 147 + ], + "score": 1.0, + "content": "Igor Mordatch", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 428, + 145, + 465, + 160 + ], + "spans": [ + { + "bbox": [ + 428, + 145, + 465, + 160 + ], + "score": 1.0, + "content": "OpenAI", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 10.5, + "bbox_fs": [ + 428, + 134, + 495, + 160 + ] + }, + { + "type": "title", + "bbox": [ + 278, + 187, + 333, + 199 + ], + "lines": [ + { + "bbox": [ + 276, + 185, + 336, + 201 + ], + "spans": [ + { + "bbox": [ + 276, + 185, + 336, + 201 + ], + "score": 1.0, + "content": "ABSTRACT", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 12 + }, + { + "type": "text", + "bbox": [ + 143, + 212, + 468, + 300 + ], + "lines": [ + { + "bbox": [ + 142, + 213, + 469, + 225 + ], + "spans": [ + { + "bbox": [ + 142, + 213, + 469, + 225 + ], + "score": 1.0, + "content": "Reinforcement learning algorithms can train agents that solve problems in com-", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 141, + 223, + 469, + 235 + ], + "spans": [ + { + "bbox": [ + 141, + 223, + 469, + 235 + ], + "score": 1.0, + "content": "plex, interesting environments. Normally, the complexity of the trained agent is", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 141, + 234, + 469, + 247 + ], + "spans": [ + { + "bbox": [ + 141, + 234, + 469, + 247 + ], + "score": 1.0, + "content": "closely related to the complexity of the environment. This suggests that a highly", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 141, + 245, + 470, + 258 + ], + "spans": [ + { + "bbox": [ + 141, + 245, + 470, + 258 + ], + "score": 1.0, + "content": "capable agent requires a complex environment for training. In this paper, we point", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 141, + 257, + 470, + 268 + ], + "spans": [ + { + "bbox": [ + 141, + 257, + 470, + 268 + ], + "score": 1.0, + "content": "out that a competitive multi-agent environment trained with self-play can produce", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 141, + 266, + 470, + 280 + ], + "spans": [ + { + "bbox": [ + 141, + 266, + 470, + 280 + ], + "score": 1.0, + "content": "behaviors that are far more complex than the environment itself. We also point out", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 141, + 278, + 469, + 290 + ], + "spans": [ + { + "bbox": [ + 141, + 278, + 469, + 290 + ], + "score": 1.0, + "content": "that such environments come with a natural curriculum, because for any skill level,", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 141, + 288, + 459, + 302 + ], + "spans": [ + { + "bbox": [ + 141, + 288, + 459, + 302 + ], + "score": 1.0, + "content": "an environment full of agents of this level will have the right level of difficulty.", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 16.5, + "bbox_fs": [ + 141, + 213, + 470, + 302 + ] + }, + { + "type": "text", + "bbox": [ + 143, + 302, + 468, + 379 + ], + "lines": [ + { + "bbox": [ + 142, + 302, + 469, + 315 + ], + "spans": [ + { + "bbox": [ + 142, + 302, + 469, + 315 + ], + "score": 1.0, + "content": "This work introduces several competitive multi-agent environments where agents", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 141, + 312, + 470, + 326 + ], + "spans": [ + { + "bbox": [ + 141, + 312, + 470, + 326 + ], + "score": 1.0, + "content": "compete in a 3D world with simulated physics. The trained agents learn a", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 141, + 324, + 470, + 336 + ], + "spans": [ + { + "bbox": [ + 141, + 324, + 470, + 336 + ], + "score": 1.0, + "content": "wide variety of complex and interesting skills, even though the environment", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 141, + 334, + 470, + 348 + ], + "spans": [ + { + "bbox": [ + 141, + 334, + 470, + 348 + ], + "score": 1.0, + "content": "themselves are relatively simple. The skills include behaviors such as running,", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 141, + 345, + 470, + 359 + ], + "spans": [ + { + "bbox": [ + 141, + 345, + 470, + 359 + ], + "score": 1.0, + "content": "blocking, ducking, tackling, fooling opponents, kicking, and defending using", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 141, + 356, + 469, + 369 + ], + "spans": [ + { + "bbox": [ + 141, + 356, + 469, + 369 + ], + "score": 1.0, + "content": "both arms and legs. A highlight of the learned behaviors can be found here:", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 141, + 367, + 234, + 380 + ], + "spans": [ + { + "bbox": [ + 141, + 367, + 234, + 380 + ], + "score": 1.0, + "content": "https://goo.gl/eR7fbX.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 24, + "bbox_fs": [ + 141, + 302, + 470, + 380 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 401, + 206, + 414 + ], + "lines": [ + { + "bbox": [ + 105, + 400, + 208, + 416 + ], + "spans": [ + { + "bbox": [ + 105, + 400, + 208, + 416 + ], + "score": 1.0, + "content": "1 INTRODUCTION", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 28 + }, + { + "type": "text", + "bbox": [ + 107, + 426, + 505, + 503 + ], + "lines": [ + { + "bbox": [ + 105, + 426, + 505, + 438 + ], + "spans": [ + { + "bbox": [ + 105, + 426, + 505, + 438 + ], + "score": 1.0, + "content": "Reinforcement Learning (RL) is exciting because good reinforcement learning algorithms exist", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 437, + 505, + 450 + ], + "spans": [ + { + "bbox": [ + 106, + 437, + 505, + 450 + ], + "score": 1.0, + "content": "(Mnih et al., 2015; Silver et al., 2016; Schulman et al., 2015a; Mnih et al., 2016; Schulman et al.,", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 448, + 505, + 460 + ], + "spans": [ + { + "bbox": [ + 106, + 448, + 505, + 460 + ], + "score": 1.0, + "content": "2015b; Lillicrap et al., 2015; Schulman et al., 2017), allowing us to train agents that accomplish a", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 459, + 505, + 472 + ], + "spans": [ + { + "bbox": [ + 105, + 459, + 505, + 472 + ], + "score": 1.0, + "content": "great variety of interesting tasks. We can train an agent to play Atari games from pixels (Mnih et al.,", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 470, + 505, + 483 + ], + "spans": [ + { + "bbox": [ + 105, + 470, + 505, + 483 + ], + "score": 1.0, + "content": "2015) or get humanoids to walk (Schulman et al., 2017). RL is exciting partly because it is easy", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 481, + 505, + 494 + ], + "spans": [ + { + "bbox": [ + 105, + 481, + 505, + 494 + ], + "score": 1.0, + "content": "to envision an RL algorithm producing a broadly competent agent when trained on an appropriate", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 493, + 222, + 504 + ], + "spans": [ + { + "bbox": [ + 106, + 493, + 222, + 504 + ], + "score": 1.0, + "content": "curriculum of environments.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 32, + "bbox_fs": [ + 105, + 426, + 505, + 504 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 510, + 505, + 652 + ], + "lines": [ + { + "bbox": [ + 106, + 510, + 504, + 522 + ], + "spans": [ + { + "bbox": [ + 106, + 510, + 504, + 522 + ], + "score": 1.0, + "content": "In general, training an agent to perform a highly complex task requires a highly complex environ-", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 520, + 505, + 532 + ], + "spans": [ + { + "bbox": [ + 105, + 520, + 505, + 532 + ], + "score": 1.0, + "content": "ment, and these can be difficult to create. However, there exists a class of environments where the", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 532, + 505, + 543 + ], + "spans": [ + { + "bbox": [ + 106, + 532, + 505, + 543 + ], + "score": 1.0, + "content": "behavior produced by the agents can be far more complex than the environments; this is the class", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 541, + 506, + 556 + ], + "spans": [ + { + "bbox": [ + 105, + 541, + 506, + 556 + ], + "score": 1.0, + "content": "of the competitive multi-agent environments trained with self-play. Such environments have two", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 554, + 505, + 566 + ], + "spans": [ + { + "bbox": [ + 106, + 554, + 505, + 566 + ], + "score": 1.0, + "content": "very attractive properties: (1) Even very simple competitive multi-agent environments can produce", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 564, + 505, + 577 + ], + "spans": [ + { + "bbox": [ + 105, + 564, + 505, + 577 + ], + "score": 1.0, + "content": "extremely complex behaviors. For example, the game of Go has very simple rules, but the strategies", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 576, + 505, + 588 + ], + "spans": [ + { + "bbox": [ + 105, + 576, + 505, + 588 + ], + "score": 1.0, + "content": "needed to win are extremely complex. This is because the complexity of these environments is pro-", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 585, + 505, + 599 + ], + "spans": [ + { + "bbox": [ + 105, + 585, + 505, + 599 + ], + "score": 1.0, + "content": "duced by the competing agents that act in it. Thus, as the other agents become more competent, the", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 596, + 506, + 611 + ], + "spans": [ + { + "bbox": [ + 105, + 596, + 506, + 611 + ], + "score": 1.0, + "content": "environment effectively becomes more complex. (2) When trained with self-play, the competitive", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 607, + 506, + 622 + ], + "spans": [ + { + "bbox": [ + 105, + 607, + 506, + 622 + ], + "score": 1.0, + "content": "multi-agent environment provides the agents with a perfect curriculum. This happens because no", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 619, + 505, + 632 + ], + "spans": [ + { + "bbox": [ + 105, + 619, + 505, + 632 + ], + "score": 1.0, + "content": "matter how weak or strong an agent is, an environment populated with other agents of comparable", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 104, + 628, + 505, + 645 + ], + "spans": [ + { + "bbox": [ + 104, + 628, + 505, + 645 + ], + "score": 1.0, + "content": "strength provides the right challenge to the agent, facilitating maximally rapid learning and avoiding", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 641, + 162, + 654 + ], + "spans": [ + { + "bbox": [ + 105, + 641, + 162, + 654 + ], + "score": 1.0, + "content": "getting stuck.", + "type": "text" + } + ], + "index": 48 + } + ], + "index": 42, + "bbox_fs": [ + 104, + 510, + 506, + 654 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 658, + 504, + 713 + ], + "lines": [ + { + "bbox": [ + 106, + 658, + 505, + 669 + ], + "spans": [ + { + "bbox": [ + 106, + 658, + 505, + 669 + ], + "score": 1.0, + "content": "Self-play in competitive multi-agent environments is not a new idea – it has already been explored", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 106, + 669, + 504, + 681 + ], + "spans": [ + { + "bbox": [ + 106, + 669, + 504, + 681 + ], + "score": 1.0, + "content": "in TD-gammon (Tesauro, 1995) and refined in AlphaGo (Silver et al., 2016) and Dota 2 (OpenAI).", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 105, + 679, + 505, + 692 + ], + "spans": [ + { + "bbox": [ + 105, + 679, + 505, + 692 + ], + "score": 1.0, + "content": "In both cases, the resulting behavior was far more complex than the environment itself, and the", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 105, + 691, + 506, + 704 + ], + "spans": [ + { + "bbox": [ + 105, + 691, + 506, + 704 + ], + "score": 1.0, + "content": "self-play approach provided the agents with a perfectly tuned curriculum for each task. In this", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 105, + 701, + 506, + 715 + ], + "spans": [ + { + "bbox": [ + 105, + 701, + 506, + 715 + ], + "score": 1.0, + "content": "paper, we investigate whether the idea of competitive multi-agent environments can yield fruit in", + "type": "text" + } + ], + "index": 53 + }, + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "other domains: specifically, in the domain of continuous control, where balance, dexterity, and", + "type": "text", + "cross_page": true + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 94, + 234, + 105 + ], + "spans": [ + { + "bbox": [ + 106, + 94, + 234, + 105 + ], + "score": 1.0, + "content": "manipulation are the key skills.", + "type": "text", + "cross_page": true + } + ], + "index": 1 + } + ], + "index": 51, + "bbox_fs": [ + 105, + 658, + 506, + 715 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 82, + 504, + 105 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "other domains: specifically, in the domain of continuous control, where balance, dexterity, and", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 94, + 234, + 105 + ], + "spans": [ + { + "bbox": [ + 106, + 94, + 234, + 105 + ], + "score": 1.0, + "content": "manipulation are the key skills.", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "text", + "bbox": [ + 106, + 110, + 505, + 221 + ], + "lines": [ + { + "bbox": [ + 105, + 110, + 505, + 123 + ], + "spans": [ + { + "bbox": [ + 105, + 110, + 505, + 123 + ], + "score": 1.0, + "content": "In more detail, we introduce several multi-agent tasks with competing goals in a 3D world with sim-", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 122, + 505, + 133 + ], + "spans": [ + { + "bbox": [ + 106, + 122, + 505, + 133 + ], + "score": 1.0, + "content": "ulated physics, using the MuJoCo framework (Todorov et al., 2012), where the agents would need", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 133, + 505, + 144 + ], + "spans": [ + { + "bbox": [ + 106, + 133, + 505, + 144 + ], + "score": 1.0, + "content": "to learn highly developed motor skills in order to succeed in the competitive environment. We train", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 143, + 505, + 156 + ], + "spans": [ + { + "bbox": [ + 106, + 143, + 505, + 156 + ], + "score": 1.0, + "content": "the agents using a distributed implementation of a recent policy gradient algorithm, Proximal Policy", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 154, + 505, + 167 + ], + "spans": [ + { + "bbox": [ + 106, + 154, + 505, + 167 + ], + "score": 1.0, + "content": "Optimization (Schulman et al., 2017). By adding a simple exploration curriculum to aid exploration", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 164, + 505, + 178 + ], + "spans": [ + { + "bbox": [ + 105, + 164, + 505, + 178 + ], + "score": 1.0, + "content": "in the environment we find that agents learn a high level of dexterity in order to achieve their goals,", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 176, + 504, + 188 + ], + "spans": [ + { + "bbox": [ + 106, + 176, + 504, + 188 + ], + "score": 1.0, + "content": "in particular we find numerous emergent skills for which it may be difficult to engineer a reward.", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 186, + 505, + 201 + ], + "spans": [ + { + "bbox": [ + 105, + 186, + 505, + 201 + ], + "score": 1.0, + "content": "Specifically, the agents learned a wide variety of skills and behaviors that include running, blocking,", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 198, + 505, + 211 + ], + "spans": [ + { + "bbox": [ + 106, + 198, + 505, + 211 + ], + "score": 1.0, + "content": "ducking, tackling, fooling opponents, kicking, and defending using arms and legs. Highlight of the", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 209, + 428, + 222 + ], + "spans": [ + { + "bbox": [ + 105, + 209, + 428, + 222 + ], + "score": 1.0, + "content": "learned behaviors on the various tasks can be found here: https://goo.gl/eR7fbX", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 6.5 + }, + { + "type": "title", + "bbox": [ + 108, + 238, + 208, + 250 + ], + "lines": [ + { + "bbox": [ + 105, + 237, + 209, + 253 + ], + "spans": [ + { + "bbox": [ + 105, + 237, + 209, + 253 + ], + "score": 1.0, + "content": "2 PRELIMINARIES", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 12 + }, + { + "type": "text", + "bbox": [ + 107, + 264, + 502, + 286 + ], + "lines": [ + { + "bbox": [ + 106, + 264, + 504, + 277 + ], + "spans": [ + { + "bbox": [ + 106, + 264, + 504, + 277 + ], + "score": 1.0, + "content": "In this section, we review some background on policy gradient methods, Proximal Policy Optimiza-", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 274, + 395, + 288 + ], + "spans": [ + { + "bbox": [ + 105, + 274, + 395, + 288 + ], + "score": 1.0, + "content": "tion and related work in the multi-agent reinforcement learning domain.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 13.5 + }, + { + "type": "text", + "bbox": [ + 106, + 291, + 505, + 405 + ], + "lines": [ + { + "bbox": [ + 105, + 291, + 506, + 305 + ], + "spans": [ + { + "bbox": [ + 105, + 291, + 465, + 305 + ], + "score": 1.0, + "content": "Notation: We consider multi-agent Markov games (Littman, 1994). A Markov game for", + "type": "text" + }, + { + "bbox": [ + 466, + 293, + 476, + 302 + ], + "score": 0.82, + "content": "N", + "type": "inline_equation" + }, + { + "bbox": [ + 476, + 291, + 506, + 305 + ], + "score": 1.0, + "content": "agents", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 302, + 505, + 316 + ], + "spans": [ + { + "bbox": [ + 105, + 302, + 451, + 316 + ], + "score": 1.0, + "content": "is a partially observable Markov decision process (MDP) defined by: a set of states", + "type": "text" + }, + { + "bbox": [ + 451, + 304, + 459, + 313 + ], + "score": 0.79, + "content": "s", + "type": "inline_equation" + }, + { + "bbox": [ + 460, + 302, + 505, + 316 + ], + "score": 1.0, + "content": "describing", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 313, + 505, + 326 + ], + "spans": [ + { + "bbox": [ + 105, + 313, + 505, + 326 + ], + "score": 1.0, + "content": "the state of the world and the possible joint configuration of all the agents, a set of observations", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 107, + 321, + 505, + 339 + ], + "spans": [ + { + "bbox": [ + 107, + 324, + 158, + 336 + ], + "score": 0.89, + "content": "\\mathcal { O } ^ { 1 } , \\ldots , \\mathcal { O } ^ { N }", + "type": "inline_equation" + }, + { + "bbox": [ + 159, + 321, + 345, + 339 + ], + "score": 1.0, + "content": "of each agent, a set of actions of each agent", + "type": "text" + }, + { + "bbox": [ + 346, + 324, + 397, + 336 + ], + "score": 0.93, + "content": "\\mathcal { A } ^ { 1 } , \\ldots , \\mathcal { A } ^ { \\tilde { N } }", + "type": "inline_equation" + }, + { + "bbox": [ + 397, + 321, + 487, + 339 + ], + "score": 1.0, + "content": ", a transition function", + "type": "text" + }, + { + "bbox": [ + 487, + 325, + 505, + 336 + ], + "score": 0.41, + "content": "\\tau :", + "type": "inline_equation" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 333, + 506, + 350 + ], + "spans": [ + { + "bbox": [ + 106, + 335, + 192, + 347 + ], + "score": 0.9, + "content": "\\mathcal { S } \\times \\mathcal { A } ^ { 1 } \\cdot \\cdot \\cdot \\mathcal { A } ^ { N } \\to \\mathcal { S }", + "type": "inline_equation" + }, + { + "bbox": [ + 193, + 333, + 472, + 350 + ], + "score": 1.0, + "content": "determining distribution over next states, and a reward for each agent", + "type": "text" + }, + { + "bbox": [ + 472, + 337, + 477, + 346 + ], + "score": 0.73, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 478, + 333, + 506, + 350 + ], + "score": 1.0, + "content": "which", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 104, + 346, + 505, + 360 + ], + "spans": [ + { + "bbox": [ + 104, + 346, + 303, + 360 + ], + "score": 1.0, + "content": "is a function of the state and the agent’s action", + "type": "text" + }, + { + "bbox": [ + 303, + 347, + 383, + 357 + ], + "score": 0.91, + "content": "r ^ { i } : \\mathcal { S } \\times \\mathcal { A } ^ { i } \\to \\mathbb { R }", + "type": "inline_equation" + }, + { + "bbox": [ + 383, + 346, + 505, + 360 + ], + "score": 1.0, + "content": ". Agents choose their actions", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 357, + 505, + 371 + ], + "spans": [ + { + "bbox": [ + 105, + 357, + 235, + 371 + ], + "score": 1.0, + "content": "according to a stochastic policy", + "type": "text" + }, + { + "bbox": [ + 236, + 357, + 331, + 370 + ], + "score": 0.92, + "content": "\\pi _ { \\theta ^ { i } } : \\mathcal { O } ^ { i } \\times \\mathcal { A } ^ { i } [ 0 , 1 ]", + "type": "inline_equation" + }, + { + "bbox": [ + 332, + 357, + 362, + 371 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 363, + 358, + 372, + 368 + ], + "score": 0.85, + "content": "\\theta ^ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 372, + 357, + 505, + 371 + ], + "score": 1.0, + "content": "are the parameters of the policy.", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 367, + 505, + 381 + ], + "spans": [ + { + "bbox": [ + 105, + 367, + 308, + 381 + ], + "score": 1.0, + "content": "For continuous control problems considered here,", + "type": "text" + }, + { + "bbox": [ + 309, + 371, + 320, + 380 + ], + "score": 0.86, + "content": "\\pi _ { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 320, + 367, + 505, + 381 + ], + "score": 1.0, + "content": "is Gaussian where the mean and variance are", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 380, + 505, + 393 + ], + "spans": [ + { + "bbox": [ + 106, + 380, + 255, + 393 + ], + "score": 1.0, + "content": "deep neural networks with parameter", + "type": "text" + }, + { + "bbox": [ + 255, + 380, + 262, + 390 + ], + "score": 0.74, + "content": "\\theta", + "type": "inline_equation" + }, + { + "bbox": [ + 262, + 380, + 312, + 393 + ], + "score": 1.0, + "content": ". Each agent", + "type": "text" + }, + { + "bbox": [ + 312, + 381, + 317, + 390 + ], + "score": 0.8, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 317, + 380, + 505, + 393 + ], + "score": 1.0, + "content": "aims to maximize its own total expected return", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 107, + 389, + 397, + 410 + ], + "spans": [ + { + "bbox": [ + 107, + 390, + 175, + 406 + ], + "score": 0.93, + "content": "\\begin{array} { r } { R ^ { i } = \\sum _ { t = 0 } ^ { T } \\gamma ^ { t } r _ { t } ^ { i } } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 175, + 389, + 205, + 410 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 205, + 394, + 213, + 405 + ], + "score": 0.82, + "content": "\\gamma", + "type": "inline_equation" + }, + { + "bbox": [ + 213, + 389, + 308, + 410 + ], + "score": 1.0, + "content": "is a discount factor and", + "type": "text" + }, + { + "bbox": [ + 309, + 393, + 317, + 403 + ], + "score": 0.83, + "content": "T", + "type": "inline_equation" + }, + { + "bbox": [ + 318, + 389, + 397, + 410 + ], + "score": 1.0, + "content": "is the time horizon", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 19.5 + }, + { + "type": "text", + "bbox": [ + 106, + 410, + 505, + 542 + ], + "lines": [ + { + "bbox": [ + 105, + 408, + 505, + 423 + ], + "spans": [ + { + "bbox": [ + 105, + 408, + 505, + 423 + ], + "score": 1.0, + "content": "Policy Gradient: Policy gradient methods work by directly computing an estimate of the gradient", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 420, + 505, + 434 + ], + "spans": [ + { + "bbox": [ + 105, + 420, + 505, + 434 + ], + "score": 1.0, + "content": "of policy parameters in order to maximize the expected return using stochastic gradient descent.", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 430, + 505, + 444 + ], + "spans": [ + { + "bbox": [ + 105, + 430, + 505, + 444 + ], + "score": 1.0, + "content": "These methods are behind much of the recent success in using deep neural networks for control", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 442, + 504, + 455 + ], + "spans": [ + { + "bbox": [ + 106, + 442, + 504, + 455 + ], + "score": 1.0, + "content": "(Schulman et al., 2015b; Heess et al., 2017; Lillicrap et al., 2015; Silver et al., 2016). Such meth-", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 454, + 505, + 465 + ], + "spans": [ + { + "bbox": [ + 106, + 454, + 505, + 465 + ], + "score": 1.0, + "content": "ods are also attractive because they don’t require an explicit model of the world. There are several", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 463, + 504, + 477 + ], + "spans": [ + { + "bbox": [ + 105, + 463, + 413, + 477 + ], + "score": 1.0, + "content": "different expressions for the policy gradient estimator which have the form", + "type": "text" + }, + { + "bbox": [ + 414, + 464, + 501, + 477 + ], + "score": 0.93, + "content": "g : = \\mathbb { E } \\left[ A _ { t } \\nabla _ { \\theta } \\log \\pi _ { \\theta } \\right]", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 463, + 504, + 477 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 476, + 505, + 488 + ], + "spans": [ + { + "bbox": [ + 106, + 476, + 187, + 488 + ], + "score": 1.0, + "content": "Different choices of", + "type": "text" + }, + { + "bbox": [ + 188, + 476, + 199, + 487 + ], + "score": 0.88, + "content": "A _ { t }", + "type": "inline_equation" + }, + { + "bbox": [ + 200, + 476, + 505, + 488 + ], + "score": 1.0, + "content": "lead to different algorithms, for example taking the sample return of a trajec-", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 486, + 505, + 499 + ], + "spans": [ + { + "bbox": [ + 105, + 486, + 125, + 499 + ], + "score": 1.0, + "content": "tory", + "type": "text" + }, + { + "bbox": [ + 126, + 486, + 175, + 499 + ], + "score": 0.92, + "content": "\\boldsymbol { A } _ { t } = \\sum _ { t } \\boldsymbol { r } _ { t }", + "type": "inline_equation" + }, + { + "bbox": [ + 175, + 486, + 505, + 499 + ], + "score": 1.0, + "content": "leads to the REINFORCE algorithm (Williams, 1992). However, such algorithms", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 496, + 506, + 510 + ], + "spans": [ + { + "bbox": [ + 105, + 496, + 506, + 510 + ], + "score": 1.0, + "content": "suffer from high variance in the gradient estimates and it’s typical to use a baseline, such as a value", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 508, + 505, + 520 + ], + "spans": [ + { + "bbox": [ + 106, + 508, + 505, + 520 + ], + "score": 1.0, + "content": "function baseline, to ameliorate the high variance. Generalized advantage estimation (Schulman", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 519, + 506, + 532 + ], + "spans": [ + { + "bbox": [ + 106, + 519, + 506, + 532 + ], + "score": 1.0, + "content": "et al., 2015b) takes this approach of using a learned value function to reduce variance at the cost of", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 531, + 443, + 543 + ], + "spans": [ + { + "bbox": [ + 106, + 531, + 443, + 543 + ], + "score": 1.0, + "content": "some bias and using an exponentially weighted estimator of the advantage function.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 30.5 + }, + { + "type": "text", + "bbox": [ + 106, + 547, + 505, + 693 + ], + "lines": [ + { + "bbox": [ + 105, + 546, + 505, + 560 + ], + "spans": [ + { + "bbox": [ + 105, + 546, + 505, + 560 + ], + "score": 1.0, + "content": "Proximal Policy Optimization (PPO): Achieving good results with policy gradient algorithms", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 558, + 505, + 570 + ], + "spans": [ + { + "bbox": [ + 106, + 558, + 505, + 570 + ], + "score": 1.0, + "content": "requires carefully tuning the step-size (Schulman et al., 2015a). Moreover, most policy gradient", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 568, + 504, + 582 + ], + "spans": [ + { + "bbox": [ + 105, + 568, + 504, + 582 + ], + "score": 1.0, + "content": "methods perform one gradient update per sampled trajectory and have high sample complexity.", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 580, + 504, + 592 + ], + "spans": [ + { + "bbox": [ + 106, + 580, + 504, + 592 + ], + "score": 1.0, + "content": "Recently, Schulman et al. (2017) proposed the PPO algorithm which addresses both these prob-", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 104, + 590, + 505, + 604 + ], + "spans": [ + { + "bbox": [ + 104, + 590, + 505, + 604 + ], + "score": 1.0, + "content": "lems. This uses a surrogate objective which is maximized while penalizing large changes to the", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 601, + 505, + 621 + ], + "spans": [ + { + "bbox": [ + 105, + 601, + 156, + 621 + ], + "score": 1.0, + "content": "policy. Let", + "type": "text" + }, + { + "bbox": [ + 157, + 602, + 239, + 620 + ], + "score": 0.93, + "content": "\\begin{array} { r } { l _ { t } ( \\theta ) ~ = ~ \\frac { \\pi _ { \\theta } ^ { - } \\left( a _ { t } | s _ { t } \\right) ^ { - } } { \\pi _ { \\theta _ { o l d } } \\left( a _ { t } | s _ { t } \\right) } } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 239, + 601, + 505, + 621 + ], + "score": 1.0, + "content": "denote the likelihood ratio. Then PPO optimizes the objective:", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 619, + 506, + 639 + ], + "spans": [ + { + "bbox": [ + 106, + 619, + 309, + 639 + ], + "score": 0.9, + "content": "L = \\mathbb { E } \\left[ \\operatorname* { m i n } ( l _ { t } ( \\theta ) \\hat { A } _ { t } , \\operatorname { c l i p } ( l _ { t } ( \\theta ) , 1 - \\epsilon , 1 + \\epsilon ) \\hat { A } _ { t } ) \\right]", + "type": "inline_equation" + }, + { + "bbox": [ + 309, + 619, + 340, + 637 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 340, + 621, + 352, + 634 + ], + "score": 0.89, + "content": "\\hat { A } _ { t }", + "type": "inline_equation" + }, + { + "bbox": [ + 353, + 619, + 506, + 637 + ], + "score": 1.0, + "content": "is the generalized advantage estimate", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 637, + 505, + 650 + ], + "spans": [ + { + "bbox": [ + 106, + 637, + 124, + 650 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 124, + 639, + 220, + 650 + ], + "score": 0.79, + "content": "\\mathrm { c l i p } ( l _ { t } ( \\theta ) , 1 - \\epsilon , 1 + \\epsilon )", + "type": "inline_equation" + }, + { + "bbox": [ + 220, + 637, + 244, + 650 + ], + "score": 1.0, + "content": "clips", + "type": "text" + }, + { + "bbox": [ + 244, + 638, + 264, + 650 + ], + "score": 0.87, + "content": "l _ { t } ( \\theta )", + "type": "inline_equation" + }, + { + "bbox": [ + 265, + 637, + 326, + 650 + ], + "score": 1.0, + "content": "in the interval", + "type": "text" + }, + { + "bbox": [ + 326, + 637, + 381, + 650 + ], + "score": 0.92, + "content": "[ 1 - \\epsilon , 1 + \\epsilon ]", + "type": "inline_equation" + }, + { + "bbox": [ + 382, + 637, + 505, + 650 + ], + "score": 1.0, + "content": ". The algorithm alternates be-", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 648, + 504, + 660 + ], + "spans": [ + { + "bbox": [ + 106, + 648, + 504, + 660 + ], + "score": 1.0, + "content": "tween sampling multiple trajectories from the policy and performing several epochs of SGD on the", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 660, + 505, + 672 + ], + "spans": [ + { + "bbox": [ + 106, + 660, + 505, + 672 + ], + "score": 1.0, + "content": "sampled dataset to optimize this surrogate objective. Since the state value function is also simulta-", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 671, + 505, + 683 + ], + "spans": [ + { + "bbox": [ + 106, + 671, + 505, + 683 + ], + "score": 1.0, + "content": "neously approximated, the error for the value function approximation is also added to the surrogate", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 682, + 417, + 693 + ], + "spans": [ + { + "bbox": [ + 106, + 682, + 417, + 693 + ], + "score": 1.0, + "content": "objective to compute the complete objective function (Schulman et al., 2017).", + "type": "text" + } + ], + "index": 48 + } + ], + "index": 42.5 + }, + { + "type": "text", + "bbox": [ + 108, + 699, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "score": 1.0, + "content": "Related Work: Tan (1993) explored the multi-agent setting with independently learning agents", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 106, + 710, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 710, + 505, + 722 + ], + "score": 1.0, + "content": "using Q-learning, in particular exploring advantages of cooperative agents over independent agents", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 106, + 721, + 505, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 505, + 733 + ], + "score": 1.0, + "content": "in a 2D grid world. This was further explored by Matignon et al. (2012) again in the cooperative", + "type": "text" + } + ], + "index": 51 + } + ], + "index": 50 + } + ], + "page_idx": 1, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2018", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 309, + 760 + ], + "lines": [ + { + "bbox": [ + 301, + 750, + 310, + 763 + ], + "spans": [ + { + "bbox": [ + 301, + 750, + 310, + 763 + ], + "score": 1.0, + "content": "2", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 82, + 504, + 105 + ], + "lines": [], + "index": 0.5, + "bbox_fs": [ + 106, + 82, + 505, + 105 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 106, + 110, + 505, + 221 + ], + "lines": [ + { + "bbox": [ + 105, + 110, + 505, + 123 + ], + "spans": [ + { + "bbox": [ + 105, + 110, + 505, + 123 + ], + "score": 1.0, + "content": "In more detail, we introduce several multi-agent tasks with competing goals in a 3D world with sim-", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 122, + 505, + 133 + ], + "spans": [ + { + "bbox": [ + 106, + 122, + 505, + 133 + ], + "score": 1.0, + "content": "ulated physics, using the MuJoCo framework (Todorov et al., 2012), where the agents would need", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 133, + 505, + 144 + ], + "spans": [ + { + "bbox": [ + 106, + 133, + 505, + 144 + ], + "score": 1.0, + "content": "to learn highly developed motor skills in order to succeed in the competitive environment. We train", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 143, + 505, + 156 + ], + "spans": [ + { + "bbox": [ + 106, + 143, + 505, + 156 + ], + "score": 1.0, + "content": "the agents using a distributed implementation of a recent policy gradient algorithm, Proximal Policy", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 154, + 505, + 167 + ], + "spans": [ + { + "bbox": [ + 106, + 154, + 505, + 167 + ], + "score": 1.0, + "content": "Optimization (Schulman et al., 2017). By adding a simple exploration curriculum to aid exploration", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 164, + 505, + 178 + ], + "spans": [ + { + "bbox": [ + 105, + 164, + 505, + 178 + ], + "score": 1.0, + "content": "in the environment we find that agents learn a high level of dexterity in order to achieve their goals,", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 176, + 504, + 188 + ], + "spans": [ + { + "bbox": [ + 106, + 176, + 504, + 188 + ], + "score": 1.0, + "content": "in particular we find numerous emergent skills for which it may be difficult to engineer a reward.", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 186, + 505, + 201 + ], + "spans": [ + { + "bbox": [ + 105, + 186, + 505, + 201 + ], + "score": 1.0, + "content": "Specifically, the agents learned a wide variety of skills and behaviors that include running, blocking,", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 198, + 505, + 211 + ], + "spans": [ + { + "bbox": [ + 106, + 198, + 505, + 211 + ], + "score": 1.0, + "content": "ducking, tackling, fooling opponents, kicking, and defending using arms and legs. Highlight of the", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 209, + 428, + 222 + ], + "spans": [ + { + "bbox": [ + 105, + 209, + 428, + 222 + ], + "score": 1.0, + "content": "learned behaviors on the various tasks can be found here: https://goo.gl/eR7fbX", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 6.5, + "bbox_fs": [ + 105, + 110, + 505, + 222 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 238, + 208, + 250 + ], + "lines": [ + { + "bbox": [ + 105, + 237, + 209, + 253 + ], + "spans": [ + { + "bbox": [ + 105, + 237, + 209, + 253 + ], + "score": 1.0, + "content": "2 PRELIMINARIES", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 12 + }, + { + "type": "text", + "bbox": [ + 107, + 264, + 502, + 286 + ], + "lines": [ + { + "bbox": [ + 106, + 264, + 504, + 277 + ], + "spans": [ + { + "bbox": [ + 106, + 264, + 504, + 277 + ], + "score": 1.0, + "content": "In this section, we review some background on policy gradient methods, Proximal Policy Optimiza-", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 274, + 395, + 288 + ], + "spans": [ + { + "bbox": [ + 105, + 274, + 395, + 288 + ], + "score": 1.0, + "content": "tion and related work in the multi-agent reinforcement learning domain.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 13.5, + "bbox_fs": [ + 105, + 264, + 504, + 288 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 291, + 505, + 405 + ], + "lines": [ + { + "bbox": [ + 105, + 291, + 506, + 305 + ], + "spans": [ + { + "bbox": [ + 105, + 291, + 465, + 305 + ], + "score": 1.0, + "content": "Notation: We consider multi-agent Markov games (Littman, 1994). A Markov game for", + "type": "text" + }, + { + "bbox": [ + 466, + 293, + 476, + 302 + ], + "score": 0.82, + "content": "N", + "type": "inline_equation" + }, + { + "bbox": [ + 476, + 291, + 506, + 305 + ], + "score": 1.0, + "content": "agents", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 302, + 505, + 316 + ], + "spans": [ + { + "bbox": [ + 105, + 302, + 451, + 316 + ], + "score": 1.0, + "content": "is a partially observable Markov decision process (MDP) defined by: a set of states", + "type": "text" + }, + { + "bbox": [ + 451, + 304, + 459, + 313 + ], + "score": 0.79, + "content": "s", + "type": "inline_equation" + }, + { + "bbox": [ + 460, + 302, + 505, + 316 + ], + "score": 1.0, + "content": "describing", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 313, + 505, + 326 + ], + "spans": [ + { + "bbox": [ + 105, + 313, + 505, + 326 + ], + "score": 1.0, + "content": "the state of the world and the possible joint configuration of all the agents, a set of observations", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 107, + 321, + 505, + 339 + ], + "spans": [ + { + "bbox": [ + 107, + 324, + 158, + 336 + ], + "score": 0.89, + "content": "\\mathcal { O } ^ { 1 } , \\ldots , \\mathcal { O } ^ { N }", + "type": "inline_equation" + }, + { + "bbox": [ + 159, + 321, + 345, + 339 + ], + "score": 1.0, + "content": "of each agent, a set of actions of each agent", + "type": "text" + }, + { + "bbox": [ + 346, + 324, + 397, + 336 + ], + "score": 0.93, + "content": "\\mathcal { A } ^ { 1 } , \\ldots , \\mathcal { A } ^ { \\tilde { N } }", + "type": "inline_equation" + }, + { + "bbox": [ + 397, + 321, + 487, + 339 + ], + "score": 1.0, + "content": ", a transition function", + "type": "text" + }, + { + "bbox": [ + 487, + 325, + 505, + 336 + ], + "score": 0.41, + "content": "\\tau :", + "type": "inline_equation" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 333, + 506, + 350 + ], + "spans": [ + { + "bbox": [ + 106, + 335, + 192, + 347 + ], + "score": 0.9, + "content": "\\mathcal { S } \\times \\mathcal { A } ^ { 1 } \\cdot \\cdot \\cdot \\mathcal { A } ^ { N } \\to \\mathcal { S }", + "type": "inline_equation" + }, + { + "bbox": [ + 193, + 333, + 472, + 350 + ], + "score": 1.0, + "content": "determining distribution over next states, and a reward for each agent", + "type": "text" + }, + { + "bbox": [ + 472, + 337, + 477, + 346 + ], + "score": 0.73, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 478, + 333, + 506, + 350 + ], + "score": 1.0, + "content": "which", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 104, + 346, + 505, + 360 + ], + "spans": [ + { + "bbox": [ + 104, + 346, + 303, + 360 + ], + "score": 1.0, + "content": "is a function of the state and the agent’s action", + "type": "text" + }, + { + "bbox": [ + 303, + 347, + 383, + 357 + ], + "score": 0.91, + "content": "r ^ { i } : \\mathcal { S } \\times \\mathcal { A } ^ { i } \\to \\mathbb { R }", + "type": "inline_equation" + }, + { + "bbox": [ + 383, + 346, + 505, + 360 + ], + "score": 1.0, + "content": ". Agents choose their actions", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 357, + 505, + 371 + ], + "spans": [ + { + "bbox": [ + 105, + 357, + 235, + 371 + ], + "score": 1.0, + "content": "according to a stochastic policy", + "type": "text" + }, + { + "bbox": [ + 236, + 357, + 331, + 370 + ], + "score": 0.92, + "content": "\\pi _ { \\theta ^ { i } } : \\mathcal { O } ^ { i } \\times \\mathcal { A } ^ { i } [ 0 , 1 ]", + "type": "inline_equation" + }, + { + "bbox": [ + 332, + 357, + 362, + 371 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 363, + 358, + 372, + 368 + ], + "score": 0.85, + "content": "\\theta ^ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 372, + 357, + 505, + 371 + ], + "score": 1.0, + "content": "are the parameters of the policy.", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 367, + 505, + 381 + ], + "spans": [ + { + "bbox": [ + 105, + 367, + 308, + 381 + ], + "score": 1.0, + "content": "For continuous control problems considered here,", + "type": "text" + }, + { + "bbox": [ + 309, + 371, + 320, + 380 + ], + "score": 0.86, + "content": "\\pi _ { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 320, + 367, + 505, + 381 + ], + "score": 1.0, + "content": "is Gaussian where the mean and variance are", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 380, + 505, + 393 + ], + "spans": [ + { + "bbox": [ + 106, + 380, + 255, + 393 + ], + "score": 1.0, + "content": "deep neural networks with parameter", + "type": "text" + }, + { + "bbox": [ + 255, + 380, + 262, + 390 + ], + "score": 0.74, + "content": "\\theta", + "type": "inline_equation" + }, + { + "bbox": [ + 262, + 380, + 312, + 393 + ], + "score": 1.0, + "content": ". Each agent", + "type": "text" + }, + { + "bbox": [ + 312, + 381, + 317, + 390 + ], + "score": 0.8, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 317, + 380, + 505, + 393 + ], + "score": 1.0, + "content": "aims to maximize its own total expected return", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 107, + 389, + 397, + 410 + ], + "spans": [ + { + "bbox": [ + 107, + 390, + 175, + 406 + ], + "score": 0.93, + "content": "\\begin{array} { r } { R ^ { i } = \\sum _ { t = 0 } ^ { T } \\gamma ^ { t } r _ { t } ^ { i } } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 175, + 389, + 205, + 410 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 205, + 394, + 213, + 405 + ], + "score": 0.82, + "content": "\\gamma", + "type": "inline_equation" + }, + { + "bbox": [ + 213, + 389, + 308, + 410 + ], + "score": 1.0, + "content": "is a discount factor and", + "type": "text" + }, + { + "bbox": [ + 309, + 393, + 317, + 403 + ], + "score": 0.83, + "content": "T", + "type": "inline_equation" + }, + { + "bbox": [ + 318, + 389, + 397, + 410 + ], + "score": 1.0, + "content": "is the time horizon", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 19.5, + "bbox_fs": [ + 104, + 291, + 506, + 410 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 410, + 505, + 542 + ], + "lines": [ + { + "bbox": [ + 105, + 408, + 505, + 423 + ], + "spans": [ + { + "bbox": [ + 105, + 408, + 505, + 423 + ], + "score": 1.0, + "content": "Policy Gradient: Policy gradient methods work by directly computing an estimate of the gradient", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 420, + 505, + 434 + ], + "spans": [ + { + "bbox": [ + 105, + 420, + 505, + 434 + ], + "score": 1.0, + "content": "of policy parameters in order to maximize the expected return using stochastic gradient descent.", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 430, + 505, + 444 + ], + "spans": [ + { + "bbox": [ + 105, + 430, + 505, + 444 + ], + "score": 1.0, + "content": "These methods are behind much of the recent success in using deep neural networks for control", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 442, + 504, + 455 + ], + "spans": [ + { + "bbox": [ + 106, + 442, + 504, + 455 + ], + "score": 1.0, + "content": "(Schulman et al., 2015b; Heess et al., 2017; Lillicrap et al., 2015; Silver et al., 2016). Such meth-", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 454, + 505, + 465 + ], + "spans": [ + { + "bbox": [ + 106, + 454, + 505, + 465 + ], + "score": 1.0, + "content": "ods are also attractive because they don’t require an explicit model of the world. There are several", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 463, + 504, + 477 + ], + "spans": [ + { + "bbox": [ + 105, + 463, + 413, + 477 + ], + "score": 1.0, + "content": "different expressions for the policy gradient estimator which have the form", + "type": "text" + }, + { + "bbox": [ + 414, + 464, + 501, + 477 + ], + "score": 0.93, + "content": "g : = \\mathbb { E } \\left[ A _ { t } \\nabla _ { \\theta } \\log \\pi _ { \\theta } \\right]", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 463, + 504, + 477 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 476, + 505, + 488 + ], + "spans": [ + { + "bbox": [ + 106, + 476, + 187, + 488 + ], + "score": 1.0, + "content": "Different choices of", + "type": "text" + }, + { + "bbox": [ + 188, + 476, + 199, + 487 + ], + "score": 0.88, + "content": "A _ { t }", + "type": "inline_equation" + }, + { + "bbox": [ + 200, + 476, + 505, + 488 + ], + "score": 1.0, + "content": "lead to different algorithms, for example taking the sample return of a trajec-", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 486, + 505, + 499 + ], + "spans": [ + { + "bbox": [ + 105, + 486, + 125, + 499 + ], + "score": 1.0, + "content": "tory", + "type": "text" + }, + { + "bbox": [ + 126, + 486, + 175, + 499 + ], + "score": 0.92, + "content": "\\boldsymbol { A } _ { t } = \\sum _ { t } \\boldsymbol { r } _ { t }", + "type": "inline_equation" + }, + { + "bbox": [ + 175, + 486, + 505, + 499 + ], + "score": 1.0, + "content": "leads to the REINFORCE algorithm (Williams, 1992). However, such algorithms", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 496, + 506, + 510 + ], + "spans": [ + { + "bbox": [ + 105, + 496, + 506, + 510 + ], + "score": 1.0, + "content": "suffer from high variance in the gradient estimates and it’s typical to use a baseline, such as a value", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 508, + 505, + 520 + ], + "spans": [ + { + "bbox": [ + 106, + 508, + 505, + 520 + ], + "score": 1.0, + "content": "function baseline, to ameliorate the high variance. 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Moreover, most policy gradient", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 568, + 504, + 582 + ], + "spans": [ + { + "bbox": [ + 105, + 568, + 504, + 582 + ], + "score": 1.0, + "content": "methods perform one gradient update per sampled trajectory and have high sample complexity.", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 580, + 504, + 592 + ], + "spans": [ + { + "bbox": [ + 106, + 580, + 504, + 592 + ], + "score": 1.0, + "content": "Recently, Schulman et al. (2017) proposed the PPO algorithm which addresses both these prob-", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 104, + 590, + 505, + 604 + ], + "spans": [ + { + "bbox": [ + 104, + 590, + 505, + 604 + ], + "score": 1.0, + "content": "lems. This uses a surrogate objective which is maximized while penalizing large changes to the", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 601, + 505, + 621 + ], + "spans": [ + { + "bbox": [ + 105, + 601, + 156, + 621 + ], + "score": 1.0, + "content": "policy. Let", + "type": "text" + }, + { + "bbox": [ + 157, + 602, + 239, + 620 + ], + "score": 0.93, + "content": "\\begin{array} { r } { l _ { t } ( \\theta ) ~ = ~ \\frac { \\pi _ { \\theta } ^ { - } \\left( a _ { t } | s _ { t } \\right) ^ { - } } { \\pi _ { \\theta _ { o l d } } \\left( a _ { t } | s _ { t } \\right) } } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 239, + 601, + 505, + 621 + ], + "score": 1.0, + "content": "denote the likelihood ratio. Then PPO optimizes the objective:", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 619, + 506, + 639 + ], + "spans": [ + { + "bbox": [ + 106, + 619, + 309, + 639 + ], + "score": 0.9, + "content": "L = \\mathbb { E } \\left[ \\operatorname* { m i n } ( l _ { t } ( \\theta ) \\hat { A } _ { t } , \\operatorname { c l i p } ( l _ { t } ( \\theta ) , 1 - \\epsilon , 1 + \\epsilon ) \\hat { A } _ { t } ) \\right]", + "type": "inline_equation" + }, + { + "bbox": [ + 309, + 619, + 340, + 637 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 340, + 621, + 352, + 634 + ], + "score": 0.89, + "content": "\\hat { A } _ { t }", + "type": "inline_equation" + }, + { + "bbox": [ + 353, + 619, + 506, + 637 + ], + "score": 1.0, + "content": "is the generalized advantage estimate", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 637, + 505, + 650 + ], + "spans": [ + { + "bbox": [ + 106, + 637, + 124, + 650 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 124, + 639, + 220, + 650 + ], + "score": 0.79, + "content": "\\mathrm { c l i p } ( l _ { t } ( \\theta ) , 1 - \\epsilon , 1 + \\epsilon )", + "type": "inline_equation" + }, + { + "bbox": [ + 220, + 637, + 244, + 650 + ], + "score": 1.0, + "content": "clips", + "type": "text" + }, + { + "bbox": [ + 244, + 638, + 264, + 650 + ], + "score": 0.87, + "content": "l _ { t } ( \\theta )", + "type": "inline_equation" + }, + { + "bbox": [ + 265, + 637, + 326, + 650 + ], + "score": 1.0, + "content": "in the interval", + "type": "text" + }, + { + "bbox": [ + 326, + 637, + 381, + 650 + ], + "score": 0.92, + "content": "[ 1 - \\epsilon , 1 + \\epsilon ]", + "type": "inline_equation" + }, + { + "bbox": [ + 382, + 637, + 505, + 650 + ], + "score": 1.0, + "content": ". The algorithm alternates be-", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 648, + 504, + 660 + ], + "spans": [ + { + "bbox": [ + 106, + 648, + 504, + 660 + ], + "score": 1.0, + "content": "tween sampling multiple trajectories from the policy and performing several epochs of SGD on the", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 660, + 505, + 672 + ], + "spans": [ + { + "bbox": [ + 106, + 660, + 505, + 672 + ], + "score": 1.0, + "content": "sampled dataset to optimize this surrogate objective. Since the state value function is also simulta-", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 671, + 505, + 683 + ], + "spans": [ + { + "bbox": [ + 106, + 671, + 505, + 683 + ], + "score": 1.0, + "content": "neously approximated, the error for the value function approximation is also added to the surrogate", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 682, + 417, + 693 + ], + "spans": [ + { + "bbox": [ + 106, + 682, + 417, + 693 + ], + "score": 1.0, + "content": "objective to compute the complete objective function (Schulman et al., 2017).", + "type": "text" + } + ], + "index": 48 + } + ], + "index": 42.5, + "bbox_fs": [ + 104, + 546, + 506, + 693 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 699, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "score": 1.0, + "content": "Related Work: Tan (1993) explored the multi-agent setting with independently learning agents", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 106, + 710, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 710, + 505, + 722 + ], + "score": 1.0, + "content": "using Q-learning, in particular exploring advantages of cooperative agents over independent agents", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 106, + 721, + 505, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 505, + 733 + ], + "score": 1.0, + "content": "in a 2D grid world. This was further explored by Matignon et al. (2012) again in the cooperative", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "setting. A lot of the work on multi-agent RL is focused on cooperative settings, see Busoniu et al.", + "type": "text", + "cross_page": true + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 92, + 505, + 108 + ], + "spans": [ + { + "bbox": [ + 105, + 92, + 505, + 108 + ], + "score": 1.0, + "content": "(2008) for a review of multi-agent RL and Panait & Luke (2005) for a review focused on coop-", + "type": "text", + "cross_page": true + } + ], + "index": 1 + }, + { + "bbox": [ + 104, + 102, + 507, + 119 + ], + "spans": [ + { + "bbox": [ + 104, + 102, + 507, + 119 + ], + "score": 1.0, + "content": "erative settings. Stanley & Miikkulainen (2004) trained agents in a competitive 2D world, using", + "type": "text", + "cross_page": true + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 505, + 128 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 505, + 128 + ], + "score": 1.0, + "content": "evolutionary strategies to evolve both weights and structure of policies with competition as a fitness", + "type": "text", + "cross_page": true + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 126, + 506, + 139 + ], + "spans": [ + { + "bbox": [ + 104, + 126, + 506, + 139 + ], + "score": 1.0, + "content": "measure. Tampuu et al. (2017) studied the application of deep Q-learning to train Pong agents with", + "type": "text", + "cross_page": true + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 137, + 505, + 150 + ], + "spans": [ + { + "bbox": [ + 105, + 137, + 505, + 150 + ], + "score": 1.0, + "content": "competitive and collaborative rewarding schemes. He et al. (2016) used deep Q-learning to model", + "type": "text", + "cross_page": true + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 146, + 506, + 163 + ], + "spans": [ + { + "bbox": [ + 104, + 146, + 506, + 163 + ], + "score": 1.0, + "content": "competitive games where only one agent is learning and the Q network implicitly models the op-", + "type": "text", + "cross_page": true + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 159, + 506, + 172 + ], + "spans": [ + { + "bbox": [ + 104, + 159, + 506, + 172 + ], + "score": 1.0, + "content": "ponent. Silver et al. (2016) used self-play with deep reinforcement learning techniques to master", + "type": "text", + "cross_page": true + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 171, + 505, + 183 + ], + "spans": [ + { + "bbox": [ + 106, + 171, + 505, + 183 + ], + "score": 1.0, + "content": "the game of Go. Sukhbaatar et al. (2017) introduced a self-play method for generating an automatic", + "type": "text", + "cross_page": true + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 181, + 505, + 193 + ], + "spans": [ + { + "bbox": [ + 105, + 181, + 505, + 193 + ], + "score": 1.0, + "content": "training curriculum in single-agent environments. From a game-theoretic perspective, Heinrich &", + "type": "text", + "cross_page": true + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 192, + 505, + 205 + ], + "spans": [ + { + "bbox": [ + 106, + 192, + 505, + 205 + ], + "score": 1.0, + "content": "Silver (2016) studied fictitious self-play for achieving approximate Nash equilibrium in zero-sum", + "type": "text", + "cross_page": true + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 202, + 505, + 217 + ], + "spans": [ + { + "bbox": [ + 105, + 202, + 505, + 217 + ], + "score": 1.0, + "content": "games like Poker. Recently, Foerster et al. (2017a) introduced an algorithm which explicitly ac-", + "type": "text", + "cross_page": true + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 215, + 505, + 226 + ], + "spans": [ + { + "bbox": [ + 106, + 215, + 505, + 226 + ], + "score": 1.0, + "content": "counts for the fact that the opponent is also learning and showed that it can achieve cooperation in", + "type": "text", + "cross_page": true + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 225, + 505, + 237 + ], + "spans": [ + { + "bbox": [ + 106, + 225, + 505, + 237 + ], + "score": 1.0, + "content": "iterated prisoner’s dilemma, however the algorithm requires access to the opponent’s parameters.", + "type": "text", + "cross_page": true + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 234, + 506, + 250 + ], + "spans": [ + { + "bbox": [ + 105, + 234, + 506, + 250 + ], + "score": 1.0, + "content": "Recently, Lowe et al. (2017) and Foerster et al. (2017b) proposed methods for centralized learning", + "type": "text", + "cross_page": true + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 248, + 504, + 259 + ], + "spans": [ + { + "bbox": [ + 106, + 248, + 504, + 259 + ], + "score": 1.0, + "content": "in multi-agent domains, where the idea is to use an actor-critic method with a central critic which", + "type": "text", + "cross_page": true + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 258, + 505, + 270 + ], + "spans": [ + { + "bbox": [ + 105, + 258, + 505, + 270 + ], + "score": 1.0, + "content": "can observe the joint state and actions of all agents in order to reduce variance, evaluating on 2D", + "type": "text", + "cross_page": true + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 268, + 506, + 283 + ], + "spans": [ + { + "bbox": [ + 105, + 268, + 506, + 283 + ], + "score": 1.0, + "content": "games and StarCraft. In this work, we do not rely on centralized training and address the variance", + "type": "text", + "cross_page": true + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 280, + 505, + 292 + ], + "spans": [ + { + "bbox": [ + 105, + 280, + 505, + 292 + ], + "score": 1.0, + "content": "problem by using very large batchsize through a distributed implementation of the PPO algorithm.", + "type": "text", + "cross_page": true + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 290, + 506, + 304 + ], + "spans": [ + { + "bbox": [ + 105, + 290, + 506, + 304 + ], + "score": 1.0, + "content": "Moreover, we study fully competitive settings in a 3D world with simulated physics whereas prior", + "type": "text", + "cross_page": true + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 300, + 506, + 317 + ], + "spans": [ + { + "bbox": [ + 105, + 300, + 506, + 317 + ], + "score": 1.0, + "content": "applications have focused on toy 2D worlds or game-theoretic problems. Recent work on learning", + "type": "text", + "cross_page": true + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 312, + 506, + 326 + ], + "spans": [ + { + "bbox": [ + 105, + 312, + 506, + 326 + ], + "score": 1.0, + "content": "dexterous locomotion skills in 3D environments by adding complexity in the agent’s environment", + "type": "text", + "cross_page": true + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 322, + 505, + 336 + ], + "spans": [ + { + "bbox": [ + 105, + 322, + 505, + 336 + ], + "score": 1.0, + "content": "(Heess et al., 2017) is also related. However, whereas Heess et al. (2017) learn complex behaviours", + "type": "text", + "cross_page": true + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 335, + 504, + 346 + ], + "spans": [ + { + "bbox": [ + 106, + 335, + 504, + 346 + ], + "score": 1.0, + "content": "by engineering complexity into the environment design and by engineering dense reward functions", + "type": "text", + "cross_page": true + } + ], + "index": 23 + }, + { + "bbox": [ + 104, + 344, + 506, + 360 + ], + "spans": [ + { + "bbox": [ + 104, + 344, + 506, + 360 + ], + "score": 1.0, + "content": "for these environments, the resultant complexity in our work is due to the presence of other learning", + "type": "text", + "cross_page": true + } + ], + "index": 24 + }, + { + "bbox": [ + 104, + 356, + 505, + 370 + ], + "spans": [ + { + "bbox": [ + 104, + 356, + 505, + 370 + ], + "score": 1.0, + "content": "agents in a simple environment. Our work is also related to early work in the graphics community", + "type": "text", + "cross_page": true + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 367, + 505, + 380 + ], + "spans": [ + { + "bbox": [ + 105, + 367, + 505, + 380 + ], + "score": 1.0, + "content": "(Sims, 1994) on evolving creature morphology in varying environments using genetic algorithm and", + "type": "text", + "cross_page": true + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 378, + 505, + 391 + ], + "spans": [ + { + "bbox": [ + 105, + 378, + 505, + 391 + ], + "score": 1.0, + "content": "work in animation (Wampler et al., 2010) for adversarial games. The competitive multi-agent learn-", + "type": "text", + "cross_page": true + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 389, + 505, + 402 + ], + "spans": [ + { + "bbox": [ + 105, + 389, + 505, + 402 + ], + "score": 1.0, + "content": "ing framework is also related to generative adversarial networks (Goodfellow et al., 2014) and work", + "type": "text", + "cross_page": true + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 401, + 417, + 414 + ], + "spans": [ + { + "bbox": [ + 106, + 401, + 417, + 414 + ], + "score": 1.0, + "content": "on learning robust grasping policies through an adversary (Pinto et al., 2017).", + "type": "text", + "cross_page": true + } + ], + "index": 29 + } + ], + "index": 50, + "bbox_fs": [ + 105, + 698, + 506, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 505, + 411 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "setting. 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Recent work on learning", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 312, + 506, + 326 + ], + "spans": [ + { + "bbox": [ + 105, + 312, + 506, + 326 + ], + "score": 1.0, + "content": "dexterous locomotion skills in 3D environments by adding complexity in the agent’s environment", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 322, + 505, + 336 + ], + "spans": [ + { + "bbox": [ + 105, + 322, + 505, + 336 + ], + "score": 1.0, + "content": "(Heess et al., 2017) is also related. However, whereas Heess et al. 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The winner gets", + "type": "text" + }, + { + "bbox": [ + 445, + 132, + 473, + 143 + ], + "score": 0.87, + "content": "+ 1 0 0 0", + "type": "inline_equation" + }, + { + "bbox": [ + 473, + 132, + 505, + 145 + ], + "score": 1.0, + "content": "and the", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 143, + 381, + 156 + ], + "spans": [ + { + "bbox": [ + 105, + 143, + 381, + 156 + ], + "score": 1.0, + "content": "other agent gets -1000. If there is a draw then both agents get -1000.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4 + }, + { + "type": "text", + "bbox": [ + 107, + 160, + 505, + 248 + ], + "lines": [ + { + "bbox": [ + 105, + 160, + 505, + 173 + ], + "spans": [ + { + "bbox": [ + 105, + 160, + 505, + 173 + ], + "score": 1.0, + "content": "Kick and Defend: This a standard penalty shootout (see Fig.1d). One agent has to kick a ball", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 171, + 505, + 183 + ], + "spans": [ + { + "bbox": [ + 105, + 171, + 505, + 183 + ], + "score": 1.0, + "content": "through the goal, which has a fixed width of 6 units, while the other agent defends. Successful kick", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 181, + 505, + 196 + ], + "spans": [ + { + "bbox": [ + 105, + 181, + 212, + 196 + ], + "score": 1.0, + "content": "or defend gives the agent", + "type": "text" + }, + { + "bbox": [ + 212, + 182, + 239, + 193 + ], + "score": 0.87, + "content": "+ 1 0 0 0", + "type": "inline_equation" + }, + { + "bbox": [ + 240, + 181, + 505, + 196 + ], + "score": 1.0, + "content": "reward and the opponent -1000 reward. The defender cannot go", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 193, + 506, + 206 + ], + "spans": [ + { + "bbox": [ + 105, + 193, + 506, + 206 + ], + "score": 1.0, + "content": "beyond the goal-keeping area which is a distance 3 units from the goal, doing so terminates the game", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 204, + 506, + 216 + ], + "spans": [ + { + "bbox": [ + 106, + 204, + 506, + 216 + ], + "score": 1.0, + "content": "with a penalty of -1000 for the defender. We give two additional rewards for defender: if defender is", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 215, + 506, + 227 + ], + "spans": [ + { + "bbox": [ + 105, + 215, + 371, + 227 + ], + "score": 1.0, + "content": "successful and it made contact with the ball then it gets additional", + "type": "text" + }, + { + "bbox": [ + 372, + 215, + 394, + 226 + ], + "score": 0.86, + "content": "+ 5 0 0", + "type": "inline_equation" + }, + { + "bbox": [ + 394, + 215, + 506, + 227 + ], + "score": 1.0, + "content": "reward, and if the defender", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 226, + 505, + 238 + ], + "spans": [ + { + "bbox": [ + 105, + 226, + 479, + 238 + ], + "score": 1.0, + "content": "is successful and still standing at the end of the game then it gets another additional reward of", + "type": "text" + }, + { + "bbox": [ + 479, + 226, + 501, + 237 + ], + "score": 0.86, + "content": "+ 5 0 0", + "type": "inline_equation" + }, + { + "bbox": [ + 502, + 226, + 505, + 238 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 236, + 445, + 249 + ], + "spans": [ + { + "bbox": [ + 106, + 236, + 445, + 249 + ], + "score": 1.0, + "content": "We found the latter two rewards to yield more realistic looking defending behaviors.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 9.5 + }, + { + "type": "title", + "bbox": [ + 108, + 264, + 299, + 277 + ], + "lines": [ + { + "bbox": [ + 105, + 263, + 300, + 279 + ], + "spans": [ + { + "bbox": [ + 105, + 263, + 300, + 279 + ], + "score": 1.0, + "content": "4 TRAINING COMPETITIVE AGENTS", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 14 + }, + { + "type": "text", + "bbox": [ + 107, + 290, + 505, + 433 + ], + "lines": [ + { + "bbox": [ + 105, + 289, + 505, + 302 + ], + "spans": [ + { + "bbox": [ + 105, + 289, + 505, + 302 + ], + "score": 1.0, + "content": "In this section we describe the multi-agent training framework. We use a policy gradient algorithm,", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 300, + 506, + 314 + ], + "spans": [ + { + "bbox": [ + 105, + 300, + 506, + 314 + ], + "score": 1.0, + "content": "Proximal Policy Optimization (PPO) (Schulman et al., 2017), described previously. We adopt a", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 312, + 506, + 325 + ], + "spans": [ + { + "bbox": [ + 105, + 312, + 506, + 325 + ], + "score": 1.0, + "content": "decentralized training approach and use a distributed implementation of PPO for very large scale", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 324, + 504, + 335 + ], + "spans": [ + { + "bbox": [ + 106, + 324, + 504, + 335 + ], + "score": 1.0, + "content": "multi-agent training. This allows us to use really large batch-sizes during training ameliorating the", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 334, + 504, + 345 + ], + "spans": [ + { + "bbox": [ + 106, + 334, + 504, + 345 + ], + "score": 1.0, + "content": "variance problem to some extent while also aiding in exploration. Our distributed PPO implemen-", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 344, + 506, + 358 + ], + "spans": [ + { + "bbox": [ + 105, + 344, + 506, + 358 + ], + "score": 1.0, + "content": "tation is similar to the implementation of Heess et al. (2017), where instead of the KL penalty we", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 356, + 506, + 369 + ], + "spans": [ + { + "bbox": [ + 105, + 356, + 506, + 369 + ], + "score": 1.0, + "content": "used the clipped objective as proposed in PPO (Schulman et al., 2017). We do multiple rollouts in", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 366, + 506, + 379 + ], + "spans": [ + { + "bbox": [ + 105, + 366, + 506, + 379 + ], + "score": 1.0, + "content": "parallel for each agent and have separate optimizers for each agent. We collect a large amount of", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 378, + 506, + 390 + ], + "spans": [ + { + "bbox": [ + 105, + 378, + 506, + 390 + ], + "score": 1.0, + "content": "rollouts from the parallel workers and for each agent optimize the objective with the collected batch", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 388, + 505, + 401 + ], + "spans": [ + { + "bbox": [ + 105, + 388, + 505, + 401 + ], + "score": 1.0, + "content": "on 4 GPUs. The approach is same as synchronous actor critic of Mnih et al. (2016). Instead of esti-", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 399, + 505, + 412 + ], + "spans": [ + { + "bbox": [ + 105, + 399, + 505, + 412 + ], + "score": 1.0, + "content": "mating a truncated generalized advantage estimate (GAE) from a small number of steps per rollout,", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 410, + 506, + 423 + ], + "spans": [ + { + "bbox": [ + 105, + 410, + 506, + 423 + ], + "score": 1.0, + "content": "as in Schulman et al. (2017); Heess et al. (2017), we estimate GAE from the full rollouts. This is", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 421, + 484, + 434 + ], + "spans": [ + { + "bbox": [ + 106, + 421, + 484, + 434 + ], + "score": 1.0, + "content": "important as the competition reward is a sparse reward given at the termination of the episode.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 21 + }, + { + "type": "text", + "bbox": [ + 108, + 438, + 502, + 472 + ], + "lines": [ + { + "bbox": [ + 106, + 437, + 505, + 452 + ], + "spans": [ + { + "bbox": [ + 106, + 437, + 505, + 452 + ], + "score": 1.0, + "content": "There are further challenges in applying distributed PPO to train multiple competitive agents. One is", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 448, + 505, + 463 + ], + "spans": [ + { + "bbox": [ + 105, + 448, + 505, + 463 + ], + "score": 1.0, + "content": "the problem of exploration with sparse reward and second is the choice of opponent during training", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 461, + 428, + 473 + ], + "spans": [ + { + "bbox": [ + 106, + 461, + 428, + 473 + ], + "score": 1.0, + "content": "which effects the stability of training. We now turn our attention to these issues.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 29 + }, + { + "type": "title", + "bbox": [ + 108, + 486, + 255, + 496 + ], + "lines": [ + { + "bbox": [ + 106, + 485, + 256, + 498 + ], + "spans": [ + { + "bbox": [ + 106, + 485, + 256, + 498 + ], + "score": 1.0, + "content": "4.1 EXPLORATION CURRICULUM", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 31 + }, + { + "type": "text", + "bbox": [ + 107, + 506, + 505, + 660 + ], + "lines": [ + { + "bbox": [ + 105, + 505, + 506, + 519 + ], + "spans": [ + { + "bbox": [ + 105, + 505, + 506, + 519 + ], + "score": 1.0, + "content": "The success of agents in the competitive games requires the agents to occasionally solve the task", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 518, + 505, + 529 + ], + "spans": [ + { + "bbox": [ + 106, + 518, + 505, + 529 + ], + "score": 1.0, + "content": "(i.e. win the competition) by random actions. The probability of this happening in most games is", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 528, + 505, + 541 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 505, + 541 + ], + "score": 1.0, + "content": "minuscule as they require as a prerequisite some fundamental motor skills like the ability to walk.", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 539, + 505, + 552 + ], + "spans": [ + { + "bbox": [ + 105, + 539, + 505, + 552 + ], + "score": 1.0, + "content": "For example, the only way a kicker in the kick-and-defend task would achieve any positive reward", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 550, + 505, + 563 + ], + "spans": [ + { + "bbox": [ + 105, + 550, + 505, + 563 + ], + "score": 1.0, + "content": "is if it moves towards the ball and causes sufficient displacement to it so as to make it go past the", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 561, + 506, + 574 + ], + "spans": [ + { + "bbox": [ + 105, + 561, + 506, + 574 + ], + "score": 1.0, + "content": "goal boundaries which is also obstructed by a defender. This is a problem of training from sparse", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 572, + 506, + 584 + ], + "spans": [ + { + "bbox": [ + 105, + 572, + 506, + 584 + ], + "score": 1.0, + "content": "reward which is an active area of current research (Andrychowicz et al., 2017). To overcome this", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 583, + 506, + 595 + ], + "spans": [ + { + "bbox": [ + 105, + 583, + 506, + 595 + ], + "score": 1.0, + "content": "problem, we can use simple dense rewards at each step to allow the agents to learn basic motor skills", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 593, + 505, + 607 + ], + "spans": [ + { + "bbox": [ + 105, + 593, + 505, + 607 + ], + "score": 1.0, + "content": "initially. Such rewards have been previously researched for tasks like walking forward and standing", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 604, + 506, + 618 + ], + "spans": [ + { + "bbox": [ + 105, + 604, + 506, + 618 + ], + "score": 1.0, + "content": "up, see for e.g. Schulman et al. (2015b) and Duan et al. (2016). However, engineering such dense", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 616, + 506, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 616, + 506, + 628 + ], + "score": 1.0, + "content": "rewards for the competitive tasks is not straight forward. Moreover, such engineered rewards defeat", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 627, + 505, + 640 + ], + "spans": [ + { + "bbox": [ + 105, + 627, + 505, + 640 + ], + "score": 1.0, + "content": "the purpose of the competitive multi-agent training as we would like the agents to benefit from", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 637, + 505, + 652 + ], + "spans": [ + { + "bbox": [ + 105, + 637, + 505, + 652 + ], + "score": 1.0, + "content": "the natural curriculum arising from the multi-agent training. To overcome this chicken-and-egg", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 649, + 381, + 662 + ], + "spans": [ + { + "bbox": [ + 105, + 649, + 381, + 662 + ], + "score": 1.0, + "content": "problem, we instead propose to use a simple curriculum for training.", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 38.5 + }, + { + "type": "text", + "bbox": [ + 107, + 666, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 665, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 106, + 665, + 505, + 678 + ], + "score": 1.0, + "content": "We use a dense reward at every step in the beginning phase of the training to allow agents to learn ba-", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 677, + 506, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 506, + 690 + ], + "score": 1.0, + "content": "sic motor skills, like walking forward or being able to stand, which would increase the probability of", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 688, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 106, + 688, + 505, + 700 + ], + "score": 1.0, + "content": "random actions from the agent yielding a positive reward. 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So, at time-step", + "type": "text" + }, + { + "bbox": [ + 357, + 722, + 361, + 730 + ], + "score": 0.68, + "content": "t", + "type": "inline_equation" + }, + { + "bbox": [ + 362, + 721, + 477, + 732 + ], + "score": 1.0, + "content": ", if the exploration reward is", + "type": "text" + }, + { + "bbox": [ + 477, + 722, + 486, + 732 + ], + "score": 0.85, + "content": "s _ { t }", + "type": "inline_equation" + }, + { + "bbox": [ + 487, + 721, + 505, + 732 + ], + "score": 1.0, + "content": ", the", + "type": "text" + } + ], + "index": 51 + } + ], + "index": 48.5 + } + ], + "page_idx": 3, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2018", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 752, + 308, + 759 + ], + "lines": [] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 108, + 82, + 503, + 115 + ], + "lines": [], + "index": 1, + "bbox_fs": [ + 105, + 81, + 506, + 116 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 107, + 121, + 504, + 155 + ], + "lines": [ + { + "bbox": [ + 105, + 120, + 506, + 134 + ], + "spans": [ + { + "bbox": [ + 105, + 120, + 506, + 134 + ], + "score": 1.0, + "content": "Sumo: The agents compete on a round arena (see Fig.1c) and the goal of each agent is to either", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 132, + 505, + 145 + ], + "spans": [ + { + "bbox": [ + 105, + 132, + 445, + 145 + ], + "score": 1.0, + "content": "knock the other agent to the ground or to push them out of the ring. The winner gets", + "type": "text" + }, + { + "bbox": [ + 445, + 132, + 473, + 143 + ], + "score": 0.87, + "content": "+ 1 0 0 0", + "type": "inline_equation" + }, + { + "bbox": [ + 473, + 132, + 505, + 145 + ], + "score": 1.0, + "content": "and the", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 143, + 381, + 156 + ], + "spans": [ + { + "bbox": [ + 105, + 143, + 381, + 156 + ], + "score": 1.0, + "content": "other agent gets -1000. If there is a draw then both agents get -1000.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4, + "bbox_fs": [ + 105, + 120, + 506, + 156 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 160, + 505, + 248 + ], + "lines": [ + { + "bbox": [ + 105, + 160, + 505, + 173 + ], + "spans": [ + { + "bbox": [ + 105, + 160, + 505, + 173 + ], + "score": 1.0, + "content": "Kick and Defend: This a standard penalty shootout (see Fig.1d). One agent has to kick a ball", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 171, + 505, + 183 + ], + "spans": [ + { + "bbox": [ + 105, + 171, + 505, + 183 + ], + "score": 1.0, + "content": "through the goal, which has a fixed width of 6 units, while the other agent defends. Successful kick", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 181, + 505, + 196 + ], + "spans": [ + { + "bbox": [ + 105, + 181, + 212, + 196 + ], + "score": 1.0, + "content": "or defend gives the agent", + "type": "text" + }, + { + "bbox": [ + 212, + 182, + 239, + 193 + ], + "score": 0.87, + "content": "+ 1 0 0 0", + "type": "inline_equation" + }, + { + "bbox": [ + 240, + 181, + 505, + 196 + ], + "score": 1.0, + "content": "reward and the opponent -1000 reward. The defender cannot go", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 193, + 506, + 206 + ], + "spans": [ + { + "bbox": [ + 105, + 193, + 506, + 206 + ], + "score": 1.0, + "content": "beyond the goal-keeping area which is a distance 3 units from the goal, doing so terminates the game", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 204, + 506, + 216 + ], + "spans": [ + { + "bbox": [ + 106, + 204, + 506, + 216 + ], + "score": 1.0, + "content": "with a penalty of -1000 for the defender. We give two additional rewards for defender: if defender is", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 215, + 506, + 227 + ], + "spans": [ + { + "bbox": [ + 105, + 215, + 371, + 227 + ], + "score": 1.0, + "content": "successful and it made contact with the ball then it gets additional", + "type": "text" + }, + { + "bbox": [ + 372, + 215, + 394, + 226 + ], + "score": 0.86, + "content": "+ 5 0 0", + "type": "inline_equation" + }, + { + "bbox": [ + 394, + 215, + 506, + 227 + ], + "score": 1.0, + "content": "reward, and if the defender", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 226, + 505, + 238 + ], + "spans": [ + { + "bbox": [ + 105, + 226, + 479, + 238 + ], + "score": 1.0, + "content": "is successful and still standing at the end of the game then it gets another additional reward of", + "type": "text" + }, + { + "bbox": [ + 479, + 226, + 501, + 237 + ], + "score": 0.86, + "content": "+ 5 0 0", + "type": "inline_equation" + }, + { + "bbox": [ + 502, + 226, + 505, + 238 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 236, + 445, + 249 + ], + "spans": [ + { + "bbox": [ + 106, + 236, + 445, + 249 + ], + "score": 1.0, + "content": "We found the latter two rewards to yield more realistic looking defending behaviors.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 9.5, + "bbox_fs": [ + 105, + 160, + 506, + 249 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 264, + 299, + 277 + ], + "lines": [ + { + "bbox": [ + 105, + 263, + 300, + 279 + ], + "spans": [ + { + "bbox": [ + 105, + 263, + 300, + 279 + ], + "score": 1.0, + "content": "4 TRAINING COMPETITIVE AGENTS", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 14 + }, + { + "type": "text", + "bbox": [ + 107, + 290, + 505, + 433 + ], + "lines": [ + { + "bbox": [ + 105, + 289, + 505, + 302 + ], + "spans": [ + { + "bbox": [ + 105, + 289, + 505, + 302 + ], + "score": 1.0, + "content": "In this section we describe the multi-agent training framework. We use a policy gradient algorithm,", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 300, + 506, + 314 + ], + "spans": [ + { + "bbox": [ + 105, + 300, + 506, + 314 + ], + "score": 1.0, + "content": "Proximal Policy Optimization (PPO) (Schulman et al., 2017), described previously. We adopt a", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 312, + 506, + 325 + ], + "spans": [ + { + "bbox": [ + 105, + 312, + 506, + 325 + ], + "score": 1.0, + "content": "decentralized training approach and use a distributed implementation of PPO for very large scale", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 324, + 504, + 335 + ], + "spans": [ + { + "bbox": [ + 106, + 324, + 504, + 335 + ], + "score": 1.0, + "content": "multi-agent training. This allows us to use really large batch-sizes during training ameliorating the", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 334, + 504, + 345 + ], + "spans": [ + { + "bbox": [ + 106, + 334, + 504, + 345 + ], + "score": 1.0, + "content": "variance problem to some extent while also aiding in exploration. Our distributed PPO implemen-", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 344, + 506, + 358 + ], + "spans": [ + { + "bbox": [ + 105, + 344, + 506, + 358 + ], + "score": 1.0, + "content": "tation is similar to the implementation of Heess et al. (2017), where instead of the KL penalty we", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 356, + 506, + 369 + ], + "spans": [ + { + "bbox": [ + 105, + 356, + 506, + 369 + ], + "score": 1.0, + "content": "used the clipped objective as proposed in PPO (Schulman et al., 2017). We do multiple rollouts in", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 366, + 506, + 379 + ], + "spans": [ + { + "bbox": [ + 105, + 366, + 506, + 379 + ], + "score": 1.0, + "content": "parallel for each agent and have separate optimizers for each agent. We collect a large amount of", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 378, + 506, + 390 + ], + "spans": [ + { + "bbox": [ + 105, + 378, + 506, + 390 + ], + "score": 1.0, + "content": "rollouts from the parallel workers and for each agent optimize the objective with the collected batch", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 388, + 505, + 401 + ], + "spans": [ + { + "bbox": [ + 105, + 388, + 505, + 401 + ], + "score": 1.0, + "content": "on 4 GPUs. The approach is same as synchronous actor critic of Mnih et al. (2016). Instead of esti-", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 399, + 505, + 412 + ], + "spans": [ + { + "bbox": [ + 105, + 399, + 505, + 412 + ], + "score": 1.0, + "content": "mating a truncated generalized advantage estimate (GAE) from a small number of steps per rollout,", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 410, + 506, + 423 + ], + "spans": [ + { + "bbox": [ + 105, + 410, + 506, + 423 + ], + "score": 1.0, + "content": "as in Schulman et al. (2017); Heess et al. (2017), we estimate GAE from the full rollouts. This is", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 421, + 484, + 434 + ], + "spans": [ + { + "bbox": [ + 106, + 421, + 484, + 434 + ], + "score": 1.0, + "content": "important as the competition reward is a sparse reward given at the termination of the episode.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 21, + "bbox_fs": [ + 105, + 289, + 506, + 434 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 438, + 502, + 472 + ], + "lines": [ + { + "bbox": [ + 106, + 437, + 505, + 452 + ], + "spans": [ + { + "bbox": [ + 106, + 437, + 505, + 452 + ], + "score": 1.0, + "content": "There are further challenges in applying distributed PPO to train multiple competitive agents. One is", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 448, + 505, + 463 + ], + "spans": [ + { + "bbox": [ + 105, + 448, + 505, + 463 + ], + "score": 1.0, + "content": "the problem of exploration with sparse reward and second is the choice of opponent during training", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 461, + 428, + 473 + ], + "spans": [ + { + "bbox": [ + 106, + 461, + 428, + 473 + ], + "score": 1.0, + "content": "which effects the stability of training. We now turn our attention to these issues.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 29, + "bbox_fs": [ + 105, + 437, + 505, + 473 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 486, + 255, + 496 + ], + "lines": [ + { + "bbox": [ + 106, + 485, + 256, + 498 + ], + "spans": [ + { + "bbox": [ + 106, + 485, + 256, + 498 + ], + "score": 1.0, + "content": "4.1 EXPLORATION CURRICULUM", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 31 + }, + { + "type": "text", + "bbox": [ + 107, + 506, + 505, + 660 + ], + "lines": [ + { + "bbox": [ + 105, + 505, + 506, + 519 + ], + "spans": [ + { + "bbox": [ + 105, + 505, + 506, + 519 + ], + "score": 1.0, + "content": "The success of agents in the competitive games requires the agents to occasionally solve the task", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 518, + 505, + 529 + ], + "spans": [ + { + "bbox": [ + 106, + 518, + 505, + 529 + ], + "score": 1.0, + "content": "(i.e. win the competition) by random actions. The probability of this happening in most games is", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 528, + 505, + 541 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 505, + 541 + ], + "score": 1.0, + "content": "minuscule as they require as a prerequisite some fundamental motor skills like the ability to walk.", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 539, + 505, + 552 + ], + "spans": [ + { + "bbox": [ + 105, + 539, + 505, + 552 + ], + "score": 1.0, + "content": "For example, the only way a kicker in the kick-and-defend task would achieve any positive reward", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 550, + 505, + 563 + ], + "spans": [ + { + "bbox": [ + 105, + 550, + 505, + 563 + ], + "score": 1.0, + "content": "is if it moves towards the ball and causes sufficient displacement to it so as to make it go past the", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 561, + 506, + 574 + ], + "spans": [ + { + "bbox": [ + 105, + 561, + 506, + 574 + ], + "score": 1.0, + "content": "goal boundaries which is also obstructed by a defender. This is a problem of training from sparse", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 572, + 506, + 584 + ], + "spans": [ + { + "bbox": [ + 105, + 572, + 506, + 584 + ], + "score": 1.0, + "content": "reward which is an active area of current research (Andrychowicz et al., 2017). To overcome this", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 583, + 506, + 595 + ], + "spans": [ + { + "bbox": [ + 105, + 583, + 506, + 595 + ], + "score": 1.0, + "content": "problem, we can use simple dense rewards at each step to allow the agents to learn basic motor skills", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 593, + 505, + 607 + ], + "spans": [ + { + "bbox": [ + 105, + 593, + 505, + 607 + ], + "score": 1.0, + "content": "initially. 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Moreover, such engineered rewards defeat", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 627, + 505, + 640 + ], + "spans": [ + { + "bbox": [ + 105, + 627, + 505, + 640 + ], + "score": 1.0, + "content": "the purpose of the competitive multi-agent training as we would like the agents to benefit from", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 637, + 505, + 652 + ], + "spans": [ + { + "bbox": [ + 105, + 637, + 505, + 652 + ], + "score": 1.0, + "content": "the natural curriculum arising from the multi-agent training. 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These", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 313, + 506, + 326 + ], + "spans": [ + { + "bbox": [ + 105, + 313, + 506, + 326 + ], + "score": 1.0, + "content": "rewards are adopted from existing work and we did not tune weights on the various reward terms. In", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 325, + 506, + 338 + ], + "spans": [ + { + "bbox": [ + 105, + 325, + 506, + 338 + ], + "score": 1.0, + "content": "particular, it is important to note that there is no dense reward term for many of the complex emergent", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 335, + 506, + 348 + ], + "spans": [ + { + "bbox": [ + 105, + 335, + 506, + 348 + ], + "score": 1.0, + "content": "behaviors and we also show in the experiment section how the learned behaviors are affected if we", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 345, + 464, + 359 + ], + "spans": [ + { + "bbox": [ + 105, + 345, + 464, + 359 + ], + "score": 1.0, + "content": "do not anneal the dense reward to benefit from optimizing the sparse competition reward.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 10.5 + }, + { + "type": "title", + "bbox": [ + 108, + 371, + 227, + 382 + ], + "lines": [ + { + "bbox": [ + 106, + 371, + 228, + 383 + ], + "spans": [ + { + "bbox": [ + 106, + 371, + 228, + 383 + ], + "score": 1.0, + "content": "4.2 OPPONENT SAMPLING", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 16 + }, + { + "type": "text", + "bbox": [ + 107, + 392, + 505, + 513 + ], + "lines": [ + { + "bbox": [ + 105, + 392, + 505, + 405 + ], + "spans": [ + { + "bbox": [ + 105, + 392, + 505, + 405 + ], + "score": 1.0, + "content": "In the competitive multi-agent framework, all agents are simultaneously training in opponent pairs.", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 403, + 505, + 416 + ], + "spans": [ + { + "bbox": [ + 106, + 403, + 505, + 416 + ], + "score": 1.0, + "content": "Thus, the skill of opponents encountered during training could have significant impact on the learn-", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 413, + 506, + 427 + ], + "spans": [ + { + "bbox": [ + 105, + 413, + 506, + 427 + ], + "score": 1.0, + "content": "ing of the agents. We found that training agents against the most recent opponent leads to imbalance", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 425, + 505, + 438 + ], + "spans": [ + { + "bbox": [ + 106, + 425, + 505, + 438 + ], + "score": 1.0, + "content": "in training where one agent becomes more skilled than the other agent early in training and the other", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 435, + 506, + 449 + ], + "spans": [ + { + "bbox": [ + 105, + 435, + 506, + 449 + ], + "score": 1.0, + "content": "agent is unable to recover. Fig. 2a shows the rewards during training with this naive approach (for", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 447, + 505, + 459 + ], + "spans": [ + { + "bbox": [ + 106, + 447, + 505, + 459 + ], + "score": 1.0, + "content": "the “run to goal” task with ant). 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We further analyze the effect of this opponent", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 490, + 505, + 504 + ], + "spans": [ + { + "bbox": [ + 105, + 490, + 505, + 504 + ], + "score": 1.0, + "content": "sampling in the experiments section. Note that for self-play this means that the policy at any time", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 501, + 463, + 515 + ], + "spans": [ + { + "bbox": [ + 105, + 501, + 463, + 515 + ], + "score": 1.0, + "content": "should be able to defeat random older versions of itself, thus ensuring continual learning.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 22 + }, + { + "type": "title", + "bbox": [ + 108, + 529, + 200, + 542 + ], + "lines": [ + { + "bbox": [ + 104, + 528, + 202, + 544 + ], + "spans": [ + { + "bbox": [ + 104, + 528, + 202, + 544 + ], + "score": 1.0, + "content": "5 EXPERIMENTS", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 28 + }, + { + "type": "text", + "bbox": [ + 107, + 554, + 505, + 621 + ], + "lines": [ + { + "bbox": [ + 107, + 555, + 505, + 566 + ], + "spans": [ + { + "bbox": [ + 107, + 555, + 505, + 566 + ], + "score": 1.0, + "content": "We train agents for the four competitive tasks using the training methods described previously. Our", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 564, + 505, + 578 + ], + "spans": [ + { + "bbox": [ + 105, + 564, + 505, + 578 + ], + "score": 1.0, + "content": "aim is to show that competitive multi-agent training provides a natural curriculum during learning", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 577, + 505, + 588 + ], + "spans": [ + { + "bbox": [ + 106, + 577, + 505, + 588 + ], + "score": 1.0, + "content": "which allows agents to learn complex behaviors. We provide additional training details and analyze", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 587, + 505, + 600 + ], + "spans": [ + { + "bbox": [ + 106, + 587, + 505, + 600 + ], + "score": 1.0, + "content": "various aspects of the competitive multi-agent training in this section. A highlight of the learned", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 597, + 505, + 610 + ], + "spans": [ + { + "bbox": [ + 105, + 597, + 505, + 610 + ], + "score": 1.0, + "content": "behaviors can be seen in the videos. Code for the environments as well as learned policy parameters", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 609, + 504, + 622 + ], + "spans": [ + { + "bbox": [ + 106, + 609, + 504, + 622 + ], + "score": 1.0, + "content": "for agents on all the environments are available: https://github.com/openai/multiagent-competition.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 31.5 + }, + { + "type": "title", + "bbox": [ + 108, + 634, + 239, + 645 + ], + "lines": [ + { + "bbox": [ + 105, + 633, + 240, + 647 + ], + "spans": [ + { + "bbox": [ + 105, + 633, + 240, + 647 + ], + "score": 1.0, + "content": "5.1 EXPERIMENTAL DETAILS", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 35 + }, + { + "type": "text", + "bbox": [ + 107, + 654, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "score": 1.0, + "content": "Policies and Value Functions: We compare both MLP and LSTM for the policies and the value", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "score": 1.0, + "content": "functions. 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We found that training agents against the most recent opponent leads to imbalance", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 425, + 505, + 438 + ], + "spans": [ + { + "bbox": [ + 106, + 425, + 505, + 438 + ], + "score": 1.0, + "content": "in training where one agent becomes more skilled than the other agent early in training and the other", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 435, + 506, + 449 + ], + "spans": [ + { + "bbox": [ + 105, + 435, + 506, + 449 + ], + "score": 1.0, + "content": "agent is unable to recover. Fig. 2a shows the rewards during training with this naive approach (for", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 447, + 505, + 459 + ], + "spans": [ + { + "bbox": [ + 106, + 447, + 505, + 459 + ], + "score": 1.0, + "content": "the “run to goal” task with ant). 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Our", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 564, + 505, + 578 + ], + "spans": [ + { + "bbox": [ + 105, + 564, + 505, + 578 + ], + "score": 1.0, + "content": "aim is to show that competitive multi-agent training provides a natural curriculum during learning", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 577, + 505, + 588 + ], + "spans": [ + { + "bbox": [ + 106, + 577, + 505, + 588 + ], + "score": 1.0, + "content": "which allows agents to learn complex behaviors. We provide additional training details and analyze", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 587, + 505, + 600 + ], + "spans": [ + { + "bbox": [ + 106, + 587, + 505, + 600 + ], + "score": 1.0, + "content": "various aspects of the competitive multi-agent training in this section. A highlight of the learned", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 597, + 505, + 610 + ], + "spans": [ + { + "bbox": [ + 105, + 597, + 505, + 610 + ], + "score": 1.0, + "content": "behaviors can be seen in the videos. Code for the environments as well as learned policy parameters", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 609, + 504, + 622 + ], + "spans": [ + { + "bbox": [ + 106, + 609, + 504, + 622 + ], + "score": 1.0, + "content": "for agents on all the environments are available: https://github.com/openai/multiagent-competition.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 31.5, + "bbox_fs": [ + 105, + 555, + 505, + 622 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 634, + 239, + 645 + ], + "lines": [ + { + "bbox": [ + 105, + 633, + 240, + 647 + ], + "spans": [ + { + "bbox": [ + 105, + 633, + 240, + 647 + ], + "score": 1.0, + "content": "5.1 EXPERIMENTAL DETAILS", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 35 + }, + { + "type": "text", + "bbox": [ + 107, + 654, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "score": 1.0, + "content": "Policies and Value Functions: We compare both MLP and LSTM for the policies and the value", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "score": 1.0, + "content": "functions. MLP had 2 hidden layers with 128 units each. For LSTM networks, the input was first", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 677, + 506, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 506, + 690 + ], + "score": 1.0, + "content": "projected to a 128 dimensional embedding using a fully connected layer with ReLU activation which", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "score": 1.0, + "content": "is then fed into a single-layer LSTM with 128 hidden state dimension and the output is projected", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 698, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 505, + 711 + ], + "score": 1.0, + "content": "to the action dimension using another fully connected layer. We used Gaussian policies with mean", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 709, + 506, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 506, + 722 + ], + "score": 1.0, + "content": "given by the output of the networks and a diagonal covariance matrix whose entries are also treated", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 721, + 505, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 721, + 505, + 733 + ], + "score": 1.0, + "content": "as trianable parameters. The policy outputs are clipped to lie within the control range. We used", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 39, + "bbox_fs": [ + 105, + 654, + 506, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 505, + 149 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "MLP policy and value functions for the run-to-goal and you-shall-not-pass environments, and LSTM", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 94, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 94, + 505, + 106 + ], + "score": 1.0, + "content": "policy and value function for sumo and kick-and-defend. This is because earlier experiments did not", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 104, + 506, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 104, + 506, + 118 + ], + "score": 1.0, + "content": "yield good results with MLP policy on these tasks. For LSTM policy we used truncated BPTT with", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 505, + 128 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 505, + 128 + ], + "score": 1.0, + "content": "a truncation of 10 timesteps. The policy and the value functions have separate parameters. For the", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 127, + 505, + 140 + ], + "spans": [ + { + "bbox": [ + 105, + 127, + 505, + 140 + ], + "score": 1.0, + "content": "asymmetric games, you-shall-not-pass and kick-and-defend, we use separate policies for the two", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 138, + 178, + 150 + ], + "spans": [ + { + "bbox": [ + 106, + 138, + 178, + 150 + ], + "score": 1.0, + "content": "agents in a game.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 2.5 + }, + { + "type": "text", + "bbox": [ + 107, + 154, + 505, + 264 + ], + "lines": [ + { + "bbox": [ + 105, + 153, + 505, + 167 + ], + "spans": [ + { + "bbox": [ + 105, + 153, + 505, + 167 + ], + "score": 1.0, + "content": "Observations: For the Ant body we use all the joint angles of the agent, its velocity of all its", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 165, + 506, + 178 + ], + "spans": [ + { + "bbox": [ + 105, + 165, + 506, + 178 + ], + "score": 1.0, + "content": "joints, the contact forces acting on the body and the relative position and all the joint angles for the", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 176, + 506, + 189 + ], + "spans": [ + { + "bbox": [ + 105, + 176, + 506, + 189 + ], + "score": 1.0, + "content": "opponent. For the Humanoid body, in addition to the above we also give the centre-of-mass based", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 188, + 505, + 199 + ], + "spans": [ + { + "bbox": [ + 106, + 188, + 505, + 199 + ], + "score": 1.0, + "content": "inertia tensor, velocity vector and the actuator forces for the body. In addition to these, there are other", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 198, + 506, + 211 + ], + "spans": [ + { + "bbox": [ + 105, + 198, + 506, + 211 + ], + "score": 1.0, + "content": "environment specific observations. For the Sumo environment, we give the torso’s orientation vector", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 209, + 505, + 222 + ], + "spans": [ + { + "bbox": [ + 105, + 209, + 505, + 222 + ], + "score": 1.0, + "content": "as the input, the radial distance from the edge of the ring of all the agents and the time remaining in", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 220, + 506, + 232 + ], + "spans": [ + { + "bbox": [ + 105, + 220, + 506, + 232 + ], + "score": 1.0, + "content": "the game. For kick-and-defend, we give the relative position of the ball from the agent, the relative", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 231, + 505, + 244 + ], + "spans": [ + { + "bbox": [ + 105, + 231, + 505, + 244 + ], + "score": 1.0, + "content": "distance of the ball from goal and the relative position of the ball from the two goal posts. Note", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 241, + 506, + 255 + ], + "spans": [ + { + "bbox": [ + 105, + 241, + 506, + 255 + ], + "score": 1.0, + "content": "that none of the agents observe the complete global state of the multi-agent world and only observe", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 253, + 505, + 265 + ], + "spans": [ + { + "bbox": [ + 105, + 253, + 505, + 265 + ], + "score": 1.0, + "content": "relevant sub-parts of the state vector to keep observations as close to real-world scenarios as possible.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 10.5 + }, + { + "type": "text", + "bbox": [ + 107, + 270, + 505, + 357 + ], + "lines": [ + { + "bbox": [ + 105, + 268, + 505, + 283 + ], + "spans": [ + { + "bbox": [ + 105, + 268, + 505, + 283 + ], + "score": 1.0, + "content": "Algorithm Parameters: We use Adam (Kingma & Ba, 2014) with learning rate 0.001. The clip-", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 281, + 506, + 294 + ], + "spans": [ + { + "bbox": [ + 105, + 281, + 201, + 294 + ], + "score": 1.0, + "content": "ping parameter in PPO", + "type": "text" + }, + { + "bbox": [ + 201, + 281, + 235, + 291 + ], + "score": 0.88, + "content": "\\epsilon = 0 . 2", + "type": "inline_equation" + }, + { + "bbox": [ + 235, + 281, + 313, + 294 + ], + "score": 1.0, + "content": ", discounting factor", + "type": "text" + }, + { + "bbox": [ + 314, + 281, + 359, + 292 + ], + "score": 0.89, + "content": "\\gamma = 0 . 9 9 5", + "type": "inline_equation" + }, + { + "bbox": [ + 359, + 281, + 506, + 294 + ], + "score": 1.0, + "content": "and generalized advantage estimate", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 291, + 505, + 305 + ], + "spans": [ + { + "bbox": [ + 105, + 291, + 149, + 305 + ], + "score": 1.0, + "content": "parameter", + "type": "text" + }, + { + "bbox": [ + 149, + 292, + 188, + 302 + ], + "score": 0.9, + "content": "\\lambda = 0 . 9 5", + "type": "inline_equation" + }, + { + "bbox": [ + 189, + 291, + 505, + 305 + ], + "score": 1.0, + "content": ". Each iteration, we collect 409600 samples from the parallel rollouts and per-", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 303, + 505, + 315 + ], + "spans": [ + { + "bbox": [ + 105, + 303, + 505, + 315 + ], + "score": 1.0, + "content": "form multiple epochs of PPO training in mini-batches consisting of 5120 samples. For MLP policies", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 313, + 505, + 327 + ], + "spans": [ + { + "bbox": [ + 105, + 313, + 505, + 327 + ], + "score": 1.0, + "content": "we did 6 epochs of SGD per iteration and for LSTM policies we did 3 epochs. We don’t use any", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 325, + 505, + 337 + ], + "spans": [ + { + "bbox": [ + 105, + 325, + 210, + 337 + ], + "score": 1.0, + "content": "entropy bonus. We found", + "type": "text" + }, + { + "bbox": [ + 210, + 325, + 219, + 336 + ], + "score": 0.86, + "content": "l _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 219, + 325, + 505, + 337 + ], + "score": 1.0, + "content": "regularization of the policy and value network parameters to be useful.", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 336, + 505, + 348 + ], + "spans": [ + { + "bbox": [ + 106, + 336, + 173, + 348 + ], + "score": 1.0, + "content": "The co-efficient", + "type": "text" + }, + { + "bbox": [ + 173, + 337, + 184, + 347 + ], + "score": 0.85, + "content": "\\alpha _ { t }", + "type": "inline_equation" + }, + { + "bbox": [ + 185, + 336, + 505, + 348 + ], + "score": 1.0, + "content": "in eq. 1 for the exploration reward is annealed to 0 in 500 iterations for all the", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 347, + 440, + 358 + ], + "spans": [ + { + "bbox": [ + 105, + 347, + 440, + 358 + ], + "score": 1.0, + "content": "environments except for kick-and-defend in which it is annealed in 1000 iterations.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 19.5 + }, + { + "type": "title", + "bbox": [ + 108, + 372, + 226, + 383 + ], + "lines": [ + { + "bbox": [ + 105, + 372, + 227, + 385 + ], + "spans": [ + { + "bbox": [ + 105, + 372, + 227, + 385 + ], + "score": 1.0, + "content": "5.2 LEARNED BEHAVIORS", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 24 + }, + { + "type": "text", + "bbox": [ + 107, + 393, + 505, + 580 + ], + "lines": [ + { + "bbox": [ + 106, + 394, + 505, + 406 + ], + "spans": [ + { + "bbox": [ + 106, + 394, + 505, + 406 + ], + "score": 1.0, + "content": "We observe numerous interesting learned behaviors demonstrated by the agents as a result of the", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 405, + 505, + 417 + ], + "spans": [ + { + "bbox": [ + 105, + 405, + 505, + 417 + ], + "score": 1.0, + "content": "complexity arising out of the competitive multi-agent training. Different random seeds often lead", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 415, + 505, + 428 + ], + "spans": [ + { + "bbox": [ + 105, + 415, + 505, + 428 + ], + "score": 1.0, + "content": "to somewhat different behaviors. Refer to the videos for highlights of the learned policies on all", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 104, + 424, + 506, + 440 + ], + "spans": [ + { + "bbox": [ + 104, + 424, + 506, + 440 + ], + "score": 1.0, + "content": "the tasks. On Run-to-Goal, we observe the quadruped Ants demonstrate behaviors like blocking,", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 104, + 437, + 506, + 451 + ], + "spans": [ + { + "bbox": [ + 104, + 437, + 506, + 451 + ], + "score": 1.0, + "content": "standing robustly, using legs to topple the opponent and running towards the goal. Humanoids", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 448, + 505, + 461 + ], + "spans": [ + { + "bbox": [ + 105, + 448, + 505, + 461 + ], + "score": 1.0, + "content": "try to avoid each other and run towards their goal really fast, occasionally they will bump into", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 460, + 505, + 471 + ], + "spans": [ + { + "bbox": [ + 105, + 460, + 505, + 471 + ], + "score": 1.0, + "content": "each other with force and try to recover from the impact. On You-Shall-Not-Pass, we observe the", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 470, + 506, + 483 + ], + "spans": [ + { + "bbox": [ + 105, + 470, + 506, + 483 + ], + "score": 1.0, + "content": "blocking humanoid learn to block by raising its hand while the other humanoid eventually learned", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 480, + 506, + 495 + ], + "spans": [ + { + "bbox": [ + 105, + 480, + 506, + 495 + ], + "score": 1.0, + "content": "to duck in order to cross. On Sumo, we observe multiple different strategies used by the Ant and", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 492, + 505, + 505 + ], + "spans": [ + { + "bbox": [ + 105, + 492, + 505, + 505 + ], + "score": 1.0, + "content": "Humanoid. Humanoids, for example, demonstrate a stable fighting stance and learned to knock the", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 503, + 506, + 517 + ], + "spans": [ + { + "bbox": [ + 105, + 503, + 506, + 517 + ], + "score": 1.0, + "content": "opponent using their heads. In a different run, we observe that one agent learned to charge towards", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 514, + 505, + 527 + ], + "spans": [ + { + "bbox": [ + 105, + 514, + 505, + 527 + ], + "score": 1.0, + "content": "the opponent whereas the opponent tried to fool it by stepping out of the opponents way at the", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 525, + 505, + 538 + ], + "spans": [ + { + "bbox": [ + 105, + 525, + 505, + 538 + ], + "score": 1.0, + "content": "edge of the ring. On kick-and-defend, we observe that the kicker learned a good kicking policy", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 536, + 505, + 548 + ], + "spans": [ + { + "bbox": [ + 105, + 536, + 505, + 548 + ], + "score": 1.0, + "content": "where it can go towards random ball positions, uses its feet to kick the ball high and tries to avoid", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 547, + 504, + 559 + ], + "spans": [ + { + "bbox": [ + 106, + 547, + 504, + 559 + ], + "score": 1.0, + "content": "the defender. We also see a fooling behavior in the kicker’s motions where it moves left and right", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 558, + 506, + 572 + ], + "spans": [ + { + "bbox": [ + 105, + 558, + 506, + 572 + ], + "score": 1.0, + "content": "quickly once close to the ball to fool the defender. The defender learned to defend by moving in", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 569, + 446, + 581 + ], + "spans": [ + { + "bbox": [ + 105, + 569, + 446, + 581 + ], + "score": 1.0, + "content": "response to the motion of the kicker and using its hands and legs to obstruct the ball.", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 33 + }, + { + "type": "text", + "bbox": [ + 107, + 586, + 504, + 663 + ], + "lines": [ + { + "bbox": [ + 106, + 586, + 506, + 598 + ], + "spans": [ + { + "bbox": [ + 106, + 586, + 506, + 598 + ], + "score": 1.0, + "content": "These movement strategies are not just useful in competition, for example the skills learned in the", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 596, + 506, + 610 + ], + "spans": [ + { + "bbox": [ + 105, + 596, + 506, + 610 + ], + "score": 1.0, + "content": "Sumo can transfer to other situations even without other agents. In one case, we took the agent", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 607, + 506, + 621 + ], + "spans": [ + { + "bbox": [ + 105, + 607, + 506, + 621 + ], + "score": 1.0, + "content": "trained on the multi-agent Sumo task and faced it with the task of standing while being perturbed by", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 619, + 506, + 631 + ], + "spans": [ + { + "bbox": [ + 105, + 619, + 506, + 631 + ], + "score": 1.0, + "content": "wind forces. The agent receives the zero vector for parts of the opponent observation. We found that", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 630, + 506, + 642 + ], + "spans": [ + { + "bbox": [ + 106, + 630, + 506, + 642 + ], + "score": 1.0, + "content": "the agent managed to stay upright despite never seeing the windy environment or observing wind", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 640, + 506, + 654 + ], + "spans": [ + { + "bbox": [ + 105, + 640, + 506, + 654 + ], + "score": 1.0, + "content": "forces. Please see Appendix B.1 for details of the experiment and quantitative results. Refer to the", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 652, + 213, + 663 + ], + "spans": [ + { + "bbox": [ + 106, + 652, + 213, + 663 + ], + "score": 1.0, + "content": "video for a demonstration.", + "type": "text" + } + ], + "index": 48 + } + ], + "index": 45 + }, + { + "type": "title", + "bbox": [ + 107, + 677, + 303, + 689 + ], + "lines": [ + { + "bbox": [ + 105, + 677, + 305, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 305, + 690 + ], + "score": 1.0, + "content": "5.3 EFFECT OF EXPLORATION CURRICULUM", + "type": "text" + } + ], + "index": 49 + } + ], + "index": 49 + }, + { + "type": "text", + "bbox": [ + 108, + 699, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "score": 1.0, + "content": "In section 4.1 we introduced an exploration curriculum to help agents explore in a 3D world. One", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 105, + 709, + 506, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 506, + 722 + ], + "score": 1.0, + "content": "question that arises is the extent to which the outcome of learning is affected by this exploration", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 106, + 721, + 506, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 506, + 733 + ], + "score": 1.0, + "content": "reward and to explore the benefit of this exploration reward. As already argued, we found the", + "type": "text" + } + ], + "index": 52 + } + ], + "index": 51 + } + ], + "page_idx": 5, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2018", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 752, + 308, + 760 + ], + "lines": [ + { + "bbox": [ + 302, + 751, + 309, + 762 + ], + "spans": [ + { + "bbox": [ + 302, + 751, + 309, + 762 + ], + "score": 1.0, + "content": "6", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 505, + 149 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "MLP policy and value functions for the run-to-goal and you-shall-not-pass environments, and LSTM", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 94, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 94, + 505, + 106 + ], + "score": 1.0, + "content": "policy and value function for sumo and kick-and-defend. This is because earlier experiments did not", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 104, + 506, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 104, + 506, + 118 + ], + "score": 1.0, + "content": "yield good results with MLP policy on these tasks. For LSTM policy we used truncated BPTT with", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 505, + 128 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 505, + 128 + ], + "score": 1.0, + "content": "a truncation of 10 timesteps. The policy and the value functions have separate parameters. For the", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 127, + 505, + 140 + ], + "spans": [ + { + "bbox": [ + 105, + 127, + 505, + 140 + ], + "score": 1.0, + "content": "asymmetric games, you-shall-not-pass and kick-and-defend, we use separate policies for the two", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 138, + 178, + 150 + ], + "spans": [ + { + "bbox": [ + 106, + 138, + 178, + 150 + ], + "score": 1.0, + "content": "agents in a game.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 2.5, + "bbox_fs": [ + 105, + 82, + 506, + 150 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 154, + 505, + 264 + ], + "lines": [ + { + "bbox": [ + 105, + 153, + 505, + 167 + ], + "spans": [ + { + "bbox": [ + 105, + 153, + 505, + 167 + ], + "score": 1.0, + "content": "Observations: For the Ant body we use all the joint angles of the agent, its velocity of all its", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 165, + 506, + 178 + ], + "spans": [ + { + "bbox": [ + 105, + 165, + 506, + 178 + ], + "score": 1.0, + "content": "joints, the contact forces acting on the body and the relative position and all the joint angles for the", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 176, + 506, + 189 + ], + "spans": [ + { + "bbox": [ + 105, + 176, + 506, + 189 + ], + "score": 1.0, + "content": "opponent. For the Humanoid body, in addition to the above we also give the centre-of-mass based", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 188, + 505, + 199 + ], + "spans": [ + { + "bbox": [ + 106, + 188, + 505, + 199 + ], + "score": 1.0, + "content": "inertia tensor, velocity vector and the actuator forces for the body. In addition to these, there are other", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 198, + 506, + 211 + ], + "spans": [ + { + "bbox": [ + 105, + 198, + 506, + 211 + ], + "score": 1.0, + "content": "environment specific observations. For the Sumo environment, we give the torso’s orientation vector", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 209, + 505, + 222 + ], + "spans": [ + { + "bbox": [ + 105, + 209, + 505, + 222 + ], + "score": 1.0, + "content": "as the input, the radial distance from the edge of the ring of all the agents and the time remaining in", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 220, + 506, + 232 + ], + "spans": [ + { + "bbox": [ + 105, + 220, + 506, + 232 + ], + "score": 1.0, + "content": "the game. For kick-and-defend, we give the relative position of the ball from the agent, the relative", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 231, + 505, + 244 + ], + "spans": [ + { + "bbox": [ + 105, + 231, + 505, + 244 + ], + "score": 1.0, + "content": "distance of the ball from goal and the relative position of the ball from the two goal posts. Note", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 241, + 506, + 255 + ], + "spans": [ + { + "bbox": [ + 105, + 241, + 506, + 255 + ], + "score": 1.0, + "content": "that none of the agents observe the complete global state of the multi-agent world and only observe", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 253, + 505, + 265 + ], + "spans": [ + { + "bbox": [ + 105, + 253, + 505, + 265 + ], + "score": 1.0, + "content": "relevant sub-parts of the state vector to keep observations as close to real-world scenarios as possible.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 10.5, + "bbox_fs": [ + 105, + 153, + 506, + 265 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 270, + 505, + 357 + ], + "lines": [ + { + "bbox": [ + 105, + 268, + 505, + 283 + ], + "spans": [ + { + "bbox": [ + 105, + 268, + 505, + 283 + ], + "score": 1.0, + "content": "Algorithm Parameters: We use Adam (Kingma & Ba, 2014) with learning rate 0.001. The clip-", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 281, + 506, + 294 + ], + "spans": [ + { + "bbox": [ + 105, + 281, + 201, + 294 + ], + "score": 1.0, + "content": "ping parameter in PPO", + "type": "text" + }, + { + "bbox": [ + 201, + 281, + 235, + 291 + ], + "score": 0.88, + "content": "\\epsilon = 0 . 2", + "type": "inline_equation" + }, + { + "bbox": [ + 235, + 281, + 313, + 294 + ], + "score": 1.0, + "content": ", discounting factor", + "type": "text" + }, + { + "bbox": [ + 314, + 281, + 359, + 292 + ], + "score": 0.89, + "content": "\\gamma = 0 . 9 9 5", + "type": "inline_equation" + }, + { + "bbox": [ + 359, + 281, + 506, + 294 + ], + "score": 1.0, + "content": "and generalized advantage estimate", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 291, + 505, + 305 + ], + "spans": [ + { + "bbox": [ + 105, + 291, + 149, + 305 + ], + "score": 1.0, + "content": "parameter", + "type": "text" + }, + { + "bbox": [ + 149, + 292, + 188, + 302 + ], + "score": 0.9, + "content": "\\lambda = 0 . 9 5", + "type": "inline_equation" + }, + { + "bbox": [ + 189, + 291, + 505, + 305 + ], + "score": 1.0, + "content": ". Each iteration, we collect 409600 samples from the parallel rollouts and per-", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 303, + 505, + 315 + ], + "spans": [ + { + "bbox": [ + 105, + 303, + 505, + 315 + ], + "score": 1.0, + "content": "form multiple epochs of PPO training in mini-batches consisting of 5120 samples. For MLP policies", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 313, + 505, + 327 + ], + "spans": [ + { + "bbox": [ + 105, + 313, + 505, + 327 + ], + "score": 1.0, + "content": "we did 6 epochs of SGD per iteration and for LSTM policies we did 3 epochs. We don’t use any", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 325, + 505, + 337 + ], + "spans": [ + { + "bbox": [ + 105, + 325, + 210, + 337 + ], + "score": 1.0, + "content": "entropy bonus. We found", + "type": "text" + }, + { + "bbox": [ + 210, + 325, + 219, + 336 + ], + "score": 0.86, + "content": "l _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 219, + 325, + 505, + 337 + ], + "score": 1.0, + "content": "regularization of the policy and value network parameters to be useful.", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 336, + 505, + 348 + ], + "spans": [ + { + "bbox": [ + 106, + 336, + 173, + 348 + ], + "score": 1.0, + "content": "The co-efficient", + "type": "text" + }, + { + "bbox": [ + 173, + 337, + 184, + 347 + ], + "score": 0.85, + "content": "\\alpha _ { t }", + "type": "inline_equation" + }, + { + "bbox": [ + 185, + 336, + 505, + 348 + ], + "score": 1.0, + "content": "in eq. 1 for the exploration reward is annealed to 0 in 500 iterations for all the", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 347, + 440, + 358 + ], + "spans": [ + { + "bbox": [ + 105, + 347, + 440, + 358 + ], + "score": 1.0, + "content": "environments except for kick-and-defend in which it is annealed in 1000 iterations.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 19.5, + "bbox_fs": [ + 105, + 268, + 506, + 358 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 372, + 226, + 383 + ], + "lines": [ + { + "bbox": [ + 105, + 372, + 227, + 385 + ], + "spans": [ + { + "bbox": [ + 105, + 372, + 227, + 385 + ], + "score": 1.0, + "content": "5.2 LEARNED BEHAVIORS", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 24 + }, + { + "type": "text", + "bbox": [ + 107, + 393, + 505, + 580 + ], + "lines": [ + { + "bbox": [ + 106, + 394, + 505, + 406 + ], + "spans": [ + { + "bbox": [ + 106, + 394, + 505, + 406 + ], + "score": 1.0, + "content": "We observe numerous interesting learned behaviors demonstrated by the agents as a result of the", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 405, + 505, + 417 + ], + "spans": [ + { + "bbox": [ + 105, + 405, + 505, + 417 + ], + "score": 1.0, + "content": "complexity arising out of the competitive multi-agent training. Different random seeds often lead", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 415, + 505, + 428 + ], + "spans": [ + { + "bbox": [ + 105, + 415, + 505, + 428 + ], + "score": 1.0, + "content": "to somewhat different behaviors. Refer to the videos for highlights of the learned policies on all", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 104, + 424, + 506, + 440 + ], + "spans": [ + { + "bbox": [ + 104, + 424, + 506, + 440 + ], + "score": 1.0, + "content": "the tasks. On Run-to-Goal, we observe the quadruped Ants demonstrate behaviors like blocking,", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 104, + 437, + 506, + 451 + ], + "spans": [ + { + "bbox": [ + 104, + 437, + 506, + 451 + ], + "score": 1.0, + "content": "standing robustly, using legs to topple the opponent and running towards the goal. Humanoids", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 448, + 505, + 461 + ], + "spans": [ + { + "bbox": [ + 105, + 448, + 505, + 461 + ], + "score": 1.0, + "content": "try to avoid each other and run towards their goal really fast, occasionally they will bump into", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 460, + 505, + 471 + ], + "spans": [ + { + "bbox": [ + 105, + 460, + 505, + 471 + ], + "score": 1.0, + "content": "each other with force and try to recover from the impact. On You-Shall-Not-Pass, we observe the", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 470, + 506, + 483 + ], + "spans": [ + { + "bbox": [ + 105, + 470, + 506, + 483 + ], + "score": 1.0, + "content": "blocking humanoid learn to block by raising its hand while the other humanoid eventually learned", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 480, + 506, + 495 + ], + "spans": [ + { + "bbox": [ + 105, + 480, + 506, + 495 + ], + "score": 1.0, + "content": "to duck in order to cross. On Sumo, we observe multiple different strategies used by the Ant and", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 492, + 505, + 505 + ], + "spans": [ + { + "bbox": [ + 105, + 492, + 505, + 505 + ], + "score": 1.0, + "content": "Humanoid. Humanoids, for example, demonstrate a stable fighting stance and learned to knock the", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 503, + 506, + 517 + ], + "spans": [ + { + "bbox": [ + 105, + 503, + 506, + 517 + ], + "score": 1.0, + "content": "opponent using their heads. In a different run, we observe that one agent learned to charge towards", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 514, + 505, + 527 + ], + "spans": [ + { + "bbox": [ + 105, + 514, + 505, + 527 + ], + "score": 1.0, + "content": "the opponent whereas the opponent tried to fool it by stepping out of the opponents way at the", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 525, + 505, + 538 + ], + "spans": [ + { + "bbox": [ + 105, + 525, + 505, + 538 + ], + "score": 1.0, + "content": "edge of the ring. On kick-and-defend, we observe that the kicker learned a good kicking policy", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 536, + 505, + 548 + ], + "spans": [ + { + "bbox": [ + 105, + 536, + 505, + 548 + ], + "score": 1.0, + "content": "where it can go towards random ball positions, uses its feet to kick the ball high and tries to avoid", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 547, + 504, + 559 + ], + "spans": [ + { + "bbox": [ + 106, + 547, + 504, + 559 + ], + "score": 1.0, + "content": "the defender. We also see a fooling behavior in the kicker’s motions where it moves left and right", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 558, + 506, + 572 + ], + "spans": [ + { + "bbox": [ + 105, + 558, + 506, + 572 + ], + "score": 1.0, + "content": "quickly once close to the ball to fool the defender. The defender learned to defend by moving in", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 569, + 446, + 581 + ], + "spans": [ + { + "bbox": [ + 105, + 569, + 446, + 581 + ], + "score": 1.0, + "content": "response to the motion of the kicker and using its hands and legs to obstruct the ball.", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 33, + "bbox_fs": [ + 104, + 394, + 506, + 581 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 586, + 504, + 663 + ], + "lines": [ + { + "bbox": [ + 106, + 586, + 506, + 598 + ], + "spans": [ + { + "bbox": [ + 106, + 586, + 506, + 598 + ], + "score": 1.0, + "content": "These movement strategies are not just useful in competition, for example the skills learned in the", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 596, + 506, + 610 + ], + "spans": [ + { + "bbox": [ + 105, + 596, + 506, + 610 + ], + "score": 1.0, + "content": "Sumo can transfer to other situations even without other agents. In one case, we took the agent", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 607, + 506, + 621 + ], + "spans": [ + { + "bbox": [ + 105, + 607, + 506, + 621 + ], + "score": 1.0, + "content": "trained on the multi-agent Sumo task and faced it with the task of standing while being perturbed by", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 619, + 506, + 631 + ], + "spans": [ + { + "bbox": [ + 105, + 619, + 506, + 631 + ], + "score": 1.0, + "content": "wind forces. The agent receives the zero vector for parts of the opponent observation. We found that", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 630, + 506, + 642 + ], + "spans": [ + { + "bbox": [ + 106, + 630, + 506, + 642 + ], + "score": 1.0, + "content": "the agent managed to stay upright despite never seeing the windy environment or observing wind", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 640, + 506, + 654 + ], + "spans": [ + { + "bbox": [ + 105, + 640, + 506, + 654 + ], + "score": 1.0, + "content": "forces. Please see Appendix B.1 for details of the experiment and quantitative results. Refer to the", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 652, + 213, + 663 + ], + "spans": [ + { + "bbox": [ + 106, + 652, + 213, + 663 + ], + "score": 1.0, + "content": "video for a demonstration.", + "type": "text" + } + ], + "index": 48 + } + ], + "index": 45, + "bbox_fs": [ + 105, + 586, + 506, + 663 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 677, + 303, + 689 + ], + "lines": [ + { + "bbox": [ + 105, + 677, + 305, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 305, + 690 + ], + "score": 1.0, + "content": "5.3 EFFECT OF EXPLORATION CURRICULUM", + "type": "text" + } + ], + "index": 49 + } + ], + "index": 49 + }, + { + "type": "text", + "bbox": [ + 108, + 699, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "score": 1.0, + "content": "In section 4.1 we introduced an exploration curriculum to help agents explore in a 3D world. One", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 105, + 709, + 506, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 506, + 722 + ], + "score": 1.0, + "content": "question that arises is the extent to which the outcome of learning is affected by this exploration", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 106, + 721, + 506, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 506, + 733 + ], + "score": 1.0, + "content": "reward and to explore the benefit of this exploration reward. As already argued, we found the", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 106, + 379, + 506, + 392 + ], + "spans": [ + { + "bbox": [ + 106, + 379, + 506, + 392 + ], + "score": 1.0, + "content": "exploration reward to be crucial for learning as otherwise the agents are unable to explore the sparse", + "type": "text", + "cross_page": true + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 390, + 506, + 402 + ], + "spans": [ + { + "bbox": [ + 105, + 390, + 506, + 402 + ], + "score": 1.0, + "content": "competition reward. However, the learned behaviors are mostly a result of the natural curriculum", + "type": "text", + "cross_page": true + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 401, + 504, + 412 + ], + "spans": [ + { + "bbox": [ + 106, + 401, + 504, + 412 + ], + "score": 1.0, + "content": "arising out of the multi-agent competition and not due to the dense exploration reward. To see this,", + "type": "text", + "cross_page": true + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 412, + 505, + 424 + ], + "spans": [ + { + "bbox": [ + 106, + 412, + 505, + 424 + ], + "score": 1.0, + "content": "first note that we do not give any reward for many of the complex learned behaviours described", + "type": "text", + "cross_page": true + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 423, + 506, + 435 + ], + "spans": [ + { + "bbox": [ + 105, + 423, + 506, + 435 + ], + "score": 1.0, + "content": "previously. We further test this by not annealing the exploration reward and always having a dense", + "type": "text", + "cross_page": true + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 433, + 505, + 446 + ], + "spans": [ + { + "bbox": [ + 105, + 433, + 505, + 446 + ], + "score": 1.0, + "content": "reward which is a sum of the exploration reward and the competition reward. We take these agents", + "type": "text", + "cross_page": true + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 444, + 505, + 457 + ], + "spans": [ + { + "bbox": [ + 105, + 444, + 505, + 457 + ], + "score": 1.0, + "content": "trained without curriculum and pit them against agents trained with exploration curriculum. We plot", + "type": "text", + "cross_page": true + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 455, + 506, + 469 + ], + "spans": [ + { + "bbox": [ + 105, + 455, + 506, + 469 + ], + "score": 1.0, + "content": "the average win-rates over 800 games at various intervals during training in Fig. 3, for the sumo", + "type": "text", + "cross_page": true + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 467, + 505, + 479 + ], + "spans": [ + { + "bbox": [ + 106, + 467, + 505, + 479 + ], + "score": 1.0, + "content": "and kick-and-defend environments. For kick-and-defend there are two plots, one where kicker is", + "type": "text", + "cross_page": true + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 477, + 505, + 489 + ], + "spans": [ + { + "bbox": [ + 106, + 477, + 505, + 489 + ], + "score": 1.0, + "content": "trained with curriculum while keeper without it and vice versa. Observe that the agents trained", + "type": "text", + "cross_page": true + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 489, + 505, + 501 + ], + "spans": [ + { + "bbox": [ + 106, + 489, + 505, + 501 + ], + "score": 1.0, + "content": "with curriculum beat the non-curriculum agents by a margin. We found agents trained without", + "type": "text", + "cross_page": true + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 498, + 506, + 513 + ], + "spans": [ + { + "bbox": [ + 105, + 498, + 506, + 513 + ], + "score": 1.0, + "content": "curriculum exhibit either non-optimal behaviors for the competition or end up optimizing for a", + "type": "text", + "cross_page": true + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 510, + 506, + 523 + ], + "spans": [ + { + "bbox": [ + 105, + 510, + 506, + 523 + ], + "score": 1.0, + "content": "particular component of the dense reward. For example, for Sumo, the agents just learn to stand and", + "type": "text", + "cross_page": true + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 520, + 506, + 535 + ], + "spans": [ + { + "bbox": [ + 105, + 520, + 506, + 535 + ], + "score": 1.0, + "content": "move towards center of the arena, and for kick-and-defend, the defender optimizes for being able to", + "type": "text", + "cross_page": true + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 532, + 505, + 545 + ], + "spans": [ + { + "bbox": [ + 105, + 532, + 505, + 545 + ], + "score": 1.0, + "content": "stand up but doesn’t learn to defend while the kicker learns a non-optimal strategy of carrying the ball", + "type": "text", + "cross_page": true + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 543, + 506, + 556 + ], + "spans": [ + { + "bbox": [ + 106, + 543, + 506, + 556 + ], + "score": 1.0, + "content": "with itself to the goal (rather than kicking) – a policy which is easily defeated by a defender trained", + "type": "text", + "cross_page": true + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 554, + 505, + 567 + ], + "spans": [ + { + "bbox": [ + 106, + 554, + 505, + 567 + ], + "score": 1.0, + "content": "with curriculum. 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For humanoid", + "type": "text" + }, + { + "bbox": [ + 410, + 334, + 447, + 345 + ], + "score": 0.9, + "content": "\\delta \\ : = \\ : 0 . 5", + "type": "inline_equation" + }, + { + "bbox": [ + 448, + 334, + 505, + 347 + ], + "score": 1.0, + "content": "gives highest", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 345, + 339, + 357 + ], + "spans": [ + { + "bbox": [ + 106, + 345, + 274, + 357 + ], + "score": 1.0, + "content": "win-rate and lowest loss, whereas for Ant", + "type": "text" + }, + { + "bbox": [ + 275, + 345, + 299, + 356 + ], + "score": 0.9, + "content": "\\delta = 0", + "type": "inline_equation" + }, + { + "bbox": [ + 299, + 345, + 339, + 357 + ], + "score": 1.0, + "content": "was best.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 16 + } + ], + "index": 13.0 + }, + { + "type": "text", + "bbox": [ + 106, + 379, + 505, + 609 + ], + "lines": [ + { + "bbox": [ + 106, + 379, + 506, + 392 + ], + "spans": [ + { + "bbox": [ + 106, + 379, + 506, + 392 + ], + "score": 1.0, + "content": "exploration reward to be crucial for learning as otherwise the agents are unable to explore the sparse", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 390, + 506, + 402 + ], + "spans": [ + { + "bbox": [ + 105, + 390, + 506, + 402 + ], + "score": 1.0, + "content": "competition reward. However, the learned behaviors are mostly a result of the natural curriculum", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 401, + 504, + 412 + ], + "spans": [ + { + "bbox": [ + 106, + 401, + 504, + 412 + ], + "score": 1.0, + "content": "arising out of the multi-agent competition and not due to the dense exploration reward. To see this,", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 412, + 505, + 424 + ], + "spans": [ + { + "bbox": [ + 106, + 412, + 505, + 424 + ], + "score": 1.0, + "content": "first note that we do not give any reward for many of the complex learned behaviours described", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 423, + 506, + 435 + ], + "spans": [ + { + "bbox": [ + 105, + 423, + 506, + 435 + ], + "score": 1.0, + "content": "previously. We further test this by not annealing the exploration reward and always having a dense", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 433, + 505, + 446 + ], + "spans": [ + { + "bbox": [ + 105, + 433, + 505, + 446 + ], + "score": 1.0, + "content": "reward which is a sum of the exploration reward and the competition reward. We take these agents", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 444, + 505, + 457 + ], + "spans": [ + { + "bbox": [ + 105, + 444, + 505, + 457 + ], + "score": 1.0, + "content": "trained without curriculum and pit them against agents trained with exploration curriculum. We plot", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 455, + 506, + 469 + ], + "spans": [ + { + "bbox": [ + 105, + 455, + 506, + 469 + ], + "score": 1.0, + "content": "the average win-rates over 800 games at various intervals during training in Fig. 3, for the sumo", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 467, + 505, + 479 + ], + "spans": [ + { + "bbox": [ + 106, + 467, + 505, + 479 + ], + "score": 1.0, + "content": "and kick-and-defend environments. For kick-and-defend there are two plots, one where kicker is", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 477, + 505, + 489 + ], + "spans": [ + { + "bbox": [ + 106, + 477, + 505, + 489 + ], + "score": 1.0, + "content": "trained with curriculum while keeper without it and vice versa. Observe that the agents trained", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 489, + 505, + 501 + ], + "spans": [ + { + "bbox": [ + 106, + 489, + 505, + 501 + ], + "score": 1.0, + "content": "with curriculum beat the non-curriculum agents by a margin. We found agents trained without", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 498, + 506, + 513 + ], + "spans": [ + { + "bbox": [ + 105, + 498, + 506, + 513 + ], + "score": 1.0, + "content": "curriculum exhibit either non-optimal behaviors for the competition or end up optimizing for a", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 510, + 506, + 523 + ], + "spans": [ + { + "bbox": [ + 105, + 510, + 506, + 523 + ], + "score": 1.0, + "content": "particular component of the dense reward. For example, for Sumo, the agents just learn to stand and", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 520, + 506, + 535 + ], + "spans": [ + { + "bbox": [ + 105, + 520, + 506, + 535 + ], + "score": 1.0, + "content": "move towards center of the arena, and for kick-and-defend, the defender optimizes for being able to", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 532, + 505, + 545 + ], + "spans": [ + { + "bbox": [ + 105, + 532, + 505, + 545 + ], + "score": 1.0, + "content": "stand up but doesn’t learn to defend while the kicker learns a non-optimal strategy of carrying the ball", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 543, + 506, + 556 + ], + "spans": [ + { + "bbox": [ + 106, + 543, + 506, + 556 + ], + "score": 1.0, + "content": "with itself to the goal (rather than kicking) – a policy which is easily defeated by a defender trained", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 554, + 505, + 567 + ], + "spans": [ + { + "bbox": [ + 106, + 554, + 505, + 567 + ], + "score": 1.0, + "content": "with curriculum. Moreover, training without curriculum also takes more samples to learn. We also", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 564, + 505, + 578 + ], + "spans": [ + { + "bbox": [ + 105, + 564, + 505, + 578 + ], + "score": 1.0, + "content": "show these behaviours qualitatively in the videos. These results echo some recent findings (albeit", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 576, + 505, + 589 + ], + "spans": [ + { + "bbox": [ + 105, + 576, + 505, + 589 + ], + "score": 1.0, + "content": "in the single agent case), like Andrychowicz et al. (2017) who found that optimizing for the sparse", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 587, + 505, + 600 + ], + "spans": [ + { + "bbox": [ + 105, + 587, + 505, + 600 + ], + "score": 1.0, + "content": "reward yields better return than optimizing for hand crafted dense rewards. For the competitive", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 599, + 478, + 610 + ], + "spans": [ + { + "bbox": [ + 106, + 599, + 478, + 610 + ], + "score": 1.0, + "content": "multi-agent case, these results shed further light on the importance of the natural curriculum.", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 28 + }, + { + "type": "title", + "bbox": [ + 108, + 623, + 275, + 634 + ], + "lines": [ + { + "bbox": [ + 106, + 623, + 277, + 636 + ], + "spans": [ + { + "bbox": [ + 106, + 623, + 277, + 636 + ], + "score": 1.0, + "content": "5.4 EFFECT OF OPPONENT SAMPLING", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 39 + }, + { + "type": "text", + "bbox": [ + 107, + 644, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 643, + 506, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 643, + 506, + 657 + ], + "score": 1.0, + "content": "In section 4.2, we introduced the past opponent sampling method for training competitive agents", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 655, + 506, + 668 + ], + "spans": [ + { + "bbox": [ + 105, + 655, + 506, + 668 + ], + "score": 1.0, + "content": "simultaneously. This choice of opponent could be important as it affects the natural curriculum for", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "score": 1.0, + "content": "the agents. We test different opponent sampling strategies by considering a threshold on the oldest", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 677, + 506, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 506, + 689 + ], + "score": 1.0, + "content": "opponent for each agent. 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Since the agents", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 506, + 108 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 506, + 108 + ], + "score": 1.0, + "content": "have different skills and strengths at various points during training, we compute a Monte Carlo", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 105, + 505, + 117 + ], + "spans": [ + { + "bbox": [ + 106, + 105, + 505, + 117 + ], + "score": 1.0, + "content": "estimate of the expected win-rate for two agents that have seen the same number of samples taken at a", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 116, + 504, + 127 + ], + "spans": [ + { + "bbox": [ + 106, + 116, + 504, + 127 + ], + "score": 1.0, + "content": "random point during training. This is done by taking average of the win-rates of 30 agents at intervals", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 125, + 506, + 140 + ], + "spans": [ + { + "bbox": [ + 105, + 125, + 506, + 140 + ], + "score": 1.0, + "content": "of 100 iterations after a burn-in of 3000 iterations, where each win-rate is computed from an average", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 136, + 506, + 151 + ], + "spans": [ + { + "bbox": [ + 104, + 136, + 506, + 151 + ], + "score": 1.0, + "content": "over 800 episodes. Table 1a reports the results for Humanoid and Table 1b reports the results for", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 147, + 505, + 162 + ], + "spans": [ + { + "bbox": [ + 105, + 147, + 505, + 162 + ], + "score": 1.0, + "content": "Ant. First note that training against the latest opponent leads to worst performance, as argued earlier.", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 159, + 506, + 172 + ], + "spans": [ + { + "bbox": [ + 105, + 159, + 292, + 172 + ], + "score": 1.0, + "content": "Surprisingly, we found that uniform random", + "type": "text" + }, + { + "bbox": [ + 292, + 159, + 328, + 170 + ], + "score": 0.86, + "content": "\\delta = 0 . 0", + "type": "inline_equation" + }, + { + "bbox": [ + 328, + 159, + 506, + 172 + ], + "score": 1.0, + "content": ") over the entire history to have the highest", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 171, + 505, + 182 + ], + "spans": [ + { + "bbox": [ + 106, + 171, + 194, + 182 + ], + "score": 1.0, + "content": "win-rate for Ant and", + "type": "text" + }, + { + "bbox": [ + 194, + 171, + 229, + 181 + ], + "score": 0.9, + "content": "\\delta = 0 . 5", + "type": "inline_equation" + }, + { + "bbox": [ + 229, + 171, + 505, + 182 + ], + "score": 1.0, + "content": "to have the highest win-rate for Humanoid. This could be because", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 181, + 504, + 194 + ], + "spans": [ + { + "bbox": [ + 105, + 181, + 504, + 194 + ], + "score": 1.0, + "content": "Ant with random policy on a small arena is still a good opponent while a Humanoid with random", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 191, + 506, + 205 + ], + "spans": [ + { + "bbox": [ + 105, + 191, + 506, + 205 + ], + "score": 1.0, + "content": "policy is unable to stand and thus always looses in a few steps. The differences in these win-rates", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 202, + 506, + 216 + ], + "spans": [ + { + "bbox": [ + 105, + 202, + 506, + 216 + ], + "score": 1.0, + "content": "for different sampling strategies show that the choice of the opponent during sampling is important", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 213, + 488, + 227 + ], + "spans": [ + { + "bbox": [ + 105, + 213, + 488, + 227 + ], + "score": 1.0, + "content": "and care must be taken while designing training algorithms for such competitive environments.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 6 + }, + { + "type": "title", + "bbox": [ + 108, + 241, + 257, + 252 + ], + "lines": [ + { + "bbox": [ + 105, + 239, + 259, + 254 + ], + "spans": [ + { + "bbox": [ + 105, + 239, + 259, + 254 + ], + "score": 1.0, + "content": "5.5 LEARNING ROBUST POLICIES", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 13 + }, + { + "type": "text", + "bbox": [ + 107, + 262, + 504, + 306 + ], + "lines": [ + { + "bbox": [ + 105, + 262, + 506, + 275 + ], + "spans": [ + { + "bbox": [ + 105, + 262, + 506, + 275 + ], + "score": 1.0, + "content": "Over-fitting to a particular dataset is often a problem in supervised learning. Similar problems can", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 273, + 506, + 285 + ], + "spans": [ + { + "bbox": [ + 105, + 273, + 506, + 285 + ], + "score": 1.0, + "content": "arise in reinforcement learning setups when there is no or little variation in the environment. We", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 283, + 506, + 298 + ], + "spans": [ + { + "bbox": [ + 105, + 283, + 506, + 298 + ], + "score": 1.0, + "content": "discovered two such problems in our competitive multi-agent training framework and we analyze", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 295, + 290, + 307 + ], + "spans": [ + { + "bbox": [ + 106, + 295, + 290, + 307 + ], + "score": 1.0, + "content": "and propose solutions to address these issues.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 15.5 + }, + { + "type": "title", + "bbox": [ + 108, + 320, + 262, + 331 + ], + "lines": [ + { + "bbox": [ + 106, + 320, + 263, + 333 + ], + "spans": [ + { + "bbox": [ + 106, + 320, + 263, + 333 + ], + "score": 1.0, + "content": "5.5.1 RANDOMIZATION IN WORLD", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 18 + }, + { + "type": "text", + "bbox": [ + 107, + 340, + 505, + 461 + ], + "lines": [ + { + "bbox": [ + 105, + 340, + 505, + 353 + ], + "spans": [ + { + "bbox": [ + 105, + 340, + 505, + 353 + ], + "score": 1.0, + "content": "In order to learn robust policies which generalize better we can introduce randomness in the environ-", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 351, + 504, + 363 + ], + "spans": [ + { + "bbox": [ + 105, + 351, + 504, + 363 + ], + "score": 1.0, + "content": "ment, for example the arena radius for the sumo environment can be randomized, the ball position", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 362, + 505, + 375 + ], + "spans": [ + { + "bbox": [ + 105, + 362, + 505, + 375 + ], + "score": 1.0, + "content": "for the kick-and-defend environment can be randomized, agent start positions can be randomized.", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 373, + 505, + 386 + ], + "spans": [ + { + "bbox": [ + 106, + 373, + 505, + 386 + ], + "score": 1.0, + "content": "However, we found that while randomization is crucial to learn policies which generalize better, it", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 384, + 505, + 397 + ], + "spans": [ + { + "bbox": [ + 105, + 384, + 505, + 397 + ], + "score": 1.0, + "content": "might hinder learning early on as there might be too many things for the agents to explore. Indeed,", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 395, + 506, + 408 + ], + "spans": [ + { + "bbox": [ + 105, + 395, + 506, + 408 + ], + "score": 1.0, + "content": "we observe that in kick-and-defend the agents are unable to learn to kick with a lot of randomization", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 406, + 505, + 419 + ], + "spans": [ + { + "bbox": [ + 105, + 406, + 505, + 419 + ], + "score": 1.0, + "content": "in both the ball and agent positions, whereas when trained with no randomization the learned poli-", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 417, + 506, + 429 + ], + "spans": [ + { + "bbox": [ + 105, + 417, + 506, + 429 + ], + "score": 1.0, + "content": "cies are overfit to the particular position of the ball (see Fig. 4). Thus, in order to learn policies that", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 428, + 505, + 440 + ], + "spans": [ + { + "bbox": [ + 105, + 428, + 505, + 440 + ], + "score": 1.0, + "content": "generalize well, we introduce a simple curriculum in the randomization where we start with a small", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 440, + 505, + 451 + ], + "spans": [ + { + "bbox": [ + 106, + 440, + 505, + 451 + ], + "score": 1.0, + "content": "amount of randomization which is easier to solve and then gradually increase the randomization", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 451, + 428, + 462 + ], + "spans": [ + { + "bbox": [ + 106, + 451, + 428, + 462 + ], + "score": 1.0, + "content": "during training. We found this curriculum to work well for all the environments.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 24 + }, + { + "type": "title", + "bbox": [ + 107, + 476, + 336, + 487 + ], + "lines": [ + { + "bbox": [ + 106, + 475, + 338, + 488 + ], + "spans": [ + { + "bbox": [ + 106, + 475, + 338, + 488 + ], + "score": 1.0, + "content": "5.5.2 COMPETING AGAINST ENSEMBLE OF POLICIES", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 30 + }, + { + "type": "text", + "bbox": [ + 107, + 495, + 505, + 649 + ], + "lines": [ + { + "bbox": [ + 105, + 495, + 505, + 508 + ], + "spans": [ + { + "bbox": [ + 105, + 495, + 505, + 508 + ], + "score": 1.0, + "content": "Another related problem that we observed is over-fitting to the behavior of the opponent when", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 506, + 505, + 519 + ], + "spans": [ + { + "bbox": [ + 105, + 506, + 505, + 519 + ], + "score": 1.0, + "content": "trained for very long. This results in policies which are good against particular types of opponents", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 518, + 505, + 530 + ], + "spans": [ + { + "bbox": [ + 105, + 518, + 505, + 530 + ], + "score": 1.0, + "content": "but do not generalize to other opponents (say opponents trained with a different random seed). This", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 528, + 505, + 541 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 505, + 541 + ], + "score": 1.0, + "content": "overfitting can also be observed in win-rates against opponent during training, where one would", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 539, + 506, + 552 + ], + "spans": [ + { + "bbox": [ + 105, + 539, + 506, + 552 + ], + "score": 1.0, + "content": "see oscillations as agents try to adapt to their particular opponent and changes in their strategies.", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 550, + 506, + 563 + ], + "spans": [ + { + "bbox": [ + 105, + 550, + 506, + 563 + ], + "score": 1.0, + "content": "To overcome this we propose learning multiple policies simultaneously. Thus, there is a pool of", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 561, + 505, + 574 + ], + "spans": [ + { + "bbox": [ + 105, + 561, + 505, + 574 + ], + "score": 1.0, + "content": "policies and in each rollout for a particular policy one of the other policies is selected at random", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 573, + 505, + 584 + ], + "spans": [ + { + "bbox": [ + 105, + 573, + 505, + 584 + ], + "score": 1.0, + "content": "as the opponent (in symmetric games, the same policy can also be an opponent). This is similar", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 583, + 506, + 596 + ], + "spans": [ + { + "bbox": [ + 105, + 583, + 506, + 596 + ], + "score": 1.0, + "content": "to multi-task learning (Caruana, 1998) where the same network is used to model multiple related", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 592, + 506, + 608 + ], + "spans": [ + { + "bbox": [ + 105, + 592, + 506, + 608 + ], + "score": 1.0, + "content": "tasks which allows sharing of statistical strength among tasks and reduces overfitting. In this case,", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 604, + 506, + 618 + ], + "spans": [ + { + "bbox": [ + 105, + 604, + 506, + 618 + ], + "score": 1.0, + "content": "the pool of all policies as opponents – current and throughout the history of training – creates a", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 617, + 505, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 617, + 505, + 628 + ], + "score": 1.0, + "content": "natural distribution over related tasks for multi-task learning. We found random policy initialization", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 104, + 626, + 506, + 641 + ], + "spans": [ + { + "bbox": [ + 104, + 626, + 506, + 641 + ], + "score": 1.0, + "content": "to provide enough diversity between agent policies, however techniques that explicitly encourage", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 638, + 407, + 651 + ], + "spans": [ + { + "bbox": [ + 105, + 638, + 407, + 651 + ], + "score": 1.0, + "content": "diversity (Liu & Wang, 2016) can potentially be incorporated in the future.", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 37.5 + }, + { + "type": "text", + "bbox": [ + 107, + 655, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 655, + 506, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 655, + 506, + 667 + ], + "score": 1.0, + "content": "In order to test the robustness of training policies in an ensemble, we experiment on the Sumo", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "score": 1.0, + "content": "environment with Ant and Humanoid bodies. We train a pool of three policies in an ensemble and", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 677, + 506, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 506, + 689 + ], + "score": 1.0, + "content": "take the policy with the highest average training reward in the last 500 iterations as the best ensemble", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 687, + 506, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 506, + 700 + ], + "score": 1.0, + "content": "policy. We also train three independent policies via self-play, that is just a single policy is trained", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 699, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 506, + 712 + ], + "score": 1.0, + "content": "in a run, and again take the policy with the highest average training reward in last 500 iterations", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 105, + 710, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 505, + 722 + ], + "score": 1.0, + "content": "as the best self-play policy. Then we pit the best ensemble policy against the best self-play policy", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 105, + 721, + 505, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 721, + 505, + 734 + ], + "score": 1.0, + "content": "and record average win-rates over 800 games. Fig. 5 shows the win-rates over training iterations", + "type": "text" + } + ], + "index": 51 + } + ], + "index": 48 + } + ], + "page_idx": 7, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2018", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 752, + 308, + 759 + ], + "lines": [ + { + "bbox": [ + 302, + 750, + 309, + 761 + ], + "spans": [ + { + "bbox": [ + 302, + 750, + 309, + 761 + ], + "score": 1.0, + "content": "8", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 83, + 505, + 225 + ], + "lines": [], + "index": 6, + "bbox_fs": [ + 104, + 82, + 506, + 227 + ], + "lines_deleted": true + }, + { + "type": "title", + "bbox": [ + 108, + 241, + 257, + 252 + ], + "lines": [ + { + "bbox": [ + 105, + 239, + 259, + 254 + ], + "spans": [ + { + "bbox": [ + 105, + 239, + 259, + 254 + ], + "score": 1.0, + "content": "5.5 LEARNING ROBUST POLICIES", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 13 + }, + { + "type": "text", + "bbox": [ + 107, + 262, + 504, + 306 + ], + "lines": [ + { + "bbox": [ + 105, + 262, + 506, + 275 + ], + "spans": [ + { + "bbox": [ + 105, + 262, + 506, + 275 + ], + "score": 1.0, + "content": "Over-fitting to a particular dataset is often a problem in supervised learning. Similar problems can", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 273, + 506, + 285 + ], + "spans": [ + { + "bbox": [ + 105, + 273, + 506, + 285 + ], + "score": 1.0, + "content": "arise in reinforcement learning setups when there is no or little variation in the environment. We", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 283, + 506, + 298 + ], + "spans": [ + { + "bbox": [ + 105, + 283, + 506, + 298 + ], + "score": 1.0, + "content": "discovered two such problems in our competitive multi-agent training framework and we analyze", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 295, + 290, + 307 + ], + "spans": [ + { + "bbox": [ + 106, + 295, + 290, + 307 + ], + "score": 1.0, + "content": "and propose solutions to address these issues.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 15.5, + "bbox_fs": [ + 105, + 262, + 506, + 307 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 320, + 262, + 331 + ], + "lines": [ + { + "bbox": [ + 106, + 320, + 263, + 333 + ], + "spans": [ + { + "bbox": [ + 106, + 320, + 263, + 333 + ], + "score": 1.0, + "content": "5.5.1 RANDOMIZATION IN WORLD", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 18 + }, + { + "type": "text", + "bbox": [ + 107, + 340, + 505, + 461 + ], + "lines": [ + { + "bbox": [ + 105, + 340, + 505, + 353 + ], + "spans": [ + { + "bbox": [ + 105, + 340, + 505, + 353 + ], + "score": 1.0, + "content": "In order to learn robust policies which generalize better we can introduce randomness in the environ-", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 351, + 504, + 363 + ], + "spans": [ + { + "bbox": [ + 105, + 351, + 504, + 363 + ], + "score": 1.0, + "content": "ment, for example the arena radius for the sumo environment can be randomized, the ball position", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 362, + 505, + 375 + ], + "spans": [ + { + "bbox": [ + 105, + 362, + 505, + 375 + ], + "score": 1.0, + "content": "for the kick-and-defend environment can be randomized, agent start positions can be randomized.", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 373, + 505, + 386 + ], + "spans": [ + { + "bbox": [ + 106, + 373, + 505, + 386 + ], + "score": 1.0, + "content": "However, we found that while randomization is crucial to learn policies which generalize better, it", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 384, + 505, + 397 + ], + "spans": [ + { + "bbox": [ + 105, + 384, + 505, + 397 + ], + "score": 1.0, + "content": "might hinder learning early on as there might be too many things for the agents to explore. Indeed,", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 395, + 506, + 408 + ], + "spans": [ + { + "bbox": [ + 105, + 395, + 506, + 408 + ], + "score": 1.0, + "content": "we observe that in kick-and-defend the agents are unable to learn to kick with a lot of randomization", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 406, + 505, + 419 + ], + "spans": [ + { + "bbox": [ + 105, + 406, + 505, + 419 + ], + "score": 1.0, + "content": "in both the ball and agent positions, whereas when trained with no randomization the learned poli-", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 417, + 506, + 429 + ], + "spans": [ + { + "bbox": [ + 105, + 417, + 506, + 429 + ], + "score": 1.0, + "content": "cies are overfit to the particular position of the ball (see Fig. 4). Thus, in order to learn policies that", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 428, + 505, + 440 + ], + "spans": [ + { + "bbox": [ + 105, + 428, + 505, + 440 + ], + "score": 1.0, + "content": "generalize well, we introduce a simple curriculum in the randomization where we start with a small", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 440, + 505, + 451 + ], + "spans": [ + { + "bbox": [ + 106, + 440, + 505, + 451 + ], + "score": 1.0, + "content": "amount of randomization which is easier to solve and then gradually increase the randomization", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 451, + 428, + 462 + ], + "spans": [ + { + "bbox": [ + 106, + 451, + 428, + 462 + ], + "score": 1.0, + "content": "during training. We found this curriculum to work well for all the environments.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 24, + "bbox_fs": [ + 105, + 340, + 506, + 462 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 476, + 336, + 487 + ], + "lines": [ + { + "bbox": [ + 106, + 475, + 338, + 488 + ], + "spans": [ + { + "bbox": [ + 106, + 475, + 338, + 488 + ], + "score": 1.0, + "content": "5.5.2 COMPETING AGAINST ENSEMBLE OF POLICIES", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 30 + }, + { + "type": "text", + "bbox": [ + 107, + 495, + 505, + 649 + ], + "lines": [ + { + "bbox": [ + 105, + 495, + 505, + 508 + ], + "spans": [ + { + "bbox": [ + 105, + 495, + 505, + 508 + ], + "score": 1.0, + "content": "Another related problem that we observed is over-fitting to the behavior of the opponent when", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 506, + 505, + 519 + ], + "spans": [ + { + "bbox": [ + 105, + 506, + 505, + 519 + ], + "score": 1.0, + "content": "trained for very long. This results in policies which are good against particular types of opponents", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 518, + 505, + 530 + ], + "spans": [ + { + "bbox": [ + 105, + 518, + 505, + 530 + ], + "score": 1.0, + "content": "but do not generalize to other opponents (say opponents trained with a different random seed). This", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 528, + 505, + 541 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 505, + 541 + ], + "score": 1.0, + "content": "overfitting can also be observed in win-rates against opponent during training, where one would", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 539, + 506, + 552 + ], + "spans": [ + { + "bbox": [ + 105, + 539, + 506, + 552 + ], + "score": 1.0, + "content": "see oscillations as agents try to adapt to their particular opponent and changes in their strategies.", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 550, + 506, + 563 + ], + "spans": [ + { + "bbox": [ + 105, + 550, + 506, + 563 + ], + "score": 1.0, + "content": "To overcome this we propose learning multiple policies simultaneously. Thus, there is a pool of", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 561, + 505, + 574 + ], + "spans": [ + { + "bbox": [ + 105, + 561, + 505, + 574 + ], + "score": 1.0, + "content": "policies and in each rollout for a particular policy one of the other policies is selected at random", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 573, + 505, + 584 + ], + "spans": [ + { + "bbox": [ + 105, + 573, + 505, + 584 + ], + "score": 1.0, + "content": "as the opponent (in symmetric games, the same policy can also be an opponent). This is similar", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 583, + 506, + 596 + ], + "spans": [ + { + "bbox": [ + 105, + 583, + 506, + 596 + ], + "score": 1.0, + "content": "to multi-task learning (Caruana, 1998) where the same network is used to model multiple related", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 592, + 506, + 608 + ], + "spans": [ + { + "bbox": [ + 105, + 592, + 506, + 608 + ], + "score": 1.0, + "content": "tasks which allows sharing of statistical strength among tasks and reduces overfitting. In this case,", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 604, + 506, + 618 + ], + "spans": [ + { + "bbox": [ + 105, + 604, + 506, + 618 + ], + "score": 1.0, + "content": "the pool of all policies as opponents – current and throughout the history of training – creates a", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 617, + 505, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 617, + 505, + 628 + ], + "score": 1.0, + "content": "natural distribution over related tasks for multi-task learning. We found random policy initialization", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 104, + 626, + 506, + 641 + ], + "spans": [ + { + "bbox": [ + 104, + 626, + 506, + 641 + ], + "score": 1.0, + "content": "to provide enough diversity between agent policies, however techniques that explicitly encourage", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 638, + 407, + 651 + ], + "spans": [ + { + "bbox": [ + 105, + 638, + 407, + 651 + ], + "score": 1.0, + "content": "diversity (Liu & Wang, 2016) can potentially be incorporated in the future.", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 37.5, + "bbox_fs": [ + 104, + 495, + 506, + 651 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 655, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 655, + 506, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 655, + 506, + 667 + ], + "score": 1.0, + "content": "In order to test the robustness of training policies in an ensemble, we experiment on the Sumo", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "score": 1.0, + "content": "environment with Ant and Humanoid bodies. We train a pool of three policies in an ensemble and", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 677, + 506, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 506, + 689 + ], + "score": 1.0, + "content": "take the policy with the highest average training reward in the last 500 iterations as the best ensemble", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 687, + 506, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 506, + 700 + ], + "score": 1.0, + "content": "policy. We also train three independent policies via self-play, that is just a single policy is trained", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 699, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 506, + 712 + ], + "score": 1.0, + "content": "in a run, and again take the policy with the highest average training reward in last 500 iterations", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 105, + 710, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 505, + 722 + ], + "score": 1.0, + "content": "as the best self-play policy. Then we pit the best ensemble policy against the best self-play policy", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 105, + 721, + 505, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 721, + 505, + 734 + ], + "score": 1.0, + "content": "and record average win-rates over 800 games. Fig. 5 shows the win-rates over training iterations", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 106, + 226, + 506, + 239 + ], + "spans": [ + { + "bbox": [ + 106, + 226, + 506, + 239 + ], + "score": 1.0, + "content": "(after 1000 iterations of training). We find that training in ensemble performs significantly better", + "type": "text", + "cross_page": true + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 237, + 505, + 250 + ], + "spans": [ + { + "bbox": [ + 105, + 237, + 505, + 250 + ], + "score": 1.0, + "content": "for the humanoid body, whereas for ant the performance is similar to training a single policy. Again", + "type": "text", + "cross_page": true + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 248, + 506, + 261 + ], + "spans": [ + { + "bbox": [ + 105, + 248, + 506, + 261 + ], + "score": 1.0, + "content": "we suspect this is because there is not enough variability in the behavior of ant across different", + "type": "text", + "cross_page": true + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 259, + 505, + 271 + ], + "spans": [ + { + "bbox": [ + 105, + 259, + 505, + 271 + ], + "score": 1.0, + "content": "runs. While training single policies might occasionally get stuck in a local minima and learn sub-", + "type": "text", + "cross_page": true + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 269, + 505, + 282 + ], + "spans": [ + { + "bbox": [ + 105, + 269, + 505, + 282 + ], + "score": 1.0, + "content": "optimal behaviors, we found that when training in an ensemble to be more robust to such minima.", + "type": "text", + "cross_page": true + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 282, + 475, + 293 + ], + "spans": [ + { + "bbox": [ + 106, + 282, + 475, + 293 + ], + "score": 1.0, + "content": "Qualitatively, we see more robust behavior of the humanoid trained in ensemble (see video).", + "type": "text", + "cross_page": true + } + ], + "index": 15 + } + ], + "index": 48, + "bbox_fs": [ + 105, + 655, + 506, + 734 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 108, + 90, + 212, + 164 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 108, + 90, + 212, + 164 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 108, + 90, + 212, + 164 + ], + "spans": [ + { + "bbox": [ + 108, + 90, + 212, + 164 + ], + "score": 0.949, + "type": "image", + "image_path": "152bfacb47e873bf346837e201498b80a5c6447de979e7d7bfc9455e1f8b8c6a.jpg" + } + ] + } + ], + "index": 1.5, + "virtual_lines": [ + { + "bbox": [ + 108, + 90, + 212, + 127.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 108, + 127.0, + 212, + 164.0 + ], + "spans": [], + "index": 3 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 173, + 216, + 206 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 172, + 217, + 185 + ], + "spans": [ + { + "bbox": [ + 106, + 172, + 217, + 185 + ], + "score": 1.0, + "content": "Figure 4: Win-rate of", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 183, + 216, + 195 + ], + "spans": [ + { + "bbox": [ + 105, + 183, + 216, + 195 + ], + "score": 1.0, + "content": "kicker vs iterations with", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 194, + 183, + 206 + ], + "spans": [ + { + "bbox": [ + 106, + 194, + 183, + 206 + ], + "score": 1.0, + "content": "full randomization", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 7 + } + ], + "index": 4.25 + }, + { + "type": "image", + "bbox": [ + 227, + 91, + 502, + 164 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 227, + 91, + 502, + 164 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 227, + 91, + 502, + 164 + ], + "spans": [ + { + "bbox": [ + 227, + 91, + 502, + 164 + ], + "score": 0.967, + "type": "image", + "image_path": "f5e400e02f6c6d1d2a0808d79e102f4c6f33d5a9225e9a4aafd4f4d34c22885b.jpg" + } + ] + } + ], + "index": 2, + "virtual_lines": [ + { + "bbox": [ + 227, + 91, + 502, + 115.33333333333333 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 227, + 115.33333333333333, + 502, + 139.66666666666666 + ], + "spans": [], + "index": 2 + }, + { + "bbox": [ + 227, + 139.66666666666666, + 502, + 164.0 + ], + "spans": [], + "index": 4 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 225, + 173, + 504, + 196 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 225, + 173, + 505, + 185 + ], + "spans": [ + { + "bbox": [ + 225, + 173, + 265, + 185 + ], + "score": 1.0, + "content": "Figure 5:", + "type": "text" + }, + { + "bbox": [ + 265, + 174, + 275, + 183 + ], + "score": 0.64, + "content": "\\%", + "type": "inline_equation" + }, + { + "bbox": [ + 276, + 173, + 505, + 185 + ], + "score": 1.0, + "content": "Win-rate of agents trained in ensemble vs agents trained", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 225, + 183, + 505, + 197 + ], + "spans": [ + { + "bbox": [ + 225, + 183, + 505, + 197 + ], + "score": 1.0, + "content": "with just a single policy. Humanoid Sumo (left) and Ant Sumo (right).", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 7.0 + } + ], + "index": 4.5 + }, + { + "type": "text", + "bbox": [ + 107, + 226, + 505, + 293 + ], + "lines": [ + { + "bbox": [ + 106, + 226, + 506, + 239 + ], + "spans": [ + { + "bbox": [ + 106, + 226, + 506, + 239 + ], + "score": 1.0, + "content": "(after 1000 iterations of training). We find that training in ensemble performs significantly better", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 237, + 505, + 250 + ], + "spans": [ + { + "bbox": [ + 105, + 237, + 505, + 250 + ], + "score": 1.0, + "content": "for the humanoid body, whereas for ant the performance is similar to training a single policy. Again", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 248, + 506, + 261 + ], + "spans": [ + { + "bbox": [ + 105, + 248, + 506, + 261 + ], + "score": 1.0, + "content": "we suspect this is because there is not enough variability in the behavior of ant across different", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 259, + 505, + 271 + ], + "spans": [ + { + "bbox": [ + 105, + 259, + 505, + 271 + ], + "score": 1.0, + "content": "runs. While training single policies might occasionally get stuck in a local minima and learn sub-", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 269, + 505, + 282 + ], + "spans": [ + { + "bbox": [ + 105, + 269, + 505, + 282 + ], + "score": 1.0, + "content": "optimal behaviors, we found that when training in an ensemble to be more robust to such minima.", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 282, + 475, + 293 + ], + "spans": [ + { + "bbox": [ + 106, + 282, + 475, + 293 + ], + "score": 1.0, + "content": "Qualitatively, we see more robust behavior of the humanoid trained in ensemble (see video).", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 12.5 + }, + { + "type": "title", + "bbox": [ + 108, + 308, + 195, + 321 + ], + "lines": [ + { + "bbox": [ + 105, + 306, + 197, + 324 + ], + "spans": [ + { + "bbox": [ + 105, + 306, + 197, + 324 + ], + "score": 1.0, + "content": "6 CONCLUSION", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 16 + }, + { + "type": "text", + "bbox": [ + 107, + 333, + 505, + 399 + ], + "lines": [ + { + "bbox": [ + 106, + 333, + 505, + 344 + ], + "spans": [ + { + "bbox": [ + 106, + 333, + 505, + 344 + ], + "score": 1.0, + "content": "We have presented several new competitive multi-agent 3D physically simulated environments. We", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 343, + 505, + 356 + ], + "spans": [ + { + "bbox": [ + 105, + 343, + 505, + 356 + ], + "score": 1.0, + "content": "demonstrate the development of highly complex skills in simple environments with simple rewards.", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 354, + 505, + 367 + ], + "spans": [ + { + "bbox": [ + 105, + 354, + 505, + 367 + ], + "score": 1.0, + "content": "In future work, it would be interesting to conduct larger scale experiments in more complex en-", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 366, + 505, + 378 + ], + "spans": [ + { + "bbox": [ + 106, + 366, + 505, + 378 + ], + "score": 1.0, + "content": "vironments that encourage agents to both compete and cooperate with each other. Incorporation of", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 376, + 505, + 389 + ], + "spans": [ + { + "bbox": [ + 106, + 376, + 505, + 389 + ], + "score": 1.0, + "content": "additional skills, such as reasoning about other agents, potentially via techniques from Foerster et al.", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 387, + 291, + 401 + ], + "spans": [ + { + "bbox": [ + 106, + 387, + 291, + 401 + ], + "score": 1.0, + "content": "(2017a), may also be important in our setting.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 19.5 + }, + { + "type": "title", + "bbox": [ + 107, + 416, + 175, + 427 + ], + "lines": [ + { + "bbox": [ + 106, + 415, + 176, + 429 + ], + "spans": [ + { + "bbox": [ + 106, + 415, + 176, + 429 + ], + "score": 1.0, + "content": "REFERENCES", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 23 + }, + { + "type": "text", + "bbox": [ + 105, + 433, + 506, + 733 + ], + "lines": [ + { + "bbox": [ + 105, + 434, + 505, + 446 + ], + "spans": [ + { + "bbox": [ + 105, + 434, + 505, + 446 + ], + "score": 1.0, + "content": "Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 115, + 445, + 505, + 458 + ], + "spans": [ + { + "bbox": [ + 115, + 445, + 505, + 458 + ], + "score": 1.0, + "content": "McGrew, Josh Tobin, Pieter Abbeel, and Wojciech Zaremba. 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Machine learning, 8(3-4):229–256, 1992.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 12.5 + }, + { + "type": "title", + "bbox": [ + 108, + 303, + 257, + 316 + ], + "lines": [ + { + "bbox": [ + 105, + 302, + 258, + 318 + ], + "spans": [ + { + "bbox": [ + 105, + 302, + 258, + 318 + ], + "score": 1.0, + "content": "A EXPLORATION REWARDS", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 14 + }, + { + "type": "text", + "bbox": [ + 106, + 328, + 505, + 406 + ], + "lines": [ + { + "bbox": [ + 106, + 328, + 505, + 341 + ], + "spans": [ + { + "bbox": [ + 106, + 328, + 505, + 341 + ], + "score": 1.0, + "content": "We define the dense exploration rewards used for the tasks in this section. Our exploration re-", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 340, + 505, + 351 + ], + "spans": [ + { + "bbox": [ + 106, + 340, + 505, + 351 + ], + "score": 1.0, + "content": "ward terms are based on adapting the rewards defined previously for the training humanoids", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 351, + 505, + 362 + ], + "spans": [ + { + "bbox": [ + 105, + 351, + 505, + 362 + ], + "score": 1.0, + "content": "and quadrupeds to walk (Duan et al., 2016; Schulman et al., 2015b). We first review this lo-", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 362, + 505, + 373 + ], + "spans": [ + { + "bbox": [ + 106, + 362, + 505, + 373 + ], + "score": 1.0, + "content": "comotion reward and then define the task-specific dense rewards. These rewards take the form", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 372, + 506, + 385 + ], + "spans": [ + { + "bbox": [ + 106, + 372, + 250, + 384 + ], + "score": 0.92, + "content": "r _ { t } ( s , a ) = v _ { f w d } + c _ { t } ( s , a ) + C _ { a l i v e }", + "type": "inline_equation" + }, + { + "bbox": [ + 250, + 372, + 278, + 385 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 278, + 374, + 299, + 385 + ], + "score": 0.89, + "content": "v _ { f w d }", + "type": "inline_equation" + }, + { + "bbox": [ + 300, + 372, + 506, + 385 + ], + "score": 1.0, + "content": "is the velocity in the forward direction, a bonus for", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 383, + 505, + 396 + ], + "spans": [ + { + "bbox": [ + 105, + 383, + 143, + 396 + ], + "score": 1.0, + "content": "standing", + "type": "text" + }, + { + "bbox": [ + 144, + 385, + 170, + 395 + ], + "score": 0.9, + "content": "C _ { a l i v e }", + "type": "inline_equation" + }, + { + "bbox": [ + 170, + 383, + 301, + 396 + ], + "score": 1.0, + "content": "and costs for impact and action", + "type": "text" + }, + { + "bbox": [ + 302, + 384, + 332, + 396 + ], + "score": 0.92, + "content": "c _ { t } ( s , a )", + "type": "inline_equation" + }, + { + "bbox": [ + 333, + 383, + 505, + 396 + ], + "score": 1.0, + "content": ". 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Mujoco: A physics engine for model-based control.", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 116, + 197, + 505, + 209 + ], + "spans": [ + { + "bbox": [ + 116, + 197, + 505, + 209 + ], + "score": 1.0, + "content": "In Intelligent Robots and Systems (IROS), 2012 IEEE/RSJ International Conference on, pp. 5026–", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 116, + 208, + 193, + 219 + ], + "spans": [ + { + "bbox": [ + 116, + 208, + 193, + 219 + ], + "score": 1.0, + "content": "5033. IEEE, 2012.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 8, + "bbox_fs": [ + 105, + 185, + 505, + 219 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 227, + 504, + 251 + ], + "lines": [ + { + "bbox": [ + 105, + 227, + 505, + 241 + ], + "spans": [ + { + "bbox": [ + 105, + 227, + 505, + 241 + ], + "score": 1.0, + "content": "Kevin Wampler, Erik Andersen, Evan Herbst, Yongjoon Lee, and Zoran Popovic. Character anima- ´", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 115, + 239, + 492, + 252 + ], + "spans": [ + { + "bbox": [ + 115, + 239, + 492, + 252 + ], + "score": 1.0, + "content": "tion in two-player adversarial games. ACM Transactions on Graphics (TOG), 29(3):26, 2010.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 10.5, + "bbox_fs": [ + 105, + 227, + 505, + 252 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 258, + 504, + 281 + ], + "lines": [ + { + "bbox": [ + 105, + 258, + 505, + 272 + ], + "spans": [ + { + "bbox": [ + 105, + 258, + 505, + 272 + ], + "score": 1.0, + "content": "Ronald J Williams. Simple statistical gradient-following algorithms for connectionist reinforcement", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 115, + 269, + 324, + 282 + ], + "spans": [ + { + "bbox": [ + 115, + 269, + 324, + 282 + ], + "score": 1.0, + "content": "learning. Machine learning, 8(3-4):229–256, 1992.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 12.5, + "bbox_fs": [ + 105, + 258, + 505, + 282 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 303, + 257, + 316 + ], + "lines": [ + { + "bbox": [ + 105, + 302, + 258, + 318 + ], + "spans": [ + { + "bbox": [ + 105, + 302, + 258, + 318 + ], + "score": 1.0, + "content": "A EXPLORATION REWARDS", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 14 + }, + { + "type": "text", + "bbox": [ + 106, + 328, + 505, + 406 + ], + "lines": [ + { + "bbox": [ + 106, + 328, + 505, + 341 + ], + "spans": [ + { + "bbox": [ + 106, + 328, + 505, + 341 + ], + "score": 1.0, + "content": "We define the dense exploration rewards used for the tasks in this section. Our exploration re-", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 340, + 505, + 351 + ], + "spans": [ + { + "bbox": [ + 106, + 340, + 505, + 351 + ], + "score": 1.0, + "content": "ward terms are based on adapting the rewards defined previously for the training humanoids", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 351, + 505, + 362 + ], + "spans": [ + { + "bbox": [ + 105, + 351, + 505, + 362 + ], + "score": 1.0, + "content": "and quadrupeds to walk (Duan et al., 2016; Schulman et al., 2015b). We first review this lo-", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 362, + 505, + 373 + ], + "spans": [ + { + "bbox": [ + 106, + 362, + 505, + 373 + ], + "score": 1.0, + "content": "comotion reward and then define the task-specific dense rewards. These rewards take the form", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 372, + 506, + 385 + ], + "spans": [ + { + "bbox": [ + 106, + 372, + 250, + 384 + ], + "score": 0.92, + "content": "r _ { t } ( s , a ) = v _ { f w d } + c _ { t } ( s , a ) + C _ { a l i v e }", + "type": "inline_equation" + }, + { + "bbox": [ + 250, + 372, + 278, + 385 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 278, + 374, + 299, + 385 + ], + "score": 0.89, + "content": "v _ { f w d }", + "type": "inline_equation" + }, + { + "bbox": [ + 300, + 372, + 506, + 385 + ], + "score": 1.0, + "content": "is the velocity in the forward direction, a bonus for", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 383, + 505, + 396 + ], + "spans": [ + { + "bbox": [ + 105, + 383, + 143, + 396 + ], + "score": 1.0, + "content": "standing", + "type": "text" + }, + { + "bbox": [ + 144, + 385, + 170, + 395 + ], + "score": 0.9, + "content": "C _ { a l i v e }", + "type": "inline_equation" + }, + { + "bbox": [ + 170, + 383, + 301, + 396 + ], + "score": 1.0, + "content": "and costs for impact and action", + "type": "text" + }, + { + "bbox": [ + 302, + 384, + 332, + 396 + ], + "score": 0.92, + "content": "c _ { t } ( s , a )", + "type": "inline_equation" + }, + { + "bbox": [ + 333, + 383, + 505, + 396 + ], + "score": 1.0, + "content": ". 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For defender,", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 709, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 145, + 723 + ], + "score": 1.0, + "content": "reward is", + "type": "text" + }, + { + "bbox": [ + 146, + 710, + 257, + 722 + ], + "score": 0.93, + "content": "c ^ { h } ( s , a ) + C _ { a l i v e } + | b _ { x } - g |", + "type": "inline_equation" + }, + { + "bbox": [ + 257, + 709, + 299, + 723 + ], + "score": 1.0, + "content": "where for", + "type": "text" + }, + { + "bbox": [ + 299, + 710, + 325, + 721 + ], + "score": 0.91, + "content": "C _ { a l i v e }", + "type": "inline_equation" + }, + { + "bbox": [ + 325, + 709, + 506, + 723 + ], + "score": 1.0, + "content": "we only gave positive reward if the defender", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 720, + 223, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 223, + 733 + ], + "score": 1.0, + "content": "was in front of the goal area.", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 40.5, + "bbox_fs": [ + 105, + 686, + 506, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 136, + 80, + 474, + 127 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 136, + 80, + 474, + 127 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 136, + 80, + 474, + 127 + ], + "spans": [ + { + "bbox": [ + 136, + 80, + 474, + 127 + ], + "score": 0.977, + "html": "
Force Magnitude
200300400500600
Sumo Agent372 ± 146327±150247± 143181 ± 114123 ± 57
Walker Agent179± 54139± 42116± 32103±2395 ± 20
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Sumo Agent refers to the agent trained in Sumo", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 145, + 505, + 159 + ], + "spans": [ + { + "bbox": [ + 105, + 145, + 505, + 159 + ], + "score": 1.0, + "content": "environment whereas Walker Agent refers to the agent trained to walk in a single agent environment.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 3.5 + } + ], + "index": 2.25 + }, + { + "type": "title", + "bbox": [ + 107, + 178, + 244, + 191 + ], + "lines": [ + { + "bbox": [ + 105, + 176, + 246, + 192 + ], + "spans": [ + { + "bbox": [ + 105, + 176, + 246, + 192 + ], + "score": 1.0, + "content": "B ADDITIONAL RESULTS", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 5 + }, + { + "type": "title", + "bbox": [ + 107, + 203, + 219, + 214 + ], + "lines": [ + { + "bbox": [ + 105, + 202, + 220, + 215 + ], + "spans": [ + { + "bbox": [ + 105, + 202, + 220, + 215 + ], + "score": 1.0, + "content": "B.1 TRANSFER RESULTS", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 6 + }, + { + "type": "text", + "bbox": [ + 106, + 223, + 505, + 312 + ], + "lines": [ + { + "bbox": [ + 106, + 223, + 505, + 236 + ], + "spans": [ + { + "bbox": [ + 106, + 223, + 505, + 236 + ], + "score": 1.0, + "content": "We took the agent trained on the multi-agent Sumo task and faced it with the task of standing while", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 234, + 506, + 248 + ], + "spans": [ + { + "bbox": [ + 105, + 234, + 506, + 248 + ], + "score": 1.0, + "content": "being perturbed by wind forces. 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We calculate the number of steps before the agent falls down", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 104, + 255, + 506, + 270 + ], + "spans": [ + { + "bbox": [ + 104, + 255, + 150, + 270 + ], + "score": 1.0, + "content": "(i.e. when", + "type": "text" + }, + { + "bbox": [ + 150, + 257, + 203, + 268 + ], + "score": 0.89, + "content": "z _ { b o d y } \\le 0 . 5", + "type": "inline_equation" + }, + { + "bbox": [ + 203, + 255, + 506, + 270 + ], + "score": 1.0, + "content": ") or the agent is pushed out of the arena and report the average steps over", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 267, + 506, + 280 + ], + "spans": [ + { + "bbox": [ + 105, + 267, + 506, + 280 + ], + "score": 1.0, + "content": "200 episodes. Episodes last a maximum of 500 time steps. In half the episodes the wind force is", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 278, + 506, + 290 + ], + "spans": [ + { + "bbox": [ + 105, + 278, + 506, + 290 + ], + "score": 1.0, + "content": "applied in a radially outwards direction and in the remaining half it is applied in the radially inwards", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 289, + 505, + 302 + ], + "spans": [ + { + "bbox": [ + 105, + 289, + 505, + 302 + ], + "score": 1.0, + "content": "direction. We allow 50 steps for the agent to stabilize and apply the force at intervals of 50 steps", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 300, + 429, + 313 + ], + "spans": [ + { + "bbox": [ + 106, + 300, + 429, + 313 + ], + "score": 1.0, + "content": "where in between the intervals the force magnitude is decayed at a constant rate:", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 10.5 + }, + { + "type": "interline_equation", + "bbox": [ + 215, + 316, + 389, + 344 + ], + "lines": [ + { + "bbox": [ + 215, + 316, + 389, + 344 + ], + "spans": [ + { + "bbox": [ + 215, + 316, + 389, + 344 + ], + "score": 0.92, + "content": "F _ { t } = { \\left\\{ \\begin{array} { l l } { \\qquad F } & { { \\mathrm { i f ~ } } t \\equiv 0 { \\pmod { 5 0 } } } \\\\ { 0 . 9 * F _ { t - 1 } } & { { \\mathrm { o t h e r w i s e } } } \\end{array} \\right. }", + "type": "interline_equation", + "image_path": "28957d3b59adcd66bdd352d2787ef82f430257231afb79ed6d116c37acc9b288.jpg" + } + ] + } + ], + "index": 15.5, + "virtual_lines": [ + { + "bbox": [ + 215, + 316, + 389, + 330.0 + ], + "spans": [], + "index": 15 + }, + { + "bbox": [ + 215, + 330.0, + 389, + 344.0 + ], + "spans": [], + "index": 16 + } + ] + }, + { + "type": "text", + "bbox": [ + 108, + 349, + 260, + 361 + ], + "lines": [ + { + "bbox": [ + 106, + 348, + 261, + 363 + ], + "spans": [ + { + "bbox": [ + 106, + 348, + 133, + 363 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 133, + 349, + 257, + 362 + ], + "score": 0.9, + "content": "F \\in \\{ 2 0 0 , 3 0 0 , 4 0 0 , 5 0 0 , 6 0 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 257, + 348, + 261, + 363 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 17 + }, + { + "type": "text", + "bbox": [ + 106, + 361, + 505, + 427 + ], + "lines": [ + { + "bbox": [ + 106, + 360, + 504, + 373 + ], + "spans": [ + { + "bbox": [ + 106, + 360, + 504, + 373 + ], + "score": 1.0, + "content": "We compare with a humanoid agent trained in a single agent environment for the task of walking.", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 371, + 505, + 384 + ], + "spans": [ + { + "bbox": [ + 105, + 371, + 505, + 384 + ], + "score": 1.0, + "content": "We used same LSTM policy architecture as used for the Sumo agent and trained the humanoid in the", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 382, + 505, + 395 + ], + "spans": [ + { + "bbox": [ + 105, + 382, + 505, + 395 + ], + "score": 1.0, + "content": "publicly available OpenAI Gym Humanoid-v1 environment using PPO. We then apply force on this", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 393, + 506, + 407 + ], + "spans": [ + { + "bbox": [ + 105, + 393, + 506, + 407 + ], + "score": 1.0, + "content": "agent using the same method as above where the direction of the force is in the direction the agent", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 405, + 506, + 417 + ], + "spans": [ + { + "bbox": [ + 105, + 405, + 506, + 417 + ], + "score": 1.0, + "content": "is walking in half the episodes and opposite to it in the remaining half. We record average number", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 415, + 360, + 429 + ], + "spans": [ + { + "bbox": [ + 105, + 415, + 360, + 429 + ], + "score": 1.0, + "content": "of steps to fall using the same condition as for the Sumo agent.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 20.5 + }, + { + "type": "text", + "bbox": [ + 107, + 427, + 504, + 460 + ], + "lines": [ + { + "bbox": [ + 105, + 426, + 505, + 438 + ], + "spans": [ + { + "bbox": [ + 105, + 426, + 505, + 438 + ], + "score": 1.0, + "content": "Table 2 shows the average number of steps over 200 episodes along with the standard deviation. We", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 437, + 505, + 449 + ], + "spans": [ + { + "bbox": [ + 105, + 437, + 505, + 449 + ], + "score": 1.0, + "content": "see that the humanoid trained in Sumo is more robust to adversarial forces and able to withstand", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 448, + 270, + 461 + ], + "spans": [ + { + "bbox": [ + 105, + 448, + 270, + 461 + ], + "score": 1.0, + "content": "large magnitude of force for many steps.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 25 + } + ], + "page_idx": 11, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2018", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 751, + 311, + 760 + ], + "lines": [ + { + "bbox": [ + 299, + 750, + 313, + 764 + ], + "spans": [ + { + "bbox": [ + 299, + 750, + 313, + 764 + ], + "score": 1.0, + "content": "12", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "table", + "bbox": [ + 136, + 80, + 474, + 127 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 136, + 80, + 474, + 127 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 136, + 80, + 474, + 127 + ], + "spans": [ + { + "bbox": [ + 136, + 80, + 474, + 127 + ], + "score": 0.977, + "html": "
Force Magnitude
200300400500600
Sumo Agent372 ± 146327±150247± 143181 ± 114123 ± 57
Walker Agent179± 54139± 42116± 32103±2395 ± 20
", + "type": "table", + "image_path": "f75253e2221d8b44fb99c2bd37b6851dec021ae2e228de525188c17d3b7ff086.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 136, + 80, + 474, + 95.66666666666667 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 136, + 95.66666666666667, + 474, + 111.33333333333334 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 136, + 111.33333333333334, + 474, + 127.00000000000001 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "table_caption", + "bbox": [ + 106, + 135, + 504, + 158 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 135, + 505, + 148 + ], + "spans": [ + { + "bbox": [ + 106, + 135, + 505, + 148 + ], + "score": 1.0, + "content": "Table 2: Average number of steps before agent falls. Sumo Agent refers to the agent trained in Sumo", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 145, + 505, + 159 + ], + "spans": [ + { + "bbox": [ + 105, + 145, + 505, + 159 + ], + "score": 1.0, + "content": "environment whereas Walker Agent refers to the agent trained to walk in a single agent environment.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 3.5 + } + ], + "index": 2.25 + }, + { + "type": "title", + "bbox": [ + 107, + 178, + 244, + 191 + ], + "lines": [ + { + "bbox": [ + 105, + 176, + 246, + 192 + ], + "spans": [ + { + "bbox": [ + 105, + 176, + 246, + 192 + ], + "score": 1.0, + "content": "B ADDITIONAL RESULTS", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 5 + }, + { + "type": "title", + "bbox": [ + 107, + 203, + 219, + 214 + ], + "lines": [ + { + "bbox": [ + 105, + 202, + 220, + 215 + ], + "spans": [ + { + "bbox": [ + 105, + 202, + 220, + 215 + ], + "score": 1.0, + "content": "B.1 TRANSFER RESULTS", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 6 + }, + { + "type": "text", + "bbox": [ + 106, + 223, + 505, + 312 + ], + "lines": [ + { + "bbox": [ + 106, + 223, + 505, + 236 + ], + "spans": [ + { + "bbox": [ + 106, + 223, + 505, + 236 + ], + "score": 1.0, + "content": "We took the agent trained on the multi-agent Sumo task and faced it with the task of standing while", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 234, + 506, + 248 + ], + "spans": [ + { + "bbox": [ + 105, + 234, + 506, + 248 + ], + "score": 1.0, + "content": "being perturbed by wind forces. The agent receives a zero vector for parts of the observation space", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 104, + 244, + 506, + 259 + ], + "spans": [ + { + "bbox": [ + 104, + 244, + 506, + 259 + ], + "score": 1.0, + "content": "which correspond to the opponent. We calculate the number of steps before the agent falls down", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 104, + 255, + 506, + 270 + ], + "spans": [ + { + "bbox": [ + 104, + 255, + 150, + 270 + ], + "score": 1.0, + "content": "(i.e. when", + "type": "text" + }, + { + "bbox": [ + 150, + 257, + 203, + 268 + ], + "score": 0.89, + "content": "z _ { b o d y } \\le 0 . 5", + "type": "inline_equation" + }, + { + "bbox": [ + 203, + 255, + 506, + 270 + ], + "score": 1.0, + "content": ") or the agent is pushed out of the arena and report the average steps over", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 267, + 506, + 280 + ], + "spans": [ + { + "bbox": [ + 105, + 267, + 506, + 280 + ], + "score": 1.0, + "content": "200 episodes. Episodes last a maximum of 500 time steps. In half the episodes the wind force is", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 278, + 506, + 290 + ], + "spans": [ + { + "bbox": [ + 105, + 278, + 506, + 290 + ], + "score": 1.0, + "content": "applied in a radially outwards direction and in the remaining half it is applied in the radially inwards", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 289, + 505, + 302 + ], + "spans": [ + { + "bbox": [ + 105, + 289, + 505, + 302 + ], + "score": 1.0, + "content": "direction. We allow 50 steps for the agent to stabilize and apply the force at intervals of 50 steps", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 300, + 429, + 313 + ], + "spans": [ + { + "bbox": [ + 106, + 300, + 429, + 313 + ], + "score": 1.0, + "content": "where in between the intervals the force magnitude is decayed at a constant rate:", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 10.5, + "bbox_fs": [ + 104, + 223, + 506, + 313 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 215, + 316, + 389, + 344 + ], + "lines": [ + { + "bbox": [ + 215, + 316, + 389, + 344 + ], + "spans": [ + { + "bbox": [ + 215, + 316, + 389, + 344 + ], + "score": 0.92, + "content": "F _ { t } = { \\left\\{ \\begin{array} { l l } { \\qquad F } & { { \\mathrm { i f ~ } } t \\equiv 0 { \\pmod { 5 0 } } } \\\\ { 0 . 9 * F _ { t - 1 } } & { { \\mathrm { o t h e r w i s e } } } \\end{array} \\right. }", + "type": "interline_equation", + "image_path": "28957d3b59adcd66bdd352d2787ef82f430257231afb79ed6d116c37acc9b288.jpg" + } + ] + } + ], + "index": 15.5, + "virtual_lines": [ + { + "bbox": [ + 215, + 316, + 389, + 330.0 + ], + "spans": [], + "index": 15 + }, + { + "bbox": [ + 215, + 330.0, + 389, + 344.0 + ], + "spans": [], + "index": 16 + } + ] + }, + { + "type": "text", + "bbox": [ + 108, + 349, + 260, + 361 + ], + "lines": [ + { + "bbox": [ + 106, + 348, + 261, + 363 + ], + "spans": [ + { + "bbox": [ + 106, + 348, + 133, + 363 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 133, + 349, + 257, + 362 + ], + "score": 0.9, + "content": "F \\in \\{ 2 0 0 , 3 0 0 , 4 0 0 , 5 0 0 , 6 0 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 257, + 348, + 261, + 363 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 17, + "bbox_fs": [ + 106, + 348, + 261, + 363 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 361, + 505, + 427 + ], + "lines": [ + { + "bbox": [ + 106, + 360, + 504, + 373 + ], + "spans": [ + { + "bbox": [ + 106, + 360, + 504, + 373 + ], + "score": 1.0, + "content": "We compare with a humanoid agent trained in a single agent environment for the task of walking.", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 371, + 505, + 384 + ], + "spans": [ + { + "bbox": [ + 105, + 371, + 505, + 384 + ], + "score": 1.0, + "content": "We used same LSTM policy architecture as used for the Sumo agent and trained the humanoid in the", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 382, + 505, + 395 + ], + "spans": [ + { + "bbox": [ + 105, + 382, + 505, + 395 + ], + "score": 1.0, + "content": "publicly available OpenAI Gym Humanoid-v1 environment using PPO. We then apply force on this", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 393, + 506, + 407 + ], + "spans": [ + { + "bbox": [ + 105, + 393, + 506, + 407 + ], + "score": 1.0, + "content": "agent using the same method as above where the direction of the force is in the direction the agent", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 405, + 506, + 417 + ], + "spans": [ + { + "bbox": [ + 105, + 405, + 506, + 417 + ], + "score": 1.0, + "content": "is walking in half the episodes and opposite to it in the remaining half. We record average number", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 415, + 360, + 429 + ], + "spans": [ + { + "bbox": [ + 105, + 415, + 360, + 429 + ], + "score": 1.0, + "content": "of steps to fall using the same condition as for the Sumo agent.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 20.5, + "bbox_fs": [ + 105, + 360, + 506, + 429 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 427, + 504, + 460 + ], + "lines": [ + { + "bbox": [ + 105, + 426, + 505, + 438 + ], + "spans": [ + { + "bbox": [ + 105, + 426, + 505, + 438 + ], + "score": 1.0, + "content": "Table 2 shows the average number of steps over 200 episodes along with the standard deviation. We", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 437, + 505, + 449 + ], + "spans": [ + { + "bbox": [ + 105, + 437, + 505, + 449 + ], + "score": 1.0, + "content": "see that the humanoid trained in Sumo is more robust to adversarial forces and able to withstand", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 448, + 270, + 461 + ], + "spans": [ + { + "bbox": [ + 105, + 448, + 270, + 461 + ], + "score": 1.0, + "content": "large magnitude of force for many steps.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 25, + "bbox_fs": [ + 105, + 426, + 505, + 461 + ] + } + ] + } + ], + "_backend": "pipeline", + "_version_name": "2.2.2" +} \ No newline at end of file diff --git a/parse/train/Sy0GnUxCb/Sy0GnUxCb_model.json b/parse/train/Sy0GnUxCb/Sy0GnUxCb_model.json new file mode 100644 index 0000000000000000000000000000000000000000..0f59ffc72643828daf7e452ed658b34aa68aa76e --- /dev/null +++ b/parse/train/Sy0GnUxCb/Sy0GnUxCb_model.json 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Force Magnitude
200300400500600
Sumo Agent372 ± 146327±150247± 143181 ± 114123 ± 57
Walker Agent179± 54139± 42116± 32103±2395 ± 20
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b/parse/train/te7PVH1sPxJ/images/f55a1bd5ecbc668b7ba6403df2db85f32a5a1c61f81dff72e4f797f5ce4f4d9e.jpg new file mode 100644 index 0000000000000000000000000000000000000000..6f2d0eb9cb00067b8bd3355ba5896fd1d3aabe60 --- /dev/null +++ b/parse/train/te7PVH1sPxJ/images/f55a1bd5ecbc668b7ba6403df2db85f32a5a1c61f81dff72e4f797f5ce4f4d9e.jpg @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:89410800213d868ba107362b23c8586557f9d9e4c3e7cd27e8ea517f3cc1cb23 +size 53482 diff --git a/parse/train/ucEXZQncukK/ucEXZQncukK.md b/parse/train/ucEXZQncukK/ucEXZQncukK.md new file mode 100644 index 0000000000000000000000000000000000000000..8d305d65a643b77fc7895a02153f4242a20e4fb9 --- /dev/null +++ b/parse/train/ucEXZQncukK/ucEXZQncukK.md @@ -0,0 +1,507 @@ +# BAYESIAN ONLINE META-LEARNING + +Anonymous authors Paper under double-blind review + +# ABSTRACT + +Neural networks are known to suffer from catastrophic forgetting when trained on sequential datasets. While there have been numerous attempts to solve this problem for large-scale supervised classification, little has been done to overcome catastrophic forgetting for few-shot classification problems. Few-shot metalearning algorithms often require all few-shot tasks to be readily available in a batch for training. The popular gradient-based model-agnostic meta-learning algorithm (MAML) is a typical algorithm that suffers from these limitations. This work introduces a Bayesian online meta-learning framework to tackle the catastrophic forgetting and the sequential few-shot tasks problems. Our framework incorporates MAML into a Bayesian online learning algorithm with Laplace approximation or variational inference. This framework enables few-shot classification on a range of sequentially arriving datasets with a single meta-learned model and training on sequentially arriving few-shot tasks. The experimental evaluations demonstrate that our framework can effectively prevent catastrophic forgetting and is capable of online meta-learning in various few-shot classification settings. + +# 1 INTRODUCTION + +Image classification models and algorithms often require an enormous amount of labelled examples for training to achieve state-of-the-art performance. Labelled examples can be expensive and time-consuming to acquire. Human visual systems, on the other hand, are able to recognise new classes after being shown a few labelled examples. Few-shot classification (Miller et al., 2000; Li et al., 2004; 2006; Lake et al., 2011) tackles this issue by learning to adapt to unseen classes (known as novel classes) with very few labelled examples from each class. Recent works show that metalearning provides promising approaches to few-shot classification problems (Santoro et al., 2016; Finn et al., 2017; Li et al., 2017; Ravi & Larochelle, 2017). Meta-learning or learning-to-learn (Schmidhuber, 1987; Thrun & Pratt, 1998) takes the learning process a level deeper – instead of learning from the labelled examples in the training classes (known as base classes), meta-learning learns the example-learning process. The training process in meta-learning that utilises the base classes is called the meta-training stage, and the evaluation process that reports the few-shot performance on the novel classes is known as the meta-evaluation stage. + +Despite being a promising solution to few-shot classification problems, meta-learning methods suffer from several limitations: + +1. Unable to continually learn from sequential few-shot tasks: It is mandatory to have all base classes readily available for meta-training. Such meta-learning algorithms often require sampling a number of few-shot tasks in every iteration for optimisation. +2. Unable to retain few-shot classification ability on sequential datasets that have evident distributional shift: A meta-learned model is restricted to perform few-shot classification on a specific dataset, in the sense that the base and novel classes have to originate from the same dataset distribution. A meta-learned model loses its few-shot classification ability on previous datasets as new ones arrive subsequently for meta-training. + +We emphasise that the task mentioned in this paper refers to the few-shot task for meta-learning. This paper considers meta-learning a single model for few-shot classification in the sequential datasets and sequential few-shot tasks settings respectively. + +We introduce a Bayesian online meta-learning framework that can train a few-shot learning model under the sequential few-shot tasks setting and train a model that is applicable to a broader scope of few-shot classification datasets by overcoming catastrophic forgetting. We extend the Bayesian online learning (BOL) framework (Opper, 1998) to a Bayesian online meta-learning framework using the model-agnostic meta-learning (MAML) algorithm (Finn et al., 2017). MAML finds a good model parameter initialisation (called meta-parameters) that can quickly adapt to novel classes using very few labelled examples, while BOL provides a principled framework for finding the posterior of the model parameters. Our framework aims to combine both BOL and MAML to find the posterior of the meta-parameters. Our work builds on Ritter et al. (2018a) which combines the BOL framework and Laplace approximation with block-diagonal Kronecker-factored Fisher approximation, and Nguyen et al. (2018) which uses variational inference with BOL to overcome catastrophic forgetting in large-scale supervised classification. + +An important reason to implement Bayesian inference over non-Bayesian methods for an online setting is that BOL provides a grounded framework that suggests using the previous posterior as the prior recursively. Bayesian inference inherits an advantage for robust meta-learning (Yoon et al., 2018) to overcome training instability problems addressed by Antoniou et al. (2019). BOL implicitly keeps a memory on previous knowledge via the posterior, in contrast to recent online meta-learning methods that explicitly accumulate previous data in a task buffer (Finn et al., 2019; Zhuang et al., 2019). Explicitly keeping a memory on previous data often triggers an important question: how should the carried-forward data be processed in future task rounds, in order to accumulate knowledge? Finn et al. (2019) update the meta-parameters at each iteration using previous few-shot tasks in the task buffer. This defeats the purpose of online learning, which by definition means to update the parameters each round using only the new data encountered. Having to re-train on previous data to avoid forgetting also increases the training time as the data accumulate (Finn et al., 2019; He et al., 2019). Certainly one can clamp the amount of data at some maximal limit and sample from the buffer, but the final performance of such an algorithm would be dependent on the samples being informative and of good quality which may vary across different seed runs. In contrast to memorising the datasets, having an implicit memory via the posterior automatically deals with the question on how to process carried-forward data and allows a better carry forward in previous experiences. + +Below are the contributions we make in this paper: + +We develop the Bayesian online meta-learning (BOML) framework for sequential few-shot classification problems. Under this framework we introduce the algorithms Bayesian online meta-learning with Laplace approximation (BOMLA) and Bayesian online meta-learning with variational inference (BOMVI). We propose a simple approximation to the Fisher corresponding to the BOMLA algorithm that carries over the desirable block-diagonal Kronecker-factored structure from the Fisher approximation in the non-meta-learning setting. We demonstrate that BOML can overcome catastrophic forgetting in the sequential few-shot datasets setting with apparent distributional shift in the datasets. +• We demonstrate that BOML can continually learn to few-shot classify the novel classes in the sequential meta-training few-shot tasks setting. + +# 2 META-LEARNING + +Most meta-learning algorithms comprise an inner loop for example-learning and an outer loop that learns the example-learning process. Such algorithms often require sampling a meta-batch of tasks at each iteration, where a task is formed by sampling a subset of classes from the pool of base classes or novel classes during meta-training or meta-evaluation respectively. The $N$ -way $K$ -shot task, for instance, refers to sampling $N$ classes and using $K$ examples per class for few-shot quick adaptation. + +An offline meta-learning algorithm learns a few-shot classification model only for a specific dataset $\mathcal { D } _ { t + 1 }$ where all base classes of $\mathcal { D } _ { t + 1 }$ have to be readily available for meta-training. For notational convenience, we drop the $t + 1$ subscript in this section, as there is only one dataset involved in offline meta-learning. The dataset $\mathcal { D } _ { t + 1 }$ is divided into the set of base classes $\widetilde { \mathcal { D } }$ and novel classes $\widehat { \mathcal { D } }$ for meta-training and meta-evaluation respectively. Upon completing meta-training on the base class set $\widetilde { \mathcal { D } }$ , the goal of few-shot classification is to perform well on an unseen task ${ \widehat { \mathcal { D } } } ^ { * }$ sampled from the novel class set $\widehat { \mathcal { D } }$ after a quick adaptation on a small subset $\widehat { \mathcal { D } } ^ { * , S }$ (known as the support set) of $\widehat { \mathcal { D } } ^ { * }$ . The performance of this unseen task is evaluated on the query set $\widehat { \mathcal { D } } ^ { * , Q }$ , where $\hat { \mathcal { D } } ^ { * , Q } = \widehat { \mathcal { D } } ^ { * } \backslash \widehat { \mathcal { D } } ^ { * , S }$ . Since $\widehat { \mathcal { D } }$ is not accessible during meta-training, this support-query split is mimicked on the base class set $\widetilde { \mathcal { D } }$ for meta-training. + +Model-agnostic meta-learning We are interested in the well-known meta-learning algorithm MAML (Finn et al., 2017). Each updating step of MAML aims to improve the ability of the metaparameters to act as a good model initialisation for a quick adaptation on unseen tasks. Each iteration of the MAML algorithm samples $M$ tasks from the base class set $\widetilde { \mathcal { D } }$ and runs a few steps of stochastic gradient descent (SGD) for an inner loop task-specific learning. The number of tasks sampled per iteration is known as the meta-batch size. For task $m$ , the inner loop outputs the task-specific parameters $\tilde { \theta } ^ { m }$ from a $k$ -step SGD quick adaptation on the objective $\mathcal { L } ( \boldsymbol { \theta } , \widetilde { \mathcal { D } } ^ { m , S } )$ with the support set $\widetilde { \mathcal { D } } ^ { m , S }$ and initialised at $\theta$ : + +$$ +\tilde { \theta } ^ { m } = S G D _ { k } ( \mathcal { L } ( \theta , \widetilde { D } ^ { m , S } ) ) , +$$ + +where $m = 1 , \ldots , M$ . The outer loop gathers all task-specific adaptations to update the metaparameters $\theta$ using the loss $\mathcal { L } ( \tilde { \theta } ^ { m } , \widetilde { D } ^ { m , Q } )$ on the query set $\bar { \mathcal { D } } ^ { m , Q }$ . + +The overall MAML optimisation objective is + +$$ +\underset { \theta } { \arg \operatorname* { m i n } } \frac { 1 } { M } \sum _ { m = 1 } ^ { M } \mathcal { L } ( S G D _ { k } ( \mathcal { L } ( \theta , \widetilde { \mathcal { D } } ^ { m , S } ) ) , \widetilde { \mathcal { D } } ^ { m , Q } ) . +$$ + +Like most offline meta-learning algorithms, MAML requires all base classes to be readily available for tasks-sampling at each iteration. We aim to overcome this limitation by meta-learning a model that can few-shot classify unseen tasks from the novel classes, while the tasks from the base classes arrive sequentially for meta-training. MAML also assumes a stationary task distribution during meta-training and meta-evaluation. Under this assumption, a meta-learned model is only applicable to a specific dataset distribution. When the model encounters a sequence of datasets with apparent distributional shift, it loses the few-shot classification ability on previous datasets as new ones arrive for meta-training. Our work also aims to meta-learn a single model for few-shot classification on multiple datasets that arrive sequentially for meta-training. We achieve these two goals by incorporating MAML into the BOL framework to give the Bayesian online meta-learning (BOML) framework that finds the posterior of the meta-parameters. + +# 3 OVERVIEW OF OUR BAYESIAN ONLINE META-LEARNING APPROACH + +Our central contribution is to extend the benefits of meta-learning to the Bayesian online scenario, thereby training models that can generalise across tasks whilst dealing with parameter uncertainty in the setting of sequential tasks or sequential datasets. + +Sequential datasets setting In this setting, online meta-training occurs sequentially on the datasets $\mathcal { D } _ { 1 } , \ldots , \mathcal { D } _ { T }$ . Each dataset $\mathcal { D } _ { i }$ can be seen as a knowledge domain with an associated underlying task distribution $p ( \mathcal T _ { i } )$ . A newly-arrived $\mathcal { D } _ { t + 1 }$ is separated into the base class set $\widetilde { \mathcal { D } } _ { t + 1 }$ and novel class set $\widehat { \mathcal { D } } _ { t + 1 }$ for meta-training and meta-evaluation respectively, where the tasks in these two stages are drawn from the task distribution $p ( \mathcal T _ { t + 1 } )$ . + +Sequential tasks setting The sequential tasks setting only involves one dataset $\mathcal { D }$ with an associated underlying task distribution $p ( \mathcal { T } )$ , where $\mathcal { D }$ is separated into the base and novel class sets. In this setting, $\widetilde { \cal D } _ { 1 } , \ldots , \widetilde { \cal D } _ { t + 1 }$ denote the non-overlapping tasks formed from the base class set and they arrive sequentially for meta-training. These tasks $\widetilde { \mathcal { D } } _ { 1 } , \ldots , \widetilde { \mathcal { D } } _ { t + 1 }$ and the meta-evaluation tasks are drawn from the task distribution $p ( \tau )$ . + +Notationally, for both sequential tasks and sequential datasets settings, let $\mathcal { \widetilde { D } } _ { t + 1 } ^ { S }$ and $\widetilde { \mathcal { D } } _ { t + 1 } ^ { Q }$ denote the collection of support sets and query sets respectively from $\widetilde { \mathcal { D } } _ { t + 1 }$ , so that $\widetilde { D } _ { t + 1 } = \widetilde { D } _ { t + 1 } ^ { S } \cup \widetilde { D } _ { t + 1 } ^ { Q }$ . + +We are interested in a MAP estimate $\theta ^ { * } = \arg \operatorname* { m a x } _ { \theta } p ( \theta | \widetilde { D } _ { 1 : t + 1 } )$ . Using Bayes’ rule on the posterior gives the recursive formula + +$$ +\begin{array} { r l } & { p ( \theta | \widetilde { D } _ { 1 : t + 1 } ) \propto p ( \widetilde { D } _ { t + 1 } ^ { S } , \widetilde { D } _ { t + 1 } ^ { Q } | \theta ) p ( \theta | \widetilde { D } _ { 1 : t } ) } \\ & { \qquad = p ( \widetilde { D } _ { t + 1 } ^ { Q } | \theta , \widetilde { D } _ { t + 1 } ^ { S } ) p ( \widetilde { D } _ { t + 1 } ^ { S } | \theta ) p ( \theta | \widetilde { D } _ { 1 : t } ) } \\ & { \qquad = \bigg \{ \int p ( \widetilde { D } _ { t + 1 } ^ { Q } | \widetilde { \theta } ) p ( \widetilde { \theta } | \theta , \widetilde { D } _ { t + 1 } ^ { S } ) d \widetilde { \theta } \bigg \} p ( \widetilde { D } _ { t + 1 } ^ { S } | \theta ) p ( \theta | \widetilde { D } _ { 1 : t } ) } \end{array} +$$ + +where Eq. (3) follows from the assumption that each dataset is independent given $\theta$ . + +From the meta-learning perspective, the parameters $\tilde { \theta }$ introduced in Eq. (5) can be viewed as the task-specific parameters in MAML. There are various choices for the distribution $p ( \tilde { \theta } | \theta , \widetilde { D } _ { t + 1 } ^ { S } )$ in Eq. (5). In particular if we choose to set it as the deterministic function of taking several steps of SGD on loss $\mathcal { L }$ with the support set collection $\mathcal { \widetilde { D } } _ { t + 1 } ^ { S }$ and initialised at $\theta$ , we have + +$$ +p ( { \tilde { \theta } } | \theta , { \widetilde { \mathcal { D } } } _ { t + 1 } ^ { S } ) = \mathbb { 1 } \{ { \tilde { \theta } } = S G D _ { k } ( { \mathcal { L } } ( \theta , { \widetilde { \mathcal { D } } } _ { t + 1 } ^ { S } ) ) \} . +$$ + +and this recovers the MAML inner loop with SGD quick adaptation in Eq. (1). The recursion given by Eq. (5) forms the basis of our approach and the remainder of this paper explains how we implement this. In order to do so we give a mini tutorial in Appendix A on Bayesian online learning, Laplace approximation and variational continual learning. + +# 4 BAYESIAN ONLINE META-LEARNING IMPLEMENTATION + +This section demonstrates how we arrive at the algorithms Bayesian online meta-learning with Laplace approximation (BOMLA) and Bayesian online meta-learning with variational inference (BOMVI) by implementing Laplace approximation and variational continual learning respectively to the posterior of the BOML framework in Eq. (5). These algorithms from the grounded BOML framework are useful for online training on the sequential few-shot classification datasets or tasks. + +# 4.1 BAYESIAN ONLINE META-LEARNING WITH LAPLACE APPROXIMATION + +We discover that the Laplace approximation method provides a well-fitted meta-training framework for Bayesian online meta-learning in Eq. (5). Each updating step in the approximation procedure can be modified to correspond to the meta-parameters for few-shot classification, instead of the model parameters for large-scale supervised classification. + +Laplace approximation rationalises the use of a Gaussian approximate posterior by Taylor expanding the log-posterior around a mode up to the second order, as described in Appendix A.2. The second order term corresponds to the log-probability of a Gaussian distribution. The BOML framework in Section 3 with a Gaussian approximate posterior $q$ of mean and precision $\phi _ { t } = \{ \mu _ { t } , \Lambda _ { t } \}$ from the Laplace approximation gives a MAP estimate: + +$$ +\theta ^ { * } = \arg \operatorname* { m a x } _ { \theta } \Bigg \{ \log \int p ( \widetilde { \mathcal { D } } _ { t + 1 } ^ { Q } | \widetilde { \theta } ) p ( \widetilde { \theta } | \theta , \widetilde { \mathcal { D } } _ { t + 1 } ^ { S } ) d \widetilde { \theta } + \log p ( \widetilde { \mathcal { D } } _ { t + 1 } ^ { S } | \theta ) - \frac { 1 } { 2 } ( \theta - \mu _ { t } ) ^ { T } \Lambda _ { t } ( \theta - \mu _ { t } ) \Bigg \} . +$$ + +For an efficient optimisation, we use the deterministic $\tilde { \theta }$ in Eq. (6). The objective in Eq. (7) can be batched (for sequential tasks) or meta-batched (for sequential datasets). This leads to minimising the objective + +$$ +\mathsf { \Pi } _ { t + 1 } ^ { \mathsf { R O M L A } } ( \theta , \mu _ { t } , \Lambda _ { t } ) = - \frac { 1 } { M } \sum _ { m = 1 } ^ { M } \log p ( \widetilde { \mathcal { D } } _ { t + 1 } ^ { m , Q } | \widetilde { \theta } ^ { m } ) - \frac { 1 } { M } \sum _ { m = 1 } ^ { M } \log p ( \widetilde { \mathcal { D } } _ { t + 1 } ^ { m , S } | \theta ) + \frac { 1 } { 2 } ( \theta - \mu _ { t } ) ^ { T } \Lambda _ { t } ( \theta - \mu _ { t } ) , +$$ + +where $\tilde { \theta } ^ { m } = S G D _ { k } ( \mathcal { L } ( \theta , \widetilde { D } _ { t + 1 } ^ { m , S } ) )$ for $m = 1 , \ldots , M$ . In the sequential datasets setting $M$ denotes the number of tasks sampled per iteration, whereas in the sequential tasks setting denotes the number of batches per epoch. The first term of the objective in Eq. (8) corresponds to the MAML objective in Eq. (2) with a cross-entropy loss, the second term can be viewed as the pre-adaptation loss on the support set and the last term can be seen as a regulariser. + +# 4.2 HESSIAN APPROXIMATION + +We calculate a block-diagonal Kronecker-factored Hessian approximation in order to update the precision $\Lambda _ { t }$ , as explained in Appendix A.3. The Hessian approximations in both sequential datasets and sequential tasks settings are very similar, except that the sequential datasets setting averages over the meta-batch size and the sequential tasks setting averages over the number of batches. + +The Hessian matrix corresponding to the first term of the BOMLA objective in Eq. (8) is + +$$ +\widetilde { H } _ { t + 1 } ^ { i j } = \frac { 1 } { M } \sum _ { m = 1 } ^ { M } - \frac { \partial ^ { 2 } } { \partial \theta ^ { ( i ) } \partial \theta ^ { ( j ) } } \log p ( \widetilde { \mathcal { D } } _ { t + 1 } ^ { m , Q } | \widetilde { \theta } ^ { m } ) ) \Bigg | _ { \theta = \mu _ { t + 1 } } . +$$ + +It is worth noting that the BOMLA Hessian deviates from the original BOL Hessian in Appendix A.2. This requires deriving an adjusted approximation to the Hessian with some further assumptions. + +The BOL Hessian for a single data point can be approximated using the Fisher information matrix $F$ to ensure its positive semi-definiteness (Martens $\&$ Grosse, 2015): + +$$ +F = \mathbb { E } _ { x , y } \bigg [ \frac { d } { d \theta } \log p ( y | x , \theta ) \frac { d } { d \theta } \log p ( y | x , \theta ) ^ { T } \bigg ] . +$$ + +Each $( x , y )$ pair for the Fisher in BOMLA is associated to a task (or a batch) $m$ . The Fisher information matrix $\widetilde { F }$ corresponding to the BOMLA Hessian in Eq. (9) for a single data point is + +$$ +\widetilde { F } = \frac { 1 } { M } \sum _ { m = 1 } ^ { M } \mathbb { E } _ { x , y } \bigg [ \bigg ( \frac { \partial \widetilde { \theta } ^ { m } } { \partial \theta } \bigg ) \frac { d } { d \widetilde { \theta } ^ { m } } \log p ( y | x , \widetilde { \theta } ^ { m } ) \frac { d } { d \widetilde { \theta } ^ { m } } \log p ( y | x , \widetilde { \theta } ^ { m } ) ^ { T } \bigg ( \frac { \partial \widetilde { \theta } ^ { m } } { \partial \theta } \bigg ) ^ { T } \bigg ] . +$$ + +The additional Jacobian matrix $\frac { \partial \tilde { \theta } ^ { m } } { \partial \theta }$ breaks the Kronecker-factored structure described by Martens & Grosse (2015) for the original Fisher in Eq. (10). + +The results in Finn et al. (2017) show that the first step of the quick adaptation in $\tilde { \theta } ^ { m }$ contributes the largest change to the meta-evaluation objective, and the remaining adaptation steps give a relatively small change to the objective. It is reasonable to assume that the quick adaptation is a one-step SGD for Fisher approximation: + +$$ +\begin{array} { r } { \tilde { \theta } ^ { m } = \theta - \nabla _ { \theta } \mathcal { L } ( \theta , \widetilde { D } _ { t + 1 } ^ { m , S } ) . } \end{array} +$$ + +By imposing this assumption, the $( i , j )$ -th entry of the Jacobian term can be interpreted as + +$$ +\left( \frac { \partial \tilde { \theta } ^ { m } } { \partial \theta } \right) ^ { i j } = I ^ { i j } - \frac { \partial ^ { 2 } ( - \log p ( \widetilde { D } _ { t + 1 } ^ { m , S } | \theta ) ) } { \partial \theta ^ { ( i ) } \partial \theta ^ { ( j ) } } , +$$ + +where $I$ is the corresponding identity matrix and the objective $\mathcal { L }$ involved is the negative loglikelihood. The Hessian for a single data point in the second term of Eq. (13) can be approximated by $F$ in Eq. (10) via the usual block-diagonal Kronecker-factored approximation. Putting the Jacobian back into Eq. (11) and expanding the factors give terms that multiply two or more Kronecker products together. The detailed derivation of $\widetilde { F }$ is explained in Appendix A.3.1. We introduce the posterior regulariser $\lambda$ when updating the precision: $\Lambda _ { t + 1 } = \lambda { \widetilde { \cal H } } _ { t + 1 } + \Lambda _ { t }$ and the rationale for introducing $\lambda$ is explained in Appendix A.3.2. The pseudo-code of the BOMLA algorithm can be found in Appendix B.1. + +# 4.3 BAYESIAN ONLINE META-LEARNING WITH VARIATIONAL INFERENCE + +The variational continual learning (VCL) framework (Nguyen et al., 2018) is directly applicable to BOML. This section demonstrates how we arrive at the BOMVI algorithm by implementing VCL to the posterior of the BOML framework in Eq. (5). + +As described in Appendix A.4, VCL approximates the posterior by minimising the KL-divergence over some pre-determined approximate posterior family $\mathcal { Q }$ . Fitting the BOML posterior in Eq. (5) into the VCL framework gives the approximate posterior: + +$$ +q ( \theta | \phi _ { t + 1 } ) = \underset { q \in \mathcal { Q } } { \operatorname { a r g m i n } } D _ { \mathrm { K L } } \Bigg ( q ( \theta | \phi ) \bigg | \bigg | \bigg \{ \int p ( \widetilde { \mathcal { D } } _ { t + 1 } ^ { Q } | \widetilde { \theta } ) p ( \widetilde { \theta } | \theta , \widetilde { \mathcal { D } } _ { t + 1 } ^ { S } ) d \widetilde { \theta } \bigg \} p ( \widetilde { \mathcal { D } } _ { t + 1 } ^ { S } | \theta ) q ( \theta | \phi _ { t } ) \Bigg ) . +$$ + +Similar to BOMLA, we use the deterministic $\tilde { \theta }$ in Eq. (6), and the objective in Eq. (14) can be batched (for sequential tasks) or meta-batched (for sequential datasets). This leads to minimising the objective + +$$ +f _ { t + 1 } ^ { \mathrm { B o n v I } } ( \phi , \phi _ { t } ) = - \frac { 1 } { M } \sum _ { m = 1 } ^ { M } \mathbb { E } _ { q ( \theta | \phi ) } \big [ \log p ( \widetilde { \mathcal { D } } _ { t + 1 } ^ { m , Q } | \widetilde { \theta } ^ { m } ) \big ] - \frac { 1 } { M } \sum _ { m = 1 } ^ { M } \mathbb { E } _ { q ( \theta | \phi ) } \big [ \log p ( \widetilde { \mathcal { D } } _ { t + 1 } ^ { m , S } | \theta ) \big ] +$$ + +where $\tilde { \theta } ^ { m } = S G D _ { k } ( \mathcal { L } ( \theta , \widetilde { D } _ { t + 1 } ^ { m , S } ) )$ for $m = 1 , \ldots , M$ . In the sequential datasets setting $M$ denotes the number of tasks sampled per iteration, whereas in the sequential tasks setting $M$ denotes the number of batches per epoch. We use a Gaussian mean-field approximate posterior $q ( \theta | \phi _ { t } ) =$ $\textstyle \prod _ { d = 1 } ^ { D } N ( \mu _ { t , d } , \sigma _ { t , d } ^ { 2 } )$ , where $\phi _ { t } ~ = ~ \{ \mu _ { t , d } , \sigma _ { t , d } \} _ { d = 1 } ^ { D }$ , $D = \dim ( \theta )$ and the objective in Eq. (15) is minimised over $\phi$ . The pseudo-code of the BOMVI algorithm can be found in Appendix B.1. + +The first term in Eq. (15) is rather cumbersome to estimate in optimisation. To compute its Monte Carlo estimator, we have to generate samples $\theta _ { r } \sim q$ for $r = 1 , \ldots , R$ , and run a quick adaptation on each sampled meta-parameters $\theta _ { r }$ before evaluating its log-likelihood. This is computationally intensive and it gives an estimator with large variance. We propose a workaround by modifying the inner loop SGD quick adaptation, and the details can be found in Appendix B.2. + +# 5 RELATED WORK + +Online Meta-Learning There are two common problem settings in the current online metalearning works: + +• Underlying task distribution: Sequential tasks are assumed to originate from the same underlying task distribution $p ( \mathcal { T } )$ in this setting. Our work in the sequential tasks setting belongs to this category. Denevi et al. (2019) introduce the online-within-online (OWO) and online-within-batch (OWB) settings, where OWO encounters tasks and examples within tasks sequentially while OWB encounters tasks sequentially but examples within tasks are in batch. The BOML framework in the sequential tasks setting corresponds to the OWB setting. On the other hand, our work in the sequential datasets setting is novel in overcoming few-shot catastrophic forgetting, where the goal is to few-shot classify tasks drawn from a sequence of distributions $p ( { \bar { \mathcal { T } } } _ { 1 } ) , \dots , p ( { \mathcal { T } } _ { T } )$ as explained in Section 3. He et al. (2019), Harrison et al. (2019) and Jerfel et al. (2019) look into continual meta-learning for nonstationary task distributions where the task boundaries are unknown to the model. Jerfel et al. (2019) consider a latent task structure to adapt to the non-stationary task distributions. + +• Regret minimisation: In this setting, the goal is to minimise the regret function, and the assumptions are made on the loss function rather than the task distribution. Recent works Finn et al. (2019); Zhuang et al. (2019) belong to this category, where the aim is to compete with the best meta-learner and supersede it. These methods accumulate data as they arrive and meta-learn using all data acquired so far. Data accumulation is not desirable as the algorithmic complexity of training grows with the amount of data accumulated, and training time increases as new data arrive (Finn et al., 2019; He et al., 2019). The agent will eventually run out of memory for a long sequence of data. The BOML framework on the other hand is advantageous, as it only takes the posterior of the meta-parameters into consideration during optimisation. This gives a framework with an algorithmic complexity independent of the length of the dataset sequence. + +Offline Meta-Learning Previous meta-learning works attempt to solve few-shot classification problems in an offline setting, under the assumption of having a stationary task distribution during meta-training and meta-evaluation. A single meta-learned model is aimed to few-shot classify one specific dataset with all base classes of the dataset readily available in a batch for meta-training. There are two general frameworks for the offline meta-learning setting: + +• Probabilistic framework: The MAML algorithm can be cast into a probabilistic inference problem (Finn et al., 2018) or with a hierarchical Bayesian structure (Grant et al., + +2018; Yoon et al., 2018). Grant et al. (2018) discuss the use of a Laplace approximation in the task-specific inner loop to improve MAML using the curvature information, whilst Yoon et al. (2018) use Stein Variational Gradient Descent (SVGD) for task-specific learning. Gordon et al. (2019) implement probabilistic inference by considering the posterior predictive distribution with amortised networks. + +• Non-probabilistic framework: Gradient-based meta-learning (Finn et al., 2017; Nichol et al., 2018; Rusu et al., 2019) updates the meta-parameters by accumulating the gradients of a meta-batch of task-specific inner loop updates. The meta-parameters will be used as a model initialisation for a quick adaptation on the novel classes. Metric-based metalearning (Koch et al., 2015; Vinyals et al., 2016; Snell et al., 2017) utilises the metric distance between labelled examples. Such methods assume that base and novel classes are from the same dataset distribution, and the metric distance estimations can be generalised to the novel classes upon meta-learning the base classes. + +Continual Learning Modern continual learning works (Goodfellow et al., 2013; Lee et al., 2017; Zenke et al., 2017) focus primarily on large-scale supervised learning, in contrast to our work that looks into continual few-shot classification across sequential tasks and datasets. Wen et al. (2018) utilise few-shot learning to improve on overcoming catastrophic forgetting via logit matching on a small sample from the previous tasks. The online learning element in this paper is closely related to (Kirkpatrick et al., 2017; Zenke et al., 2017; Ritter et al., 2018a; Nguyen et al., 2018) that overcome catastrophic forgetting for large-scale supervised classification. In particular, our work builds on the online Laplace approximation method in (Ritter et al., 2018a). We extend this to the meta-learning scenario to avoid forgetting in few-shot classification problems. Nguyen et al. (2018) provide the alternative of using variational inference instead of Laplace approximation for approximating the posterior. It is a reasonable approach to adapt variational approximation methods to approximate the posterior of the meta-parameters by adjusting the KL-divergence objective. + +# 6 EXPERIMENTS + +# 6.1 OMNIGLOT: SEQUENTIAL TASKS + +We run the sequential tasks experiment on the Omniglot dataset. To increase the difficulty level, we split the datasets based on the alphabets (super-classes) instead of the characters (classes). The goal of this experiment is to classify the 5-way 5-shot novel tasks sampled from the meta-evaluation alphabets. The experimental details and the alphabet splits can be found in Appendix C.1. + +We compare our algorithms to the following baselines: + +1. Train-On-Everything (TOE): When a new task (or dataset) arrives for meta-training, we randomly re-initialise the meta-parameters and perform meta-training on all tasks (or datasets) encountered so far. Once meta-training is completed in this stage, we do not update the posterior of the meta-parameters like we would in BOMLA and BOMVI. 2. Train-From-Scratch (TFS): Upon the arrival of a new task (or dataset), we randomly reinitialise the meta-parameters and meta-train only on the newly-arrived task (or dataset). Similar to TOE, the posterior of the meta-parameters is not updated in TFS. 3. Follow The Meta-Leader (FTML): We introduce a slight modification to FTML (Finn et al., 2019) on its evaluation method, as FTML is not designed for few-shot learning on unseen tasks. In our experiment, we apply Update-Procedure in FTML to the data from unseen tasks, rather than the data from the same training task as in the original FTML. + +As the tasks arrive sequentially for meta-training, Figure 1 shows that BOMLA and BOMVI can accumulate the few-shot classification ability on the novel tasks over time. The knowledge acquired from previous meta-training tasks are carried forward in the form of a posterior, which is then used as the prior when a new task arrives for meta-training. The baselines TOE and TFS have similar performances. Despite having access to all previous tasks, TOE shows no positive forward transfer in the meta-evaluation accuracy each time it encounters a new task. BOMLA with $\lambda = 0 . 1$ gives the best performance in this experiment. + +![](images/f1b81faadf230be434c4056a4a78621223884d73db008b674c0cea1f3e45bc91.jpg) +Figure 1: Meta-evaluation accuracy across 3 seed runs on the novel tasks along meta-training. Left: compares BOMLA to the baselines, centre: compares BOMVI to the baselines, right: compares BOMLA with different $\lambda$ values to BOMVI. + +# 6.2 PENTATHLON: SEQUENTIAL DATASETS + +We implement BOMLA and BOMVI to the pentathlon 5-way 1-shot classification sequence: + +Omniglot CIFAR-FS miniImageNet VGG-Flowers Aircraft + +The details of this experiment and the datasets can be found in Appendix C.2. We compare BOMLA and BOMVI to the baseline TOE, and running MAML continuously on the sequential datasets for meta-training. + +Figure 2 shows that BOMLA and BOMVI are able to prevent few-shot catastrophic forgetting. TOE is also able to retain the few-shot performance as it has access to all datasets encountered so far. However, since it learns all datasets from random re-initialisation each time it encounters a new dataset, the meta-training time required to achieve a similarly good meta-evaluation performance is longer compared to other runs. The sequential MAML, on the other hand, catastrophically forgets the previously learned datasets but has the best performance on new datasets compared to other runs. TOE can be memory-intensive as the dataset sequence becomes longer. It takes the bruteforce approach to prevent forgetting by memorising all datasets. Unlike TOE, our BOML approach only takes the posterior of the meta-parameters into consideration during optimisation. This gives a framework with an algorithmic complexity independent of the length of the dataset sequence. + +$@ \ @ \left( { \widehat { a } } \right)$ New2: errorband + +Tuning the posterior regulariser $\lambda$ mentioned in Section 4.2 corresponds to balancing between a smaller performance trade-off on a new dataset and less forgetting on previous datasets. As shown in Appendix C.2 Figure 4, a larger $\lambda = 1 0 0 0$ results in a more concentrated Gaussian posterior and is therefore unable to learn new datasets well, but can better retain the performances on previous datasets. A smaller value $\lambda = 1$ on the other hand gives a widespread Gaussian posterior and learns better on new datasets by sacrificing the performance on the previous datasets. In this experiment, the value $\lambda = 1 0 0$ gives the best balance between old and new datasets. Ideally we seek for a good performance on both old and new datasets, but in reality there is a trade-off between retaining performance on old datasets and learning well on new datasets due to posterior approximation errors. + +As shown in Figures 1 and 2, BOMLA with appropriate $\lambda$ is superior to BOMVI. This is due to BOMLA having a better posterior approximation than BOMVI. Whilst BOMLA has a Gaussian approximate posterior with block-diagonal precision, BOMVI uses a Gaussian mean-field approximate posterior. Trippe & Turner (2017) compared the performances of variational inference with different covariance structures, and discovered that variational inference with block-diagonal covariance performs worse than mean-field approximation. This is because the block-diagonal covariance in variational inference prohibits variance reduction methods such as local reparameterisation trick for Monte Carlo estimation. The variance of the Monte Carlo estimate has been proven problematic (Kingma et al., 2015; Trippe & Turner, 2017). We address this issue in Section 4.3 and Appendix B.2 specifically to the meta-learning setting by modifying the inner loop quick adaptation. + +$@ \ @ \left( { \widehat { a } } \right)$ New2: $\lambda { \cdot }$ - comparing plot in App. C.2 + +![](images/e2f5052bde38ab7aad480616153346453a41dffe2b36ad7c864932e1cf0d6269.jpg) +Figure 2: Meta-evaluation accuracy across 3 seed runs on each dataset along meta-training (refer to Figure 3 for the enlarged version). Higher accuracy values indicate better results with less forgetting as we proceed to new datasets. BOMLA with $\lambda = 1 0 0$ gives good performance in the offdiagonal plots (retains performances on previously learned datasets), and has a minor performance trade-off in the diagonal plots (learns less well on new datasets). Sequential MAML gives better performance in the diagonal plots (learns well on new datasets) but worse performance in the offdiagonal plots (forgets previously learned datasets). BOMVI is also able to retain performance on previous datasets, although it may be unable to perform as good as BOMLA due to sampling and estimator variance. + +# 7 CONCLUSION + +We introduced the Bayesian online meta-learning (BOML) framework with two algorithms: BOMLA and BOMVI. Our framework can overcome catastrophic forgetting in few-shot classification problems and can handle sequentially arriving few-shot tasks for online meta-learning. BOML merged the BOL framework and the MAML algorithm via Laplace approximation or variational continual learning. We proposed the necessary adjustments in the Hessian and Fisher approximation for BOMLA, as we are optimising the meta-parameters for few-shot classification instead of the usual model parameters in large-scale supervised classification. 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Few-Shot Self Reminder to Overcome Catastrophic Forgetting. arXiv preprint, arXiv:1812.00543, 2018. +J. Yoon, T. Kim, O. Dia, S. Kim, Y. Bengio, and S. Ahn. Bayesian Model-Agnostic Meta-Learning. In Advances in Neural Information Processing Systems 31, 2018. +F. Zenke, B. Poole, and S. Ganguli. Continual Learning through Synaptic Intelligence. In Proceedings of the 34th International Conference on Machine Learning, 2017. +Z. Zhuang, Y. Wang, K. Yu, and S. Lu. No-Regret Non-Convex Online Meta-Learning. arXiv preprint, arXiv:1910.10196, 2019. + +# A BACKGROUND + +This section provides a background explanation of using BOL to find the posterior of a model parameters and overcome catastrophic forgetting, commonly for large-scale supervised classification. We will then apply this approach to our recursion in Eq. (5). + +The posterior is typically intractable due to the enormous size of the modern neural network architectures. This leads to the requirement for a good approximation of the posterior of the metaparameters. A particularly suitable candidate for this purpose in meta-learning is the Laplace approximation (MacKay, 1992; Ritter et al., 2018b), as it simply adds a quadratic regulariser to the training objective. Variational inference is another possible method to obtain an approximation for the posterior of the meta-parameters. + +# A.1 BAYESIAN ONLINE LEARNING + +Upon the arrival of the new $\mathcal { D } _ { t + 1 }$ , we are interested in a MAP estimate $\theta ^ { * } = \arg \operatorname* { m a x } _ { \theta } p ( \theta | \mathcal { D } _ { 1 : t + 1 } )$ for the parameters $\theta$ of a neural network. Using Bayes’ rule on the posterior gives the recursive formula + +$$ +p ( \theta | \mathcal { D } _ { 1 : t + 1 } ) \propto p ( \mathcal { D } _ { t + 1 } | \theta ) p ( \theta | \mathcal { D } _ { 1 : t } ) +$$ + +where Eq. (16) follows from the assumption that each dataset is independent given $\theta$ . As the normalised posterior $p ( \theta | \mathcal { D } _ { 1 : t } )$ is usually intractable, it may be approximated by a parametric distribution $q$ with parameter $\phi _ { t }$ . The BOL framework consists of the update step and the projection step (Opper, 1998). The update step uses the approximate posterior $q ( \theta | \phi _ { t } )$ obtained from the previous step for an update in the form of Eq. (16): + +$$ +p ( \theta | \mathcal { D } _ { 1 : t + 1 } , \phi _ { t } ) \propto p ( \mathcal { D } _ { t + 1 } | \theta ) q ( \theta | \phi _ { t } ) . +$$ + +The new posterior $p ( \theta | \mathcal { D } _ { 1 : t + 1 } , \phi _ { t } )$ might not belong to the same parametric family as $q ( \theta | \phi _ { t } )$ . In this case, the new posterior has to be projected into the same parametric family to obtain $q ( \theta | \phi _ { t + 1 } )$ . Opper (1998) performs this projection by minimising the KL-divergence between the new posterior and the parametric $q$ , while Ritter et al. (2018a) use the Laplace approximation and Nguyen et al. (2018) use variational inference. + +# A.2 LAPLACE APPROXIMATION + +We consider finding a MAP estimate following from Eq. (16): + +$$ +\theta _ { t + 1 } ^ { * } = \arg \operatorname* { m a x } _ { \theta } p ( \theta | \mathcal { D } _ { 1 : t + 1 } ) = \arg \operatorname* { m a x } _ { \theta } \{ \log p ( \mathcal { D } _ { t + 1 } | \theta ) + \log p ( \theta | \mathcal { D } _ { 1 : t } ) \} . +$$ + +Since the posterior $p ( \theta | \mathcal { D } _ { 1 : t } )$ of a neural network is intractable except for small architectures, the unnormalised posterior $\tilde { p } ( \theta | \mathcal { D } _ { 1 : t } )$ is considered instead. Performing Taylor expansion on the logarithm of the unnormalised posterior around a mode ${ \boldsymbol { \theta } } _ { t } ^ { * }$ gives + +$$ +\log \tilde { p } ( \theta | \mathcal { D } _ { 1 : t } ) \simeq \log \tilde { p } ( \theta | \mathcal { D } _ { 1 : t } ) \big | _ { \theta = \theta _ { t } ^ { * } } - \frac { 1 } { 2 } ( \theta - \theta _ { t } ^ { * } ) ^ { T } A _ { t } ( \theta - \theta _ { t } ^ { * } ) , +$$ + +where $A _ { t }$ denotes the Hessian matrix of the negative log-posterior evaluated at $\theta _ { t } ^ { * }$ . The expansion in Eq. (19) suggests using a Gaussian approximate posterior. Given the parameter $\phi _ { t } = \{ \mu _ { t } , \Lambda _ { t } \}$ , a mean $\mu _ { t + 1 }$ for step $t + 1$ can be obtained by finding a mode of the approximate posterior as follows via standard gradient-based optimisation: + +$$ +\mu _ { t + 1 } = \arg \operatorname* { m a x } _ { \boldsymbol { \theta } } \log p ( \mathcal { D } _ { t + 1 } | \boldsymbol { \theta } ) - \frac { 1 } { 2 } ( \boldsymbol { \theta } - \boldsymbol { \mu } _ { t } ) ^ { T } \Lambda _ { t } ( \boldsymbol { \theta } - \boldsymbol { \mu } _ { t } ) . +$$ + +The precision matrix is updated as $\Lambda _ { t + 1 } = H _ { t + 1 } + \Lambda _ { t }$ , where $H _ { t + 1 }$ is the Hessian matrix of the negative log-likelihood for $\mathcal { D } _ { t + 1 }$ evaluated at $\mu _ { t + 1 }$ with entries + +$$ +H _ { t + 1 } ^ { i j } = - \frac { \partial ^ { 2 } } { \partial \theta ^ { ( i ) } \partial \theta ^ { ( j ) } } \log p ( \mathcal { D } _ { t + 1 } \vert \theta ) \bigg \vert _ { \theta = \mu _ { t + 1 } } . +$$ + +For a neural network model, gradient-based optimisation methods such as SGD (Robbins & Monro, 1951) and Adam (Kingma & Ba, 2015) are the standard gradient-based methods in finding a mode for the Laplace approximation in Eq. (20). We show in Section 4.1 that this provides a well-suited skeleton to implement Bayesian online meta-learning in Eq. (5) with the mode-seeking optimisation procedure. + +# A.3 BLOCK-DIAGONAL HESSIAN APPROXIMATION + +Since the full Hessian matrix in Eq. (21) is intractable for large neural networks, we seek for an efficient and relatively close approximation to the Hessian matrix. Diagonal approximations (Denker & LeCun, 1991; Kirkpatrick et al., 2017) are memory and computationally efficient, but sacrifice approximation accuracy as they ignore the interaction between parameters. Consider instead separating the Hessian matrix into blocks where different blocks are associated to different layers of a neural network. A particular diagonal block corresponds to the Hessian for a particular layer of the neural network. The block-diagonal Kronecker-factored approximation (Martens & Grosse, 2015; Grosse & Martens, 2016; Botev et al., 2017) utilises the fact that each diagonal block of the Hessian is Kronecker-factored for a single data point. This provides a better Hessian approximation as it takes the parameter interactions within a layer into consideration. + +# A.3.1 KRONECKER-FACTORED APPROXIMATION + +Consider a neural network with $L$ layers and parameter $\theta = [ \mathrm { v e c } ( W _ { 1 } ) ^ { T } , \dots , \mathrm { v e c } ( W _ { L } ) ^ { T } ] ^ { T }$ where $W _ { \ell }$ is the weight of layer $\ell$ for $\ell = \{ 1 , \dots , L \}$ and vec denotes stacking the columns of a matrix into a vector. We denote the input of the neural network as $a _ { 0 } = x$ and the output of the neural network as $h _ { L }$ . As the input passes through each layer of the neural network, we have the pre-activation for layer $\ell$ as $h _ { \ell } = W _ { \ell } a _ { \ell - 1 }$ and the activation as $a _ { \ell } = f _ { \ell } ( h _ { \ell } )$ where $f _ { \ell }$ is the activation function of layer $\ell$ . If a bias vector is applicable in calculating the pre-activation of a layer, we append the bias vector to the last column of the weight matrix and append a scalar one to the last element of the activation. The gradient $g _ { \ell }$ of loss $L _ { \theta } ( \dot { x _ { \star } } y ) = - \log p ( \bar { y } | \dot { x } , \theta )$ with respect to $h _ { \ell }$ for an input-target pair $( x , y )$ is the pre-activation gradient for layer $\ell$ . + +Martens $\&$ Grosse (2015) show that the $\ell$ -th diagonal block $F _ { \ell }$ of the Fisher information matrix $F$ can be approximated by the Kronecker product between the expectation of the outer product of the $( \ell - 1 )$ -th layer activation and the $\ell$ -th layer pre-activation gradient: + +$$ +\begin{array} { r l } & { F _ { \ell } = \mathbb { E } _ { x , y } \bigl [ a _ { \ell - 1 } a _ { \ell - 1 } ^ { T } \otimes g _ { \ell } g _ { \ell } ^ { T } \bigr ] } \\ & { \qquad \approx \mathbb { E } _ { x } \bigl [ a _ { \ell - 1 } a _ { \ell - 1 } ^ { T } \bigr ] \otimes \mathbb { E } _ { y | x } \bigl [ g _ { \ell } g _ { \ell } ^ { T } \bigr ] } \\ & { \qquad = A _ { \ell - 1 } \otimes G _ { \ell } , } \end{array} +$$ + +where $A _ { \ell - 1 } = \mathbb { E } _ { x } [ a _ { \ell - 1 } a _ { \ell - 1 } ^ { T } ]$ and $G _ { \ell } = \mathbb { E } _ { y | x } [ g _ { \ell } g _ { \ell } ^ { T } ]$ . Grosse $\&$ Martens (2016) extend the blockdiagonal Kronecker-factored Fisher approximation for fully-connected layers to that for convolution layers. The Gaussian log-probability term can be calculated efficiently without expanding the Kronecker product using the identity + +$$ +\begin{array} { r } { ( A _ { \ell - 1 } \otimes G _ { \ell } ) \operatorname { v e c } ( W _ { \ell } - W _ { \ell } ^ { * } ) = \operatorname { v e c } ( G _ { \ell } ( W _ { \ell } - W _ { \ell } ^ { * } ) A _ { \ell - 1 } ^ { T } ) . } \end{array} +$$ + +As we mentioned in Section 4.2, approximating the Hessian with the one-step SGD inner loop assumption results in having terms that multiply two or more Kronecker products together. The $\ell$ -th diagonal block of $\widetilde { F }$ in Eq. (11) is + +$$ +\widetilde { F } _ { \ell } = \frac { 1 } { M } \sum _ { m = 1 } ^ { M } ( I - A _ { \ell - 1 } ^ { m } \otimes G _ { \ell } ^ { m } ) ( \widetilde { A } _ { \ell - 1 } ^ { m } \otimes \widetilde { G } _ { \ell } ^ { m } ) ( I - A _ { \ell - 1 } ^ { m } \otimes G _ { \ell } ^ { m } ) ^ { T } , +$$ + +where $A _ { \ell - 1 } ^ { m } \otimes G _ { \ell } ^ { m }$ is the Kronecker product corresponding to the Hessian in Eq. (13) for task or batch $m$ . We expand $\widetilde { F } _ { \ell }$ using the Kronecker product property: + +$$ +\begin{array} { r } { ( A _ { \ell - 1 } ^ { m } \otimes G _ { \ell } ^ { m } ) ( \widetilde { A } _ { \ell - 1 } ^ { m } \otimes \widetilde { G } _ { \ell } ^ { m } ) = A _ { \ell - 1 } ^ { m } \widetilde { A } _ { \ell - 1 } ^ { m } \otimes G _ { \ell } ^ { m } \widetilde { G } _ { \ell } ^ { m } . } \end{array} +$$ + +This gives + +$$ +\begin{array} { r l r } { \widetilde { F } _ { \ell } = \frac { 1 } { M } \sum _ { m = 1 } ^ { M } \Big \{ \widetilde { A } _ { \ell - 1 } ^ { m } \otimes \widetilde { G } _ { \ell } ^ { m } - A _ { \ell - 1 } ^ { m } \widetilde { A } _ { \ell - 1 } ^ { m } \otimes G _ { \ell } ^ { m } \widetilde { G } _ { \ell } ^ { m } - \widetilde { A } _ { \ell - 1 } ^ { m } ( A _ { \ell - 1 } ^ { m } ) ^ { T } \otimes \widetilde { G } _ { \ell } ^ { m } ( G _ { \ell } ^ { m } ) ^ { T } } \\ & { } & { + A _ { \ell - 1 } ^ { m } \widetilde { A } _ { \ell - 1 } ^ { m } ( A _ { \ell - 1 } ^ { m } ) ^ { T } \otimes G _ { \ell } ^ { m } \widetilde { G } _ { \ell } ^ { m } ( G _ { \ell } ^ { m } ) ^ { T } \Big \} . } \end{array} +$$ + +Finally, moving the meta-batch (or batch) averaging into the Kronecker factors gives the approximation: + +$$ +\begin{array} { r l } & { \widetilde { F } _ { \ell } \approx \widetilde { A } _ { \ell - 1 } \otimes \widetilde { G } _ { \ell } - A _ { \ell - 1 } \widetilde { A } _ { \ell - 1 } \otimes G _ { \ell } \widetilde { G } _ { \ell } - \widetilde { A } _ { \ell - 1 } ( A _ { \ell - 1 } ) ^ { T } \otimes \widetilde { G } _ { \ell } ( G _ { \ell } ) ^ { T } } \\ & { \qquad + A _ { \ell - 1 } \widetilde { A } _ { \ell - 1 } ( A _ { \ell - 1 } ) ^ { T } \otimes G _ { \ell } \widetilde { G } _ { \ell } ( G _ { \ell } ) ^ { T } , } \end{array} +$$ + +where $\begin{array} { r } { \tilde { A } _ { \ell - 1 } = \frac { 1 } { M } \sum _ { m } \tilde { A } _ { \ell - 1 } ^ { m } , \tilde { G } _ { \ell } = \frac { 1 } { M } \sum _ { m } \tilde { G } _ { \ell } ^ { m } , A _ { \ell - 1 } \tilde { A } _ { \ell - 1 } = \frac { 1 } { M } \sum _ { m } A _ { \ell - 1 } ^ { m } \tilde { A } _ { \ell - 1 } ^ { m } . } \end{array}$ and so on. + +A.3.2 POSTERIOR REGULARISING HYPERPARAMETER FOR PRECISION UPDATE + +Ritter et al. (2018a) use a hyperparameter $\lambda$ as a multiplier to the Hessian when updating the precision: + +$$ +\Lambda _ { t + 1 } = \lambda H _ { t + 1 } + \Lambda _ { t } . +$$ + +In the large-scale supervised classification setting, this hyperparameter has a regularising effect on the Gaussian posterior approximation for a balance between having a good performance on a new dataset and maintaining the performance on previous datasets (Ritter et al., 2018a). A large $\lambda$ results in a sharply peaked Gaussian posterior and is therefore unable to learn new datasets well, but can prevent forgetting previously learned datasets. A small $\lambda$ on the other hand gives a dispersed Gaussian posterior and allows better performance on new datasets by sacrificing the performance on the previous datasets. + +# A.4 VARIATIONAL CONTINUAL LEARNING + +The variational continual learning method (Nguyen et al., 2018) also provides a suitable metatraining framework for Bayesian online meta-learning in Eq. (5). Consider approximating the posterior $q$ by minimising the KL-divergence between the parametric $q$ and the new posterior as in the projection step in Eq. (17), where $q$ belongs to some pre-determined approximate posterior family $\mathcal { Q }$ with parameters $\phi _ { t }$ : + +$$ +\begin{array} { r l } & { q ( \theta | \phi _ { t + 1 } ) = \underset { q \in \mathcal { Q } } { \arg \operatorname* { m i n } } D _ { \mathrm { K L } } ( q ( \theta | \phi ) \| p ( \mathcal { D } _ { t + 1 } | \theta ) q ( \theta | \phi _ { t } ) ) } \\ & { \qquad = \underset { q \in \mathcal { Q } } { \arg \operatorname* { m i n } } \big \{ - \mathbb { E } _ { q ( \theta | \phi ) } [ \log p ( \mathcal { D } _ { t + 1 } | \theta ) ] + D _ { \mathrm { K L } } ( q ( \theta | \phi ) \| q ( \theta | \phi _ { t } ) ) \big \} . } \end{array} +$$ + +The optimisation in Eq. (32) leads to the objective + +$$ +\phi _ { t + 1 } = \underset { \phi } { \arg \operatorname* { m i n } } \big \{ - \mathbb { E } _ { q ( \theta | \phi ) } [ \log p ( \mathcal { D } _ { t + 1 } | \theta ) ] + D _ { \mathrm { K L } } ( q ( \theta | \phi ) \| q ( \theta | \phi _ { t } ) ) \big \} . +$$ + +One can use a Gaussian mean-field approximate posterior $\begin{array} { r } { q ( \theta | \phi _ { t } ) = \prod _ { d = 1 } ^ { D } N ( \mu _ { t , d } , \sigma _ { t , d } ^ { 2 } ) } \end{array}$ , where $\phi _ { t } = \{ \mu _ { t , d } , \sigma _ { t , d } \} _ { d = 1 } ^ { D }$ and $D = \dim ( \theta )$ . The first term in Eq. (33) can be estimated via Monte Carlo with local reparameterisation trick (Kingma et al., 2015), and the second KL-divergence term has a closed form for Gaussian distributions. + +# B ALGORITHMS + +# B.1 BOMLA AND BOMVI + +Algorithm 1 gives the pseudo-code of the BOMLA algorithm for the sequential datasets setting, with the corresponding variation for the sequential tasks setting in brackets. The algorithm is formed of three main elements: meta-training on a specific dataset or task (line 4 – 11), updating the Gaussian mean (line 12) and updating the Gaussian precision (line 13 – 16). For the precision update, we approximate the Hessian using block-diagonal Kronecker-factored approximation (BD-KFA). + +Algorithm 2 gives the pseudo-code of the BOMVI algorithm for the sequential datasets setting, with the corresponding variation for the sequential tasks setting in brackets. The algorithm is formed of two main elements: meta-training on a specific dataset or task (line 4 – 11) and updating the parameters of the Gaussian mean-field approximate posterior (line 12). + +1: Require: sequential datasets (or tasks) $\widetilde { \mathcal { D } } _ { 1 } , \ldots , \widetilde { \mathcal { D } } _ { T }$ , learning rate $\alpha$ , posterior regulariser $\lambda$ , +number of meta-training iterations (or epochs) $J$ , meta-batch size (or number of batches) $M$ +2: Initialise: $\mu _ { 0 } , \Lambda _ { 0 }$ , $\theta$ +3: for $t = 1$ to $T$ do +4: for $i = 1 , \dots , J$ do $\triangleright$ meta-training on dataset or task $\widetilde { \cal D } _ { t } \quad$ New: added $\cdot$ +5: for $m = 1$ to $M$ do +6: Sample task (or split the batch) $\widetilde { \mathcal { D } } _ { t } ^ { m } = \widetilde { \mathcal { D } } _ { t } ^ { m , S } \cup \widetilde { \mathcal { D } } _ { t } ^ { m , Q }$ +7: Inner update $\tilde { \theta } ^ { m } = S G D _ { k } ( \mathcal { L } ( \theta , \widetilde { D } _ { t } ^ { m , S } ) )$ +8: end for +9: Evaluate loss $f _ { t } ^ { \mathrm { B o u L A } } ( \theta , \mu _ { t - 1 } , \Lambda _ { t - 1 } )$ in Eq. (8) +10: Outer update $\theta \gets \theta - \alpha \nabla _ { \theta } f _ { t } ^ { \mathrm { B o M L A } } ( \theta , \mu _ { t - 1 } , \Lambda _ { t - 1 } )$ +11: end for +12: Update mean $\mu _ { t } \gets \theta$ $\triangleright$ update posterior mean +13: For sequential datasets, sample $M$ tasks for Hessian approximation +14: Run inner update in line 7 for each task (or for each batch) +15: Approximate $\widetilde { H } _ { t }$ with BD-KFA to $\widetilde { F }$ in Eq. (11) +16: Update precision $\Lambda _ { t } \gets \lambda \widetilde { H } _ { t } + \Lambda _ { t - 1 }$ $\triangleright$ update posterior precision +17: end for + +# Algorithm 2 Bayesian online meta-learning with variational inference (BOMVI) + +1: Require: sequential datasets (or tasks) $\widetilde { \mathcal { D } } _ { 1 } , \ldots , \widetilde { \mathcal { D } } _ { T }$ , learning rate $\alpha$ , number of meta-training +iterations (or epochs) $J$ , meta-batch size (or number of batches) $M$ +2: Initialise: $\phi _ { 0 } = \{ \mu _ { 0 } , \sigma _ { 0 } \}$ +3: for $t = 1$ to $T$ do +4: for $i = 1 , 2 , \dots , J$ do $\triangleright$ meta-training on dataset or task $\widetilde { \cal D } _ { t } \quad$ New: added $\cdot$ +5: for $m = 1$ to $M$ do +6: Sample task (or split the batch) $\widetilde { \mathcal { D } } _ { t } ^ { m } = \widetilde { \mathcal { D } } _ { t } ^ { m , S } \cup \widetilde { \mathcal { D } } _ { t } ^ { m , Q }$ +7: Inner update $\tilde { \theta } ^ { m } = S G D _ { k } ( \mathcal { L } ( \theta , \widetilde { D } _ { t } ^ { m , S } ) )$ +8: end for +9: Evaluate loss $f _ { t } ^ { \mathrm { B o u V I } } ( \phi , \phi _ { t - 1 } )$ in Eq. (15) +10: Outer update $\bar { \mu } \mu - \alpha \nabla _ { \mu } f _ { t } ^ { \mathrm { B o M V I } } ( \phi , \phi _ { t - 1 } )$ , and $\sigma \gets \sigma - \alpha \nabla _ { \sigma } f _ { t } ^ { \mathrm { B o M V I } } ( \phi , \phi _ { t - 1 } )$ +11: end for +12: Update $\mu _ { t } \mu$ and $\sigma _ { t } \gets \sigma$ . update posterior parameters +13: end for + +# B.2 BOMVI MONTE CARLO ESTIMATOR + +Recall that the BOMVI objective is: + +$$ +f _ { t + 1 } ^ { \mathrm { B o M V I } } ( \phi , \phi _ { t } ) = - \frac { 1 } { M } \sum _ { m = 1 } ^ { M } \mathbb { E } _ { q ( \theta | \phi ) } \big [ \log p ( \widetilde { \mathcal { D } } _ { t + 1 } ^ { m , Q } | \widetilde { \theta } ^ { m } ) \big ] - \frac { 1 } { M } \sum _ { m = 1 } ^ { M } \mathbb { E } _ { q ( \theta | \phi ) } \big [ \log p ( \widetilde { \mathcal { D } } _ { t + 1 } ^ { m , S } | \theta ) \big ] +$$ + +where term o $\tilde { \theta } ^ { m } = S G D _ { k } ( \mathcal { L } ( \theta , \widetilde { D } _ { t + 1 } ^ { m , S } ) )$ for diffic $m = 1 , \ldots , M$ . The Monte Carlo estimator for th as every sampled meta-parameters firstfor $\theta _ { r }$ $r = 1 , \ldots , R$ has to undergo a few-shot quick adaptation prior to the log-likelihood evaluation. As a consequence the estimator is prone to a large variance. Moreover, every quickly-adapted sample $\theta _ { r }$ contributes to the meta-learning gradients of the posterior mean and covariance, resulting in a high computational cost when taking the meta-gradients. + +To solve these impediments, we introduce a slight modification to the SGD quick adaptation ${ \widetilde { \theta } } ^ { m }$ . Instead of taking the gradients with respect to the sampled meta-parameters, we consider the gradients with respect to the posterior mean. A one-step SGD quick adaptation, for instance, becomes: + +$$ +\tilde { \theta } ^ { m } = \theta - \alpha \nabla _ { \mu _ { t } } \mathcal { L } ( \mu _ { t } , \mathcal { \tilde { D } } _ { t + 1 } ^ { m , S } ) . +$$ + +This gives $\widetilde { \theta } ^ { m } \sim N ( \widetilde { \mu } _ { t } , \mathrm { d i a g } ( \sigma _ { t } ^ { 2 } ) )$ where + +$$ +\widetilde { \mu } _ { t } = \mu _ { t } - \alpha \nabla _ { \mu _ { t } } \mathcal { L } ( \mu _ { t } , \widetilde { D } _ { t + 1 } ^ { m , S } ) , +$$ + +since $\theta \sim N ( \mu _ { t } , \mathrm { d i a g } ( \sigma _ { t } ^ { 2 } ) )$ . A quick adaptation with more steps works in a similar fashion. With this modification, we can calculate the Monte Carlo estimator for the first term using the local reparameterisation trick as usual. + +# C EXPERIMENTS + +# C.1 OMNIGLOT: SEQUENTIAL TASKS + +In this experiment, we use the model architecture proposed by Vinyals et al. (2016) that takes 4 modules with 64 filters of size $3 \times 3$ , followed by a batch normalisation, a ReLU activation and a $2 \times 2$ max-pooling. A fully-connected layer is appended to the final module before getting the class probabilities with softmax. Table 1 shows the hyperparameters used in this experiment. + +The Omniglot dataset comprises 50 alphabets (super-classes). Each alphabet has numerous characters (classes) and each character has 20 instances. As the meta-training alphabets arrive sequentially, we form non-overlapping sequential tasks from each arriving alphabet, and the tasks also do not overlap in the characters. We use 35 alphabets for meta-training, 7 alphabets for validation and 8 alphabets for meta-evaluation. The alphabet splits are as follows: + +# 35 alphabets for meta-training: + +Kannada, Burmese_(Myanmar), Malay_(Jawi_-_Arabic), Grantha, Atlantean, Ojibwe_(Canadian_Aboriginal_Syllabics), Balinese, Japanese_(katakana), Hebrew, Japanese_(hiragana), Keble, ’Old_Church_Slavonic_(Cyrillic), Asomtavruli_(Georgian), Tengwar, Aurek-Besh, Sanskrit, Manipuri, Early_Aramaic, Oriya, Mongolian, Avesta, Malayalam, Tifinagh, Angelic, Latin, Braille, Inuktitut_(Canadian_Aboriginal_Syllabics), Alphabet_of_the_Magi, Armenian, Korean, Gurmukhi, ULOG, Bengali, Gujarati, Sylheti + +7 alphabets for validation: + +Ge_ez, Cyrillic, Glagolitic, N_Ko, Arcadian, Anglo-Saxon_Futhorc, Blackfoot_(Canadian_Aboriginal_Syllabics) + +8 alphabets for meta-evaluation: + +Syriac_(Serto), Atemayar_Qelisayer, Tibetan, Futurama, Mkhedruli_(Georgian), Syriac_(Estrangelo), Tagalog, Greek + +Table 1: Hyperparameters for the Omniglot sequential tasks experiment + +
HyperparameterBOMLABOMVI
Posterior regulariser 入0.1
Precision initialisation values10-4~10-2
Covariance initialisation values1exp(-10)
NumberofMonte Carlo samples=5
Number of batch M11
Number of query samples per class (meta-evaluation)1515
Number of epochs per task5050
Number of inner SGD steps in meta-training (k)55
Inner SGD learning rate (α)0.10.1
Outer loop optimiserAdamAdam
Outer loop learning rate0.0010.001
Number of tasks sampled for meta-evaluation100100
Number of inner SGD steps in meta-evaluation (k)1010
+ +# C.2 PENTATHLON: SEQUENTIAL DATASETS + +We use the model architecture proposed by Vinyals et al. (2016) in this experiment, as we did for the sequential tasks experiment. Tables 2 and 3 are the hyperparameters used in this experiment. + +Omniglot: The Omniglot dataset (Lake et al., 2011) comprises 1623 characters from 50 alphabets and each character has 20 instances. New classes with rotations in the multiples of $9 0 °$ are formed after splitting the classes for meta-training, validation and meta-evaluation. We use 1100 characters for meta-training, 100 characters for validation and the remaining for meta-evaluation. + +CIFAR-FS: The CIFAR-FS dataset (Bertinetto et al., 2019) has 100 classes of objects and each class comprises 600 images. We use the same split as Bertinetto et al. (2019): 64 classes for metatraining, 16 classes for validation and 20 classes for meta-evaluation. + +miniImageNet: The miniImageNet dataset (Vinyals et al., 2016) takes 100 classes and 600 instances in each class from the ImageNet dataset. We use the same split as Ravi & Larochelle (2017): 64 classes for meta-training, 16 classes for validation and 20 classes for meta-evaluation. + +VGG-Flowers: The VGG-Flowers dataset (Nilsback & Zisserman, 2008) comprises 102 different types of flowers as the classes. This dataset has 8,189 instances in total. We randomly split 66 classes for meta-training, 16 classes for validation and 20 classes for meta-evaluation. + +Aircraft: The Aircraft dataset (Maji et al., 2013) is a fine-grained dataset consisting of 100 different aircraft models as the classes and each class has 100 instances. We randomly split 64 classes for meta-training, 16 classes for validation and 20 classes for meta-evaluation. + +Table 2: Hyperparameters for the pentathlon experiment (same value for all datasets) + +
HyperparameterBOMLABOMVI
Posterior regulariser 入(various values)
Precision initialisation values10-4~ 10-2
Number of tasks sampled for Hessian approx.5000
Covariance initialisation valuesexp(-5)
Number of Monte Carlo samples=20
Meta-batch size M= 3232
Number of query samples per class1515
Number of iterations per dataset5000
Outer loop optimiserAdam5000
Outer loop learning rateAdam
Number of tasks sampled for meta-evaluation0.001 1000.001 100
+ +Table 3: Hyperparameters for the pentathlon sequential datasets experiment (individual datasets) + +
HyperparameterOmniglotCIFAR-FSminiImageNetVGG-FlowersAircraft
Number of inner SGD steps in meta-training (k)15555
Inner SGD learning rate0.40.10.10.10.1
(a) Outer learning rate decay-×0.1×0.1 halfway×0.1 per 1000x0.1
schedule Number of inner SGD steps in meta-evaluation3halfway 1010iterations 10halfway 10
+ +![](images/e4c0f6de57d020e55a0adba80739413b67359f38476dfa77ec263a2bdb85913e.jpg) +Figure 3: Meta-evaluation accuracy across 3 seed runs on each dataset along meta-training. Higher accuracy values indicate better results with less forgetting as we proceed to new datasets. BOMLA with $\lambda = 1 0 0$ gives better performance in the off-diagonal plots (retains performances on previously learned datasets), and has a minor performance trade-off in the diagonal plots (learns less well on new datasets). Sequential MAML gives better performance in the diagonal plots (learns well on new datasets) but worse performance in the off-diagonal plots (forgets previously learned datasets). BOMVI is also able to retain performance on previous datasets, although it may be unable to perform as good as BOMLA due to sampling and estimator variance. + +![](images/8b2b41f7bbda229777423d37569a5dc851b7bef2d0b560bb5db9e6b27a775de1.jpg) +Figure 4: Meta-evaluation accuracy across 3 seed runs on each dataset along meta-training. Higher accuracy values indicate better results with less forgetting as we proceed to new datasets. BOMLA with a large $\lambda = 1 0 0 0$ gives better performance in the off-diagonal plots (retains performances on previously learned datasets) but worse performance in the diagonal plots (does not learn well on new datasets). A small $\lambda = 1$ gives better performance in the diagonal plots (learns well on new datasets) but worse performance in the off-diagonal plots (forgets previously learned datasets). BOMVI is also able to retain performance on previous datasets, although it may be unable to learn new datasets as good as BOMLA due to sampling and estimator variance. \ No newline at end of file diff --git a/parse/train/ucEXZQncukK/ucEXZQncukK_content_list.json b/parse/train/ucEXZQncukK/ucEXZQncukK_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..86ffbb0803ee67cef87847ce836a53f3b53c90b9 --- /dev/null +++ b/parse/train/ucEXZQncukK/ucEXZQncukK_content_list.json @@ -0,0 +1,2137 @@ +[ + { + "type": "text", + "text": "BAYESIAN ONLINE META-LEARNING ", + "text_level": 1, + "bbox": [ + 174, + 99, + 624, + 121 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Anonymous authors Paper under double-blind review ", + "bbox": [ + 183, + 145, + 398, + 172 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ABSTRACT ", + "text_level": 1, + "bbox": [ + 454, + 210, + 544, + 224 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Neural networks are known to suffer from catastrophic forgetting when trained on sequential datasets. While there have been numerous attempts to solve this problem for large-scale supervised classification, little has been done to overcome catastrophic forgetting for few-shot classification problems. Few-shot metalearning algorithms often require all few-shot tasks to be readily available in a batch for training. The popular gradient-based model-agnostic meta-learning algorithm (MAML) is a typical algorithm that suffers from these limitations. This work introduces a Bayesian online meta-learning framework to tackle the catastrophic forgetting and the sequential few-shot tasks problems. Our framework incorporates MAML into a Bayesian online learning algorithm with Laplace approximation or variational inference. This framework enables few-shot classification on a range of sequentially arriving datasets with a single meta-learned model and training on sequentially arriving few-shot tasks. The experimental evaluations demonstrate that our framework can effectively prevent catastrophic forgetting and is capable of online meta-learning in various few-shot classification settings. ", + "bbox": [ + 233, + 244, + 764, + 452 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 INTRODUCTION ", + "text_level": 1, + "bbox": [ + 176, + 484, + 336, + 501 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Image classification models and algorithms often require an enormous amount of labelled examples for training to achieve state-of-the-art performance. Labelled examples can be expensive and time-consuming to acquire. Human visual systems, on the other hand, are able to recognise new classes after being shown a few labelled examples. Few-shot classification (Miller et al., 2000; Li et al., 2004; 2006; Lake et al., 2011) tackles this issue by learning to adapt to unseen classes (known as novel classes) with very few labelled examples from each class. Recent works show that metalearning provides promising approaches to few-shot classification problems (Santoro et al., 2016; Finn et al., 2017; Li et al., 2017; Ravi & Larochelle, 2017). Meta-learning or learning-to-learn (Schmidhuber, 1987; Thrun & Pratt, 1998) takes the learning process a level deeper – instead of learning from the labelled examples in the training classes (known as base classes), meta-learning learns the example-learning process. The training process in meta-learning that utilises the base classes is called the meta-training stage, and the evaluation process that reports the few-shot performance on the novel classes is known as the meta-evaluation stage. ", + "bbox": [ + 174, + 520, + 825, + 699 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite being a promising solution to few-shot classification problems, meta-learning methods suffer from several limitations: ", + "bbox": [ + 174, + 707, + 821, + 734 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Unable to continually learn from sequential few-shot tasks: It is mandatory to have all base classes readily available for meta-training. Such meta-learning algorithms often require sampling a number of few-shot tasks in every iteration for optimisation. \n2. Unable to retain few-shot classification ability on sequential datasets that have evident distributional shift: A meta-learned model is restricted to perform few-shot classification on a specific dataset, in the sense that the base and novel classes have to originate from the same dataset distribution. A meta-learned model loses its few-shot classification ability on previous datasets as new ones arrive subsequently for meta-training. ", + "bbox": [ + 212, + 747, + 825, + 868 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We emphasise that the task mentioned in this paper refers to the few-shot task for meta-learning. This paper considers meta-learning a single model for few-shot classification in the sequential datasets and sequential few-shot tasks settings respectively. ", + "bbox": [ + 176, + 882, + 823, + 924 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We introduce a Bayesian online meta-learning framework that can train a few-shot learning model under the sequential few-shot tasks setting and train a model that is applicable to a broader scope of few-shot classification datasets by overcoming catastrophic forgetting. We extend the Bayesian online learning (BOL) framework (Opper, 1998) to a Bayesian online meta-learning framework using the model-agnostic meta-learning (MAML) algorithm (Finn et al., 2017). MAML finds a good model parameter initialisation (called meta-parameters) that can quickly adapt to novel classes using very few labelled examples, while BOL provides a principled framework for finding the posterior of the model parameters. Our framework aims to combine both BOL and MAML to find the posterior of the meta-parameters. Our work builds on Ritter et al. (2018a) which combines the BOL framework and Laplace approximation with block-diagonal Kronecker-factored Fisher approximation, and Nguyen et al. (2018) which uses variational inference with BOL to overcome catastrophic forgetting in large-scale supervised classification. ", + "bbox": [ + 174, + 103, + 825, + 270 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "An important reason to implement Bayesian inference over non-Bayesian methods for an online setting is that BOL provides a grounded framework that suggests using the previous posterior as the prior recursively. Bayesian inference inherits an advantage for robust meta-learning (Yoon et al., 2018) to overcome training instability problems addressed by Antoniou et al. (2019). BOL implicitly keeps a memory on previous knowledge via the posterior, in contrast to recent online meta-learning methods that explicitly accumulate previous data in a task buffer (Finn et al., 2019; Zhuang et al., 2019). Explicitly keeping a memory on previous data often triggers an important question: how should the carried-forward data be processed in future task rounds, in order to accumulate knowledge? Finn et al. (2019) update the meta-parameters at each iteration using previous few-shot tasks in the task buffer. This defeats the purpose of online learning, which by definition means to update the parameters each round using only the new data encountered. Having to re-train on previous data to avoid forgetting also increases the training time as the data accumulate (Finn et al., 2019; He et al., 2019). Certainly one can clamp the amount of data at some maximal limit and sample from the buffer, but the final performance of such an algorithm would be dependent on the samples being informative and of good quality which may vary across different seed runs. In contrast to memorising the datasets, having an implicit memory via the posterior automatically deals with the question on how to process carried-forward data and allows a better carry forward in previous experiences. ", + "bbox": [ + 174, + 277, + 825, + 513 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Below are the contributions we make in this paper: ", + "bbox": [ + 174, + 520, + 506, + 534 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We develop the Bayesian online meta-learning (BOML) framework for sequential few-shot classification problems. Under this framework we introduce the algorithms Bayesian online meta-learning with Laplace approximation (BOMLA) and Bayesian online meta-learning with variational inference (BOMVI). We propose a simple approximation to the Fisher corresponding to the BOMLA algorithm that carries over the desirable block-diagonal Kronecker-factored structure from the Fisher approximation in the non-meta-learning setting. We demonstrate that BOML can overcome catastrophic forgetting in the sequential few-shot datasets setting with apparent distributional shift in the datasets. \n• We demonstrate that BOML can continually learn to few-shot classify the novel classes in the sequential meta-training few-shot tasks setting. ", + "bbox": [ + 215, + 545, + 825, + 710 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2 META-LEARNING ", + "text_level": 1, + "bbox": [ + 174, + 729, + 351, + 746 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Most meta-learning algorithms comprise an inner loop for example-learning and an outer loop that learns the example-learning process. Such algorithms often require sampling a meta-batch of tasks at each iteration, where a task is formed by sampling a subset of classes from the pool of base classes or novel classes during meta-training or meta-evaluation respectively. The $N$ -way $K$ -shot task, for instance, refers to sampling $N$ classes and using $K$ examples per class for few-shot quick adaptation. ", + "bbox": [ + 174, + 761, + 825, + 844 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "An offline meta-learning algorithm learns a few-shot classification model only for a specific dataset $\\mathcal { D } _ { t + 1 }$ where all base classes of $\\mathcal { D } _ { t + 1 }$ have to be readily available for meta-training. For notational convenience, we drop the $t + 1$ subscript in this section, as there is only one dataset involved in offline meta-learning. The dataset $\\mathcal { D } _ { t + 1 }$ is divided into the set of base classes $\\widetilde { \\mathcal { D } }$ and novel classes $\\widehat { \\mathcal { D } }$ for meta-training and meta-evaluation respectively. Upon completing meta-training on the base class set $\\widetilde { \\mathcal { D } }$ , the goal of few-shot classification is to perform well on an unseen task ${ \\widehat { \\mathcal { D } } } ^ { * }$ sampled from the novel class set $\\widehat { \\mathcal { D } }$ after a quick adaptation on a small subset $\\widehat { \\mathcal { D } } ^ { * , S }$ (known as the support set) of $\\widehat { \\mathcal { D } } ^ { * }$ . The performance of this unseen task is evaluated on the query set $\\widehat { \\mathcal { D } } ^ { * , Q }$ , where $\\hat { \\mathcal { D } } ^ { * , Q } = \\widehat { \\mathcal { D } } ^ { * } \\backslash \\widehat { \\mathcal { D } } ^ { * , S }$ . Since $\\widehat { \\mathcal { D } }$ is not accessible during meta-training, this support-query split is mimicked on the base class set $\\widetilde { \\mathcal { D } }$ for meta-training. ", + "bbox": [ + 174, + 851, + 825, + 924 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "", + "bbox": [ + 173, + 99, + 825, + 184 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Model-agnostic meta-learning We are interested in the well-known meta-learning algorithm MAML (Finn et al., 2017). Each updating step of MAML aims to improve the ability of the metaparameters to act as a good model initialisation for a quick adaptation on unseen tasks. Each iteration of the MAML algorithm samples $M$ tasks from the base class set $\\widetilde { \\mathcal { D } }$ and runs a few steps of stochastic gradient descent (SGD) for an inner loop task-specific learning. The number of tasks sampled per iteration is known as the meta-batch size. For task $m$ , the inner loop outputs the task-specific parameters $\\tilde { \\theta } ^ { m }$ from a $k$ -step SGD quick adaptation on the objective $\\mathcal { L } ( \\boldsymbol { \\theta } , \\widetilde { \\mathcal { D } } ^ { m , S } )$ with the support set $\\widetilde { \\mathcal { D } } ^ { m , S }$ and initialised at $\\theta$ : ", + "bbox": [ + 173, + 198, + 825, + 316 + ], + "page_idx": 2 + }, + { + "type": "equation", + "img_path": "images/7eca1273e68ec69039e51c7a6b2fa9df631d9ebf7fce7921499424209291ac69.jpg", + "text": "$$\n\\tilde { \\theta } ^ { m } = S G D _ { k } ( \\mathcal { L } ( \\theta , \\widetilde { D } ^ { m , S } ) ) ,\n$$", + "text_format": "latex", + "bbox": [ + 405, + 314, + 589, + 333 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $m = 1 , \\ldots , M$ . The outer loop gathers all task-specific adaptations to update the metaparameters $\\theta$ using the loss $\\mathcal { L } ( \\tilde { \\theta } ^ { m } , \\widetilde { D } ^ { m , Q } )$ on the query set $\\bar { \\mathcal { D } } ^ { m , Q }$ . ", + "bbox": [ + 176, + 337, + 825, + 368 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The overall MAML optimisation objective is ", + "bbox": [ + 176, + 375, + 470, + 388 + ], + "page_idx": 2 + }, + { + "type": "equation", + "img_path": "images/92a2ef5fcf69515e3b21eb37f25efa013c1be58b6f0ef4335d7d4f09097f34c7.jpg", + "text": "$$\n\\underset { \\theta } { \\arg \\operatorname* { m i n } } \\frac { 1 } { M } \\sum _ { m = 1 } ^ { M } \\mathcal { L } ( S G D _ { k } ( \\mathcal { L } ( \\theta , \\widetilde { \\mathcal { D } } ^ { m , S } ) ) , \\widetilde { \\mathcal { D } } ^ { m , Q } ) .\n$$", + "text_format": "latex", + "bbox": [ + 336, + 396, + 663, + 439 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Like most offline meta-learning algorithms, MAML requires all base classes to be readily available for tasks-sampling at each iteration. We aim to overcome this limitation by meta-learning a model that can few-shot classify unseen tasks from the novel classes, while the tasks from the base classes arrive sequentially for meta-training. MAML also assumes a stationary task distribution during meta-training and meta-evaluation. Under this assumption, a meta-learned model is only applicable to a specific dataset distribution. When the model encounters a sequence of datasets with apparent distributional shift, it loses the few-shot classification ability on previous datasets as new ones arrive for meta-training. Our work also aims to meta-learn a single model for few-shot classification on multiple datasets that arrive sequentially for meta-training. We achieve these two goals by incorporating MAML into the BOL framework to give the Bayesian online meta-learning (BOML) framework that finds the posterior of the meta-parameters. ", + "bbox": [ + 173, + 452, + 825, + 606 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3 OVERVIEW OF OUR BAYESIAN ONLINE META-LEARNING APPROACH", + "text_level": 1, + "bbox": [ + 173, + 626, + 766, + 642 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our central contribution is to extend the benefits of meta-learning to the Bayesian online scenario, thereby training models that can generalise across tasks whilst dealing with parameter uncertainty in the setting of sequential tasks or sequential datasets. ", + "bbox": [ + 174, + 657, + 823, + 700 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Sequential datasets setting In this setting, online meta-training occurs sequentially on the datasets $\\mathcal { D } _ { 1 } , \\ldots , \\mathcal { D } _ { T }$ . Each dataset $\\mathcal { D } _ { i }$ can be seen as a knowledge domain with an associated underlying task distribution $p ( \\mathcal T _ { i } )$ . A newly-arrived $\\mathcal { D } _ { t + 1 }$ is separated into the base class set $\\widetilde { \\mathcal { D } } _ { t + 1 }$ and novel class set $\\widehat { \\mathcal { D } } _ { t + 1 }$ for meta-training and meta-evaluation respectively, where the tasks in these two stages are drawn from the task distribution $p ( \\mathcal T _ { t + 1 } )$ . ", + "bbox": [ + 173, + 715, + 825, + 791 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Sequential tasks setting The sequential tasks setting only involves one dataset $\\mathcal { D }$ with an associated underlying task distribution $p ( \\mathcal { T } )$ , where $\\mathcal { D }$ is separated into the base and novel class sets. In this setting, $\\widetilde { \\cal D } _ { 1 } , \\ldots , \\widetilde { \\cal D } _ { t + 1 }$ denote the non-overlapping tasks formed from the base class set and they arrive sequentially for meta-training. These tasks $\\widetilde { \\mathcal { D } } _ { 1 } , \\ldots , \\widetilde { \\mathcal { D } } _ { t + 1 }$ and the meta-evaluation tasks are drawn from the task distribution $p ( \\tau )$ . ", + "bbox": [ + 173, + 805, + 825, + 883 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Notationally, for both sequential tasks and sequential datasets settings, let $\\mathcal { \\widetilde { D } } _ { t + 1 } ^ { S }$ and $\\widetilde { \\mathcal { D } } _ { t + 1 } ^ { Q }$ denote the collection of support sets and query sets respectively from $\\widetilde { \\mathcal { D } } _ { t + 1 }$ , so that $\\widetilde { D } _ { t + 1 } = \\widetilde { D } _ { t + 1 } ^ { S } \\cup \\widetilde { D } _ { t + 1 } ^ { Q }$ . ", + "bbox": [ + 174, + 888, + 823, + 925 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We are interested in a MAP estimate $\\theta ^ { * } = \\arg \\operatorname* { m a x } _ { \\theta } p ( \\theta | \\widetilde { D } _ { 1 : t + 1 } )$ . Using Bayes’ rule on the posterior gives the recursive formula ", + "bbox": [ + 173, + 102, + 823, + 132 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/1a8e95d40de872338dbc14d6059f9cc8b3bb5ce6f016109a516aedb5ff29e140.jpg", + "text": "$$\n\\begin{array} { r l } & { p ( \\theta | \\widetilde { D } _ { 1 : t + 1 } ) \\propto p ( \\widetilde { D } _ { t + 1 } ^ { S } , \\widetilde { D } _ { t + 1 } ^ { Q } | \\theta ) p ( \\theta | \\widetilde { D } _ { 1 : t } ) } \\\\ & { \\qquad = p ( \\widetilde { D } _ { t + 1 } ^ { Q } | \\theta , \\widetilde { D } _ { t + 1 } ^ { S } ) p ( \\widetilde { D } _ { t + 1 } ^ { S } | \\theta ) p ( \\theta | \\widetilde { D } _ { 1 : t } ) } \\\\ & { \\qquad = \\bigg \\{ \\int p ( \\widetilde { D } _ { t + 1 } ^ { Q } | \\widetilde { \\theta } ) p ( \\widetilde { \\theta } | \\theta , \\widetilde { D } _ { t + 1 } ^ { S } ) d \\widetilde { \\theta } \\bigg \\} p ( \\widetilde { D } _ { t + 1 } ^ { S } | \\theta ) p ( \\theta | \\widetilde { D } _ { 1 : t } ) } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 267, + 137, + 728, + 218 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where Eq. (3) follows from the assumption that each dataset is independent given $\\theta$ . ", + "bbox": [ + 171, + 222, + 722, + 237 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "From the meta-learning perspective, the parameters $\\tilde { \\theta }$ introduced in Eq. (5) can be viewed as the task-specific parameters in MAML. There are various choices for the distribution $p ( \\tilde { \\theta } | \\theta , \\widetilde { D } _ { t + 1 } ^ { S } )$ in Eq. (5). In particular if we choose to set it as the deterministic function of taking several steps of SGD on loss $\\mathcal { L }$ with the support set collection $\\mathcal { \\widetilde { D } } _ { t + 1 } ^ { S }$ and initialised at $\\theta$ , we have ", + "bbox": [ + 173, + 243, + 825, + 306 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/40c0d0a3235433880a84fe4a976870153a480de768d4c9151bbe5804f3f2a947.jpg", + "text": "$$\np ( { \\tilde { \\theta } } | \\theta , { \\widetilde { \\mathcal { D } } } _ { t + 1 } ^ { S } ) = \\mathbb { 1 } \\{ { \\tilde { \\theta } } = S G D _ { k } ( { \\mathcal { L } } ( \\theta , { \\widetilde { \\mathcal { D } } } _ { t + 1 } ^ { S } ) ) \\} .\n$$", + "text_format": "latex", + "bbox": [ + 348, + 313, + 650, + 334 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and this recovers the MAML inner loop with SGD quick adaptation in Eq. (1). The recursion given by Eq. (5) forms the basis of our approach and the remainder of this paper explains how we implement this. In order to do so we give a mini tutorial in Appendix A on Bayesian online learning, Laplace approximation and variational continual learning. ", + "bbox": [ + 173, + 338, + 825, + 396 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4 BAYESIAN ONLINE META-LEARNING IMPLEMENTATION ", + "text_level": 1, + "bbox": [ + 174, + 416, + 663, + 433 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This section demonstrates how we arrive at the algorithms Bayesian online meta-learning with Laplace approximation (BOMLA) and Bayesian online meta-learning with variational inference (BOMVI) by implementing Laplace approximation and variational continual learning respectively to the posterior of the BOML framework in Eq. (5). These algorithms from the grounded BOML framework are useful for online training on the sequential few-shot classification datasets or tasks. ", + "bbox": [ + 174, + 446, + 825, + 517 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1 BAYESIAN ONLINE META-LEARNING WITH LAPLACE APPROXIMATION ", + "text_level": 1, + "bbox": [ + 174, + 534, + 697, + 549 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We discover that the Laplace approximation method provides a well-fitted meta-training framework for Bayesian online meta-learning in Eq. (5). Each updating step in the approximation procedure can be modified to correspond to the meta-parameters for few-shot classification, instead of the model parameters for large-scale supervised classification. ", + "bbox": [ + 174, + 559, + 825, + 616 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Laplace approximation rationalises the use of a Gaussian approximate posterior by Taylor expanding the log-posterior around a mode up to the second order, as described in Appendix A.2. The second order term corresponds to the log-probability of a Gaussian distribution. The BOML framework in Section 3 with a Gaussian approximate posterior $q$ of mean and precision $\\phi _ { t } = \\{ \\mu _ { t } , \\Lambda _ { t } \\}$ from the Laplace approximation gives a MAP estimate: ", + "bbox": [ + 173, + 622, + 825, + 693 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/d4f655828fc7d9c372db6d9131ab554473fb2952db5ee5acd5614d86a29d3385.jpg", + "text": "$$\n\\theta ^ { * } = \\arg \\operatorname* { m a x } _ { \\theta } \\Bigg \\{ \\log \\int p ( \\widetilde { \\mathcal { D } } _ { t + 1 } ^ { Q } | \\widetilde { \\theta } ) p ( \\widetilde { \\theta } | \\theta , \\widetilde { \\mathcal { D } } _ { t + 1 } ^ { S } ) d \\widetilde { \\theta } + \\log p ( \\widetilde { \\mathcal { D } } _ { t + 1 } ^ { S } | \\theta ) - \\frac { 1 } { 2 } ( \\theta - \\mu _ { t } ) ^ { T } \\Lambda _ { t } ( \\theta - \\mu _ { t } ) \\Bigg \\} .\n$$", + "text_format": "latex", + "bbox": [ + 179, + 699, + 799, + 733 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For an efficient optimisation, we use the deterministic $\\tilde { \\theta }$ in Eq. (6). The objective in Eq. (7) can be batched (for sequential tasks) or meta-batched (for sequential datasets). This leads to minimising the objective ", + "bbox": [ + 174, + 747, + 826, + 791 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/d42e6d885d731b8872483f64658c48686a601629b7b799ed3b5091a561277731.jpg", + "text": "$$\n\\mathsf { \\Pi } _ { t + 1 } ^ { \\mathsf { R O M L A } } ( \\theta , \\mu _ { t } , \\Lambda _ { t } ) = - \\frac { 1 } { M } \\sum _ { m = 1 } ^ { M } \\log p ( \\widetilde { \\mathcal { D } } _ { t + 1 } ^ { m , Q } | \\widetilde { \\theta } ^ { m } ) - \\frac { 1 } { M } \\sum _ { m = 1 } ^ { M } \\log p ( \\widetilde { \\mathcal { D } } _ { t + 1 } ^ { m , S } | \\theta ) + \\frac { 1 } { 2 } ( \\theta - \\mu _ { t } ) ^ { T } \\Lambda _ { t } ( \\theta - \\mu _ { t } ) ,\n$$", + "text_format": "latex", + "bbox": [ + 181, + 797, + 825, + 842 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\tilde { \\theta } ^ { m } = S G D _ { k } ( \\mathcal { L } ( \\theta , \\widetilde { D } _ { t + 1 } ^ { m , S } ) )$ for $m = 1 , \\ldots , M$ . In the sequential datasets setting $M$ denotes the number of tasks sampled per iteration, whereas in the sequential tasks setting denotes the number of batches per epoch. The first term of the objective in Eq. (8) corresponds to the MAML objective in Eq. (2) with a cross-entropy loss, the second term can be viewed as the pre-adaptation loss on the support set and the last term can be seen as a regulariser. ", + "bbox": [ + 173, + 852, + 825, + 924 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2 HESSIAN APPROXIMATION ", + "text_level": 1, + "bbox": [ + 174, + 103, + 398, + 117 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We calculate a block-diagonal Kronecker-factored Hessian approximation in order to update the precision $\\Lambda _ { t }$ , as explained in Appendix A.3. The Hessian approximations in both sequential datasets and sequential tasks settings are very similar, except that the sequential datasets setting averages over the meta-batch size and the sequential tasks setting averages over the number of batches. ", + "bbox": [ + 173, + 128, + 825, + 185 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The Hessian matrix corresponding to the first term of the BOMLA objective in Eq. (8) is ", + "bbox": [ + 171, + 191, + 753, + 207 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/343db103ae61129fa73d7ad5c6538f7344b3d54d2a428145c9173df606c0dbfc.jpg", + "text": "$$\n\\widetilde { H } _ { t + 1 } ^ { i j } = \\frac { 1 } { M } \\sum _ { m = 1 } ^ { M } - \\frac { \\partial ^ { 2 } } { \\partial \\theta ^ { ( i ) } \\partial \\theta ^ { ( j ) } } \\log p ( \\widetilde { \\mathcal { D } } _ { t + 1 } ^ { m , Q } | \\widetilde { \\theta } ^ { m } ) ) \\Bigg | _ { \\theta = \\mu _ { t + 1 } } .\n$$", + "text_format": "latex", + "bbox": [ + 312, + 210, + 686, + 255 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "It is worth noting that the BOMLA Hessian deviates from the original BOL Hessian in Appendix A.2. This requires deriving an adjusted approximation to the Hessian with some further assumptions. ", + "bbox": [ + 174, + 257, + 825, + 300 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The BOL Hessian for a single data point can be approximated using the Fisher information matrix $F$ to ensure its positive semi-definiteness (Martens $\\&$ Grosse, 2015): ", + "bbox": [ + 171, + 306, + 823, + 335 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/cf0c4d7d663b09b3e560637d67790ea757514eefcaa97699217cf1453a6a0fd8.jpg", + "text": "$$\nF = \\mathbb { E } _ { x , y } \\bigg [ \\frac { d } { d \\theta } \\log p ( y | x , \\theta ) \\frac { d } { d \\theta } \\log p ( y | x , \\theta ) ^ { T } \\bigg ] .\n$$", + "text_format": "latex", + "bbox": [ + 343, + 340, + 655, + 375 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Each $( x , y )$ pair for the Fisher in BOMLA is associated to a task (or a batch) $m$ . The Fisher information matrix $\\widetilde { F }$ corresponding to the BOMLA Hessian in Eq. (9) for a single data point is ", + "bbox": [ + 173, + 378, + 823, + 410 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/8baa73ad4baba1475c9a3370fe3004bb5cbaa3b00d996bdebeddf1cace34611c.jpg", + "text": "$$\n\\widetilde { F } = \\frac { 1 } { M } \\sum _ { m = 1 } ^ { M } \\mathbb { E } _ { x , y } \\bigg [ \\bigg ( \\frac { \\partial \\widetilde { \\theta } ^ { m } } { \\partial \\theta } \\bigg ) \\frac { d } { d \\widetilde { \\theta } ^ { m } } \\log p ( y | x , \\widetilde { \\theta } ^ { m } ) \\frac { d } { d \\widetilde { \\theta } ^ { m } } \\log p ( y | x , \\widetilde { \\theta } ^ { m } ) ^ { T } \\bigg ( \\frac { \\partial \\widetilde { \\theta } ^ { m } } { \\partial \\theta } \\bigg ) ^ { T } \\bigg ] .\n$$", + "text_format": "latex", + "bbox": [ + 227, + 414, + 769, + 458 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The additional Jacobian matrix $\\frac { \\partial \\tilde { \\theta } ^ { m } } { \\partial \\theta }$ breaks the Kronecker-factored structure described by Martens & Grosse (2015) for the original Fisher in Eq. (10). ", + "bbox": [ + 173, + 463, + 825, + 494 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The results in Finn et al. (2017) show that the first step of the quick adaptation in $\\tilde { \\theta } ^ { m }$ contributes the largest change to the meta-evaluation objective, and the remaining adaptation steps give a relatively small change to the objective. It is reasonable to assume that the quick adaptation is a one-step SGD for Fisher approximation: ", + "bbox": [ + 173, + 501, + 825, + 558 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/010371dd5f0c91339f5ccb1951cdebe2358e8321e7db27767127020481d5f5f9.jpg", + "text": "$$\n\\begin{array} { r } { \\tilde { \\theta } ^ { m } = \\theta - \\nabla _ { \\theta } \\mathcal { L } ( \\theta , \\widetilde { D } _ { t + 1 } ^ { m , S } ) . } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 410, + 556, + 588, + 577 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "By imposing this assumption, the $( i , j )$ -th entry of the Jacobian term can be interpreted as ", + "bbox": [ + 178, + 577, + 764, + 593 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/fb6d2e8697e39d339370645ea1db417c8e2841845d468d841f06e573d0b06a95.jpg", + "text": "$$\n\\left( \\frac { \\partial \\tilde { \\theta } ^ { m } } { \\partial \\theta } \\right) ^ { i j } = I ^ { i j } - \\frac { \\partial ^ { 2 } ( - \\log p ( \\widetilde { D } _ { t + 1 } ^ { m , S } | \\theta ) ) } { \\partial \\theta ^ { ( i ) } \\partial \\theta ^ { ( j ) } } ,\n$$", + "text_format": "latex", + "bbox": [ + 356, + 597, + 640, + 635 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $I$ is the corresponding identity matrix and the objective $\\mathcal { L }$ involved is the negative loglikelihood. The Hessian for a single data point in the second term of Eq. (13) can be approximated by $F$ in Eq. (10) via the usual block-diagonal Kronecker-factored approximation. Putting the Jacobian back into Eq. (11) and expanding the factors give terms that multiply two or more Kronecker products together. The detailed derivation of $\\widetilde { F }$ is explained in Appendix A.3.1. We introduce the posterior regulariser $\\lambda$ when updating the precision: $\\Lambda _ { t + 1 } = \\lambda { \\widetilde { \\cal H } } _ { t + 1 } + \\Lambda _ { t }$ and the rationale for introducing $\\lambda$ is explained in Appendix A.3.2. The pseudo-code of the BOMLA algorithm can be found in Appendix B.1. ", + "bbox": [ + 173, + 637, + 825, + 755 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3 BAYESIAN ONLINE META-LEARNING WITH VARIATIONAL INFERENCE ", + "text_level": 1, + "bbox": [ + 174, + 771, + 691, + 785 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The variational continual learning (VCL) framework (Nguyen et al., 2018) is directly applicable to BOML. This section demonstrates how we arrive at the BOMVI algorithm by implementing VCL to the posterior of the BOML framework in Eq. (5). ", + "bbox": [ + 174, + 796, + 825, + 839 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As described in Appendix A.4, VCL approximates the posterior by minimising the KL-divergence over some pre-determined approximate posterior family $\\mathcal { Q }$ . Fitting the BOML posterior in Eq. (5) into the VCL framework gives the approximate posterior: ", + "bbox": [ + 174, + 845, + 825, + 888 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/23bd8d9eb209877e105b8e2387ef7e368d77d8125637c2486211c36eb40e27cd.jpg", + "text": "$$\nq ( \\theta | \\phi _ { t + 1 } ) = \\underset { q \\in \\mathcal { Q } } { \\operatorname { a r g m i n } } D _ { \\mathrm { K L } } \\Bigg ( q ( \\theta | \\phi ) \\bigg | \\bigg | \\bigg \\{ \\int p ( \\widetilde { \\mathcal { D } } _ { t + 1 } ^ { Q } | \\widetilde { \\theta } ) p ( \\widetilde { \\theta } | \\theta , \\widetilde { \\mathcal { D } } _ { t + 1 } ^ { S } ) d \\widetilde { \\theta } \\bigg \\} p ( \\widetilde { \\mathcal { D } } _ { t + 1 } ^ { S } | \\theta ) q ( \\theta | \\phi _ { t } ) \\Bigg ) .\n$$", + "text_format": "latex", + "bbox": [ + 184, + 892, + 785, + 928 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Similar to BOMLA, we use the deterministic $\\tilde { \\theta }$ in Eq. (6), and the objective in Eq. (14) can be batched (for sequential tasks) or meta-batched (for sequential datasets). This leads to minimising the objective ", + "bbox": [ + 176, + 102, + 823, + 146 + ], + "page_idx": 5 + }, + { + "type": "equation", + "img_path": "images/ee7b2e2e580f20188f5f558ef8418de608a8ef60ce3e4fd0e30c87ce3702de47.jpg", + "text": "$$\nf _ { t + 1 } ^ { \\mathrm { B o n v I } } ( \\phi , \\phi _ { t } ) = - \\frac { 1 } { M } \\sum _ { m = 1 } ^ { M } \\mathbb { E } _ { q ( \\theta | \\phi ) } \\big [ \\log p ( \\widetilde { \\mathcal { D } } _ { t + 1 } ^ { m , Q } | \\widetilde { \\theta } ^ { m } ) \\big ] - \\frac { 1 } { M } \\sum _ { m = 1 } ^ { M } \\mathbb { E } _ { q ( \\theta | \\phi ) } \\big [ \\log p ( \\widetilde { \\mathcal { D } } _ { t + 1 } ^ { m , S } | \\theta ) \\big ]\n$$", + "text_format": "latex", + "bbox": [ + 189, + 152, + 781, + 217 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\tilde { \\theta } ^ { m } = S G D _ { k } ( \\mathcal { L } ( \\theta , \\widetilde { D } _ { t + 1 } ^ { m , S } ) )$ for $m = 1 , \\ldots , M$ . In the sequential datasets setting $M$ denotes the number of tasks sampled per iteration, whereas in the sequential tasks setting $M$ denotes the number of batches per epoch. We use a Gaussian mean-field approximate posterior $q ( \\theta | \\phi _ { t } ) =$ $\\textstyle \\prod _ { d = 1 } ^ { D } N ( \\mu _ { t , d } , \\sigma _ { t , d } ^ { 2 } )$ , where $\\phi _ { t } ~ = ~ \\{ \\mu _ { t , d } , \\sigma _ { t , d } \\} _ { d = 1 } ^ { D }$ , $D = \\dim ( \\theta )$ and the objective in Eq. (15) is minimised over $\\phi$ . The pseudo-code of the BOMVI algorithm can be found in Appendix B.1. ", + "bbox": [ + 174, + 223, + 825, + 300 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The first term in Eq. (15) is rather cumbersome to estimate in optimisation. To compute its Monte Carlo estimator, we have to generate samples $\\theta _ { r } \\sim q$ for $r = 1 , \\ldots , R$ , and run a quick adaptation on each sampled meta-parameters $\\theta _ { r }$ before evaluating its log-likelihood. This is computationally intensive and it gives an estimator with large variance. We propose a workaround by modifying the inner loop SGD quick adaptation, and the details can be found in Appendix B.2. ", + "bbox": [ + 174, + 306, + 825, + 377 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5 RELATED WORK ", + "text_level": 1, + "bbox": [ + 176, + 397, + 341, + 412 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Online Meta-Learning There are two common problem settings in the current online metalearning works: ", + "bbox": [ + 173, + 429, + 821, + 458 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "• Underlying task distribution: Sequential tasks are assumed to originate from the same underlying task distribution $p ( \\mathcal { T } )$ in this setting. Our work in the sequential tasks setting belongs to this category. Denevi et al. (2019) introduce the online-within-online (OWO) and online-within-batch (OWB) settings, where OWO encounters tasks and examples within tasks sequentially while OWB encounters tasks sequentially but examples within tasks are in batch. The BOML framework in the sequential tasks setting corresponds to the OWB setting. On the other hand, our work in the sequential datasets setting is novel in overcoming few-shot catastrophic forgetting, where the goal is to few-shot classify tasks drawn from a sequence of distributions $p ( { \\bar { \\mathcal { T } } } _ { 1 } ) , \\dots , p ( { \\mathcal { T } } _ { T } )$ as explained in Section 3. He et al. (2019), Harrison et al. (2019) and Jerfel et al. (2019) look into continual meta-learning for nonstationary task distributions where the task boundaries are unknown to the model. Jerfel et al. (2019) consider a latent task structure to adapt to the non-stationary task distributions. ", + "bbox": [ + 215, + 472, + 823, + 638 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "• Regret minimisation: In this setting, the goal is to minimise the regret function, and the assumptions are made on the loss function rather than the task distribution. Recent works Finn et al. (2019); Zhuang et al. (2019) belong to this category, where the aim is to compete with the best meta-learner and supersede it. These methods accumulate data as they arrive and meta-learn using all data acquired so far. Data accumulation is not desirable as the algorithmic complexity of training grows with the amount of data accumulated, and training time increases as new data arrive (Finn et al., 2019; He et al., 2019). The agent will eventually run out of memory for a long sequence of data. The BOML framework on the other hand is advantageous, as it only takes the posterior of the meta-parameters into consideration during optimisation. This gives a framework with an algorithmic complexity independent of the length of the dataset sequence. ", + "bbox": [ + 215, + 643, + 825, + 796 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Offline Meta-Learning Previous meta-learning works attempt to solve few-shot classification problems in an offline setting, under the assumption of having a stationary task distribution during meta-training and meta-evaluation. A single meta-learned model is aimed to few-shot classify one specific dataset with all base classes of the dataset readily available in a batch for meta-training. There are two general frameworks for the offline meta-learning setting: ", + "bbox": [ + 176, + 811, + 823, + 882 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "• Probabilistic framework: The MAML algorithm can be cast into a probabilistic inference problem (Finn et al., 2018) or with a hierarchical Bayesian structure (Grant et al., ", + "bbox": [ + 217, + 895, + 823, + 924 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "2018; Yoon et al., 2018). Grant et al. (2018) discuss the use of a Laplace approximation in the task-specific inner loop to improve MAML using the curvature information, whilst Yoon et al. (2018) use Stein Variational Gradient Descent (SVGD) for task-specific learning. Gordon et al. (2019) implement probabilistic inference by considering the posterior predictive distribution with amortised networks. ", + "bbox": [ + 230, + 103, + 825, + 172 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "• Non-probabilistic framework: Gradient-based meta-learning (Finn et al., 2017; Nichol et al., 2018; Rusu et al., 2019) updates the meta-parameters by accumulating the gradients of a meta-batch of task-specific inner loop updates. The meta-parameters will be used as a model initialisation for a quick adaptation on the novel classes. Metric-based metalearning (Koch et al., 2015; Vinyals et al., 2016; Snell et al., 2017) utilises the metric distance between labelled examples. Such methods assume that base and novel classes are from the same dataset distribution, and the metric distance estimations can be generalised to the novel classes upon meta-learning the base classes. ", + "bbox": [ + 217, + 179, + 825, + 290 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Continual Learning Modern continual learning works (Goodfellow et al., 2013; Lee et al., 2017; Zenke et al., 2017) focus primarily on large-scale supervised learning, in contrast to our work that looks into continual few-shot classification across sequential tasks and datasets. Wen et al. (2018) utilise few-shot learning to improve on overcoming catastrophic forgetting via logit matching on a small sample from the previous tasks. The online learning element in this paper is closely related to (Kirkpatrick et al., 2017; Zenke et al., 2017; Ritter et al., 2018a; Nguyen et al., 2018) that overcome catastrophic forgetting for large-scale supervised classification. In particular, our work builds on the online Laplace approximation method in (Ritter et al., 2018a). We extend this to the meta-learning scenario to avoid forgetting in few-shot classification problems. Nguyen et al. (2018) provide the alternative of using variational inference instead of Laplace approximation for approximating the posterior. It is a reasonable approach to adapt variational approximation methods to approximate the posterior of the meta-parameters by adjusting the KL-divergence objective. ", + "bbox": [ + 174, + 308, + 825, + 474 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6 EXPERIMENTS ", + "text_level": 1, + "bbox": [ + 174, + 497, + 326, + 513 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.1 OMNIGLOT: SEQUENTIAL TASKS ", + "text_level": 1, + "bbox": [ + 176, + 530, + 439, + 544 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We run the sequential tasks experiment on the Omniglot dataset. To increase the difficulty level, we split the datasets based on the alphabets (super-classes) instead of the characters (classes). The goal of this experiment is to classify the 5-way 5-shot novel tasks sampled from the meta-evaluation alphabets. The experimental details and the alphabet splits can be found in Appendix C.1. ", + "bbox": [ + 176, + 556, + 825, + 613 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We compare our algorithms to the following baselines: ", + "bbox": [ + 176, + 619, + 532, + 633 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "1. Train-On-Everything (TOE): When a new task (or dataset) arrives for meta-training, we randomly re-initialise the meta-parameters and perform meta-training on all tasks (or datasets) encountered so far. Once meta-training is completed in this stage, we do not update the posterior of the meta-parameters like we would in BOMLA and BOMVI. 2. Train-From-Scratch (TFS): Upon the arrival of a new task (or dataset), we randomly reinitialise the meta-parameters and meta-train only on the newly-arrived task (or dataset). Similar to TOE, the posterior of the meta-parameters is not updated in TFS. 3. Follow The Meta-Leader (FTML): We introduce a slight modification to FTML (Finn et al., 2019) on its evaluation method, as FTML is not designed for few-shot learning on unseen tasks. In our experiment, we apply Update-Procedure in FTML to the data from unseen tasks, rather than the data from the same training task as in the original FTML. ", + "bbox": [ + 212, + 646, + 825, + 814 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As the tasks arrive sequentially for meta-training, Figure 1 shows that BOMLA and BOMVI can accumulate the few-shot classification ability on the novel tasks over time. The knowledge acquired from previous meta-training tasks are carried forward in the form of a posterior, which is then used as the prior when a new task arrives for meta-training. The baselines TOE and TFS have similar performances. Despite having access to all previous tasks, TOE shows no positive forward transfer in the meta-evaluation accuracy each time it encounters a new task. BOMLA with $\\lambda = 0 . 1$ gives the best performance in this experiment. ", + "bbox": [ + 174, + 827, + 825, + 924 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f1b81faadf230be434c4056a4a78621223884d73db008b674c0cea1f3e45bc91.jpg", + "image_caption": [ + "Figure 1: Meta-evaluation accuracy across 3 seed runs on the novel tasks along meta-training. Left: compares BOMLA to the baselines, centre: compares BOMVI to the baselines, right: compares BOMLA with different $\\lambda$ values to BOMVI. " + ], + "image_footnote": [], + "bbox": [ + 174, + 103, + 823, + 268 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6.2 PENTATHLON: SEQUENTIAL DATASETS ", + "text_level": 1, + "bbox": [ + 176, + 372, + 480, + 387 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We implement BOMLA and BOMVI to the pentathlon 5-way 1-shot classification sequence: ", + "bbox": [ + 169, + 398, + 777, + 414 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Omniglot CIFAR-FS miniImageNet VGG-Flowers Aircraft ", + "bbox": [ + 261, + 424, + 736, + 439 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The details of this experiment and the datasets can be found in Appendix C.2. We compare BOMLA and BOMVI to the baseline TOE, and running MAML continuously on the sequential datasets for meta-training. ", + "bbox": [ + 174, + 457, + 823, + 500 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Figure 2 shows that BOMLA and BOMVI are able to prevent few-shot catastrophic forgetting. TOE is also able to retain the few-shot performance as it has access to all datasets encountered so far. However, since it learns all datasets from random re-initialisation each time it encounters a new dataset, the meta-training time required to achieve a similarly good meta-evaluation performance is longer compared to other runs. The sequential MAML, on the other hand, catastrophically forgets the previously learned datasets but has the best performance on new datasets compared to other runs. TOE can be memory-intensive as the dataset sequence becomes longer. It takes the bruteforce approach to prevent forgetting by memorising all datasets. Unlike TOE, our BOML approach only takes the posterior of the meta-parameters into consideration during optimisation. This gives a framework with an algorithmic complexity independent of the length of the dataset sequence. ", + "bbox": [ + 174, + 506, + 825, + 646 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "$@ \\ @ \\left( { \\widehat { a } } \\right)$ New2: errorband ", + "bbox": [ + 839, + 507, + 883, + 561 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Tuning the posterior regulariser $\\lambda$ mentioned in Section 4.2 corresponds to balancing between a smaller performance trade-off on a new dataset and less forgetting on previous datasets. As shown in Appendix C.2 Figure 4, a larger $\\lambda = 1 0 0 0$ results in a more concentrated Gaussian posterior and is therefore unable to learn new datasets well, but can better retain the performances on previous datasets. A smaller value $\\lambda = 1$ on the other hand gives a widespread Gaussian posterior and learns better on new datasets by sacrificing the performance on the previous datasets. In this experiment, the value $\\lambda = 1 0 0$ gives the best balance between old and new datasets. Ideally we seek for a good performance on both old and new datasets, but in reality there is a trade-off between retaining performance on old datasets and learning well on new datasets due to posterior approximation errors. ", + "bbox": [ + 174, + 652, + 825, + 777 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As shown in Figures 1 and 2, BOMLA with appropriate $\\lambda$ is superior to BOMVI. This is due to BOMLA having a better posterior approximation than BOMVI. Whilst BOMLA has a Gaussian approximate posterior with block-diagonal precision, BOMVI uses a Gaussian mean-field approximate posterior. Trippe & Turner (2017) compared the performances of variational inference with different covariance structures, and discovered that variational inference with block-diagonal covariance performs worse than mean-field approximation. This is because the block-diagonal covariance in variational inference prohibits variance reduction methods such as local reparameterisation trick for Monte Carlo estimation. The variance of the Monte Carlo estimate has been proven problematic (Kingma et al., 2015; Trippe & Turner, 2017). We address this issue in Section 4.3 and Appendix B.2 specifically to the meta-learning setting by modifying the inner loop quick adaptation. ", + "bbox": [ + 174, + 784, + 825, + 924 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "$@ \\ @ \\left( { \\widehat { a } } \\right)$ New2: $\\lambda { \\cdot }$ - comparing plot in App. C.2 ", + "bbox": [ + 838, + 654, + 911, + 737 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e2f5052bde38ab7aad480616153346453a41dffe2b36ad7c864932e1cf0d6269.jpg", + "image_caption": [ + "Figure 2: Meta-evaluation accuracy across 3 seed runs on each dataset along meta-training (refer to Figure 3 for the enlarged version). Higher accuracy values indicate better results with less forgetting as we proceed to new datasets. BOMLA with $\\lambda = 1 0 0$ gives good performance in the offdiagonal plots (retains performances on previously learned datasets), and has a minor performance trade-off in the diagonal plots (learns less well on new datasets). Sequential MAML gives better performance in the diagonal plots (learns well on new datasets) but worse performance in the offdiagonal plots (forgets previously learned datasets). BOMVI is also able to retain performance on previous datasets, although it may be unable to perform as good as BOMLA due to sampling and estimator variance. " + ], + "image_footnote": [], + "bbox": [ + 174, + 111, + 818, + 434 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "7 CONCLUSION ", + "text_level": 1, + "bbox": [ + 176, + 619, + 318, + 636 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We introduced the Bayesian online meta-learning (BOML) framework with two algorithms: BOMLA and BOMVI. Our framework can overcome catastrophic forgetting in few-shot classification problems and can handle sequentially arriving few-shot tasks for online meta-learning. BOML merged the BOL framework and the MAML algorithm via Laplace approximation or variational continual learning. We proposed the necessary adjustments in the Hessian and Fisher approximation for BOMLA, as we are optimising the meta-parameters for few-shot classification instead of the usual model parameters in large-scale supervised classification. The experiments show that BOMLA and BOMVI are able to retain the few-shot classification ability when trained on sequential datasets with evident distributional shift, resulting in the ability to perform few-shot classification on multiple datasets with a single meta-learned model. BOMLA and BOMVI are also able to continually learn to few-shot classify novel tasks as the meta-training tasks arrive sequentially for learning. ", + "bbox": [ + 174, + 652, + 825, + 806 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "REFERENCES ", + "text_level": 1, + "bbox": [ + 174, + 829, + 285, + 844 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "A. Antoniou, H. Edwards, and A. Storkey. How to Train Your MAML. In International Conference on Learning Representations, 2019. L. Bertinetto, J. F. Henriques, P. Torr, and A. Vedaldi. Meta-Learning with Differentiable ClosedForm Solvers. In International Conference on Learning Representations, 2019. 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In Proceedings of the 36th International Conference on Machine Learning, 2019. \nI. J. Goodfellow, M. Mirza, D. Xiao, A. Courville, and Y. Bengio. An Empirical Investigation of Catastrophic Forgetting in Gradient-Based Neural Networks. arXiv preprint, arXiv:1312.6211, 2013. \nJ. Gordon, J. Bronskill, M. Bauer, S. Nowozin, and R. Turner. Meta-Learning Probabilistic Inference for Prediction. In International Conference on Learning Representations, 2019. URL https: //openreview.net/forum?id ${ . } = { }$ HkxStoC5F7. \nE. Grant, C. Finn, S. Levine, T. Darrell, and T. Griffiths. Recasting Gradient-Based Meta-Learning as Hierarchical Bayes. In International Conference on Learning Representations, 2018. \nR. Grosse and J. Martens. A Kronecker-Factored Approximate Fisher Matrix for Convolution Layers. In Proceedings of the 33rd International Conference on Machine Learning, 2016. \nJ. Harrison, A. Sharma, C. Finn, and M. Pavone. Continuous Meta-Learning without Tasks. arXiv preprint, arXiv:1912.08866, 2019. \nX. He, J. Sygnowski, A. Galashov, A. A. Rusu, Y. Teh, and R. Pascanu. Task Agnostic Continual Learning via Meta Learning. arXiv preprint, arXiv:1906.05201, 2019. \nG. Jerfel, E. Grant, T. Griffiths, and K. A. Heller. Reconciling Meta-Learning and Continual Learning with Online Mixtures of Tasks. In Advances in Neural Information Processing Systems 32, 2019. \nD. P. Kingma and J. Ba. Adam: A Method for Stochastic Optimization. In International Conference on Learning Representations, 2015. \nD. P. Kingma, T. Salimans, and M. Welling. Variational Dropout and the Local Reparameterization Trick. In Advances in Neural Information Processing Systems 28, 2015. \nJ. Kirkpatrick, R. Pascanu, N. Rabinowitz, J. Veness, G. Desjardins, A. A. Rusu, K. Milan, J. Quan, T. Ramalho, A. Grabska-Barwinska, D. Hassabis, C. Clopath, D. Kumaran, and R. Hadsell. Overcoming Catastrophic Forgetting in Neural Networks. Proceedings of the National Academy of Sciences, 2017. \nG. Koch, R. Zemel, and R. Salakhutdinov. Siamese Neural Networks for One-Shot Image Recognition. In 32th International Conference on Machine Learning Deep Learning Workshop, 2015. \nB. Lake, R. Salakhutdinov, J. Gross, and J.B. Tenenbaum. One Shot Learning of Simple Visual Concepts. In Proceedings of the 33rd Annual Conference of the Cognitive Science Society, 2011. \nS. Lee, J. Kim, J. Jun, J. Ha, and B. Zhang. Overcoming Catastrophic Forgetting by Incremental Moment Matching. In Advances in Neural Information Processing Systems 30, 2017. \nF. Li, R. Fergus, and P. Perona. Learning Generative Visual Models from Few Training Examples: An Incremental Bayesian Approach Tested on 101 Object Categories. In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, 2004. \nF. Li, R. Fergus, and P. Perona. One-Shot Learning of Object Categories. 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Sygnowski, O. Vinyals, R. Pascanu, S. Osindero, and R. Hadsell. MetaLearning with Latent Embedding Optimization. In International Conference on Learning Representations, 2019. \nA. Santoro, S. Bartunov, M. Botvinick, D. Wierstra, and T. Lillicrap. Meta-Learning with MemoryAugmented Neural Networks. In Proceedings of the 33rd International Conference on Machine Learning, 2016. \nJ. Schmidhuber. Evolutionary Principles in Self-Referential Learning. On Learning How to Learn: The Meta-Meta-Meta...-Hook. Diploma thesis, Institut fur Informatik, Technische Universit ¨ at¨ Munchen, 1987. ¨ \nJ. Snell, K. Swersky, and R. Zemel. Prototypical Networks for Few-Shot Learning. In Advances in Neural Information Processing Systems 30, 2017. \nS. Thrun and L. Pratt. Learning to Learn: Introduction and Overview. Springer, Boston, MA, 1998. \nB. L. Trippe and R. E. Turner. Overpruning in Variational Bayesian Neural Networks. In Advances in Neural Information Processing Systems 30 – Advances in Approximate Bayesian Inference Workshop, 2017. \nO. Vinyals, C. Blundell, T. Lillicrap, K. Kavukcuoglu, and D. Wierstra. Matching Networks for One Shot Learning. In Advances in Neural Information Processing Systems 29, 2016. \nJ. Wen, Y. Cao, and R. Huang. Few-Shot Self Reminder to Overcome Catastrophic Forgetting. arXiv preprint, arXiv:1812.00543, 2018. \nJ. Yoon, T. Kim, O. Dia, S. Kim, Y. Bengio, and S. Ahn. Bayesian Model-Agnostic Meta-Learning. In Advances in Neural Information Processing Systems 31, 2018. \nF. Zenke, B. Poole, and S. Ganguli. Continual Learning through Synaptic Intelligence. In Proceedings of the 34th International Conference on Machine Learning, 2017. \nZ. Zhuang, Y. Wang, K. Yu, and S. Lu. No-Regret Non-Convex Online Meta-Learning. arXiv preprint, arXiv:1910.10196, 2019. ", + "bbox": [ + 169, + 85, + 828, + 934 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "", + "bbox": [ + 169, + 65, + 828, + 929 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "", + "bbox": [ + 169, + 102, + 826, + 246 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "A BACKGROUND ", + "text_level": 1, + "bbox": [ + 176, + 102, + 331, + 118 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "This section provides a background explanation of using BOL to find the posterior of a model parameters and overcome catastrophic forgetting, commonly for large-scale supervised classification. We will then apply this approach to our recursion in Eq. (5). ", + "bbox": [ + 174, + 132, + 823, + 175 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "The posterior is typically intractable due to the enormous size of the modern neural network architectures. This leads to the requirement for a good approximation of the posterior of the metaparameters. A particularly suitable candidate for this purpose in meta-learning is the Laplace approximation (MacKay, 1992; Ritter et al., 2018b), as it simply adds a quadratic regulariser to the training objective. Variational inference is another possible method to obtain an approximation for the posterior of the meta-parameters. ", + "bbox": [ + 174, + 181, + 825, + 266 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "A.1 BAYESIAN ONLINE LEARNING ", + "text_level": 1, + "bbox": [ + 176, + 281, + 426, + 295 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "Upon the arrival of the new $\\mathcal { D } _ { t + 1 }$ , we are interested in a MAP estimate $\\theta ^ { * } = \\arg \\operatorname* { m a x } _ { \\theta } p ( \\theta | \\mathcal { D } _ { 1 : t + 1 } )$ for the parameters $\\theta$ of a neural network. Using Bayes’ rule on the posterior gives the recursive formula ", + "bbox": [ + 174, + 306, + 825, + 348 + ], + "page_idx": 12 + }, + { + "type": "equation", + "img_path": "images/50c4eeba784d039aea493d055edcf74d0628b62536ebcf5612919a59d04374f0.jpg", + "text": "$$\np ( \\theta | \\mathcal { D } _ { 1 : t + 1 } ) \\propto p ( \\mathcal { D } _ { t + 1 } | \\theta ) p ( \\theta | \\mathcal { D } _ { 1 : t } )\n$$", + "text_format": "latex", + "bbox": [ + 380, + 348, + 616, + 364 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "where Eq. (16) follows from the assumption that each dataset is independent given $\\theta$ . As the normalised posterior $p ( \\theta | \\mathcal { D } _ { 1 : t } )$ is usually intractable, it may be approximated by a parametric distribution $q$ with parameter $\\phi _ { t }$ . The BOL framework consists of the update step and the projection step (Opper, 1998). The update step uses the approximate posterior $q ( \\theta | \\phi _ { t } )$ obtained from the previous step for an update in the form of Eq. (16): ", + "bbox": [ + 173, + 366, + 825, + 434 + ], + "page_idx": 12 + }, + { + "type": "equation", + "img_path": "images/053143aefc5a8d71314f3d247199e8e8c233a1d5a7f82df99d9438bd84bcefc4.jpg", + "text": "$$\np ( \\theta | \\mathcal { D } _ { 1 : t + 1 } , \\phi _ { t } ) \\propto p ( \\mathcal { D } _ { t + 1 } | \\theta ) q ( \\theta | \\phi _ { t } ) .\n$$", + "text_format": "latex", + "bbox": [ + 374, + 436, + 622, + 454 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "The new posterior $p ( \\theta | \\mathcal { D } _ { 1 : t + 1 } , \\phi _ { t } )$ might not belong to the same parametric family as $q ( \\theta | \\phi _ { t } )$ . In this case, the new posterior has to be projected into the same parametric family to obtain $q ( \\theta | \\phi _ { t + 1 } )$ . Opper (1998) performs this projection by minimising the KL-divergence between the new posterior and the parametric $q$ , while Ritter et al. (2018a) use the Laplace approximation and Nguyen et al. (2018) use variational inference. ", + "bbox": [ + 174, + 455, + 825, + 525 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "A.2 LAPLACE APPROXIMATION ", + "text_level": 1, + "bbox": [ + 176, + 541, + 405, + 556 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "We consider finding a MAP estimate following from Eq. (16): ", + "bbox": [ + 174, + 566, + 588, + 582 + ], + "page_idx": 12 + }, + { + "type": "equation", + "img_path": "images/9d85b6ebff62fbeeb39d1d697c4878400e7b766c9cde0013e04e871b1e5d123f.jpg", + "text": "$$\n\\theta _ { t + 1 } ^ { * } = \\arg \\operatorname* { m a x } _ { \\theta } p ( \\theta | \\mathcal { D } _ { 1 : t + 1 } ) = \\arg \\operatorname* { m a x } _ { \\theta } \\{ \\log p ( \\mathcal { D } _ { t + 1 } | \\theta ) + \\log p ( \\theta | \\mathcal { D } _ { 1 : t } ) \\} .\n$$", + "text_format": "latex", + "bbox": [ + 254, + 583, + 743, + 608 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "Since the posterior $p ( \\theta | \\mathcal { D } _ { 1 : t } )$ of a neural network is intractable except for small architectures, the unnormalised posterior $\\tilde { p } ( \\theta | \\mathcal { D } _ { 1 : t } )$ is considered instead. Performing Taylor expansion on the logarithm of the unnormalised posterior around a mode ${ \\boldsymbol { \\theta } } _ { t } ^ { * }$ gives ", + "bbox": [ + 173, + 611, + 821, + 654 + ], + "page_idx": 12 + }, + { + "type": "equation", + "img_path": "images/6e164b79457e9d746c6db551d3aec927946fffa4599c2c369f8bc272ac1af928.jpg", + "text": "$$\n\\log \\tilde { p } ( \\theta | \\mathcal { D } _ { 1 : t } ) \\simeq \\log \\tilde { p } ( \\theta | \\mathcal { D } _ { 1 : t } ) \\big | _ { \\theta = \\theta _ { t } ^ { * } } - \\frac { 1 } { 2 } ( \\theta - \\theta _ { t } ^ { * } ) ^ { T } A _ { t } ( \\theta - \\theta _ { t } ^ { * } ) ,\n$$", + "text_format": "latex", + "bbox": [ + 294, + 655, + 704, + 685 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "where $A _ { t }$ denotes the Hessian matrix of the negative log-posterior evaluated at $\\theta _ { t } ^ { * }$ . The expansion in Eq. (19) suggests using a Gaussian approximate posterior. Given the parameter $\\phi _ { t } = \\{ \\mu _ { t } , \\Lambda _ { t } \\}$ , a mean $\\mu _ { t + 1 }$ for step $t + 1$ can be obtained by finding a mode of the approximate posterior as follows via standard gradient-based optimisation: ", + "bbox": [ + 174, + 685, + 825, + 741 + ], + "page_idx": 12 + }, + { + "type": "equation", + "img_path": "images/e30a9fc2b0abe8259f6075a61a749cf139f06448d9e71a45118af62aa94d8b78.jpg", + "text": "$$\n\\mu _ { t + 1 } = \\arg \\operatorname* { m a x } _ { \\boldsymbol { \\theta } } \\log p ( \\mathcal { D } _ { t + 1 } | \\boldsymbol { \\theta } ) - \\frac { 1 } { 2 } ( \\boldsymbol { \\theta } - \\boldsymbol { \\mu } _ { t } ) ^ { T } \\Lambda _ { t } ( \\boldsymbol { \\theta } - \\boldsymbol { \\mu } _ { t } ) .\n$$", + "text_format": "latex", + "bbox": [ + 305, + 743, + 692, + 775 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "The precision matrix is updated as $\\Lambda _ { t + 1 } = H _ { t + 1 } + \\Lambda _ { t }$ , where $H _ { t + 1 }$ is the Hessian matrix of the negative log-likelihood for $\\mathcal { D } _ { t + 1 }$ evaluated at $\\mu _ { t + 1 }$ with entries ", + "bbox": [ + 176, + 776, + 820, + 806 + ], + "page_idx": 12 + }, + { + "type": "equation", + "img_path": "images/3d76cacc8904531fc2e50381c54e1d3f2b06f30c94bcb0c2d8e5d129428e2753.jpg", + "text": "$$\nH _ { t + 1 } ^ { i j } = - \\frac { \\partial ^ { 2 } } { \\partial \\theta ^ { ( i ) } \\partial \\theta ^ { ( j ) } } \\log p ( \\mathcal { D } _ { t + 1 } \\vert \\theta ) \\bigg \\vert _ { \\theta = \\mu _ { t + 1 } } .\n$$", + "text_format": "latex", + "bbox": [ + 351, + 808, + 647, + 845 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "For a neural network model, gradient-based optimisation methods such as SGD (Robbins & Monro, 1951) and Adam (Kingma & Ba, 2015) are the standard gradient-based methods in finding a mode for the Laplace approximation in Eq. (20). We show in Section 4.1 that this provides a well-suited skeleton to implement Bayesian online meta-learning in Eq. (5) with the mode-seeking optimisation procedure. ", + "bbox": [ + 174, + 853, + 825, + 924 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "A.3 BLOCK-DIAGONAL HESSIAN APPROXIMATION ", + "text_level": 1, + "bbox": [ + 176, + 103, + 532, + 117 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "Since the full Hessian matrix in Eq. (21) is intractable for large neural networks, we seek for an efficient and relatively close approximation to the Hessian matrix. Diagonal approximations (Denker & LeCun, 1991; Kirkpatrick et al., 2017) are memory and computationally efficient, but sacrifice approximation accuracy as they ignore the interaction between parameters. Consider instead separating the Hessian matrix into blocks where different blocks are associated to different layers of a neural network. A particular diagonal block corresponds to the Hessian for a particular layer of the neural network. The block-diagonal Kronecker-factored approximation (Martens & Grosse, 2015; Grosse & Martens, 2016; Botev et al., 2017) utilises the fact that each diagonal block of the Hessian is Kronecker-factored for a single data point. This provides a better Hessian approximation as it takes the parameter interactions within a layer into consideration. ", + "bbox": [ + 173, + 130, + 825, + 270 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "A.3.1 KRONECKER-FACTORED APPROXIMATION ", + "text_level": 1, + "bbox": [ + 176, + 286, + 521, + 300 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "Consider a neural network with $L$ layers and parameter $\\theta = [ \\mathrm { v e c } ( W _ { 1 } ) ^ { T } , \\dots , \\mathrm { v e c } ( W _ { L } ) ^ { T } ] ^ { T }$ where $W _ { \\ell }$ is the weight of layer $\\ell$ for $\\ell = \\{ 1 , \\dots , L \\}$ and vec denotes stacking the columns of a matrix into a vector. We denote the input of the neural network as $a _ { 0 } = x$ and the output of the neural network as $h _ { L }$ . As the input passes through each layer of the neural network, we have the pre-activation for layer $\\ell$ as $h _ { \\ell } = W _ { \\ell } a _ { \\ell - 1 }$ and the activation as $a _ { \\ell } = f _ { \\ell } ( h _ { \\ell } )$ where $f _ { \\ell }$ is the activation function of layer $\\ell$ . If a bias vector is applicable in calculating the pre-activation of a layer, we append the bias vector to the last column of the weight matrix and append a scalar one to the last element of the activation. The gradient $g _ { \\ell }$ of loss $L _ { \\theta } ( \\dot { x _ { \\star } } y ) = - \\log p ( \\bar { y } | \\dot { x } , \\theta )$ with respect to $h _ { \\ell }$ for an input-target pair $( x , y )$ is the pre-activation gradient for layer $\\ell$ . ", + "bbox": [ + 173, + 310, + 825, + 438 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "Martens $\\&$ Grosse (2015) show that the $\\ell$ -th diagonal block $F _ { \\ell }$ of the Fisher information matrix $F$ can be approximated by the Kronecker product between the expectation of the outer product of the $( \\ell - 1 )$ -th layer activation and the $\\ell$ -th layer pre-activation gradient: ", + "bbox": [ + 174, + 443, + 825, + 486 + ], + "page_idx": 13 + }, + { + "type": "equation", + "img_path": "images/01d6f1816d037e2fc2773e2e0641af57f957eeb4d764a0fa28da0a46ab8d5996.jpg", + "text": "$$\n\\begin{array} { r l } & { F _ { \\ell } = \\mathbb { E } _ { x , y } \\bigl [ a _ { \\ell - 1 } a _ { \\ell - 1 } ^ { T } \\otimes g _ { \\ell } g _ { \\ell } ^ { T } \\bigr ] } \\\\ & { \\qquad \\approx \\mathbb { E } _ { x } \\bigl [ a _ { \\ell - 1 } a _ { \\ell - 1 } ^ { T } \\bigr ] \\otimes \\mathbb { E } _ { y | x } \\bigl [ g _ { \\ell } g _ { \\ell } ^ { T } \\bigr ] } \\\\ & { \\qquad = A _ { \\ell - 1 } \\otimes G _ { \\ell } , } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 385, + 492, + 612, + 555 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "where $A _ { \\ell - 1 } = \\mathbb { E } _ { x } [ a _ { \\ell - 1 } a _ { \\ell - 1 } ^ { T } ]$ and $G _ { \\ell } = \\mathbb { E } _ { y | x } [ g _ { \\ell } g _ { \\ell } ^ { T } ]$ . Grosse $\\&$ Martens (2016) extend the blockdiagonal Kronecker-factored Fisher approximation for fully-connected layers to that for convolution layers. The Gaussian log-probability term can be calculated efficiently without expanding the Kronecker product using the identity ", + "bbox": [ + 174, + 561, + 823, + 619 + ], + "page_idx": 13 + }, + { + "type": "equation", + "img_path": "images/8f8bc2f05c3b8eb69e818f06083bed3fdcb836a3458238e31051d0c193a81042.jpg", + "text": "$$\n\\begin{array} { r } { ( A _ { \\ell - 1 } \\otimes G _ { \\ell } ) \\operatorname { v e c } ( W _ { \\ell } - W _ { \\ell } ^ { * } ) = \\operatorname { v e c } ( G _ { \\ell } ( W _ { \\ell } - W _ { \\ell } ^ { * } ) A _ { \\ell - 1 } ^ { T } ) . } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 303, + 627, + 694, + 647 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "As we mentioned in Section 4.2, approximating the Hessian with the one-step SGD inner loop assumption results in having terms that multiply two or more Kronecker products together. The $\\ell$ -th diagonal block of $\\widetilde { F }$ in Eq. (11) is ", + "bbox": [ + 174, + 661, + 825, + 707 + ], + "page_idx": 13 + }, + { + "type": "equation", + "img_path": "images/c0cc31057c73ef43fe3c70286e31fc7ef0fd43efcf4487b653b25d8250b1bc59.jpg", + "text": "$$\n\\widetilde { F } _ { \\ell } = \\frac { 1 } { M } \\sum _ { m = 1 } ^ { M } ( I - A _ { \\ell - 1 } ^ { m } \\otimes G _ { \\ell } ^ { m } ) ( \\widetilde { A } _ { \\ell - 1 } ^ { m } \\otimes \\widetilde { G } _ { \\ell } ^ { m } ) ( I - A _ { \\ell - 1 } ^ { m } \\otimes G _ { \\ell } ^ { m } ) ^ { T } ,\n$$", + "text_format": "latex", + "bbox": [ + 276, + 714, + 722, + 758 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "where $A _ { \\ell - 1 } ^ { m } \\otimes G _ { \\ell } ^ { m }$ is the Kronecker product corresponding to the Hessian in Eq. (13) for task or batch $m$ . We expand $\\widetilde { F } _ { \\ell }$ using the Kronecker product property: ", + "bbox": [ + 176, + 765, + 823, + 799 + ], + "page_idx": 13 + }, + { + "type": "equation", + "img_path": "images/b9369fd3cf80040f481e2e2351109b05137f442bca53c0c61fab746d7ecd9e03.jpg", + "text": "$$\n\\begin{array} { r } { ( A _ { \\ell - 1 } ^ { m } \\otimes G _ { \\ell } ^ { m } ) ( \\widetilde { A } _ { \\ell - 1 } ^ { m } \\otimes \\widetilde { G } _ { \\ell } ^ { m } ) = A _ { \\ell - 1 } ^ { m } \\widetilde { A } _ { \\ell - 1 } ^ { m } \\otimes G _ { \\ell } ^ { m } \\widetilde { G } _ { \\ell } ^ { m } . } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 320, + 806, + 678, + 828 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "This gives ", + "bbox": [ + 173, + 834, + 245, + 849 + ], + "page_idx": 13 + }, + { + "type": "equation", + "img_path": "images/0d88d94963f128eab55eecbc9315a4c835701fc077ce460c2229d058604d9c5d.jpg", + "text": "$$\n\\begin{array} { r l r } { \\widetilde { F } _ { \\ell } = \\frac { 1 } { M } \\sum _ { m = 1 } ^ { M } \\Big \\{ \\widetilde { A } _ { \\ell - 1 } ^ { m } \\otimes \\widetilde { G } _ { \\ell } ^ { m } - A _ { \\ell - 1 } ^ { m } \\widetilde { A } _ { \\ell - 1 } ^ { m } \\otimes G _ { \\ell } ^ { m } \\widetilde { G } _ { \\ell } ^ { m } - \\widetilde { A } _ { \\ell - 1 } ^ { m } ( A _ { \\ell - 1 } ^ { m } ) ^ { T } \\otimes \\widetilde { G } _ { \\ell } ^ { m } ( G _ { \\ell } ^ { m } ) ^ { T } } \\\\ & { } & { + A _ { \\ell - 1 } ^ { m } \\widetilde { A } _ { \\ell - 1 } ^ { m } ( A _ { \\ell - 1 } ^ { m } ) ^ { T } \\otimes G _ { \\ell } ^ { m } \\widetilde { G } _ { \\ell } ^ { m } ( G _ { \\ell } ^ { m } ) ^ { T } \\Big \\} . } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 207, + 858, + 761, + 930 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "Finally, moving the meta-batch (or batch) averaging into the Kronecker factors gives the approximation: ", + "bbox": [ + 171, + 103, + 823, + 132 + ], + "page_idx": 14 + }, + { + "type": "equation", + "img_path": "images/79017d6ac10f7bd4d154b80b7a499facd06abe7c9ae7a9273c24d017271f9433.jpg", + "text": "$$\n\\begin{array} { r l } & { \\widetilde { F } _ { \\ell } \\approx \\widetilde { A } _ { \\ell - 1 } \\otimes \\widetilde { G } _ { \\ell } - A _ { \\ell - 1 } \\widetilde { A } _ { \\ell - 1 } \\otimes G _ { \\ell } \\widetilde { G } _ { \\ell } - \\widetilde { A } _ { \\ell - 1 } ( A _ { \\ell - 1 } ) ^ { T } \\otimes \\widetilde { G } _ { \\ell } ( G _ { \\ell } ) ^ { T } } \\\\ & { \\qquad + A _ { \\ell - 1 } \\widetilde { A } _ { \\ell - 1 } ( A _ { \\ell - 1 } ) ^ { T } \\otimes G _ { \\ell } \\widetilde { G } _ { \\ell } ( G _ { \\ell } ) ^ { T } , } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 261, + 136, + 736, + 180 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "where $\\begin{array} { r } { \\tilde { A } _ { \\ell - 1 } = \\frac { 1 } { M } \\sum _ { m } \\tilde { A } _ { \\ell - 1 } ^ { m } , \\tilde { G } _ { \\ell } = \\frac { 1 } { M } \\sum _ { m } \\tilde { G } _ { \\ell } ^ { m } , A _ { \\ell - 1 } \\tilde { A } _ { \\ell - 1 } = \\frac { 1 } { M } \\sum _ { m } A _ { \\ell - 1 } ^ { m } \\tilde { A } _ { \\ell - 1 } ^ { m } . } \\end{array}$ and so on. ", + "bbox": [ + 173, + 186, + 795, + 209 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "A.3.2 POSTERIOR REGULARISING HYPERPARAMETER FOR PRECISION UPDATE ", + "bbox": [ + 174, + 222, + 727, + 237 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "Ritter et al. (2018a) use a hyperparameter $\\lambda$ as a multiplier to the Hessian when updating the precision: ", + "bbox": [ + 173, + 246, + 821, + 273 + ], + "page_idx": 14 + }, + { + "type": "equation", + "img_path": "images/6bf45a96e5aabdd9e5a0e8a4301df23f10090ac658485151fff6efd9fe5c8268.jpg", + "text": "$$\n\\Lambda _ { t + 1 } = \\lambda H _ { t + 1 } + \\Lambda _ { t } .\n$$", + "text_format": "latex", + "bbox": [ + 426, + 275, + 571, + 292 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "In the large-scale supervised classification setting, this hyperparameter has a regularising effect on the Gaussian posterior approximation for a balance between having a good performance on a new dataset and maintaining the performance on previous datasets (Ritter et al., 2018a). A large $\\lambda$ results in a sharply peaked Gaussian posterior and is therefore unable to learn new datasets well, but can prevent forgetting previously learned datasets. A small $\\lambda$ on the other hand gives a dispersed Gaussian posterior and allows better performance on new datasets by sacrificing the performance on the previous datasets. ", + "bbox": [ + 173, + 296, + 825, + 395 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "A.4 VARIATIONAL CONTINUAL LEARNING ", + "text_level": 1, + "bbox": [ + 176, + 414, + 478, + 428 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "The variational continual learning method (Nguyen et al., 2018) also provides a suitable metatraining framework for Bayesian online meta-learning in Eq. (5). Consider approximating the posterior $q$ by minimising the KL-divergence between the parametric $q$ and the new posterior as in the projection step in Eq. (17), where $q$ belongs to some pre-determined approximate posterior family $\\mathcal { Q }$ with parameters $\\phi _ { t }$ : ", + "bbox": [ + 176, + 439, + 823, + 511 + ], + "page_idx": 14 + }, + { + "type": "equation", + "img_path": "images/d9274b26e342e6942600d43106c57c106ad5c5fc74a1e9cf7cb8f03a8668d6e4.jpg", + "text": "$$\n\\begin{array} { r l } & { q ( \\theta | \\phi _ { t + 1 } ) = \\underset { q \\in \\mathcal { Q } } { \\arg \\operatorname* { m i n } } D _ { \\mathrm { K L } } ( q ( \\theta | \\phi ) \\| p ( \\mathcal { D } _ { t + 1 } | \\theta ) q ( \\theta | \\phi _ { t } ) ) } \\\\ & { \\qquad = \\underset { q \\in \\mathcal { Q } } { \\arg \\operatorname* { m i n } } \\big \\{ - \\mathbb { E } _ { q ( \\theta | \\phi ) } [ \\log p ( \\mathcal { D } _ { t + 1 } | \\theta ) ] + D _ { \\mathrm { K L } } ( q ( \\theta | \\phi ) \\| q ( \\theta | \\phi _ { t } ) ) \\big \\} . } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 246, + 516, + 748, + 575 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "The optimisation in Eq. (32) leads to the objective ", + "bbox": [ + 174, + 588, + 504, + 604 + ], + "page_idx": 14 + }, + { + "type": "equation", + "img_path": "images/2e930ae7499d5b3ec81d6291b95368d3720d81d32369c6162a5a05c122d07e72.jpg", + "text": "$$\n\\phi _ { t + 1 } = \\underset { \\phi } { \\arg \\operatorname* { m i n } } \\big \\{ - \\mathbb { E } _ { q ( \\theta | \\phi ) } [ \\log p ( \\mathcal { D } _ { t + 1 } | \\theta ) ] + D _ { \\mathrm { K L } } ( q ( \\theta | \\phi ) \\| q ( \\theta | \\phi _ { t } ) ) \\big \\} .\n$$", + "text_format": "latex", + "bbox": [ + 264, + 611, + 735, + 640 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "One can use a Gaussian mean-field approximate posterior $\\begin{array} { r } { q ( \\theta | \\phi _ { t } ) = \\prod _ { d = 1 } ^ { D } N ( \\mu _ { t , d } , \\sigma _ { t , d } ^ { 2 } ) } \\end{array}$ , where $\\phi _ { t } = \\{ \\mu _ { t , d } , \\sigma _ { t , d } \\} _ { d = 1 } ^ { D }$ and $D = \\dim ( \\theta )$ . The first term in Eq. (33) can be estimated via Monte Carlo with local reparameterisation trick (Kingma et al., 2015), and the second KL-divergence term has a closed form for Gaussian distributions. ", + "bbox": [ + 173, + 648, + 825, + 710 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "B ALGORITHMS ", + "text_level": 1, + "bbox": [ + 176, + 732, + 325, + 748 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "B.1 BOMLA AND BOMVI", + "text_level": 1, + "bbox": [ + 176, + 763, + 367, + 779 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "Algorithm 1 gives the pseudo-code of the BOMLA algorithm for the sequential datasets setting, with the corresponding variation for the sequential tasks setting in brackets. The algorithm is formed of three main elements: meta-training on a specific dataset or task (line 4 – 11), updating the Gaussian mean (line 12) and updating the Gaussian precision (line 13 – 16). For the precision update, we approximate the Hessian using block-diagonal Kronecker-factored approximation (BD-KFA). ", + "bbox": [ + 174, + 790, + 825, + 861 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "Algorithm 2 gives the pseudo-code of the BOMVI algorithm for the sequential datasets setting, with the corresponding variation for the sequential tasks setting in brackets. The algorithm is formed of two main elements: meta-training on a specific dataset or task (line 4 – 11) and updating the parameters of the Gaussian mean-field approximate posterior (line 12). ", + "bbox": [ + 174, + 867, + 825, + 924 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "1: Require: sequential datasets (or tasks) $\\widetilde { \\mathcal { D } } _ { 1 } , \\ldots , \\widetilde { \\mathcal { D } } _ { T }$ , learning rate $\\alpha$ , posterior regulariser $\\lambda$ , \nnumber of meta-training iterations (or epochs) $J$ , meta-batch size (or number of batches) $M$ \n2: Initialise: $\\mu _ { 0 } , \\Lambda _ { 0 }$ , $\\theta$ \n3: for $t = 1$ to $T$ do \n4: for $i = 1 , \\dots , J$ do $\\triangleright$ meta-training on dataset or task $\\widetilde { \\cal D } _ { t } \\quad$ New: added $\\cdot$ \n5: for $m = 1$ to $M$ do \n6: Sample task (or split the batch) $\\widetilde { \\mathcal { D } } _ { t } ^ { m } = \\widetilde { \\mathcal { D } } _ { t } ^ { m , S } \\cup \\widetilde { \\mathcal { D } } _ { t } ^ { m , Q }$ \n7: Inner update $\\tilde { \\theta } ^ { m } = S G D _ { k } ( \\mathcal { L } ( \\theta , \\widetilde { D } _ { t } ^ { m , S } ) )$ \n8: end for \n9: Evaluate loss $f _ { t } ^ { \\mathrm { B o u L A } } ( \\theta , \\mu _ { t - 1 } , \\Lambda _ { t - 1 } )$ in Eq. (8) \n10: Outer update $\\theta \\gets \\theta - \\alpha \\nabla _ { \\theta } f _ { t } ^ { \\mathrm { B o M L A } } ( \\theta , \\mu _ { t - 1 } , \\Lambda _ { t - 1 } )$ \n11: end for \n12: Update mean $\\mu _ { t } \\gets \\theta$ $\\triangleright$ update posterior mean \n13: For sequential datasets, sample $M$ tasks for Hessian approximation \n14: Run inner update in line 7 for each task (or for each batch) \n15: Approximate $\\widetilde { H } _ { t }$ with BD-KFA to $\\widetilde { F }$ in Eq. (11) \n16: Update precision $\\Lambda _ { t } \\gets \\lambda \\widetilde { H } _ { t } + \\Lambda _ { t - 1 }$ $\\triangleright$ update posterior precision \n17: end for ", + "bbox": [ + 176, + 119, + 826, + 381 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "Algorithm 2 Bayesian online meta-learning with variational inference (BOMVI) ", + "text_level": 1, + "bbox": [ + 173, + 398, + 704, + 415 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "1: Require: sequential datasets (or tasks) $\\widetilde { \\mathcal { D } } _ { 1 } , \\ldots , \\widetilde { \\mathcal { D } } _ { T }$ , learning rate $\\alpha$ , number of meta-training \niterations (or epochs) $J$ , meta-batch size (or number of batches) $M$ \n2: Initialise: $\\phi _ { 0 } = \\{ \\mu _ { 0 } , \\sigma _ { 0 } \\}$ \n3: for $t = 1$ to $T$ do \n4: for $i = 1 , 2 , \\dots , J$ do $\\triangleright$ meta-training on dataset or task $\\widetilde { \\cal D } _ { t } \\quad$ New: added $\\cdot$ \n5: for $m = 1$ to $M$ do \n6: Sample task (or split the batch) $\\widetilde { \\mathcal { D } } _ { t } ^ { m } = \\widetilde { \\mathcal { D } } _ { t } ^ { m , S } \\cup \\widetilde { \\mathcal { D } } _ { t } ^ { m , Q }$ \n7: Inner update $\\tilde { \\theta } ^ { m } = S G D _ { k } ( \\mathcal { L } ( \\theta , \\widetilde { D } _ { t } ^ { m , S } ) )$ \n8: end for \n9: Evaluate loss $f _ { t } ^ { \\mathrm { B o u V I } } ( \\phi , \\phi _ { t - 1 } )$ in Eq. (15) \n10: Outer update $\\bar { \\mu } \\mu - \\alpha \\nabla _ { \\mu } f _ { t } ^ { \\mathrm { B o M V I } } ( \\phi , \\phi _ { t - 1 } )$ , and $\\sigma \\gets \\sigma - \\alpha \\nabla _ { \\sigma } f _ { t } ^ { \\mathrm { B o M V I } } ( \\phi , \\phi _ { t - 1 } )$ \n11: end for \n12: Update $\\mu _ { t } \\mu$ and $\\sigma _ { t } \\gets \\sigma$ . update posterior parameters \n13: end for ", + "bbox": [ + 178, + 417, + 826, + 619 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "B.2 BOMVI MONTE CARLO ESTIMATOR", + "text_level": 1, + "bbox": [ + 176, + 645, + 467, + 660 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "Recall that the BOMVI objective is: ", + "bbox": [ + 174, + 671, + 410, + 686 + ], + "page_idx": 15 + }, + { + "type": "equation", + "img_path": "images/678b43c1f0a68aeca4af82d036852f4b1f5ef45bccb79aff2378b8efe0c30363.jpg", + "text": "$$\nf _ { t + 1 } ^ { \\mathrm { B o M V I } } ( \\phi , \\phi _ { t } ) = - \\frac { 1 } { M } \\sum _ { m = 1 } ^ { M } \\mathbb { E } _ { q ( \\theta | \\phi ) } \\big [ \\log p ( \\widetilde { \\mathcal { D } } _ { t + 1 } ^ { m , Q } | \\widetilde { \\theta } ^ { m } ) \\big ] - \\frac { 1 } { M } \\sum _ { m = 1 } ^ { M } \\mathbb { E } _ { q ( \\theta | \\phi ) } \\big [ \\log p ( \\widetilde { \\mathcal { D } } _ { t + 1 } ^ { m , S } | \\theta ) \\big ]\n$$", + "text_format": "latex", + "bbox": [ + 200, + 691, + 794, + 756 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "where term o $\\tilde { \\theta } ^ { m } = S G D _ { k } ( \\mathcal { L } ( \\theta , \\widetilde { D } _ { t + 1 } ^ { m , S } ) )$ for diffic $m = 1 , \\ldots , M$ . The Monte Carlo estimator for th as every sampled meta-parameters firstfor $\\theta _ { r }$ $r = 1 , \\ldots , R$ has to undergo a few-shot quick adaptation prior to the log-likelihood evaluation. As a consequence the estimator is prone to a large variance. Moreover, every quickly-adapted sample $\\theta _ { r }$ contributes to the meta-learning gradients of the posterior mean and covariance, resulting in a high computational cost when taking the meta-gradients. ", + "bbox": [ + 173, + 761, + 826, + 848 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "To solve these impediments, we introduce a slight modification to the SGD quick adaptation ${ \\widetilde { \\theta } } ^ { m }$ . Instead of taking the gradients with respect to the sampled meta-parameters, we consider the gradients with respect to the posterior mean. A one-step SGD quick adaptation, for instance, becomes: ", + "bbox": [ + 174, + 856, + 825, + 900 + ], + "page_idx": 15 + }, + { + "type": "equation", + "img_path": "images/77ca9b68f79603d9329d84362522d23df65f4bb92faed2f1cf7c9cf9d6a699ef.jpg", + "text": "$$\n\\tilde { \\theta } ^ { m } = \\theta - \\alpha \\nabla _ { \\mu _ { t } } \\mathcal { L } ( \\mu _ { t } , \\mathcal { \\tilde { D } } _ { t + 1 } ^ { m , S } ) .\n$$", + "text_format": "latex", + "bbox": [ + 398, + 905, + 599, + 926 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "This gives $\\widetilde { \\theta } ^ { m } \\sim N ( \\widetilde { \\mu } _ { t } , \\mathrm { d i a g } ( \\sigma _ { t } ^ { 2 } ) )$ where ", + "bbox": [ + 176, + 102, + 442, + 119 + ], + "page_idx": 16 + }, + { + "type": "equation", + "img_path": "images/bc98546152e2a855f7709b260cba28d4761b62fd3ccf9110ad7afd71d3b6ae7a.jpg", + "text": "$$\n\\widetilde { \\mu } _ { t } = \\mu _ { t } - \\alpha \\nabla _ { \\mu _ { t } } \\mathcal { L } ( \\mu _ { t } , \\widetilde { D } _ { t + 1 } ^ { m , S } ) ,\n$$", + "text_format": "latex", + "bbox": [ + 397, + 121, + 599, + 142 + ], + "page_idx": 16 + }, + { + "type": "text", + "text": "since $\\theta \\sim N ( \\mu _ { t } , \\mathrm { d i a g } ( \\sigma _ { t } ^ { 2 } ) )$ . A quick adaptation with more steps works in a similar fashion. With this modification, we can calculate the Monte Carlo estimator for the first term using the local reparameterisation trick as usual. ", + "bbox": [ + 173, + 145, + 825, + 188 + ], + "page_idx": 16 + }, + { + "type": "text", + "text": "C EXPERIMENTS ", + "text_level": 1, + "bbox": [ + 176, + 208, + 331, + 224 + ], + "page_idx": 16 + }, + { + "type": "text", + "text": "C.1 OMNIGLOT: SEQUENTIAL TASKS ", + "text_level": 1, + "bbox": [ + 176, + 238, + 442, + 253 + ], + "page_idx": 16 + }, + { + "type": "text", + "text": "In this experiment, we use the model architecture proposed by Vinyals et al. (2016) that takes 4 modules with 64 filters of size $3 \\times 3$ , followed by a batch normalisation, a ReLU activation and a $2 \\times 2$ max-pooling. A fully-connected layer is appended to the final module before getting the class probabilities with softmax. Table 1 shows the hyperparameters used in this experiment. ", + "bbox": [ + 174, + 263, + 825, + 320 + ], + "page_idx": 16 + }, + { + "type": "text", + "text": "The Omniglot dataset comprises 50 alphabets (super-classes). Each alphabet has numerous characters (classes) and each character has 20 instances. As the meta-training alphabets arrive sequentially, we form non-overlapping sequential tasks from each arriving alphabet, and the tasks also do not overlap in the characters. We use 35 alphabets for meta-training, 7 alphabets for validation and 8 alphabets for meta-evaluation. The alphabet splits are as follows: ", + "bbox": [ + 174, + 327, + 825, + 397 + ], + "page_idx": 16 + }, + { + "type": "text", + "text": "35 alphabets for meta-training: ", + "text_level": 1, + "bbox": [ + 176, + 405, + 377, + 419 + ], + "page_idx": 16 + }, + { + "type": "text", + "text": "Kannada, Burmese_(Myanmar), Malay_(Jawi_-_Arabic), Grantha, Atlantean, Ojibwe_(Canadian_Aboriginal_Syllabics), Balinese, Japanese_(katakana), Hebrew, Japanese_(hiragana), Keble, ’Old_Church_Slavonic_(Cyrillic), Asomtavruli_(Georgian), Tengwar, Aurek-Besh, Sanskrit, Manipuri, Early_Aramaic, Oriya, Mongolian, Avesta, Malayalam, Tifinagh, Angelic, Latin, Braille, Inuktitut_(Canadian_Aboriginal_Syllabics), Alphabet_of_the_Magi, Armenian, Korean, Gurmukhi, ULOG, Bengali, Gujarati, Sylheti ", + "bbox": [ + 173, + 429, + 802, + 541 + ], + "page_idx": 16 + }, + { + "type": "text", + "text": "7 alphabets for validation: ", + "bbox": [ + 176, + 547, + 346, + 561 + ], + "page_idx": 16 + }, + { + "type": "text", + "text": "Ge_ez, Cyrillic, Glagolitic, N_Ko, Arcadian, Anglo-Saxon_Futhorc, Blackfoot_(Canadian_Aboriginal_Syllabics) ", + "bbox": [ + 176, + 573, + 808, + 601 + ], + "page_idx": 16 + }, + { + "type": "text", + "text": "8 alphabets for meta-evaluation: ", + "bbox": [ + 174, + 608, + 385, + 621 + ], + "page_idx": 16 + }, + { + "type": "text", + "text": "Syriac_(Serto), Atemayar_Qelisayer, Tibetan, Futurama, Mkhedruli_(Georgian), Syriac_(Estrangelo), Tagalog, Greek ", + "bbox": [ + 174, + 633, + 735, + 661 + ], + "page_idx": 16 + }, + { + "type": "table", + "img_path": "images/abfc71c479179f152a296dc801a02e8baf1b4db935788c253f7ca12863ee2625.jpg", + "table_caption": [ + "Table 1: Hyperparameters for the Omniglot sequential tasks experiment " + ], + "table_footnote": [], + "table_body": "
HyperparameterBOMLABOMVI
Posterior regulariser 入0.1
Precision initialisation values10-4~10-2
Covariance initialisation values1exp(-10)
NumberofMonte Carlo samples=5
Number of batch M11
Number of query samples per class (meta-evaluation)1515
Number of epochs per task5050
Number of inner SGD steps in meta-training (k)55
Inner SGD learning rate (α)0.10.1
Outer loop optimiserAdamAdam
Outer loop learning rate0.0010.001
Number of tasks sampled for meta-evaluation100100
Number of inner SGD steps in meta-evaluation (k)1010
", + "bbox": [ + 218, + 702, + 779, + 916 + ], + "page_idx": 16 + }, + { + "type": "text", + "text": "C.2 PENTATHLON: SEQUENTIAL DATASETS ", + "text_level": 1, + "bbox": [ + 176, + 104, + 483, + 117 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "We use the model architecture proposed by Vinyals et al. (2016) in this experiment, as we did for the sequential tasks experiment. Tables 2 and 3 are the hyperparameters used in this experiment. ", + "bbox": [ + 173, + 128, + 823, + 159 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "Omniglot: The Omniglot dataset (Lake et al., 2011) comprises 1623 characters from 50 alphabets and each character has 20 instances. New classes with rotations in the multiples of $9 0 °$ are formed after splitting the classes for meta-training, validation and meta-evaluation. We use 1100 characters for meta-training, 100 characters for validation and the remaining for meta-evaluation. ", + "bbox": [ + 174, + 172, + 825, + 229 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "CIFAR-FS: The CIFAR-FS dataset (Bertinetto et al., 2019) has 100 classes of objects and each class comprises 600 images. We use the same split as Bertinetto et al. (2019): 64 classes for metatraining, 16 classes for validation and 20 classes for meta-evaluation. ", + "bbox": [ + 174, + 244, + 825, + 286 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "miniImageNet: The miniImageNet dataset (Vinyals et al., 2016) takes 100 classes and 600 instances in each class from the ImageNet dataset. We use the same split as Ravi & Larochelle (2017): 64 classes for meta-training, 16 classes for validation and 20 classes for meta-evaluation. ", + "bbox": [ + 176, + 301, + 821, + 344 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "VGG-Flowers: The VGG-Flowers dataset (Nilsback & Zisserman, 2008) comprises 102 different types of flowers as the classes. This dataset has 8,189 instances in total. We randomly split 66 classes for meta-training, 16 classes for validation and 20 classes for meta-evaluation. ", + "bbox": [ + 174, + 359, + 825, + 401 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "Aircraft: The Aircraft dataset (Maji et al., 2013) is a fine-grained dataset consisting of 100 different aircraft models as the classes and each class has 100 instances. We randomly split 64 classes for meta-training, 16 classes for validation and 20 classes for meta-evaluation. ", + "bbox": [ + 173, + 416, + 825, + 459 + ], + "page_idx": 17 + }, + { + "type": "table", + "img_path": "images/0c04a6f448fd725ce5decae0ec7f8f61c218a242e7997579f16fd45972d36a60.jpg", + "table_caption": [ + "Table 2: Hyperparameters for the pentathlon experiment (same value for all datasets) " + ], + "table_footnote": [], + "table_body": "
HyperparameterBOMLABOMVI
Posterior regulariser 入(various values)
Precision initialisation values10-4~ 10-2
Number of tasks sampled for Hessian approx.5000
Covariance initialisation valuesexp(-5)
Number of Monte Carlo samples=20
Meta-batch size M= 3232
Number of query samples per class1515
Number of iterations per dataset5000
Outer loop optimiserAdam5000
Outer loop learning rateAdam
Number of tasks sampled for meta-evaluation0.001 1000.001 100
", + "bbox": [ + 233, + 502, + 771, + 688 + ], + "page_idx": 17 + }, + { + "type": "table", + "img_path": "images/792d3d021b75bc928e7ebb45cd35d3377b79f40b295a20a86dd3e8b6f4bad6ab.jpg", + "table_caption": [ + "Table 3: Hyperparameters for the pentathlon sequential datasets experiment (individual datasets) " + ], + "table_footnote": [], + "table_body": "
HyperparameterOmniglotCIFAR-FSminiImageNetVGG-FlowersAircraft
Number of inner SGD steps in meta-training (k)15555
Inner SGD learning rate0.40.10.10.10.1
(a) Outer learning rate decay-×0.1×0.1 halfway×0.1 per 1000x0.1
schedule Number of inner SGD steps in meta-evaluation3halfway 1010iterations 10halfway 10
", + "bbox": [ + 178, + 753, + 859, + 895 + ], + "page_idx": 17 + }, + { + "type": "image", + "img_path": "images/e4c0f6de57d020e55a0adba80739413b67359f38476dfa77ec263a2bdb85913e.jpg", + "image_caption": [ + "Figure 3: Meta-evaluation accuracy across 3 seed runs on each dataset along meta-training. Higher accuracy values indicate better results with less forgetting as we proceed to new datasets. BOMLA with $\\lambda = 1 0 0$ gives better performance in the off-diagonal plots (retains performances on previously learned datasets), and has a minor performance trade-off in the diagonal plots (learns less well on new datasets). Sequential MAML gives better performance in the diagonal plots (learns well on new datasets) but worse performance in the off-diagonal plots (forgets previously learned datasets). BOMVI is also able to retain performance on previous datasets, although it may be unable to perform as good as BOMLA due to sampling and estimator variance. " + ], + "image_footnote": [], + "bbox": [ + 230, + 104, + 785, + 792 + ], + "page_idx": 18 + }, + { + "type": "image", + "img_path": "images/8b2b41f7bbda229777423d37569a5dc851b7bef2d0b560bb5db9e6b27a775de1.jpg", + "image_caption": [ + "Figure 4: Meta-evaluation accuracy across 3 seed runs on each dataset along meta-training. Higher accuracy values indicate better results with less forgetting as we proceed to new datasets. BOMLA with a large $\\lambda = 1 0 0 0$ gives better performance in the off-diagonal plots (retains performances on previously learned datasets) but worse performance in the diagonal plots (does not learn well on new datasets). A small $\\lambda = 1$ gives better performance in the diagonal plots (learns well on new datasets) but worse performance in the off-diagonal plots (forgets previously learned datasets). BOMVI is also able to retain performance on previous datasets, although it may be unable to learn new datasets as good as BOMLA due to sampling and estimator variance. 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Few-shot meta-", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 141, + 238, + 470, + 249 + ], + "spans": [ + { + "bbox": [ + 141, + 238, + 470, + 249 + ], + "score": 1.0, + "content": "learning algorithms often require all few-shot tasks to be readily available in a", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 141, + 248, + 469, + 261 + ], + "spans": [ + { + "bbox": [ + 141, + 248, + 469, + 261 + ], + "score": 1.0, + "content": "batch for training. The popular gradient-based model-agnostic meta-learning al-", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 141, + 260, + 470, + 271 + ], + "spans": [ + { + "bbox": [ + 141, + 260, + 470, + 271 + ], + "score": 1.0, + "content": "gorithm (MAML) is a typical algorithm that suffers from these limitations. This", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 141, + 271, + 469, + 282 + ], + "spans": [ + { + "bbox": [ + 141, + 271, + 469, + 282 + ], + "score": 1.0, + "content": "work introduces a Bayesian online meta-learning framework to tackle the catas-", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 141, + 281, + 470, + 293 + ], + "spans": [ + { + "bbox": [ + 141, + 281, + 470, + 293 + ], + "score": 1.0, + "content": "trophic forgetting and the sequential few-shot tasks problems. 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The experimental evaluations", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 141, + 336, + 469, + 348 + ], + "spans": [ + { + "bbox": [ + 141, + 336, + 469, + 348 + ], + "score": 1.0, + "content": "demonstrate that our framework can effectively prevent catastrophic forgetting and", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 141, + 347, + 450, + 360 + ], + "spans": [ + { + "bbox": [ + 141, + 347, + 450, + 360 + ], + "score": 1.0, + "content": "is capable of online meta-learning in various few-shot classification settings.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 11, + "bbox_fs": [ + 141, + 193, + 470, + 360 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 384, + 206, + 397 + ], + "lines": [ + { + "bbox": [ + 105, + 383, + 208, + 400 + ], + "spans": [ + { + "bbox": [ + 105, + 383, + 208, + 400 + ], + "score": 1.0, + "content": "1 INTRODUCTION", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 19 + }, + { + "type": "text", + "bbox": [ + 107, + 412, + 505, + 554 + ], + "lines": [ + { + "bbox": [ + 106, + 411, + 505, + 424 + ], + "spans": [ + { + "bbox": [ + 106, + 411, + 505, + 424 + ], + "score": 1.0, + "content": "Image classification models and algorithms often require an enormous amount of labelled exam-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 423, + 505, + 434 + ], + "spans": [ + { + "bbox": [ + 105, + 423, + 505, + 434 + ], + "score": 1.0, + "content": "ples for training to achieve state-of-the-art performance. Labelled examples can be expensive and", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 434, + 505, + 446 + ], + "spans": [ + { + "bbox": [ + 105, + 434, + 505, + 446 + ], + "score": 1.0, + "content": "time-consuming to acquire. Human visual systems, on the other hand, are able to recognise new", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 445, + 505, + 456 + ], + "spans": [ + { + "bbox": [ + 105, + 445, + 505, + 456 + ], + "score": 1.0, + "content": "classes after being shown a few labelled examples. 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Our framework aims to combine both BOL and MAML to find the", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 170, + 505, + 182 + ], + "spans": [ + { + "bbox": [ + 105, + 170, + 505, + 182 + ], + "score": 1.0, + "content": "posterior of the meta-parameters. Our work builds on Ritter et al. (2018a) which combines the BOL", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 180, + 505, + 194 + ], + "spans": [ + { + "bbox": [ + 105, + 180, + 505, + 194 + ], + "score": 1.0, + "content": "framework and Laplace approximation with block-diagonal Kronecker-factored Fisher approxima-", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 191, + 505, + 205 + ], + "spans": [ + { + "bbox": [ + 105, + 191, + 505, + 205 + ], + "score": 1.0, + "content": "tion, and Nguyen et al. 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Bayesian inference inherits an advantage for robust meta-learning (Yoon et al.,", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 251, + 505, + 266 + ], + "spans": [ + { + "bbox": [ + 105, + 251, + 505, + 266 + ], + "score": 1.0, + "content": "2018) to overcome training instability problems addressed by Antoniou et al. (2019). 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This defeats the purpose of online learning, which by definition means to update", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 330, + 506, + 343 + ], + "spans": [ + { + "bbox": [ + 105, + 330, + 506, + 343 + ], + "score": 1.0, + "content": "the parameters each round using only the new data encountered. Having to re-train on previous data", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 340, + 506, + 353 + ], + "spans": [ + { + "bbox": [ + 105, + 340, + 506, + 353 + ], + "score": 1.0, + "content": "to avoid forgetting also increases the training time as the data accumulate (Finn et al., 2019; He", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 352, + 505, + 365 + ], + "spans": [ + { + "bbox": [ + 105, + 352, + 505, + 365 + ], + "score": 1.0, + "content": "et al., 2019). Certainly one can clamp the amount of data at some maximal limit and sample from", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 361, + 505, + 376 + ], + "spans": [ + { + "bbox": [ + 105, + 361, + 505, + 376 + ], + "score": 1.0, + "content": "the buffer, but the final performance of such an algorithm would be dependent on the samples being", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 372, + 505, + 388 + ], + "spans": [ + { + "bbox": [ + 105, + 372, + 505, + 388 + ], + "score": 1.0, + "content": "informative and of good quality which may vary across different seed runs. In contrast to memoris-", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 385, + 504, + 397 + ], + "spans": [ + { + "bbox": [ + 106, + 385, + 504, + 397 + ], + "score": 1.0, + "content": "ing the datasets, having an implicit memory via the posterior automatically deals with the question", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 396, + 498, + 408 + ], + "spans": [ + { + "bbox": [ + 105, + 396, + 498, + 408 + ], + "score": 1.0, + "content": "on how to process carried-forward data and allows a better carry forward in previous experiences.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 20 + }, + { + "type": "text", + "bbox": [ + 107, + 412, + 310, + 423 + ], + "lines": [ + { + "bbox": [ + 105, + 410, + 312, + 426 + ], + "spans": [ + { + "bbox": [ + 105, + 410, + 312, + 426 + ], + "score": 1.0, + "content": "Below are the contributions we make in this paper:", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 29 + }, + { + "type": "text", + "bbox": [ + 132, + 432, + 505, + 563 + ], + "lines": [ + { + "bbox": [ + 137, + 432, + 505, + 444 + ], + "spans": [ + { + "bbox": [ + 137, + 432, + 505, + 444 + ], + "score": 1.0, + "content": "We develop the Bayesian online meta-learning (BOML) framework for sequential few-shot", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 141, + 443, + 505, + 456 + ], + "spans": [ + { + "bbox": [ + 141, + 443, + 505, + 456 + ], + "score": 1.0, + "content": "classification problems. Under this framework we introduce the algorithms Bayesian online", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 141, + 453, + 505, + 468 + ], + "spans": [ + { + "bbox": [ + 141, + 453, + 505, + 468 + ], + "score": 1.0, + "content": "meta-learning with Laplace approximation (BOMLA) and Bayesian online meta-learning", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 141, + 465, + 290, + 477 + ], + "spans": [ + { + "bbox": [ + 141, + 465, + 290, + 477 + ], + "score": 1.0, + "content": "with variational inference (BOMVI).", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 141, + 479, + 505, + 492 + ], + "spans": [ + { + "bbox": [ + 141, + 479, + 505, + 492 + ], + "score": 1.0, + "content": "We propose a simple approximation to the Fisher corresponding to the BOMLA algorithm", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 142, + 490, + 504, + 501 + ], + "spans": [ + { + "bbox": [ + 142, + 490, + 504, + 501 + ], + "score": 1.0, + "content": "that carries over the desirable block-diagonal Kronecker-factored structure from the Fisher", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 141, + 501, + 335, + 515 + ], + "spans": [ + { + "bbox": [ + 141, + 501, + 335, + 515 + ], + "score": 1.0, + "content": "approximation in the non-meta-learning setting.", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 140, + 515, + 505, + 528 + ], + "spans": [ + { + "bbox": [ + 140, + 515, + 505, + 528 + ], + "score": 1.0, + "content": "We demonstrate that BOML can overcome catastrophic forgetting in the sequential few-shot", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 141, + 527, + 399, + 539 + ], + "spans": [ + { + "bbox": [ + 141, + 527, + 399, + 539 + ], + "score": 1.0, + "content": "datasets setting with apparent distributional shift in the datasets.", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 133, + 540, + 505, + 554 + ], + "spans": [ + { + "bbox": [ + 133, + 540, + 505, + 554 + ], + "score": 1.0, + "content": "• We demonstrate that BOML can continually learn to few-shot classify the novel classes in", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 141, + 551, + 347, + 565 + ], + "spans": [ + { + "bbox": [ + 141, + 551, + 347, + 565 + ], + "score": 1.0, + "content": "the sequential meta-training few-shot tasks setting.", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 35 + }, + { + "type": "title", + "bbox": [ + 107, + 578, + 215, + 591 + ], + "lines": [ + { + "bbox": [ + 105, + 577, + 217, + 593 + ], + "spans": [ + { + "bbox": [ + 105, + 577, + 217, + 593 + ], + "score": 1.0, + "content": "2 META-LEARNING", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 41 + }, + { + "type": "text", + "bbox": [ + 107, + 603, + 505, + 669 + ], + "lines": [ + { + "bbox": [ + 105, + 603, + 505, + 615 + ], + "spans": [ + { + "bbox": [ + 105, + 603, + 505, + 615 + ], + "score": 1.0, + "content": "Most meta-learning algorithms comprise an inner loop for example-learning and an outer loop that", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 615, + 505, + 626 + ], + "spans": [ + { + "bbox": [ + 106, + 615, + 505, + 626 + ], + "score": 1.0, + "content": "learns the example-learning process. 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MAML finds a good", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 137, + 505, + 150 + ], + "spans": [ + { + "bbox": [ + 105, + 137, + 505, + 150 + ], + "score": 1.0, + "content": "model parameter initialisation (called meta-parameters) that can quickly adapt to novel classes", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 149, + 505, + 161 + ], + "spans": [ + { + "bbox": [ + 106, + 149, + 505, + 161 + ], + "score": 1.0, + "content": "using very few labelled examples, while BOL provides a principled framework for finding the pos-", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 159, + 505, + 171 + ], + "spans": [ + { + "bbox": [ + 105, + 159, + 505, + 171 + ], + "score": 1.0, + "content": "terior of the model parameters. 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(2018) which uses variational inference with BOL to overcome catastrophic", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 203, + 306, + 216 + ], + "spans": [ + { + "bbox": [ + 105, + 203, + 306, + 216 + ], + "score": 1.0, + "content": "forgetting in large-scale supervised classification.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 5.5, + "bbox_fs": [ + 105, + 83, + 506, + 216 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 220, + 505, + 407 + ], + "lines": [ + { + "bbox": [ + 106, + 221, + 505, + 232 + ], + "spans": [ + { + "bbox": [ + 106, + 221, + 505, + 232 + ], + "score": 1.0, + "content": "An important reason to implement Bayesian inference over non-Bayesian methods for an online", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 231, + 505, + 243 + ], + "spans": [ + { + "bbox": [ + 106, + 231, + 505, + 243 + ], + "score": 1.0, + "content": "setting is that BOL provides a grounded framework that suggests using the previous posterior as", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 241, + 506, + 255 + ], + "spans": [ + { + "bbox": [ + 105, + 241, + 506, + 255 + ], + "score": 1.0, + "content": "the prior recursively. Bayesian inference inherits an advantage for robust meta-learning (Yoon et al.,", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 251, + 505, + 266 + ], + "spans": [ + { + "bbox": [ + 105, + 251, + 505, + 266 + ], + "score": 1.0, + "content": "2018) to overcome training instability problems addressed by Antoniou et al. (2019). BOL implicitly", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 264, + 505, + 277 + ], + "spans": [ + { + "bbox": [ + 105, + 264, + 505, + 277 + ], + "score": 1.0, + "content": "keeps a memory on previous knowledge via the posterior, in contrast to recent online meta-learning", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 275, + 505, + 288 + ], + "spans": [ + { + "bbox": [ + 105, + 275, + 505, + 288 + ], + "score": 1.0, + "content": "methods that explicitly accumulate previous data in a task buffer (Finn et al., 2019; Zhuang et al.,", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 285, + 506, + 299 + ], + "spans": [ + { + "bbox": [ + 105, + 285, + 506, + 299 + ], + "score": 1.0, + "content": "2019). Explicitly keeping a memory on previous data often triggers an important question: how", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 296, + 505, + 309 + ], + "spans": [ + { + "bbox": [ + 105, + 296, + 505, + 309 + ], + "score": 1.0, + "content": "should the carried-forward data be processed in future task rounds, in order to accumulate knowl-", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 307, + 505, + 320 + ], + "spans": [ + { + "bbox": [ + 105, + 307, + 505, + 320 + ], + "score": 1.0, + "content": "edge? Finn et al. (2019) update the meta-parameters at each iteration using previous few-shot tasks", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 318, + 505, + 331 + ], + "spans": [ + { + "bbox": [ + 105, + 318, + 505, + 331 + ], + "score": 1.0, + "content": "in the task buffer. This defeats the purpose of online learning, which by definition means to update", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 330, + 506, + 343 + ], + "spans": [ + { + "bbox": [ + 105, + 330, + 506, + 343 + ], + "score": 1.0, + "content": "the parameters each round using only the new data encountered. Having to re-train on previous data", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 340, + 506, + 353 + ], + "spans": [ + { + "bbox": [ + 105, + 340, + 506, + 353 + ], + "score": 1.0, + "content": "to avoid forgetting also increases the training time as the data accumulate (Finn et al., 2019; He", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 352, + 505, + 365 + ], + "spans": [ + { + "bbox": [ + 105, + 352, + 505, + 365 + ], + "score": 1.0, + "content": "et al., 2019). Certainly one can clamp the amount of data at some maximal limit and sample from", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 361, + 505, + 376 + ], + "spans": [ + { + "bbox": [ + 105, + 361, + 505, + 376 + ], + "score": 1.0, + "content": "the buffer, but the final performance of such an algorithm would be dependent on the samples being", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 372, + 505, + 388 + ], + "spans": [ + { + "bbox": [ + 105, + 372, + 505, + 388 + ], + "score": 1.0, + "content": "informative and of good quality which may vary across different seed runs. 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We achieve these two goals by", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 458, + 505, + 470 + ], + "spans": [ + { + "bbox": [ + 105, + 458, + 505, + 470 + ], + "score": 1.0, + "content": "incorporating MAML into the BOL framework to give the Bayesian online meta-learning (BOML)", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 468, + 342, + 482 + ], + "spans": [ + { + "bbox": [ + 105, + 468, + 342, + 482 + ], + "score": 1.0, + "content": "framework that finds the posterior of the meta-parameters.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 24, + "bbox_fs": [ + 104, + 358, + 506, + 482 + ] + }, + { + "type": "title", + "bbox": [ + 106, + 496, + 469, + 509 + ], + "lines": [ + { + "bbox": [ + 104, + 495, + 471, + 511 + ], + "spans": [ + { + "bbox": [ + 104, + 495, + 471, + 511 + ], + "score": 1.0, + "content": "3 OVERVIEW OF OUR BAYESIAN ONLINE META-LEARNING APPROACH", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 30 + }, + { + "type": "text", + "bbox": [ + 107, + 521, + 504, + 555 + ], + "lines": [ + { + "bbox": [ + 105, + 520, + 505, + 534 + ], + "spans": [ + { + "bbox": [ + 105, + 520, + 505, + 534 + ], + "score": 1.0, + "content": "Our central contribution is to extend the benefits of meta-learning to the Bayesian online scenario,", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 532, + 504, + 546 + ], + "spans": [ + { + "bbox": [ + 105, + 532, + 504, + 546 + ], + "score": 1.0, + "content": "thereby training models that can generalise across tasks whilst dealing with parameter uncertainty", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 542, + 327, + 556 + ], + "spans": [ + { + "bbox": [ + 105, + 542, + 327, + 556 + ], + "score": 1.0, + "content": "in the setting of sequential tasks or sequential datasets.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 32, + "bbox_fs": [ + 105, + 520, + 505, + 556 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 567, + 505, + 627 + ], + "lines": [ + { + "bbox": [ + 106, + 566, + 505, + 579 + ], + "spans": [ + { + "bbox": [ + 106, + 566, + 505, + 579 + ], + "score": 1.0, + "content": "Sequential datasets setting In this setting, online meta-training occurs sequentially on the", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 577, + 505, + 591 + ], + "spans": [ + { + "bbox": [ + 105, + 577, + 141, + 591 + ], + "score": 1.0, + "content": "datasets", + "type": "text" + }, + { + "bbox": [ + 141, + 578, + 190, + 590 + ], + "score": 0.92, + "content": "\\mathcal { D } _ { 1 } , \\ldots , \\mathcal { D } _ { T }", + "type": "inline_equation" + }, + { + "bbox": [ + 191, + 577, + 250, + 591 + ], + "score": 1.0, + "content": ". 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(1). The recursion", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 280, + 505, + 293 + ], + "spans": [ + { + "bbox": [ + 105, + 280, + 505, + 293 + ], + "score": 1.0, + "content": "given by Eq. (5) forms the basis of our approach and the remainder of this paper explains how we", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 291, + 505, + 305 + ], + "spans": [ + { + "bbox": [ + 106, + 291, + 505, + 305 + ], + "score": 1.0, + "content": "implement this. 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These algorithms from the grounded BOML", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 398, + 500, + 410 + ], + "spans": [ + { + "bbox": [ + 105, + 398, + 500, + 410 + ], + "score": 1.0, + "content": "framework are useful for online training on the sequential few-shot classification datasets or tasks.", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 18 + }, + { + "type": "title", + "bbox": [ + 107, + 423, + 427, + 435 + ], + "lines": [ + { + "bbox": [ + 106, + 424, + 429, + 435 + ], + "spans": [ + { + "bbox": [ + 106, + 424, + 429, + 435 + ], + "score": 1.0, + "content": "4.1 BAYESIAN ONLINE META-LEARNING WITH LAPLACE APPROXIMATION", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 21 + }, + { + "type": "text", + "bbox": [ + 107, + 443, + 505, + 488 + ], + "lines": [ + { + "bbox": [ + 105, + 443, + 505, + 457 + ], + "spans": [ + { + "bbox": [ + 105, + 443, + 505, + 457 + ], + "score": 1.0, + "content": "We discover that the Laplace approximation method provides a well-fitted meta-training framework", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 454, + 505, + 467 + ], + "spans": [ + { + "bbox": [ + 105, + 454, + 505, + 467 + ], + "score": 1.0, + "content": "for Bayesian online meta-learning in Eq. 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(5). These algorithms from the grounded BOML", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 398, + 500, + 410 + ], + "spans": [ + { + "bbox": [ + 105, + 398, + 500, + 410 + ], + "score": 1.0, + "content": "framework are useful for online training on the sequential few-shot classification datasets or tasks.", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 18, + "bbox_fs": [ + 105, + 353, + 506, + 410 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 423, + 427, + 435 + ], + "lines": [ + { + "bbox": [ + 106, + 424, + 429, + 435 + ], + "spans": [ + { + "bbox": [ + 106, + 424, + 429, + 435 + ], + "score": 1.0, + "content": "4.1 BAYESIAN ONLINE META-LEARNING WITH LAPLACE APPROXIMATION", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 21 + }, + { + "type": "text", + "bbox": [ + 107, + 443, + 505, + 488 + ], + "lines": [ + { + "bbox": [ + 105, + 443, + 505, + 457 + ], + "spans": [ + { + "bbox": [ + 105, + 443, + 505, + 457 + ], + "score": 1.0, + "content": "We discover that the Laplace approximation method provides a well-fitted meta-training framework", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 454, + 505, + 467 + ], + "spans": [ + { + "bbox": [ + 105, + 454, + 505, + 467 + ], + "score": 1.0, + "content": "for Bayesian online meta-learning in Eq. 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Each updating step in the approximation procedure can", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 466, + 506, + 479 + ], + "spans": [ + { + "bbox": [ + 105, + 466, + 506, + 479 + ], + "score": 1.0, + "content": "be modified to correspond to the meta-parameters for few-shot classification, instead of the model", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 477, + 315, + 489 + ], + "spans": [ + { + "bbox": [ + 105, + 477, + 315, + 489 + ], + "score": 1.0, + "content": "parameters for large-scale supervised classification.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 23.5, + "bbox_fs": [ + 105, + 443, + 506, + 489 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 493, + 505, + 549 + ], + "lines": [ + { + "bbox": [ + 105, + 493, + 505, + 507 + ], + "spans": [ + { + "bbox": [ + 105, + 493, + 505, + 507 + ], + "score": 1.0, + "content": "Laplace approximation rationalises the use of a Gaussian approximate posterior by Taylor expanding", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 504, + 505, + 517 + ], + "spans": [ + { + "bbox": [ + 106, + 504, + 505, + 517 + ], + "score": 1.0, + "content": "the log-posterior around a mode up to the second order, as described in Appendix A.2. The second", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 515, + 505, + 528 + ], + "spans": [ + { + "bbox": [ + 105, + 515, + 505, + 528 + ], + "score": 1.0, + "content": "order term corresponds to the log-probability of a Gaussian distribution. The BOML framework in", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 104, + 525, + 506, + 540 + ], + "spans": [ + { + "bbox": [ + 104, + 525, + 306, + 540 + ], + "score": 1.0, + "content": "Section 3 with a Gaussian approximate posterior", + "type": "text" + }, + { + "bbox": [ + 306, + 529, + 312, + 538 + ], + "score": 0.79, + "content": "q", + "type": "inline_equation" + }, + { + "bbox": [ + 313, + 525, + 406, + 540 + ], + "score": 1.0, + "content": "of mean and precision", + "type": "text" + }, + { + "bbox": [ + 407, + 526, + 466, + 538 + ], + "score": 0.94, + "content": "\\phi _ { t } = \\{ \\mu _ { t } , \\Lambda _ { t } \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 467, + 525, + 506, + 540 + ], + "score": 1.0, + "content": "from the", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 538, + 293, + 550 + ], + "spans": [ + { + "bbox": [ + 106, + 538, + 293, + 550 + ], + "score": 1.0, + "content": "Laplace approximation gives a MAP estimate:", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 28, + "bbox_fs": [ + 104, + 493, + 506, + 550 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 110, + 554, + 489, + 581 + ], + "lines": [ + { + "bbox": [ + 110, + 554, + 489, + 581 + ], + "spans": [ + { + "bbox": [ + 110, + 554, + 489, + 581 + ], + "score": 0.93, + "content": "\\theta ^ { * } = \\arg \\operatorname* { m a x } _ { \\theta } \\Bigg \\{ \\log \\int p ( \\widetilde { \\mathcal { D } } _ { t + 1 } ^ { Q } | \\widetilde { \\theta } ) p ( \\widetilde { \\theta } | \\theta , \\widetilde { \\mathcal { D } } _ { t + 1 } ^ { S } ) d \\widetilde { \\theta } + \\log p ( \\widetilde { \\mathcal { D } } _ { t + 1 } ^ { S } | \\theta ) - \\frac { 1 } { 2 } ( \\theta - \\mu _ { t } ) ^ { T } \\Lambda _ { t } ( \\theta - \\mu _ { t } ) \\Bigg \\} .", + "type": "interline_equation", + "image_path": "d4f655828fc7d9c372db6d9131ab554473fb2952db5ee5acd5614d86a29d3385.jpg" + } + ] + } + ], + "index": 31, + "virtual_lines": [ + { + "bbox": [ + 110, + 554, + 489, + 581 + ], + "spans": [], + "index": 31 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 592, + 506, + 627 + ], + "lines": [ + { + "bbox": [ + 105, + 592, + 505, + 606 + ], + "spans": [ + { + "bbox": [ + 105, + 592, + 325, + 606 + ], + "score": 1.0, + "content": "For an efficient optimisation, we use the deterministic", + "type": "text" + }, + { + "bbox": [ + 326, + 592, + 332, + 604 + ], + "score": 0.84, + "content": "\\tilde { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 332, + 592, + 505, + 606 + ], + "score": 1.0, + "content": "in Eq. 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(2019) introduce the online-within-online (OWO) and", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 142, + 407, + 505, + 419 + ], + "spans": [ + { + "bbox": [ + 142, + 407, + 505, + 419 + ], + "score": 1.0, + "content": "online-within-batch (OWB) settings, where OWO encounters tasks and examples within", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 142, + 418, + 505, + 430 + ], + "spans": [ + { + "bbox": [ + 142, + 418, + 505, + 430 + ], + "score": 1.0, + "content": "tasks sequentially while OWB encounters tasks sequentially but examples within tasks are", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 141, + 428, + 505, + 442 + ], + "spans": [ + { + "bbox": [ + 141, + 428, + 505, + 442 + ], + "score": 1.0, + "content": "in batch. 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(2019),", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 141, + 471, + 505, + 485 + ], + "spans": [ + { + "bbox": [ + 141, + 471, + 505, + 485 + ], + "score": 1.0, + "content": "Harrison et al. (2019) and Jerfel et al. (2019) look into continual meta-learning for non-", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 142, + 483, + 505, + 496 + ], + "spans": [ + { + "bbox": [ + 142, + 483, + 505, + 496 + ], + "score": 1.0, + "content": "stationary task distributions where the task boundaries are unknown to the model. Jerfel", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 141, + 494, + 505, + 507 + ], + "spans": [ + { + "bbox": [ + 141, + 494, + 505, + 507 + ], + "score": 1.0, + "content": "et al. (2019) consider a latent task structure to adapt to the non-stationary task distributions.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 24.5 + }, + { + "type": "text", + "bbox": [ + 132, + 510, + 505, + 631 + ], + "lines": [ + { + "bbox": [ + 132, + 510, + 506, + 522 + ], + "spans": [ + { + "bbox": [ + 132, + 510, + 506, + 522 + ], + "score": 1.0, + "content": "• Regret minimisation: In this setting, the goal is to minimise the regret function, and", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 142, + 521, + 506, + 533 + ], + "spans": [ + { + "bbox": [ + 142, + 521, + 506, + 533 + ], + "score": 1.0, + "content": "the assumptions are made on the loss function rather than the task distribution. Recent", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 141, + 531, + 506, + 544 + ], + "spans": [ + { + "bbox": [ + 141, + 531, + 506, + 544 + ], + "score": 1.0, + "content": "works Finn et al. (2019); Zhuang et al. (2019) belong to this category, where the aim is to", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 142, + 543, + 506, + 555 + ], + "spans": [ + { + "bbox": [ + 142, + 543, + 506, + 555 + ], + "score": 1.0, + "content": "compete with the best meta-learner and supersede it. These methods accumulate data as", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 142, + 554, + 505, + 565 + ], + "spans": [ + { + "bbox": [ + 142, + 554, + 505, + 565 + ], + "score": 1.0, + "content": "they arrive and meta-learn using all data acquired so far. Data accumulation is not desirable", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 141, + 565, + 505, + 576 + ], + "spans": [ + { + "bbox": [ + 141, + 565, + 505, + 576 + ], + "score": 1.0, + "content": "as the algorithmic complexity of training grows with the amount of data accumulated, and", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 141, + 576, + 506, + 588 + ], + "spans": [ + { + "bbox": [ + 141, + 576, + 506, + 588 + ], + "score": 1.0, + "content": "training time increases as new data arrive (Finn et al., 2019; He et al., 2019). The agent", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 142, + 586, + 506, + 599 + ], + "spans": [ + { + "bbox": [ + 142, + 586, + 506, + 599 + ], + "score": 1.0, + "content": "will eventually run out of memory for a long sequence of data. 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To compute its Monte", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 252, + 505, + 268 + ], + "spans": [ + { + "bbox": [ + 105, + 252, + 291, + 268 + ], + "score": 1.0, + "content": "Carlo estimator, we have to generate samples", + "type": "text" + }, + { + "bbox": [ + 291, + 254, + 321, + 266 + ], + "score": 0.91, + "content": "\\theta _ { r } \\sim q", + "type": "inline_equation" + }, + { + "bbox": [ + 321, + 252, + 336, + 268 + ], + "score": 1.0, + "content": "for", + "type": "text" + }, + { + "bbox": [ + 337, + 254, + 392, + 266 + ], + "score": 0.92, + "content": "r = 1 , \\ldots , R", + "type": "inline_equation" + }, + { + "bbox": [ + 392, + 252, + 505, + 268 + ], + "score": 1.0, + "content": ", and run a quick adaptation", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 265, + 504, + 278 + ], + "spans": [ + { + "bbox": [ + 105, + 265, + 246, + 278 + ], + "score": 1.0, + "content": "on each sampled meta-parameters", + "type": "text" + }, + { + "bbox": [ + 246, + 266, + 257, + 276 + ], + "score": 0.89, + "content": "\\theta _ { r }", + "type": "inline_equation" + }, + { + "bbox": [ + 257, + 265, + 504, + 278 + ], + "score": 1.0, + "content": "before evaluating its log-likelihood. This is computationally", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 276, + 505, + 289 + ], + "spans": [ + { + "bbox": [ + 105, + 276, + 505, + 289 + ], + "score": 1.0, + "content": "intensive and it gives an estimator with large variance. We propose a workaround by modifying the", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 288, + 428, + 299 + ], + "spans": [ + { + "bbox": [ + 106, + 288, + 428, + 299 + ], + "score": 1.0, + "content": "inner loop SGD quick adaptation, and the details can be found in Appendix B.2.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 13, + "bbox_fs": [ + 105, + 242, + 505, + 299 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 315, + 209, + 327 + ], + "lines": [ + { + "bbox": [ + 105, + 313, + 211, + 330 + ], + "spans": [ + { + "bbox": [ + 105, + 313, + 211, + 330 + ], + "score": 1.0, + "content": "5 RELATED WORK", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 16 + }, + { + "type": "text", + "bbox": [ + 106, + 340, + 503, + 363 + ], + "lines": [ + { + "bbox": [ + 105, + 339, + 505, + 354 + ], + "spans": [ + { + "bbox": [ + 105, + 339, + 505, + 354 + ], + "score": 1.0, + "content": "Online Meta-Learning There are two common problem settings in the current online meta-", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 352, + 171, + 363 + ], + "spans": [ + { + "bbox": [ + 106, + 352, + 171, + 363 + ], + "score": 1.0, + "content": "learning works:", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 17.5, + "bbox_fs": [ + 105, + 339, + 505, + 363 + ] + }, + { + "type": "text", + "bbox": [ + 132, + 374, + 504, + 506 + ], + "lines": [ + { + "bbox": [ + 136, + 373, + 505, + 386 + ], + "spans": [ + { + "bbox": [ + 136, + 373, + 505, + 386 + ], + "score": 1.0, + "content": "• Underlying task distribution: Sequential tasks are assumed to originate from the same", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 142, + 385, + 504, + 397 + ], + "spans": [ + { + "bbox": [ + 142, + 385, + 253, + 397 + ], + "score": 1.0, + "content": "underlying task distribution", + "type": "text" + }, + { + "bbox": [ + 253, + 385, + 275, + 397 + ], + "score": 0.92, + "content": "p ( \\mathcal { T } )", + "type": "inline_equation" + }, + { + "bbox": [ + 275, + 385, + 504, + 397 + ], + "score": 1.0, + "content": "in this setting. Our work in the sequential tasks setting be-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 142, + 396, + 505, + 408 + ], + "spans": [ + { + "bbox": [ + 142, + 396, + 505, + 408 + ], + "score": 1.0, + "content": "longs to this category. Denevi et al. (2019) introduce the online-within-online (OWO) and", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 142, + 407, + 505, + 419 + ], + "spans": [ + { + "bbox": [ + 142, + 407, + 505, + 419 + ], + "score": 1.0, + "content": "online-within-batch (OWB) settings, where OWO encounters tasks and examples within", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 142, + 418, + 505, + 430 + ], + "spans": [ + { + "bbox": [ + 142, + 418, + 505, + 430 + ], + "score": 1.0, + "content": "tasks sequentially while OWB encounters tasks sequentially but examples within tasks are", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 141, + 428, + 505, + 442 + ], + "spans": [ + { + "bbox": [ + 141, + 428, + 505, + 442 + ], + "score": 1.0, + "content": "in batch. The BOML framework in the sequential tasks setting corresponds to the OWB set-", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 141, + 439, + 505, + 453 + ], + "spans": [ + { + "bbox": [ + 141, + 439, + 505, + 453 + ], + "score": 1.0, + "content": "ting. On the other hand, our work in the sequential datasets setting is novel in overcoming", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 142, + 451, + 505, + 463 + ], + "spans": [ + { + "bbox": [ + 142, + 451, + 505, + 463 + ], + "score": 1.0, + "content": "few-shot catastrophic forgetting, where the goal is to few-shot classify tasks drawn from", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 140, + 461, + 505, + 474 + ], + "spans": [ + { + "bbox": [ + 140, + 461, + 254, + 474 + ], + "score": 1.0, + "content": "a sequence of distributions", + "type": "text" + }, + { + "bbox": [ + 254, + 461, + 324, + 473 + ], + "score": 0.93, + "content": "p ( { \\bar { \\mathcal { T } } } _ { 1 } ) , \\dots , p ( { \\mathcal { T } } _ { T } )", + "type": "inline_equation" + }, + { + "bbox": [ + 325, + 461, + 505, + 474 + ], + "score": 1.0, + "content": "as explained in Section 3. He et al. (2019),", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 141, + 471, + 505, + 485 + ], + "spans": [ + { + "bbox": [ + 141, + 471, + 505, + 485 + ], + "score": 1.0, + "content": "Harrison et al. (2019) and Jerfel et al. (2019) look into continual meta-learning for non-", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 142, + 483, + 505, + 496 + ], + "spans": [ + { + "bbox": [ + 142, + 483, + 505, + 496 + ], + "score": 1.0, + "content": "stationary task distributions where the task boundaries are unknown to the model. Jerfel", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 141, + 494, + 505, + 507 + ], + "spans": [ + { + "bbox": [ + 141, + 494, + 505, + 507 + ], + "score": 1.0, + "content": "et al. (2019) consider a latent task structure to adapt to the non-stationary task distributions.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 24.5, + "bbox_fs": [ + 136, + 373, + 505, + 507 + ] + }, + { + "type": "text", + "bbox": [ + 132, + 510, + 505, + 631 + ], + "lines": [ + { + "bbox": [ + 132, + 510, + 506, + 522 + ], + "spans": [ + { + "bbox": [ + 132, + 510, + 506, + 522 + ], + "score": 1.0, + "content": "• Regret minimisation: In this setting, the goal is to minimise the regret function, and", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 142, + 521, + 506, + 533 + ], + "spans": [ + { + "bbox": [ + 142, + 521, + 506, + 533 + ], + "score": 1.0, + "content": "the assumptions are made on the loss function rather than the task distribution. Recent", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 141, + 531, + 506, + 544 + ], + "spans": [ + { + "bbox": [ + 141, + 531, + 506, + 544 + ], + "score": 1.0, + "content": "works Finn et al. (2019); Zhuang et al. (2019) belong to this category, where the aim is to", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 142, + 543, + 506, + 555 + ], + "spans": [ + { + "bbox": [ + 142, + 543, + 506, + 555 + ], + "score": 1.0, + "content": "compete with the best meta-learner and supersede it. These methods accumulate data as", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 142, + 554, + 505, + 565 + ], + "spans": [ + { + "bbox": [ + 142, + 554, + 505, + 565 + ], + "score": 1.0, + "content": "they arrive and meta-learn using all data acquired so far. Data accumulation is not desirable", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 141, + 565, + 505, + 576 + ], + "spans": [ + { + "bbox": [ + 141, + 565, + 505, + 576 + ], + "score": 1.0, + "content": "as the algorithmic complexity of training grows with the amount of data accumulated, and", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 141, + 576, + 506, + 588 + ], + "spans": [ + { + "bbox": [ + 141, + 576, + 506, + 588 + ], + "score": 1.0, + "content": "training time increases as new data arrive (Finn et al., 2019; He et al., 2019). The agent", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 142, + 586, + 506, + 599 + ], + "spans": [ + { + "bbox": [ + 142, + 586, + 506, + 599 + ], + "score": 1.0, + "content": "will eventually run out of memory for a long sequence of data. The BOML framework on", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 142, + 598, + 505, + 609 + ], + "spans": [ + { + "bbox": [ + 142, + 598, + 505, + 609 + ], + "score": 1.0, + "content": "the other hand is advantageous, as it only takes the posterior of the meta-parameters into", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 141, + 608, + 504, + 621 + ], + "spans": [ + { + "bbox": [ + 141, + 608, + 504, + 621 + ], + "score": 1.0, + "content": "consideration during optimisation. This gives a framework with an algorithmic complexity", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 142, + 619, + 343, + 632 + ], + "spans": [ + { + "bbox": [ + 142, + 619, + 343, + 632 + ], + "score": 1.0, + "content": "independent of the length of the dataset sequence.", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 36, + "bbox_fs": [ + 132, + 510, + 506, + 632 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 643, + 504, + 699 + ], + "lines": [ + { + "bbox": [ + 106, + 643, + 506, + 656 + ], + "spans": [ + { + "bbox": [ + 106, + 643, + 506, + 656 + ], + "score": 1.0, + "content": "Offline Meta-Learning Previous meta-learning works attempt to solve few-shot classification", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 655, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 505, + 667 + ], + "score": 1.0, + "content": "problems in an offline setting, under the assumption of having a stationary task distribution dur-", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 665, + 504, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 504, + 678 + ], + "score": 1.0, + "content": "ing meta-training and meta-evaluation. A single meta-learned model is aimed to few-shot classify", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 104, + 675, + 506, + 690 + ], + "spans": [ + { + "bbox": [ + 104, + 675, + 506, + 690 + ], + "score": 1.0, + "content": "one specific dataset with all base classes of the dataset readily available in a batch for meta-training.", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 685, + 392, + 702 + ], + "spans": [ + { + "bbox": [ + 105, + 685, + 392, + 702 + ], + "score": 1.0, + "content": "There are two general frameworks for the offline meta-learning setting:", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 44, + "bbox_fs": [ + 104, + 643, + 506, + 702 + ] + }, + { + "type": "text", + "bbox": [ + 133, + 709, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 133, + 708, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 133, + 708, + 505, + 722 + ], + "score": 1.0, + "content": "• Probabilistic framework: The MAML algorithm can be cast into a probabilistic infer-", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 141, + 720, + 505, + 733 + ], + "spans": [ + { + "bbox": [ + 141, + 720, + 505, + 733 + ], + "score": 1.0, + "content": "ence problem (Finn et al., 2018) or with a hierarchical Bayesian structure (Grant et al.,", + "type": "text" + } + ], + "index": 48 + } + ], + "index": 47.5, + "bbox_fs": [ + 133, + 708, + 505, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 141, + 82, + 505, + 137 + ], + "lines": [ + { + "bbox": [ + 141, + 82, + 506, + 95 + ], + "spans": [ + { + "bbox": [ + 141, + 82, + 506, + 95 + ], + "score": 1.0, + "content": "2018; Yoon et al., 2018). Grant et al. (2018) discuss the use of a Laplace approximation", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 141, + 93, + 506, + 106 + ], + "spans": [ + { + "bbox": [ + 141, + 93, + 506, + 106 + ], + "score": 1.0, + "content": "in the task-specific inner loop to improve MAML using the curvature information, whilst", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 141, + 104, + 505, + 117 + ], + "spans": [ + { + "bbox": [ + 141, + 104, + 505, + 117 + ], + "score": 1.0, + "content": "Yoon et al. (2018) use Stein Variational Gradient Descent (SVGD) for task-specific learn-", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 141, + 115, + 506, + 128 + ], + "spans": [ + { + "bbox": [ + 141, + 115, + 506, + 128 + ], + "score": 1.0, + "content": "ing. Gordon et al. (2019) implement probabilistic inference by considering the posterior", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 141, + 127, + 335, + 138 + ], + "spans": [ + { + "bbox": [ + 141, + 127, + 335, + 138 + ], + "score": 1.0, + "content": "predictive distribution with amortised networks.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 2 + }, + { + "type": "text", + "bbox": [ + 133, + 142, + 505, + 230 + ], + "lines": [ + { + "bbox": [ + 132, + 142, + 506, + 155 + ], + "spans": [ + { + "bbox": [ + 132, + 142, + 506, + 155 + ], + "score": 1.0, + "content": "• Non-probabilistic framework: Gradient-based meta-learning (Finn et al., 2017; Nichol", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 141, + 153, + 505, + 166 + ], + "spans": [ + { + "bbox": [ + 141, + 153, + 505, + 166 + ], + "score": 1.0, + "content": "et al., 2018; Rusu et al., 2019) updates the meta-parameters by accumulating the gradients", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 142, + 165, + 505, + 177 + ], + "spans": [ + { + "bbox": [ + 142, + 165, + 505, + 177 + ], + "score": 1.0, + "content": "of a meta-batch of task-specific inner loop updates. The meta-parameters will be used", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 141, + 176, + 505, + 188 + ], + "spans": [ + { + "bbox": [ + 141, + 176, + 505, + 188 + ], + "score": 1.0, + "content": "as a model initialisation for a quick adaptation on the novel classes. Metric-based meta-", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 141, + 187, + 505, + 199 + ], + "spans": [ + { + "bbox": [ + 141, + 187, + 505, + 199 + ], + "score": 1.0, + "content": "learning (Koch et al., 2015; Vinyals et al., 2016; Snell et al., 2017) utilises the metric", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 141, + 197, + 505, + 210 + ], + "spans": [ + { + "bbox": [ + 141, + 197, + 505, + 210 + ], + "score": 1.0, + "content": "distance between labelled examples. Such methods assume that base and novel classes are", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 142, + 209, + 505, + 220 + ], + "spans": [ + { + "bbox": [ + 142, + 209, + 505, + 220 + ], + "score": 1.0, + "content": "from the same dataset distribution, and the metric distance estimations can be generalised", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 141, + 219, + 370, + 231 + ], + "spans": [ + { + "bbox": [ + 141, + 219, + 370, + 231 + ], + "score": 1.0, + "content": "to the novel classes upon meta-learning the base classes.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 8.5 + }, + { + "type": "text", + "bbox": [ + 107, + 244, + 505, + 376 + ], + "lines": [ + { + "bbox": [ + 106, + 245, + 506, + 257 + ], + "spans": [ + { + "bbox": [ + 106, + 245, + 506, + 257 + ], + "score": 1.0, + "content": "Continual Learning Modern continual learning works (Goodfellow et al., 2013; Lee et al., 2017;", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 255, + 506, + 269 + ], + "spans": [ + { + "bbox": [ + 105, + 255, + 506, + 269 + ], + "score": 1.0, + "content": "Zenke et al., 2017) focus primarily on large-scale supervised learning, in contrast to our work that", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 104, + 265, + 505, + 280 + ], + "spans": [ + { + "bbox": [ + 104, + 265, + 505, + 280 + ], + "score": 1.0, + "content": "looks into continual few-shot classification across sequential tasks and datasets. Wen et al. (2018)", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 277, + 506, + 291 + ], + "spans": [ + { + "bbox": [ + 105, + 277, + 506, + 291 + ], + "score": 1.0, + "content": "utilise few-shot learning to improve on overcoming catastrophic forgetting via logit matching on a", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 289, + 505, + 301 + ], + "spans": [ + { + "bbox": [ + 105, + 289, + 505, + 301 + ], + "score": 1.0, + "content": "small sample from the previous tasks. The online learning element in this paper is closely related to", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 300, + 505, + 312 + ], + "spans": [ + { + "bbox": [ + 105, + 300, + 505, + 312 + ], + "score": 1.0, + "content": "(Kirkpatrick et al., 2017; Zenke et al., 2017; Ritter et al., 2018a; Nguyen et al., 2018) that overcome", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 311, + 505, + 323 + ], + "spans": [ + { + "bbox": [ + 105, + 311, + 505, + 323 + ], + "score": 1.0, + "content": "catastrophic forgetting for large-scale supervised classification. In particular, our work builds on the", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 104, + 320, + 506, + 335 + ], + "spans": [ + { + "bbox": [ + 104, + 320, + 506, + 335 + ], + "score": 1.0, + "content": "online Laplace approximation method in (Ritter et al., 2018a). We extend this to the meta-learning", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 333, + 504, + 345 + ], + "spans": [ + { + "bbox": [ + 105, + 333, + 504, + 345 + ], + "score": 1.0, + "content": "scenario to avoid forgetting in few-shot classification problems. Nguyen et al. (2018) provide the", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 342, + 505, + 357 + ], + "spans": [ + { + "bbox": [ + 105, + 342, + 505, + 357 + ], + "score": 1.0, + "content": "alternative of using variational inference instead of Laplace approximation for approximating the", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 355, + 505, + 367 + ], + "spans": [ + { + "bbox": [ + 105, + 355, + 505, + 367 + ], + "score": 1.0, + "content": "posterior. It is a reasonable approach to adapt variational approximation methods to approximate", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 366, + 423, + 378 + ], + "spans": [ + { + "bbox": [ + 105, + 366, + 423, + 378 + ], + "score": 1.0, + "content": "the posterior of the meta-parameters by adjusting the KL-divergence objective.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 18.5 + }, + { + "type": "title", + "bbox": [ + 107, + 394, + 200, + 407 + ], + "lines": [ + { + "bbox": [ + 105, + 393, + 201, + 409 + ], + "spans": [ + { + "bbox": [ + 105, + 393, + 201, + 409 + ], + "score": 1.0, + "content": "6 EXPERIMENTS", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 25 + }, + { + "type": "title", + "bbox": [ + 108, + 420, + 269, + 431 + ], + "lines": [ + { + "bbox": [ + 106, + 420, + 270, + 433 + ], + "spans": [ + { + "bbox": [ + 106, + 420, + 270, + 433 + ], + "score": 1.0, + "content": "6.1 OMNIGLOT: SEQUENTIAL TASKS", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 26 + }, + { + "type": "text", + "bbox": [ + 108, + 441, + 505, + 486 + ], + "lines": [ + { + "bbox": [ + 106, + 442, + 505, + 453 + ], + "spans": [ + { + "bbox": [ + 106, + 442, + 505, + 453 + ], + "score": 1.0, + "content": "We run the sequential tasks experiment on the Omniglot dataset. To increase the difficulty level,", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 452, + 505, + 465 + ], + "spans": [ + { + "bbox": [ + 105, + 452, + 505, + 465 + ], + "score": 1.0, + "content": "we split the datasets based on the alphabets (super-classes) instead of the characters (classes). The", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 464, + 506, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 464, + 506, + 475 + ], + "score": 1.0, + "content": "goal of this experiment is to classify the 5-way 5-shot novel tasks sampled from the meta-evaluation", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 475, + 467, + 486 + ], + "spans": [ + { + "bbox": [ + 106, + 475, + 467, + 486 + ], + "score": 1.0, + "content": "alphabets. The experimental details and the alphabet splits can be found in Appendix C.1.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 28.5 + }, + { + "type": "text", + "bbox": [ + 108, + 491, + 326, + 502 + ], + "lines": [ + { + "bbox": [ + 106, + 490, + 328, + 505 + ], + "spans": [ + { + "bbox": [ + 106, + 490, + 328, + 505 + ], + "score": 1.0, + "content": "We compare our algorithms to the following baselines:", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 31 + }, + { + "type": "text", + "bbox": [ + 130, + 512, + 505, + 645 + ], + "lines": [ + { + "bbox": [ + 129, + 512, + 505, + 526 + ], + "spans": [ + { + "bbox": [ + 129, + 512, + 505, + 526 + ], + "score": 1.0, + "content": "1. Train-On-Everything (TOE): When a new task (or dataset) arrives for meta-training,", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 142, + 524, + 505, + 537 + ], + "spans": [ + { + "bbox": [ + 142, + 524, + 505, + 537 + ], + "score": 1.0, + "content": "we randomly re-initialise the meta-parameters and perform meta-training on all tasks (or", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 142, + 535, + 505, + 547 + ], + "spans": [ + { + "bbox": [ + 142, + 535, + 505, + 547 + ], + "score": 1.0, + "content": "datasets) encountered so far. Once meta-training is completed in this stage, we do not", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 141, + 546, + 480, + 558 + ], + "spans": [ + { + "bbox": [ + 141, + 546, + 480, + 558 + ], + "score": 1.0, + "content": "update the posterior of the meta-parameters like we would in BOMLA and BOMVI.", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 130, + 562, + 505, + 574 + ], + "spans": [ + { + "bbox": [ + 130, + 562, + 505, + 574 + ], + "score": 1.0, + "content": "2. Train-From-Scratch (TFS): Upon the arrival of a new task (or dataset), we randomly re-", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 142, + 574, + 504, + 585 + ], + "spans": [ + { + "bbox": [ + 142, + 574, + 504, + 585 + ], + "score": 1.0, + "content": "initialise the meta-parameters and meta-train only on the newly-arrived task (or dataset).", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 141, + 583, + 446, + 597 + ], + "spans": [ + { + "bbox": [ + 141, + 583, + 446, + 597 + ], + "score": 1.0, + "content": "Similar to TOE, the posterior of the meta-parameters is not updated in TFS.", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 128, + 599, + 505, + 613 + ], + "spans": [ + { + "bbox": [ + 128, + 599, + 505, + 613 + ], + "score": 1.0, + "content": "3. Follow The Meta-Leader (FTML): We introduce a slight modification to FTML (Finn", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 141, + 611, + 505, + 624 + ], + "spans": [ + { + "bbox": [ + 141, + 611, + 505, + 624 + ], + "score": 1.0, + "content": "et al., 2019) on its evaluation method, as FTML is not designed for few-shot learning on", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 142, + 622, + 505, + 635 + ], + "spans": [ + { + "bbox": [ + 142, + 622, + 505, + 635 + ], + "score": 1.0, + "content": "unseen tasks. 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The knowledge acquired", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 677, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 505, + 689 + ], + "score": 1.0, + "content": "from previous meta-training tasks are carried forward in the form of a posterior, which is then used", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 688, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 688, + 505, + 700 + ], + "score": 1.0, + "content": "as the prior when a new task arrives for meta-training. The baselines TOE and TFS have similar", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 699, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 505, + 711 + ], + "score": 1.0, + "content": "performances. Despite having access to all previous tasks, TOE shows no positive forward transfer", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 433, + 722 + ], + "score": 1.0, + "content": "in the meta-evaluation accuracy each time it encounters a new task. 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Grant et al. (2018) discuss the use of a Laplace approximation", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 141, + 93, + 506, + 106 + ], + "spans": [ + { + "bbox": [ + 141, + 93, + 506, + 106 + ], + "score": 1.0, + "content": "in the task-specific inner loop to improve MAML using the curvature information, whilst", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 141, + 104, + 505, + 117 + ], + "spans": [ + { + "bbox": [ + 141, + 104, + 505, + 117 + ], + "score": 1.0, + "content": "Yoon et al. (2018) use Stein Variational Gradient Descent (SVGD) for task-specific learn-", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 141, + 115, + 506, + 128 + ], + "spans": [ + { + "bbox": [ + 141, + 115, + 506, + 128 + ], + "score": 1.0, + "content": "ing. Gordon et al. (2019) implement probabilistic inference by considering the posterior", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 141, + 127, + 335, + 138 + ], + "spans": [ + { + "bbox": [ + 141, + 127, + 335, + 138 + ], + "score": 1.0, + "content": "predictive distribution with amortised networks.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 2, + "bbox_fs": [ + 141, + 82, + 506, + 138 + ] + }, + { + "type": "text", + "bbox": [ + 133, + 142, + 505, + 230 + ], + "lines": [ + { + "bbox": [ + 132, + 142, + 506, + 155 + ], + "spans": [ + { + "bbox": [ + 132, + 142, + 506, + 155 + ], + "score": 1.0, + "content": "• Non-probabilistic framework: Gradient-based meta-learning (Finn et al., 2017; Nichol", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 141, + 153, + 505, + 166 + ], + "spans": [ + { + "bbox": [ + 141, + 153, + 505, + 166 + ], + "score": 1.0, + "content": "et al., 2018; Rusu et al., 2019) updates the meta-parameters by accumulating the gradients", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 142, + 165, + 505, + 177 + ], + "spans": [ + { + "bbox": [ + 142, + 165, + 505, + 177 + ], + "score": 1.0, + "content": "of a meta-batch of task-specific inner loop updates. The meta-parameters will be used", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 141, + 176, + 505, + 188 + ], + "spans": [ + { + "bbox": [ + 141, + 176, + 505, + 188 + ], + "score": 1.0, + "content": "as a model initialisation for a quick adaptation on the novel classes. Metric-based meta-", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 141, + 187, + 505, + 199 + ], + "spans": [ + { + "bbox": [ + 141, + 187, + 505, + 199 + ], + "score": 1.0, + "content": "learning (Koch et al., 2015; Vinyals et al., 2016; Snell et al., 2017) utilises the metric", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 141, + 197, + 505, + 210 + ], + "spans": [ + { + "bbox": [ + 141, + 197, + 505, + 210 + ], + "score": 1.0, + "content": "distance between labelled examples. Such methods assume that base and novel classes are", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 142, + 209, + 505, + 220 + ], + "spans": [ + { + "bbox": [ + 142, + 209, + 505, + 220 + ], + "score": 1.0, + "content": "from the same dataset distribution, and the metric distance estimations can be generalised", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 141, + 219, + 370, + 231 + ], + "spans": [ + { + "bbox": [ + 141, + 219, + 370, + 231 + ], + "score": 1.0, + "content": "to the novel classes upon meta-learning the base classes.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 8.5, + "bbox_fs": [ + 132, + 142, + 506, + 231 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 244, + 505, + 376 + ], + "lines": [ + { + "bbox": [ + 106, + 245, + 506, + 257 + ], + "spans": [ + { + "bbox": [ + 106, + 245, + 506, + 257 + ], + "score": 1.0, + "content": "Continual Learning Modern continual learning works (Goodfellow et al., 2013; Lee et al., 2017;", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 255, + 506, + 269 + ], + "spans": [ + { + "bbox": [ + 105, + 255, + 506, + 269 + ], + "score": 1.0, + "content": "Zenke et al., 2017) focus primarily on large-scale supervised learning, in contrast to our work that", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 104, + 265, + 505, + 280 + ], + "spans": [ + { + "bbox": [ + 104, + 265, + 505, + 280 + ], + "score": 1.0, + "content": "looks into continual few-shot classification across sequential tasks and datasets. Wen et al. (2018)", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 277, + 506, + 291 + ], + "spans": [ + { + "bbox": [ + 105, + 277, + 506, + 291 + ], + "score": 1.0, + "content": "utilise few-shot learning to improve on overcoming catastrophic forgetting via logit matching on a", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 289, + 505, + 301 + ], + "spans": [ + { + "bbox": [ + 105, + 289, + 505, + 301 + ], + "score": 1.0, + "content": "small sample from the previous tasks. The online learning element in this paper is closely related to", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 300, + 505, + 312 + ], + "spans": [ + { + "bbox": [ + 105, + 300, + 505, + 312 + ], + "score": 1.0, + "content": "(Kirkpatrick et al., 2017; Zenke et al., 2017; Ritter et al., 2018a; Nguyen et al., 2018) that overcome", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 311, + 505, + 323 + ], + "spans": [ + { + "bbox": [ + 105, + 311, + 505, + 323 + ], + "score": 1.0, + "content": "catastrophic forgetting for large-scale supervised classification. In particular, our work builds on the", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 104, + 320, + 506, + 335 + ], + "spans": [ + { + "bbox": [ + 104, + 320, + 506, + 335 + ], + "score": 1.0, + "content": "online Laplace approximation method in (Ritter et al., 2018a). We extend this to the meta-learning", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 333, + 504, + 345 + ], + "spans": [ + { + "bbox": [ + 105, + 333, + 504, + 345 + ], + "score": 1.0, + "content": "scenario to avoid forgetting in few-shot classification problems. Nguyen et al. (2018) provide the", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 342, + 505, + 357 + ], + "spans": [ + { + "bbox": [ + 105, + 342, + 505, + 357 + ], + "score": 1.0, + "content": "alternative of using variational inference instead of Laplace approximation for approximating the", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 355, + 505, + 367 + ], + "spans": [ + { + "bbox": [ + 105, + 355, + 505, + 367 + ], + "score": 1.0, + "content": "posterior. It is a reasonable approach to adapt variational approximation methods to approximate", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 366, + 423, + 378 + ], + "spans": [ + { + "bbox": [ + 105, + 366, + 423, + 378 + ], + "score": 1.0, + "content": "the posterior of the meta-parameters by adjusting the KL-divergence objective.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 18.5, + "bbox_fs": [ + 104, + 245, + 506, + 378 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 394, + 200, + 407 + ], + "lines": [ + { + "bbox": [ + 105, + 393, + 201, + 409 + ], + "spans": [ + { + "bbox": [ + 105, + 393, + 201, + 409 + ], + "score": 1.0, + "content": "6 EXPERIMENTS", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 25 + }, + { + "type": "title", + "bbox": [ + 108, + 420, + 269, + 431 + ], + "lines": [ + { + "bbox": [ + 106, + 420, + 270, + 433 + ], + "spans": [ + { + "bbox": [ + 106, + 420, + 270, + 433 + ], + "score": 1.0, + "content": "6.1 OMNIGLOT: SEQUENTIAL TASKS", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 26 + }, + { + "type": "text", + "bbox": [ + 108, + 441, + 505, + 486 + ], + "lines": [ + { + "bbox": [ + 106, + 442, + 505, + 453 + ], + "spans": [ + { + "bbox": [ + 106, + 442, + 505, + 453 + ], + "score": 1.0, + "content": "We run the sequential tasks experiment on the Omniglot dataset. To increase the difficulty level,", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 452, + 505, + 465 + ], + "spans": [ + { + "bbox": [ + 105, + 452, + 505, + 465 + ], + "score": 1.0, + "content": "we split the datasets based on the alphabets (super-classes) instead of the characters (classes). The", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 464, + 506, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 464, + 506, + 475 + ], + "score": 1.0, + "content": "goal of this experiment is to classify the 5-way 5-shot novel tasks sampled from the meta-evaluation", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 475, + 467, + 486 + ], + "spans": [ + { + "bbox": [ + 106, + 475, + 467, + 486 + ], + "score": 1.0, + "content": "alphabets. The experimental details and the alphabet splits can be found in Appendix C.1.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 28.5, + "bbox_fs": [ + 105, + 442, + 506, + 486 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 491, + 326, + 502 + ], + "lines": [ + { + "bbox": [ + 106, + 490, + 328, + 505 + ], + "spans": [ + { + "bbox": [ + 106, + 490, + 328, + 505 + ], + "score": 1.0, + "content": "We compare our algorithms to the following baselines:", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 31, + "bbox_fs": [ + 106, + 490, + 328, + 505 + ] + }, + { + "type": "text", + "bbox": [ + 130, + 512, + 505, + 645 + ], + "lines": [ + { + "bbox": [ + 129, + 512, + 505, + 526 + ], + "spans": [ + { + "bbox": [ + 129, + 512, + 505, + 526 + ], + "score": 1.0, + "content": "1. Train-On-Everything (TOE): When a new task (or dataset) arrives for meta-training,", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 142, + 524, + 505, + 537 + ], + "spans": [ + { + "bbox": [ + 142, + 524, + 505, + 537 + ], + "score": 1.0, + "content": "we randomly re-initialise the meta-parameters and perform meta-training on all tasks (or", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 142, + 535, + 505, + 547 + ], + "spans": [ + { + "bbox": [ + 142, + 535, + 505, + 547 + ], + "score": 1.0, + "content": "datasets) encountered so far. Once meta-training is completed in this stage, we do not", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 141, + 546, + 480, + 558 + ], + "spans": [ + { + "bbox": [ + 141, + 546, + 480, + 558 + ], + "score": 1.0, + "content": "update the posterior of the meta-parameters like we would in BOMLA and BOMVI.", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 130, + 562, + 505, + 574 + ], + "spans": [ + { + "bbox": [ + 130, + 562, + 505, + 574 + ], + "score": 1.0, + "content": "2. Train-From-Scratch (TFS): Upon the arrival of a new task (or dataset), we randomly re-", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 142, + 574, + 504, + 585 + ], + "spans": [ + { + "bbox": [ + 142, + 574, + 504, + 585 + ], + "score": 1.0, + "content": "initialise the meta-parameters and meta-train only on the newly-arrived task (or dataset).", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 141, + 583, + 446, + 597 + ], + "spans": [ + { + "bbox": [ + 141, + 583, + 446, + 597 + ], + "score": 1.0, + "content": "Similar to TOE, the posterior of the meta-parameters is not updated in TFS.", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 128, + 599, + 505, + 613 + ], + "spans": [ + { + "bbox": [ + 128, + 599, + 505, + 613 + ], + "score": 1.0, + "content": "3. Follow The Meta-Leader (FTML): We introduce a slight modification to FTML (Finn", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 141, + 611, + 505, + 624 + ], + "spans": [ + { + "bbox": [ + 141, + 611, + 505, + 624 + ], + "score": 1.0, + "content": "et al., 2019) on its evaluation method, as FTML is not designed for few-shot learning on", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 142, + 622, + 505, + 635 + ], + "spans": [ + { + "bbox": [ + 142, + 622, + 505, + 635 + ], + "score": 1.0, + "content": "unseen tasks. 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Left:", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 252, + 505, + 264 + ], + "spans": [ + { + "bbox": [ + 105, + 252, + 505, + 264 + ], + "score": 1.0, + "content": "compares BOMLA to the baselines, centre: compares BOMVI to the baselines, right: compares", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 263, + 285, + 274 + ], + "spans": [ + { + "bbox": [ + 106, + 263, + 201, + 274 + ], + "score": 1.0, + "content": "BOMLA with different", + "type": "text" + }, + { + "bbox": [ + 201, + 264, + 208, + 273 + ], + "score": 0.76, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 209, + 263, + 285, + 274 + ], + "score": 1.0, + "content": "values to BOMVI.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4 + } + ], + "index": 2.5 + }, + { + "type": "title", + "bbox": [ + 108, + 295, + 294, + 307 + ], + "lines": [ + { + "bbox": [ + 106, + 295, + 296, + 308 + ], + "spans": [ + { + "bbox": [ + 106, + 295, + 296, + 308 + ], + "score": 1.0, + "content": "6.2 PENTATHLON: SEQUENTIAL DATASETS", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 6 + }, + { + "type": "text", + "bbox": [ + 104, + 316, + 476, + 328 + ], + "lines": [ + { + "bbox": [ + 105, + 315, + 478, + 331 + ], + "spans": [ + { + "bbox": [ + 105, + 315, + 478, + 331 + ], + "score": 1.0, + "content": "We implement BOMLA and BOMVI to the pentathlon 5-way 1-shot classification sequence:", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 7 + }, + { + "type": "text", + "bbox": [ + 160, + 336, + 451, + 348 + ], + "lines": [ + { + "bbox": [ + 159, + 335, + 452, + 351 + ], + "spans": [ + { + "bbox": [ + 159, + 335, + 200, + 351 + ], + "score": 1.0, + "content": "Omniglot", + "type": "text" + }, + { + "bbox": [ + 201, + 338, + 214, + 347 + ], + "score": 0.75, + "content": "", + "type": "inline_equation" + }, + { + "bbox": [ + 214, + 335, + 259, + 351 + ], + "score": 1.0, + "content": "CIFAR-FS", + "type": "text" + }, + { + "bbox": [ + 259, + 338, + 272, + 347 + ], + "score": 0.7, + "content": "", + "type": "inline_equation" + }, + { + "bbox": [ + 273, + 335, + 331, + 351 + ], + "score": 1.0, + "content": "miniImageNet", + "type": "text" + }, + { + "bbox": [ + 331, + 338, + 345, + 347 + ], + "score": 0.77, + "content": "", + "type": "inline_equation" + }, + { + "bbox": [ + 345, + 335, + 403, + 351 + ], + "score": 1.0, + "content": "VGG-Flowers", + "type": "text" + }, + { + "bbox": [ + 404, + 338, + 417, + 347 + ], + "score": 0.8, + "content": "", + "type": "inline_equation" + }, + { + "bbox": [ + 417, + 335, + 452, + 351 + ], + "score": 1.0, + "content": "Aircraft", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 8 + }, + { + "type": "text", + "bbox": [ + 107, + 362, + 504, + 396 + ], + "lines": [ + { + "bbox": [ + 106, + 363, + 504, + 375 + ], + "spans": [ + { + "bbox": [ + 106, + 363, + 504, + 375 + ], + "score": 1.0, + "content": "The details of this experiment and the datasets can be found in Appendix C.2. 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TOE", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 413, + 505, + 424 + ], + "spans": [ + { + "bbox": [ + 105, + 413, + 505, + 424 + ], + "score": 1.0, + "content": "is also able to retain the few-shot performance as it has access to all datasets encountered so far.", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 423, + 505, + 437 + ], + "spans": [ + { + "bbox": [ + 105, + 423, + 505, + 437 + ], + "score": 1.0, + "content": "However, since it learns all datasets from random re-initialisation each time it encounters a new", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 434, + 506, + 447 + ], + "spans": [ + { + "bbox": [ + 105, + 434, + 506, + 447 + ], + "score": 1.0, + "content": "dataset, the meta-training time required to achieve a similarly good meta-evaluation performance is", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 447, + 505, + 458 + ], + "spans": [ + { + "bbox": [ + 106, + 447, + 505, + 458 + ], + "score": 1.0, + "content": "longer compared to other runs. 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Left:", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 252, + 505, + 264 + ], + "spans": [ + { + "bbox": [ + 105, + 252, + 505, + 264 + ], + "score": 1.0, + "content": "compares BOMLA to the baselines, centre: compares BOMVI to the baselines, right: compares", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 263, + 285, + 274 + ], + "spans": [ + { + "bbox": [ + 106, + 263, + 201, + 274 + ], + "score": 1.0, + "content": "BOMLA with different", + "type": "text" + }, + { + "bbox": [ + 201, + 264, + 208, + 273 + ], + "score": 0.76, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 209, + 263, + 285, + 274 + ], + "score": 1.0, + "content": "values to BOMVI.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4 + } + ], + "index": 2.5 + }, + { + "type": "title", + "bbox": [ + 108, + 295, + 294, + 307 + ], + "lines": [ + { + "bbox": [ + 106, + 295, + 296, + 308 + ], + "spans": [ + { + "bbox": [ + 106, + 295, + 296, + 308 + ], + "score": 1.0, + "content": "6.2 PENTATHLON: SEQUENTIAL DATASETS", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 6 + }, + { + "type": "text", + "bbox": [ + 104, + 316, + 476, + 328 + ], + "lines": [ + { + "bbox": [ + 105, + 315, + 478, + 331 + ], + "spans": [ + { + "bbox": [ + 105, + 315, + 478, + 331 + ], + "score": 1.0, + "content": "We implement BOMLA and BOMVI to the pentathlon 5-way 1-shot classification sequence:", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 7, + "bbox_fs": [ + 105, + 315, + 478, + 331 + ] + }, + { + "type": "text", + "bbox": [ + 160, + 336, + 451, + 348 + ], + "lines": [ + { + "bbox": [ + 159, + 335, + 452, + 351 + ], + "spans": [ + { + "bbox": [ + 159, + 335, + 200, + 351 + ], + "score": 1.0, + "content": "Omniglot", + "type": "text" + }, + { + "bbox": [ + 201, + 338, + 214, + 347 + ], + "score": 0.75, + "content": "", + "type": "inline_equation" + }, + { + "bbox": [ + 214, + 335, + 259, + 351 + ], + "score": 1.0, + "content": "CIFAR-FS", + "type": "text" + }, + { + "bbox": [ + 259, + 338, + 272, + 347 + ], + "score": 0.7, + "content": "", + "type": "inline_equation" + }, + { + "bbox": [ + 273, + 335, + 331, + 351 + ], + "score": 1.0, + "content": "miniImageNet", + "type": "text" + }, + { + "bbox": [ + 331, + 338, + 345, + 347 + ], + "score": 0.77, + "content": "", + "type": "inline_equation" + }, + { + "bbox": [ + 345, + 335, + 403, + 351 + ], + "score": 1.0, + "content": "VGG-Flowers", + "type": "text" + }, + { + "bbox": [ + 404, + 338, + 417, + 347 + ], + "score": 0.8, + "content": "", + "type": "inline_equation" + }, + { + "bbox": [ + 417, + 335, + 452, + 351 + ], + "score": 1.0, + "content": "Aircraft", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 8, + "bbox_fs": [ + 159, + 335, + 452, + 351 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 362, + 504, + 396 + ], + "lines": [ + { + "bbox": [ + 106, + 363, + 504, + 375 + ], + "spans": [ + { + "bbox": [ + 106, + 363, + 504, + 375 + ], + "score": 1.0, + "content": "The details of this experiment and the datasets can be found in Appendix C.2. We compare BOMLA", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 374, + 505, + 386 + ], + "spans": [ + { + "bbox": [ + 106, + 374, + 505, + 386 + ], + "score": 1.0, + "content": "and BOMVI to the baseline TOE, and running MAML continuously on the sequential datasets for", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 384, + 166, + 398 + ], + "spans": [ + { + "bbox": [ + 106, + 384, + 166, + 398 + ], + "score": 1.0, + "content": "meta-training.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 10, + "bbox_fs": [ + 106, + 363, + 505, + 398 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 401, + 505, + 512 + ], + "lines": [ + { + "bbox": [ + 106, + 402, + 505, + 414 + ], + "spans": [ + { + "bbox": [ + 106, + 402, + 505, + 414 + ], + "score": 1.0, + "content": "Figure 2 shows that BOMLA and BOMVI are able to prevent few-shot catastrophic forgetting. TOE", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 413, + 505, + 424 + ], + "spans": [ + { + "bbox": [ + 105, + 413, + 505, + 424 + ], + "score": 1.0, + "content": "is also able to retain the few-shot performance as it has access to all datasets encountered so far.", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 423, + 505, + 437 + ], + "spans": [ + { + "bbox": [ + 105, + 423, + 505, + 437 + ], + "score": 1.0, + "content": "However, since it learns all datasets from random re-initialisation each time it encounters a new", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 434, + 506, + 447 + ], + "spans": [ + { + "bbox": [ + 105, + 434, + 506, + 447 + ], + "score": 1.0, + "content": "dataset, the meta-training time required to achieve a similarly good meta-evaluation performance is", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 447, + 505, + 458 + ], + "spans": [ + { + "bbox": [ + 106, + 447, + 505, + 458 + ], + "score": 1.0, + "content": "longer compared to other runs. The sequential MAML, on the other hand, catastrophically forgets", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 457, + 506, + 469 + ], + "spans": [ + { + "bbox": [ + 105, + 457, + 506, + 469 + ], + "score": 1.0, + "content": "the previously learned datasets but has the best performance on new datasets compared to other", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 466, + 505, + 479 + ], + "spans": [ + { + "bbox": [ + 105, + 466, + 505, + 479 + ], + "score": 1.0, + "content": "runs. TOE can be memory-intensive as the dataset sequence becomes longer. It takes the brute-", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 479, + 505, + 491 + ], + "spans": [ + { + "bbox": [ + 105, + 479, + 505, + 491 + ], + "score": 1.0, + "content": "force approach to prevent forgetting by memorising all datasets. 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As shown", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 540, + 505, + 551 + ], + "spans": [ + { + "bbox": [ + 106, + 540, + 249, + 551 + ], + "score": 1.0, + "content": "in Appendix C.2 Figure 4, a larger", + "type": "text" + }, + { + "bbox": [ + 249, + 540, + 290, + 550 + ], + "score": 0.91, + "content": "\\lambda = 1 0 0 0", + "type": "inline_equation" + }, + { + "bbox": [ + 290, + 540, + 505, + 551 + ], + "score": 1.0, + "content": "results in a more concentrated Gaussian posterior and", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 549, + 505, + 563 + ], + "spans": [ + { + "bbox": [ + 105, + 549, + 505, + 563 + ], + "score": 1.0, + "content": "is therefore unable to learn new datasets well, but can better retain the performances on previous", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 560, + 505, + 574 + ], + "spans": [ + { + "bbox": [ + 105, + 560, + 208, + 574 + ], + "score": 1.0, + "content": "datasets. A smaller value", + "type": "text" + }, + { + "bbox": [ + 209, + 561, + 234, + 572 + ], + "score": 0.9, + "content": "\\lambda = 1", + "type": "inline_equation" + }, + { + "bbox": [ + 235, + 560, + 505, + 574 + ], + "score": 1.0, + "content": "on the other hand gives a widespread Gaussian posterior and learns", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 571, + 505, + 585 + ], + "spans": [ + { + "bbox": [ + 105, + 571, + 505, + 585 + ], + "score": 1.0, + "content": "better on new datasets by sacrificing the performance on the previous datasets. 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Ideally we seek for a", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 593, + 506, + 609 + ], + "spans": [ + { + "bbox": [ + 105, + 593, + 506, + 609 + ], + "score": 1.0, + "content": "good performance on both old and new datasets, but in reality there is a trade-off between retaining", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 605, + 505, + 618 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 505, + 618 + ], + "score": 1.0, + "content": "performance on old datasets and learning well on new datasets due to posterior approximation errors.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 30, + "bbox_fs": [ + 105, + 517, + 506, + 618 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 621, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 622, + 505, + 633 + ], + "spans": [ + { + "bbox": [ + 106, + 622, + 340, + 633 + ], + "score": 1.0, + "content": "As shown in Figures 1 and 2, BOMLA with appropriate", + "type": "text" + }, + { + "bbox": [ + 341, + 622, + 348, + 632 + ], + "score": 0.76, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 348, + 622, + 505, + 633 + ], + "score": 1.0, + "content": "is superior to BOMVI. This is due to", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 633, + 506, + 645 + ], + "spans": [ + { + "bbox": [ + 105, + 633, + 506, + 645 + ], + "score": 1.0, + "content": "BOMLA having a better posterior approximation than BOMVI. Whilst BOMLA has a Gaussian", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 644, + 506, + 656 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 506, + 656 + ], + "score": 1.0, + "content": "approximate posterior with block-diagonal precision, BOMVI uses a Gaussian mean-field approx-", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 655, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 655, + 505, + 667 + ], + "score": 1.0, + "content": "imate posterior. 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No-Regret Non-Convex Online Meta-Learning. arXiv", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 115, + 184, + 257, + 196 + ], + "spans": [ + { + "bbox": [ + 115, + 184, + 257, + 196 + ], + "score": 1.0, + "content": "preprint, arXiv:1910.10196, 2019.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 3.5 + } + ], + "page_idx": 11, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 300, + 751, + 311, + 760 + ], + "lines": [ + { + "bbox": [ + 299, + 750, + 313, + 764 + ], + "spans": [ + { + "bbox": [ + 299, + 750, + 313, + 764 + ], + "score": 1.0, + "content": "12", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 107, + 26, + 307, + 38 + ], + "lines": [ + { + "bbox": [ + 106, + 25, + 308, + 39 + ], + "spans": [ + { + "bbox": [ + 106, + 25, + 308, + 39 + ], + "score": 1.0, + "content": "Under review as a conference paper at ICLR 2021", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "list", + "bbox": [ + 104, + 81, + 506, + 195 + ], + "lines": [], + "index": 3.5, + "bbox_fs": [ + 104, + 82, + 505, + 196 + ], + "lines_deleted": true + } + ] + }, + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 108, + 81, + 203, + 94 + ], + "lines": [ + { + "bbox": [ + 105, + 80, + 205, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 80, + 205, + 96 + ], + "score": 1.0, + "content": "A BACKGROUND", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 107, + 105, + 504, + 139 + ], + "lines": [ + { + "bbox": [ + 105, + 104, + 504, + 119 + ], + "spans": [ + { + "bbox": [ + 105, + 104, + 504, + 119 + ], + "score": 1.0, + "content": "This section provides a background explanation of using BOL to find the posterior of a model pa-", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 116, + 505, + 129 + ], + "spans": [ + { + "bbox": [ + 105, + 116, + 505, + 129 + ], + "score": 1.0, + "content": "rameters and overcome catastrophic forgetting, commonly for large-scale supervised classification.", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 127, + 348, + 141 + ], + "spans": [ + { + "bbox": [ + 105, + 127, + 348, + 141 + ], + "score": 1.0, + "content": "We will then apply this approach to our recursion in Eq. (5).", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 2 + }, + { + "type": "text", + "bbox": [ + 107, + 144, + 505, + 211 + ], + "lines": [ + { + "bbox": [ + 106, + 145, + 505, + 156 + ], + "spans": [ + { + "bbox": [ + 106, + 145, + 505, + 156 + ], + "score": 1.0, + "content": "The posterior is typically intractable due to the enormous size of the modern neural network ar-", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 154, + 505, + 168 + ], + "spans": [ + { + "bbox": [ + 105, + 154, + 505, + 168 + ], + "score": 1.0, + "content": "chitectures. This leads to the requirement for a good approximation of the posterior of the meta-", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 166, + 505, + 180 + ], + "spans": [ + { + "bbox": [ + 105, + 166, + 505, + 180 + ], + "score": 1.0, + "content": "parameters. A particularly suitable candidate for this purpose in meta-learning is the Laplace ap-", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 176, + 506, + 190 + ], + "spans": [ + { + "bbox": [ + 105, + 176, + 506, + 190 + ], + "score": 1.0, + "content": "proximation (MacKay, 1992; Ritter et al., 2018b), as it simply adds a quadratic regulariser to the", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 188, + 505, + 201 + ], + "spans": [ + { + "bbox": [ + 105, + 188, + 505, + 201 + ], + "score": 1.0, + "content": "training objective. 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In", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 371, + 505, + 385 + ], + "spans": [ + { + "bbox": [ + 105, + 371, + 460, + 385 + ], + "score": 1.0, + "content": "this case, the new posterior has to be projected into the same parametric family to obtain", + "type": "text" + }, + { + "bbox": [ + 461, + 372, + 501, + 384 + ], + "score": 0.92, + "content": "q ( \\theta | \\phi _ { t + 1 } )", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 371, + 505, + 385 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 383, + 506, + 396 + ], + "spans": [ + { + "bbox": [ + 105, + 383, + 506, + 396 + ], + "score": 1.0, + "content": "Opper (1998) performs this projection by minimising the KL-divergence between the new posterior", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 393, + 505, + 407 + ], + "spans": [ + { + "bbox": [ + 105, + 393, + 184, + 407 + ], + "score": 1.0, + "content": "and the parametric", + "type": "text" + }, + { + "bbox": [ + 185, + 396, + 191, + 406 + ], + "score": 0.79, + "content": "q", + "type": "inline_equation" + }, + { + "bbox": [ + 191, + 393, + 505, + 407 + ], + "score": 1.0, + "content": ", while Ritter et al. (2018a) use the Laplace approximation and Nguyen et al.", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 404, + 238, + 417 + ], + "spans": [ + { + "bbox": [ + 106, + 404, + 238, + 417 + ], + "score": 1.0, + "content": "(2018) use variational inference.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 23 + }, + { + "type": "title", + "bbox": [ + 108, + 429, + 248, + 441 + ], + "lines": [ + { + "bbox": [ + 106, + 429, + 248, + 441 + ], + "spans": [ + { + "bbox": [ + 106, + 429, + 248, + 441 + ], + "score": 1.0, + "content": "A.2 LAPLACE APPROXIMATION", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 26 + }, + { + "type": "text", + "bbox": [ + 107, + 449, + 360, + 461 + ], + "lines": [ + { + "bbox": [ + 105, + 447, + 356, + 464 + ], + "spans": [ + { + "bbox": [ + 105, + 447, + 356, + 464 + ], + "score": 1.0, + "content": "We consider finding a MAP estimate following from Eq. (16):", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 27 + }, + { + "type": "interline_equation", + "bbox": [ + 156, + 462, + 455, + 482 + ], + "lines": [ + { + "bbox": [ + 156, + 462, + 455, + 482 + ], + "spans": [ + { + "bbox": [ + 156, + 462, + 455, + 482 + ], + "score": 0.91, + "content": "\\theta _ { t + 1 } ^ { * } = \\arg \\operatorname* { m a x } _ { \\theta } p ( \\theta | \\mathcal { D } _ { 1 : t + 1 } ) = \\arg \\operatorname* { m a x } _ { \\theta } \\{ \\log p ( \\mathcal { D } _ { t + 1 } | \\theta ) + \\log p ( \\theta | \\mathcal { D } _ { 1 : t } ) \\} .", + "type": "interline_equation", + "image_path": "9d85b6ebff62fbeeb39d1d697c4878400e7b766c9cde0013e04e871b1e5d123f.jpg" + } + ] + } + ], + "index": 28, + "virtual_lines": [ + { + "bbox": [ + 156, + 462, + 455, + 482 + ], + "spans": [], + "index": 28 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 484, + 503, + 518 + ], + "lines": [ + { + "bbox": [ + 105, + 483, + 505, + 498 + ], + "spans": [ + { + "bbox": [ + 105, + 483, + 182, + 498 + ], + "score": 1.0, + "content": "Since the posterior", + "type": "text" + }, + { + "bbox": [ + 183, + 485, + 221, + 496 + ], + "score": 0.91, + "content": "p ( \\theta | \\mathcal { D } _ { 1 : t } )", + "type": "inline_equation" + }, + { + "bbox": [ + 222, + 483, + 505, + 498 + ], + "score": 1.0, + "content": "of a neural network is intractable except for small architectures, the un-", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 496, + 504, + 508 + ], + "spans": [ + { + "bbox": [ + 106, + 496, + 191, + 508 + ], + "score": 1.0, + "content": "normalised posterior", + "type": "text" + }, + { + "bbox": [ + 191, + 496, + 230, + 507 + ], + "score": 0.91, + "content": "\\tilde { p } ( \\theta | \\mathcal { D } _ { 1 : t } )", + "type": "inline_equation" + }, + { + "bbox": [ + 230, + 496, + 504, + 508 + ], + "score": 1.0, + "content": "is considered instead. Performing Taylor expansion on the logarithm", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 506, + 324, + 519 + ], + "spans": [ + { + "bbox": [ + 106, + 506, + 288, + 519 + ], + "score": 1.0, + "content": "of the unnormalised posterior around a mode", + "type": "text" + }, + { + "bbox": [ + 288, + 507, + 299, + 518 + ], + "score": 0.88, + "content": "{ \\boldsymbol { \\theta } } _ { t } ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 299, + 506, + 324, + 519 + ], + "score": 1.0, + "content": "gives", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 30 + }, + { + "type": "interline_equation", + "bbox": [ + 180, + 519, + 431, + 543 + ], + "lines": [ + { + "bbox": [ + 180, + 519, + 431, + 543 + ], + "spans": [ + { + "bbox": [ + 180, + 519, + 431, + 543 + ], + "score": 0.92, + "content": "\\log \\tilde { p } ( \\theta | \\mathcal { D } _ { 1 : t } ) \\simeq \\log \\tilde { p } ( \\theta | \\mathcal { D } _ { 1 : t } ) \\big | _ { \\theta = \\theta _ { t } ^ { * } } - \\frac { 1 } { 2 } ( \\theta - \\theta _ { t } ^ { * } ) ^ { T } A _ { t } ( \\theta - \\theta _ { t } ^ { * } ) ,", + "type": "interline_equation", + "image_path": "6e164b79457e9d746c6db551d3aec927946fffa4599c2c369f8bc272ac1af928.jpg" + } + ] + } + ], + "index": 32, + "virtual_lines": [ + { + "bbox": [ + 180, + 519, + 431, + 543 + ], + "spans": [], + "index": 32 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 543, + 505, + 587 + ], + "lines": [ + { + "bbox": [ + 105, + 543, + 504, + 556 + ], + "spans": [ + { + "bbox": [ + 105, + 543, + 134, + 556 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 134, + 544, + 146, + 555 + ], + "score": 0.88, + "content": "A _ { t }", + "type": "inline_equation" + }, + { + "bbox": [ + 146, + 543, + 427, + 556 + ], + "score": 1.0, + "content": "denotes the Hessian matrix of the negative log-posterior evaluated at", + "type": "text" + }, + { + "bbox": [ + 428, + 544, + 438, + 555 + ], + "score": 0.87, + "content": "\\theta _ { t } ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 438, + 543, + 504, + 556 + ], + "score": 1.0, + "content": ". 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Given the parameter", + "type": "text" + }, + { + "bbox": [ + 436, + 555, + 494, + 567 + ], + "score": 0.92, + "content": "\\phi _ { t } = \\{ \\mu _ { t } , \\Lambda _ { t } \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 494, + 554, + 505, + 568 + ], + "score": 1.0, + "content": ", a", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 566, + 505, + 579 + ], + "spans": [ + { + "bbox": [ + 105, + 566, + 131, + 579 + ], + "score": 1.0, + "content": "mean", + "type": "text" + }, + { + "bbox": [ + 131, + 569, + 151, + 578 + ], + "score": 0.81, + "content": "\\mu _ { t + 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 151, + 566, + 185, + 579 + ], + "score": 1.0, + "content": "for step", + "type": "text" + }, + { + "bbox": [ + 185, + 567, + 207, + 576 + ], + "score": 0.85, + "content": "t + 1", + "type": "inline_equation" + }, + { + "bbox": [ + 207, + 566, + 505, + 579 + ], + "score": 1.0, + "content": "can be obtained by finding a mode of the approximate posterior as follows", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 576, + 273, + 589 + ], + "spans": [ + { + "bbox": [ + 106, + 576, + 273, + 589 + ], + "score": 1.0, + "content": "via standard gradient-based optimisation:", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 34.5 + }, + { + "type": "interline_equation", + "bbox": [ + 187, + 589, + 424, + 614 + ], + "lines": [ + { + "bbox": [ + 187, + 589, + 424, + 614 + ], + "spans": [ + { + "bbox": [ + 187, + 589, + 424, + 614 + ], + "score": 0.92, + "content": "\\mu _ { t + 1 } = \\arg \\operatorname* { m a x } _ { \\boldsymbol { \\theta } } \\log p ( \\mathcal { D } _ { t + 1 } | \\boldsymbol { \\theta } ) - \\frac { 1 } { 2 } ( \\boldsymbol { \\theta } - \\boldsymbol { \\mu } _ { t } ) ^ { T } \\Lambda _ { t } ( \\boldsymbol { \\theta } - \\boldsymbol { \\mu } _ { t } ) .", + "type": "interline_equation", + "image_path": "e30a9fc2b0abe8259f6075a61a749cf139f06448d9e71a45118af62aa94d8b78.jpg" + } + ] + } + ], + "index": 37, + "virtual_lines": [ + { + "bbox": [ + 187, + 589, + 424, + 614 + ], + "spans": [], + "index": 37 + } + ] + }, + { + "type": "text", + "bbox": [ + 108, + 615, + 502, + 639 + ], + "lines": [ + { + "bbox": [ + 106, + 615, + 504, + 628 + ], + "spans": [ + { + "bbox": [ + 106, + 615, + 250, + 628 + ], + "score": 1.0, + "content": "The precision matrix is updated as", + "type": "text" + }, + { + "bbox": [ + 250, + 616, + 333, + 628 + ], + "score": 0.91, + "content": "\\Lambda _ { t + 1 } = H _ { t + 1 } + \\Lambda _ { t }", + "type": "inline_equation" + }, + { + "bbox": [ + 333, + 615, + 365, + 628 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 365, + 616, + 388, + 628 + ], + "score": 0.91, + "content": "H _ { t + 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 388, + 615, + 504, + 628 + ], + "score": 1.0, + "content": "is the Hessian matrix of the", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 626, + 361, + 640 + ], + "spans": [ + { + "bbox": [ + 106, + 626, + 215, + 640 + ], + "score": 1.0, + "content": "negative log-likelihood for", + "type": "text" + }, + { + "bbox": [ + 216, + 628, + 237, + 639 + ], + "score": 0.91, + "content": "\\mathcal { D } _ { t + 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 238, + 626, + 289, + 640 + ], + "score": 1.0, + "content": "evaluated at", + "type": "text" + }, + { + "bbox": [ + 289, + 629, + 309, + 639 + ], + "score": 0.89, + "content": "\\mu _ { t + 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 310, + 626, + 361, + 640 + ], + "score": 1.0, + "content": "with entries", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 38.5 + }, + { + "type": "interline_equation", + "bbox": [ + 215, + 640, + 396, + 670 + ], + "lines": [ + { + "bbox": [ + 215, + 640, + 396, + 670 + ], + "spans": [ + { + "bbox": [ + 215, + 640, + 396, + 670 + ], + "score": 0.93, + "content": "H _ { t + 1 } ^ { i j } = - 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A fully-connected layer is appended to the final module before getting the class", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 243, + 456, + 256 + ], + "spans": [ + { + "bbox": [ + 105, + 243, + 456, + 256 + ], + "score": 1.0, + "content": "probabilities with softmax. Table 1 shows the hyperparameters used in this experiment.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 8.5 + }, + { + "type": "text", + "bbox": [ + 107, + 259, + 505, + 315 + ], + "lines": [ + { + "bbox": [ + 106, + 260, + 505, + 272 + ], + "spans": [ + { + "bbox": [ + 106, + 260, + 505, + 272 + ], + "score": 1.0, + "content": "The Omniglot dataset comprises 50 alphabets (super-classes). Each alphabet has numerous charac-", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 270, + 505, + 284 + ], + "spans": [ + { + "bbox": [ + 105, + 270, + 505, + 284 + ], + "score": 1.0, + "content": "ters (classes) and each character has 20 instances. 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HyperparameterBOMLABOMVI
Posterior regulariser 入0.1
Precision initialisation values10-4~10-2
Covariance initialisation values1exp(-10)
NumberofMonte Carlo samples=5
Number of batch M11
Number of query samples per class (meta-evaluation)1515
Number of epochs per task5050
Number of inner SGD steps in meta-training (k)55
Inner SGD learning rate (α)0.10.1
Outer loop optimiserAdamAdam
Outer loop learning rate0.0010.001
Number of tasks sampled for meta-evaluation100100
Number of inner SGD steps in meta-evaluation (k)1010
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A quick adaptation with more steps works in a similar fashion. With", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 127, + 504, + 138 + ], + "spans": [ + { + "bbox": [ + 106, + 127, + 504, + 138 + ], + "score": 1.0, + "content": "this modification, we can calculate the Monte Carlo estimator for the first term using the local", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 138, + 240, + 149 + ], + "spans": [ + { + "bbox": [ + 105, + 138, + 240, + 149 + ], + "score": 1.0, + "content": "reparameterisation trick as usual.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 3, + "bbox_fs": [ + 105, + 115, + 505, + 149 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 165, + 203, + 178 + ], + "lines": [ + { + "bbox": [ + 105, + 163, + 204, + 180 + ], + "spans": [ + { + "bbox": [ + 105, + 163, + 204, + 180 + ], + "score": 1.0, + "content": "C EXPERIMENTS", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 5 + }, + { + "type": "title", + "bbox": [ + 108, + 189, + 271, + 201 + ], + "lines": [ + { + "bbox": [ + 106, + 189, + 272, + 202 + ], + "spans": [ + { + "bbox": [ + 106, + 189, + 272, + 202 + ], + "score": 1.0, + "content": "C.1 OMNIGLOT: SEQUENTIAL TASKS", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 6 + }, + { + "type": "text", + "bbox": [ + 107, + 209, + 505, + 254 + ], + "lines": [ + { + "bbox": [ + 105, + 210, + 506, + 222 + ], + "spans": [ + { + "bbox": [ + 105, + 210, + 506, + 222 + ], + "score": 1.0, + "content": "In this experiment, we use the model architecture proposed by Vinyals et al. (2016) that takes 4", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 221, + 506, + 233 + ], + "spans": [ + { + "bbox": [ + 105, + 221, + 232, + 233 + ], + "score": 1.0, + "content": "modules with 64 filters of size", + "type": "text" + }, + { + "bbox": [ + 232, + 221, + 257, + 232 + ], + "score": 0.89, + "content": "3 \\times 3", + "type": "inline_equation" + }, + { + "bbox": [ + 257, + 221, + 506, + 233 + ], + "score": 1.0, + "content": ", followed by a batch normalisation, a ReLU activation and a", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 107, + 232, + 505, + 244 + ], + "spans": [ + { + "bbox": [ + 107, + 232, + 129, + 243 + ], + "score": 0.87, + "content": "2 \\times 2", + "type": "inline_equation" + }, + { + "bbox": [ + 130, + 232, + 505, + 244 + ], + "score": 1.0, + "content": "max-pooling. A fully-connected layer is appended to the final module before getting the class", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 243, + 456, + 256 + ], + "spans": [ + { + "bbox": [ + 105, + 243, + 456, + 256 + ], + "score": 1.0, + "content": "probabilities with softmax. Table 1 shows the hyperparameters used in this experiment.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 8.5, + "bbox_fs": [ + 105, + 210, + 506, + 256 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 259, + 505, + 315 + ], + "lines": [ + { + "bbox": [ + 106, + 260, + 505, + 272 + ], + "spans": [ + { + "bbox": [ + 106, + 260, + 505, + 272 + ], + "score": 1.0, + "content": "The Omniglot dataset comprises 50 alphabets (super-classes). Each alphabet has numerous charac-", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 270, + 505, + 284 + ], + "spans": [ + { + "bbox": [ + 105, + 270, + 505, + 284 + ], + "score": 1.0, + "content": "ters (classes) and each character has 20 instances. As the meta-training alphabets arrive sequentially,", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 282, + 505, + 294 + ], + "spans": [ + { + "bbox": [ + 106, + 282, + 505, + 294 + ], + "score": 1.0, + "content": "we form non-overlapping sequential tasks from each arriving alphabet, and the tasks also do not", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 293, + 506, + 306 + ], + "spans": [ + { + "bbox": [ + 105, + 293, + 506, + 306 + ], + "score": 1.0, + "content": "overlap in the characters. We use 35 alphabets for meta-training, 7 alphabets for validation and 8", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 303, + 369, + 317 + ], + "spans": [ + { + "bbox": [ + 105, + 303, + 369, + 317 + ], + "score": 1.0, + "content": "alphabets for meta-evaluation. The alphabet splits are as follows:", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 13, + "bbox_fs": [ + 105, + 260, + 506, + 317 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 321, + 231, + 332 + ], + "lines": [ + { + "bbox": [ + 106, + 319, + 232, + 334 + ], + "spans": [ + { + "bbox": [ + 106, + 319, + 232, + 334 + ], + "score": 1.0, + "content": "35 alphabets for meta-training:", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 16 + }, + { + "type": "text", + "bbox": [ + 106, + 340, + 491, + 429 + ], + "lines": [ + { + "bbox": [ + 105, + 340, + 460, + 353 + ], + "spans": [ + { + "bbox": [ + 105, + 340, + 460, + 353 + ], + "score": 1.0, + "content": "Kannada, Burmese_(Myanmar), Malay_(Jawi_-_Arabic), Grantha,", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 352, + 466, + 364 + ], + "spans": [ + { + "bbox": [ + 105, + 352, + 466, + 364 + ], + "score": 1.0, + "content": "Atlantean, Ojibwe_(Canadian_Aboriginal_Syllabics), Balinese,", 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HyperparameterBOMLABOMVI
Posterior regulariser 入0.1
Precision initialisation values10-4~10-2
Covariance initialisation values1exp(-10)
NumberofMonte Carlo samples=5
Number of batch M11
Number of query samples per class (meta-evaluation)1515
Number of epochs per task5050
Number of inner SGD steps in meta-training (k)55
Inner SGD learning rate (α)0.10.1
Outer loop optimiserAdamAdam
Outer loop learning rate0.0010.001
Number of tasks sampled for meta-evaluation100100
Number of inner SGD steps in meta-evaluation (k)1010
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HyperparameterBOMLABOMVI
Posterior regulariser 入(various values)
Precision initialisation values10-4~ 10-2
Number of tasks sampled for Hessian approx.5000
Covariance initialisation valuesexp(-5)
Number of Monte Carlo samples=20
Meta-batch size M= 3232
Number of query samples per class1515
Number of iterations per dataset5000
Outer loop optimiserAdam5000
Outer loop learning rateAdam
Number of tasks sampled for meta-evaluation0.001 1000.001 100
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HyperparameterOmniglotCIFAR-FSminiImageNetVGG-FlowersAircraft
Number of inner SGD steps in meta-training (k)15555
Inner SGD learning rate0.40.10.10.10.1
(a) Outer learning rate decay-×0.1×0.1 halfway×0.1 per 1000x0.1
schedule Number of inner SGD steps in meta-evaluation3halfway 1010iterations 10halfway 10
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HyperparameterBOMLABOMVI
Posterior regulariser 入(various values)
Precision initialisation values10-4~ 10-2
Number of tasks sampled for Hessian approx.5000
Covariance initialisation valuesexp(-5)
Number of Monte Carlo samples=20
Meta-batch size M= 3232
Number of query samples per class1515
Number of iterations per dataset5000
Outer loop optimiserAdam5000
Outer loop learning rateAdam
Number of tasks sampled for meta-evaluation0.001 1000.001 100
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HyperparameterOmniglotCIFAR-FSminiImageNetVGG-FlowersAircraft
Number of inner SGD steps in meta-training (k)15555
Inner SGD learning rate0.40.10.10.10.1
(a) Outer learning rate decay-×0.1×0.1 halfway×0.1 per 1000x0.1
schedule Number of inner SGD steps in meta-evaluation3halfway 1010iterations 10halfway 10
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HyperparameterBOMLABOMVI
Posterior regulariser 入0.1
Precision initialisation values10-4~10-2
Covariance initialisation values1exp(-10)
NumberofMonte Carlo samples=5
Number of batch M11
Number of query samples per class (meta-evaluation)1515
Number of epochs per task5050
Number of inner SGD steps in meta-training (k)55
Inner SGD learning rate (α)0.10.1
Outer loop optimiserAdamAdam
Outer loop learning rate0.0010.001
Number of tasks sampled for meta-evaluation100100
Number of inner SGD steps in meta-evaluation (k)1010
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HyperparameterOmniglotCIFAR-FSminiImageNetVGG-FlowersAircraft
Number of inner SGD steps in meta-training (k)15555
Inner SGD learning rate0.40.10.10.10.1
(a) Outer learning rate decay-×0.1×0.1 halfway×0.1 per 1000x0.1
schedule Number of inner SGD steps in meta-evaluation3halfway 1010iterations 10halfway 10
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HyperparameterBOMLABOMVI
Posterior regulariser 入(various values)
Precision initialisation values10-4~ 10-2
Number of tasks sampled for Hessian approx.5000
Covariance initialisation valuesexp(-5)
Number of Monte Carlo samples=20
Meta-batch size M= 3232
Number of query samples per class1515
Number of iterations per dataset5000
Outer loop optimiserAdam5000
Outer loop learning rateAdam
Number of tasks sampled for meta-evaluation0.001 1000.001 100
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