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+# FR-GAN: FAIR AND ROBUST TRAINING
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+We consider the problem of fair and robust model training in the presence of data poisoning. Ensuring fairness usually involves a tradeoff against accuracy, so if the data poisoning is mistakenly viewed as additional bias to be fixed, the accuracy will be sacrificed even more. We demonstrate that this phenomenon indeed holds for state-of-the-art model fairness techniques. We then propose FR-GAN, which holistically performs fair and robust model training using generative adversarial networks (GANs). We first use a generator that attempts to classify examples as accurately as possible. In addition, we deploy two discriminators: (1) a fairness discriminator that predicts the sensitive attribute from classification results and (2) a robustness discriminator that distinguishes examples and predictions from a clean validation set. Our framework respects all the prominent fairness measures: disparate impact, equalized odds, and equal opportunity. Also, FR-GAN optimizes fairness without requiring the knowledge of prior statistics of the sensitive attributes. In our experiments, FR-GAN shows almost no decrease in fairness and accuracy in the presence of data poisoning unlike other state-of-the-art fairness methods, which are vulnerable. In addition, FR-GAN can be adjusted using parameters to maintain reasonable accuracy and fairness even if the validation set is too small or unavailable.
+
+# 1 INTRODUCTION
+
+As machine learning becomes widespread in the Software 2.0 era (Karpathy, 2017), there is an urgent need to address the issues of fairness and robustness. For sensitive applications like healthcare, finance, and self-driving cars, a trained model must not discriminate customers based on sensitive attributes including age, sex, or religion. In addition, as applications often rely on external data sets for their training data, the model training must be resilient against noisy or even adversarial data.
+
+Traditionally, model fairness research (Venkatasubramanian, 2019; Chouldechova & Roth, 2018; Verma & Rubin, 2018) has focused on developing metrics such as disparate impact (Feldman et al., 2015), equalized odds (Hardt et al., 2016), and equal opportunity (Hardt et al., 2016), which capture various notions of discrimination. More recently, there has been a surge in unfairness mitigation techniques (Bellamy et al., 2018), which improve the model fairness by either fixing the training data, training process, or trained model. Unfairness mitigation usually involves some tradeoff between the model’s accuracy and fairness. Most recently, generative adversarial networks (GANs) are being adapted to a fairness setting (Zhang et al., 2018). The architecture of GANs is suitable because it can be used to compete the training between two objectives: accuracy and fairness.
+
+Robust model training is also important and needs to be concurrently taken into consideration. There has been a proliferation of algorithms that make model training resilient against noisy and even adversarial data (Natarajan et al., 2013; Biggio et al., 2011; Frenay & Verleysen, 2014). The latter ´ scenario may occur when the source of the training data is external, and we cannot control the data that is being added. For example, any public dataset on the Web may contain intentionallyfalse information. Moreover, one must have a robust training algorithm if the data set comes from diverse users’ inputs that cannot be fully trusted (Konecnˇ y et al., 2016). Recently, data poisoning \` attacks have become increasingly sophisticated where it is becoming difficult to sanitize the data against all of them (Koh et al., 2018). In addition, dataset searching is becoming mainstream as demonstrated by Google Dataset Search (Goods) (Halevy et al., 2016) and its public version for searching scientific datasets (Noy et al., 2019). While data lakes within companies may consist of refined datasets, datasets in the public are easy to poison. And anyone can poison public datasets using attacks in the literature and share them. We thus believe that it is essential to address both bias and poisoning as a preventive measure.
+
+Solving model fairness without addressing data poisoning may lead to a worse tradeoff between accuracy and fairness. For example, consider a banking system that is giving out loans where there are two sensitive groups: men and women. According to disparate impact, the two groups must have similar ratios of positive predictions. A perfect disparate impact would have a value of 1. Suppose the clean training data has no bias and a perfect (or high) disparate impact score. Now suppose this data is poisoned where half of the positive labels of men are flipped to negative labels. If the model is fitted so as to make more negative predictions on men than women, then disparate impact would worsen. To address this problem, one may suggest using data sanitization techniques prior to the model training, but it is challenging to do so without any knowledge of the model. Even though many data sanitization methods are proposed, there have been newer attacks that can easily evade such defenses (Koh et al., 2018).
+
+Our main contribution is the development of a new framework called FR-GAN, which trains accurate models that are also fair and robust to poisoning. FR-GAN consists of a generator used for classification, a discriminator that distinguishes predictions from one sensitive group against others, and a second discriminator that distinguishes {examples, predictions $\}$ of the training data from {examples, labels $\}$ of a separate and clean validation set. The first discriminator ensures that the prediction $\hat { y }$ is independent of the sensitive attribute $z$ . We show that variations of this approach can be used to maximize any of the following prominent fairness measures: disparate impact, equalized odds, and equal opportunity. The second discriminator ensures that the model predictions on the training data are “consistent” with labels on clean data. We theoretically show that FR-GAN optimizes fairness without requiring the knowledge of prior statistics of sensitive attributes. In addition, the parameters of FR-GAN can be adjusted to maintain reasonable accuracy and fairness even if the validation set is too small or unavailable. In the following sections, we present the related work, demonstrate the weaknesses of current fairness methods, and propose FR-GAN.
+
+# 2 RELATED WORK
+
+Model fairness The notion of discrimination has many definitions and usually comes from certain social goals that one wants to guarantee. Fairness research has been focused on defining fairness measures that capture a variety of notions of fairness (Verma & Rubin, 2018). There are largely two types of fairness measures: (1) group fairness (Barocas & Selbst, 2016; Hardt et al., 2016), which ensures similar statistics between two sensitive groups; (2) individual fairness (Dwork et al., 2012), which guarantees similar prediction results across nearby examples. Group fairness measures are widely studied in general applications, even though these cannot be simultaneously satisfied in certain circumstances (Kleinberg et al., 2017). In addition, there are also recent significant works that focus on individual fairness (Garg et al., 2018; Yurochkin et al., 2019; Kearns et al., 2019; Jung et al., 2019). Among the two types of fairness with different aspects, we focus on group fairness as our initial research. Recently, there has also been a surge of research on unfairness mitigation techniques (Bellamy et al., 2018). Depending on where a fix occurs, there are mainly three approaches: (1) pre-processing techniques (Kamiran & Calders, 2011; du Pin Calmon et al., 2017; Zemel et al., 2013; Feldman et al., 2015) that fix the training data; (2) in-processing techniques (Zafar et al., 2017; Jiang & Nachum, 2019; Zhang et al., 2018; Kamishima et al., 2012; Cotter et al., 2019; 2018; Agarwal et al., 2018) that address the issue during model training; and (3) post-processing techniques (Hardt et al., 2016; Pleiss et al., 2017; Kamiran et al., 2012) that manipulate predictions while maintaining the model.
+
+Among the three, the in-processing techniques have the advantages that one can work with any data and that there is more control on model training (Venkatasubramanian, 2019). FAIRNESS CONSTRAINTS (Zafar et al., 2017) incorporates a regularization term that reflects fairness constraints in the context of convex margin-based classifiers such as logistic regression and support vector machines (SVMs). The main hyperparameter is the $\lambda$ term, which serves to balance the accuracy and fairness objectives. LABEL BIAS CORRECTION (Jiang & Nachum, 2019) assumes the existence of true yet possibly biased labels. A reweighting algorithm is proposed with theoretical guarantees that training on the resulting loss corresponds to training on the true unbiased labels, which yields a fair model. Here the hyperparameters include the number of training iterations. Finally, ADVERSARIAL
+
+![](images/587d93eae3dc45b7462314f369f8fbc58049c38195c3a2af8d5cd0cbe2723540.jpg)  
+Figure 1: The left figure shows a synthetic dataset with a certain poisoning. Examples are divided into $z = 0$ (marked with circles) and $z = 1$ (crosses) as per a sensitive attribute $z$ . The blue points indicate positive labels while the red points denote negative ones. For data poisoning, we flipped $z$ values that reduce the model accuracy the most (similar to label flipping (Paudice et al., 2018), but specialized for fairness). The right figure shows that poisoning significantly worsens the accuracyfairness tradeoff (i.e., shifts to the left) of the FAIRNESS CONSTRAINTS method (Zafar et al., 2017).
+
+DEBIASING (Zhang et al., 2018) trains a classifier so that an adversary cannot predict the sensitive attributes based on the output of the classifier. Hence, the classifier achieves fairness when its predictions do not have any correlation with sensitive attributes. This idea of adversarial training is similar to GANs (Goodfellow et al., 2014). ADVERSARIAL DEBIASING provides insights of using adversarial training to minimize mutual information between the prediction and sensitive attributes. In this paper, we strengthen the theoretical results of ADVERSARIAL DEBIASING using information theory, and this motivates us to provide systematic methodology for various fairness metrics (Section 4.1).
+
+As we demonstrate in Section 3, the existing techniques are not tailored for robust training, so are vulnerable to data poisoning attacks. In comparison, FR-GAN addresses both model fairness and robust training within the same model training process.
+
+Robust training There is a heavy literature on how to make the model training robust against noisy or even adversarial data (Natarajan et al., 2013; Biggio et al., 2011; Frenay & Verleysen, 2014;´ Kurakin et al., 2017). A major challenge is that there can be a wide range of data poisoning attacks that keep on evolving. One defense approach is to sanitize the training data and thus fix the root cause. A fundamental limitation is that we do not know in general what kind of poisoning will occur, so a universal defense against all possible attacks does not seem feasible as demonstrated by Koh et al. (2018). A more recent trend is to develop general defense algorithms for any attack during model training using meta learning (Veit et al., 2017; Li et al., 2017; Xiao et al., 2015; Hendrycks et al., 2018). Ren et al. (2018) propose a meta-learning framework that employs a clean validation set for the purpose of preventing the model training from being influenced by poisoned data. By using the validation loss as a meta objective, it intends to defend against any poisoning attack. Our FR-GAN framework is inspired by this approach, but employs a GAN-based model to support fair and robust training without using meta learning. In particular, the design of FR-GAN’s robustness discriminator is based on mutual-information-based theoretical insights (Section 4.2). Another line of research is defending against adversarial attacks during test time (Biggio et al., 2013; Goodfellow et al., 2015; Wong & Kolter, 2018). In comparison, our focus is on defending against data poisoning on the training data.
+
+# 3 VULNERABILITY OF FAIRNESS METHODS
+
+We perform experiments to demonstrate that state-of-the-art fairness methods are indeed vulnerable even to simple poisoning attacks. We generate a synthetic dataset as shown in Figure 1a (see the generation details in Section 5.1). There are two non-sensitive attributes $a$ and $b$ , which are reflected in the $\mathbf { X }$ -axis and y-axis, respectively. The examples are further divided into two classes based on the sensitive attribute $z$ . To generate poisoned data, we measure accuracy degradation for a flipping of each $z$ . We then choose the top- $10 \%$ of the $z$ values with the highest degradation and flip them. This approach is similar to the existing label flipping method (Paudice et al., 2018), except that the $z$ value is being flipped instead of the label so that the model fairness is also affected. To make a validation set, we randomly select clean examples that amount to $10 \%$ of the entire training data.
+
+![](images/5ce3b0098e0441d312415d8d3cf93b0e03452037ee45f1e0fe753a8a781d3cb0.jpg)  
+Figure 2: The architecture of FR-GAN.
+
+We use disparate impact (Feldman et al., 2015) as a fairness measure and evaluate one fairness method, called FAIRNESS CONSTRAINTS (Zafar et al., 2017). As this method involves a regularization factor $\lambda$ that balances the accuracy and fairness objectives, we can obtain a tradeoff curve by adjusting its value. Figure 1b shows two accuracy-fairness tradeoff curves obtained with the clean and poisoned synthetic datasets. Notice that adding data poisoning clearly shifts the curve to the left, which means both accuracy and fairness decrease. This coincides with our intuition. The poisoning confuses the model so that there are more biased examples to fix, which in turn makes it overreact and thus sacrifice more on accuracy. In the supplementary, we show similar trends when the data is poisoned via label flipping. In Section 5, we will show how data poisoning affects LABEL BIAS CORRECTION (Jiang & Nachum, 2019) and ADVERSARIAL DEBIASING (Zhang et al., 2018).
+
+# 4 FR-GAN
+
+We now describe FR-GAN, which is shown in Figure 2. Unlike traditional GANs, the generator is a classifier that receives an example $x \in X$ and returns a prediction $\hat { y }$ . The other two discriminators optimize fairness and robustness as we describe in the following sections.
+
+# 4.1 FAIRNESS
+
+We denote by $\mathcal { D } _ { t r }$ the training data set. Suppose $\mathcal { D } _ { t r }$ has $m$ examples $\{ ( \boldsymbol { x } ^ { ( i ) } , \boldsymbol { z } ^ { ( i ) } , \boldsymbol { y } ^ { ( i ) } ) \} _ { i = 1 } ^ { m }$ where $\boldsymbol { x } ^ { ( i ) }$ contains the non-sensitive attributes, $z ^ { ( i ) }$ contains the sensitive attributes, and $\boldsymbol y ^ { ( i ) }$ is the label. Both the sensitive attribute and label can be multi-class, i.e., they can have one of multiple values. For notational simplicity, we assume there is one sensitive attribute, which can be viewed as a merged result of multiple sensitive attributes with a larger alphabet size. For illustrative purposes, we focus on disparate impact, leaving in the supplementary our formulation for equalized odds and equal opportunity.
+
+The first discriminator in FR-GAN distinguishes predictions w.r.t. one sensitive group from those in the others. Disparate impact intends the sensitive attribute to be independent of the model’s prediction, i.e.,
+
+$$
+I ( Z ; { \hat { Y } } ) = 0 .
+$$
+
+We explain how FR-GAN can enforce the above constraint. Let $P _ { Z } ( z )$ be the distribution of $Z$ where $z \in { \mathcal { Z } }$ and $\mathcal { Z }$ is the set of possible sensitive attribute values. Let $\hat { Y } | Z = z \sim P _ { \hat { Y } | z } ( \cdot )$ and $\hat { Y } \sim P _ { \hat { Y } } ( \cdot )$ . Then $\begin{array} { r } { P _ { \hat { Y } } ( \cdot ) = \sum _ { z \in \mathcal { Z } } P _ { Z } ( z ) P _ { \hat { Y } | z } ( \cdot ) } \end{array}$ .
+
+We show that mutual information is equivalent to the following expression where the optimal discriminator $\begin{array} { r } { D _ { z } ^ { \star } ( \hat { y } ) = \frac { P _ { \hat { Y } , z } ( \hat { y } , z ) } { P _ { \hat { Y } } ( \hat { y } ) } } \end{array}$ and $\begin{array} { r } { \sum _ { z \in \mathcal { Z } } D _ { z } ^ { \star } ( \hat { y } ) = 1 \forall \hat { y } \in \mathcal { V } } \end{array}$ .
+
+$$
+\begin{array} { r } { I ( Z ; \hat { Y } ) = \operatorname* { m a x } _ { D _ { z } ( \hat { y } ) : \sum _ { z } D _ { z } ( \hat { y } ) = 1 \forall \hat { y } } \sum _ { z \in \mathcal { Z } } P _ { Z } ( z ) \mathbb { E } _ { P _ { \hat { Y } | z } } \left[ \log D _ { z } ( \hat { Y } ) \right] + H ( Z ) . } \end{array}
+$$
+
+While deferring the detailed proof to the supplemental materials, we provide a brief overview of the proof. As the optimization problem in the RHS is convex, we find the optimal dicriminator by solving the KKT conditions. We then show that the maximum value attained by the optimal discriminator is equal to the mutual information by using the properties of mutual information and the generalized Jensen-Shannon divergence (Lin, 1991).
+
+What is more involved than showing the above equality is designing a right optimization problem. One needs to carefully handcraft a plausible optimization problem so that its unique solution matches the desired quantity. Here, we design the above optimization problem via a ‘guess- $\&$ -check’ approach aided by the structural insights across the KL divergences that appear in an alternative expression of mutual information.
+
+We now discuss how to implement the above expression. Since we do not know $P _ { \hat { Y } | z } ( \cdot )$ exactly, we compute the following empirical version:
+
+$$
+\operatorname* { m a x } _ { D _ { z } ( \hat { y } ) : \sum _ { z } D _ { z } ( \hat { y } ) = 1 \forall \hat { y } } \sum _ { z \in \mathcal { Z } } P _ { Z } ( z ) \sum _ { i : z ^ { ( i ) } = z } \frac { 1 } { m _ { z } } \log D _ { z } ( \hat { y } ^ { ( i ) } ) + H ( Z ) .
+$$
+
+Now for sufficiently large $m$ , the number $m _ { z }$ of examples with $z ^ { ( i ) } = z$ is approximately the same as $P _ { Z } ( z ) m$ . Therefore, the above expression becomes:
+
+$$
+\operatorname* { m a x } _ { D _ { z } ( \hat { y } ) : \sum _ { z } D _ { z } ( \hat { y } ) = 1 \forall \hat { y } } \sum _ { z \in \mathcal { Z } } \sum _ { i : z ^ { ( i ) } = z } \frac { 1 } { m } \log D _ { z } ( \hat { y } ^ { ( i ) } ) + H ( Z ) .
+$$
+
+Interestingly, this formulation is exactly the same as that in the original GAN (Goodfellow et al., 2014) when $| \mathcal { Z } | = 2$ . We also remark that our formulation does not require a prior knowledge on $P _ { Z } ( z )$ .
+
+# 4.2 ROBUSTNESS
+
+We utilize a clean yet small validation set to ensure robust training. In particular, we add a second discriminator that distinguishes the training data with predictions $\{ ( \bar { x ^ { ( i ) } } , z ^ { ( i ) } , \hat { y } ^ { ( i ) } ) \} _ { i = 1 } ^ { m }$ from the validation set {(x(i)val, z(i)val, y(i)val)}mvali=1 . Intuitively, if the classifier is confused by data poisoning in the training data, then its predictions will not be consistent with the labels of the clean data, and the discriminator would be able to detect that difference. While using a validation set is inspired by the meta learning approach by Ren et al. (2018), we take an adversarial learning approach. A key motivation behind this choice is that our GAN approach introduces a knob that controls the emphasis of robust training. We find that this knob enables FR-GAN to be more robust to the validation set size. See details in Section 5.1.
+
+Our formulation is as follows. Let $V \sim B e r n ( \beta )$ denote whether an example comes from training data $V = 1$ ) or from the validation set $V = 0$ ). We then want to ensure that $V$ is independent of the training data and predictions, i.e., $I ( V ; X , Z , \hat { Y } ) = 0$ , which means the predictions on the training data are indistinguishable from labels of the validation set. This way we can mimic the clean data set while expecting an indirect sanitization effect. We optimize this independence using a formulation similar to that of fairness. Another possible formulation is to use the hard decision value from $D ( \hat { Y } )$ , say $\hat { Z }$ , instead of $Z$ . However, this discriminator can only be trained after the fairness discriminator is trained. Instead, we take an approach that allows us to train the two discriminators at the same time.
+
+# 4.3 ARCHITECTURE
+
+Figure 2 illustrates the architecture of FR-GAN. For the loss function in the generator, we employ the cross entropy loss:
+
+$$
+L _ { 1 } = \frac { 1 } { m } \sum _ { i = 1 } ^ { m } - y ^ { ( i ) } \log \hat { y } ^ { ( i ) } - ( 1 - y ^ { ( i ) } ) \log ( 1 - \hat { y } ^ { ( i ) } ) .
+$$
+
+As per Theorem 1, we set the loss function w.r.t. the fairness discriminator as:
+
+$$
+L _ { 2 } = \operatorname* { m a x } _ { D ( \cdot ) } \sum _ { z \in \mathcal { Z } } \sum _ { i : z ^ { ( i ) } = z } \frac { 1 } { m } \log D _ { z } ( \hat { y } ^ { ( i ) } ) + H ( Z )
+$$
+
+where $D ( \cdot ) : = ( D _ { 1 } ( \cdot ) , \ldots , D _ { | \mathcal { Z } | } ( \cdot ) )$ . The condition $\begin{array} { r } { \sum _ { z \in \mathcal { Z } } D _ { z } ^ { \star } ( \hat { Y } ) = 1 } \end{array}$ can be enforced by adding a softmax layer to the discriminator.
+
+Table 1: Accuracy and fairness performances on the clean and poisoned synthetic datasets w.r.t. disparate impact. Two types of methods are compared: (1) non-fairness methods: logistic regression (LR), the meta learning by Ren et al. (2018) (ML), and R-GAN (FR-GAN with $\lambda _ { 1 } = 0$ ); (2) fairness-only methods: FAIRNESS CONSTRAINTS (Zafar et al., 2017) (FC), LABEL BIAS CORRECTION (Jiang & Nachum, 2019) (LBC), and ADVERSARIAL DEBIASING (Zhang et al., 2018) (AD). Also $ { { ^ { 6 } + \mathrm { L D } ^ { \prime } } }$ denotes loss defense (Koh et al., 2018) (a data sanitization technique that is applied prior to model training). For FR-GAN, the validation set is $10 \%$ of $\mathcal { D } _ { t r }$ . For each fairness or accuracy result of the poisoned data, we make a comparison with the clean data result and show the percentage increase or decrease.
+
+<table><tr><td>Type</td><td>Method</td><td colspan="2">Clean data</td><td colspan="2">Poisoned data</td></tr><tr><td></td><td></td><td>D. impact</td><td>Acc.</td><td>D. impact</td><td>Acc.</td></tr><tr><td rowspan="3">Non-fair</td><td>LR</td><td>0.409</td><td>0.885</td><td>0.436 (6.60% ↑)</td><td>0.876 (1.02% ↓)</td></tr><tr><td>ML</td><td>0.429</td><td>0.883</td><td>0.386 (10.0% ↓)</td><td>0.884 (0.11% ↑)</td></tr><tr><td>R-GAN</td><td>0.414</td><td>0.883</td><td>0.338 (18.4% ↓)</td><td>0.884 (0.11% ↑)</td></tr><tr><td rowspan="6">Fair-only</td><td>FC</td><td>0.822</td><td>0.806</td><td>0.756 (8.03% ↓</td><td>0.655 (18.7% ↓)</td></tr><tr><td>LBC</td><td>0.819</td><td>0.760</td><td>0.816 (0.37% √</td><td>0.738 (2.89% ↓)</td></tr><tr><td>AD</td><td>0.807</td><td>0.811</td><td>0.711 (11.9% ↓</td><td>0.812 (0.12% ↑)</td></tr><tr><td>FC+LD</td><td>0.822</td><td>0.806</td><td>0.763 3 (7.18% ↓</td><td>0.651 (19.2% ↓)</td></tr><tr><td>LBC+LD</td><td>0.819</td><td>0.760</td><td>0.513 (37.4% ↓</td><td>0.859 (13.0% ↑)</td></tr><tr><td>AD+LD</td><td>0.807</td><td>0.811</td><td>0.730 (9.54% ↓)</td><td>0.818 (0.86% ↑)</td></tr><tr><td>Both</td><td>FR-GAN</td><td>0.813</td><td>0.809</td><td>0.830 (2.09% ↑)</td><td>0.808 (0.12% ↓)</td></tr></table>
+
+Finally, implementing $I ( V ; X , Z , { \hat { Y } } )$ as advised by Theorem 1, we set the loss function w.r.t. the robustness discriminator as:
+
+$$
+L _ { 3 } = \operatorname* { m a x } _ { D ^ { r } ( \cdot ) } \sum _ { i : v ^ { ( i ) } = 0 } \frac { 1 } { m } \log D ^ { r } ( x ^ { ( i ) } , z ^ { ( i ) } , \hat { y } ^ { ( i ) } ) + \sum _ { i : v ^ { ( i ) } = 1 } \frac { 1 } { m } \log ( 1 - D ^ { r } ( x ^ { ( i ) } , z ^ { ( i ) } , \hat { y } ^ { ( i ) } ) ) + H ( V ) .
+$$
+
+The final objective function is to minimize the weighted sum of these value functions:
+
+$$
+\operatorname * { m i n } _ { G ( \cdot ) } L _ { 1 } + \lambda _ { 1 } L _ { 2 } + \lambda _ { 2 } L _ { 3 } .
+$$
+
+Here $\lambda _ { 1 }$ and $\lambda _ { 2 }$ are tuning knobs that play roles to emphasize fair and robust training, respectively.
+
+# 5 EXPERIMENTS
+
+We provide experimental results for disparate impact, while leaving in the supplementary those for equalized odds and equal opportunity. All of our results are on a separate test set. More implementation details are also in the supplementary.
+
+# 5.1 SYNTHETIC DATA RESULTS
+
+For the synthetic data, we generate 2,000 examples with two non-sensitive attributes $a$ and $b$ , a sensitive attribute $z$ , and a label $y$ , using a method similar to the algorithm proposed by Zafar et al. (2017). Both $z$ and $y$ are binary and generated uniformly at random. For the four possible $( z , y )$ combinations, we generate different normal distributions for $a$ and $b$ . Finally for each example, the $a$ and $b$ values are sampled as per the normal distribution associated with the $( z , y )$ pair. For data poisoning, we flip the $z$ values of examples so as to lower the model’s accuracy the most as described in Section 3.
+
+To make a fair comparison in the context of robust training, we also improve the existing fairness methods with data sanitization and compare them with FR-GAN. Since FR-GAN is one of the first works to address both fairness and robustness, there are few baselines to compare with. Hence, we employed one reasonable baseline, which first sanitizes the poisoned data using a well-known sanitization technique and then performs each fairness algorithm. There are several sanitization techniques surveyed in Koh et al. (2018), and we choose the loss defense method. Here examples that are not well fit by the model and result in a high loss are considered poisoned and are subsequently discarded. Loss defense is the only method that utilizes the trained model and thus has the best chance of defending poisoning attacks.
+
+![](images/ac4f63a08631dca21653d0b3eb1db537af5a3468c9de0cabedee83a448f2adb6.jpg)  
+Figure 3: Accuracy-fairness tradeoff curves.
+
+Accuracy and fairness We compare FR-GAN with FAIRNESS CONSTRAINTS (Zafar et al., 2017), LABEL BIAS CORRECTION (Jiang & Nachum, 2019), ADVERSARIAL DEBIASING (Zhang et al., 2018), and a plain non-fairness method, logistic regression. We also compare with the meta learning approach by Ren et al. (2018), which focuses on robust training. For this comparison, we tailor our framework to a setting where $\lambda _ { 1 } = 0$ (no fairness constraint), and name it R-GAN. For FR-GAN, we use a validation set that amounts to $10 \%$ of $\mathcal { D } _ { t r }$ . When setting $\lambda _ { 1 }$ and $\lambda _ { 2 }$ , we usually fix $\lambda _ { 2 }$ to some value and then adjust $\lambda _ { 1 }$ . For the clean data, we apply proper hyperparameters so that the disparate impacts are similar (around 0.8) across all distinct methods. We do the same for the poisoned data. There is no such hyperparameter tuning for logistic regression and the meta learning by Ren et al. (2018), as the frameworks have no knob for adjusting fairness. We find that this leads to poor disparate impacts. For the three fairness methods, data poisoning aggravates performances in accuracy, fairness or both. For example, the disparate impact and accuracy of FAIRNESS CONSTRAINTS fall by $8 . 0 3 \%$ and $1 8 . 7 \%$ , respectively. On the other hand, the performance changes for FR-GAN are negligible: disparate impact increases by $2 . 0 9 \%$ , and accuracy decreases by $0 . 1 2 \%$ . Table 1 also shows that combining the fairness methods with loss defense (rows 6–8) does not always yield better accuracy and fairness. In fact, using the loss defense may lower the accuracy or fairness (e.g., $\mathrm { L B C + L D }$ has a disparate impact of 0.513 on poisoned data while LBC has 0.816). Perhaps this is because the data sanitization sometimes mistakenly discards clean data as well. The results demonstrate that even a data sanitization technique may not help much. In the supplementary, we also perform experiments using equalized odds and show that FR-GAN has similar benefits.
+
+We observe how accuracy trades off with fairness on clean and poisoned datasets. The results for FAIRNESS CONSTRAINTS are shown in Figure 1b. For LABEL BIAS CORRECTION, we employ the number of training iterations as a knob to trade accuracy off fairness. As shown in Figure 3a, the tradeoff curve shifts to the left, which demonstrates a clear tradeoff degradation. For ADVERSARIAL DEBIASING, we employ the $\alpha$ parameter (Zhang et al., 2018) analogous to $\lambda _ { 1 }$ as a knob to trade accuracy off fairness. We see in Figure 3b that the tradeoff curve again shifts to the left.
+
+Validation set size Figures 3c to 3e show how the validation set size affects the robustness of FRGAN. In particular, we compare the accuracy-fairness tradeoff of FR-GAN on clean data and that on poisoned data while varying the size of the validation set. When running on poisoned data, we fixed $\lambda _ { 2 } = 0 . 2$ and varied $\lambda _ { 1 }$ . We see that even $2 \%$ validation set (Figure 3d) is sufficient to maintain the accuracy and fairness obtained on the clean data. When using $0 . 5 \%$ (Figure 3e), the validation set is too small and has an adverse effect on the training. However, our framework includes a tuning knob $\lambda _ { 2 }$ , so by decreasing $\lambda _ { 2 }$ down to 0.1, we could de-emphasize robust training, thereby avoiding the adverse effect (Figure 3f). This is in contrast to the meta learning approach, which suffers from a non-negligible performance degradation for a very small validation set. See details in the supplementary. The results show that only a holistic framework like FR-GAN can achieve both excellent model fairness and training robustness. In comparison, other methods tailored for only one of these objectives lose either accuracy, fairness or both.
+
+Ablation study (Without ‘R’) For a small value of $\lambda _ { 2 }$ , we observe in Figure 3f that the accuracyfairness tradeoff curve shifts to the left, just like other fairness-only methods. To make the comparison clearer, we also plot them together in the supplementary. (Without ‘F’) When $\lambda _ { 1 } = 0$ , FR-GAN is expected to behave similarly to the other non-fair algorithms. The performance of FR-GAN with $\lambda _ { 1 } = 0$ , which we dub as R-GAN, is reported in Table 1. One can observe that R-GAN achieves a poor fairness performance just like the other non-fair algorithms.
+
+# 5.2 REAL DATA RESULTS
+
+We use the following benchmark datasets: ProPublica COMPAS (Angwin et al., 2016) and Adult Census (Kohavi, 1996). For sensitive attributes, we use SEX for both datasets. We do not employ the German Credit data set (Dua & Graff, 2017) as its highly biased towards positive labels. With such dataset, it is nearly impossible to observe any meaningful tradeoff.
+
+For data poisoning, we use the same method employed on synthetic data: flipping the $z$ values so as to maximize the accuracy performance degradation. While there may be stronger attacks, this poisoning attack is effective enough to fool the three fairness methods. In the supplementary, we also evaluate FR-GAN against label flipping attacks and show similar results. We use the same constructions for the validation set and poisoning as described in Section 3.
+
+Accuracy and fairness See Table 2. As in Table 1, we apply proper hyperparameters so that disparate impacts are similar across all distinct methods, both for the clean and poisoned datasets. The results are similar to Table 1: logistic regression and meta learning exhibit poor disparate impacts; the three fairness methods have worse disparate impact and accuracy due to data poisoning; and FR-GAN again shows little degradation both in fairness and accuracy. Table 2 also shows that combining the fairness methods with loss defense (rows 6–8 and 15–17) does not always yield better accuracy and fairness and may even lower them, which is consistent to the results on synthetic data.
+
+# 6 DISCUSSION
+
+In this section, we discuss possible ways to extend FR-GAN.
+
+Subjective labels FR-GAN can be generalized to a setting where labels are subjective instead of being clean or poisoned. Here the dataset without the undesirable human biases becomes the clean validation set. In general, given two datasets with different distributions where one of them is desirable, FR-GAN can train robustly against the other distribution.
+
+Constructing real datasets We propose a general methodology for constructing a real dataset that has both bias and poisoning, as well as a “clean” validation set. Suppose that we are performing evaluation tasks (say loan decisions) where there is a high chance of human bias (i.e., poisoning) due to the high workload. We can construct a clean validation set by selecting a few tasks, assigning more evaluators, and taking a majority vote of the evaluations to minimize the bias. While employing more evaluators can be expensive, constructing a small validation set is sufficient for robust training, which makes this method practical.
+
+Generalizing to all attacks An interesting question is whether FR-GAN can defend against all poisoning attacks. If we know all the possible attacks, we can construct a training set containing these attacks. In the more challenging case where we do not know which attacks even exist, there seems to be a fundamental limitation in protecting against the attacks. Generalization is a universal problem in machine learning where a model trained on one dataset is not guaranteed to perform well in another dataset with a different distribution. Although the generalization is a critical issue to address, it is currently beyond the scope of this paper.
+
+Table 2: Accuracy and fairness performances on real data for disparate impact. Two types of methods are compared: (1) non-fairness methods: logistic regression (LR), the meta learning by Ren et al. (2018) (ML), and R-GAN (FR-GAN with $\lambda _ { 1 } = 0$ ); (2) fairness-only methods: FAIRNESS CONSTRAINTS (Zafar et al., 2017) (FC), LABEL BIAS CORRECTION (Jiang & Nachum, 2019) (LBC), and ADVERSARIAL DEBIASING (Zhang et al., 2018) (AD). Also $ { { ^ { 6 } + \mathrm { L D } ^ { \prime } } }$ denotes loss defense (Koh et al., 2018) (a data sanitization technique that is applied prior to model training). For FR-GAN, the validation set is $10 \%$ of $\mathcal { D } _ { t r }$ . For each fairness or accuracy result of the poisoned data, we compare with the clean data result and show the percentage increase or decrease.   
+
+<table><tr><td>Dataset</td><td>Type</td><td>Method</td><td colspan="2">Clean data</td><td colspan="2">Poisoned data</td></tr><tr><td></td><td></td><td></td><td>D. impact</td><td>Acc.</td><td>D. impact</td><td>Acc.</td></tr><tr><td rowspan="10"></td><td>Non-fair</td><td>LR</td><td>0.465</td><td>0.674</td><td>0.431 (7.31% ↓)</td><td>0.667 (1.04% ↓)</td></tr><tr><td></td><td>ML</td><td>0.493</td><td>0.680</td><td>0.164 (66.7% ↓)</td><td>0.661 (2.79% ↓)</td></tr><tr><td></td><td>R-GAN</td><td>0.574</td><td>0.683</td><td>0.393 (31.5% ↓)</td><td>0.650 (4.83% ↓)</td></tr><tr><td></td><td>FC</td><td>0.777</td><td>0.682</td><td>0.790 (1.67% ↑)</td><td>0.671 (1.61% ↓)</td></tr><tr><td>Fair-only</td><td>LBC</td><td>0.866</td><td>0.671</td><td>0.807 (6.81% ↓)</td><td>0.615 (8.35% ↓)</td></tr><tr><td></td><td>AD</td><td>0.846</td><td>0.680</td><td>0.822 (2.84% ↓)</td><td>0.655 (3.68% ↓)</td></tr><tr><td></td><td>FC + LD</td><td>0.777</td><td>0.682</td><td>0.790 (1.67% ↑)</td><td>0.668 (2.05% ↓)</td></tr><tr><td></td><td>LBC +LD AD + LD</td><td>0.866</td><td>0.671</td><td>0.822 (5.08% ↓)</td><td>0.628 (6.41% ↓)</td></tr><tr><td></td><td></td><td>0.846</td><td>0.680</td><td>0.836 (1.18% ↓)</td><td>0.620 (8.82% ↓)</td></tr><tr><td>Both</td><td>FR-GAN</td><td>0.936</td><td>0.667</td><td>0.947 (1.18% ↑)</td><td>0.660 (1.05% ↓)</td></tr><tr><td rowspan="10">Adult</td><td>Non-fair</td><td>LR</td><td>0.328</td><td>0.847</td><td>0.230 (29.9% ↓)</td><td>0.848 (0.12% 个)</td></tr><tr><td></td><td>ML</td><td>0.346</td><td>0.844</td><td>0.215 (37.9% ↓)</td><td>0.843 (0.12% ↓)</td></tr><tr><td></td><td>R-GAN</td><td>0.335</td><td>0.847</td><td>0.285 (14.9% ↓)</td><td>0.834 (1.53% ↓)</td></tr><tr><td></td><td>FC</td><td>0.825</td><td>0.826</td><td>0.816 (1.09% ↓)</td><td>0.828 (0.24% ↑)</td></tr><tr><td></td><td>LBC</td><td>0.825</td><td>0.825</td><td>0.825 (0.00% -)</td><td>0.795 (3.64% ↓)</td></tr><tr><td>Fair-only</td><td>AD</td><td>0.850</td><td>0.767</td><td>0.679 (20.1% ↓)</td><td>0.754 (1.69% ↓)</td></tr><tr><td></td><td>FC + LD</td><td>0.825</td><td>0.826</td><td>0.798 (3.27% ↓)</td><td>0.807 (2.30% ↓)</td></tr><tr><td></td><td>LBC + LD</td><td>0.825</td><td>0.825</td><td>0.815 (1.21% ↓)</td><td>0.811 (1.70% ↓)</td></tr><tr><td></td><td>AD + LD</td><td>0.850</td><td>0.767</td><td>0.821 1 (3.41% ↓)</td><td>0.728 (5.08% ↓)</td></tr><tr><td>Both</td><td>FR-GAN</td><td>0.870</td><td>0.819</td><td>0.866 (0.46% ↓)</td><td>0.827 (0.98% ↑)</td></tr></table>
+
+# 7 CONCLUSION
+
+We proposed FR-GAN, which is a holistic framework that enables both unfairness mitigation and robust training. Our key contribution is proposing a novel GAN architecture that enjoys the synergistic effect of combining two approaches: (1) employing a fairness discriminator that distinguishes predictions w.r.t. one sensitive group from others and (2) employing a robust discriminator that distinguishes training data with predictions from a clean yet small validation set. We showed that existing fairness methods are vulnerable to data poisoning, even when combined with data sanitization techniques. In comparison, FR-GAN is robust to the poisoning and can be adjusted to maintain reasonable accuracy and fairness even if the validation set is too small or unavailable. We showed that FR-GAN is guaranteed to maximize fairness and supports all the prominent fairness measures: disparate impact, equalized odds, and equal opportunity.
+
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+
+# A APPENDIX
+
+# A.1 PROOF FOR THEOREM 1
+
+Before we present the proof of the main theorem, we first recall our notation. Let $P _ { Z } ( z )$ be the distribution of $Z$ where $z \in { \mathcal { Z } }$ and $\mathcal { Z }$ is the set of possible sensitive attribute values. Let ${ \hat { Y } } | Z =$ $z \sim P _ { \hat { Y } | z } ( \cdot )$ and $\hat { Y } \sim P _ { \hat { Y } } ( \cdot )$ . Then $\begin{array} { r } { P _ { \hat { Y } } ( \cdot ) = \sum _ { z \in \mathcal { Z } } P _ { Z } ( z ) P _ { \hat { Y } | z } ( \cdot ) } \end{array}$ . Also, let $Y \sim P _ { Y } ( \cdot )$ .
+
+For convenience, let us repeat the statement of Theorem 1 here:
+
+$$
+I ( Z ; \hat { Y } ) = \operatorname* { m a x } _ { \substack { D _ { z } ( \hat { y } ) : \sum _ { z } D _ { z } ( \hat { y } ) = 1 , \forall \hat { y } } } \ \sum _ { z \in Z } P _ { Z } ( z ) \mathbb { E } _ { P _ { \hat { Y } | z } } \left[ \log D _ { z } ( \hat { Y } ) \right] + H ( Z ) .
+$$
+
+We now prove the theorem.
+
+Proof. Denote by $_ D$ the collection of $D _ { z } ( \hat { y } )$ for all possible values of $z$ and $\hat { y }$ , and by $\pmb { \nu }$ the collection of $\nu _ { \hat { y } }$ for all values of $\hat { y }$ . We can construct the Lagrangian function as follows:
+
+$$
+\mathcal { L } ( D , \nu ) = \sum _ { z \in \mathcal { Z } } P _ { \mathcal { Z } } ( z ) \mathbb { E } _ { P _ { \hat { Y } | z } } \left[ \log D _ { z } ( \hat { Y } ) \right] + H ( Z ) + \sum _ { \hat { y } \in \mathcal { Y } } \nu _ { \hat { y } } \left( 1 - \sum _ { z \in \mathcal { Z } } D _ { z } ( \hat { y } ) \right) .
+$$
+
+We use the following KKT conditions:
+
+$$
+\begin{array} { r l r l } & { \displaystyle \frac { \partial \mathcal { L } ( D , \nu ) } { \partial D _ { z } ( \hat { y } ) } = P _ { Z } ( z ) \frac { P _ { \hat { Y } | z } ( \hat { y } ) } { D _ { z } ^ { \star } ( \hat { y } ) } - \nu _ { \hat { y } } ^ { \star } = 0 , \quad } & & { \forall ( \hat { y } , z ) \in \mathcal { Y } \times \mathcal { Z } , } \\ & { 1 - \displaystyle \sum _ { z \in \mathcal { Z } } D _ { z } ^ { \star } ( \hat { y } ) = 0 , \quad } & & { \forall \hat { y } \in \mathcal { Y } . } \end{array}
+$$
+
+Solving the two equations, we obtain $\nu _ { \hat { y } } ^ { \star } = P _ { \hat { Y } } ( \hat { y } )$ for all $\hat { y }$ . Thus,
+
+$$
+D _ { z } ^ { \star } ( \hat { y } ) = \frac { P _ { Z } ( z ) P _ { \hat { Y } | z } ( \hat { y } ) } { P _ { \hat { Y } } ( \hat { y } ) } .
+$$
+
+Putting this to the above optimization,
+
+$$
+\begin{array} { r l } & { \quad \displaystyle \sum _ { z \in \mathcal { Z } } F _ { \mathcal { Z } } ( z ) \mathbb { E } _ { P _ { \hat { \mathcal { Y } } _ { 1 } } } \left[ \log \frac { P _ { \mathcal { Z } } ( z ) P _ { \hat { \mathcal { Y } } _ { 1 } | z } ( \hat { \mathcal { Y } } ) } { P _ { \hat { \mathcal { Y } } _ { 1 } } ( \hat { \mathcal { Y } } ) } \right] + H ( Z ) } \\ & { = \displaystyle \sum _ { z \in \mathcal { Z } } P _ { \mathcal { Z } } ( z ) \mathbb { E } _ { P _ { \hat { \mathcal { Y } } _ { 1 } | z } } \left[ \log \frac { P _ { \mathcal { Z } } ( z ) P _ { \hat { \mathcal { Y } } _ { 1 } | z } ( \hat { \mathcal { Y } } ) } { P _ { \hat { \mathcal { Y } } } ( \hat { \mathcal { Y } } ) } \right] + \displaystyle \sum _ { z \in \mathcal { Z } } P _ { \mathcal { Z } } ( z ) \log \frac { 1 } { P _ { \mathcal { Z } } ( z ) } } \\ & { = \displaystyle \sum _ { z \in \mathcal { Z } } P _ { \mathcal { Z } } ( z ) \mathbb { E } _ { P _ { \hat { \mathcal { Y } } _ { 1 } | z } } \left[ \log \frac { P _ { \hat { \mathcal { Y } } _ { 1 } | z } ( \hat { \mathcal { Y } } ) } { P _ { \hat { \mathcal { Y } } } ( \hat { \mathcal { Y } } ) } \right] } \\ & { = \displaystyle \sum _ { z \in \mathcal { Z } } P _ { \mathcal { Z } } ( z ) D _ { \mathrm { R L } } ( P _ { \hat { \mathcal { Y } } _ { 1 } | z } | \mathbb { P } _ { \hat { \mathcal { Y } } } ) } \\ & { \overset { \mathrm { ( a ) } } { \ = } \displaystyle \sum _ { z \in \mathcal { Z } } \left( P _ { \mathcal { Y } } \mathbf { _ { \hat { \mathcal { Y } } _ { 1 } | z } } , \mathbf { ( ) } P _ { \hat { \mathcal { Y } } _ { 1 } | z } \right) = I ( \mathcal { Z } ; \hat { \mathcal { Y } } ) . } \end{array}
+$$
+
+Here, the second last equality is due to the definition of the generalized JS divergence, and the last equality is due to its equivalence to the mutual information (Lin, 1991). □
+
+# A.2 EXTENSIONS TO OTHER FAIRNESS MEASURES
+
+The following theorem relates the conditional mutual information $I ( Z ; { \hat { Y } } | Y )$ to the solution of an optimization problem.
+
+# Theorem 2.
+
+$$
+I ( Z ; \hat { Y } | Y ) = \operatorname* { m a x } _ { \substack { D _ { z | y ( \hat { y } ) } : \sum _ { z \in \mathcal { Z } } D _ { z | y } ( \hat { y } ) = 1 ; \forall \hat { y } } } \sum _ { y \in \mathcal { Y } } \sum _ { y \in \mathcal { Z } } P _ { Y , Z } ( y , z ) \mathbb { E } _ { P _ { \hat { Y } | y , z } } \left[ \log D _ { z | y } ( \hat { Y } ) \right] + H ( Z | Y ) .
+$$
+
+Recall that this conditional mutual information term can be used to capture equalized odds, which is another important fairness metric. We also note that the following theorem can be modified in a straightforward manner so that it can handle $I ( Z ; { \hat { Y } } | Y = 1 )$ , which can be used to capture equal opportunity.
+
+We now prove the theorem.
+
+Proof. Denote by $_ D$ the collection of $D _ { z | y } ( \hat { y } )$ for all possible values of $( z , \hat { y }$ , and $y$ ) and by $\pmb { \nu }$ the collection of $\nu _ { y , \hat { y } }$ for all values of $y$ and $\hat { y }$ . We can construct the Lagrangian function as follows:
+
+$$
+: ( D , \nu ) = \sum _ { y \in \mathcal { Y } } \sum _ { z \in \mathcal { Z } } P _ { Y , \mathcal { Z } } ( y , z ) \mathbb { E } _ { P _ { \mathcal { Y } | y , z } } \left[ \log D _ { z | y } ( \hat { Y } ) \right] + H ( Z | Y ) + \sum _ { \hat { y } \in \mathcal { Y } } \sum _ { y \in \mathcal { Y } } \nu _ { y , \hat { y } } \left( 1 - \sum _ { z \in \mathcal { Z } } D _ { z | y } ( \hat { y } ) \right)
+$$
+
+We use the following KKT conditions:
+
+$$
+\begin{array} { l l } { \displaystyle \frac { \partial \mathcal { L } ( D , \nu ) } { \partial D _ { z | y } ( \hat { y } ) } = P _ { Y , Z } ( y , z ) \frac { P _ { \hat { Y } | y , z } ( \hat { y } ) } { D _ { z | y } ^ { \star } ( \hat { y } ) } - \nu _ { y , \hat { y } } = 0 , \qquad } & { \forall ( \hat { y } , y , z ) \in \mathcal { Y } \times \mathcal { Y } \times \mathcal { Z } } \\ { \displaystyle 1 - \sum _ { z \in \mathcal { Z } } D _ { z | y } ^ { \star } ( \hat { y } ) = 0 , \qquad } & { \forall ( \hat { y } , y ) \in \mathcal { Y } \times \mathcal { Y } . } \end{array}
+$$
+
+Solving the two equations, we obtain $\nu _ { y , \hat { y } } ^ { \star } = P _ { Y , \hat { Y } } ( y , \hat { y } )$ for all $( y , \hat { y } ) \in \mathcal { V } \times \mathcal { V }$ . Thus,
+
+$$
+D _ { z | y } ^ { \star } ( \hat { y } ) = \frac { P _ { Z | y } ( z ) P _ { \hat { Y } | y , z } ( \hat { y } ) } { P _ { \hat { Y } | y } ( \hat { y } ) } , \forall y , \hat { y } \in \mathcal { V } \times \mathcal { V } .
+$$
+
+Putting this to the above optimization,
+
+$$
+\begin{array} { r l } & { \quad \displaystyle \sum _ { y \geq \tau \leq t } \sum _ { w \leq t } \hat { \gamma } _ { x \geq t } \| w _ { \hat { \gamma } _ { x \geq t } } \| _ { \mathcal { X } _ { t - 1 } } \left[ \exp ^ { \beta _ { t } } \hat { \gamma } _ { y \geq t } ( \hat { \gamma } _ { y \geq t } ) \right] ^ { \top } \mid \mathcal { H } ( \mathcal { L } | \mathcal { Y } ) } \\ & { \quad = \displaystyle \sum _ { y \leq t \leq t } \sum _ { w \leq t } \hat { \gamma } _ { x \geq t } \| \mathbf { E } _ { \hat { \gamma } _ { x \geq t } } \left[ \exp ^ { \beta _ { t } } \frac { \hat { \gamma } _ { x \geq t } ( \hat { \gamma } _ { y \geq t } ) \cdot \mathbf { S } _ { y \geq t } \mathcal { Y } _ { t } } { \hat { \gamma } _ { y \geq t } ( \hat { \gamma } _ { t } ) } \right] ^ { \top } + \displaystyle \sum _ { x \leq t \leq t } \sum _ { w \leq t } \hat { \gamma } _ { x \leq t } \hat { \gamma } _ { x \geq t } \| \mathbf { E } _ { \hat { \gamma } _ { x \geq t } } \frac { 1 } { \hat { \gamma } _ { x \geq t } ( \hat { \gamma } _ { t } ) } } \\ & { \quad \quad \quad - \displaystyle \sum _ { y \leq t \leq t } \sum _ { x \leq t } \hat { \gamma } _ { x \geq t } \sum _ { y \leq t } \Big [ \exp ^ { \beta _ { t } } \frac { \hat { \gamma } _ { x \geq t } ( \hat { \gamma } _ { x \geq t } ) } { \hat { \gamma } _ { x \geq t } ( \hat { \gamma } _ { t } ) } \Big ] ^ { \top } } \\ & { \quad \quad = \displaystyle \sum _ { y \leq t \leq t } \sum _ { w \leq t } \hat { \gamma } _ { x \geq t } \| \mathbf { E } _ { \hat { \gamma } _ { x \geq t } } \Big [ \exp ^ { \beta _ { t } } \hat { \gamma } _ { x \geq t } ( \hat { \gamma } _ { t } ) \Big ] } \\ &  \quad \quad = \displaystyle \sum _ { y \leq t \leq t } \sum _ { w \leq t } \hat { \gamma } _ { x \geq t } \| \mathbf { E } _ { \hat { \gamma } _ { x \geq t } } \Big [ \exp ^ { \beta _ { t } } \exp ^ { \beta _ { t } } \exp ^ { \beta _ { t } } \Big [ \exp ^ { \beta _ { t } } \exp ^ { \beta _ { t } } \big [ \exp ^  \beta _  t \end{array}
+$$
+
+The third last equality is due to the definition of the generalized JS divergence; the second last equality is due to its equivalence to the mutual information (Lin, 1991); and the last equality is due to the definition of conditional mutual information. □
+
+We now discuss how to actually compute the mutual information. We compute the following empirical version using the example $\{ ( x ^ { ( i ) } , z ^ { ( i ) } , y ^ { ( i ) } ) \} _ { i = 1 } ^ { m }$ .
+
+$$
+\operatorname* { m a x } _ { \substack { D _ { z | y } ( \hat { y } ) : \sum _ { z \in \mathcal { Z } } D _ { z | y } ( \hat { y } ) = 1 ; \forall \hat { y } } } \sum _ { y \in \mathcal { Y } } \sum _ { z \in \mathcal { Z } } P _ { Y , Z } ( y , z ) \sum _ { \substack { i : ( y ^ { ( i ) } , z ^ { ( i ) } ) = ( y , z ) } } \frac { 1 } { m _ { y , z } } \log D _ { z | y } ( \hat { y } ^ { ( i ) } ) + H ( Z | Y ) .
+$$
+
+![](images/e63154594e7fa2dafeef2ca41ed32600b22ea91cfa4d80b53b27489adca510a0.jpg)  
+Figure 4: The architecture of FR-GAN for equalized odds.
+
+![](images/194ecc6c20785f8f923ae3e10a1b8d08ed63144c03aed7b19466e0c33f92e456.jpg)  
+Figure 5: Accuracy-fairness tradeoff curves for poisoned synthetic data with label flipping $( 7 \% )$ . Now for a sufficiently large value of $m$ , $m _ { y , z } \approx P _ { Y , Z } ( y , z ) m$ . Therefore, the above expression is approximated as:
+
+$$
+\operatorname* { m a x } _ { \substack { D _ { z | y } ( \hat { y } ) : \sum _ { z \in \mathcal { Z } } D _ { z | y } ( \hat { y } ) = 1 ; \forall \hat { y } } } \sum _ { y \in \mathcal { Y } } \sum _ { z \in \mathcal { Z } } \sum _ { \substack { i : ( y ^ { ( i ) } , z ^ { ( i ) } ) = ( y , z ) } } \frac { 1 } { m } \log D _ { z | y } ( \hat { y } ^ { ( i ) } ) + H ( Z | Y ) .
+$$
+
+Hence, we can set $L _ { 2 }$ (i.e., the loss w.r.t. the fairness discriminator) to the above expression. The rest of the objective function is the same. Figure 4 shows the resulting FR-GAN architecture.
+
+# A.3 ADDITIONAL EXPERIMENTS
+
+# A.3.1 SYNTHETIC DATA
+
+We continue our experiments from Sections 3 and 5.1.
+
+Label flipping for data poisoning Figure 5a to 5d show the experimental results when the data is poisoned via label flipping. We used the same synthetic data, as illustrated in Figure 1a, and flipped $7 \%$ of labels from the clean data to make a poisoned data. Figures 5a, 5b, and 5c show the accuracy-fairness tradeoff curves of FAIRNESS CONSTRAINTS, LABEL BIAS CORRECTION, and ADVERSARIAL DEBIASING, respectively. While the tradeoff curves in Figure 5a to 5c considerably shift to the left, Figure 5d shows that FR-GAN is noticeably robust against label flipping.
+
+![](images/d90a163df5d95e49b275f6da4a3905aa1eb677dabb77ed3dea93d5a17d648e3a.jpg)  
+Figure 6: Comparison between ADVERSARIAL DEBIASING (AD) and FR-GAN with small validation set $( 0 . 5 \% )$ on synthetic data.
+
+Meta learning with different validation set sizes Table 3 shows the accuracy and fairness results for the meta learning method by Ren et al. (2018) (ML) for different validation set sizes. We observe a drastic decrease of accuracy when the validation set size is $0 . 1 \%$ of the training data.
+
+Ablation study for fairness Figure 6 shows the accuracy-fairness tradeoff curves for ADVERSARIAL DEBIASING and FR-GAN on the synthetic dataset. ADVERSARIAL DEBIASING tradeoff curves are from Figure 3b, and the FR-GAN curve comes from Figure 3f. We observe in Figure 6 that the accuracy-fairness tradeoff of FR-GAN using a small value of $\lambda _ { 2 }$ on the poisoned data is similar to the results of fairness-only methods.
+
+# A.3.2 REAL DATA
+
+We continue our experiments from Section 5.2.
+
+Label flipping for data poisoning Table 4 uses the same experimental setting as in Table 2, except that data poisoning is label flipping (not w.r.t. sensitive attributes). We observe similar trends as in Table 2. For the non-fairness methods, the fairness results are significantly worse than other methods. For the fairness-only methods, both fairness and accuracy tend to be high on the clean data, but at least one of them decreases significantly on the poisoned data. On the other hand, FR-GAN yields high fairness and accuracy on the clean data and is also the most resilient against poisoned data. The results emphasize our holistic technique that takes both fairness and accuracy into consideration.
+
+# A.3.3 FR-GAN USING OTHER FAIRNESS MEASURES
+
+As we showed in Appendix A.2, FR-GAN respects equalized odds and equal opportunity. Table 5 shows the experimental results on the synthetic and real datasets for equalized odds. We see that FR-GAN significantly improves equalized odds with reasonable accuracy. The results w.r.t. equal opportunity are similar and thus not shown here.
+
+Table 4: Accuracy and fairness performances on real data for disparate impact where the data is poisoned using a label flipping attack (Paudice et al., 2018). Two types of methods are compared: (1) non-fairness methods: logistic regression (LR), the meta learning by Ren et al. (2018) (ML), and R-GAN (FR-GAN with $\lambda _ { 1 } = 0$ ); (2) fairness-only methods: FAIRNESS CONSTRAINTS (Zafar et al., 2017) (FC), LABEL BIAS CORRECTION (Jiang & Nachum, 2019) (LBC), and ADVERSARIAL DEBIASING (Zhang et al., 2018) (AD). Also $ { { ^ { 6 } + \mathrm { L D } ^ { \prime } } }$ denotes loss defense (Koh et al., 2018) (a data sanitization technique that is applied prior to model training). For FR-GAN, the validation set is $10 \%$ of $\mathcal { D } _ { t r }$ . For each fairness or accuracy result of the poisoned data, we make a comparison with the clean data result and show the percentage increase or decrease.   
+
+<table><tr><td>Dataset</td><td>Type</td><td>Method</td><td colspan="2">Clean data</td><td colspan="2">Poisoned data</td></tr><tr><td></td><td></td><td></td><td>D. impact</td><td>Acc.</td><td>D. impact</td><td>Acc.</td></tr><tr><td rowspan="9"></td><td rowspan="3">Non-fair</td><td>LR</td><td>0.465</td><td>0.674</td><td>0.856 (84.1% 个)</td><td>0.487 (27.7% ↓)</td></tr><tr><td>ML</td><td>0.493</td><td>0.680</td><td>0.608 (23.3% 个)</td><td>0.629 (7.50% ↓)</td></tr><tr><td>R-GAN</td><td>0.574</td><td>0.683</td><td>0.919 (60.1% ↑)</td><td>0.621 (9.08% ↓)</td></tr><tr><td rowspan="6">Fair-only</td><td>FC</td><td>0.777</td><td>0.682</td><td>0.931 (19.8% ↑)</td><td>0.490 (28.2% ↓)</td></tr><tr><td>LBC</td><td>0.866</td><td>0.671</td><td>0.945 (9.12% ↑)</td><td>0.488 (27.3% ↓)</td></tr><tr><td>AD</td><td>0.846</td><td>0.680</td><td>0.941 (11.2% ↑)</td><td>0.615 (9.56% ↓)</td></tr><tr><td>FC +LD</td><td>0.777</td><td>0.682</td><td>0.820 (5.53% ↑)</td><td>0.544 (20.2% ↓)</td></tr><tr><td>LBC +LD</td><td>0.866</td><td>0.671</td><td>0.928 (7.16% ↑)</td><td>0.550 (18.0% ↓)</td></tr><tr><td>AD + LD</td><td>0.846</td><td>0.680</td><td>0.822 (2.84% ↓)</td><td>0.614 (9.71% ↓)</td></tr><tr><td rowspan="9"></td><td rowspan="3">Both Non-fair</td><td>FR-GAN</td><td>0.936</td><td>0.667</td><td>0.964 (2.99% ↑)</td><td>0.621 (6.90% ↓)</td></tr><tr><td>LR</td><td>0.328</td><td>0.847</td><td>0.316 (3.66% ↓)</td><td>0.824 (2.72% ↓)</td></tr><tr><td>ML R-GAN</td><td>0.346 0.335</td><td>0.844</td><td>0.413 (19.4% ↑)</td><td>0.826 (2.13% ↓) 0.833 (2.13% ↓)</td></tr><tr><td rowspan="6">Fair-only</td><td>FC</td><td></td><td>0.847</td><td>0.342 (2.09% ↑)</td><td></td></tr><tr><td>LBC</td><td>0.825</td><td>0.826</td><td>0.814 (1.33% ↓)</td><td>0.802 (2.91% ↓)</td></tr><tr><td>AD</td><td>0.825 0.850</td><td>0.825</td><td>0.734 (11.0% ↓) 0.652 (23.3% ↓)</td><td>0.819 (0.73% ↓)</td></tr><tr><td>FC +LD</td><td>0.825</td><td>0.767 0.826</td><td>0.762 (7.64% ↓)</td><td>0.749 (2.35% ↓)</td></tr><tr><td></td><td>0.825</td><td></td><td>0.720 (12.7% ↓)</td><td>0.831 (0.61% ↑)</td></tr><tr><td>LBC +LD AD + LD</td><td>0.850</td><td>0.825 0.767</td><td>0.761 (10.5% ↓)</td><td>0.827 (0.24% 个)</td></tr><tr><td>Both</td><td>FR-GAN</td><td>0.870</td><td>0.819</td><td>0.859 (1.26% ↓)</td><td>0.803 (4.69% ↑) 0.789 (3.66% ↓)</td></tr></table>
+
+Table 5: Accuracy and fairness performances on synthetic and real datasets w.r.t. equalized odds. Two algorithms are compared: (1) logistic regression (LR, non-fairness method) and (2) FR-GAN.   
+
+<table><tr><td>Dataset</td><td>Method</td><td>Equalized odds</td><td></td><td> Accuracy</td></tr><tr><td></td><td></td><td>Y=0</td><td>Y=1</td><td></td></tr><tr><td rowspan="2">Synthetic Data</td><td>LR</td><td>0.351</td><td>0.804</td><td>0.885</td></tr><tr><td>FR-GAN</td><td>0.888</td><td>0.936</td><td>0.865</td></tr><tr><td rowspan="2">Compas</td><td>LR</td><td>0.427</td><td>0.557</td><td>0.674</td></tr><tr><td>FR-GAN</td><td>0.718</td><td>0.959</td><td>0.628</td></tr><tr><td rowspan="2">AdultCensus</td><td>LR</td><td>0.286</td><td>0.909</td><td>0.848</td></tr><tr><td>FR-GAN</td><td>0.503</td><td>0.917</td><td>0.842</td></tr></table>
+
+# A.4 TRAINING METHODOLOGY
+
+We implement all algorithms in PyTorch (Paszke et al., 2017), and all experiments are performed on a server with Intel i7-6850 CPUs.
+
+The generator $G$ is a neural network with zero or one hidden layer. The discriminator $D ^ { f }$ is a single layer neural network, and the discriminator $D ^ { r }$ is a neural network with one hidden layer. We used 8 or 16 nodes in the hidden layers. We set an Adam optimizer (Kingma & Ba, 2014) for the generator, and a stochastic gradient descent (SGD) optimizer for each discriminator. We empirically observe that one can stabilize the training procedure by freezing the parameters of the fairness discriminator $D ^ { f }$ for the initial phase of training. Thus, we choose to freeze the parameters of the fairness discriminator $D ^ { f }$ for the first few epochs until the generator achieves a certain accuracy. We use the generator/discriminator update ratio of 1:1 for the first 300 epochs and use the update ratio of 1:3 (or 1:5) for the rest of training.
+
+Table 6: Confusion matrix on poisoned AdultCensus dataset w.r.t. disparate impact. Two algorithms are compared: (1) AD and (2) FR-GAN. For a fair comparison, we use data sanitization before running AD.   
+
+<table><tr><td></td><td></td><td colspan="2">Female</td><td colspan="2">Male</td></tr><tr><td>Method</td><td></td><td>Prediction = 0</td><td>Prediction = 1</td><td>Prediction = 0</td><td>Prediction = 1</td></tr><tr><td rowspan="2">AD + LD</td><td>True = 0</td><td>2,502</td><td>566</td><td>4,330</td><td>583</td></tr><tr><td>True = 1</td><td>191</td><td>194</td><td>1,551</td><td>714</td></tr><tr><td rowspan="2">FR-GAN</td><td>True = 0</td><td>2,765</td><td>303</td><td>4,611</td><td>302</td></tr><tr><td>True = 1</td><td>95</td><td>290</td><td>1,144</td><td>1,121</td></tr></table>
+
+Table 7: Confusion matrix on poisoned AdultCensus dataset w.r.t. equalized odds. Two algorithms are compared: (1) AD and (2) FR-GAN. For a fair comparison, we use data sanitization before running AD.   
+
+<table><tr><td colspan="2"></td><td colspan="2">Female</td><td colspan="2">Male</td></tr><tr><td colspan="2">Method</td><td>Prediction = 0</td><td>Prediction = 1</td><td>Prediction = 0</td><td>Prediction = 1</td></tr><tr><td rowspan="2">AD + LD</td><td>True = 0</td><td>2,935</td><td>133</td><td>4,629</td><td>284</td></tr><tr><td>True = 1</td><td>249</td><td>136</td><td>1,590</td><td>675</td></tr><tr><td rowspan="2">FR-GAN</td><td>True = 0</td><td>2,859</td><td>209</td><td>4,480</td><td>443</td></tr><tr><td>True = 1</td><td>116</td><td>269</td><td>960</td><td>1,305</td></tr></table>
+
+Also, we use the following details for choosing the values of $\lambda _ { 1 }$ and $\lambda _ { 2 }$ . For clean data, we set $\lambda _ { 2 }$ as a small value (e.g., 0.01) and vary $\lambda _ { 1 }$ from 0 to 0.95. For poisoned data, we set $\lambda _ { 2 }$ as 0.2, 0.3, or 0.4, and vary $\lambda _ { 1 }$ from 0 to $0 . 9 5 - \lambda _ { 2 }$ . Given the values of $\lambda _ { 1 }$ and $\lambda _ { 2 }$ , we also normalize $L _ { 1 }$ (the generator loss) by multiplying it with $\left( 1 - \lambda _ { 1 } - \lambda _ { 2 } \right)$ .
+
+# A.5 ADDITIONAL EXPERIMENTS ON ADULT DATASET
+
+We compare FR-GAN and AD using the AdultCensus dataset and the same poisoning in Section 3. For a fair comparison, we use loss defense (LD) as data sanitization prior to running AD. We generate confusion matrices both for disparate impact (DI) and equalized odds (EO). Overall, FRGAN performs better than AD because of its robustness discriminator. The robustness discriminator successfully ignores the poisoned distribution in the training data, and FR-GAN’s TPR is higher than AD with sanitization. Table 6 shows confusion matrices as results of disparate-impact-focused experiment. The results are reported when AD achieves (Acc, $\mathrm { D I } ) = ( 0 . 7 2 8 $ , 0.821), and FR-GAN achieves (Acc, $\mathrm { D I } ) = ( 0 . 8 2 7$ , 0.866). In addition, Table 7 represents confusion matrices as results of equalized-odds-focused experiment. The results are reported when AD achieves (Acc, EO when $y =$ 1, EO when $y = 0 ) = ( 0 . 7 8 8 , 0 . 8 4 4 , 0 . 7 5 0 ) _ { \ L }$ , and FR-GAN achieves (Acc, EO when $y = 1$ , EO when $y = 0 ) = ( 0 . 8 3 8$ , 0.824, 0.773).

parse/train/SkgzYiRqtX/SkgzYiRqtX.md

@@ -0,0 +1,269 @@
+# GRAPH NEURAL NETWORKS WITH GENERATED PARAMETERS FOR RELATION EXTRACTION
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+Recently, progress has been made towards improving relational reasoning in machine learning field. Among existing models, graph neural networks (GNNs) is one of the most effective approaches for multi-hop relational reasoning. In fact, multi-hop relational reasoning is indispensable in many natural language processing tasks such as relation extraction. In this paper, we propose to generate the parameters of graph neural networks (GP-GNNs) according to natural language sentences, which enables GNNs to process relational reasoning on unstructured text inputs. We verify GP-GNNs in relation extraction from text. Experimental results on a human-annotated dataset and two distantly supervised datasets show that our model achieves significant improvements compared to baselines. We also perform a qualitative analysis to demonstrate that our model could discover more accurate relations by multi-hop relational reasoning.
+
+# 1 INTRODUCTION
+
+Recent years, graph neural networks (GNNs) have been applied to various fields of machine learning, including node classification (Kipf & Welling, 2016), relation classification (Schlichtkrull et al., 2017), molecular property prediction (Gilmer et al., 2017), few-shot learning (Garcia & Bruna, 2018), and achieve promising results on these tasks. These works have demonstrated GNNs’ strong power to process relational reasoning on graphs.
+
+Relational reasoning aims to abstractly reason about entities/objects and their relations, which is an important part of human intelligence. Besides graphs, relational reasoning is also of great importance in many natural language processing tasks such as question answering, relation extraction, summarization, etc. Consider the example shown in Fig. 1, existing relation extraction models could easily extract the facts that Luc Besson directed a film Leon: The Professional ´ and that the film is in English, but fail to infer the relationship between Luc Besson and English without multi-hop relational reasoning. By considering the reasoning patterns, one can discover that Luc Besson could speak English following a reasoning logic that Luc Besson directed Leon: The Professional ´ and this film is in English indicates Luc Besson could speak English. However, most existing GNNs can only process multi-hop relational reasoning on pre-defined graphs and cannot be directly applied in natural language relational reasoning. Enabling multi-hop relational reasoning in natural languages remains an open problem.
+
+To address this issue, in this paper, we propose graph neural networks with generated parameters (GP-GNNs), to adapt graph neural networks to solve the natural language relational reasoning task. GP-GNNs first constructs a fully-connected graph with the entities in the sequence of text. After that, it employs three modules to process relational reasoning: (1) an encoding module which enables edges to encode rich information from natural languages, (2) a propagation module which propagates relational information among various nodes, and (3) a classification module which makes predictions with node representations. As compared to traditional GNNs, GP-GNNs could learn edges’ parameters from natural languages, extending it from performing inferring on only non-relational graphs or graphs with a limited number of edge types to unstructured inputs such as texts.
+
+In the experiments, we apply GP-GNNs to a classic natural language relational reasoning task: relation extraction from text. We carry out experiments on Wikipedia corpus aligned with Wikidata knowledge base (Vrandeciˇ c & Kr ´ otzsch, 2014) and build a human annotated test set as well as ¨ two distantly labeled test sets with different levels of denseness.Experiment results show that our model outperforms other state-of-the-art models on relation extraction task by considering multihop relational reasoning. We also perform a qualitative analysis which shows that our model could discover more relations by reasoning more robustly as compared to baseline models.
+
+![](images/82a0d23c9b35c47677e0e5c518a67caec7c3c543be55937df03c888ebfb4fb8d.jpg)  
+Figure 1: An example of relation extraction from plain text. Given a sentence with several entities marked, we model the interaction between these entities by generating the weights of graph neural networks. Modeling the relationship between “Leon” and “English” as well as “Luc Besson” helps ´ discover the relationship between “Luc Besson” and “English”.
+
+Our main contributions are in two-fold:
+
+(1) We extend a novel graph neural network model with generated parameters, to enable relational message-passing with rich text information, which could be applied to process relational reasoning on unstructured inputs such as natural languages.
+
+(2) We verify our GP-GNNs in the task of relation extraction from text, which demonstrates its ability on multi-hop relational reasoning as compared to those models which extract relationships separately. Moreover, we also present three datasets, which could help future researchers compare their models in different settings.
+
+# 2 RELATED WORK
+
+# 2.1 GRAPH NEURAL NETWORKS (GNNS)
+
+GNNs were first proposed in (Scarselli et al., 2009) and are trained via the Almeida-Pineda algorithm (Almeida, 1987). Later the authors in Li et al. (2016) replace the Almeida-Pineda algorithm with the more generic backpropagation and demonstrate its effectiveness empirically. Gilmer et al. (2017) propose to apply GNNs to molecular property prediction tasks. Garcia & Bruna (2018) shows how to use GNNs to learn classifiers on image datasets in a few-shot manner. Gilmer et al. (2017) study the effectiveness of message-passing in quantum chemistry. Dhingra et al. (2017) apply message-passing on a graph constructed by coreference links to answer relational questions. There are relatively fewer papers discussing how to adapt GNNs to natural language tasks. For example, Marcheggiani & Titov (2017) propose to apply GNNs to semantic role labeling and Schlichtkrull et al. (2017) apply GNNs to knowledge base completion tasks. Zhang et al. (2018) apply GNNs to relation extraction by encoding dependency trees, and De Cao et al. (2018) apply GNNs to multi-hop question answering by encoding co-occurence and co-reference relationships. Although they also consider applying GNNs to natural language processing tasks, they still perform message-passing on predefined graphs. Johnson (2017) introduces a novel neural architecture to generate a graph based on the textual input and dynamically update the relationship during the learning process. In sharp contrast, this paper focuses on extracting relations from real-world relation datasets.
+
+# 2.2 RELATIONAL REASONING
+
+Relational reasoning has been explored in various fields. For example, Santoro et al. (2017) propose a simple neural network to reason the relationship of objects in a picture, Xu et al. (2017) build up a scene graph according to an image, and Kipf et al. (2018) model the interaction of physical objects.
+
+In this paper, we focus on the relational reasoning in natural language domain. Existing works (Zeng et al., 2014; 2015; Lin et al., 2016) have demonstrated that neural networks are capable of capturing the pair-wise relationship between entities in certain situations. For example, (Zeng et al., 2014) is one of the earliest works that applies a simple CNN to this task, and (Zeng et al., 2015) further extends it with piece-wise max-pooling. Nguyen & Grishman (2015) propose a multi-window version of CNN for relation extraction. Lin et al. (2016) study an attention mechanism for relation extraction tasks. Peng et al. (2017) predict n-ary relations of entities in different sentences with Graph LSTMs. Le & Titov (2018) treat relations as latent variables which are capable of inducing the relations without any supervision signals. Zeng et al. (2017) show that the relation path has an important role in relation extraction. Miwa & Bansal (2016) show the effectiveness of LSTMs (Hochreiter & Schmidhuber, 1997) in relation extraction. Christopoulou et al. (2018) proposed a walk-based model to do relation extraction. The most related work is (Sorokin & Gurevych, 2017), where the proposed model incorporates contextual relations with attention mechanism when predicting the relation of a target entity pair. The drawback of existing approaches is that they could not make full use of the multi-hop inference patterns among multiple entity pairs and their relations within the sentence.
+
+![](images/c210b6cb0340bef734b6e9ea7ec0fccf709f426fd20d6fb9ee6018227b464f5a.jpg)  
+Figure 2: Overall architecture: the encoding module takes a sequence of vector representations as inputs, and output a transition matrix as output; the propagation module propagates the hidden states from nodes to its neighbours with the generated transition matrix; the classification module provides task-related predictions according to nodes representations.
+
+# 3 GRAPH NEURAL NETWORK WITH GENERATED PARAMETERS (GP-GNNS)
+
+We first define the task of natural language relational reasoning. Given a sequence of text with $m$ entities, it aims to reason on both the text and entities and make a prediction of the labels of the entities or entity pairs.
+
+In this section, we will introduce the general framework of GP-GNNs. GP-GNNs first build a fullyconnected graph $\mathcal { G } = ( \nu , \mathcal { E } )$ , where $\nu$ is the set of entities, and each edge $( v _ { i } , v _ { j } ) \in \mathcal { E } , v _ { i } , v _ { j } \in \mathcal { V }$ corresponds to a sequence s = xi,j0 , xi,j1 , . . . , xi,jl−1 extracted from the text. After that, GP-GNNs employ three modules including (1) encoding module, (2) propagation module and (3) classification module to proceed relational reasoning, as shown in Fig. 2.
+
+# 3.1 ENCODING MODULE
+
+The encoding module converts sequences into transition matrices corresponding to edges, i.e. the parameters of the propagation module, by
+
+$$
+\mathcal { A } _ { i , j } ^ { ( n ) } = f ( E ( x _ { 0 } ^ { i , j } ) , E ( x _ { 1 } ^ { i , j } ) , \cdot \cdot \cdot , E ( x _ { l - 1 } ^ { i , j } ) ; \theta _ { e } ^ { n } ) ,
+$$
+
+where $f ( \cdot )$ could be any model that could encode sequential data, such as LSTMs, GRUs, CNNs, $E ( \cdot )$ indicates an embedding function, and $\theta _ { e } ^ { n }$ denotes the parameters of the encoding module of $n$ -th layer.
+
+# 3.2 PROPAGATION MODULE
+
+The propagation module learns representations for nodes layer by layer. The initial embeddings of nodes, i.e. the representations of layer 0, are task-related, which could be embeddings that encode
+
+features of nodes or just one-hot embeddings. Given representations of layer $n$ , the representations of layer $n + 1$ are calculated by
+
+$$
+\mathbf { h } _ { i } ^ { ( n + 1 ) } = \sum _ { v _ { j } \in \mathcal { N } ( v _ { i } ) } \sigma ( \mathcal { A } _ { i , j } ^ { ( n ) } \mathbf { h } _ { j } ^ { ( n ) } ) ,
+$$
+
+where $\mathcal { N } ( v _ { i } )$ denotes the neighbours of node $v _ { i }$ in graph $\mathcal { G }$ and $\sigma ( \cdot )$ denotes non-linear activation function.
+
+# 3.3 CLASSIFICATION MODULE
+
+Generally, the classification module takes node representations as inputs and outputs predictions. Therefore, the loss of GP-GNNs could be calculated as
+
+$$
+\mathcal { L } = g ( \mathbf { h } _ { 0 : | \mathcal { V } | - 1 } ^ { 0 } , \mathbf { h } _ { 0 : | \mathcal { V } | - 1 } ^ { 1 } , \dots , \mathbf { h } _ { 0 : | \mathcal { V } | - 1 } ^ { K } , Y ; \theta _ { c } ) ,
+$$
+
+where $\theta _ { c }$ denotes the parameters of the classification module, $K$ is the number of layers in propagation module and $Y$ denotes the ground truth label. The parameters in GP-GNNs are trained by gradient descent methods.
+
+# 4 RELATION EXTRACTION WITH GP-GNNS
+
+Relation extraction from text is a classic natural language relational reasoning task. Given a sentence $s ~ = ~ ( x _ { 0 } , x _ { 1 } , \ldots , x _ { l - 1 } )$ , a set of relations $\mathcal { R }$ and a set of entities in this sentence ${ \mathcal V } _ { s } = \{ v _ { 1 } , v _ { 2 } , \ldots , v _ { | { \mathcal V } _ { s } | } \}$ , where each $v _ { i }$ consists of one or a sequence of tokens, relation extraction from text is to identify the pairwise relationship $r _ { v _ { i } , v _ { j } } \in \mathcal { R }$ between each entity pair $( v _ { i } , v _ { j } )$ .
+
+In this section, we will introduce how to apply GP-GNNs to relation extraction.
+
+# 4.1 ENCODING MODULE
+
+To encode the context of entity pairs (or edges in the graph), we first concatenate the position embeddings with word embeddings in the sentence:
+
+$$
+E ( x _ { t } ^ { i , j } ) = [ { \pmb x } _ { t } ; { \pmb p } _ { t } ^ { i , j } ] ,
+$$
+
+where $\mathbf { \Delta } _ { \mathbf { \mathcal { X } } _ { t } }$ denotes the word embedding of word $x _ { t }$ and $\mathbf { \Delta } _ { \mathbf { \mathcal { P } } _ { t } ^ { i , j } }$ denotes the position embedding of word position $t$ relative to the entity pair’s position $i , j$ (Details of these two embeddings are introduced in the next two paragraphs.) After that, we feed the representations of entity pairs into encoder $f ( \cdot )$ which contains a bi-directional LSTM and a multi-layer perceptron:
+
+$$
+\begin{array} { r } { \boldsymbol { \mathcal { A } } _ { i , j } ^ { ( n ) } = [ \mathtt { M L P } _ { n } ( \mathtt { B i L S T M } _ { n } ( ( E ( x _ { 0 } ^ { i , j } ) , E ( x _ { 1 } ^ { i , j } ) , \cdots , E ( x _ { l - 1 } ^ { i , j } ) ) ] , } \end{array}
+$$
+
+where $n$ denotes the index of layer 1, $[ \cdot ]$ means reshaping a vector as a matrix, BiLSTM encodes a sequence by concatenating tail hidden states of the forward LSTM and head hidden states of the backward LSTM together and MLP denotes a multi-layer perceptron with non-linear activation $\sigma$ .
+
+Word Representations We first map each token $x _ { t }$ of sentence $\{ x _ { 0 } , x _ { 1 } , \dotsc , x _ { l - 1 } \}$ to a $k$ - dimensional embedding vector $\mathbf { \Delta } _ { \mathbf { \mathcal { X } } _ { t } }$ using a word embedding matrix $W _ { e } \in \mathbb { R } ^ { | V | \times d _ { w } }$ , where $| V |$ is the size of the vocabulary. Throughout this paper, we stick to 50-dimensional GloVe embeddings pre-trained on a 6 billion corpus (Pennington et al., 2014).
+
+Position Embedding In this work, we consider a simple entity marking scheme2: we mark each token in the sentence as either belonging to the first entity $v _ { i }$ , the second entity $v _ { j }$ or to neither of those. Each position marker is also mapped to a $d _ { p }$ -dimensional vector by a position embedding matrix $P \in \mathbb { R } ^ { 3 \times d _ { p } }$ . We use notation $\mathbf { \Delta } _ { \mathbf { \mathcal { P } } _ { t } ^ { i , j } }$ to represent the position embedding for $x _ { t }$ corresponding to entity pair $( v _ { i } , v _ { j } )$ .
+
+# 4.2 PROPAGATION MODULE
+
+Next, we use Eq. (2) to propagate information among nodes where the initial embeddings of nodes and number of layers are further specified as follows.
+
+The Initial Embeddings of Nodes Suppose we are focusing on extracting the relationship between entity $v _ { i }$ and entity $v _ { j }$ , the initial embeddings of them are annotated as $\mathbf { h } _ { v _ { i } } ^ { ( 0 ) } = \pmb { a } _ { \mathrm { s u b j e c t } }$ , and $h _ { v _ { j } } ^ { ( 0 ) } = a _ { \mathrm { o b j e c t } }$ , while the initial embeddings of other entities are set to all zeros. We set special values for the head and tail entity’s initial embeddings as a kind of “flag” messages which we expect to be passed through propagation. Annotators $\mathbf { \pmb { a } } _ { \mathrm { s u b j e c t } }$ and $\mathbf { \phi } _ { a _ { \mathrm { o b j e c t } } }$ could also carry the prior knowledge about subject entity and object entity. In our experiments, we generalize the idea of Gated Graph Neural Networks (Li et al., 2016) by setting $\pmb { a } _ { \mathrm { s u b j e c t } } = [ \mathbf { 1 } ; \mathbf { 0 } ] ^ { \top }$ and $\mathbf { \Delta } \mathbf { a } _ { \mathrm { o b j e c t } } = [ \mathbf { 0 } ; \mathbf { 1 } ] ^ { \top 3 }$ .
+
+Number of Layers In general graphs, the number of layers $K$ is chosen to be of the order of the graph diameter so that all nodes obtain information from the entire graph. In our context, however, since the graph is densely connected, the depth is interpreted simply as giving the model more expressive power. We treat $K$ as a hyper-parameter, the effectiveness of which will be discussed in detail (Sect. 5.4).
+
+# 4.3 CLASSIFICATION MODULE
+
+The output module takes the embeddings of the target entity pair $( v _ { i } , v _ { j } )$ as input, which are first converted by:
+
+$$
+\pmb { r } _ { v _ { i } , v _ { j } } = [ [ \pmb { h } _ { v _ { i } } ^ { ( 1 ) } \odot \pmb { h } _ { v _ { j } } ^ { ( 1 ) } ] ^ { \top } ; [ \pmb { h } _ { v _ { i } } ^ { ( 2 ) } \odot \pmb { h } _ { v _ { j } } ^ { ( 2 ) } ] ^ { \top } ; \dots ; [ \pmb { h } _ { v _ { i } } ^ { ( K ) } \odot \pmb { h } _ { v _ { j } } ^ { ( K ) } ] ^ { \top } ] ,
+$$
+
+where $\odot$ represents element-wise multiplication. This could be used for classification:
+
+$$
+\mathbb { P } ( r _ { v _ { i } , v _ { j } } | h , t , s ) = \mathsf { s o f t m a x } \big ( \mathtt { M L P } ( r _ { v _ { i } , v _ { j } } ) \big ) ,
+$$
+
+where $r _ { v _ { i } , v _ { j } } \in \mathcal { R }$ , and MLP denotes a multi-layer perceptron module.
+
+We use cross entropy here as the classification loss
+
+$$
+\mathcal { L } = \sum _ { s \in S } \sum _ { i \neq j } \log \mathbb { P } ( r _ { v _ { i } , v _ { j } } | i , j , s ) ,
+$$
+
+where $r _ { v _ { i } , v _ { j } }$ denotes the relation label for entity pair $( v _ { i } , v _ { j } )$ and $S$ denotes the whole corpus.
+
+In practice, we stack the embeddings for every target entity pairs together to infer the underlying relationship between each pair of entities. We use PyTorch (Paszke et al., 2017) to implement our models. To make it more efficient, we avoid using loop-based, scalar-oriented code by matrix and vector operations.
+
+# 5 EXPERIMENTS
+
+Our experiments mainly aim to: (1) showing that our best models could improve the performance of relation extraction under a variety of settings; (2) illustrating that how the number of layers affect the performance of our model; and (3) performing a qualitative investigation to highlight the difference between our models and baseline models. In both part (1) and part (2), we do three subparts of experiments: (i) we will first show that our models could improve instance-level relation extraction on a human annotated test set, and (ii) then we will show that our models could also help enhance the performance of bag-level relation extraction on a distantly labeled test set 4, and (iii) we also split a subset of distantly labeled test set, where the number of entities and edges is large.
+
+# 5.1 EXPERIMENT SETTINGS
+
+# 5.1.1 DATASETS
+
+Distantly labeled set Sorokin & Gurevych (2017) have proposed a dataset with Wikipedia corpora. There is a small difference between our task and theirs: our task is to extract the relationship between every pair of entities in the sentence, whereas their task is to extract the relationship between the given entity pair and the context entity pairs. Therefore, we need to modify their dataset: (1) We added reversed edges if they are missing from a given triple, e.g. if triple (Earth, part of, Solar System) exists in the sentence, we add a reversed label, (Solar System, has a member, Earth), to it; (2) For all of the entity pairs with no relations, we added “NA” labels to them.5 We use the same training set for all of the experiments.
+
+Human annotated test set Based on the test set provided by (Sorokin & Gurevych, 2017), 5 annotators6 are asked to label the dataset. They are asked to decide whether or not the distant supervision is right for every pair of entities. Only the instances accepted by all 5 annotators are incorporated into the human annotated test set. There are 350 sentences and 1,230 triples in this test set.
+
+Dense distantly labeled test set We further split a dense test set from the distantly labeled test set. Our criteria are: (1) the number of entities should be strictly larger than 2; and (2) there must be at least one circle (with at least three entities) in the ground-truth label of the sentence 7. This test set could be used to test our methods’ performance on sentences with the complex interaction between entities. There are 1,350 sentences and more than 17,915 triples and 7,906 relational facts in this test set.
+
+# 5.1.2 MODELS FOR COMPARISON
+
+We select the following models for comparison, the first four of which are our baseline models.
+
+Context-Aware RE, proposed by Sorokin & Gurevych (2017). This model utilizes attention mechanism to encode the context relations for predicting target relations. It was the state-of-the-art models on Wikipedia dataset. This baseline is implemented by ourselves based on authors’ public repo8.
+
+Multi-Window CNN. Zeng et al. (2014) utilize convolutional neural networks to classify relations. Different from the original version of CNN proposed in (Zeng et al., 2014), our implementation, follows (Nguyen & Grishman, 2015), concatenates features extracted by three different window sizes: 3, 5, 7.
+
+PCNN, proposed by Zeng et al. (2015). This model divides the whole sentence into three pieces and applies max-pooling after convolution layer piece-wisely. For CNN and following PCNN, the entity markers are the same as originally proposed in (Zeng et al., 2014; 2015).
+
+LSTM or GP-GNN with $K = 1$ layer. Bi-directional LSTM (Schuster & Paliwal, 1997) could be seen as an 1-layer variant of our model.
+
+GP-GNN with $K = 2$ or $K = 3$ layerss. These models are capable of performing 2-hop reasoning and 3-hop reasoning, respectively.
+
+# 5.1.3 HYPER-PARAMETERS
+
+We select the best parameters for the validation set. We select non-linear activation functions between relu and tanh, and select $d _ { n }$ among $\{ 2 , 4 , 8 , 1 2 , 1 6 \} ^ { 9 }$ . We have also tried two forms of adjacent matrices: tied-weights (set $\mathcal { A } ^ { ( n ) } = \mathcal { A } ^ { ( n + 1 ) } )$ and untied-weights. Table 1 shows our best hyper-parameter settings, which are used in all of our experiments.
+
+Table 1: Hyper-parameters settings.   
+
+<table><tr><td>Hyper-parameters</td><td>Value</td></tr><tr><td>learning rate</td><td>0.001</td></tr><tr><td>batch size</td><td>50</td></tr><tr><td>dropout ratio</td><td>0.5</td></tr><tr><td>hidden state size</td><td>256</td></tr><tr><td>non-linear activation o</td><td>relu</td></tr><tr><td>embedding size for #layers =1</td><td>8</td></tr><tr><td>embedding size for #layers =2 and 3</td><td>12</td></tr><tr><td>adjacent matrices</td><td>untied</td></tr></table>
+
+# 5.2 EVALUATION DETAILS
+
+So far, we have only talked about the way to implement sentence-level relation extraction. To evaluate our models and baseline models in bag-level, we utilize a bag of sentences with given entity pair to score the relations between them. Zeng et al. (2015) formalize the bag-level relation extraction as multi-instance learning. Here, we follow their idea and define the score function of entity pair and its corresponding relation $r$ as a max-one setting:
+
+$$
+E ( r | v _ { i } , v _ { j } , S ) = \displaystyle \operatorname* { m a x } _ { s \in S } \mathbb { P } ( r _ { v _ { i } , v _ { j } } | i , j , s ) .
+$$
+
+Table 2: Results on human annotated dataset   
+
+<table><tr><td>Dataset Metric</td><td>Human Annotated Test Set Acc Macro F1</td></tr><tr><td>Multi-Window CNN</td><td>47.3 17.5</td></tr><tr><td>PCNN</td><td>30.8 3.2</td></tr><tr><td>Context-Aware RE</td><td>68.9 44.9</td></tr><tr><td>GP-GNN (#layers=1)</td><td>62.9 44.1</td></tr><tr><td>GP-GNN (#layers=2)</td><td>69.5 44.2</td></tr><tr><td>GP-GNN (#layers=3)</td><td>75.3 47.9</td></tr></table>
+
+Table 3: Results on distantly labeled test set   
+
+<table><tr><td rowspan="2">Dataset Metric</td><td colspan="4">Distantly Labeled Test Set</td><td colspan="4">Dense Distantly Labeled Test Set</td></tr><tr><td>P@5%</td><td>P@10%</td><td>P@15%</td><td>P@20%</td><td>P@5%</td><td>P@10%</td><td>P@15%</td><td>P@20%</td></tr><tr><td>Multi-Window CNN</td><td>78.9</td><td>78.4</td><td>76.2</td><td>72.9</td><td>86.2</td><td>83.4</td><td>81.4</td><td>79.1</td></tr><tr><td>PCNN</td><td>73.0</td><td>65.4</td><td>58.1</td><td>51.2</td><td>85.3</td><td>79.1</td><td>72.4</td><td>68.1</td></tr><tr><td>Context-Aware RE</td><td>90.8</td><td>89.9</td><td>88.5</td><td>87.2</td><td>93.5</td><td>93.0</td><td>93.8</td><td>93.0</td></tr><tr><td>GP-GNN (#layers=1)</td><td>90.5</td><td>89.9</td><td>88.2</td><td>87.2</td><td>97.4</td><td>93.5</td><td>92.4</td><td>91.9</td></tr><tr><td>GP-GNN (#layers=2)</td><td>92.5</td><td>92.0</td><td>89.3</td><td>87.1</td><td>95.0</td><td>94.6</td><td>95.2</td><td>94.2</td></tr><tr><td>GP-GNN (#layers=3)</td><td>94.2</td><td>92.0</td><td>89.7</td><td>88.3</td><td>98.5</td><td>97.4</td><td>96.6</td><td>96.1</td></tr></table>
+
+# 5.3 EFFECTIVENESS OF REASONING MECHANISM
+
+From Table 2 and 3, we can see that our best models outperform all the baseline models significantly on all three test sets. These results indicate our model could successfully conduct reasoning on the fully-connected graph with generated parameters from natural language. These results also indicate that our model not only performs well on sentence-level relation extraction but also improves on bag-level relation extraction. Note that Context-Aware RE also incorporates context information to predict the relation of the target entity pair, however, we argue that Context-Aware RE only models the co-occurrence of various relations, ignoring whether the context relation participates in the reasoning process of relation extraction of the target entity pair. Context-Aware RE may introduce more noise, for it may mistakenly increase the probability of a relation with the similar topic with the context relations. We will give samples to illustrate this issue in Sect. 5.5. Another interesting observation is that our #layers=1 version outperforms CNN and PCNN in these three datasets. One probable reason is that sentences from Wikipedia corpus are always complex, which may be hard to model for CNN and PCNN. Similar conclusions are also reached by Zhang & Wang (2015).
+
+![](images/5a6061a24c0341d261606729c0c97258d87cce32a42396aa1f6067102048ba98.jpg)  
+Figure 3: The aggregated precision-recall curves of our models with different number of layers on distantly labeled test set (left) and dense distantly labeled test set (right). We also add Context Aware RE for comparison.   
+Table 4: Sample predictions from the baseline models and our GP-GNN model. Ground truth graphs are the subgraph in Wikidata knowledge graph induced by the sets of entities in the sentences. The models take sentences and entity markers as input and produce a graph containing entities (colored and bold) and relations between them. Although “No Relation” is also be seen as a type of relation, we only show other relation types in the graphs.
+
+<table><tr><td rowspan=1 colspan=1>Sentence</td><td rowspan=1 colspan=1>Context AwareRelation Extraction</td><td rowspan=1 colspan=1>LSTM</td><td rowspan=1 colspan=1>GP-GNN (#layers = 3)</td><td rowspan=1 colspan=1>Ground Truth</td></tr><tr><td rowspan=1 colspan=1>Oozham(or Uzham)is anupcoming 2016 Malayalamdrama film written anddirected by Jeethu Josephwith Prithviraj Sukumaranin the lead role.</td><td rowspan=1 colspan=1>Prithviraj Sukumaran7cast memberOozham1directororiginal language★        1Jeethu Joseph       Malayalam</td><td rowspan=1 colspan=1>Prithviraj Sukumaran?cast memberOozhamdirectororiginal language↓Jeethu Joseph        Malayalam</td><td rowspan=1 colspan=1>Prithviraj Sukumaran?cast memberOozham1         language spokendirectororiginal language?        1Jeethu Joseph       Malayalam</td><td rowspan=1 colspan=1>Prithviraj Sukumaran中cast memberOozhamlanguage spokendirectororiginal language↓Jeethu Joseph       Malayalam</td></tr><tr><td rowspan=1 colspan=1>The third annual of the 2006Premios Juventud (YouthAwards) edition will be heldon July 13,2006 at theBankUnited Center fromthe University of Miami inCoralGables,Florida</td><td rowspan=1 colspan=1>University of Miami located in the admini-BankUnited Centerstrative territorial entityTCoral Gables, Florida</td><td rowspan=1 colspan=1>University of Miamilocated in the admini-BankUnited Centerstrative terrtorial entityCoral Gables, Florida</td><td rowspan=1 colspan=1>University of Miami中owned byBankUnited Center  Iocated in the admini-strative territorial entitylocated in the admini-strative territorial entityCoral Gables, Florida</td><td rowspan=1 colspan=1>University of Miami7owned byBankUnited Center located in the admini-strative territorial entity1Coral Gables, Florida</td></tr><tr><td rowspan=1 colspan=1>The association wasorganized in Enterprise (nowknown as Redbush)Johnson County,Kentucky in 1894 and wasincorporated in 1955,afterrelocating to Gallipolis,Ohio.</td><td rowspan=1 colspan=1>Johnson CountyIlocated in the admini-strative teritorial entitylocated in the admini-strative territorial entityRedbush4Ohio share   Kentuckyboarder with</td><td rowspan=1 colspan=1>Johnson Countylocated in the admini-strative territorial entityIocated in the admini-strative territorial entityRedbushOhio       Kentucky</td><td rowspan=1 colspan=1>Johnson CountyIocated in the admini-strative territorial entityIocated in the admini-strative territorial entityRedbush1Ohio       Kentucky</td><td rowspan=1 colspan=1>Johnson CountyIlocated in the admini-strative teritorial entityIocated in the admini-strative territorial entityRedbushOhio       Kentucky</td></tr></table>
+
+# 5.4 THE EFFECTIVENESS OF THE NUMBER OF LAYERS
+
+The number of layers represents the reasoning ability of our models. A $K$ -layer version has the ability to infer $K$ -hop relations. To demonstrate the effects of the number of layers, we also compare our models with different numbers of layers. From Table 2 and Table 3, we could see that on all three datasets, 3-layer version achieves the best. We could also see from Fig. 3 that as the number of layers grows, the curves get higher and higher precision, indicating considering more hops in reasoning leads to better performance. However, the improvement of the third layer is much smaller on the overall distantly supervised test set than the one on the dense subset. This observation reveals that the reasoning mechanism could help us identify relations especially on sentences where there are more entities. We could also see that on the human annotated test set 3-layer version to have a greater improvement over 2-layer version as compared with 2-layer version over 1-layer version. It is probably due to the reason that bag-level relation extraction is much easier. In real applications, different variants could be selected for different kind of sentences or we can also ensemble the prediction from different models. We leave these explorations for future work.
+
+# 5.5 QUALITATIVE RESULTS: CASE STUDY
+
+Tab. 4 shows qualitative results that compare our GP-GNN model and the baseline models. The results show that GP-GNN has the ability to infer the relationship between two entities with reasoning. In the first case, GP-GNN implicitly learns a logic rule $\exists y , x \xrightarrow { \sim \mathrm { c a s t - m e m b e r } } y$ original language z $x \xrightarrow { \xrightarrow { \cdots } \infty ^ { \infty } \cdots } z$ language spoken to derive (Oozham, language spoken, Malayalam) and in the second case our model implicitly learns another logic rule $\exists y , x \xrightarrow { \mathrm { { o w n e d } \cdot b y } } y \xrightarrow { \mathrm { { l o c a t e d i n } } } z \Rightarrow x \xrightarrow { \mathrm { { l o c a t e d i n } } } z$ to find the fact (BankUnited Center, located in, English). Note that (BankUnited Center, located in, English) is even not in Wikidata, but our model could identify this fact through reasoning. We also find that Context-Aware RE tends to predict relations with similar topics. For example, in the third case, share boarder with and located in are both relations about territory issues. Consequently, Context-Aware RE makes a mistake by predicting (Kentucky, share boarder with, Ohio). As we have discussed before, this is due to its mechanism to model co-occurrence of multiple relations. However, in our model, since Ohio and Johnson County have no relationship, this wrong relation is not predicted.
+
+# 6 CONCLUSION AND FUTURE WORK
+
+We addressed the problem of utilizing GNNs to perform relational reasoning with natural languages. Our proposed models, GP-GNNs, solves the relational message-passing task by encoding natural language as parameters and performing propagation from layer to layer. Our model can also be considered as a more generic framework for graph generation problem with unstructured input other than text, e.g. images, videos, audios. In this work, we demonstrate its effectiveness in predicting the relationship between entities in natural language and bag-level and show that by considering more hops in reasoning the performance of relation extraction could be significantly improved.
+
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+Michael Schlichtkrull, Thomas N Kipf, Peter Bloem, Rianne van den Berg, Ivan Titov, and Max Welling. Modeling relational data with graph convolutional networks. arXiv preprint arXiv:1703.06103, 2017.
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+Mike Schuster and Kuldip K Paliwal. Bidirectional recurrent neural networks. IEEE Transactions on Signal Processing, pp. 2673–2681, 1997.
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+Daniil Sorokin and Iryna Gurevych. Context-aware representations for knowledge base relation extraction. In Proceedings of EMNLP, pp. 1784–1789, 2017.
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parse/train/SkgzYiRqtX/SkgzYiRqtX_content_list.json

@@ -0,0 +1,1407 @@
+[
+    {
+        "type": "text",
+        "text": "GRAPH NEURAL NETWORKS WITH GENERATED PARAMETERS FOR RELATION EXTRACTION ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Anonymous authors Paper under double-blind review ",
+        "bbox": [
+            183,
+            171,
+            398,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            234,
+            544,
+            251
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Recently, progress has been made towards improving relational reasoning in machine learning field. Among existing models, graph neural networks (GNNs) is one of the most effective approaches for multi-hop relational reasoning. In fact, multi-hop relational reasoning is indispensable in many natural language processing tasks such as relation extraction. In this paper, we propose to generate the parameters of graph neural networks (GP-GNNs) according to natural language sentences, which enables GNNs to process relational reasoning on unstructured text inputs. We verify GP-GNNs in relation extraction from text. Experimental results on a human-annotated dataset and two distantly supervised datasets show that our model achieves significant improvements compared to baselines. We also perform a qualitative analysis to demonstrate that our model could discover more accurate relations by multi-hop relational reasoning. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            454,
+            336,
+            470
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Recent years, graph neural networks (GNNs) have been applied to various fields of machine learning, including node classification (Kipf & Welling, 2016), relation classification (Schlichtkrull et al., 2017), molecular property prediction (Gilmer et al., 2017), few-shot learning (Garcia & Bruna, 2018), and achieve promising results on these tasks. These works have demonstrated GNNs’ strong power to process relational reasoning on graphs. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Relational reasoning aims to abstractly reason about entities/objects and their relations, which is an important part of human intelligence. Besides graphs, relational reasoning is also of great importance in many natural language processing tasks such as question answering, relation extraction, summarization, etc. Consider the example shown in Fig. 1, existing relation extraction models could easily extract the facts that Luc Besson directed a film Leon: The Professional ´ and that the film is in English, but fail to infer the relationship between Luc Besson and English without multi-hop relational reasoning. By considering the reasoning patterns, one can discover that Luc Besson could speak English following a reasoning logic that Luc Besson directed Leon: The Professional ´ and this film is in English indicates Luc Besson could speak English. However, most existing GNNs can only process multi-hop relational reasoning on pre-defined graphs and cannot be directly applied in natural language relational reasoning. Enabling multi-hop relational reasoning in natural languages remains an open problem. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "To address this issue, in this paper, we propose graph neural networks with generated parameters (GP-GNNs), to adapt graph neural networks to solve the natural language relational reasoning task. GP-GNNs first constructs a fully-connected graph with the entities in the sequence of text. After that, it employs three modules to process relational reasoning: (1) an encoding module which enables edges to encode rich information from natural languages, (2) a propagation module which propagates relational information among various nodes, and (3) a classification module which makes predictions with node representations. As compared to traditional GNNs, GP-GNNs could learn edges’ parameters from natural languages, extending it from performing inferring on only non-relational graphs or graphs with a limited number of edge types to unstructured inputs such as texts. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In the experiments, we apply GP-GNNs to a classic natural language relational reasoning task: relation extraction from text. We carry out experiments on Wikipedia corpus aligned with Wikidata knowledge base (Vrandeciˇ c & Kr ´ otzsch, 2014) and build a human annotated test set as well as ¨ two distantly labeled test sets with different levels of denseness.Experiment results show that our model outperforms other state-of-the-art models on relation extraction task by considering multihop relational reasoning. We also perform a qualitative analysis which shows that our model could discover more relations by reasoning more robustly as compared to baseline models. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/82a0d23c9b35c47677e0e5c518a67caec7c3c543be55937df03c888ebfb4fb8d.jpg",
+        "image_caption": [
+            "Figure 1: An example of relation extraction from plain text. Given a sentence with several entities marked, we model the interaction between these entities by generating the weights of graph neural networks. Modeling the relationship between “Leon” and “English” as well as “Luc Besson” helps ´ discover the relationship between “Luc Besson” and “English”. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+            329,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Our main contributions are in two-fold: ",
+        "bbox": [
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+            377,
+            431,
+            392
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "(1) We extend a novel graph neural network model with generated parameters, to enable relational message-passing with rich text information, which could be applied to process relational reasoning on unstructured inputs such as natural languages. ",
+        "bbox": [
+            174,
+            398,
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "(2) We verify our GP-GNNs in the task of relation extraction from text, which demonstrates its ability on multi-hop relational reasoning as compared to those models which extract relationships separately. Moreover, we also present three datasets, which could help future researchers compare their models in different settings. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            523,
+            344,
+            540
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.1 GRAPH NEURAL NETWORKS (GNNS) ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            555,
+            477,
+            570
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "GNNs were first proposed in (Scarselli et al., 2009) and are trained via the Almeida-Pineda algorithm (Almeida, 1987). Later the authors in Li et al. (2016) replace the Almeida-Pineda algorithm with the more generic backpropagation and demonstrate its effectiveness empirically. Gilmer et al. (2017) propose to apply GNNs to molecular property prediction tasks. Garcia & Bruna (2018) shows how to use GNNs to learn classifiers on image datasets in a few-shot manner. Gilmer et al. (2017) study the effectiveness of message-passing in quantum chemistry. Dhingra et al. (2017) apply message-passing on a graph constructed by coreference links to answer relational questions. There are relatively fewer papers discussing how to adapt GNNs to natural language tasks. For example, Marcheggiani & Titov (2017) propose to apply GNNs to semantic role labeling and Schlichtkrull et al. (2017) apply GNNs to knowledge base completion tasks. Zhang et al. (2018) apply GNNs to relation extraction by encoding dependency trees, and De Cao et al. (2018) apply GNNs to multi-hop question answering by encoding co-occurence and co-reference relationships. Although they also consider applying GNNs to natural language processing tasks, they still perform message-passing on predefined graphs. Johnson (2017) introduces a novel neural architecture to generate a graph based on the textual input and dynamically update the relationship during the learning process. In sharp contrast, this paper focuses on extracting relations from real-world relation datasets. ",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.2 RELATIONAL REASONING ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            820,
+            395,
+            834
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Relational reasoning has been explored in various fields. For example, Santoro et al. (2017) propose a simple neural network to reason the relationship of objects in a picture, Xu et al. (2017) build up a scene graph according to an image, and Kipf et al. (2018) model the interaction of physical objects. ",
+        "bbox": [
+            174,
+            847,
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+            888
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we focus on the relational reasoning in natural language domain. Existing works (Zeng et al., 2014; 2015; Lin et al., 2016) have demonstrated that neural networks are capable of capturing the pair-wise relationship between entities in certain situations. For example, (Zeng et al., 2014) is one of the earliest works that applies a simple CNN to this task, and (Zeng et al., 2015) further extends it with piece-wise max-pooling. Nguyen & Grishman (2015) propose a multi-window version of CNN for relation extraction. Lin et al. (2016) study an attention mechanism for relation extraction tasks. Peng et al. (2017) predict n-ary relations of entities in different sentences with Graph LSTMs. Le & Titov (2018) treat relations as latent variables which are capable of inducing the relations without any supervision signals. Zeng et al. (2017) show that the relation path has an important role in relation extraction. Miwa & Bansal (2016) show the effectiveness of LSTMs (Hochreiter & Schmidhuber, 1997) in relation extraction. Christopoulou et al. (2018) proposed a walk-based model to do relation extraction. The most related work is (Sorokin & Gurevych, 2017), where the proposed model incorporates contextual relations with attention mechanism when predicting the relation of a target entity pair. The drawback of existing approaches is that they could not make full use of the multi-hop inference patterns among multiple entity pairs and their relations within the sentence. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/c210b6cb0340bef734b6e9ea7ec0fccf709f426fd20d6fb9ee6018227b464f5a.jpg",
+        "image_caption": [
+            "Figure 2: Overall architecture: the encoding module takes a sequence of vector representations as inputs, and output a transition matrix as output; the propagation module propagates the hidden states from nodes to its neighbours with the generated transition matrix; the classification module provides task-related predictions according to nodes representations. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 GRAPH NEURAL NETWORK WITH GENERATED PARAMETERS (GP-GNNS) ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            541,
+            820,
+            559
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We first define the task of natural language relational reasoning. Given a sequence of text with $m$ entities, it aims to reason on both the text and entities and make a prediction of the labels of the entities or entity pairs. ",
+        "bbox": [
+            174,
+            574,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this section, we will introduce the general framework of GP-GNNs. GP-GNNs first build a fullyconnected graph $\\mathcal { G } = ( \\nu , \\mathcal { E } )$ , where $\\nu$ is the set of entities, and each edge $( v _ { i } , v _ { j } ) \\in \\mathcal { E } , v _ { i } , v _ { j } \\in \\mathcal { V }$ corresponds to a sequence s = xi,j0 , xi,j1 , . . . , xi,jl−1 extracted from the text. After that, GP-GNNs employ three modules including (1) encoding module, (2) propagation module and (3) classification module to proceed relational reasoning, as shown in Fig. 2. ",
+        "bbox": [
+            173,
+            622,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1 ENCODING MODULE ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            713,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The encoding module converts sequences into transition matrices corresponding to edges, i.e. the parameters of the propagation module, by ",
+        "bbox": [
+            173,
+            739,
+            823,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/1186e7ba347961d0f1c1aba69745bdd29407bc0f42052665c3ee1c596a4188c1.jpg",
+        "text": "$$\n\\mathcal { A } _ { i , j } ^ { ( n ) } = f ( E ( x _ { 0 } ^ { i , j } ) , E ( x _ { 1 } ^ { i , j } ) , \\cdot \\cdot \\cdot , E ( x _ { l - 1 } ^ { i , j } ) ; \\theta _ { e } ^ { n } ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+            784,
+            653,
+            806
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where $f ( \\cdot )$ could be any model that could encode sequential data, such as LSTMs, GRUs, CNNs, $E ( \\cdot )$ indicates an embedding function, and $\\theta _ { e } ^ { n }$ denotes the parameters of the encoding module of $n$ -th layer. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2 PROPAGATION MODULE ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            869,
+            382,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The propagation module learns representations for nodes layer by layer. The initial embeddings of nodes, i.e. the representations of layer 0, are task-related, which could be embeddings that encode ",
+        "bbox": [
+            174,
+            895,
+            823,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "features of nodes or just one-hot embeddings. Given representations of layer $n$ , the representations of layer $n + 1$ are calculated by ",
+        "bbox": [
+            173,
+            103,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/ec48d811dbe0ac74e397a8f13e307a3538658937df38e48513c124dda4641549.jpg",
+        "text": "$$\n\\mathbf { h } _ { i } ^ { ( n + 1 ) } = \\sum _ { v _ { j } \\in \\mathcal { N } ( v _ { i } ) } \\sigma ( \\mathcal { A } _ { i , j } ^ { ( n ) } \\mathbf { h } _ { j } ^ { ( n ) } ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            388,
+            135,
+            607,
+            171
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $\\mathcal { N } ( v _ { i } )$ denotes the neighbours of node $v _ { i }$ in graph $\\mathcal { G }$ and $\\sigma ( \\cdot )$ denotes non-linear activation function. ",
+        "bbox": [
+            174,
+            176,
+            825,
+            204
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3 CLASSIFICATION MODULE ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            220,
+            400,
+            236
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Generally, the classification module takes node representations as inputs and outputs predictions. Therefore, the loss of GP-GNNs could be calculated as ",
+        "bbox": [
+            174,
+            246,
+            823,
+            275
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/8458f178c2acdcd7ca4372ed74ad3e2698e93cc29c7da493bcc8a02f04cef63b.jpg",
+        "text": "$$\n\\mathcal { L } = g ( \\mathbf { h } _ { 0 : | \\mathcal { V } | - 1 } ^ { 0 } , \\mathbf { h } _ { 0 : | \\mathcal { V } | - 1 } ^ { 1 } , \\dots , \\mathbf { h } _ { 0 : | \\mathcal { V } | - 1 } ^ { K } , Y ; \\theta _ { c } ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            341,
+            277,
+            653,
+            299
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $\\theta _ { c }$ denotes the parameters of the classification module, $K$ is the number of layers in propagation module and $Y$ denotes the ground truth label. The parameters in GP-GNNs are trained by gradient descent methods. ",
+        "bbox": [
+            174,
+            301,
+            825,
+            344
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4 RELATION EXTRACTION WITH GP-GNNS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            363,
+            553,
+            381
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Relation extraction from text is a classic natural language relational reasoning task. Given a sentence $s ~ = ~ ( x _ { 0 } , x _ { 1 } , \\ldots , x _ { l - 1 } )$ , a set of relations $\\mathcal { R }$ and a set of entities in this sentence ${ \\mathcal V } _ { s } = \\{ v _ { 1 } , v _ { 2 } , \\ldots , v _ { | { \\mathcal V } _ { s } | } \\}$ , where each $v _ { i }$ consists of one or a sequence of tokens, relation extraction from text is to identify the pairwise relationship $r _ { v _ { i } , v _ { j } } \\in \\mathcal { R }$ between each entity pair $( v _ { i } , v _ { j } )$ . ",
+        "bbox": [
+            173,
+            393,
+            825,
+            453
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In this section, we will introduce how to apply GP-GNNs to relation extraction. ",
+        "bbox": [
+            174,
+            458,
+            694,
+            474
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.1 ENCODING MODULE ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            489,
+            359,
+            503
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To encode the context of entity pairs (or edges in the graph), we first concatenate the position embeddings with word embeddings in the sentence: ",
+        "bbox": [
+            173,
+            515,
+            823,
+            545
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/d6bbcf8f56fdeafab3a5282800a3c1a5a4e16df46a2412c3fb220e1e3ff54f52.jpg",
+        "text": "$$\nE ( x _ { t } ^ { i , j } ) = [ { \\pmb x } _ { t } ; { \\pmb p } _ { t } ^ { i , j } ] ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            429,
+            560,
+            566,
+            580
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $\\mathbf { \\Delta } _ { \\mathbf { \\mathcal { X } } _ { t } }$ denotes the word embedding of word $x _ { t }$ and $\\mathbf { \\Delta } _ { \\mathbf { \\mathcal { P } } _ { t } ^ { i , j } }$ denotes the position embedding of word position $t$ relative to the entity pair’s position $i , j$ (Details of these two embeddings are introduced in the next two paragraphs.) After that, we feed the representations of entity pairs into encoder $f ( \\cdot )$ which contains a bi-directional LSTM and a multi-layer perceptron: ",
+        "bbox": [
+            173,
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/cf38de968c329dc016572044eee567131cd4af73a0e435bc7dcae5f7cc955545.jpg",
+        "text": "$$\n\\begin{array} { r } { \\boldsymbol { \\mathcal { A } } _ { i , j } ^ { ( n ) } = [ \\mathtt { M L P } _ { n } ( \\mathtt { B i L S T M } _ { n } ( ( E ( x _ { 0 } ^ { i , j } ) , E ( x _ { 1 } ^ { i , j } ) , \\cdots , E ( x _ { l - 1 } ^ { i , j } ) ) ] , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $n$ denotes the index of layer 1, $[ \\cdot ]$ means reshaping a vector as a matrix, BiLSTM encodes a sequence by concatenating tail hidden states of the forward LSTM and head hidden states of the backward LSTM together and MLP denotes a multi-layer perceptron with non-linear activation $\\sigma$ . ",
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+    },
+    {
+        "type": "text",
+        "text": "Word Representations We first map each token $x _ { t }$ of sentence $\\{ x _ { 0 } , x _ { 1 } , \\dotsc , x _ { l - 1 } \\}$ to a $k$ - dimensional embedding vector $\\mathbf { \\Delta } _ { \\mathbf { \\mathcal { X } } _ { t } }$ using a word embedding matrix $W _ { e } \\in \\mathbb { R } ^ { | V | \\times d _ { w } }$ , where $| V |$ is the size of the vocabulary. Throughout this paper, we stick to 50-dimensional GloVe embeddings pre-trained on a 6 billion corpus (Pennington et al., 2014). ",
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+    },
+    {
+        "type": "text",
+        "text": "Position Embedding In this work, we consider a simple entity marking scheme2: we mark each token in the sentence as either belonging to the first entity $v _ { i }$ , the second entity $v _ { j }$ or to neither of those. Each position marker is also mapped to a $d _ { p }$ -dimensional vector by a position embedding matrix $P \\in \\mathbb { R } ^ { 3 \\times d _ { p } }$ . We use notation $\\mathbf { \\Delta } _ { \\mathbf { \\mathcal { P } } _ { t } ^ { i , j } }$ to represent the position embedding for $x _ { t }$ corresponding to entity pair $( v _ { i } , v _ { j } )$ . ",
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+    {
+        "type": "text",
+        "text": "4.2 PROPAGATION MODULE ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Next, we use Eq. (2) to propagate information among nodes where the initial embeddings of nodes and number of layers are further specified as follows. ",
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+    },
+    {
+        "type": "text",
+        "text": "The Initial Embeddings of Nodes Suppose we are focusing on extracting the relationship between entity $v _ { i }$ and entity $v _ { j }$ , the initial embeddings of them are annotated as $\\mathbf { h } _ { v _ { i } } ^ { ( 0 ) } = \\pmb { a } _ { \\mathrm { s u b j e c t } }$ , and $h _ { v _ { j } } ^ { ( 0 ) } = a _ { \\mathrm { o b j e c t } }$ , while the initial embeddings of other entities are set to all zeros. We set special values for the head and tail entity’s initial embeddings as a kind of “flag” messages which we expect to be passed through propagation. Annotators $\\mathbf { \\pmb { a } } _ { \\mathrm { s u b j e c t } }$ and $\\mathbf { \\phi } _ { a _ { \\mathrm { o b j e c t } } }$ could also carry the prior knowledge about subject entity and object entity. In our experiments, we generalize the idea of Gated Graph Neural Networks (Li et al., 2016) by setting $\\pmb { a } _ { \\mathrm { s u b j e c t } } = [ \\mathbf { 1 } ; \\mathbf { 0 } ] ^ { \\top }$ and $\\mathbf { \\Delta } \\mathbf { a } _ { \\mathrm { o b j e c t } } = [ \\mathbf { 0 } ; \\mathbf { 1 } ] ^ { \\top 3 }$ . ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Number of Layers In general graphs, the number of layers $K$ is chosen to be of the order of the graph diameter so that all nodes obtain information from the entire graph. In our context, however, since the graph is densely connected, the depth is interpreted simply as giving the model more expressive power. We treat $K$ as a hyper-parameter, the effectiveness of which will be discussed in detail (Sect. 5.4). ",
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+    {
+        "type": "text",
+        "text": "4.3 CLASSIFICATION MODULE ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "The output module takes the embeddings of the target entity pair $( v _ { i } , v _ { j } )$ as input, which are first converted by: ",
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+    {
+        "type": "equation",
+        "img_path": "images/406705cf98e48f001a12d3cd5f6fe40f059045f6de814b46ee6d3590f9758e65.jpg",
+        "text": "$$\n\\pmb { r } _ { v _ { i } , v _ { j } } = [ [ \\pmb { h } _ { v _ { i } } ^ { ( 1 ) } \\odot \\pmb { h } _ { v _ { j } } ^ { ( 1 ) } ] ^ { \\top } ; [ \\pmb { h } _ { v _ { i } } ^ { ( 2 ) } \\odot \\pmb { h } _ { v _ { j } } ^ { ( 2 ) } ] ^ { \\top } ; \\dots ; [ \\pmb { h } _ { v _ { i } } ^ { ( K ) } \\odot \\pmb { h } _ { v _ { j } } ^ { ( K ) } ] ^ { \\top } ] ,\n$$",
+        "text_format": "latex",
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $\\odot$ represents element-wise multiplication. This could be used for classification: ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/ddbf69d1bc402f18c35cea397eceee9f5631cdf04c6e501d9e508b1b54b2823b.jpg",
+        "text": "$$\n\\mathbb { P } ( r _ { v _ { i } , v _ { j } } | h , t , s ) = \\mathsf { s o f t m a x } \\big ( \\mathtt { M L P } ( r _ { v _ { i } , v _ { j } } ) \\big ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $r _ { v _ { i } , v _ { j } } \\in \\mathcal { R }$ , and MLP denotes a multi-layer perceptron module. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We use cross entropy here as the classification loss ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/4f82298534b4e615fc41f66d99e59589f564ad0080132f28900fcd81e24589ec.jpg",
+        "text": "$$\n\\mathcal { L } = \\sum _ { s \\in S } \\sum _ { i \\neq j } \\log \\mathbb { P } ( r _ { v _ { i } , v _ { j } } | i , j , s ) ,\n$$",
+        "text_format": "latex",
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+    },
+    {
+        "type": "text",
+        "text": "where $r _ { v _ { i } , v _ { j } }$ denotes the relation label for entity pair $( v _ { i } , v _ { j } )$ and $S$ denotes the whole corpus. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In practice, we stack the embeddings for every target entity pairs together to infer the underlying relationship between each pair of entities. We use PyTorch (Paszke et al., 2017) to implement our models. To make it more efficient, we avoid using loop-based, scalar-oriented code by matrix and vector operations. ",
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+    },
+    {
+        "type": "text",
+        "text": "5 EXPERIMENTS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Our experiments mainly aim to: (1) showing that our best models could improve the performance of relation extraction under a variety of settings; (2) illustrating that how the number of layers affect the performance of our model; and (3) performing a qualitative investigation to highlight the difference between our models and baseline models. In both part (1) and part (2), we do three subparts of experiments: (i) we will first show that our models could improve instance-level relation extraction on a human annotated test set, and (ii) then we will show that our models could also help enhance the performance of bag-level relation extraction on a distantly labeled test set 4, and (iii) we also split a subset of distantly labeled test set, where the number of entities and edges is large. ",
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+    {
+        "type": "text",
+        "text": "5.1 EXPERIMENT SETTINGS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "5.1.1 DATASETS ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Distantly labeled set Sorokin & Gurevych (2017) have proposed a dataset with Wikipedia corpora. There is a small difference between our task and theirs: our task is to extract the relationship between every pair of entities in the sentence, whereas their task is to extract the relationship between the given entity pair and the context entity pairs. Therefore, we need to modify their dataset: (1) We added reversed edges if they are missing from a given triple, e.g. if triple (Earth, part of, Solar System) exists in the sentence, we add a reversed label, (Solar System, has a member, Earth), to it; (2) For all of the entity pairs with no relations, we added “NA” labels to them.5 We use the same training set for all of the experiments. ",
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+    {
+        "type": "text",
+        "text": "Human annotated test set Based on the test set provided by (Sorokin & Gurevych, 2017), 5 annotators6 are asked to label the dataset. They are asked to decide whether or not the distant supervision is right for every pair of entities. Only the instances accepted by all 5 annotators are incorporated into the human annotated test set. There are 350 sentences and 1,230 triples in this test set. ",
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+    },
+    {
+        "type": "text",
+        "text": "Dense distantly labeled test set We further split a dense test set from the distantly labeled test set. Our criteria are: (1) the number of entities should be strictly larger than 2; and (2) there must be at least one circle (with at least three entities) in the ground-truth label of the sentence 7. This test set could be used to test our methods’ performance on sentences with the complex interaction between entities. There are 1,350 sentences and more than 17,915 triples and 7,906 relational facts in this test set. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.1.2 MODELS FOR COMPARISON ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We select the following models for comparison, the first four of which are our baseline models. ",
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Context-Aware RE, proposed by Sorokin & Gurevych (2017). This model utilizes attention mechanism to encode the context relations for predicting target relations. It was the state-of-the-art models on Wikipedia dataset. This baseline is implemented by ourselves based on authors’ public repo8. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Multi-Window CNN. Zeng et al. (2014) utilize convolutional neural networks to classify relations. Different from the original version of CNN proposed in (Zeng et al., 2014), our implementation, follows (Nguyen & Grishman, 2015), concatenates features extracted by three different window sizes: 3, 5, 7. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "PCNN, proposed by Zeng et al. (2015). This model divides the whole sentence into three pieces and applies max-pooling after convolution layer piece-wisely. For CNN and following PCNN, the entity markers are the same as originally proposed in (Zeng et al., 2014; 2015). ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "LSTM or GP-GNN with $K = 1$ layer. Bi-directional LSTM (Schuster & Paliwal, 1997) could be seen as an 1-layer variant of our model. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "GP-GNN with $K = 2$ or $K = 3$ layerss. These models are capable of performing 2-hop reasoning and 3-hop reasoning, respectively. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.1.3 HYPER-PARAMETERS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We select the best parameters for the validation set. We select non-linear activation functions between relu and tanh, and select $d _ { n }$ among $\\{ 2 , 4 , 8 , 1 2 , 1 6 \\} ^ { 9 }$ . We have also tried two forms of adjacent matrices: tied-weights (set $\\mathcal { A } ^ { ( n ) } = \\mathcal { A } ^ { ( n + 1 ) } )$ and untied-weights. Table 1 shows our best hyper-parameter settings, which are used in all of our experiments. ",
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+    {
+        "type": "table",
+        "img_path": "images/fcb5879d5b27a32bfd58b47ed4b63e72c5f7a3c988e21aba28fa8e3449c913ca.jpg",
+        "table_caption": [
+            "Table 1: Hyper-parameters settings. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Hyper-parameters</td><td>Value</td></tr><tr><td>learning rate</td><td>0.001</td></tr><tr><td>batch size</td><td>50</td></tr><tr><td>dropout ratio</td><td>0.5</td></tr><tr><td>hidden state size</td><td>256</td></tr><tr><td>non-linear activation o</td><td>relu</td></tr><tr><td>embedding size for #layers =1</td><td>8</td></tr><tr><td>embedding size for #layers =2 and 3</td><td>12</td></tr><tr><td>adjacent matrices</td><td>untied</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.2 EVALUATION DETAILS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "So far, we have only talked about the way to implement sentence-level relation extraction. To evaluate our models and baseline models in bag-level, we utilize a bag of sentences with given entity pair to score the relations between them. Zeng et al. (2015) formalize the bag-level relation extraction as multi-instance learning. Here, we follow their idea and define the score function of entity pair and its corresponding relation $r$ as a max-one setting: ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "img_path": "images/d2691d72ecd319f7c80240ee3da12d12bb7674209332b506537a328b43b22f06.jpg",
+        "text": "$$\nE ( r | v _ { i } , v _ { j } , S ) = \\displaystyle \\operatorname* { m a x } _ { s \\in S } \\mathbb { P } ( r _ { v _ { i } , v _ { j } } | i , j , s ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/6f77a658226f1af821887c7eeacb7630f96f947520d0bd269d1b3b2a535a9580.jpg",
+        "table_caption": [
+            "Table 2: Results on human annotated dataset "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset Metric</td><td>Human Annotated Test Set Acc Macro F1</td></tr><tr><td>Multi-Window CNN</td><td>47.3 17.5</td></tr><tr><td>PCNN</td><td>30.8 3.2</td></tr><tr><td>Context-Aware RE</td><td>68.9 44.9</td></tr><tr><td>GP-GNN (#layers=1)</td><td>62.9 44.1</td></tr><tr><td>GP-GNN (#layers=2)</td><td>69.5 44.2</td></tr><tr><td>GP-GNN (#layers=3)</td><td>75.3 47.9</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/921bf1275781b7eb477d7df0b6d3dd3e726c880931b75cda1ad3c33c24b5bef6.jpg",
+        "table_caption": [
+            "Table 3: Results on distantly labeled test set "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Dataset Metric</td><td colspan=\"4\">Distantly Labeled Test Set</td><td colspan=\"4\">Dense Distantly Labeled Test Set</td></tr><tr><td>P@5%</td><td>P@10%</td><td>P@15%</td><td>P@20%</td><td>P@5%</td><td>P@10%</td><td>P@15%</td><td>P@20%</td></tr><tr><td>Multi-Window CNN</td><td>78.9</td><td>78.4</td><td>76.2</td><td>72.9</td><td>86.2</td><td>83.4</td><td>81.4</td><td>79.1</td></tr><tr><td>PCNN</td><td>73.0</td><td>65.4</td><td>58.1</td><td>51.2</td><td>85.3</td><td>79.1</td><td>72.4</td><td>68.1</td></tr><tr><td>Context-Aware RE</td><td>90.8</td><td>89.9</td><td>88.5</td><td>87.2</td><td>93.5</td><td>93.0</td><td>93.8</td><td>93.0</td></tr><tr><td>GP-GNN (#layers=1)</td><td>90.5</td><td>89.9</td><td>88.2</td><td>87.2</td><td>97.4</td><td>93.5</td><td>92.4</td><td>91.9</td></tr><tr><td>GP-GNN (#layers=2)</td><td>92.5</td><td>92.0</td><td>89.3</td><td>87.1</td><td>95.0</td><td>94.6</td><td>95.2</td><td>94.2</td></tr><tr><td>GP-GNN (#layers=3)</td><td>94.2</td><td>92.0</td><td>89.7</td><td>88.3</td><td>98.5</td><td>97.4</td><td>96.6</td><td>96.1</td></tr></table>",
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.3 EFFECTIVENESS OF REASONING MECHANISM ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "From Table 2 and 3, we can see that our best models outperform all the baseline models significantly on all three test sets. These results indicate our model could successfully conduct reasoning on the fully-connected graph with generated parameters from natural language. These results also indicate that our model not only performs well on sentence-level relation extraction but also improves on bag-level relation extraction. Note that Context-Aware RE also incorporates context information to predict the relation of the target entity pair, however, we argue that Context-Aware RE only models the co-occurrence of various relations, ignoring whether the context relation participates in the reasoning process of relation extraction of the target entity pair. Context-Aware RE may introduce more noise, for it may mistakenly increase the probability of a relation with the similar topic with the context relations. We will give samples to illustrate this issue in Sect. 5.5. Another interesting observation is that our #layers=1 version outperforms CNN and PCNN in these three datasets. One probable reason is that sentences from Wikipedia corpus are always complex, which may be hard to model for CNN and PCNN. Similar conclusions are also reached by Zhang & Wang (2015). ",
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+        "type": "text",
+        "text": "",
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/5a6061a24c0341d261606729c0c97258d87cce32a42396aa1f6067102048ba98.jpg",
+        "image_caption": [
+            "Figure 3: The aggregated precision-recall curves of our models with different number of layers on distantly labeled test set (left) and dense distantly labeled test set (right). We also add Context Aware RE for comparison. ",
+            "Table 4: Sample predictions from the baseline models and our GP-GNN model. Ground truth graphs are the subgraph in Wikidata knowledge graph induced by the sets of entities in the sentences. The models take sentences and entity markers as input and produce a graph containing entities (colored and bold) and relations between them. Although “No Relation” is also be seen as a type of relation, we only show other relation types in the graphs. "
+        ],
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+    },
+    {
+        "type": "table",
+        "img_path": "images/73d293f05613444f90b3520f9037be521f3f78e8378fe4c9a771c37de199e7a0.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=1>Sentence</td><td rowspan=1 colspan=1>Context AwareRelation Extraction</td><td rowspan=1 colspan=1>LSTM</td><td rowspan=1 colspan=1>GP-GNN (#layers = 3)</td><td rowspan=1 colspan=1>Ground Truth</td></tr><tr><td rowspan=1 colspan=1>Oozham(or Uzham)is anupcoming 2016 Malayalamdrama film written anddirected by Jeethu Josephwith Prithviraj Sukumaranin the lead role.</td><td rowspan=1 colspan=1>Prithviraj Sukumaran7cast memberOozham1directororiginal language★        1Jeethu Joseph       Malayalam</td><td rowspan=1 colspan=1>Prithviraj Sukumaran?cast memberOozhamdirectororiginal language↓Jeethu Joseph        Malayalam</td><td rowspan=1 colspan=1>Prithviraj Sukumaran?cast memberOozham1         language spokendirectororiginal language?        1Jeethu Joseph       Malayalam</td><td rowspan=1 colspan=1>Prithviraj Sukumaran中cast memberOozhamlanguage spokendirectororiginal language↓Jeethu Joseph       Malayalam</td></tr><tr><td rowspan=1 colspan=1>The third annual of the 2006Premios Juventud (YouthAwards) edition will be heldon July 13,2006 at theBankUnited Center fromthe University of Miami inCoralGables,Florida</td><td rowspan=1 colspan=1>University of Miami located in the admini-BankUnited Centerstrative territorial entityTCoral Gables, Florida</td><td rowspan=1 colspan=1>University of Miamilocated in the admini-BankUnited Centerstrative terrtorial entityCoral Gables, Florida</td><td rowspan=1 colspan=1>University of Miami中owned byBankUnited Center  Iocated in the admini-strative territorial entitylocated in the admini-strative territorial entityCoral Gables, Florida</td><td rowspan=1 colspan=1>University of Miami7owned byBankUnited Center located in the admini-strative territorial entity1Coral Gables, Florida</td></tr><tr><td rowspan=1 colspan=1>The association wasorganized in Enterprise (nowknown as Redbush)Johnson County,Kentucky in 1894 and wasincorporated in 1955,afterrelocating to Gallipolis,Ohio.</td><td rowspan=1 colspan=1>Johnson CountyIlocated in the admini-strative teritorial entitylocated in the admini-strative territorial entityRedbush4Ohio share   Kentuckyboarder with</td><td rowspan=1 colspan=1>Johnson Countylocated in the admini-strative territorial entityIocated in the admini-strative territorial entityRedbushOhio       Kentucky</td><td rowspan=1 colspan=1>Johnson CountyIocated in the admini-strative territorial entityIocated in the admini-strative territorial entityRedbush1Ohio       Kentucky</td><td rowspan=1 colspan=1>Johnson CountyIlocated in the admini-strative teritorial entityIocated in the admini-strative territorial entityRedbushOhio       Kentucky</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.4 THE EFFECTIVENESS OF THE NUMBER OF LAYERS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            772,
+            565,
+            786
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "The number of layers represents the reasoning ability of our models. A $K$ -layer version has the ability to infer $K$ -hop relations. To demonstrate the effects of the number of layers, we also compare our models with different numbers of layers. From Table 2 and Table 3, we could see that on all three datasets, 3-layer version achieves the best. We could also see from Fig. 3 that as the number of layers grows, the curves get higher and higher precision, indicating considering more hops in reasoning leads to better performance. However, the improvement of the third layer is much smaller on the overall distantly supervised test set than the one on the dense subset. This observation reveals that the reasoning mechanism could help us identify relations especially on sentences where there are more entities. We could also see that on the human annotated test set 3-layer version to have a greater improvement over 2-layer version as compared with 2-layer version over 1-layer version. It is probably due to the reason that bag-level relation extraction is much easier. In real applications, different variants could be selected for different kind of sentences or we can also ensemble the prediction from different models. We leave these explorations for future work. ",
+        "bbox": [
+            173,
+            797,
+            825,
+            924
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            174,
+            103,
+            825,
+            159
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "5.5 QUALITATIVE RESULTS: CASE STUDY ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            176,
+            478,
+            190
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Tab. 4 shows qualitative results that compare our GP-GNN model and the baseline models. The results show that GP-GNN has the ability to infer the relationship between two entities with reasoning. In the first case, GP-GNN implicitly learns a logic rule $\\exists y , x \\xrightarrow { \\sim \\mathrm { c a s t - m e m b e r } } y$ original language z $x \\xrightarrow { \\xrightarrow { \\cdots } \\infty ^ { \\infty } \\cdots } z$ language spoken to derive (Oozham, language spoken, Malayalam) and in the second case our model implicitly learns another logic rule $\\exists y , x \\xrightarrow { \\mathrm { { o w n e d } \\cdot b y } } y \\xrightarrow { \\mathrm { { l o c a t e d i n } } } z \\Rightarrow x \\xrightarrow { \\mathrm { { l o c a t e d i n } } } z$ to find the fact (BankUnited Center, located in, English). Note that (BankUnited Center, located in, English) is even not in Wikidata, but our model could identify this fact through reasoning. We also find that Context-Aware RE tends to predict relations with similar topics. For example, in the third case, share boarder with and located in are both relations about territory issues. Consequently, Context-Aware RE makes a mistake by predicting (Kentucky, share boarder with, Ohio). As we have discussed before, this is due to its mechanism to model co-occurrence of multiple relations. However, in our model, since Ohio and Johnson County have no relationship, this wrong relation is not predicted. ",
+        "bbox": [
+            173,
+            202,
+            825,
+            398
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "6 CONCLUSION AND FUTURE WORK ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            417,
+            495,
+            434
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We addressed the problem of utilizing GNNs to perform relational reasoning with natural languages. Our proposed models, GP-GNNs, solves the relational message-passing task by encoding natural language as parameters and performing propagation from layer to layer. Our model can also be considered as a more generic framework for graph generation problem with unstructured input other than text, e.g. images, videos, audios. In this work, we demonstrate its effectiveness in predicting the relationship between entities in natural language and bag-level and show that by considering more hops in reasoning the performance of relation extraction could be significantly improved. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 8
+    },
+    {
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parse/train/bMLeGGwptZk/bMLeGGwptZk.md

@@ -0,0 +1,497 @@
+# The Role of Adaptive Optimizers for Honest Private Hyperparameter Selection
+
+Anonymous Author(s)   
+Affiliation   
+Address   
+email
+
+# Abstract
+
+Hyperparameter optimization is a ubiquitous challenge in machine learning, and the performance of a trained model depends crucially upon their effective selection. While a rich set of tools exist for this purpose, there are currently no practical hyperparameter selection methods under the constraint of differential privacy (DP). We study honest hyperparameter selection for differentially private machine learning, in which the process of hyperparameter tuning is accounted for in the overall privacy budget. To this end, we i) show that standard composition tools outperform more advanced techniques in many settings, ii) empirically and theoretically demonstrate an intrinsic connection between the learning rate and clipping norm hyperparameters, iii) show that adaptive optimizers like DPAdam enjoy a significant advantage in the process of honest hyperparameter tuning, and iv) draw upon novel limiting behaviour of Adam in the DP setting to design a new and more efficient optimizer.
+
+# 14 1 Introduction
+
+15 Over the last several decades, the field of machine learning has flourished. However, training machine   
+16 learning models frequently involves personal data, which leaves data contributors susceptible to   
+17 privacy attacks. This isn’t purely hypothetical: recent results have shown that models are vulnerable   
+18 to membership inference [SSSS17, $\mathrm { \bar { C } L E ^ { + } } 1 9$ , NSH19] and model inversion attacks [FJR15, SRS17].   
+19 The leading approaches for privacy-preserving machine learning are based on differential privacy   
+20 (DP) [DMNS06]. Informally, DP rigorously limits and masks the contribution that an individual   
+21 datapoint can have on an algorithm’s output. To address the aforementioned issues, DP training   
+22 procedures have been developed [WM10, BST14, SCS13, $\mathrm { A C G ^ { + } } 1 6 ]$ , which generally resemble non  
+23 private gradient-based methods, but with the incorporation of gradient clipping and noise injection.   
+24 In both the private and non-private settings, hyperparameter selection is instrumental to achieving   
+25 high accuracy. The most common methods are grid search or random search, both of which incur   
+26 a computational overhead scaling with the number of hyperparameters under consideration. In   
+27 the private setting, this issue is often magnified as most private training procedures introduce new   
+28 hyperparameters. Regardless, and more importantly, hyperparameter tuning on a sensitive dataset   
+29 also costs in terms of privacy, naively incurring a multiplicative cost which scales as the square root   
+30 of the number of candidates (based on composition properties of differential privacy [KOV15]).   
+31 Most prior works on private learning choose not to account for this cost $[ \mathrm { A C G ^ { + } } 1 6$ , $\mathrm { Y L P ^ { + } 1 9 }$ , TB21],   
+32 focusing instead on demonstrating the accuracy achievable by private learning under idealized condi  
+33 tions, that is, if the best hyperparameters were somehow known ahead of time. Some works assume   
+34 the presence of supplementary public data resembling the sensitive dataset $[ \mathrm { A G D } ^ { + } 2 0$ , $\mathrm { R T M } ^ { + } 2 0 ]$ ,   
+35 which may be freely used for hyperparameter tuning. Naturally, such public data may be scarce or   
+36 nonexistent in settings where privacy is a concern, leaving practitioners with little guidance on how   
+37 to choose hyperparameters in practice. As explored in our paper, poor hyperparameter selection with   
+38 standard private optimizers can have catastrophic effects on model accuracy.   
+39 Hope is afforded by the success of adaptive optimizers in the non-private setting. The canonical   
+40 example is Adam [KB14], which exploits moments of the gradients to adaptively and dynamically   
+41 determine the learning rate. It works out of the box in many cases, providing accuracy comparable   
+42 with tuned SGD. We navigate the different options available to a practitioner to solve the honest   
+43 private hyperparameter tuning problem and ask, are there optimizers which provide strong privacy,   
+44 require minimal hyperparameter tuning, and perform competitively with tuned counterparts?
+
+# 45 Our Contributions
+
+46 1. We investigate techniques for private tuning of hyperparameters. We perform the first empirical   
+47 evaluation of the proposed theoretical method of Liu and Talwar [LT19], and demonstrate that it can   
+48 be relatively expensive. That is, in certain cases, one can tune over sufficiently many hyperparameters   
+49 using standard composition tools such as moments accountant $[ \mathrm { A C G ^ { + } } 1 6 ]$ .   
+50 2. We empirically and theoretically demonstrate that two hyperparameters, the learning rate and   
+51 clipping threshold, are intrinsically coupled for non-adaptive optimizers. While other hyperparameters   
+52 and the model architecture are restricted by the scope of the task, privacy and utility targets, and   
+53 computational resources, the learning rate and clipping norm have no a priori bounds. Since the   
+54 resulting hyperparameter grid adds up to the privacy cost while tuning to achieve the model with the   
+55 best utility, we explore leveraging adaptive optimizers to reduce the hyperparameter space.   
+56 3. We empirically demonstrate the DPAdam optimizer (with default values for most hyperparameters),   
+57 can match the performance of tuned non-adaptive optimizers on a variety of datasets, thus enabling   
+58 private learning with honest hyperparameter selection. This finding complements a prior claim   
+59 of Papernot et al. $[ \mathrm { P C S ^ { + } } 2 0 ]$ , which suggests that a well-tuned DPSGD can outperform DPAdam.   
+60 However, our findings show that this difference in performance is relatively insignificant. Furthermore,   
+61 in the realistic setting where hyperparameter tuning must be accounted for in the privacy loss, we   
+62 show that DPAdam is much more likely to produce non-catastrophic results.   
+63 4. We show that the adaptive learning rate of DPAdam converges to a static value. To leverage this,   
+64 we introduce a new private optimizer, DPAdamWOSM that matches the performance of DPAdam   
+65 without computing the second moments.
+
+# 66 1.1 Related Work
+
+67 Hyperparameter tuning plays a vital role in machine learning practice. In the non-private setting,   
+68 ML practitioners use grid search, random search, Bayesian optimization techniques [SSA13] or   
+69 AutoML [HZC21] techniques to tune their models. However, there hasn’t been much research   
+70 on private hyperparameter tuning procedures due to the significant associated privacy costs. Each   
+71 set of hyperparameter configuration results in a privacy-utility tradeoff. This tradeoff for multiple   
+72 configurations can be captured by Pareto frontiers using multivariate Bayesian optimization over   
+73 parameter dimensions $[ \bar { \mathbf { A } } \mathbf { G } \mathbf { D } ^ { + } 2 0 ]$ . However, this method asks the model curator to query the   
+74 dataset multiple times which requires non-private access to the dataset. There have been some   
+75 end-to-end private tuning procedures [CMS11, CV13, KGGW15] which work for a selected number   
+76 of hyperparameter sets. These results work either in restricted settings for few combinations of   
+77 candidates or under relaxations of differential privacy. The most relevant work to ours is an approach   
+78 for private selection from private candidates [LT19]. Their work provides two methods, one which   
+79 outputs a candidate with accuracy greater than a given input threshold, and another which randomly   
+80 stops and outputs the best candidate seen so far. The first approach is of limited utility in practice as   
+81 it requires a prior accuracy bound for the dataset. The second variant incurs a considerable overhead   
+82 in the privacy cost. We study this second approach and compare it with naive approaches based on   
+83 Moments Accountant $[ \mathsf { A C G } ^ { + } 1 6 ]$ which would scale as the square root of the number of candidates.
+
+# 84 2 Problem Setup and Overview
+
+85 Consider a sensitive dataset $D$ which lies beyond a privacy firewall and has $n$ points of the form   
+86 $( x _ { 1 } , y _ { 1 } ) , ( x _ { 2 } , y _ { 2 } ) , \ldots , ( x _ { n } , y _ { n } )$ where $x _ { i } \in \mathcal X$ is the feature vector of the ith point and $y _ { i } \in \mathcal { V }$ is its   
+87 desired output. Though our experiments are carried out in the supervised setting, all results can be   
+88 translated to unsupervised setting as well. The dataset has been divided into two parts, the training set   
+89 and the validation set. A trusted curator wants to train a machine learning model by making queries   
+90 on the dataset with a total end-to-end training privacy budget of $( \varepsilon _ { f } , \delta _ { f } )$ such that the model can   
+91 perform with high accuracy on the validation set. The curator wants to try multiple hyperparameter   
+92 candidates for the model to figure out which candidate gives the maximum accuracy. However, as the   
+93 model is private, each candidate requires multiple queries made on the dataset and all of them need to   
+94 be accounted in the total privacy budget of $( \varepsilon _ { f } , \delta _ { f } )$ .   
+95 Note that any validation accuracy must also be measured privately. Since this accuracy is a low  
+96 sensitivity query with a scalar output, and must only be computed once per choice of hyperparameters,   
+97 the cost of this procedure is generally a lower order term versus the main training procedure. Thus for   
+98 simplicity, we do not noise these validation accuracy queries. As we will see later, some optimizers   
+99 require more candidates to tune and hence would also require more privacy budget than others.   
+100 To tackle private hyperparameter selection, we first compare the available private tuning procedures   
+101 in Section 3. We show that the privacy cost for training a model depends on the hyperparameter   
+102 grid size and standard composition theorems provide the best guarantees when the grid is small. In   
+103 Section 4, we investigate different optimizers to see how many candidates are required to output   
+104 a good solution. In Section 4.1 we provide theoretical and empirical evidence to demonstrate an   
+105 intrinsic coupling between two hyperparameters – the learning rate and clipping norm in DPSGD.   
+106 We show that this coupling makes DPSGD sensitive to these parameter choices, which can drastically   
+107 affect the validation accuracy. In Section 4.2 we demonstrate that an adaptive optimizer, DPAdam,   
+108 translates well from the non-private setting and obviates tuning of the learning rate. In Section 5, we   
+109 empirically compare DPAdam with DPSGD and DPMomentum to show that DPAdam performs at par   
+110 with less hyperparameter tuning. Finally, in Section 6, we establish that DPAdam converges to a static   
+111 learning rate in restricted settings, and unveil a new optimizer DPAdamWOSM which can leverage   
+112 this converged value without computing the second moments. In the interest of space, we defer   
+113 standard preliminaries such as DP definitions, hyperparameters, and optimizers to the appendix.
+
+# 114 3 The Cost of Privately Tuning DP Optimizers
+
+115 Effective hyperparameter tuning is crucial in extracting good utility from an optimizer. Unlike   
+116 the non-private setting, DP optimizers typically i) have more hyperparameters to tune; ii) require   
+117 additional privacy budget for tuning. Existing work on DP optimizers acknowledge this problem (e.g.,   
+118 $\mathrm { [ A C G ^ { + } 1 6 \bar ] } ,$ ), but do not address the privacy cost incurred during hyperparameter tuning $[ \mathrm { A C G ^ { + } } 1 6$ ,   
+119 $\mathrm { Y L P ^ { + } } 1 9$ , TB21]. There are two main prior general-purpose approaches for private hyperparameter   
+120 selection. The first performs composition via Moments Accountant $[ \mathrm { A C G ^ { + } } 1 6 ]$ , and the second is   
+121 the algorithm of Liu and Talwar (LT) [LT19]. The latter is a theoretical result, and to the best of our   
+122 knowledge, has not been previously evaluated in practice. We investigate the privacy cost of these   
+123 two techniques in practice and discuss situations in which each method is preferred.
+
+# 124 3.1 Hyperparameter Selection via [LT19]
+
+125 Liu and Talwar [LT19] propose a random stopping algorithm (LT) to output a ‘good’ hyperparameter   
+126 candidate from a pool of $K$ candidates, $\{ x _ { 1 } , \ldots , x _ { K } \}$ . They assume sampling access to a randomized   
+127 mechanism $Q ( D )$ which samples $i \sim [ K ]$ , and returns the $i$ -th candidate $x _ { i }$ , and a score $q _ { i }$ for this   
+128 candidate. It is a random stopping algorithm, in which at every iteration, a candidate is picked from   
+129 $Q$ i.i.d. with replacement and a $\gamma$ -biased coin is flipped to randomly stop the algorithm. When the   
+130 algorithm stops, the candidate with the maximum score seen so far is outputted. In the approximate   
+131 DP version of this algorithm, an extra parameter $\Upsilon$ is set to limit the total of number of iterations.   
+132 The pseudocode of this algorithm is deferred to the appendix.
+
+Theorem 1 ([LT19], Theorem 3.4). Fix any 133 $\gamma \in [ 0 , 1 ]$ , $\delta _ { 2 } > 0$ and let $\begin{array} { r } { \Upsilon = \frac { 1 } { \gamma } \log \frac { 1 } { \delta _ { 2 } } } \end{array}$ . If $Q$ is 134 $( \varepsilon _ { 1 } , \delta _ { 1 } )$ -DP, then the LT algorithm is $( \varepsilon _ { f } , \delta _ { f } )$ -DP for $\varepsilon _ { f } = 3 \varepsilon _ { 1 } + 3 \sqrt { 2 \delta _ { 1 } }$ and $\delta _ { f } = \sqrt { 2 \delta _ { 1 } } \Upsilon + \delta _ { 2 }$ .
+
+135 Theorem 1 expresses the privacy cost of the algorithm in terms of the privacy cost of individual   
+136 learners, and parameters of the algorithm itself. The $\delta _ { 2 }$ parameter does not significantly affect the   
+137 final epsilon $\varepsilon _ { f }$ of the algorithm and in practice, one can set it to a very small value $( 1 0 ^ { - 2 0 } )$ . Though   
+138 a small value of $\delta _ { 2 }$ has little effect on $\delta _ { f }$ , it increases the hard stopping time of the algorithm, $\Upsilon$ .   
+139 To understand the LT algorithm, we will compare the privacy costs of training a single hyperparameter   
+140 candidate with a final $\varepsilon _ { f } , \delta _ { f }$ budget via LT and compare it with the privacy cost $\varepsilon _ { 1 } , \delta _ { 1 }$ of the underlying   
+141 individual learner. This setting might seem unnatural for LT as it was designed to select from a pool   
+142 of candidates but we choose this setting to show the minimum privacy cost overhead associated with   
+143 LT and later show how the privacy cost changes for multiple candidates (varying $\gamma$ ). To use LT, one   
+144 needs to figure out the $\varepsilon _ { 1 } , \delta _ { 1 }$ via Theorem 1 using the final $\varepsilon _ { f } , \delta _ { f }$ values and in this case, $\gamma = 1$ (as   
+145 we have just one candidate). The individual learner is then trained using $\varepsilon _ { 1 } , \delta _ { 1 }$ budget.   
+146 Due to the delicate balance of $\delta _ { f }$ in Theorem 1, one can see the $\delta _ { 1 }$ comes out to be much smaller than   
+147 $\delta _ { f }$ . This change in $\delta _ { 1 }$ results in a blowup of $\varepsilon _ { 1 }$ and hence, the final privacy cost of the LT algorithm   
+148 $( \dot { 3 } \varepsilon _ { 1 } + 3 \sqrt { 2 \delta _ { 1 } } )$ , is much larger than what it would have been for learning one candidate without LT.   
+149 We call this increase the blowup of privacy. We measure this blowup in Figure 1(left), for the setting   
+150 of $\sigma = 4$ , $L = 2 5 0$ , $T = 1 0 , 0 0 0$ with varying dataset sizes $( n )$ . It can be seen that for $n = 5 , 0 0 0$ ,   
+151 the blowup is $4 . 8 \mathrm { x }$ whereas for for $n = 9 5 0 , 0 0 0$ , the blowup is almost $7 . 3 \mathrm { x }$ (note the log scale on   
+152 y-axis). Qualitatively similar trends persist for other choices of noise multiplier, lot size and iterations.   
+153 We add more experiments to compare LT vs MA with varying candidate sizes in the appendix.   
+154 Furthermore, we show that although LT entails a privacy blowup, decreasing $\gamma$ , which corresponds   
+155 to training more individual learners with $\varepsilon _ { 1 } , \delta _ { 1 }$ , doesn’t result in a significant difference in the final   
+156 epsilon guaranteed by LT. In Figure 1(middle), we show the final epsilon cost for different dataset   
+157 size and varying values of $\gamma \in [ 0 . 0 0 1 , 0 . 0 1 , 0 . 1 , 1 ]$ . It is interesting to note here that with smaller   
+158 $\gamma$ values, one can train many candidates (in expectation, $\textstyle { \frac { 1 } { \gamma } } .$ ) for negligible additional privacy cost.   
+159 The blowup to train 1 candidate $( \gamma = 1 )$ ) versus $1 , 0 0 0$ candidates $\gamma = 0 . 0 0 1 )$ increases from 33   
+160 to 39 for $n = 5 , 0 0 0$ and increases from 0.49 to 0.69, for $n = 9 5 0 , 0 0 0$ . This increase is minimal√   
+161 in comparison to advanced composition, which grows proportional to $\mathcal { O } ( \sqrt { k } )$ . However, another   
+162 resource at play is the total training time, which is proportional to $1 / \gamma$ (i.e., the total number of   
+163 candidates). In summary, the LT algorithm is effective if an analyst has the privacy budget to afford   
+164 the initial blowup, as the privacy cost of testing additional hyperparameters is insignificant.
+
+![](images/fdcf93c0067febffde4404d041f4e336e7098670fb31e1690a597572ef7e263c.jpg)  
+Figure 1: Comparing the privacy cost of LT versus Moments Accountant. The minimal privacy overhead incurred by LT is at least ${ \sim } 5 \mathrm { x }$ , and increases with the dataset size (left). However, as we allow LT to sample and test more candidate hyperparameters, the privacy cost barely increases (middle). Moments Accountant is able to test a significant number of candidates at the same cost as the minimal privacy overhead of LT (right).
+
+# 165 3.2 Hyperparameter Selection via Moments Accountant
+
+166 We learnt from the previous section that, LT permits selection from a large pool of hyperparameters   
+167 (depending on the $\gamma$ value) but incurs a constant privacy blowup. We compare LT with tuning   
+168 using Moments Accountant (MA). We notice using that with the same initial privacy blowup of   
+169 the LT algorithm, MA is able to compose a considerable number of hyperparameter candidates. In   
+170 Figure 1(right), we show the number of candidates that can be composed using MA for the minimum   
+171 privacy cost for running the LT algorithm $( \gamma = 1 )$ ), for the setting of $\sigma = 4$ , $L = 2 5 0$ , $T = 1 0$ , 000   
+172 and varying dataset size $( n )$ on the $\mathbf { X }$ -axis. As the $T$ and $L$ is set constant, bigger $n$ values in this   
+173 graph correspond to fewer epochs of training and hence, worse utility. Depending on dataset size,   
+174 MA can compose 14 candidates for $n = 5 0 0 0$ and up to 175 candidates when $n = 1 0 0 0 0 0$ . It is   
+175 perhaps surprising how well a standard composition technique performs versus LT. This information   
+176 can be highly valuable to a practitioner who has limited privacy budget. Qualitatively similar trends   
+177 persist for other choices of batch size, noise multiplier, and iterations.   
+178 From our experiments for both these tuning procedures, we conclude that while tuning with LT entails   
+179 an initial privacy blowup, and the additional privacy cost for trying more candidates (smaller $\gamma$ ) is   
+180 minimal. Even though this has an additional computation cost, it can be appealing when an analyst   
+181 wants to try numerous hyperparameters. On the other hand, for the same overall privacy cost, MA   
+182 can be used to compose a significant number of hyperparameter candidates. Additionally, MA allows   
+183 access to all intermediate learners, whereas LT allows access to only the final output parameters. In   
+184 the sequel, this conclusion will be useful in making the naive MA approach a more appealing tool for   
+185 some settings (e.g., tighter privacy budgets).
+
+# 186 4 Tuning DP Optimizers
+
+187 We detail aspects of tuning both non-adaptive and adaptive optimizers. We start with tuning non  
+188 adaptive optimizers (Section 4.1). We theoretically and empirically demonstrate a connection between   
+189 the learning rate and clipping threshold. We also establish that non-adaptive optimizers inevitably   
+190 require searching over a large LR-clip grid to extract performant models. Adaptive optimizers forego   
+191 this problem as they do not need to tune the hyperparameter dimension of learning rate. However,   
+192 they introduce other hyperparameters that have known good choices in the non-private setting, and   
+193 we empirically show that they are good candidates in the private setting (Section 4.2).
+
+# 194 4.1 Tuning DP non-adaptive optimizers
+
+While many hyperparameters are restricted due to computational and privacy/utility targets, the learning rate $\alpha$ and the clipping threshold $C$ have no a priori bounds. In what follows, we show an interplay between these parameters by first theoretically analyzing the convergence of DPSGD. We then explore an illustrative experiment which demonstrates their entanglement. In the following theorem, we derive a bound on the expected excess risk of DPSGD and while doing so, show that the optimal learning rate, $\alpha _ { o p t }$ , is proportional to the inverse of $C$ . The proof appears in Appendix D.
+
+Theorem 2. Let $f$ be a convex and $\beta$ -smooth function, and let $x ^ { * } = \arg \operatorname* { m i n } _ { x \in S } f ( x )$ . Let $x _ { 0 }$ be an arbitrary point in $s$ , and $x _ { t + 1 } = \Pi _ { S } ( x _ { t } - \alpha ( g _ { t } + z _ { t } ) )$ , where $\begin{array} { r } { g _ { t } = \operatorname* { m i n } ( 1 , \frac { C } { \| \nabla f ( x ) \| ^ { 2 } } ) \nabla f ( x ) } \end{array}$ and $z _ { t } \sim \mathcal { N } ( 0 , \sigma ^ { 2 } C ^ { 2 } )$ is the noise due to privacy. After $T$ iterations, the optimal learning rate is $\begin{array} { r } { \alpha _ { o p t } = \frac { R } { C T \sqrt { 1 + \sigma ^ { 2 } } } } \end{array}$ , where $\begin{array} { r } { \mathbb { E } [ f ( \frac { 1 } { T } \sum _ { i } ^ { T } x _ { t } ) - f ( x ^ { * } ) ] \leq \frac { R C \sqrt { 1 + \sigma ^ { 2 } } } { \sqrt { T } } } \end{array}$ and $R = \mathbb { E } [ \| x _ { 0 } - x ^ { * } \| ]$ .
+
+Though Theorem 2 gives a closed-form expression for the optimum learning rate, it is a function of the parameter $R$ , which is unknown a priori to the analyst. Given constant $T$ and $\sigma$ , the optimal learning rate $\alpha _ { o p t }$ is inversely proportional to the clipping norm $C$ . This is crucial information in practice because these parameters vary among datasets and are unbounded. This unboundedness property thus requires us to search over very large ranges of $C$ and $\alpha$ when we have no prior knowledge of the dataset. It is natural to ask whether one can fix the clipping norm $C$ and search only over a wide range for the learning rate $\alpha$ (or vice versa). We explore this relationship experimentally, showing that fixing one of these two hyperparameters may often but not always result in an optimal model.
+
+![](images/0f218e874ffce118de2302a9b4024f19a6fd8a62fdbc4f10706873ff6e14b9d2.jpg)  
+Figure 2: Log of training loss for simulation experiment at $\sigma = 4$ on a synthetic dataset. The black pixels correspond to lowest training loss. Note that most best loss values lie on a diagonal expressing the inverse connection between $\alpha$ and $C$ .
+
+219 In this experiment, we train a linear regression model on a   
+220 10-dimensional synthetic dataset of input-label pairs $( x , y )$   
+221 sampled from a distribution $\mathcal { D }$ as follows: $x _ { 1 } , \ldots , x _ { d } \sim$   
+222 $\mathcal { U } ( 0 , 1 ) , y = x \cdot w ^ { * } , w ^ { * } = 1 0 \cdot \mathbf { 1 } ^ { d }$ . We use the initialization   
+223 $w _ { 0 } = \mathbf { 0 } ^ { d }$ and train for 100 iterations. In the non-private   
+224 setting, this model converges quickly with any reasonable   
+225 learning rate, but in the private setting, we notice that the
+
+6 training loss depends heavily on the choice of $\alpha$ and $C$ . Figure 2 shows a heat map for the log training loss when trained on $( \alpha , C )$ pairs taken from a large grid consisting of [1, 2, 4, 5, 8] at scales of 8 $[ 1 0 ^ { - 4 } , 1 0 ^ { - 3 } , 1 0 ^ { - 2 } , 1 0 ^ { - 1 } , 1 0 ^ { 0 } , 1 0 ^ { \hat { 1 } } ]$ . The best training is observed when the loss is 0 (black pixels).
+
+![](images/70cbc929f5f8ba00ffaeeb33681c766a28a61c55db5750a4f553523f7c03bf6f.jpg)  
+Figure 3: Ranking hyperparameter candidates across datasets. The black points correspond to the candidates with $\alpha = 0 . 0 0 1$ (with all permutations of $\beta _ { 1 } , \beta _ { 2 }$ from our searchgrid); the gold corresponds to the candidate with $\alpha = 0 . 0 0 1 , \beta _ { 1 } = 0 . 9 , \beta _ { 2 } = 0 . 9 9 9$
+
+229 We observe two fundamental phenomena from this figure. First, to achieve the best accuracy, $\alpha$ and   
+230 $C$ need to be tuned on a large grid spanning several orders of magnitude for each of these parameters.   
+231 Second, multiple $( \alpha , C )$ pairs achieve the best accuracy and all lie on the same diagonal, validating   
+232 our theory for an inverse relation between learning rate and clipping norm. As mentioned earlier, one   
+233 might hypothesize that by setting the clipping norm $C$ constant and tuning $\alpha$ (corresponding to a   
+234 vertical line in Figure 2) or vice versa, one could eliminate tuning a hyperparameter. However, note   
+235 that not all $C$ and $\alpha$ values correspond to the lowest loss. This phenomenon is evident by noticing   
+236 that not all vertical or horizontal lines on this figure have black pixels. This happens, for example,   
+237 at the extremes (e.g., at the top-right corner), but also for several intermediate and standard choices   
+238 (e.g., $C = 0 . 1$ or 0.2). Again, the analyst has no way of knowing this a priori. We conclude that to   
+239 privately tune non-adaptive optimizers, we require a large grid of hyperparameter options.
+
+# 4.2 Tuning DP adaptive optimizers
+
+In the interest of reducing this space of tuning we turn to adaptive optimizers, where we can at least reduce one dimension of this search space. These approaches automatically adapt over the learning rate $\alpha$ , requiring us to tune only over the clipping norm $C$ . But recall our key question: can we train models that perform competitively with the fine-tuned counterparts from DPSGD?
+
+Adam [KB14], the canonical adaptive optimizer introduces two new hyperparameters, which are the first and second moment exponential decay parameters ( $\beta _ { 1 }$ and $\beta _ { 2 }$ ). In the non-private setting, these parameters are relatively insensitive, and default values of $\alpha = 0 . 0 0 1 , \beta _ { 1 } = 0 . 9$ , and $\beta _ { 2 } = 0 . 9 9 9$ are recommended based on empirical findings, requiring no additional tuning for this hyperparameter triple. Hence before we compare DPAdam and DPSGD, we first find and establish such recommended values for this hyperparameter triple in the DP setting next, and then show that DPAdam with a small hyperparameter space performs competitively with DPSGD in Section 5.
+
+252 To establish default choices of $\alpha$ , $\beta _ { 1 }$ , and $\beta _ { 2 }$ for DPAdam, we evaluate this private optimizer over four   
+253 diverse datasets (details in Appendix B, Table 2) and two learning models including logistic regression   
+254 and a neural network with one 100 neurons hidden layer (TLNN). These selected datasets include   
+255 both low-dimensional data (where the number of samples greatly outnumbers the dimensionality) and   
+256 high-dimensional data (where the number of samples and dimensionality are at same scale). Since   
+257 we still have a large hyperparameter space to tune over, for the rest of this work, we fix a constant lot   
+258 size $L = 2 5 0$ ), and consider tuning over three different noise levels, $\sigma \in [ 2 , 4 , 8 ]$ , so that we can   
+259 study the effects of tuning the other hyperparameters more thoroughly. All experiments are repeated   
+260 three times and averaged before reporting. Additionally, in this particular experiment since we focus   
+261 on $\alpha , \beta _ { 1 }$ , and $\beta _ { 2 }$ , we also fix the clipping threshold $C = 0 . 5$ , and $T = 2 5 0 0$ iterations of training.   
+262 For each dataset and model, we run DPAdam three times with hyperparameters $( \alpha , \beta _ { 1 } , \beta _ { 2 } )$ from the   
+263 grids, $\alpha \in [ 0 . 0 0 1 , 0 . 0 5 , 0 . 0 1 , 0 . 2 , 0 . 5$ ], $\beta _ { 1 } , \beta _ { 2 } \in [ 0 . 8 , 0 . 8 5 , 0 . 9 , 0 . 9 5 , 0 . 9 9 . 0 . 9 9 9 ]$ .   
+264 We show that the default hyperparameter choice $( \alpha , \beta _ { 1 } , \beta _ { 2 } )$ of Adam in the non-private setting also   
+265 works well for DPAdam. Figure 3 shows the boxplots of testing accuracies of DPAdam over the   
+266 different hyperparameter choices. When $\alpha$ is 0.001 (same as in the non-private setting), all the   
+267 datasets and models have final testing accuracies (marked in black) close to the best possible (and   
+268 in most cases it is in fact the best) accuracy. Furthermore, we also highlight the accuracy of the   
+269 suggested default choice $( \alpha = 0 . 0 0 1 , \beta _ { 1 } = 0 . 9 , \beta _ { 2 } = 0 . 9 9 9 )$ using gold dots. Hence, for the ease of   
+270 using DPAdam, we suggest the non-private default values for these parameters in the private setting   
+271 as well and hence in all our subsequent experiments.
+
+![](images/07b3acf8c43c0c543b3db127cea0f262ac95a45815938bafb21b45bbc241b8a1.jpg)  
+Figure 4: Comparing the testing accuracy curves of DPAdam, DPSGD and DPMomentum models across their hyperparameter tuning grids with $\sigma = 4$ . The limits for y-axis are adjusted based on the dataset while maintaining a $15 \%$ range for all.
+
+# 5 Advantages of tuning using DPAdam
+
+In the non-private setting, adaptive optimizers like Adam enjoy a smaller hyperparameter tuning space than SGD. We ask two questions in this section. First, can DPAdam (with little tuning) achieve accuracy comparable to a well-tuned DPSGD? Second, what is the privacy-accuracy tradeoff one incurs when using either of the two methods we detail in Section 3 for hyperparameter selection.
+
+To answer both questions, we compare DPAdam and DPSGD over the same set of datasets and models from the previous section. We report the accuracy of DPSGD with a range of learning rates and clipping values shown in Table 3 (Appendix C), and the testing accuracy of DPAdam with default parameter choice from Section 4.2 $\mathbf { \Phi } _ { \mathrm { { ( } } \alpha } = 0 . 0 0 1 $ , $\beta _ { 1 } = 0 . 9$ , $\beta _ { 2 } = 0 . 9 9 9 \rangle$ ) and a range of clipping values $C$ in Table 3. In total, DPSGD has 40 candidates to tune over, and DPAdam has 4. This is because we have shown in Section 4.1 that DPSGD needs a wide grid to obtain the best accuracy when data distributions are unknown. Additionally, we also consider the DPMomentum optimizer. Similar to how we searched for default tuning choices for DPAdam in Section 4.2, we investigate if there exists a qualitatively good choice for the momentum hyperparameter, and unfortunately our results show that there is no such choice. We detail this process in the supplement.
+
+In order to show the comparison from both sides of the privacy-accuracy tradeoff, we compare the three optimizers through i) the privacy cost when extracting the best accuracy from these optimizers, and ii) the accuracy one would obtain from them under the tight privacy constraints.
+
+# 5.1 Prioritizing Accuracy
+
+For brevity, we show experiments for $\sigma = 4$ in Figure 4, results for other values of $\sigma$ are displayed in the supplement. For each dataset and model, we train three times for each hyperparameter candidate and report the max every 100 iterations, corresponding to the dark lines for each optimizer. We note that their maxima are extremely similar. However, Table 1 shows the final privacy costs incurred by each of these max accuracy lines, and reflects our claims from Section 3.1 that using fewer hyperparameter candidates and composing privacy via MA gives a much tighter privacy guarantee.
+
+# 5.2 Prioritizing Privacy
+
+298 Additionally in Figure 4, DPSGD and DPMomentum have pastel dotted lines corresponding to their   
+299 mean accuracy attained using the MA composition that provides the tightest privacy guarantees for   
+300 DPAdam. These pastel lines are the mean accuracies (with $9 5 \%$ CI) from 100 repetitions of this   
+301 experiment. Since DPAdam has only 4 hyperparameter candidates, for this experiment, we sample 4   
+302 of the candidates at random for DPSGD and DPMomentum so that they all incur the same privacy   
+303 cost. Since the candidate pool is significantly larger for DPSGD and DPMomentum, we additionally   
+304 scrutinize the parameter grid for them and prune the learning rates that perform poorly. Our pruning   
+305 process (detailed in the supplement) is quite generous, and favours minimizing the hyperparameter   
+306 space of DPSGD and DPMomentum as much possible. 1 Despite the pruning advantage we see that   
+307 these optimizers perform subpar than DPAdam when constrained with tight privacy requirements.
+
+Table 1: Final $\varepsilon$ (at $\delta \ : = \ : 1 0 ^ { - 6 }$ ) for optimizers for the LR Models (Figure 4). DPSGD and DPMomentum use LT for privacy accounting; DPAdam uses MA.   
+
+<table><tr><td rowspan=1 colspan=1>Dataset</td><td rowspan=1 colspan=1>DPSGD (LT)</td><td rowspan=1 colspan=1>DPMomentum (LT)</td><td rowspan=1 colspan=1>DPAdam (MA)</td></tr><tr><td rowspan=1 colspan=1>Adult</td><td rowspan=1 colspan=1>5.01</td><td rowspan=1 colspan=1>5.23</td><td rowspan=1 colspan=1>1.91</td></tr><tr><td rowspan=1 colspan=1>ENRON</td><td rowspan=1 colspan=1>30.86</td><td rowspan=1 colspan=1>32.31</td><td rowspan=1 colspan=1>12.80</td></tr><tr><td rowspan=1 colspan=1>Gisette</td><td rowspan=1 colspan=1>26.40</td><td rowspan=1 colspan=1>27.64</td><td rowspan=1 colspan=1>10.76</td></tr><tr><td rowspan=1 colspan=1>MNIST</td><td rowspan=1 colspan=1>3.01</td><td rowspan=1 colspan=1>3.14</td><td rowspan=1 colspan=1>1.14</td></tr></table>
+
+# 308 6 DPAdam without second moment: DPAdamWOSM
+
+309 As illustrated in the previous section, adaptivity can indeed be a boon, enabling DPAdam to match   
+310 the performance of tuned DPSGD while consuming roughly a third of the privacy budget as seen   
+311 in Table 1. However, in addition to a decaying average of the past gradient updates, DPAdam   
+312 also requires maintaining a decaying average of their second moments. In this section, we design   
+313 DPAdamWOSM, a new DP optimizer that operates only using a decaying average of past gradients,   
+314 as well as eliminates the need to tune the learning rate parameter. We achieve this by analyzing the   
+315 convergence behavior of the second-moment decaying average in DPAdam in regimes where the scale   
+316 of noise added is much higher than the scale of the clipped gradients. Setting the effective step size   
+317 (ESS) of DPAdam to the converged constant, and removing all computations related to the second  
+318 moment updates, results in DPAdamWOSM. We empirically demonstrate that DPAdamWOSM   
+319 matches the utility of DPAdam, while requiring less computation than DPAdam.   
+320 Observe that removing the second-moment updates from DPAdam reduces it to DPMomentum with   
+321 one additional feature: bias-correction to the first-moment decaying average, which DPAdam does   
+322 to account for its initialization at the origin. While the resultant optimizer still requires tuning the   
+323 learning rate (in addition to other hyperparameters like the clipping threshold), DPAdamWOSM can   
+324 be viewed as self-tuning the learning rate by fixing it to the converged effective step size in DPAdam.
+
+# 6.1 Effective step size (ESS) in DPAdam
+
+DPAdam produces results with a smaller variance than DPSGD due to its adaptive learning rate. To understand this phenomenon better, we look closely into the update step of DPAdam [KB14]. DPAdam being an adaptive optimizer picks per-parameter ESS as $\frac { \alpha } { \sqrt { \hat { v } _ { t } } + \xi }$ , which is the base learning rate $\alpha$ scaled by the second moment of the individual parameter gradients. We notice that when $g \to 0$ , the ESS for DPAdam converges for the first moment gradient, which innately accounts for the clip bound one is training with. This may happen at later iterations, when the model is close to its minima and the gradients get close to zero.
+
+Theorem 3. The effective step size (ESS) for DPAdam with g → 0 converges to ESS∗ = α(σC/L)+ξ33 .
+
+Proof. Recall that the average noisy gradient over a lot is $\tilde { g } = g + { \mathcal N } ( 0 , \sigma ^ { 2 } C ^ { 2 } ) / L$ . We now look at the effect of this noisy gradient on the effective step size (ESS) of DPAdam. As $g \to 0$ , the second moment of DPAdam converges to $\frac { \sigma ^ { 2 } C ^ { 2 } } { L ^ { 2 } }$ This gives us the converging value for ESS:
+
+$$
+E S S ^ { * } = \frac { \alpha } { \sqrt { \hat { v } _ { t } } + \xi } = \frac { \alpha } { \sqrt { \frac { \sigma ^ { 2 } C ^ { 2 } } { L ^ { 2 } } } + \xi } = \frac { \alpha } { \left( \sigma C / L \right) + \xi }
+$$
+
+![](images/400b3e3a256416bb3bc94337e26d69e1a0cc1a23efdd2f9799cfef51025cb0e7.jpg)  
+Figure 5: Comparing the testing accuracy curves of DPAdam, ADADP and DPAdamWOSM models across hyperparameter tuning grid from Table 3 with $\sigma = 4$ . The limits for the y-axes are adjusted based on the dataset while maintaining a $15 \%$ range for all.
+
+337 Theorem 3 gives a closed form expression that ESS converges to. We can use this value in place   
+338 of $\frac { \alpha } { \sqrt { \hat { v } _ { t } } + \xi }$ in the update step from the inception of the learning process. Since the second-moment   
+339 updates (e.g., $\hat { v } _ { t }$ ) are not used anymore, removing them results in our new optimizer DPAdamWOSM.   
+340 We provide a pseudo-code for DPAdamWOSM in the appendix.
+
+# 341 6.2 Comparing Adaptive Optimizers
+
+342 We evaluate DPAdamWOSM by running it alongside DPAdam and ADADP with the same hyperpa  
+343 rameter grid in the appendix. For brevity, we show experiments on $\sigma = 4$ and others appear in the   
+344 supplement. In Figure 5, we show the maximum and median accuracy curves for all the optimizers.   
+345 We display the median accuracy curves (shown in dotted), as an indicator of the quality of the entire   
+346 pool of hyperparameter candidates for a given optimizer; which in this case is strictly over the choices   
+347 of clip. The max lines for ADADP lies beneath DPAdam and DPAdamWOSM for all dataset except   
+348 Adult. Also, the max accuracy line for DPAdamWOSM runs alongside DPAdam which means that   
+349 it can perform as good as DPAdam throughout training. The median line for DPAdamWOSM also   
+350 performs alongside DPAdam and in some cases is able to beat it (e.g, the median for DPAdamWOSM   
+351 for MNIST-LR and MNIST-TLNN lies above the median line of DPAdam). This occurrence is seen   
+352 because DPAdamWOSM uses the converged ESS from the first iteration of training.
+
+# 353 7 Conclusion
+
+354 In this paper, we performed a thorough investigation of honest hyperparameter selection for DP   
+355 Optimizers. We compared two existing private methods, LT and MA to search for hyperparameter   
+356 candidates and showed that, the former incurs a significant privacy cost but can compose a great many   
+357 candidates, while the latter is helpful when the number of candidates is small. Next, we explored   
+358 connections between the clipping norm and the step size hyperparameter to show an inverse relation  
+359 ship between them. Additionally, we compared non-adaptive and adaptive optimizers, demonstrating   
+360 that the latter typically achieves more consistent performance over a variety of hyperparameter   
+361 settings. This can be vital for applications where public data is scarce, resulting in difficulties when   
+362 tuning hyperparameters. Finally, we brought to light that DPAdam converges to a static learning rate   
+363 when the noise starts dominating the gradients. This insight allowed us to derive a novel optimizer   
+364 DPAdamWOSM, a variant of DPAdam which avoids the second-moment computation and enjoys   
+365 better accuracy especially at earlier iterations. Future work remains to investigate further implications   
+366 of these results to provide tuning-free end-to-end private ML optimizers.   
+367 References   
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+
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+
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+
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+(b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [Yes]   
+(c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? [Yes]   
+(d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)? [Yes]
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+4. If you are using existing assets (e.g., code, data, models) or curating/releasing new assets...
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parse/train/bMLeGGwptZk/bMLeGGwptZk_content_list.json

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+        "text": "The Role of Adaptive Optimizers for Honest Private Hyperparameter Selection ",
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+        "text": "Hyperparameter optimization is a ubiquitous challenge in machine learning, and the performance of a trained model depends crucially upon their effective selection. While a rich set of tools exist for this purpose, there are currently no practical hyperparameter selection methods under the constraint of differential privacy (DP). We study honest hyperparameter selection for differentially private machine learning, in which the process of hyperparameter tuning is accounted for in the overall privacy budget. To this end, we i) show that standard composition tools outperform more advanced techniques in many settings, ii) empirically and theoretically demonstrate an intrinsic connection between the learning rate and clipping norm hyperparameters, iii) show that adaptive optimizers like DPAdam enjoy a significant advantage in the process of honest hyperparameter tuning, and iv) draw upon novel limiting behaviour of Adam in the DP setting to design a new and more efficient optimizer. ",
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+        "text": "14 1 Introduction ",
+        "text_level": 1,
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+        "text": "15 Over the last several decades, the field of machine learning has flourished. However, training machine   \n16 learning models frequently involves personal data, which leaves data contributors susceptible to   \n17 privacy attacks. This isn’t purely hypothetical: recent results have shown that models are vulnerable   \n18 to membership inference [SSSS17, $\\mathrm { \\bar { C } L E ^ { + } } 1 9$ , NSH19] and model inversion attacks [FJR15, SRS17].   \n19 The leading approaches for privacy-preserving machine learning are based on differential privacy   \n20 (DP) [DMNS06]. Informally, DP rigorously limits and masks the contribution that an individual   \n21 datapoint can have on an algorithm’s output. To address the aforementioned issues, DP training   \n22 procedures have been developed [WM10, BST14, SCS13, $\\mathrm { A C G ^ { + } } 1 6 ]$ , which generally resemble non  \n23 private gradient-based methods, but with the incorporation of gradient clipping and noise injection.   \n24 In both the private and non-private settings, hyperparameter selection is instrumental to achieving   \n25 high accuracy. The most common methods are grid search or random search, both of which incur   \n26 a computational overhead scaling with the number of hyperparameters under consideration. In   \n27 the private setting, this issue is often magnified as most private training procedures introduce new   \n28 hyperparameters. Regardless, and more importantly, hyperparameter tuning on a sensitive dataset   \n29 also costs in terms of privacy, naively incurring a multiplicative cost which scales as the square root   \n30 of the number of candidates (based on composition properties of differential privacy [KOV15]).   \n31 Most prior works on private learning choose not to account for this cost $[ \\mathrm { A C G ^ { + } } 1 6$ , $\\mathrm { Y L P ^ { + } 1 9 }$ , TB21],   \n32 focusing instead on demonstrating the accuracy achievable by private learning under idealized condi  \n33 tions, that is, if the best hyperparameters were somehow known ahead of time. Some works assume   \n34 the presence of supplementary public data resembling the sensitive dataset $[ \\mathrm { A G D } ^ { + } 2 0$ , $\\mathrm { R T M } ^ { + } 2 0 ]$ ,   \n35 which may be freely used for hyperparameter tuning. Naturally, such public data may be scarce or   \n36 nonexistent in settings where privacy is a concern, leaving practitioners with little guidance on how   \n37 to choose hyperparameters in practice. As explored in our paper, poor hyperparameter selection with   \n38 standard private optimizers can have catastrophic effects on model accuracy.   \n39 Hope is afforded by the success of adaptive optimizers in the non-private setting. The canonical   \n40 example is Adam [KB14], which exploits moments of the gradients to adaptively and dynamically   \n41 determine the learning rate. It works out of the box in many cases, providing accuracy comparable   \n42 with tuned SGD. We navigate the different options available to a practitioner to solve the honest   \n43 private hyperparameter tuning problem and ask, are there optimizers which provide strong privacy,   \n44 require minimal hyperparameter tuning, and perform competitively with tuned counterparts? ",
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+        "text": "45 Our Contributions ",
+        "text_level": 1,
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+        "text": "46 1. We investigate techniques for private tuning of hyperparameters. We perform the first empirical   \n47 evaluation of the proposed theoretical method of Liu and Talwar [LT19], and demonstrate that it can   \n48 be relatively expensive. That is, in certain cases, one can tune over sufficiently many hyperparameters   \n49 using standard composition tools such as moments accountant $[ \\mathrm { A C G ^ { + } } 1 6 ]$ .   \n50 2. We empirically and theoretically demonstrate that two hyperparameters, the learning rate and   \n51 clipping threshold, are intrinsically coupled for non-adaptive optimizers. While other hyperparameters   \n52 and the model architecture are restricted by the scope of the task, privacy and utility targets, and   \n53 computational resources, the learning rate and clipping norm have no a priori bounds. Since the   \n54 resulting hyperparameter grid adds up to the privacy cost while tuning to achieve the model with the   \n55 best utility, we explore leveraging adaptive optimizers to reduce the hyperparameter space.   \n56 3. We empirically demonstrate the DPAdam optimizer (with default values for most hyperparameters),   \n57 can match the performance of tuned non-adaptive optimizers on a variety of datasets, thus enabling   \n58 private learning with honest hyperparameter selection. This finding complements a prior claim   \n59 of Papernot et al. $[ \\mathrm { P C S ^ { + } } 2 0 ]$ , which suggests that a well-tuned DPSGD can outperform DPAdam.   \n60 However, our findings show that this difference in performance is relatively insignificant. Furthermore,   \n61 in the realistic setting where hyperparameter tuning must be accounted for in the privacy loss, we   \n62 show that DPAdam is much more likely to produce non-catastrophic results.   \n63 4. We show that the adaptive learning rate of DPAdam converges to a static value. To leverage this,   \n64 we introduce a new private optimizer, DPAdamWOSM that matches the performance of DPAdam   \n65 without computing the second moments. ",
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+        "text": "66 1.1 Related Work ",
+        "text_level": 1,
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+        "text": "67 Hyperparameter tuning plays a vital role in machine learning practice. In the non-private setting,   \n68 ML practitioners use grid search, random search, Bayesian optimization techniques [SSA13] or   \n69 AutoML [HZC21] techniques to tune their models. However, there hasn’t been much research   \n70 on private hyperparameter tuning procedures due to the significant associated privacy costs. Each   \n71 set of hyperparameter configuration results in a privacy-utility tradeoff. This tradeoff for multiple   \n72 configurations can be captured by Pareto frontiers using multivariate Bayesian optimization over   \n73 parameter dimensions $[ \\bar { \\mathbf { A } } \\mathbf { G } \\mathbf { D } ^ { + } 2 0 ]$ . However, this method asks the model curator to query the   \n74 dataset multiple times which requires non-private access to the dataset. There have been some   \n75 end-to-end private tuning procedures [CMS11, CV13, KGGW15] which work for a selected number   \n76 of hyperparameter sets. These results work either in restricted settings for few combinations of   \n77 candidates or under relaxations of differential privacy. The most relevant work to ours is an approach   \n78 for private selection from private candidates [LT19]. Their work provides two methods, one which   \n79 outputs a candidate with accuracy greater than a given input threshold, and another which randomly   \n80 stops and outputs the best candidate seen so far. The first approach is of limited utility in practice as   \n81 it requires a prior accuracy bound for the dataset. The second variant incurs a considerable overhead   \n82 in the privacy cost. We study this second approach and compare it with naive approaches based on   \n83 Moments Accountant $[ \\mathsf { A C G } ^ { + } 1 6 ]$ which would scale as the square root of the number of candidates. ",
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+        "type": "text",
+        "text": "84 2 Problem Setup and Overview ",
+        "text_level": 1,
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+        "text": "85 Consider a sensitive dataset $D$ which lies beyond a privacy firewall and has $n$ points of the form   \n86 $( x _ { 1 } , y _ { 1 } ) , ( x _ { 2 } , y _ { 2 } ) , \\ldots , ( x _ { n } , y _ { n } )$ where $x _ { i } \\in \\mathcal X$ is the feature vector of the ith point and $y _ { i } \\in \\mathcal { V }$ is its   \n87 desired output. Though our experiments are carried out in the supervised setting, all results can be   \n88 translated to unsupervised setting as well. The dataset has been divided into two parts, the training set   \n89 and the validation set. A trusted curator wants to train a machine learning model by making queries   \n90 on the dataset with a total end-to-end training privacy budget of $( \\varepsilon _ { f } , \\delta _ { f } )$ such that the model can   \n91 perform with high accuracy on the validation set. The curator wants to try multiple hyperparameter   \n92 candidates for the model to figure out which candidate gives the maximum accuracy. However, as the   \n93 model is private, each candidate requires multiple queries made on the dataset and all of them need to   \n94 be accounted in the total privacy budget of $( \\varepsilon _ { f } , \\delta _ { f } )$ .   \n95 Note that any validation accuracy must also be measured privately. Since this accuracy is a low  \n96 sensitivity query with a scalar output, and must only be computed once per choice of hyperparameters,   \n97 the cost of this procedure is generally a lower order term versus the main training procedure. Thus for   \n98 simplicity, we do not noise these validation accuracy queries. As we will see later, some optimizers   \n99 require more candidates to tune and hence would also require more privacy budget than others.   \n100 To tackle private hyperparameter selection, we first compare the available private tuning procedures   \n101 in Section 3. We show that the privacy cost for training a model depends on the hyperparameter   \n102 grid size and standard composition theorems provide the best guarantees when the grid is small. In   \n103 Section 4, we investigate different optimizers to see how many candidates are required to output   \n104 a good solution. In Section 4.1 we provide theoretical and empirical evidence to demonstrate an   \n105 intrinsic coupling between two hyperparameters – the learning rate and clipping norm in DPSGD.   \n106 We show that this coupling makes DPSGD sensitive to these parameter choices, which can drastically   \n107 affect the validation accuracy. In Section 4.2 we demonstrate that an adaptive optimizer, DPAdam,   \n108 translates well from the non-private setting and obviates tuning of the learning rate. In Section 5, we   \n109 empirically compare DPAdam with DPSGD and DPMomentum to show that DPAdam performs at par   \n110 with less hyperparameter tuning. Finally, in Section 6, we establish that DPAdam converges to a static   \n111 learning rate in restricted settings, and unveil a new optimizer DPAdamWOSM which can leverage   \n112 this converged value without computing the second moments. In the interest of space, we defer   \n113 standard preliminaries such as DP definitions, hyperparameters, and optimizers to the appendix. ",
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+    {
+        "type": "text",
+        "text": "114 3 The Cost of Privately Tuning DP Optimizers ",
+        "text_level": 1,
+        "bbox": [
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+        "text": "115 Effective hyperparameter tuning is crucial in extracting good utility from an optimizer. Unlike   \n116 the non-private setting, DP optimizers typically i) have more hyperparameters to tune; ii) require   \n117 additional privacy budget for tuning. Existing work on DP optimizers acknowledge this problem (e.g.,   \n118 $\\mathrm { [ A C G ^ { + } 1 6 \\bar ] } ,$ ), but do not address the privacy cost incurred during hyperparameter tuning $[ \\mathrm { A C G ^ { + } } 1 6$ ,   \n119 $\\mathrm { Y L P ^ { + } } 1 9$ , TB21]. There are two main prior general-purpose approaches for private hyperparameter   \n120 selection. The first performs composition via Moments Accountant $[ \\mathrm { A C G ^ { + } } 1 6 ]$ , and the second is   \n121 the algorithm of Liu and Talwar (LT) [LT19]. The latter is a theoretical result, and to the best of our   \n122 knowledge, has not been previously evaluated in practice. We investigate the privacy cost of these   \n123 two techniques in practice and discuss situations in which each method is preferred. ",
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+    {
+        "type": "text",
+        "text": "124 3.1 Hyperparameter Selection via [LT19] ",
+        "text_level": 1,
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+        "text": "125 Liu and Talwar [LT19] propose a random stopping algorithm (LT) to output a ‘good’ hyperparameter   \n126 candidate from a pool of $K$ candidates, $\\{ x _ { 1 } , \\ldots , x _ { K } \\}$ . They assume sampling access to a randomized   \n127 mechanism $Q ( D )$ which samples $i \\sim [ K ]$ , and returns the $i$ -th candidate $x _ { i }$ , and a score $q _ { i }$ for this   \n128 candidate. It is a random stopping algorithm, in which at every iteration, a candidate is picked from   \n129 $Q$ i.i.d. with replacement and a $\\gamma$ -biased coin is flipped to randomly stop the algorithm. When the   \n130 algorithm stops, the candidate with the maximum score seen so far is outputted. In the approximate   \n131 DP version of this algorithm, an extra parameter $\\Upsilon$ is set to limit the total of number of iterations.   \n132 The pseudocode of this algorithm is deferred to the appendix. ",
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+        "type": "text",
+        "text": "Theorem 1 ([LT19], Theorem 3.4). Fix any 133 $\\gamma \\in [ 0 , 1 ]$ , $\\delta _ { 2 } > 0$ and let $\\begin{array} { r } { \\Upsilon = \\frac { 1 } { \\gamma } \\log \\frac { 1 } { \\delta _ { 2 } } } \\end{array}$ . If $Q$ is 134 $( \\varepsilon _ { 1 } , \\delta _ { 1 } )$ -DP, then the LT algorithm is $( \\varepsilon _ { f } , \\delta _ { f } )$ -DP for $\\varepsilon _ { f } = 3 \\varepsilon _ { 1 } + 3 \\sqrt { 2 \\delta _ { 1 } }$ and $\\delta _ { f } = \\sqrt { 2 \\delta _ { 1 } } \\Upsilon + \\delta _ { 2 }$ . ",
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+        "type": "text",
+        "text": "135 Theorem 1 expresses the privacy cost of the algorithm in terms of the privacy cost of individual   \n136 learners, and parameters of the algorithm itself. The $\\delta _ { 2 }$ parameter does not significantly affect the   \n137 final epsilon $\\varepsilon _ { f }$ of the algorithm and in practice, one can set it to a very small value $( 1 0 ^ { - 2 0 } )$ . Though   \n138 a small value of $\\delta _ { 2 }$ has little effect on $\\delta _ { f }$ , it increases the hard stopping time of the algorithm, $\\Upsilon$ .   \n139 To understand the LT algorithm, we will compare the privacy costs of training a single hyperparameter   \n140 candidate with a final $\\varepsilon _ { f } , \\delta _ { f }$ budget via LT and compare it with the privacy cost $\\varepsilon _ { 1 } , \\delta _ { 1 }$ of the underlying   \n141 individual learner. This setting might seem unnatural for LT as it was designed to select from a pool   \n142 of candidates but we choose this setting to show the minimum privacy cost overhead associated with   \n143 LT and later show how the privacy cost changes for multiple candidates (varying $\\gamma$ ). To use LT, one   \n144 needs to figure out the $\\varepsilon _ { 1 } , \\delta _ { 1 }$ via Theorem 1 using the final $\\varepsilon _ { f } , \\delta _ { f }$ values and in this case, $\\gamma = 1$ (as   \n145 we have just one candidate). The individual learner is then trained using $\\varepsilon _ { 1 } , \\delta _ { 1 }$ budget.   \n146 Due to the delicate balance of $\\delta _ { f }$ in Theorem 1, one can see the $\\delta _ { 1 }$ comes out to be much smaller than   \n147 $\\delta _ { f }$ . This change in $\\delta _ { 1 }$ results in a blowup of $\\varepsilon _ { 1 }$ and hence, the final privacy cost of the LT algorithm   \n148 $( \\dot { 3 } \\varepsilon _ { 1 } + 3 \\sqrt { 2 \\delta _ { 1 } } )$ , is much larger than what it would have been for learning one candidate without LT.   \n149 We call this increase the blowup of privacy. We measure this blowup in Figure 1(left), for the setting   \n150 of $\\sigma = 4$ , $L = 2 5 0$ , $T = 1 0 , 0 0 0$ with varying dataset sizes $( n )$ . It can be seen that for $n = 5 , 0 0 0$ ,   \n151 the blowup is $4 . 8 \\mathrm { x }$ whereas for for $n = 9 5 0 , 0 0 0$ , the blowup is almost $7 . 3 \\mathrm { x }$ (note the log scale on   \n152 y-axis). Qualitatively similar trends persist for other choices of noise multiplier, lot size and iterations.   \n153 We add more experiments to compare LT vs MA with varying candidate sizes in the appendix.   \n154 Furthermore, we show that although LT entails a privacy blowup, decreasing $\\gamma$ , which corresponds   \n155 to training more individual learners with $\\varepsilon _ { 1 } , \\delta _ { 1 }$ , doesn’t result in a significant difference in the final   \n156 epsilon guaranteed by LT. In Figure 1(middle), we show the final epsilon cost for different dataset   \n157 size and varying values of $\\gamma \\in [ 0 . 0 0 1 , 0 . 0 1 , 0 . 1 , 1 ]$ . It is interesting to note here that with smaller   \n158 $\\gamma$ values, one can train many candidates (in expectation, $\\textstyle { \\frac { 1 } { \\gamma } } .$ ) for negligible additional privacy cost.   \n159 The blowup to train 1 candidate $( \\gamma = 1 )$ ) versus $1 , 0 0 0$ candidates $\\gamma = 0 . 0 0 1 )$ increases from 33   \n160 to 39 for $n = 5 , 0 0 0$ and increases from 0.49 to 0.69, for $n = 9 5 0 , 0 0 0$ . This increase is minimal√   \n161 in comparison to advanced composition, which grows proportional to $\\mathcal { O } ( \\sqrt { k } )$ . However, another   \n162 resource at play is the total training time, which is proportional to $1 / \\gamma$ (i.e., the total number of   \n163 candidates). In summary, the LT algorithm is effective if an analyst has the privacy budget to afford   \n164 the initial blowup, as the privacy cost of testing additional hyperparameters is insignificant. ",
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+        "image_caption": [
+            "Figure 1: Comparing the privacy cost of LT versus Moments Accountant. The minimal privacy overhead incurred by LT is at least ${ \\sim } 5 \\mathrm { x }$ , and increases with the dataset size (left). However, as we allow LT to sample and test more candidate hyperparameters, the privacy cost barely increases (middle). Moments Accountant is able to test a significant number of candidates at the same cost as the minimal privacy overhead of LT (right). "
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+        "type": "text",
+        "text": "165 3.2 Hyperparameter Selection via Moments Accountant ",
+        "text_level": 1,
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+        "text": "166 We learnt from the previous section that, LT permits selection from a large pool of hyperparameters   \n167 (depending on the $\\gamma$ value) but incurs a constant privacy blowup. We compare LT with tuning   \n168 using Moments Accountant (MA). We notice using that with the same initial privacy blowup of   \n169 the LT algorithm, MA is able to compose a considerable number of hyperparameter candidates. In   \n170 Figure 1(right), we show the number of candidates that can be composed using MA for the minimum   \n171 privacy cost for running the LT algorithm $( \\gamma = 1 )$ ), for the setting of $\\sigma = 4$ , $L = 2 5 0$ , $T = 1 0$ , 000   \n172 and varying dataset size $( n )$ on the $\\mathbf { X }$ -axis. As the $T$ and $L$ is set constant, bigger $n$ values in this   \n173 graph correspond to fewer epochs of training and hence, worse utility. Depending on dataset size,   \n174 MA can compose 14 candidates for $n = 5 0 0 0$ and up to 175 candidates when $n = 1 0 0 0 0 0$ . It is   \n175 perhaps surprising how well a standard composition technique performs versus LT. This information   \n176 can be highly valuable to a practitioner who has limited privacy budget. Qualitatively similar trends   \n177 persist for other choices of batch size, noise multiplier, and iterations.   \n178 From our experiments for both these tuning procedures, we conclude that while tuning with LT entails   \n179 an initial privacy blowup, and the additional privacy cost for trying more candidates (smaller $\\gamma$ ) is   \n180 minimal. Even though this has an additional computation cost, it can be appealing when an analyst   \n181 wants to try numerous hyperparameters. On the other hand, for the same overall privacy cost, MA   \n182 can be used to compose a significant number of hyperparameter candidates. Additionally, MA allows   \n183 access to all intermediate learners, whereas LT allows access to only the final output parameters. In   \n184 the sequel, this conclusion will be useful in making the naive MA approach a more appealing tool for   \n185 some settings (e.g., tighter privacy budgets). ",
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+        "type": "text",
+        "text": "186 4 Tuning DP Optimizers ",
+        "text_level": 1,
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+        "text": "187 We detail aspects of tuning both non-adaptive and adaptive optimizers. We start with tuning non  \n188 adaptive optimizers (Section 4.1). We theoretically and empirically demonstrate a connection between   \n189 the learning rate and clipping threshold. We also establish that non-adaptive optimizers inevitably   \n190 require searching over a large LR-clip grid to extract performant models. Adaptive optimizers forego   \n191 this problem as they do not need to tune the hyperparameter dimension of learning rate. However,   \n192 they introduce other hyperparameters that have known good choices in the non-private setting, and   \n193 we empirically show that they are good candidates in the private setting (Section 4.2). ",
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+        "type": "text",
+        "text": "194 4.1 Tuning DP non-adaptive optimizers ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "While many hyperparameters are restricted due to computational and privacy/utility targets, the learning rate $\\alpha$ and the clipping threshold $C$ have no a priori bounds. In what follows, we show an interplay between these parameters by first theoretically analyzing the convergence of DPSGD. We then explore an illustrative experiment which demonstrates their entanglement. In the following theorem, we derive a bound on the expected excess risk of DPSGD and while doing so, show that the optimal learning rate, $\\alpha _ { o p t }$ , is proportional to the inverse of $C$ . The proof appears in Appendix D. ",
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+    {
+        "type": "text",
+        "text": "Theorem 2. Let $f$ be a convex and $\\beta$ -smooth function, and let $x ^ { * } = \\arg \\operatorname* { m i n } _ { x \\in S } f ( x )$ . Let $x _ { 0 }$ be an arbitrary point in $s$ , and $x _ { t + 1 } = \\Pi _ { S } ( x _ { t } - \\alpha ( g _ { t } + z _ { t } ) )$ , where $\\begin{array} { r } { g _ { t } = \\operatorname* { m i n } ( 1 , \\frac { C } { \\| \\nabla f ( x ) \\| ^ { 2 } } ) \\nabla f ( x ) } \\end{array}$ and $z _ { t } \\sim \\mathcal { N } ( 0 , \\sigma ^ { 2 } C ^ { 2 } )$ is the noise due to privacy. After $T$ iterations, the optimal learning rate is $\\begin{array} { r } { \\alpha _ { o p t } = \\frac { R } { C T \\sqrt { 1 + \\sigma ^ { 2 } } } } \\end{array}$ , where $\\begin{array} { r } { \\mathbb { E } [ f ( \\frac { 1 } { T } \\sum _ { i } ^ { T } x _ { t } ) - f ( x ^ { * } ) ] \\leq \\frac { R C \\sqrt { 1 + \\sigma ^ { 2 } } } { \\sqrt { T } } } \\end{array}$ and $R = \\mathbb { E } [ \\| x _ { 0 } - x ^ { * } \\| ]$ . ",
+        "bbox": [
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+        "type": "text",
+        "text": "Though Theorem 2 gives a closed-form expression for the optimum learning rate, it is a function of the parameter $R$ , which is unknown a priori to the analyst. Given constant $T$ and $\\sigma$ , the optimal learning rate $\\alpha _ { o p t }$ is inversely proportional to the clipping norm $C$ . This is crucial information in practice because these parameters vary among datasets and are unbounded. This unboundedness property thus requires us to search over very large ranges of $C$ and $\\alpha$ when we have no prior knowledge of the dataset. It is natural to ask whether one can fix the clipping norm $C$ and search only over a wide range for the learning rate $\\alpha$ (or vice versa). We explore this relationship experimentally, showing that fixing one of these two hyperparameters may often but not always result in an optimal model. ",
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+        "img_path": "images/0f218e874ffce118de2302a9b4024f19a6fd8a62fdbc4f10706873ff6e14b9d2.jpg",
+        "image_caption": [
+            "Figure 2: Log of training loss for simulation experiment at $\\sigma = 4$ on a synthetic dataset. The black pixels correspond to lowest training loss. Note that most best loss values lie on a diagonal expressing the inverse connection between $\\alpha$ and $C$ . "
+        ],
+        "image_footnote": [],
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+        "text": "219 In this experiment, we train a linear regression model on a   \n220 10-dimensional synthetic dataset of input-label pairs $( x , y )$   \n221 sampled from a distribution $\\mathcal { D }$ as follows: $x _ { 1 } , \\ldots , x _ { d } \\sim$   \n222 $\\mathcal { U } ( 0 , 1 ) , y = x \\cdot w ^ { * } , w ^ { * } = 1 0 \\cdot \\mathbf { 1 } ^ { d }$ . We use the initialization   \n223 $w _ { 0 } = \\mathbf { 0 } ^ { d }$ and train for 100 iterations. In the non-private   \n224 setting, this model converges quickly with any reasonable   \n225 learning rate, but in the private setting, we notice that the ",
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+        "type": "text",
+        "text": "6 training loss depends heavily on the choice of $\\alpha$ and $C$ . Figure 2 shows a heat map for the log training loss when trained on $( \\alpha , C )$ pairs taken from a large grid consisting of [1, 2, 4, 5, 8] at scales of 8 $[ 1 0 ^ { - 4 } , 1 0 ^ { - 3 } , 1 0 ^ { - 2 } , 1 0 ^ { - 1 } , 1 0 ^ { 0 } , 1 0 ^ { \\hat { 1 } } ]$ . The best training is observed when the loss is 0 (black pixels). ",
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+        "image_caption": [
+            "Figure 3: Ranking hyperparameter candidates across datasets. The black points correspond to the candidates with $\\alpha = 0 . 0 0 1$ (with all permutations of $\\beta _ { 1 } , \\beta _ { 2 }$ from our searchgrid); the gold corresponds to the candidate with $\\alpha = 0 . 0 0 1 , \\beta _ { 1 } = 0 . 9 , \\beta _ { 2 } = 0 . 9 9 9$ "
+        ],
+        "image_footnote": [],
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+        "type": "text",
+        "text": "229 We observe two fundamental phenomena from this figure. First, to achieve the best accuracy, $\\alpha$ and   \n230 $C$ need to be tuned on a large grid spanning several orders of magnitude for each of these parameters.   \n231 Second, multiple $( \\alpha , C )$ pairs achieve the best accuracy and all lie on the same diagonal, validating   \n232 our theory for an inverse relation between learning rate and clipping norm. As mentioned earlier, one   \n233 might hypothesize that by setting the clipping norm $C$ constant and tuning $\\alpha$ (corresponding to a   \n234 vertical line in Figure 2) or vice versa, one could eliminate tuning a hyperparameter. However, note   \n235 that not all $C$ and $\\alpha$ values correspond to the lowest loss. This phenomenon is evident by noticing   \n236 that not all vertical or horizontal lines on this figure have black pixels. This happens, for example,   \n237 at the extremes (e.g., at the top-right corner), but also for several intermediate and standard choices   \n238 (e.g., $C = 0 . 1$ or 0.2). Again, the analyst has no way of knowing this a priori. We conclude that to   \n239 privately tune non-adaptive optimizers, we require a large grid of hyperparameter options. ",
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+    {
+        "type": "text",
+        "text": "4.2 Tuning DP adaptive optimizers ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In the interest of reducing this space of tuning we turn to adaptive optimizers, where we can at least reduce one dimension of this search space. These approaches automatically adapt over the learning rate $\\alpha$ , requiring us to tune only over the clipping norm $C$ . But recall our key question: can we train models that perform competitively with the fine-tuned counterparts from DPSGD? ",
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+    {
+        "type": "text",
+        "text": "Adam [KB14], the canonical adaptive optimizer introduces two new hyperparameters, which are the first and second moment exponential decay parameters ( $\\beta _ { 1 }$ and $\\beta _ { 2 }$ ). In the non-private setting, these parameters are relatively insensitive, and default values of $\\alpha = 0 . 0 0 1 , \\beta _ { 1 } = 0 . 9$ , and $\\beta _ { 2 } = 0 . 9 9 9$ are recommended based on empirical findings, requiring no additional tuning for this hyperparameter triple. Hence before we compare DPAdam and DPSGD, we first find and establish such recommended values for this hyperparameter triple in the DP setting next, and then show that DPAdam with a small hyperparameter space performs competitively with DPSGD in Section 5. ",
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+        "text": "252 To establish default choices of $\\alpha$ , $\\beta _ { 1 }$ , and $\\beta _ { 2 }$ for DPAdam, we evaluate this private optimizer over four   \n253 diverse datasets (details in Appendix B, Table 2) and two learning models including logistic regression   \n254 and a neural network with one 100 neurons hidden layer (TLNN). These selected datasets include   \n255 both low-dimensional data (where the number of samples greatly outnumbers the dimensionality) and   \n256 high-dimensional data (where the number of samples and dimensionality are at same scale). Since   \n257 we still have a large hyperparameter space to tune over, for the rest of this work, we fix a constant lot   \n258 size $L = 2 5 0$ ), and consider tuning over three different noise levels, $\\sigma \\in [ 2 , 4 , 8 ]$ , so that we can   \n259 study the effects of tuning the other hyperparameters more thoroughly. All experiments are repeated   \n260 three times and averaged before reporting. Additionally, in this particular experiment since we focus   \n261 on $\\alpha , \\beta _ { 1 }$ , and $\\beta _ { 2 }$ , we also fix the clipping threshold $C = 0 . 5$ , and $T = 2 5 0 0$ iterations of training.   \n262 For each dataset and model, we run DPAdam three times with hyperparameters $( \\alpha , \\beta _ { 1 } , \\beta _ { 2 } )$ from the   \n263 grids, $\\alpha \\in [ 0 . 0 0 1 , 0 . 0 5 , 0 . 0 1 , 0 . 2 , 0 . 5$ ], $\\beta _ { 1 } , \\beta _ { 2 } \\in [ 0 . 8 , 0 . 8 5 , 0 . 9 , 0 . 9 5 , 0 . 9 9 . 0 . 9 9 9 ]$ .   \n264 We show that the default hyperparameter choice $( \\alpha , \\beta _ { 1 } , \\beta _ { 2 } )$ of Adam in the non-private setting also   \n265 works well for DPAdam. Figure 3 shows the boxplots of testing accuracies of DPAdam over the   \n266 different hyperparameter choices. When $\\alpha$ is 0.001 (same as in the non-private setting), all the   \n267 datasets and models have final testing accuracies (marked in black) close to the best possible (and   \n268 in most cases it is in fact the best) accuracy. Furthermore, we also highlight the accuracy of the   \n269 suggested default choice $( \\alpha = 0 . 0 0 1 , \\beta _ { 1 } = 0 . 9 , \\beta _ { 2 } = 0 . 9 9 9 )$ using gold dots. Hence, for the ease of   \n270 using DPAdam, we suggest the non-private default values for these parameters in the private setting   \n271 as well and hence in all our subsequent experiments. ",
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+    {
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+        "image_caption": [
+            "Figure 4: Comparing the testing accuracy curves of DPAdam, DPSGD and DPMomentum models across their hyperparameter tuning grids with $\\sigma = 4$ . The limits for y-axis are adjusted based on the dataset while maintaining a $15 \\%$ range for all. "
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+    {
+        "type": "text",
+        "text": "5 Advantages of tuning using DPAdam ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In the non-private setting, adaptive optimizers like Adam enjoy a smaller hyperparameter tuning space than SGD. We ask two questions in this section. First, can DPAdam (with little tuning) achieve accuracy comparable to a well-tuned DPSGD? Second, what is the privacy-accuracy tradeoff one incurs when using either of the two methods we detail in Section 3 for hyperparameter selection. ",
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+    {
+        "type": "text",
+        "text": "To answer both questions, we compare DPAdam and DPSGD over the same set of datasets and models from the previous section. We report the accuracy of DPSGD with a range of learning rates and clipping values shown in Table 3 (Appendix C), and the testing accuracy of DPAdam with default parameter choice from Section 4.2 $\\mathbf { \\Phi } _ { \\mathrm { { ( } } \\alpha } = 0 . 0 0 1 $ , $\\beta _ { 1 } = 0 . 9$ , $\\beta _ { 2 } = 0 . 9 9 9 \\rangle$ ) and a range of clipping values $C$ in Table 3. In total, DPSGD has 40 candidates to tune over, and DPAdam has 4. This is because we have shown in Section 4.1 that DPSGD needs a wide grid to obtain the best accuracy when data distributions are unknown. Additionally, we also consider the DPMomentum optimizer. Similar to how we searched for default tuning choices for DPAdam in Section 4.2, we investigate if there exists a qualitatively good choice for the momentum hyperparameter, and unfortunately our results show that there is no such choice. We detail this process in the supplement. ",
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+    {
+        "type": "text",
+        "text": "In order to show the comparison from both sides of the privacy-accuracy tradeoff, we compare the three optimizers through i) the privacy cost when extracting the best accuracy from these optimizers, and ii) the accuracy one would obtain from them under the tight privacy constraints. ",
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+    {
+        "type": "text",
+        "text": "5.1 Prioritizing Accuracy ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "For brevity, we show experiments for $\\sigma = 4$ in Figure 4, results for other values of $\\sigma$ are displayed in the supplement. For each dataset and model, we train three times for each hyperparameter candidate and report the max every 100 iterations, corresponding to the dark lines for each optimizer. We note that their maxima are extremely similar. However, Table 1 shows the final privacy costs incurred by each of these max accuracy lines, and reflects our claims from Section 3.1 that using fewer hyperparameter candidates and composing privacy via MA gives a much tighter privacy guarantee. ",
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+    {
+        "type": "text",
+        "text": "5.2 Prioritizing Privacy ",
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+        "text": "298 Additionally in Figure 4, DPSGD and DPMomentum have pastel dotted lines corresponding to their   \n299 mean accuracy attained using the MA composition that provides the tightest privacy guarantees for   \n300 DPAdam. These pastel lines are the mean accuracies (with $9 5 \\%$ CI) from 100 repetitions of this   \n301 experiment. Since DPAdam has only 4 hyperparameter candidates, for this experiment, we sample 4   \n302 of the candidates at random for DPSGD and DPMomentum so that they all incur the same privacy   \n303 cost. Since the candidate pool is significantly larger for DPSGD and DPMomentum, we additionally   \n304 scrutinize the parameter grid for them and prune the learning rates that perform poorly. Our pruning   \n305 process (detailed in the supplement) is quite generous, and favours minimizing the hyperparameter   \n306 space of DPSGD and DPMomentum as much possible. 1 Despite the pruning advantage we see that   \n307 these optimizers perform subpar than DPAdam when constrained with tight privacy requirements. ",
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+            "Table 1: Final $\\varepsilon$ (at $\\delta \\ : = \\ : 1 0 ^ { - 6 }$ ) for optimizers for the LR Models (Figure 4). DPSGD and DPMomentum use LT for privacy accounting; DPAdam uses MA. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=1>Dataset</td><td rowspan=1 colspan=1>DPSGD (LT)</td><td rowspan=1 colspan=1>DPMomentum (LT)</td><td rowspan=1 colspan=1>DPAdam (MA)</td></tr><tr><td rowspan=1 colspan=1>Adult</td><td rowspan=1 colspan=1>5.01</td><td rowspan=1 colspan=1>5.23</td><td rowspan=1 colspan=1>1.91</td></tr><tr><td rowspan=1 colspan=1>ENRON</td><td rowspan=1 colspan=1>30.86</td><td rowspan=1 colspan=1>32.31</td><td rowspan=1 colspan=1>12.80</td></tr><tr><td rowspan=1 colspan=1>Gisette</td><td rowspan=1 colspan=1>26.40</td><td rowspan=1 colspan=1>27.64</td><td rowspan=1 colspan=1>10.76</td></tr><tr><td rowspan=1 colspan=1>MNIST</td><td rowspan=1 colspan=1>3.01</td><td rowspan=1 colspan=1>3.14</td><td rowspan=1 colspan=1>1.14</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "308 6 DPAdam without second moment: DPAdamWOSM ",
+        "text_level": 1,
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+        "text": "309 As illustrated in the previous section, adaptivity can indeed be a boon, enabling DPAdam to match   \n310 the performance of tuned DPSGD while consuming roughly a third of the privacy budget as seen   \n311 in Table 1. However, in addition to a decaying average of the past gradient updates, DPAdam   \n312 also requires maintaining a decaying average of their second moments. In this section, we design   \n313 DPAdamWOSM, a new DP optimizer that operates only using a decaying average of past gradients,   \n314 as well as eliminates the need to tune the learning rate parameter. We achieve this by analyzing the   \n315 convergence behavior of the second-moment decaying average in DPAdam in regimes where the scale   \n316 of noise added is much higher than the scale of the clipped gradients. Setting the effective step size   \n317 (ESS) of DPAdam to the converged constant, and removing all computations related to the second  \n318 moment updates, results in DPAdamWOSM. We empirically demonstrate that DPAdamWOSM   \n319 matches the utility of DPAdam, while requiring less computation than DPAdam.   \n320 Observe that removing the second-moment updates from DPAdam reduces it to DPMomentum with   \n321 one additional feature: bias-correction to the first-moment decaying average, which DPAdam does   \n322 to account for its initialization at the origin. While the resultant optimizer still requires tuning the   \n323 learning rate (in addition to other hyperparameters like the clipping threshold), DPAdamWOSM can   \n324 be viewed as self-tuning the learning rate by fixing it to the converged effective step size in DPAdam. ",
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+        "type": "text",
+        "text": "6.1 Effective step size (ESS) in DPAdam ",
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+        "text": "DPAdam produces results with a smaller variance than DPSGD due to its adaptive learning rate. To understand this phenomenon better, we look closely into the update step of DPAdam [KB14]. DPAdam being an adaptive optimizer picks per-parameter ESS as $\\frac { \\alpha } { \\sqrt { \\hat { v } _ { t } } + \\xi }$ , which is the base learning rate $\\alpha$ scaled by the second moment of the individual parameter gradients. We notice that when $g \\to 0$ , the ESS for DPAdam converges for the first moment gradient, which innately accounts for the clip bound one is training with. This may happen at later iterations, when the model is close to its minima and the gradients get close to zero. ",
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+        "type": "text",
+        "text": "Theorem 3. The effective step size (ESS) for DPAdam with g → 0 converges to ESS∗ = α(σC/L)+ξ33 . ",
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+        "text": "Proof. Recall that the average noisy gradient over a lot is $\\tilde { g } = g + { \\mathcal N } ( 0 , \\sigma ^ { 2 } C ^ { 2 } ) / L$ . We now look at the effect of this noisy gradient on the effective step size (ESS) of DPAdam. As $g \\to 0$ , the second moment of DPAdam converges to $\\frac { \\sigma ^ { 2 } C ^ { 2 } } { L ^ { 2 } }$ This gives us the converging value for ESS: ",
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+        "img_path": "images/88d3d3eadfd84fcb53ade4fbf8930cd049953964d54dcf0a25486070f7350b92.jpg",
+        "text": "$$\nE S S ^ { * } = \\frac { \\alpha } { \\sqrt { \\hat { v } _ { t } } + \\xi } = \\frac { \\alpha } { \\sqrt { \\frac { \\sigma ^ { 2 } C ^ { 2 } } { L ^ { 2 } } } + \\xi } = \\frac { \\alpha } { \\left( \\sigma C / L \\right) + \\xi }\n$$",
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+        "img_path": "images/400b3e3a256416bb3bc94337e26d69e1a0cc1a23efdd2f9799cfef51025cb0e7.jpg",
+        "image_caption": [
+            "Figure 5: Comparing the testing accuracy curves of DPAdam, ADADP and DPAdamWOSM models across hyperparameter tuning grid from Table 3 with $\\sigma = 4$ . The limits for the y-axes are adjusted based on the dataset while maintaining a $15 \\%$ range for all. "
+        ],
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+    {
+        "type": "text",
+        "text": "337 Theorem 3 gives a closed form expression that ESS converges to. We can use this value in place   \n338 of $\\frac { \\alpha } { \\sqrt { \\hat { v } _ { t } } + \\xi }$ in the update step from the inception of the learning process. Since the second-moment   \n339 updates (e.g., $\\hat { v } _ { t }$ ) are not used anymore, removing them results in our new optimizer DPAdamWOSM.   \n340 We provide a pseudo-code for DPAdamWOSM in the appendix. ",
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+    {
+        "type": "text",
+        "text": "341 6.2 Comparing Adaptive Optimizers ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "342 We evaluate DPAdamWOSM by running it alongside DPAdam and ADADP with the same hyperpa  \n343 rameter grid in the appendix. For brevity, we show experiments on $\\sigma = 4$ and others appear in the   \n344 supplement. In Figure 5, we show the maximum and median accuracy curves for all the optimizers.   \n345 We display the median accuracy curves (shown in dotted), as an indicator of the quality of the entire   \n346 pool of hyperparameter candidates for a given optimizer; which in this case is strictly over the choices   \n347 of clip. The max lines for ADADP lies beneath DPAdam and DPAdamWOSM for all dataset except   \n348 Adult. Also, the max accuracy line for DPAdamWOSM runs alongside DPAdam which means that   \n349 it can perform as good as DPAdam throughout training. The median line for DPAdamWOSM also   \n350 performs alongside DPAdam and in some cases is able to beat it (e.g, the median for DPAdamWOSM   \n351 for MNIST-LR and MNIST-TLNN lies above the median line of DPAdam). This occurrence is seen   \n352 because DPAdamWOSM uses the converged ESS from the first iteration of training. ",
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+    {
+        "type": "text",
+        "text": "353 7 Conclusion ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "354 In this paper, we performed a thorough investigation of honest hyperparameter selection for DP   \n355 Optimizers. We compared two existing private methods, LT and MA to search for hyperparameter   \n356 candidates and showed that, the former incurs a significant privacy cost but can compose a great many   \n357 candidates, while the latter is helpful when the number of candidates is small. Next, we explored   \n358 connections between the clipping norm and the step size hyperparameter to show an inverse relation  \n359 ship between them. Additionally, we compared non-adaptive and adaptive optimizers, demonstrating   \n360 that the latter typically achieves more consistent performance over a variety of hyperparameter   \n361 settings. This can be vital for applications where public data is scarce, resulting in difficulties when   \n362 tuning hyperparameters. Finally, we brought to light that DPAdam converges to a static learning rate   \n363 when the noise starts dominating the gradients. This insight allowed us to derive a novel optimizer   \n364 DPAdamWOSM, a variant of DPAdam which avoids the second-moment computation and enjoys   \n365 better accuracy especially at earlier iterations. Future work remains to investigate further implications   \n366 of these results to provide tuning-free end-to-end private ML optimizers.   \n367 References   \n368 $[ \\mathrm { A C G ^ { + } } 1 6 ]$ Martin Abadi, Andy Chu, Ian Goodfellow, H. Brendan McMahan, Ilya Mironov, Kunal   \n369 Talwar, and Li Zhang. Deep learning with differential privacy. In Proceedings of the   \n370 2016 ACM SIGSAC Conference on Computer and Communications Security (CCS’16),   \n371 2016.   \n372 $[ \\mathrm { A G D } ^ { + } 2 0 ]$ Brendan Avent, Javier González, Tom Diethe, Andrei Paleyes, and Borja Balle. Auto  \n373 matic discovery of privacy–utility pareto fronts. Proceedings on Privacy Enhancing   \n374 Technologies, 2020(4):5–23, 2020.   \n375 [BBG18] Borja Balle, Gilles Barthe, and Marco Gaboardi. Privacy amplification by subsampling:   \n376 Tight analyses via couplings and divergences. In Advances in Neural Information   \n377 Processing Systems 31, NeurIPS ’18, pages 6277–6287. Curran Associates, Inc., 2018.   \n378 [BST14] Raef Bassily, Adam D. Smith, and Abhradeep Thakurta. Private empirical risk min  \n379 imization: Efficient algorithms and tight error bounds. In FOCS, pages 464–473,   \n380 2014.   \n381 $[ \\mathrm { C L E ^ { + } } 1 9 ]$ Nicholas Carlini, Chang Liu, Úlfar Erlingsson, Jernej Kos, and Dawn Song. The secret   \n382 sharer: Evaluating and testing unintended memorization in neural networks. In $2 8 t h$   \n383 USENIX Security Symposium (USENIX Security 19), pages 267–284, Santa Clara, CA,   \n384 August 2019. USENIX Association.   \n385 [CMS11] Kamalika Chaudhuri, Claire Monteleoni, and Anand D Sarwate. Differentially private   \n386 empirical risk minimization. Journal of Machine Learning Research, 12(3), 2011.   \n387 [CV13] Kamalika Chaudhuri and Staal A Vinterbo. A stability-based validation procedure for   \n388 differentially private machine learning. Advances in Neural Information Processing   \n389 Systems, 26:2652–2660, 2013.   \n390 [DHS11] John Duchi, Elad Hazan, and Yoram Singer. Adaptive subgradient methods for online   \n391 learning and stochastic optimization. Journal of machine learning research, 12(7),   \n392 2011.   \n393 $\\mathrm { [ D K M ^ { + } 0 6 ] }$ Cynthia Dwork, Krishnaram Kenthapadi, Frank McSherry, Ilya Mironov, and Moni   \n394 Naor. Our data, ourselves: Privacy via distributed noise generation. In EUROCRYPT,   \n395 volume 4004, pages 486–503. Springer, 2006.   \n396 [DMNS06] Cynthia Dwork, Frank McSherry, Kobbi Nissim, and Adam Smith. Calibrating noise to   \n397 sensitivity in private data analysis. 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Automl: A survey of the state-of-the-art.   \n408 Knowledge-Based Systems, 212:106622, 2021.   \n409 [KB14] Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv   \n410 preprint arXiv:1412.6980, 2014.   \n411 [KGGW15] Matt Kusner, Jacob Gardner, Roman Garnett, and Kilian Weinberger. Differentially   \n412 private bayesian optimization. In International conference on machine learning, pages   \n413 918–927. PMLR, 2015.   \n414 [KH20] Antti Koskela and Antti Honkela. Learning rate adaptation for differentially private   \n415 learning. In International Conference on Artificial Intelligence and Statistics, pages   \n416 2465–2475. PMLR, 2020.   \n417 [KOV15] Peter Kairouz, Sewoong Oh, and Pramod Viswanath. The composition theorem for   \n418 differential privacy. In International conference on machine learning, pages 1376–1385.   \n419 PMLR, 2015.   \n420 [LT19] Jingcheng Liu and Kunal Talwar. Private selection from private candidates. 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In 2019 IEEE Symposium on Security and Privacy (SP’19), 2019.   \n455 $[ \\boldsymbol { Z } \\mathrm { F M } ^ { + } 2 0 ]$ Pan Zhou, Jiashi Feng, Chao Ma, Caiming Xiong, Steven HOI, et al. Towards theo  \n456 retically understanding why sgd generalizes better than adam in deep learning. arXiv   \n457 preprint arXiv:2010.05627, 2020. ",
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parse/train/nIL7Q-p7-Sh/nIL7Q-p7-Sh.md

@@ -0,0 +1,292 @@
+# Auto-Encoding Knowledge Graph for Unsupervised Medical Report Generation
+
+Fenglin Liu1,2, Chenyu $\mathbf { V o u } ^ { 4 }$ , Xian $\mathbf { W } \mathbf { u } ^ { 5 }$ , Shen $\mathbf { G e ^ { 5 } }$ , Sheng Wang3∗, $\mathbf { X } \mathbf { u } \mathbf { S } \mathbf { u } \mathbf { n } ^ { 1 * }$   
+1MOE Key Laboratory of Computational Linguistics, School of EECS, Peking University 2School of ECE, Peking University   
+3Paul G. Allen School of Computer Science and Engineering, University of Washington 4Department of Electrical Engineering, Yale University 5Tencent {fenglinliu98, xusun}@pku.edu.cn, chenyu.you@yale.edu {kevinxwu, shenge}@tencent.com, swang@cs.washington.edu
+
+# Abstract
+
+Medical report generation, which aims to automatically generate a long and coherent report of a given medical image, has been receiving growing research interests. Existing approaches mainly adopt a supervised manner and heavily rely on coupled image-report pairs. However, in the medical domain, building a large-scale image-report paired dataset is both time-consuming and expensive. To relax the dependency on paired data, we propose an unsupervised model Knowledge Graph Auto-Encoder (KGAE) which accepts independent sets of images and reports in training. KGAE consists of a pre-constructed knowledge graph, a knowledgedriven encoder and a knowledge-driven decoder. The knowledge graph works as the shared latent space to bridge the visual and textual domains; The knowledge-driven encoder projects medical images and reports to the corresponding coordinates in this latent space and the knowledge-driven decoder generates a medical report given a coordinate in this space. Since the knowledge-driven encoder and decoder can be trained with independent sets of images and reports, KGAE is unsupervised. The experiments show that the unsupervised KGAE generates desirable medical reports without using any image-report training pairs. Moreover, KGAE can also work in both semi-supervised and supervised settings, and accept paired images and reports in training. By further fine-tuning with image-report pairs, KGAE consistently outperforms the current state-of-the-art models on two datasets.
+
+# 1 Introduction
+
+Medical images, such as radiology and pathology images, and their corresponding reports are widely used for clinical diagnosis and treatment [8, 11]. A medical report is usually a paragraph of multiple sentences which describes both the normal and abnormal findings in the medical image. In clinical practice, writing a report can be time-consuming and tedious for experienced radiologists, and error-prone for inexperienced radiologists [4]. Therefore, given the large volume of medical images, automatically generating reports can improve current clinical practice in diagnostic radiology and assist radiologists in clinical decision-making [15, 25]. Specifically, it can relieve radiologists from such heavy workload and alert radiologists of the abnormalities to avoid misdiagnosis and missed diagnosis. Therefore, automatic medical report generation attracts remarkable attention in both artificial intelligence and clinical medicine.
+
+Recently, inspired by the great success of neural machine translation [2, 38, 49, 50, 48], image captioning [44, 39, 46, 28, 30, 29] and medical imaging analysis [47, 51, 52], the data-driven deep neural models, particularly those based on the encoder-decoder frameworks [15, 16, 25, 22, 41, 45, 53, 54, 6], have achieved great success in advancing the state-of-the-art of medical report generation. However, these models are trained in a supervised learning manner and heavily rely on labeled paired image-report datasets [9, 17], which are not easy to acquire in the real world. Specifically, the medical-related data can only be manually labeled by professional radiologists, and also involves privacy issues. Therefore, the medical report generation datasets are particularly labor-intensive and expensive to obtain. As a result, the scales of existing widely-used datasets for medical report generation models [16, 25, 22, 23], i.e., MIMIC-CXR (0.22M samples) [17] and IU X-ray (4K samples) [9], are relatively small compared to image recognition datasets, e.g., ImageNet (14M samples) [10], and image captioning datasets, e.g., Conceptual Captions (3.3M samples) [36]. In addition, the MIMIC-CXR and IU X-Ray datasets only include Chest X-Ray images, for other types of medical images (MRI, Dermoscopy, Retinal, etc.) of other body parts (brain, skin, eye, etc.), the image-report pairs could be much less or even unavailable. Therefore, to relax the reliance on the paired data sets, making use of all available data, like independent image or report sets, is becoming increasingly important.
+
+![](images/afd8a513e722a0d7580732c419f634a6b81e954681b7596839e01ae7aa180bf4.jpg)  
+Figure 1: Illustration of our Knowledge Graph Auto-Encoder, which consists of a pre-constructed knowledge graph, a knowledge-driven encoder and a knowledge-driven decoder. The Green and Red lines denote the data flow in the training process and testing process of report generation, respectively.
+
+In this paper, we propose an unsupervised model Knowledge Graph Auto-Encoder (KGAE), which utilizes independent sets of images and reports in training (the image and report set are separate and have no overlap). KGAE consists of a pre-constructed knowledge graph, a knowledge-driven encoder and a knowledge-driven decoder. As shown in Figure 1, the knowledge graph works as the shared latent space of images and reports. The knowledge-driven encoder can take either the image $I$ or the report $R$ as queries and project them to corresponding coordinates $\mathcal { G } _ { I }$ and $\mathcal { G } _ { R }$ in the latent space. In this manner, since $\mathcal { G } _ { I }$ and $\mathcal { G } _ { R }$ share the same latent space, we can use positions in latent space to measure the relationship between images and reports which narrows the gap between visual and textual domains. In brief, to bridge the gap between vision and language domains without training on the pairs of images and reports, we adopt the knowledge graph to create a latent space and propose a knowledge-driven encoder, which includes a common mapping function to project images and reports to the same latent space. As a result, our encoder can extract the image and report knowledge representations, i.e., the knowledge related to the image and report, they (image, report knowledge) share the common latent space, which allows our model to bridge the gap between vision and language domains without the training on the pairs of image and report. Next, we introduce the knowledge-driven decoder to exploit $\mathcal { G } _ { I }$ and $\mathcal { G } _ { R }$ to generate the report. In the training stage, we estimate the parameters of the decoder by reconstructing the input report $R$ based on $\mathcal { G } _ { R }$ , i.e., $R  \mathcal { G } _ { R }  R$ auto-encoding pipeline; In the prediction stage, we directly input $\mathcal { G } _ { I }$ into the trained decoder to generate the report. In this way, our approach can produce desirable reports without any labeled image-report pairs.
+
+Overall, the contributions of this paper are as follows:
+
+• In this paper, we make the first attempt to conduct unsupervised medical report generation where the image-report pairs are not available. To this end, we propose the Knowledge Graph Auto-Encoder (KGAE). By leveraging a pre-constructed knowledge graph, we introduce the knowledge-driven encoder and decoder which are trained with independent sets of images and reports. According to the experimental results, the unsupervised KGAE can even outperform several supervised approaches.
+
+• In addition to the unsupervised mode, KGAE can also be applied in a semi-supervised or supervised manner. Under the semi-supervised setting, by using only $60 \%$ of paired dataset, KGAE is able to achieve competitive results with current state-of-art models; Under the supervised setting, by training on fully paired datasets as in existing works, KGAE can set new state-of-the-art performances on the IU X-ray and MIMIC-CXR, respectively. • The analysis, both quantitative and qualitative, as well as a human evaluation conducted by professional radiologists, further proves the effectiveness of our approach.
+
+# 2 Related Works
+
+Medical report generation aims to generate a relatively long paragraph to describe a given medical image. It is similar to the image captioning task [5], which aims to generate a sentence to describe a given image. In image captioning, the encoder-decoder framework [39], where the encoder [20, 12] computes visual representations for the image and the decoder [13, 38] generates a target sentence based on the visual representations, has achieved great success [1, 31, 35, 44]. However, instead of only generating one single sentence, medical report generation aims to generate a long paragraph including multiple structured sentences that describe both the normal and abnormal parts [25, 15]. To this end, given the success of encoder-decoder framework on image captioning, most existing medical report generation models attempt to exploit the hierarchical LSTM (HLSTM) [15, 16, 19] or Transformer [6] to generate an accurate, long and coherent report. However, existing models require the paired image-report datasets, which are time-consuming and expensive to collect. In this paper, we propose the unsupervised model Knowledge Graph Auto-Encoder (KGAE) which doesn’t need paired images and reports.
+
+Note that although the knowledge graph has been integrated in existing medical report generation models [54, 22], these approaches are supervised and require paired images and reports. Thus, their objectives and motivations of using knowledge graph are different from our work. In detail, existing knowledge-graph based medical report generation methods aim to adopt the knowledge graph to boost the performance of supervised models. However, in our work, we aim to generate a medical report without using any coupled image-report training pairs, i.e., unsupervised medical report generation. A key challenge of unsupervised medical report generation is to bridge the gap between vision and language domains. To this end, we adopt the knowledge graph to create a latent space and propose a knowledge-driven encoder to project image and report to the same latent space.
+
+# 3 Approach
+
+We first formulate the conventional supervised medical report generation problems; Then, we describe the proposed Knowledge Graph Auto-Encoder for unsupervised medical report generation in detail.
+
+# 3.1 Conventional Supervised Medical Report Generation Models
+
+Given a medical image $I$ , the goal is to generate a descriptive report $R$ . Most models [15, 16, 6] normally include an image encoder and a report decoder, which can be formulated as:
+
+$$
+{ \mathrm { I m a g e ~ E n c o d e r : ~ } } I  I ^ { \prime } ; { \mathrm { ~ ~ R e p o r t ~ D e c o d e r : ~ } } I ^ { \prime }  R ,
+$$
+
+where $I ^ { \prime } \in \mathbb { R } ^ { N _ { I } \times d }$ denotes the image embeddings extracted by the image encoder, e.g., ResNet-50 [12]. Then, $I ^ { \prime }$ is used to guide the generation of the target report $R$ in the report decoder, e.g., LSTM [13] and Transformer [38]. During training, given the ground truth report for the input image, we can train the encoder-decoder model by minimizing a supervised training loss, e.g., cross-entropy loss. However, paired image-report $( I { - } R )$ datasets are particularly labor-intensive and expensive to obtain. Therefore, in this paper, we aim to relax the reliance on the paired datasets and make use of the independent sets of images and reports instead.
+
+# 3.2 Knowledge Graph Auto-Encoder
+
+As shown in Figure 1, the proposed KGAE includes a knowledge graph, a knowledge-driven encoder and a knowledge-driven decoder, which will be described in detail in the following sections.
+
+Knowledge Graph The motivation of using the knowledge graph is that writing medical reports usually requires particular domain knowledge [11, 22]. Therefore, we can utilize the knowledge graph, which models the domain-specific knowledge structure, to serve as a bridge to correlate the knowledge representations of the visual and textual domains. In particular, we construct an off-the-shelf global medical knowledge graph $\mathcal { G } = ( V , E )$ covering the common abnormalities and normalities, where $V = \{ v _ { i } \} _ { i = 1 : N _ { \mathrm { K G } } } \in \mathbb { R } ^ { N _ { \mathrm { K G } } \times d }$ is a set of nodes and $E = \{ e _ { i , j } \} _ { i , j = 1 : N _ { \mathrm { K G } } }$ is a set of edges. In detail, based on the report corpus, i.e., MIMIC-CXR [17], we consider the $N _ { \mathrm { K G } }$ frequent clinical abnormalities (e.g., "enlarged heart size", "pleural effusion", and "bibasilar consolidation") and normalities (e.g., "heart size is normal" and "lungs are clear") as nodes. The edge weights are calculated by the normalized co-occurrence of different nodes computed from report corpus. Please note that this knowledge graph is built purely from the training set of MIMIC-CXR, thus there is no label leakage. After that, the knowledge graph is embedded by a graph embedding module, i.e., graph convolution network [32, 24], which is implemented as follows:
+
+$$
+v _ { i } ^ { \prime } = v _ { i } + \mathrm { R e L U } ( \sum _ { j = 1 } ^ { N _ { \mathrm { K G } } } e _ { i , j } W _ { v } v _ { j } ) ,
+$$
+
+where $\mathrm { R e L U } ( \cdot )$ represents the ReLU activation function and $W _ { v } \in \mathbb { R } ^ { d \times d }$ is the learnable matrix. As a result, we can acquire a set of node embeddings $V ^ { \prime } = \{ v _ { 1 } ^ { \prime } , v _ { 2 } ^ { \prime } , \ldots , v _ { N _ { \mathrm { K G } } } ^ { \prime } \} \in \mathbb { R } ^ { N _ { \mathrm { K G } } \times d }$ . It is worth noting that more complex graph structures could be constructed by using more large-scale medical textbooks. Therefore, our model is not limited to the currently constructed graph and could provide a good basis for the research of unsupervised medical report generation for other domains.
+
+Knowledge-driven Encoder The knowledge-driven encoder (KE) is designed to utilize the knowledge graph $\mathcal { G }$ to extract knowledge representations $( \mathcal { G } _ { I } \in \mathbb { R } ^ { N _ { I } \times d }$ and $\mathcal { G } _ { R } \in \overline { { \mathbb { R } } } ^ { N _ { R } \times d } )$ of both image $I$ and report $R$ to bridge the vision and the language domains, which can be formulated as:
+
+$$
+{ \mathcal G } _ { I } = \mathrm { K E } _ { I } ( I , { \mathcal G } ) ; { \mathcal G } _ { R } = \mathrm { K E } _ { R } ( R , { \mathcal G } ) .
+$$
+
+In implementations, as shown in Figure 1, we first adopt the ResNet-50 [12] and the Transformer [38] as the image embedding module and report embedding module to embed the image $I$ and report $R$ , acquiring the image embeddings $I ^ { \prime } \in \mathbb { R } ^ { \bar { N } _ { I } \times d }$ and report embeddings $R ^ { \prime } \in \mathbb { R } ^ { N _ { R } \times \breve { d } }$ , respectively. Next, to extract the knowledge representations from knowledge graph $\mathcal { G }$ , we adopt the attention mechanism [38] to implement the KE. The motivation stems from that the attention mechanism can compute the association weights between different features and allows probabilistic many-to-many relations instead of monotonic relations, as in [38, 44, 29]. As a result, we take $I ^ { \prime }$ and $R ^ { \prime }$ as the queries, and take the knowledge graph $\mathcal { G }$ (i.e., $V ^ { \prime } = \{ v _ { 1 } ^ { \prime } , v _ { 2 } ^ { \prime } , \ldots , v _ { N _ { \mathrm { K G } } } ^ { \prime } \} \in \mathbb { R } ^ { N _ { \mathrm { K G } } \times d } )$ as the lookup matrix:
+
+$$
+\begin{array} { r l } & { \mathcal { G } _ { I } = \mathrm { K E } _ { I } ( I , \mathcal { G } ) = \mathcal { F } ( \mathrm { A t t e n t i o n } _ { I } ( I ^ { \prime } , V ^ { \prime } ) ) ; \mathcal { G } _ { R } = \mathrm { K E } _ { R } ( R , \mathcal { G } ) = \mathcal { F } ( \mathrm { A t t e n t i o n } _ { R } ( R ^ { \prime } , V ^ { \prime } ) ) } \\ & { \quad \quad \quad \quad \quad \mathrm { A t t e n t i o n } ( x , y ) = \mathrm { s o f t m a x } \left( \frac { x W _ { \ P } \left( y W _ { \mathbf { k } } \right) ^ { \top } } { \sqrt { d } } \right) y W _ { \mathbf { v } } . } \end{array}
+$$
+
+where $x \in \mathbb { R } ^ { N _ { x } \times d _ { x } } , y \in \mathbb { R } ^ { N _ { y } \times d _ { y } }$ ; $W _ { \mathrm { q } } \in \mathbb { R } ^ { d _ { x } \times d _ { x } }$ , $W _ { \mathbf { k } } \in \mathbb { R } ^ { d _ { y } \times d _ { y } }$ and $W _ { \mathrm { v } } \in \mathbb { R } ^ { d _ { y } \times d _ { y } }$ $\langle d _ { x } = d _ { y }$ ) are learnable parameters. $\mathcal { F }$ is implemented as two fully-connected (FC) layers with a ReLU in between, i.e., FC-ReLU-FC. The resulted $\mathcal { G } _ { I } \in \mathbb { R } ^ { N _ { I } \times d }$ and $\dot { \mathcal { G } } _ { R } \in \mathbb { R } ^ { N _ { R } \times d }$ turn out to be a set of attended (i.e., extracted) knowledge related to the image and report. The knowledge representations $\mathcal { G } _ { I }$ and $\mathcal { G } _ { R }$ share the common latent space which bridges the vision and the language domains. Note that the $\mathcal { F }$ used in $\mathrm { K E } _ { I }$ and $\mathrm { K E } _ { R }$ shares the same parameters and is thus introduced to further boost the bridging capabilities of different modalities. It means that we adopt two KEs, i.e., $\mathrm { K E } _ { I }$ and $\mathrm { K E } _ { R }$ , and each KE includes an attention model as well as a common mapping function $\mathcal { F }$ . The only shared weights of $\mathrm { K E } _ { I }$ and $\mathrm { K E } _ { R }$ are the parameters of $\mathcal { F }$ , and the parameters of attention models are independent.
+
+Knowledge-driven Decoder The decoder is designed to generate the reports based on the graph representations $\mathcal { G } _ { I }$ or $\mathcal { G } _ { R }$ . For clarity, we use $\mathcal { G } _ { k }$ to represent the $\mathcal { G } _ { R }$ and $\mathcal { G } _ { I }$ during the training and testing stages, respectively. In implementations, since medical report generation requires generating a long paragraph, we choose the (three-layer) Transformer [38] as the basic module of our decoder and incorporate the proposed Knowledge-driven Attention (KA) to effectively model the long sequences.
+
+At each decoding step $t$ , the decoder takes the embedding of current input word $x _ { t } = w _ { t } + e _ { t } \in \mathbb { R } ^ { 2 d }$ as input, where $w _ { t }$ and $e _ { t }$ denote the word embedding and fixed position embedding, respectively, and generate each word $r _ { t }$ in report $R = \{ r _ { 1 } , r _ { 2 } , . . . , r _ { T } \}$ , which can be defined as follows:
+
+$$
+\begin{array}{c} \begin{array} { r } { \begin{array} { r } { h _ { t } = \mathrm { A t t e n t i o n } ( x _ { t } , x _ { 1 : t } ) } \\ { h _ { t } ^ { \prime } = \mathrm { K A } ( h _ { t } , \mathcal { G } _ { k } , B ) } \end{array} , \mathrm { ~ w h e r e ~ } \mathcal { G } _ { k } = \left\{ \begin{array} { r l } { \mathcal { G } _ { R } , } & { \mathrm { T r a i n i n g } } \\ { \mathcal { G } _ { I } , } & { \mathrm { T e s t i n g } } \end{array} \right. ; r _ { t } \sim p _ { t } = \mathrm { s o f t m a x } ( \mathrm { F F N } ( h _ { t } ^ { \prime } ) \mathbb { W } _ { p } ) , } \end{array}  \end{array}
+$$
+
+where FFN stands for Feed-Forward Network in the original Transformer [38]; $\mathbf { W } _ { p } \in \mathbb { R } ^ { 2 d \times | D | }$ is the learnable parameter $| | D | |$ denotes the vocabulary size); $B$ represents the knowledge bank in the KA.
+
+In particular, the knowledge-driven attention (KA) is inspired by the success of many works that attempt to augment a working memory into the network, e.g., memory network. Memory network preserves a dynamic knowledge base for subsequent inference [37, 21, 42, 43, 40, 46, 33]. For example, [37, 21] and [42, 43] proposed to preserve the context of a document and visual knowledge to solve language modeling and visual question answering, respectively. In this paper, since the knowledge representations $\mathcal { G } _ { k }$ are extracted from the off-the-shelf global knowledge graph $\mathcal { G }$ , we incorporate a knowledge memory mechanism to distill and preserve the fine-grained medical knowledge related to report generation task, which encourages our decoder to generate more accurate and desirable reports. Specifically, we introduce the knowledge bank $B = \{ b _ { 1 } , b _ { 2 } , \ldots , b _ { N _ { \mathrm { B } } } \} \in \mathbb { R } ^ { N _ { \mathrm { B } } \times d }$ , where $N _ { \mathrm { B } }$ stands for the total number of the knowledge corresponding to report generation. As a result, given the graph representations $\mathcal { G } _ { k } \in \mathbb { R } ^ { N _ { k } \times d }$ , the knowledge memory mechanism is defined as follows:
+
+$$
+B _ { k } = \operatorname { s o f t m a x } \left( \mathcal { G } _ { k } B ^ { \top } \right) B .
+$$
+
+Through above operation, each feature/vector in the $\mathcal { G } _ { k } \in \mathbb { R } ^ { N _ { k } \times d }$ can distill the fine-grained knowledge preserved in $B$ to acquire $B _ { k } \in \mathbb { R } ^ { N _ { k } \times d }$ for accurate report generation.
+
+Based on the above mechanism, the knowledge-driven attention in Eq. (5) is defined as:
+
+$$
+h _ { t } ^ { \prime } = \mathrm { K A } ( h _ { t } , \mathcal { G } _ { k } , B ) = \mathrm { A t t e n t i o n } ( h _ { t } , [ \mathcal { G } _ { k } ; B _ { k } ] ) = \mathrm { A t t e n t i o n } \left( h _ { t } , \left[ \mathcal { G } _ { k } ; \operatorname { s o f t m a x } \left( \mathcal { G } _ { k } B ^ { \top } \right) B \right] \right) .
+$$
+
+where $[ \cdot ; \cdot ]$ denotes the concatenation operation. It is worth noting that these operations are all differentiable, thus the bank $B$ can be learned in an end-to-end fashion.
+
+In our subsequent analysis, we will show that the introduced knowledge memory mechanism indeed distills and preserves the desired medical knowledge, and thus boost the generation of reports.
+
+# 3.3 Implementation Details
+
+Unsupervised Training Details To train our KGAE in an unsupervised manner, instead of using the paired image-report dataset in the conventional supervised model, we only require an image set CheXpert [14], which includes 224,316 X-ray images, and a separate report corpus MIMIC-CXR $[ 1 7 ] + \mathrm { I U }$ X-ray [9], which includes $2 2 2 , 7 5 8 + 2 , 7 7 { \bar { 0 } } = 2 2 5 , 5 2 8 \ \cdot$ reports2.
+
+In detail, to train our knowledge-driven encoder $\mathrm { K E } _ { I }$ and $\mathrm { K E } _ { R }$ (see Eq. (4)), we feed the $\mathcal { G } _ { I }$ and $\mathcal { G } _ { R }$ into a common multi-label classification network [54, 15] trained with binary cross entropy loss for 14 common radiographic observations classification3. In this way, our encoder can extract the knowledge representations $\mathcal { G } _ { I }$ and $\mathcal { G } _ { R }$ of both image and report in a common latent space, effectively bridging the vision and the language domains. To train the knowledge-driven decoder, as well as the knowledge bank $B$ (see Eq. (5)), since there are no coupled image-report pairs, we propose to reconstruct the report $R$ based on the $\mathcal { G } _ { R }$ . Therefore, through Eq. (5), taking the input report $R = \{ r _ { 1 } , r _ { 2 } , \ldots , r _ { T } \}$ as the ground truth report, we can train our approach by minimizing the cross-entropy loss:
+
+$$
+L _ { \mathrm { C E } } = - \sum _ { t = 1 } ^ { T } \log \left( p \left( r _ { t } \mid r _ { 1 : t - 1 } \right) \right) .
+$$
+
+In this way, we can train our decoder in the $R  \mathcal { G } _ { R }  R$ auto-encoding pipeline.
+
+During testing, we first adopt the knowledge-driven encoder to extract the knowledge representations $\mathcal { G } _ { I }$ of the test image (see Eq. (4)). Then, we directly feed $\mathcal { G } _ { I }$ into the decoder to generate final report in the $I  { \mathcal { G } } _ { I }  R$ pipeline (see Eq. (5)). In this way, our approach can relax the reliance on the image-report pairs. In our following experiments, we validate the effectiveness of our approach, which even outperforms some supervised approaches.
+
+Semi-Supervised and Supervised Training Details To further validate the effectiveness of our approach, we fine-tune the unsupervised $K G A E$ using partial and full image-report pairs to acquire the KGAE-Semi(-Supervised) and KGAE-Supervised, respectively, where the former can evaluate the performance of our approach under limited labeled pairs for training and the latter can compare the performance of KGAE with state-of-the-art supervised approaches. In the (semi-)supervised setting, given the image-report pairs, i.e., $I { - } R$ , we first incorporate the original visual information into the knowledge representation $\mathcal { G } _ { I }$ , and then train our KGAE by generating the ground truth report in the $I  { \mathcal { G } } _ { I }  R$ pipeline and minimizing the cross-entropy loss in Eq. (8). During testing, we also follow the unsupervised setting to generate the final report in the $I  { \mathcal { G } } _ { I }  R$ pipeline.
+
+# 4 Experiments
+
+We first introduce the datasets, metrics and detailed settings used for evaluation. Then, we present the evaluation of our approach under the unsupervised, semi-supervised and supervised training settings.
+
+# 4.1 Datasets, Metrics and Settings
+
+Datasets In this paper, we adopt the test sets of IU X-ray [9] and MIMIC-CXR [17] for evaluation. All protected health information (e.g., patient name and date of birth) was de-identified. In particular, the IU X-ray [9] is a widely-used public benchmark dataset for medical report generation and contains 7,470 chest X-ray images associated with 3,955 fully de-identified medical reports. Each report is composed of impression, findings and indication sections, etc. [22]. Following [25], our method also focuses on the findings section as it is the most important component of reports. Then, following [16, 22, 25, 6], we randomly select $7 0 \% - 1 0 \% - 2 0 \%$ image-report pairs of dataset to form the trainingvalidation-testing sets. The MIMIC-CXR [17] includes 377,110 chest $\mathbf { X }$ -ray images associated with 227,835 reports. The dataset is officially split into 368,960 images (222,758 reports) for training, 2,991 images (1,808 reports) for validation and 5,159 images (3,269 reports) for testing. It is worth noting that we focus on the unsupervised medical report generation, where the image-report pairs are not available, thus the image-report training pairs of both the IU X-ray and MIMIC-CXR datasets are discarded and are not used in our unsupervised training stage. Only the training reports of MIMIC-CXR and IU $\mathbf { X }$ -ray, i.e., $2 2 2 , 7 5 8 + 2 , 7 7 0 = 2 2 5 , 5 2 8$ reports, are used as the independent report corpus to train our unsupervised model. Only under the (semi-)supervised training setting, we will adopt the image-report training pairs to train our approach.
+
+Metrics To fairly compare with existing models [25, 6], we adopt the evaluation toolkit [5] to calculate the widely-used natural language generation metrics, i.e., BLEU [34], METEOR [3] and ROUGE-L [26], which measure the match between the generated reports and ground truth reports, but are not specialized for the abnormalities in the reports. Therefore, to measure the accuracy of descriptions for clinical abnormalities, we further report clinical efficacy metrics following the work of Chen et al. [6]. The clinical efficacy metrics are calculated by comparing the generated reports with ground truth reports in 14 different categories related to thoracic diseases and support devices, producing the Precision, Recall and F1 scores.
+
+Settings The size $d$ is set to 256. For the attention mechanism in Eq. (4) and Eq. (5), we adopt the multi-head attention [38], the number of heads $n$ in multi-head attention is set to 8. The intermediate dimension in $\mathcal { F }$ , i.e., Eq. (4), is set to 1024. Based on the average performance on the validation set, the $N _ { \mathrm { B } }$ in knowledge bank, i.e., Eq. (6), is set to 10,000. The $N _ { \mathrm { K G } }$ in the knowledge graph is set to 200. In our knowledge-driven encoder, the image embedding module adopts the ResNet-50 [12] pretrained on ImageNet [10] and fine-tuned on CheXpert dataset [14] to extract the image embeddings in the shape of $7 \times 7 \times 2 0 4 8$ , which will be projected to $d = 2 5 6$ , acquiring $I ^ { \prime } \in \mathbb { R } ^ { 4 9 \times 2 5 6 }$ , i.e., $N _ { I } = 4 9$ ; The report embedding module is implemented by the Transformer [38] equipping with the self-attention mechanism provided in Lin et al. [27]; $N _ { R } = N _ { I } = 4 9$ . In both unsupervised and (semi-)supervised settings (see Section 3.3), the batch size is set to 16 and Adam optimizer [18] with a learning rate of 1e-4 is used for parameter optimization. Before testing on the IU X-ray/MIMICCXR, we further only employ the training data from IU X-ray/MIMIC-CXR to train the model. All re-implementations and our experiments were run on 8 V100 GPUs.
+
+# 4.2 Automatic Evaluation
+
+We evaluate the performance of our approach under unsupervised, semi-supervised and supervised settings. The results are shown in Table 1, Table 2 and Figure 2. We select several supervised methods, including a recently state-of-the-art model R2Gen [6], for comparison. These models follow the encoder-decoder architecture, trained on the full pairs of images and reports.
+
+Unsupervised Setting As shown in Table 1 and Table 2, our unsupervised model KGAE achieves competitive results with some supervised models in both IU X-ray and MIMIC-CXR datasets, and even outperforms several supervised models. Specifically, on the IU X-ray dataset, Table 1 shows that KGAE surpasses the NIC [44], AdaAtt [31] and Att2in [35] in terms of all metrics, and the Transformer [6] in terms of BLEU-1,2,3. On the MIMIC-CXR dataset, Table 2 shows that KGAE outperforms the $\mathcal { M } ^ { 2 }$ Trans. [7] in terms of Precision, Recall and F1. The competitive results prove the effectiveness of our approach in addressing the unsupervised medical report generation, and thus can generate desirable medical reports without the training on the pairs of image and report.
+
+Table 1: Performance in terms of natural language generation metrics on the IU X-ray and MIMICCXR. B-n, M and R-L are short for BLEU-n, METEOR and ROUGE-L, respectively. Higher is better in all columns. It is worth noting that the KGAE is trained in an unsupervised manner, KGAE-Semi is trained $60 \%$ paired data, KGAE-Supervised and existing methods are trained with full paired data.   
+
+<table><tr><td rowspan="2">Methods</td><td rowspan="2">Year</td><td rowspan="2">Ratio of Pairs</td><td colspan="6">IU X-ray [9]</td><td colspan="6">MIMIC-CXR [17]</td></tr><tr><td>B-1</td><td>B-2</td><td>B-3</td><td>B-4</td><td>M</td><td>R-L</td><td>B-1</td><td>B-2</td><td>B-3</td><td>B-4</td><td>M</td><td>R-L</td></tr><tr><td>NIC [39]</td><td>2015</td><td>100%</td><td>0.216</td><td>0.124</td><td>0.087</td><td>0.066</td><td>-</td><td>0.306</td><td>0.299</td><td>0.184</td><td>0.121</td><td>0.084</td><td>0.124</td><td>0.263</td></tr><tr><td>AdaAtt [31]</td><td>2017</td><td>100%</td><td>0.220</td><td>0.127</td><td>0.089</td><td>0.068</td><td>=</td><td>0.308</td><td>0.299</td><td>0.185</td><td>0.124</td><td>0.088</td><td>0.118</td><td>0.266</td></tr><tr><td>Att2in [35]</td><td>2017</td><td>100%</td><td>0.224</td><td>0.129</td><td>0.089</td><td>0.068</td><td>=</td><td>0.308</td><td>0.325</td><td>0.203</td><td>0.136</td><td>0.096</td><td>0.134</td><td>0.276</td></tr><tr><td>Transformer [6]</td><td>2020</td><td>100%</td><td>0.396</td><td>0.254</td><td>0.179</td><td>0.135</td><td>0.164</td><td>0.342</td><td>0.314</td><td>0.192</td><td>0.127</td><td>0.090</td><td>0.125</td><td>0.265</td></tr><tr><td>M² Trans.[7]</td><td>2020</td><td>100%</td><td>0.437</td><td>0.290</td><td>0.205</td><td>0.152</td><td>0.176</td><td>0.353</td><td>0.238</td><td>0.151</td><td>0.102</td><td>0.067</td><td>0.110</td><td>0.249</td></tr><tr><td>R2Gen [6]</td><td>2020</td><td>100%</td><td>0.470</td><td>0.304</td><td>0.219</td><td>0.165</td><td>0.187</td><td>0.371</td><td>0.353</td><td>0.218</td><td>0.145</td><td>0.103</td><td>0.142</td><td>0.277</td></tr><tr><td>KGAE</td><td></td><td>0%</td><td>0.417</td><td>0.263</td><td>0.181</td><td>0.126</td><td>0.149</td><td>0.318</td><td>0.221</td><td>0.144</td><td>0.096</td><td>0.062</td><td>0.097</td><td>0.208</td></tr><tr><td>KGAE-Semi</td><td>Ours</td><td>60%</td><td>0.497</td><td>0.320</td><td>0.232</td><td>0.171</td><td>0.189</td><td>0.379</td><td>0.352</td><td>0.219</td><td>0.149</td><td>0.108</td><td>0.147</td><td>0.290</td></tr><tr><td>KGAE-Supervised</td><td></td><td>100%</td><td>0.512</td><td>0.327</td><td>0.240</td><td>0.179</td><td>0.195</td><td>0.383</td><td>0.369</td><td>0.231</td><td>0.156</td><td>0.118</td><td>0.153</td><td>0.295</td></tr></table>
+
+Table 2: Performance of automatic evaluation in terms of clinical efficacy metrics, which measure the accuracy of descriptions for clinical abnormalities, on the test set of MIMIC-CXR dataset. Higher is better in all columns.   
+
+<table><tr><td rowspan="3">Methods</td><td rowspan="3">Year</td><td rowspan="3">Ratio of Pairs</td><td colspan="3">MIMIC-CXR[17]</td></tr><tr><td>Precision Recall</td><td></td><td>F1</td></tr><tr><td></td><td></td><td></td></tr><tr><td>NIC[39]</td><td>2015</td><td>100%</td><td>0.249</td><td>0.203</td><td>0.204</td></tr><tr><td>AdaAtt [31]</td><td>2017 2017</td><td>100% 100%</td><td>0.268</td><td>0.186</td><td>0.181</td></tr><tr><td>Att2in [35] Up-Down [1]</td><td>2018</td><td>100%</td><td>0.322 0.320</td><td>0.239 0.231</td><td>0.249</td></tr><tr><td>M² Trans.[7]</td><td>2020</td><td>100%</td><td>0.197</td><td>0.145</td><td>0.238</td></tr><tr><td>Transformer [6]</td><td>2020</td><td>100%</td><td>0.331</td><td>0.224</td><td>0.133 0.228</td></tr><tr><td>R2Gen [6]</td><td>2020</td><td>100%</td><td>0.333</td><td>0.273</td><td>0.276</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>KGAE</td><td></td><td>0%</td><td>0.214</td><td>0.158</td><td>0.156</td></tr><tr><td>KGAE-Semi</td><td>Ours</td><td>60%</td><td>0.360</td><td>0.302</td><td>0.307</td></tr><tr><td>KGAE-Supervised</td><td></td><td>100%</td><td>0.389</td><td>0.362</td><td>0.355</td></tr></table>
+
+![](images/714ee8d17da130941633988e5374eacaa4fa87c8d55ee2af6783dfd8393d379c.jpg)  
+Figure 2: Performance of re-implemented state-of-theart model R2Gen [6] and our approach on the test sets with respect to various amount of paired data used for training. The margins in different ratios are shown with the polyline and the right y-axis. As we can see, our approach consistently outperforms the R2Gen.
+
+Semi-Supervised Setting To further prove the effectiveness of our approach, we fine-tune the unsupervised KGAE using partial downstream paired image-report datasets (see Section 3.3), resulting in the KGAE-Semi. To this end, in Figure 2, we evaluate the performance of our approach on both IU X-ray and MIMIC-CXR datasets with respect to the increasing amount of paired data. For a fair comparison, we also re-train the state-of-the-art model R2Gen [6] using the same amount of pairs. As we can see, our model outperforms the R2Gen under all ratios of paired dataset used for training. It is worth noting that the fewer the image-report pairs, the larger the margins, e.g., under the very limited pairs setting ( $20 \%$ of paired datasets), our approach significantly surpasses the R2Gen by $8 . 5 \%$ absolute BLEU-4 score on IU $\mathrm { X }$ -ray and $9 . 8 \%$ absolute F1 score on MIMIC-CXR. Intuitively, since our approach can relax the reliance on the paired datasets, we can make use of available unpaired image and report data as a solid bias for medical report generation task. Table 1 and Table 2 further prove the effectiveness of our approach, which achieves results competitive with current state-of-the-art models by using only $60 \%$ of paired dataset.
+
+Supervised Setting We fine-tune the unsupervised KGAE using full image-report pairs, acquiring the KGAE-Supervised model (see Section 3.3). Table 1 and Table 2 show that KGAE-Supervised sets the new state-of-the-art results on the two datasets in all metrics. Moreover, in terms of the clinical efficacy metrics, our approach achieves 0.389 precision score, 0.362 recall score and $0 . 3 5 5 \mathrm { F } 1$ score, outperforming the state-of-the-art model R2Gen [6]. The superior clinical efficacy scores demonstrate the capability of our approach to produce higher quality descriptions for clinical abnormalities than existing models.
+
+Table 3: We invite three professional clinicians to conduct human evaluation for comparing our approach with $\mathcal { M } ^ { 2 }$ Trans. [7] and R2Gen [6] under various amount of pairs for training in terms of the comprehensiveness of the generated true abnormalities and the faithfulness of the generated normalities and abnormalities to the ground truth reports. All values are reported in percentage $( \% )$ .   
+
+<table><tr><td rowspan="3">Metrics</td><td colspan="3">KGAE (0%) vs.M² Trans. (100%)</td><td colspan="3">KGAE (0%) vs.R2Gen (100%)</td><td colspan="3">KGAE-Semi (20%) vs.R2Gen (20%)</td><td colspan="3">KGAE-Supervised (100%) vs.R2Gen (100%)</td></tr><tr><td>Loss</td><td>Tie</td><td>Win</td><td>Loss</td><td>Tie</td><td>Win</td><td>Loss</td><td>Tie</td><td>Win</td><td>Loss</td><td>Tie</td><td>Win</td></tr><tr><td>Faithfulness</td><td>34</td><td>18</td><td>48</td><td>62</td><td>15</td><td>23</td><td>21</td><td>10</td><td>69</td><td>25</td><td>22</td><td>53</td></tr><tr><td>Comprehensiveness</td><td>27</td><td>20</td><td>53</td><td>57</td><td>17</td><td>26</td><td>24</td><td>11</td><td>65</td><td>32</td><td>21</td><td>47</td></tr></table>
+
+Overall Combining the results of unsupervised, semi-supervised and supervised settings, the proposed KGAE can relax the dependency on the paired datasets, and thus makes the medical report generation model use the available separate image and report data to boost the performance. The advantages under the scenarios with limited labeled pairs (i.e., semi-supervised setting) show that KGAE might be applied to other medical images (MRI, Dermoscopy, Retinal, etc.), where the coupled images and reports pairs could be much less or even unavailable.
+
+# 4.3 Human Evaluation
+
+We conduct human evaluations to verify the effectiveness of KGAE in clinical practice. Specifically, to assist radiologists in clinical decision-making and reduce their workload, it is important to generate accurate reports (faithfulness), i.e., the model does not generate normalities and abnormalities that does not exist according to doctors, with comprehensive abnormalities (comprehensiveness), the model does not leave out the abnormalities. Therefore, we randomly select 100 samples from the MIMIC-CXR and invite three professional clinicians to compare our approach and baselines independently. The clinicians are unaware of which model generates these reports. The results are shown in Table 3. As we can see, under the unsupervised setting, our approach achieves competitive results with the supervised model, outperforming the $\mathcal { M } ^ { 2 }$ Trans with winning pick-up percentages. Under the (semi-)supervised setting, our method is better than state-of-the-art model R2Gen [6] in all metrics, especially for the semi-supervised setting $20 \%$ of paired dataset), our method substantially surpasses the R2Gen, which is in accordance with the automatic evaluation, by $6 9 - 2 1 = 4 8$ and $6 5 - 2 4 = 4 1$ points in terms of the faithfulness and comprehensiveness metrics, respectively.
+
+# 5 Analysis
+
+In this section, we conduct several analysis to better understand our proposed approach.
+
+# 5.1 Knowledge Graph Sensitivity
+
+In this section, to evaluate the knowledge graph sensitivity, we evaluate the performances using different knowledge graphs defined on IU X-Ray only, MIMIC-CXR only, both MIMIC-CXR and IU X-Ray. Table 4 shows the results of KGAE $( 0 \% )$ and KGAE-Supervised $( 1 0 0 \% )$ on the IU X-ray dataset. As we can see, our KGAE using different knowledge graphs can consistently outperform several existing supervised models, i.e., NIC, AdaAtt, Att2in, across all metrics (Table 1). Similarly, our KGAE-Supervised with different knowledge graphs can also consistently outperform existing state-of-the-art model, i.e., R2Gen (Table 1). The results prove the robustness of our proposed model to the pre-defined knowledge graph. Therefore, this work could provide a good basis or starting point for the research of unsupervised medical report generation in other clinical domains such as MRI and Dermoscopy.
+
+# 5.2 Ablation Study
+
+In Table 5, we conduct quantitative analysis to better understand our approach under both the unsupervised and supervised training settings. For different ablation settings, the KGAE-Supervised is acquired by further fine-tuning the KGAE using image-report pairs.
+
+Table 4: Analysis of the knowledge graph sensitivity. Performance of our approach using different knowledge graphs defined on IU X-Ray only, MIMIC-CXR only, both MIMIC-CXR and IU X-Ray.   
+
+<table><tr><td rowspan="3">Methods</td><td rowspan="3">Ratio of Pairs</td><td rowspan="3">Knowledge Graphs</td><td colspan="6">IU X-ray [9]</td></tr><tr><td>B-1</td><td>B-2</td><td>B-3</td><td>B-4</td><td>M</td><td>R-L</td></tr><tr><td rowspan="3">KGAE</td><td rowspan="3">0%</td><td>IU X-Ray</td><td>0.425</td><td>0.271</td><td>0.185</td><td>0.114</td><td>0.123</td><td>0.310</td></tr><tr><td>MIMIC-CXR</td><td>0.417</td><td>0.263</td><td>0.181</td><td>0.126</td><td>0.149</td><td>0.318</td></tr><tr><td>MIMIC-CXR + IU X-Ray</td><td>0.419</td><td>0.260</td><td>0.180</td><td>0.124</td><td>0.143</td><td>0.321</td></tr><tr><td rowspan="3">KGAE-Supervised</td><td rowspan="3">100%</td><td>IU X-Ray</td><td>0.519</td><td>0.331</td><td>0.235</td><td>0.174</td><td>0.191</td><td>0.376</td></tr><tr><td>MIMIC-CXR</td><td>0.512</td><td>0.327</td><td>0.240</td><td>0.179</td><td>0.195</td><td>0.383</td></tr><tr><td>MIMIC-CXR + IUX-Ray</td><td>0.505</td><td>0.323</td><td>0.239</td><td>0.181</td><td>0.198</td><td>0.385</td></tr></table>
+
+Table 5: We conduct the quantitative analysis under both the unsupervised setting (KGAE) and supervised setting (KGAE-Supervised). We analysis the effect of the shared $\mathcal { F }$ in the encoder (Eq. (4)), and the effect of the number of the knowledge in the decoder’s knowledge bank $B$ (Eq. (6)).   
+
+<table><tr><td rowspan="2">Methods</td><td rowspan="2">Settings</td><td rowspan="2">F</td><td rowspan="2">B</td><td colspan="6">IU X-ray [9]</td><td colspan="6">MIMIC-CXR [17]</td></tr><tr><td>B-1</td><td>B-2</td><td>B-3</td><td>B-4</td><td>M</td><td>R-L</td><td>B-1</td><td>B-2</td><td>B-3</td><td>B-4</td><td>M</td><td>R-L</td></tr><tr><td rowspan="5">KGAE (0%)</td><td>(a)</td><td>-</td><td>-</td><td>0.291</td><td>0.170</td><td>0.127</td><td>0.086</td><td>0.120</td><td>0.301</td><td>0.166</td><td>0.095</td><td>0.064</td><td>0.032</td><td>0.070</td><td>0.174</td></tr><tr><td>(b)</td><td>?</td><td>-</td><td>0.352</td><td>0.227</td><td>0.154</td><td>0.109</td><td>0.133</td><td>0.313</td><td>0.192</td><td>0.118</td><td>0.079</td><td>0.045</td><td>0.085</td><td>0.187</td></tr><tr><td>(c)</td><td></td><td>5,000</td><td>0.403</td><td>0.252</td><td>0.170</td><td>0.117</td><td>0.144</td><td>0.316</td><td>0.211</td><td>0.137</td><td>0.093</td><td>0.058</td><td>0.093</td><td>0.202</td></tr><tr><td>(d)</td><td>√</td><td>15.000</td><td>0.412</td><td>0.260</td><td>0.178</td><td>0.121</td><td>0.148</td><td>0.320</td><td>0.217</td><td>0.140</td><td>0.092</td><td>0.059</td><td>0.101</td><td>0.205</td></tr><tr><td>Full Model</td><td>√</td><td>10.000</td><td>0.417</td><td>0.263</td><td>0.181</td><td>0.126</td><td>0.149</td><td>0.318</td><td>0.221</td><td>0.144</td><td>0.096</td><td>0.062</td><td>0.097</td><td>0.208</td></tr><tr><td rowspan="5">KGAE-Supervised (100%)</td><td>(e)</td><td>-</td><td>-</td><td>0.482</td><td>0.310</td><td>0.219</td><td>0.166</td><td>0.184</td><td>0.373</td><td>0.323</td><td>0.204</td><td>0.128</td><td>0.104</td><td>0.115</td><td>0.266</td></tr><tr><td>(f)</td><td></td><td>-</td><td>0.470</td><td>0.304</td><td>0.217</td><td>0.162</td><td>0.181</td><td>0.368</td><td>0.320</td><td>0.206</td><td>0.129</td><td>0.101</td><td>0.118</td><td>0.267</td></tr><tr><td>（g）</td><td>?</td><td>5,000</td><td>0.505</td><td>0.323</td><td>0.232</td><td>0.178</td><td>0.190</td><td>0.379</td><td>0.363</td><td>0.228</td><td>0.152</td><td>0.115</td><td>0.147</td><td>0.290</td></tr><tr><td>(h)</td><td>√</td><td>15,000</td><td>0.498</td><td>0.315</td><td>0.221</td><td>0.170</td><td>0.186</td><td>0.374</td><td>0.368</td><td>0.235</td><td>0.158</td><td>0.114</td><td>0.150</td><td>0.293</td></tr><tr><td>Full Model</td><td>&lt;</td><td>10,000</td><td>0.512</td><td>0.327</td><td>0.240</td><td>0.179</td><td>0.195</td><td>0.383</td><td>0.369</td><td>0.231</td><td>0.156</td><td>0.118</td><td>0.153</td><td>0.295</td></tr></table>
+
+As we can see, under the unsupervised setting, both the introduced shared $\mathcal { F }$ and knowledge bank $B$ can significantly boost the performance, which proves our arguments and verifies the effectiveness of our approach in performing the unsupervised medical report generation.
+
+Under the supervised setting, as shown in settings (e,f), applying shared $\mathcal { F }$ generates unchanged and impaired performance on the MIMIC-CXR and IU $\mathbf { X }$ -ray datasets, respectively. We speculate the reason is that the supervised model no longer requires the $\mathcal { F }$ to bridge the vision and the language domains. Therefore, the performance is unchanged on the large dataset MIMIC-CXR. However, the increased parameters introduced by $\mathcal { F }$ might bring overfitting or increase the difficulty in optimization on the small dataset IU X-ray, which somewhat hinders the performance. For the knowledge bank $B$ , we can find that the results of setting (h) outperforms (g) on the MIMIC-CXR dataset, but underperforms (g) on the IU X-ray dataset. We speculate the reason is that the large MIMIC-CXR dataset contains more knowledge than the small IU X-ray dataset, so a larger knowledge bank may learn more knowledge of MIMIC-CXR to boost the performance while introducing more noisy knowledge into the IU X-ray dataset to degrade the performance.
+
+# 5.3 Qualitative Analysis
+
+In Figure 3, we conduct the qualitative analysis to better understand our approach. As we can see, the visualization verifies the effectiveness of our knowledge-driven encoder in extracting the knowledge representations of both image and report. For the generated reports, our unsupervised KGAE generates a desirable report, which correctly describes “innumerable nodules are present” and “heart size is normal”. When removing the bank $B$ , the model tends to generate plausible general reports with no prominent abnormal narratives and some repeated reports, which shows that the knowledge memory mechanism can indeed distill and preserve the desired medical knowledge to boost the generation of reports. Under the semi-supervised setting, the R2Gen can not well handle the medical report generation task and generates some repeated sentences of normalities (Underlined text) and fails to depict some rare but important abnormalities, i.e., “nodules” and “scoliosis”, while our approach can generate fluent report supported by accurate abnormalities. Under the supervised setting, our approach can generate an accurate report showing significant alignment with the ground truth report. It further prove our arguments and the effectiveness of our proposed approach.
+
+![](images/8c460bd3702e10b9395e98ce52155c7f2169ebbb0324da253a96e135fc5afcc8.jpg)  
+Figure 3: Reports generated by our approach and a state-of-the-art model R2Gen [6]. Under the unsupervised setting, we show four nodes with top-4 attention weights in Eq. (4) to visualize $\mathcal { G } _ { I }$ and $\mathcal { G } _ { R }$ . The Purple and Blue colored text denote the generated wrong sentences (Faithfulness) and true abnormalities (Comprehensiveness), respectively; Underlined text denotes the repeated sentences.
+
+# 6 Conclusions and Discussions
+
+In this paper, we propose the Knowledge Graph Auto-Encoder (KGAE). Without any image-report pairs, KGAE can extract the knowledge representations of both image and report from the knowledge graph to bridge the visual and textual domains, and generate desirable reports by being trained in the auto-encoding pipeline. The experiments verify the effectiveness of our approach, which even exceeds several supervised models. Moreover, by further fine-tuning KGAE using paired datasets, we achieve the state-of-the-art results on two public datasets with the best human preference.
+
+In the future, 1) since we can relax the dependency on paired data, it can be interesting to apply the KGAE to other types of medical images of other body parts, where the image-report pairs could be much less or even unavailable, to assist radiologists in clinical decision-making and reduce their workload; 2) We can replace the explicit pre-defined knowledge graph with an implicit large matrix (e.g., knowledge bank in our decoder) to improve the generalization ability of our approach.
+
+Societal Impacts: In this paper, we target the problem of medical report generation. Although the proposed model outperforms state-of-the-art approaches, it aims to assist the radiologists instead of replacing them. For experienced radiologists, given a large amount of medical images, our model can automatically generate medical reports, the radiologists only need to make revisions rather than write a new report from scratch. However, it is possible that some radiologists direct copy the generated report as the final report. Also for less experienced radiologists, they may not be able to correct the errors in machine-generated reports. In order to apply the proposed model in clinical practice, it is required to add process control to avoid unintended use.
+
+Limitations: Although the proposed KGAE can work in an unsupervised manner, we still need the independent sets of medical images and medical reports which may still be difficult to collect for some types of medical images. In addition, our approach introduces the knowledge graph to bridge visual and textual domain, in the paper, we collect the frequent clinical findings as nodes and build the knowledge graph from the set of reports automatically. When applying to new domains, we need to collect a new set of clinical findings.
+
+# Acknowledgments
+
+We would like to sincerely thank the clinicians (Xiaoxia Xie, Jing Zhang, etc.) of the Harbin Chest Hospital in China for providing the human evaluation. We also sincerely thank all the anonymous reviewers and chairs for their constructive comments and suggestions that substantially improved this paper. Xu Sun and Sheng Wang are the corresponding authors of this paper.
+
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+
+# Checklist
+
+1. For all authors...
+
+(a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? [Yes] See the claimed contributions in Introduction.   
+(b) Did you describe the limitations of your work? [Yes] See Section 6.   
+(c) Did you discuss any potential negative societal impacts of your work? [Yes] See Section 6.   
+(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes] We ensured that our paper conforms to them.
+
+2. If you are including theoretical results...
+
+(a) Did you state the full set of assumptions of all theoretical results? [N/A] (b) Did you include complete proofs of all theoretical results? [N/A]
+
+3. If you ran experiments...
+
+(a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [Yes] See our supplemental material.
+
+(b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [Yes] See Section 4.1.   
+(c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? [No] Error bars are not reported because it would be too computationally expensive. Besides, many previous works on medical report generation did not provide error bars as well.   
+(d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)? [Yes] See Settings in Section 4.1.
+
+4. If you are using existing assets (e.g., code, data, models) or curating/releasing new assets...
+
+(a) If your work uses existing assets, did you cite the creators? [Yes] See Section 4.1.   
+(b) Did you mention the license of the assets? [Yes] See Section 4.1. Specifically, PhysioNet Credentialed Health Data License 1.5.0 (https://physionet. org/content/mimic-cxr/view-license/2.0.0/) is used for MIMIC-CXR; Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (http://creativecommons.org/licenses/by-nc-nd/4.0/) is used for IU Xray.   
+(c) Did you include any new assets either in the supplemental material or as a URL? [No]   
+(d) Did you discuss whether and how consent was obtained from people whose data you’re using/curating? [Yes] See Section 4.1. The used datasets are publicly available. All necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived.   
+(e) Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content? [Yes] See Datasets in Section 4.1. All protected health information was de-identified. De-identification was performed in compliance with Health Insurance Portability and Accountability Act (HIPAA) standards in order to facilitate public access to the datasets. Deletion of protected health information (PHI) from structured data sources (e.g., database fields that provide patient name or date of birth) was straightforward. All necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived.
+
+5. If you used crowdsourcing or conducted research with human subjects...
+
+(a) Did you include the full text of instructions given to participants and screenshots, if applicable? [N/A]   
+(b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable? [N/A]   
+(c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? [N/A]

parse/train/nIL7Q-p7-Sh/nIL7Q-p7-Sh_content_list.json

@@ -0,0 +1,1274 @@
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+    {
+        "type": "text",
+        "text": "Auto-Encoding Knowledge Graph for Unsupervised Medical Report Generation ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Fenglin Liu1,2, Chenyu $\\mathbf { V o u } ^ { 4 }$ , Xian $\\mathbf { W } \\mathbf { u } ^ { 5 }$ , Shen $\\mathbf { G e ^ { 5 } }$ , Sheng Wang3∗, $\\mathbf { X } \\mathbf { u } \\mathbf { S } \\mathbf { u } \\mathbf { n } ^ { 1 * }$   \n1MOE Key Laboratory of Computational Linguistics, School of EECS, Peking University 2School of ECE, Peking University   \n3Paul G. Allen School of Computer Science and Engineering, University of Washington 4Department of Electrical Engineering, Yale University 5Tencent {fenglinliu98, xusun}@pku.edu.cn, chenyu.you@yale.edu {kevinxwu, shenge}@tencent.com, swang@cs.washington.edu ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Abstract ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Medical report generation, which aims to automatically generate a long and coherent report of a given medical image, has been receiving growing research interests. Existing approaches mainly adopt a supervised manner and heavily rely on coupled image-report pairs. However, in the medical domain, building a large-scale image-report paired dataset is both time-consuming and expensive. To relax the dependency on paired data, we propose an unsupervised model Knowledge Graph Auto-Encoder (KGAE) which accepts independent sets of images and reports in training. KGAE consists of a pre-constructed knowledge graph, a knowledgedriven encoder and a knowledge-driven decoder. The knowledge graph works as the shared latent space to bridge the visual and textual domains; The knowledge-driven encoder projects medical images and reports to the corresponding coordinates in this latent space and the knowledge-driven decoder generates a medical report given a coordinate in this space. Since the knowledge-driven encoder and decoder can be trained with independent sets of images and reports, KGAE is unsupervised. The experiments show that the unsupervised KGAE generates desirable medical reports without using any image-report training pairs. Moreover, KGAE can also work in both semi-supervised and supervised settings, and accept paired images and reports in training. By further fine-tuning with image-report pairs, KGAE consistently outperforms the current state-of-the-art models on two datasets. ",
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+    {
+        "type": "text",
+        "text": "1 Introduction ",
+        "text_level": 1,
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Medical images, such as radiology and pathology images, and their corresponding reports are widely used for clinical diagnosis and treatment [8, 11]. A medical report is usually a paragraph of multiple sentences which describes both the normal and abnormal findings in the medical image. In clinical practice, writing a report can be time-consuming and tedious for experienced radiologists, and error-prone for inexperienced radiologists [4]. Therefore, given the large volume of medical images, automatically generating reports can improve current clinical practice in diagnostic radiology and assist radiologists in clinical decision-making [15, 25]. Specifically, it can relieve radiologists from such heavy workload and alert radiologists of the abnormalities to avoid misdiagnosis and missed diagnosis. Therefore, automatic medical report generation attracts remarkable attention in both artificial intelligence and clinical medicine. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Recently, inspired by the great success of neural machine translation [2, 38, 49, 50, 48], image captioning [44, 39, 46, 28, 30, 29] and medical imaging analysis [47, 51, 52], the data-driven deep neural models, particularly those based on the encoder-decoder frameworks [15, 16, 25, 22, 41, 45, 53, 54, 6], have achieved great success in advancing the state-of-the-art of medical report generation. However, these models are trained in a supervised learning manner and heavily rely on labeled paired image-report datasets [9, 17], which are not easy to acquire in the real world. Specifically, the medical-related data can only be manually labeled by professional radiologists, and also involves privacy issues. Therefore, the medical report generation datasets are particularly labor-intensive and expensive to obtain. As a result, the scales of existing widely-used datasets for medical report generation models [16, 25, 22, 23], i.e., MIMIC-CXR (0.22M samples) [17] and IU X-ray (4K samples) [9], are relatively small compared to image recognition datasets, e.g., ImageNet (14M samples) [10], and image captioning datasets, e.g., Conceptual Captions (3.3M samples) [36]. In addition, the MIMIC-CXR and IU X-Ray datasets only include Chest X-Ray images, for other types of medical images (MRI, Dermoscopy, Retinal, etc.) of other body parts (brain, skin, eye, etc.), the image-report pairs could be much less or even unavailable. Therefore, to relax the reliance on the paired data sets, making use of all available data, like independent image or report sets, is becoming increasingly important. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/afd8a513e722a0d7580732c419f634a6b81e954681b7596839e01ae7aa180bf4.jpg",
+        "image_caption": [
+            "Figure 1: Illustration of our Knowledge Graph Auto-Encoder, which consists of a pre-constructed knowledge graph, a knowledge-driven encoder and a knowledge-driven decoder. The Green and Red lines denote the data flow in the training process and testing process of report generation, respectively. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In this paper, we propose an unsupervised model Knowledge Graph Auto-Encoder (KGAE), which utilizes independent sets of images and reports in training (the image and report set are separate and have no overlap). KGAE consists of a pre-constructed knowledge graph, a knowledge-driven encoder and a knowledge-driven decoder. As shown in Figure 1, the knowledge graph works as the shared latent space of images and reports. The knowledge-driven encoder can take either the image $I$ or the report $R$ as queries and project them to corresponding coordinates $\\mathcal { G } _ { I }$ and $\\mathcal { G } _ { R }$ in the latent space. In this manner, since $\\mathcal { G } _ { I }$ and $\\mathcal { G } _ { R }$ share the same latent space, we can use positions in latent space to measure the relationship between images and reports which narrows the gap between visual and textual domains. In brief, to bridge the gap between vision and language domains without training on the pairs of images and reports, we adopt the knowledge graph to create a latent space and propose a knowledge-driven encoder, which includes a common mapping function to project images and reports to the same latent space. As a result, our encoder can extract the image and report knowledge representations, i.e., the knowledge related to the image and report, they (image, report knowledge) share the common latent space, which allows our model to bridge the gap between vision and language domains without the training on the pairs of image and report. Next, we introduce the knowledge-driven decoder to exploit $\\mathcal { G } _ { I }$ and $\\mathcal { G } _ { R }$ to generate the report. In the training stage, we estimate the parameters of the decoder by reconstructing the input report $R$ based on $\\mathcal { G } _ { R }$ , i.e., $R  \\mathcal { G } _ { R }  R$ auto-encoding pipeline; In the prediction stage, we directly input $\\mathcal { G } _ { I }$ into the trained decoder to generate the report. In this way, our approach can produce desirable reports without any labeled image-report pairs. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Overall, the contributions of this paper are as follows: ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "• In this paper, we make the first attempt to conduct unsupervised medical report generation where the image-report pairs are not available. To this end, we propose the Knowledge Graph Auto-Encoder (KGAE). By leveraging a pre-constructed knowledge graph, we introduce the knowledge-driven encoder and decoder which are trained with independent sets of images and reports. According to the experimental results, the unsupervised KGAE can even outperform several supervised approaches. ",
+        "bbox": [
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+        "type": "text",
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+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "• In addition to the unsupervised mode, KGAE can also be applied in a semi-supervised or supervised manner. Under the semi-supervised setting, by using only $60 \\%$ of paired dataset, KGAE is able to achieve competitive results with current state-of-art models; Under the supervised setting, by training on fully paired datasets as in existing works, KGAE can set new state-of-the-art performances on the IU X-ray and MIMIC-CXR, respectively. • The analysis, both quantitative and qualitative, as well as a human evaluation conducted by professional radiologists, further proves the effectiveness of our approach. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2 Related Works ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Medical report generation aims to generate a relatively long paragraph to describe a given medical image. It is similar to the image captioning task [5], which aims to generate a sentence to describe a given image. In image captioning, the encoder-decoder framework [39], where the encoder [20, 12] computes visual representations for the image and the decoder [13, 38] generates a target sentence based on the visual representations, has achieved great success [1, 31, 35, 44]. However, instead of only generating one single sentence, medical report generation aims to generate a long paragraph including multiple structured sentences that describe both the normal and abnormal parts [25, 15]. To this end, given the success of encoder-decoder framework on image captioning, most existing medical report generation models attempt to exploit the hierarchical LSTM (HLSTM) [15, 16, 19] or Transformer [6] to generate an accurate, long and coherent report. However, existing models require the paired image-report datasets, which are time-consuming and expensive to collect. In this paper, we propose the unsupervised model Knowledge Graph Auto-Encoder (KGAE) which doesn’t need paired images and reports. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Note that although the knowledge graph has been integrated in existing medical report generation models [54, 22], these approaches are supervised and require paired images and reports. Thus, their objectives and motivations of using knowledge graph are different from our work. In detail, existing knowledge-graph based medical report generation methods aim to adopt the knowledge graph to boost the performance of supervised models. However, in our work, we aim to generate a medical report without using any coupled image-report training pairs, i.e., unsupervised medical report generation. A key challenge of unsupervised medical report generation is to bridge the gap between vision and language domains. To this end, we adopt the knowledge graph to create a latent space and propose a knowledge-driven encoder to project image and report to the same latent space. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "3 Approach ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We first formulate the conventional supervised medical report generation problems; Then, we describe the proposed Knowledge Graph Auto-Encoder for unsupervised medical report generation in detail. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "3.1 Conventional Supervised Medical Report Generation Models ",
+        "text_level": 1,
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Given a medical image $I$ , the goal is to generate a descriptive report $R$ . Most models [15, 16, 6] normally include an image encoder and a report decoder, which can be formulated as: ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/b1113f598df9f5da69387dda0a2f7510dc687825af98010488d01ddd8b7e139e.jpg",
+        "text": "$$\n{ \\mathrm { I m a g e ~ E n c o d e r : ~ } } I  I ^ { \\prime } ; { \\mathrm { ~ ~ R e p o r t ~ D e c o d e r : ~ } } I ^ { \\prime }  R ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where $I ^ { \\prime } \\in \\mathbb { R } ^ { N _ { I } \\times d }$ denotes the image embeddings extracted by the image encoder, e.g., ResNet-50 [12]. Then, $I ^ { \\prime }$ is used to guide the generation of the target report $R$ in the report decoder, e.g., LSTM [13] and Transformer [38]. During training, given the ground truth report for the input image, we can train the encoder-decoder model by minimizing a supervised training loss, e.g., cross-entropy loss. However, paired image-report $( I { - } R )$ datasets are particularly labor-intensive and expensive to obtain. Therefore, in this paper, we aim to relax the reliance on the paired datasets and make use of the independent sets of images and reports instead. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2 Knowledge Graph Auto-Encoder ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            828,
+            442,
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "As shown in Figure 1, the proposed KGAE includes a knowledge graph, a knowledge-driven encoder and a knowledge-driven decoder, which will be described in detail in the following sections. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Knowledge Graph The motivation of using the knowledge graph is that writing medical reports usually requires particular domain knowledge [11, 22]. Therefore, we can utilize the knowledge graph, which models the domain-specific knowledge structure, to serve as a bridge to correlate the knowledge representations of the visual and textual domains. In particular, we construct an off-the-shelf global medical knowledge graph $\\mathcal { G } = ( V , E )$ covering the common abnormalities and normalities, where $V = \\{ v _ { i } \\} _ { i = 1 : N _ { \\mathrm { K G } } } \\in \\mathbb { R } ^ { N _ { \\mathrm { K G } } \\times d }$ is a set of nodes and $E = \\{ e _ { i , j } \\} _ { i , j = 1 : N _ { \\mathrm { K G } } }$ is a set of edges. In detail, based on the report corpus, i.e., MIMIC-CXR [17], we consider the $N _ { \\mathrm { K G } }$ frequent clinical abnormalities (e.g., \"enlarged heart size\", \"pleural effusion\", and \"bibasilar consolidation\") and normalities (e.g., \"heart size is normal\" and \"lungs are clear\") as nodes. The edge weights are calculated by the normalized co-occurrence of different nodes computed from report corpus. Please note that this knowledge graph is built purely from the training set of MIMIC-CXR, thus there is no label leakage. After that, the knowledge graph is embedded by a graph embedding module, i.e., graph convolution network [32, 24], which is implemented as follows: ",
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+        "text": "",
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+    {
+        "type": "equation",
+        "img_path": "images/aaeb2d9a8808e9d4735408b7d0a4f248c57068a378d3fc29021a77d361319f0f.jpg",
+        "text": "$$\nv _ { i } ^ { \\prime } = v _ { i } + \\mathrm { R e L U } ( \\sum _ { j = 1 } ^ { N _ { \\mathrm { K G } } } e _ { i , j } W _ { v } v _ { j } ) ,\n$$",
+        "text_format": "latex",
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+    },
+    {
+        "type": "text",
+        "text": "where $\\mathrm { R e L U } ( \\cdot )$ represents the ReLU activation function and $W _ { v } \\in \\mathbb { R } ^ { d \\times d }$ is the learnable matrix. As a result, we can acquire a set of node embeddings $V ^ { \\prime } = \\{ v _ { 1 } ^ { \\prime } , v _ { 2 } ^ { \\prime } , \\ldots , v _ { N _ { \\mathrm { K G } } } ^ { \\prime } \\} \\in \\mathbb { R } ^ { N _ { \\mathrm { K G } } \\times d }$ . It is worth noting that more complex graph structures could be constructed by using more large-scale medical textbooks. Therefore, our model is not limited to the currently constructed graph and could provide a good basis for the research of unsupervised medical report generation for other domains. ",
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+        "text": "Knowledge-driven Encoder The knowledge-driven encoder (KE) is designed to utilize the knowledge graph $\\mathcal { G }$ to extract knowledge representations $( \\mathcal { G } _ { I } \\in \\mathbb { R } ^ { N _ { I } \\times d }$ and $\\mathcal { G } _ { R } \\in \\overline { { \\mathbb { R } } } ^ { N _ { R } \\times d } )$ of both image $I$ and report $R$ to bridge the vision and the language domains, which can be formulated as: ",
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/7812325f7057e666ef1c49b3416922a6919e20846f0d1de257cf61489030935f.jpg",
+        "text": "$$\n{ \\mathcal G } _ { I } = \\mathrm { K E } _ { I } ( I , { \\mathcal G } ) ; { \\mathcal G } _ { R } = \\mathrm { K E } _ { R } ( R , { \\mathcal G } ) .\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "In implementations, as shown in Figure 1, we first adopt the ResNet-50 [12] and the Transformer [38] as the image embedding module and report embedding module to embed the image $I$ and report $R$ , acquiring the image embeddings $I ^ { \\prime } \\in \\mathbb { R } ^ { \\bar { N } _ { I } \\times d }$ and report embeddings $R ^ { \\prime } \\in \\mathbb { R } ^ { N _ { R } \\times \\breve { d } }$ , respectively. Next, to extract the knowledge representations from knowledge graph $\\mathcal { G }$ , we adopt the attention mechanism [38] to implement the KE. The motivation stems from that the attention mechanism can compute the association weights between different features and allows probabilistic many-to-many relations instead of monotonic relations, as in [38, 44, 29]. As a result, we take $I ^ { \\prime }$ and $R ^ { \\prime }$ as the queries, and take the knowledge graph $\\mathcal { G }$ (i.e., $V ^ { \\prime } = \\{ v _ { 1 } ^ { \\prime } , v _ { 2 } ^ { \\prime } , \\ldots , v _ { N _ { \\mathrm { K G } } } ^ { \\prime } \\} \\in \\mathbb { R } ^ { N _ { \\mathrm { K G } } \\times d } )$ as the lookup matrix: ",
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+    {
+        "type": "equation",
+        "img_path": "images/111fc65509c8e19f26d1e1d2bb2ae062fc168504649b6b143dddcd03711aa27b.jpg",
+        "text": "$$\n\\begin{array} { r l } & { \\mathcal { G } _ { I } = \\mathrm { K E } _ { I } ( I , \\mathcal { G } ) = \\mathcal { F } ( \\mathrm { A t t e n t i o n } _ { I } ( I ^ { \\prime } , V ^ { \\prime } ) ) ; \\mathcal { G } _ { R } = \\mathrm { K E } _ { R } ( R , \\mathcal { G } ) = \\mathcal { F } ( \\mathrm { A t t e n t i o n } _ { R } ( R ^ { \\prime } , V ^ { \\prime } ) ) } \\\\ & { \\quad \\quad \\quad \\quad \\quad \\mathrm { A t t e n t i o n } ( x , y ) = \\mathrm { s o f t m a x } \\left( \\frac { x W _ { \\ P } \\left( y W _ { \\mathbf { k } } \\right) ^ { \\top } } { \\sqrt { d } } \\right) y W _ { \\mathbf { v } } . } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $x \\in \\mathbb { R } ^ { N _ { x } \\times d _ { x } } , y \\in \\mathbb { R } ^ { N _ { y } \\times d _ { y } }$ ; $W _ { \\mathrm { q } } \\in \\mathbb { R } ^ { d _ { x } \\times d _ { x } }$ , $W _ { \\mathbf { k } } \\in \\mathbb { R } ^ { d _ { y } \\times d _ { y } }$ and $W _ { \\mathrm { v } } \\in \\mathbb { R } ^ { d _ { y } \\times d _ { y } }$ $\\langle d _ { x } = d _ { y }$ ) are learnable parameters. $\\mathcal { F }$ is implemented as two fully-connected (FC) layers with a ReLU in between, i.e., FC-ReLU-FC. The resulted $\\mathcal { G } _ { I } \\in \\mathbb { R } ^ { N _ { I } \\times d }$ and $\\dot { \\mathcal { G } } _ { R } \\in \\mathbb { R } ^ { N _ { R } \\times d }$ turn out to be a set of attended (i.e., extracted) knowledge related to the image and report. The knowledge representations $\\mathcal { G } _ { I }$ and $\\mathcal { G } _ { R }$ share the common latent space which bridges the vision and the language domains. Note that the $\\mathcal { F }$ used in $\\mathrm { K E } _ { I }$ and $\\mathrm { K E } _ { R }$ shares the same parameters and is thus introduced to further boost the bridging capabilities of different modalities. It means that we adopt two KEs, i.e., $\\mathrm { K E } _ { I }$ and $\\mathrm { K E } _ { R }$ , and each KE includes an attention model as well as a common mapping function $\\mathcal { F }$ . The only shared weights of $\\mathrm { K E } _ { I }$ and $\\mathrm { K E } _ { R }$ are the parameters of $\\mathcal { F }$ , and the parameters of attention models are independent. ",
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+    {
+        "type": "text",
+        "text": "Knowledge-driven Decoder The decoder is designed to generate the reports based on the graph representations $\\mathcal { G } _ { I }$ or $\\mathcal { G } _ { R }$ . For clarity, we use $\\mathcal { G } _ { k }$ to represent the $\\mathcal { G } _ { R }$ and $\\mathcal { G } _ { I }$ during the training and testing stages, respectively. In implementations, since medical report generation requires generating a long paragraph, we choose the (three-layer) Transformer [38] as the basic module of our decoder and incorporate the proposed Knowledge-driven Attention (KA) to effectively model the long sequences. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "At each decoding step $t$ , the decoder takes the embedding of current input word $x _ { t } = w _ { t } + e _ { t } \\in \\mathbb { R } ^ { 2 d }$ as input, where $w _ { t }$ and $e _ { t }$ denote the word embedding and fixed position embedding, respectively, and generate each word $r _ { t }$ in report $R = \\{ r _ { 1 } , r _ { 2 } , . . . , r _ { T } \\}$ , which can be defined as follows: ",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/76403d2c4eeac99fa6af5036a877f9ed6f1e4148334a775fcde6690e6e51edee.jpg",
+        "text": "$$\n\\begin{array}{c} \\begin{array} { r } { \\begin{array} { r } { h _ { t } = \\mathrm { A t t e n t i o n } ( x _ { t } , x _ { 1 : t } ) } \\\\ { h _ { t } ^ { \\prime } = \\mathrm { K A } ( h _ { t } , \\mathcal { G } _ { k } , B ) } \\end{array} , \\mathrm { ~ w h e r e ~ } \\mathcal { G } _ { k } = \\left\\{ \\begin{array} { r l } { \\mathcal { G } _ { R } , } & { \\mathrm { T r a i n i n g } } \\\\ { \\mathcal { G } _ { I } , } & { \\mathrm { T e s t i n g } } \\end{array} \\right. ; r _ { t } \\sim p _ { t } = \\mathrm { s o f t m a x } ( \\mathrm { F F N } ( h _ { t } ^ { \\prime } ) \\mathbb { W } _ { p } ) , } \\end{array}  \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where FFN stands for Feed-Forward Network in the original Transformer [38]; $\\mathbf { W } _ { p } \\in \\mathbb { R } ^ { 2 d \\times | D | }$ is the learnable parameter $| | D | |$ denotes the vocabulary size); $B$ represents the knowledge bank in the KA. ",
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+    {
+        "type": "text",
+        "text": "In particular, the knowledge-driven attention (KA) is inspired by the success of many works that attempt to augment a working memory into the network, e.g., memory network. Memory network preserves a dynamic knowledge base for subsequent inference [37, 21, 42, 43, 40, 46, 33]. For example, [37, 21] and [42, 43] proposed to preserve the context of a document and visual knowledge to solve language modeling and visual question answering, respectively. In this paper, since the knowledge representations $\\mathcal { G } _ { k }$ are extracted from the off-the-shelf global knowledge graph $\\mathcal { G }$ , we incorporate a knowledge memory mechanism to distill and preserve the fine-grained medical knowledge related to report generation task, which encourages our decoder to generate more accurate and desirable reports. Specifically, we introduce the knowledge bank $B = \\{ b _ { 1 } , b _ { 2 } , \\ldots , b _ { N _ { \\mathrm { B } } } \\} \\in \\mathbb { R } ^ { N _ { \\mathrm { B } } \\times d }$ , where $N _ { \\mathrm { B } }$ stands for the total number of the knowledge corresponding to report generation. As a result, given the graph representations $\\mathcal { G } _ { k } \\in \\mathbb { R } ^ { N _ { k } \\times d }$ , the knowledge memory mechanism is defined as follows: ",
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+    {
+        "type": "equation",
+        "img_path": "images/55e556f0532c418e15666290c821fe186d2ca5e6a243f0dae63583e180bdc76d.jpg",
+        "text": "$$\nB _ { k } = \\operatorname { s o f t m a x } \\left( \\mathcal { G } _ { k } B ^ { \\top } \\right) B .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Through above operation, each feature/vector in the $\\mathcal { G } _ { k } \\in \\mathbb { R } ^ { N _ { k } \\times d }$ can distill the fine-grained knowledge preserved in $B$ to acquire $B _ { k } \\in \\mathbb { R } ^ { N _ { k } \\times d }$ for accurate report generation. ",
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+    {
+        "type": "text",
+        "text": "Based on the above mechanism, the knowledge-driven attention in Eq. (5) is defined as: ",
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+    {
+        "type": "equation",
+        "img_path": "images/f16d2e95546a09969aa83c79ca74da6fd86d376cbbeece8653d37cbf97eafcb5.jpg",
+        "text": "$$\nh _ { t } ^ { \\prime } = \\mathrm { K A } ( h _ { t } , \\mathcal { G } _ { k } , B ) = \\mathrm { A t t e n t i o n } ( h _ { t } , [ \\mathcal { G } _ { k } ; B _ { k } ] ) = \\mathrm { A t t e n t i o n } \\left( h _ { t } , \\left[ \\mathcal { G } _ { k } ; \\operatorname { s o f t m a x } \\left( \\mathcal { G } _ { k } B ^ { \\top } \\right) B \\right] \\right) .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
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+    {
+        "type": "text",
+        "text": "where $[ \\cdot ; \\cdot ]$ denotes the concatenation operation. It is worth noting that these operations are all differentiable, thus the bank $B$ can be learned in an end-to-end fashion. ",
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+        "type": "text",
+        "text": "In our subsequent analysis, we will show that the introduced knowledge memory mechanism indeed distills and preserves the desired medical knowledge, and thus boost the generation of reports. ",
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+    {
+        "type": "text",
+        "text": "3.3 Implementation Details ",
+        "text_level": 1,
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+        "text": "Unsupervised Training Details To train our KGAE in an unsupervised manner, instead of using the paired image-report dataset in the conventional supervised model, we only require an image set CheXpert [14], which includes 224,316 X-ray images, and a separate report corpus MIMIC-CXR $[ 1 7 ] + \\mathrm { I U }$ X-ray [9], which includes $2 2 2 , 7 5 8 + 2 , 7 7 { \\bar { 0 } } = 2 2 5 , 5 2 8 \\ \\cdot$ reports2. ",
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+        "type": "text",
+        "text": "In detail, to train our knowledge-driven encoder $\\mathrm { K E } _ { I }$ and $\\mathrm { K E } _ { R }$ (see Eq. (4)), we feed the $\\mathcal { G } _ { I }$ and $\\mathcal { G } _ { R }$ into a common multi-label classification network [54, 15] trained with binary cross entropy loss for 14 common radiographic observations classification3. In this way, our encoder can extract the knowledge representations $\\mathcal { G } _ { I }$ and $\\mathcal { G } _ { R }$ of both image and report in a common latent space, effectively bridging the vision and the language domains. To train the knowledge-driven decoder, as well as the knowledge bank $B$ (see Eq. (5)), since there are no coupled image-report pairs, we propose to reconstruct the report $R$ based on the $\\mathcal { G } _ { R }$ . Therefore, through Eq. (5), taking the input report $R = \\{ r _ { 1 } , r _ { 2 } , \\ldots , r _ { T } \\}$ as the ground truth report, we can train our approach by minimizing the cross-entropy loss: ",
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+    {
+        "type": "equation",
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+        "text": "$$\nL _ { \\mathrm { C E } } = - \\sum _ { t = 1 } ^ { T } \\log \\left( p \\left( r _ { t } \\mid r _ { 1 : t - 1 } \\right) \\right) .\n$$",
+        "text_format": "latex",
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+        "type": "text",
+        "text": "In this way, we can train our decoder in the $R  \\mathcal { G } _ { R }  R$ auto-encoding pipeline. ",
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+    {
+        "type": "text",
+        "text": "During testing, we first adopt the knowledge-driven encoder to extract the knowledge representations $\\mathcal { G } _ { I }$ of the test image (see Eq. (4)). Then, we directly feed $\\mathcal { G } _ { I }$ into the decoder to generate final report in the $I  { \\mathcal { G } } _ { I }  R$ pipeline (see Eq. (5)). In this way, our approach can relax the reliance on the image-report pairs. In our following experiments, we validate the effectiveness of our approach, which even outperforms some supervised approaches. ",
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+    {
+        "type": "text",
+        "text": "Semi-Supervised and Supervised Training Details To further validate the effectiveness of our approach, we fine-tune the unsupervised $K G A E$ using partial and full image-report pairs to acquire the KGAE-Semi(-Supervised) and KGAE-Supervised, respectively, where the former can evaluate the performance of our approach under limited labeled pairs for training and the latter can compare the performance of KGAE with state-of-the-art supervised approaches. In the (semi-)supervised setting, given the image-report pairs, i.e., $I { - } R$ , we first incorporate the original visual information into the knowledge representation $\\mathcal { G } _ { I }$ , and then train our KGAE by generating the ground truth report in the $I  { \\mathcal { G } } _ { I }  R$ pipeline and minimizing the cross-entropy loss in Eq. (8). During testing, we also follow the unsupervised setting to generate the final report in the $I  { \\mathcal { G } } _ { I }  R$ pipeline. ",
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+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "4 Experiments ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We first introduce the datasets, metrics and detailed settings used for evaluation. Then, we present the evaluation of our approach under the unsupervised, semi-supervised and supervised training settings. ",
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+    {
+        "type": "text",
+        "text": "4.1 Datasets, Metrics and Settings ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Datasets In this paper, we adopt the test sets of IU X-ray [9] and MIMIC-CXR [17] for evaluation. All protected health information (e.g., patient name and date of birth) was de-identified. In particular, the IU X-ray [9] is a widely-used public benchmark dataset for medical report generation and contains 7,470 chest X-ray images associated with 3,955 fully de-identified medical reports. Each report is composed of impression, findings and indication sections, etc. [22]. Following [25], our method also focuses on the findings section as it is the most important component of reports. Then, following [16, 22, 25, 6], we randomly select $7 0 \\% - 1 0 \\% - 2 0 \\%$ image-report pairs of dataset to form the trainingvalidation-testing sets. The MIMIC-CXR [17] includes 377,110 chest $\\mathbf { X }$ -ray images associated with 227,835 reports. The dataset is officially split into 368,960 images (222,758 reports) for training, 2,991 images (1,808 reports) for validation and 5,159 images (3,269 reports) for testing. It is worth noting that we focus on the unsupervised medical report generation, where the image-report pairs are not available, thus the image-report training pairs of both the IU X-ray and MIMIC-CXR datasets are discarded and are not used in our unsupervised training stage. Only the training reports of MIMIC-CXR and IU $\\mathbf { X }$ -ray, i.e., $2 2 2 , 7 5 8 + 2 , 7 7 0 = 2 2 5 , 5 2 8$ reports, are used as the independent report corpus to train our unsupervised model. Only under the (semi-)supervised training setting, we will adopt the image-report training pairs to train our approach. ",
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+    {
+        "type": "text",
+        "text": "Metrics To fairly compare with existing models [25, 6], we adopt the evaluation toolkit [5] to calculate the widely-used natural language generation metrics, i.e., BLEU [34], METEOR [3] and ROUGE-L [26], which measure the match between the generated reports and ground truth reports, but are not specialized for the abnormalities in the reports. Therefore, to measure the accuracy of descriptions for clinical abnormalities, we further report clinical efficacy metrics following the work of Chen et al. [6]. The clinical efficacy metrics are calculated by comparing the generated reports with ground truth reports in 14 different categories related to thoracic diseases and support devices, producing the Precision, Recall and F1 scores. ",
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+    {
+        "type": "text",
+        "text": "Settings The size $d$ is set to 256. For the attention mechanism in Eq. (4) and Eq. (5), we adopt the multi-head attention [38], the number of heads $n$ in multi-head attention is set to 8. The intermediate dimension in $\\mathcal { F }$ , i.e., Eq. (4), is set to 1024. Based on the average performance on the validation set, the $N _ { \\mathrm { B } }$ in knowledge bank, i.e., Eq. (6), is set to 10,000. The $N _ { \\mathrm { K G } }$ in the knowledge graph is set to 200. In our knowledge-driven encoder, the image embedding module adopts the ResNet-50 [12] pretrained on ImageNet [10] and fine-tuned on CheXpert dataset [14] to extract the image embeddings in the shape of $7 \\times 7 \\times 2 0 4 8$ , which will be projected to $d = 2 5 6$ , acquiring $I ^ { \\prime } \\in \\mathbb { R } ^ { 4 9 \\times 2 5 6 }$ , i.e., $N _ { I } = 4 9$ ; The report embedding module is implemented by the Transformer [38] equipping with the self-attention mechanism provided in Lin et al. [27]; $N _ { R } = N _ { I } = 4 9$ . In both unsupervised and (semi-)supervised settings (see Section 3.3), the batch size is set to 16 and Adam optimizer [18] with a learning rate of 1e-4 is used for parameter optimization. Before testing on the IU X-ray/MIMICCXR, we further only employ the training data from IU X-ray/MIMIC-CXR to train the model. All re-implementations and our experiments were run on 8 V100 GPUs. ",
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+    {
+        "type": "text",
+        "text": "4.2 Automatic Evaluation ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We evaluate the performance of our approach under unsupervised, semi-supervised and supervised settings. The results are shown in Table 1, Table 2 and Figure 2. We select several supervised methods, including a recently state-of-the-art model R2Gen [6], for comparison. These models follow the encoder-decoder architecture, trained on the full pairs of images and reports. ",
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+        "text": "Unsupervised Setting As shown in Table 1 and Table 2, our unsupervised model KGAE achieves competitive results with some supervised models in both IU X-ray and MIMIC-CXR datasets, and even outperforms several supervised models. Specifically, on the IU X-ray dataset, Table 1 shows that KGAE surpasses the NIC [44], AdaAtt [31] and Att2in [35] in terms of all metrics, and the Transformer [6] in terms of BLEU-1,2,3. On the MIMIC-CXR dataset, Table 2 shows that KGAE outperforms the $\\mathcal { M } ^ { 2 }$ Trans. [7] in terms of Precision, Recall and F1. The competitive results prove the effectiveness of our approach in addressing the unsupervised medical report generation, and thus can generate desirable medical reports without the training on the pairs of image and report. ",
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+        "type": "table",
+        "img_path": "images/25ef589aeb28dd3a8b4430fd53ad6c9f037a99296d850efb4b7f1727bdb742b1.jpg",
+        "table_caption": [
+            "Table 1: Performance in terms of natural language generation metrics on the IU X-ray and MIMICCXR. B-n, M and R-L are short for BLEU-n, METEOR and ROUGE-L, respectively. Higher is better in all columns. It is worth noting that the KGAE is trained in an unsupervised manner, KGAE-Semi is trained $60 \\%$ paired data, KGAE-Supervised and existing methods are trained with full paired data. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Methods</td><td rowspan=\"2\">Year</td><td rowspan=\"2\">Ratio of Pairs</td><td colspan=\"6\">IU X-ray [9]</td><td colspan=\"6\">MIMIC-CXR [17]</td></tr><tr><td>B-1</td><td>B-2</td><td>B-3</td><td>B-4</td><td>M</td><td>R-L</td><td>B-1</td><td>B-2</td><td>B-3</td><td>B-4</td><td>M</td><td>R-L</td></tr><tr><td>NIC [39]</td><td>2015</td><td>100%</td><td>0.216</td><td>0.124</td><td>0.087</td><td>0.066</td><td>-</td><td>0.306</td><td>0.299</td><td>0.184</td><td>0.121</td><td>0.084</td><td>0.124</td><td>0.263</td></tr><tr><td>AdaAtt [31]</td><td>2017</td><td>100%</td><td>0.220</td><td>0.127</td><td>0.089</td><td>0.068</td><td>=</td><td>0.308</td><td>0.299</td><td>0.185</td><td>0.124</td><td>0.088</td><td>0.118</td><td>0.266</td></tr><tr><td>Att2in [35]</td><td>2017</td><td>100%</td><td>0.224</td><td>0.129</td><td>0.089</td><td>0.068</td><td>=</td><td>0.308</td><td>0.325</td><td>0.203</td><td>0.136</td><td>0.096</td><td>0.134</td><td>0.276</td></tr><tr><td>Transformer [6]</td><td>2020</td><td>100%</td><td>0.396</td><td>0.254</td><td>0.179</td><td>0.135</td><td>0.164</td><td>0.342</td><td>0.314</td><td>0.192</td><td>0.127</td><td>0.090</td><td>0.125</td><td>0.265</td></tr><tr><td>M² Trans.[7]</td><td>2020</td><td>100%</td><td>0.437</td><td>0.290</td><td>0.205</td><td>0.152</td><td>0.176</td><td>0.353</td><td>0.238</td><td>0.151</td><td>0.102</td><td>0.067</td><td>0.110</td><td>0.249</td></tr><tr><td>R2Gen [6]</td><td>2020</td><td>100%</td><td>0.470</td><td>0.304</td><td>0.219</td><td>0.165</td><td>0.187</td><td>0.371</td><td>0.353</td><td>0.218</td><td>0.145</td><td>0.103</td><td>0.142</td><td>0.277</td></tr><tr><td>KGAE</td><td></td><td>0%</td><td>0.417</td><td>0.263</td><td>0.181</td><td>0.126</td><td>0.149</td><td>0.318</td><td>0.221</td><td>0.144</td><td>0.096</td><td>0.062</td><td>0.097</td><td>0.208</td></tr><tr><td>KGAE-Semi</td><td>Ours</td><td>60%</td><td>0.497</td><td>0.320</td><td>0.232</td><td>0.171</td><td>0.189</td><td>0.379</td><td>0.352</td><td>0.219</td><td>0.149</td><td>0.108</td><td>0.147</td><td>0.290</td></tr><tr><td>KGAE-Supervised</td><td></td><td>100%</td><td>0.512</td><td>0.327</td><td>0.240</td><td>0.179</td><td>0.195</td><td>0.383</td><td>0.369</td><td>0.231</td><td>0.156</td><td>0.118</td><td>0.153</td><td>0.295</td></tr></table>",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/ca2c382c56dd32757cc94909957087f7fb4a5279ebfefbdafba17175ebe27d06.jpg",
+        "table_caption": [
+            "Table 2: Performance of automatic evaluation in terms of clinical efficacy metrics, which measure the accuracy of descriptions for clinical abnormalities, on the test set of MIMIC-CXR dataset. Higher is better in all columns. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"3\">Methods</td><td rowspan=\"3\">Year</td><td rowspan=\"3\">Ratio of Pairs</td><td colspan=\"3\">MIMIC-CXR[17]</td></tr><tr><td>Precision Recall</td><td></td><td>F1</td></tr><tr><td></td><td></td><td></td></tr><tr><td>NIC[39]</td><td>2015</td><td>100%</td><td>0.249</td><td>0.203</td><td>0.204</td></tr><tr><td>AdaAtt [31]</td><td>2017 2017</td><td>100% 100%</td><td>0.268</td><td>0.186</td><td>0.181</td></tr><tr><td>Att2in [35] Up-Down [1]</td><td>2018</td><td>100%</td><td>0.322 0.320</td><td>0.239 0.231</td><td>0.249</td></tr><tr><td>M² Trans.[7]</td><td>2020</td><td>100%</td><td>0.197</td><td>0.145</td><td>0.238</td></tr><tr><td>Transformer [6]</td><td>2020</td><td>100%</td><td>0.331</td><td>0.224</td><td>0.133 0.228</td></tr><tr><td>R2Gen [6]</td><td>2020</td><td>100%</td><td>0.333</td><td>0.273</td><td>0.276</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>KGAE</td><td></td><td>0%</td><td>0.214</td><td>0.158</td><td>0.156</td></tr><tr><td>KGAE-Semi</td><td>Ours</td><td>60%</td><td>0.360</td><td>0.302</td><td>0.307</td></tr><tr><td>KGAE-Supervised</td><td></td><td>100%</td><td>0.389</td><td>0.362</td><td>0.355</td></tr></table>",
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+    {
+        "type": "image",
+        "img_path": "images/714ee8d17da130941633988e5374eacaa4fa87c8d55ee2af6783dfd8393d379c.jpg",
+        "image_caption": [
+            "Figure 2: Performance of re-implemented state-of-theart model R2Gen [6] and our approach on the test sets with respect to various amount of paired data used for training. The margins in different ratios are shown with the polyline and the right y-axis. As we can see, our approach consistently outperforms the R2Gen. "
+        ],
+        "image_footnote": [],
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+        "text": "",
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+    {
+        "type": "text",
+        "text": "Semi-Supervised Setting To further prove the effectiveness of our approach, we fine-tune the unsupervised KGAE using partial downstream paired image-report datasets (see Section 3.3), resulting in the KGAE-Semi. To this end, in Figure 2, we evaluate the performance of our approach on both IU X-ray and MIMIC-CXR datasets with respect to the increasing amount of paired data. For a fair comparison, we also re-train the state-of-the-art model R2Gen [6] using the same amount of pairs. As we can see, our model outperforms the R2Gen under all ratios of paired dataset used for training. It is worth noting that the fewer the image-report pairs, the larger the margins, e.g., under the very limited pairs setting ( $20 \\%$ of paired datasets), our approach significantly surpasses the R2Gen by $8 . 5 \\%$ absolute BLEU-4 score on IU $\\mathrm { X }$ -ray and $9 . 8 \\%$ absolute F1 score on MIMIC-CXR. Intuitively, since our approach can relax the reliance on the paired datasets, we can make use of available unpaired image and report data as a solid bias for medical report generation task. Table 1 and Table 2 further prove the effectiveness of our approach, which achieves results competitive with current state-of-the-art models by using only $60 \\%$ of paired dataset. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Supervised Setting We fine-tune the unsupervised KGAE using full image-report pairs, acquiring the KGAE-Supervised model (see Section 3.3). Table 1 and Table 2 show that KGAE-Supervised sets the new state-of-the-art results on the two datasets in all metrics. Moreover, in terms of the clinical efficacy metrics, our approach achieves 0.389 precision score, 0.362 recall score and $0 . 3 5 5 \\mathrm { F } 1$ score, outperforming the state-of-the-art model R2Gen [6]. The superior clinical efficacy scores demonstrate the capability of our approach to produce higher quality descriptions for clinical abnormalities than existing models. ",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/8e56457adfb15a012e2067e25473b2ff36336044573405a5de5554dff5cc1ce1.jpg",
+        "table_caption": [
+            "Table 3: We invite three professional clinicians to conduct human evaluation for comparing our approach with $\\mathcal { M } ^ { 2 }$ Trans. [7] and R2Gen [6] under various amount of pairs for training in terms of the comprehensiveness of the generated true abnormalities and the faithfulness of the generated normalities and abnormalities to the ground truth reports. All values are reported in percentage $( \\% )$ . "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"3\">Metrics</td><td colspan=\"3\">KGAE (0%) vs.M² Trans. (100%)</td><td colspan=\"3\">KGAE (0%) vs.R2Gen (100%)</td><td colspan=\"3\">KGAE-Semi (20%) vs.R2Gen (20%)</td><td colspan=\"3\">KGAE-Supervised (100%) vs.R2Gen (100%)</td></tr><tr><td>Loss</td><td>Tie</td><td>Win</td><td>Loss</td><td>Tie</td><td>Win</td><td>Loss</td><td>Tie</td><td>Win</td><td>Loss</td><td>Tie</td><td>Win</td></tr><tr><td>Faithfulness</td><td>34</td><td>18</td><td>48</td><td>62</td><td>15</td><td>23</td><td>21</td><td>10</td><td>69</td><td>25</td><td>22</td><td>53</td></tr><tr><td>Comprehensiveness</td><td>27</td><td>20</td><td>53</td><td>57</td><td>17</td><td>26</td><td>24</td><td>11</td><td>65</td><td>32</td><td>21</td><td>47</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "Overall Combining the results of unsupervised, semi-supervised and supervised settings, the proposed KGAE can relax the dependency on the paired datasets, and thus makes the medical report generation model use the available separate image and report data to boost the performance. The advantages under the scenarios with limited labeled pairs (i.e., semi-supervised setting) show that KGAE might be applied to other medical images (MRI, Dermoscopy, Retinal, etc.), where the coupled images and reports pairs could be much less or even unavailable. ",
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+    {
+        "type": "text",
+        "text": "4.3 Human Evaluation ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We conduct human evaluations to verify the effectiveness of KGAE in clinical practice. Specifically, to assist radiologists in clinical decision-making and reduce their workload, it is important to generate accurate reports (faithfulness), i.e., the model does not generate normalities and abnormalities that does not exist according to doctors, with comprehensive abnormalities (comprehensiveness), the model does not leave out the abnormalities. Therefore, we randomly select 100 samples from the MIMIC-CXR and invite three professional clinicians to compare our approach and baselines independently. The clinicians are unaware of which model generates these reports. The results are shown in Table 3. As we can see, under the unsupervised setting, our approach achieves competitive results with the supervised model, outperforming the $\\mathcal { M } ^ { 2 }$ Trans with winning pick-up percentages. Under the (semi-)supervised setting, our method is better than state-of-the-art model R2Gen [6] in all metrics, especially for the semi-supervised setting $20 \\%$ of paired dataset), our method substantially surpasses the R2Gen, which is in accordance with the automatic evaluation, by $6 9 - 2 1 = 4 8$ and $6 5 - 2 4 = 4 1$ points in terms of the faithfulness and comprehensiveness metrics, respectively. ",
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+    {
+        "type": "text",
+        "text": "5 Analysis ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In this section, we conduct several analysis to better understand our proposed approach. ",
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+    {
+        "type": "text",
+        "text": "5.1 Knowledge Graph Sensitivity ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this section, to evaluate the knowledge graph sensitivity, we evaluate the performances using different knowledge graphs defined on IU X-Ray only, MIMIC-CXR only, both MIMIC-CXR and IU X-Ray. Table 4 shows the results of KGAE $( 0 \\% )$ and KGAE-Supervised $( 1 0 0 \\% )$ on the IU X-ray dataset. As we can see, our KGAE using different knowledge graphs can consistently outperform several existing supervised models, i.e., NIC, AdaAtt, Att2in, across all metrics (Table 1). Similarly, our KGAE-Supervised with different knowledge graphs can also consistently outperform existing state-of-the-art model, i.e., R2Gen (Table 1). The results prove the robustness of our proposed model to the pre-defined knowledge graph. Therefore, this work could provide a good basis or starting point for the research of unsupervised medical report generation in other clinical domains such as MRI and Dermoscopy. ",
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+    {
+        "type": "text",
+        "text": "5.2 Ablation Study ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In Table 5, we conduct quantitative analysis to better understand our approach under both the unsupervised and supervised training settings. For different ablation settings, the KGAE-Supervised is acquired by further fine-tuning the KGAE using image-report pairs. ",
+        "bbox": [
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+    {
+        "type": "table",
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+        "table_caption": [
+            "Table 4: Analysis of the knowledge graph sensitivity. Performance of our approach using different knowledge graphs defined on IU X-Ray only, MIMIC-CXR only, both MIMIC-CXR and IU X-Ray. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"3\">Methods</td><td rowspan=\"3\">Ratio of Pairs</td><td rowspan=\"3\">Knowledge Graphs</td><td colspan=\"6\">IU X-ray [9]</td></tr><tr><td>B-1</td><td>B-2</td><td>B-3</td><td>B-4</td><td>M</td><td>R-L</td></tr><tr><td rowspan=\"3\">KGAE</td><td rowspan=\"3\">0%</td><td>IU X-Ray</td><td>0.425</td><td>0.271</td><td>0.185</td><td>0.114</td><td>0.123</td><td>0.310</td></tr><tr><td>MIMIC-CXR</td><td>0.417</td><td>0.263</td><td>0.181</td><td>0.126</td><td>0.149</td><td>0.318</td></tr><tr><td>MIMIC-CXR + IU X-Ray</td><td>0.419</td><td>0.260</td><td>0.180</td><td>0.124</td><td>0.143</td><td>0.321</td></tr><tr><td rowspan=\"3\">KGAE-Supervised</td><td rowspan=\"3\">100%</td><td>IU X-Ray</td><td>0.519</td><td>0.331</td><td>0.235</td><td>0.174</td><td>0.191</td><td>0.376</td></tr><tr><td>MIMIC-CXR</td><td>0.512</td><td>0.327</td><td>0.240</td><td>0.179</td><td>0.195</td><td>0.383</td></tr><tr><td>MIMIC-CXR + IUX-Ray</td><td>0.505</td><td>0.323</td><td>0.239</td><td>0.181</td><td>0.198</td><td>0.385</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/b3c06b0ed00df127bde60b17f8e7b887b094710b79990edfe20f3c64db02b719.jpg",
+        "table_caption": [
+            "Table 5: We conduct the quantitative analysis under both the unsupervised setting (KGAE) and supervised setting (KGAE-Supervised). We analysis the effect of the shared $\\mathcal { F }$ in the encoder (Eq. (4)), and the effect of the number of the knowledge in the decoder’s knowledge bank $B$ (Eq. (6)). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Methods</td><td rowspan=\"2\">Settings</td><td rowspan=\"2\">F</td><td rowspan=\"2\">B</td><td colspan=\"6\">IU X-ray [9]</td><td colspan=\"6\">MIMIC-CXR [17]</td></tr><tr><td>B-1</td><td>B-2</td><td>B-3</td><td>B-4</td><td>M</td><td>R-L</td><td>B-1</td><td>B-2</td><td>B-3</td><td>B-4</td><td>M</td><td>R-L</td></tr><tr><td rowspan=\"5\">KGAE (0%)</td><td>(a)</td><td>-</td><td>-</td><td>0.291</td><td>0.170</td><td>0.127</td><td>0.086</td><td>0.120</td><td>0.301</td><td>0.166</td><td>0.095</td><td>0.064</td><td>0.032</td><td>0.070</td><td>0.174</td></tr><tr><td>(b)</td><td>?</td><td>-</td><td>0.352</td><td>0.227</td><td>0.154</td><td>0.109</td><td>0.133</td><td>0.313</td><td>0.192</td><td>0.118</td><td>0.079</td><td>0.045</td><td>0.085</td><td>0.187</td></tr><tr><td>(c)</td><td></td><td>5,000</td><td>0.403</td><td>0.252</td><td>0.170</td><td>0.117</td><td>0.144</td><td>0.316</td><td>0.211</td><td>0.137</td><td>0.093</td><td>0.058</td><td>0.093</td><td>0.202</td></tr><tr><td>(d)</td><td>√</td><td>15.000</td><td>0.412</td><td>0.260</td><td>0.178</td><td>0.121</td><td>0.148</td><td>0.320</td><td>0.217</td><td>0.140</td><td>0.092</td><td>0.059</td><td>0.101</td><td>0.205</td></tr><tr><td>Full Model</td><td>√</td><td>10.000</td><td>0.417</td><td>0.263</td><td>0.181</td><td>0.126</td><td>0.149</td><td>0.318</td><td>0.221</td><td>0.144</td><td>0.096</td><td>0.062</td><td>0.097</td><td>0.208</td></tr><tr><td rowspan=\"5\">KGAE-Supervised (100%)</td><td>(e)</td><td>-</td><td>-</td><td>0.482</td><td>0.310</td><td>0.219</td><td>0.166</td><td>0.184</td><td>0.373</td><td>0.323</td><td>0.204</td><td>0.128</td><td>0.104</td><td>0.115</td><td>0.266</td></tr><tr><td>(f)</td><td></td><td>-</td><td>0.470</td><td>0.304</td><td>0.217</td><td>0.162</td><td>0.181</td><td>0.368</td><td>0.320</td><td>0.206</td><td>0.129</td><td>0.101</td><td>0.118</td><td>0.267</td></tr><tr><td>（g）</td><td>?</td><td>5,000</td><td>0.505</td><td>0.323</td><td>0.232</td><td>0.178</td><td>0.190</td><td>0.379</td><td>0.363</td><td>0.228</td><td>0.152</td><td>0.115</td><td>0.147</td><td>0.290</td></tr><tr><td>(h)</td><td>√</td><td>15,000</td><td>0.498</td><td>0.315</td><td>0.221</td><td>0.170</td><td>0.186</td><td>0.374</td><td>0.368</td><td>0.235</td><td>0.158</td><td>0.114</td><td>0.150</td><td>0.293</td></tr><tr><td>Full Model</td><td>&lt;</td><td>10,000</td><td>0.512</td><td>0.327</td><td>0.240</td><td>0.179</td><td>0.195</td><td>0.383</td><td>0.369</td><td>0.231</td><td>0.156</td><td>0.118</td><td>0.153</td><td>0.295</td></tr></table>",
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+        "text": "As we can see, under the unsupervised setting, both the introduced shared $\\mathcal { F }$ and knowledge bank $B$ can significantly boost the performance, which proves our arguments and verifies the effectiveness of our approach in performing the unsupervised medical report generation. ",
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+        "text": "Under the supervised setting, as shown in settings (e,f), applying shared $\\mathcal { F }$ generates unchanged and impaired performance on the MIMIC-CXR and IU $\\mathbf { X }$ -ray datasets, respectively. We speculate the reason is that the supervised model no longer requires the $\\mathcal { F }$ to bridge the vision and the language domains. Therefore, the performance is unchanged on the large dataset MIMIC-CXR. However, the increased parameters introduced by $\\mathcal { F }$ might bring overfitting or increase the difficulty in optimization on the small dataset IU X-ray, which somewhat hinders the performance. For the knowledge bank $B$ , we can find that the results of setting (h) outperforms (g) on the MIMIC-CXR dataset, but underperforms (g) on the IU X-ray dataset. We speculate the reason is that the large MIMIC-CXR dataset contains more knowledge than the small IU X-ray dataset, so a larger knowledge bank may learn more knowledge of MIMIC-CXR to boost the performance while introducing more noisy knowledge into the IU X-ray dataset to degrade the performance. ",
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+        "text": "5.3 Qualitative Analysis ",
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+        "text": "In Figure 3, we conduct the qualitative analysis to better understand our approach. As we can see, the visualization verifies the effectiveness of our knowledge-driven encoder in extracting the knowledge representations of both image and report. For the generated reports, our unsupervised KGAE generates a desirable report, which correctly describes “innumerable nodules are present” and “heart size is normal”. When removing the bank $B$ , the model tends to generate plausible general reports with no prominent abnormal narratives and some repeated reports, which shows that the knowledge memory mechanism can indeed distill and preserve the desired medical knowledge to boost the generation of reports. Under the semi-supervised setting, the R2Gen can not well handle the medical report generation task and generates some repeated sentences of normalities (Underlined text) and fails to depict some rare but important abnormalities, i.e., “nodules” and “scoliosis”, while our approach can generate fluent report supported by accurate abnormalities. Under the supervised setting, our approach can generate an accurate report showing significant alignment with the ground truth report. It further prove our arguments and the effectiveness of our proposed approach. ",
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+            "Figure 3: Reports generated by our approach and a state-of-the-art model R2Gen [6]. Under the unsupervised setting, we show four nodes with top-4 attention weights in Eq. (4) to visualize $\\mathcal { G } _ { I }$ and $\\mathcal { G } _ { R }$ . The Purple and Blue colored text denote the generated wrong sentences (Faithfulness) and true abnormalities (Comprehensiveness), respectively; Underlined text denotes the repeated sentences. "
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+        "text": "6 Conclusions and Discussions ",
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+        "text": "In this paper, we propose the Knowledge Graph Auto-Encoder (KGAE). Without any image-report pairs, KGAE can extract the knowledge representations of both image and report from the knowledge graph to bridge the visual and textual domains, and generate desirable reports by being trained in the auto-encoding pipeline. The experiments verify the effectiveness of our approach, which even exceeds several supervised models. Moreover, by further fine-tuning KGAE using paired datasets, we achieve the state-of-the-art results on two public datasets with the best human preference. ",
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+        "text": "In the future, 1) since we can relax the dependency on paired data, it can be interesting to apply the KGAE to other types of medical images of other body parts, where the image-report pairs could be much less or even unavailable, to assist radiologists in clinical decision-making and reduce their workload; 2) We can replace the explicit pre-defined knowledge graph with an implicit large matrix (e.g., knowledge bank in our decoder) to improve the generalization ability of our approach. ",
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+        "text": "Societal Impacts: In this paper, we target the problem of medical report generation. Although the proposed model outperforms state-of-the-art approaches, it aims to assist the radiologists instead of replacing them. For experienced radiologists, given a large amount of medical images, our model can automatically generate medical reports, the radiologists only need to make revisions rather than write a new report from scratch. However, it is possible that some radiologists direct copy the generated report as the final report. Also for less experienced radiologists, they may not be able to correct the errors in machine-generated reports. In order to apply the proposed model in clinical practice, it is required to add process control to avoid unintended use. ",
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+        "text": "Limitations: Although the proposed KGAE can work in an unsupervised manner, we still need the independent sets of medical images and medical reports which may still be difficult to collect for some types of medical images. In addition, our approach introduces the knowledge graph to bridge visual and textual domain, in the paper, we collect the frequent clinical findings as nodes and build the knowledge graph from the set of reports automatically. When applying to new domains, we need to collect a new set of clinical findings. ",
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+        "type": "text",
+        "text": "Acknowledgments ",
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+        "text": "We would like to sincerely thank the clinicians (Xiaoxia Xie, Jing Zhang, etc.) of the Harbin Chest Hospital in China for providing the human evaluation. We also sincerely thank all the anonymous reviewers and chairs for their constructive comments and suggestions that substantially improved this paper. Xu Sun and Sheng Wang are the corresponding authors of this paper. ",
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+        "text": "References ",
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+        "text": "(a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? [Yes] See the claimed contributions in Introduction.   \n(b) Did you describe the limitations of your work? [Yes] See Section 6.   \n(c) Did you discuss any potential negative societal impacts of your work? [Yes] See Section 6.   \n(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes] We ensured that our paper conforms to them. ",
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+        "text": "(a) Did you state the full set of assumptions of all theoretical results? [N/A] (b) Did you include complete proofs of all theoretical results? [N/A] ",
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+        "text": "(a) If your work uses existing assets, did you cite the creators? [Yes] See Section 4.1.   \n(b) Did you mention the license of the assets? [Yes] See Section 4.1. Specifically, PhysioNet Credentialed Health Data License 1.5.0 (https://physionet. org/content/mimic-cxr/view-license/2.0.0/) is used for MIMIC-CXR; Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (http://creativecommons.org/licenses/by-nc-nd/4.0/) is used for IU Xray.   \n(c) Did you include any new assets either in the supplemental material or as a URL? [No]   \n(d) Did you discuss whether and how consent was obtained from people whose data you’re using/curating? [Yes] See Section 4.1. The used datasets are publicly available. All necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived.   \n(e) Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content? [Yes] See Datasets in Section 4.1. All protected health information was de-identified. De-identification was performed in compliance with Health Insurance Portability and Accountability Act (HIPAA) standards in order to facilitate public access to the datasets. Deletion of protected health information (PHI) from structured data sources (e.g., database fields that provide patient name or date of birth) was straightforward. All necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived. ",
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+        "text": "(a) Did you include the full text of instructions given to participants and screenshots, if applicable? [N/A]   \n(b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable? [N/A]   \n(c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? [N/A] ",
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parse/train/r1eiu2VtwH/r1eiu2VtwH.md

@@ -0,0 +1,303 @@
+# NEURAL OBLIVIOUS DECISION ENSEMBLES FOR DEEP LEARNING ON TABULAR DATA
+
+Sergei Popov   
+Yandex   
+sapopov@yandex-team.ru Stanislav Morozov   
+Yandex   
+Lomonosov Moscow State University stanis-morozov@yandex.ru
+
+# Artem Babenko
+
+Yandex National Research University Higher School of Economics artem.babenko@phystech.edu
+
+# ABSTRACT
+
+Nowadays, deep neural networks (DNNs) have become the main instrument for machine learning tasks within a wide range of domains, including vision, NLP, and speech. Meanwhile, in an important case of heterogenous tabular data, the advantage of DNNs over shallow counterparts remains questionable. In particular, there is no sufficient evidence that deep learning machinery allows constructing methods that outperform gradient boosting decision trees (GBDT), which are often the top choice for tabular problems. In this paper, we introduce Neural Oblivious Decision Ensembles (NODE), a new deep learning architecture, designed to work with any tabular data. In a nutshell, the proposed NODE architecture generalizes ensembles of oblivious decision trees, but benefits from both end-to-end gradient-based optimization and the power of multi-layer hierarchical representation learning. With an extensive experimental comparison to the leading GBDT packages on a large number of tabular datasets, we demonstrate the advantage of the proposed NODE architecture, which outperforms the competitors on most of the tasks. We open-source the PyTorch implementation of NODE and believe that it will become a universal framework for machine learning on tabular data.
+
+# 1 INTRODUCTION
+
+The recent rise of deep neural networks (DNN) resulted in a substantial breakthrough for a large number of machine learning tasks in computer vision, natural language processing, speech recognition, reinforcement learning (Goodfellow et al., 2016). Both gradient-based optimization via backpropagation (Rumelhart et al., 1985) and hierarchical representation learning appear to be crucial in increasing the performance of machine learning for these problems by a large margin.
+
+While the superiority of deep architectures in these domains is undoubtful, machine learning for tabular data still did not fully benefit from the DNN power. Namely, the state-of-the-art performance in problems with tabular heterogeneous data is often achieved by “shallow” models, such as gradient boosted decision trees (GBDT) (Friedman, 2001; Chen & Guestrin, 2016; Ke et al., 2017; Prokhorenkova et al., 2018). While the importance of deep learning on tabular data is recognized by the ML community, and many works address this problem (Zhou & Feng, 2017; Yang et al., 2018; Miller et al., 2017; Lay et al., 2018; Feng et al., 2018; Ke et al., 2018), the proposed DNN approaches do not consistently outperform the state-of-the-art shallow models by a notable margin. In particular, to the best of our knowledge, there is still no universal DNN approach that was shown to systematically outperform the leading GBDT packages (e.g., XGBoost (Chen & Guestrin, 2016)). As additional evidence, a large number of Kaggle ML competitions with tabular data are still won by the shallow GBDT methods (Harasymiv, 2015). Overall, at the moment, there is no dominant deep learning solution for tabular data problems, and we aim to reduce this gap by our paper.
+
+We introduce Neural Oblivious Decision Ensembles (NODE), a new DNN architecture, designed to work with tabular problems. The NODE architecture is partially inspired by the recent CatBoost package (Prokhorenkova et al., 2018), which was shown to provide state-of-the-art performance on a large number of tabular datasets. In a nutshell, CatBoost performs gradient boosting on oblivious decision trees (decision tables) (Kohavi, 1994; Lou & Obukhov, 2017), which makes inference very efficient, and the method is quite resistant to overfitting. In its essence, the proposed NODE architecture generalizes CatBoost, making the splitting feature choice and decision tree routing differentiable. As a result, the NODE architecture is fully differentiable and could be incorporated in any computational graph of existing DL packages, such as TensorFlow or PyTorch. Furthermore, NODE allows constructing multi-layer architectures, which resembles ”deep” GBDT that is trained end-to-end, which was never proposed before. Besides the usage of oblivious decision tables, another important design choice is the recent entmax transformation (Peters et al., 2019), which effectively performs a ”soft” splitting feature choice in decision trees inside the NODE architecture. As discussed in the following sections, these design choices are critical to obtain state-of-the-art performance. In a large number of experiments, we compare the proposed approach with the leading GBDT implementations with tuned hyperparameters and demonstrate that NODE outperforms competitors consistently on most of the datasets.
+
+Overall, the main contributions of our paper can be summarized as follows:
+
+1. We introduce a new DNN architecture for machine learning on tabular data. To the best of our knowledge, our method is the first successful example of deep architectures that substantially outperforms leading GBDT packages on tabular data.   
+2. Via an extensive experimental evaluation on a large number of datasets, we show that the proposed NODE architecture outperforms existing GBDT implementations.   
+3. The PyTorch implementation of NODE is available online1.
+
+The rest of the paper is organized as follows. In Section 2 we review prior work relevant to our method. The proposed Neural Oblivious Decision Ensembles architecture is described in Section 3 and experimentally evaluated in Section 4. Section 5 concludes the paper.
+
+# 2 RELATED WORK
+
+In this section, we briefly review the main ideas from prior work that are relevant to our method.
+
+The state-of-the-art for tabular data. Ensembles of decision trees, such as GBDT (Friedman, 2001) or random forests (Barandiaran, 1998), are currently the top choice for tabular data problems. Currently, there are several leading GBDT packages, such as XGBoost (Chen & Guestrin, 2016), LightGBM (Ke et al., 2017), CatBoost (Prokhorenkova et al., 2018), which are widely used by both academicians and ML practitioners. While these implementations vary in details, on most of the tasks their performances do not differ much (Prokhorenkova et al., 2018; Anghel et al.). The most important distinction of CatBoost is that it uses oblivious decision trees (ODTs) as weak learners. As ODTs are also an important ingredient of our NODE architecture, we discuss them below.
+
+Oblivious Decision Trees. An oblivious decision tree is a regular tree of depth $d$ that is constrained to use the same splitting feature and splitting threshold in all internal nodes of the same depth. This constraint essentially allows representing an ODT as a table with $2 ^ { d }$ entries, corresponding to all possible combinations of $d$ splits (Lou & Obukhov, 2017). Of course, due to the constraints above, ODTs are significantly weaker learners compared to unconstrained decision trees. However, when used in an ensemble, such trees are less prone to overfitting, which was shown to synergize well with gradient boosting (Prokhorenkova et al., 2018). Furthermore, the inference in ODTs is very efficient: one can compute $d$ independent binary splits in parallel and return the appropriate table entry. In contrast, non-oblivious decision trees require evaluating $d$ splits sequentially.
+
+Differentiable trees. The significant drawback of tree-based approaches is that they usually do not allow end-to-end optimization and employ greedy, local optimization procedures for tree construction. Thus, they cannot be used as a component for pipelines, trained in an end-to-end fashion. To address this issue, several works (Kontschieder et al., 2015; Yang et al., 2018; Lay et al., 2018)
+
+propose to ”soften” decision functions in the internal tree nodes to make the overall tree function and tree routing differentiable. In our work, we advocate the usage of the recent entmax transformation (Peters et al., 2019) to ”soften” decision trees. We confirm its advantages over the previously proposed approaches in the experimental section.
+
+Entmax. The key building block of our model is the entmax transformation (Peters et al., 2019), which maps a vector of real-valued scores to a discrete probability distribution. This transformation generalizes the traditional softmax and its sparsity-enforcing alternative sparsemax (Martins & Astudillo, 2016), which has already received significant attention in a wide range of applications: probabilistic inference, topic modeling, neural attention (Niculae & Blondel, 2017; Niculae et al., 2018; Lin et al., 2019). The entmax is capable to produce sparse probability distributions, where the majority of probabilities are exactly equal to 0. In this work, we argue that entmax is also an appropriate inductive bias in our model, which allows differentiable split decision construction in the internal tree nodes. Intuitively, entmax can learn splitting decisions based on a small subset of data features (up to one, as in classical decision trees), avoiding undesired influence from others. As an additional advantage, using entmax for feature selection allows for computationally efficient inference using the sparse pre-computed choice vectors as described below in Section 3.
+
+Multi-layer non-differentiable architectures. Another line of work (Miller et al., 2017; Zhou & Feng, 2017; Feng et al., 2018) promotes the construction of multi-layer architectures from nondifferentiable blocks, such as random forests or GBDT ensembles. For instance, (Zhou & Feng, 2017; Miller et al., 2017) propose to use stacking of several random forests, which are trained separately. In recent work, (Feng et al., 2018) introduces the multi-layer GBDTs and proposes a training procedure that does not require each layer component to be differentiable. While these works report marginal improvements over shallow counterparts, they lack the capability for end-to-end training, which could result in inferior performance. In contrast, we argue that end-to-end training is crucial and confirm this claim in the experimental section.
+
+Specific DNN for tabular data. While a number of prior works propose architectures designed for tabular data (Ke et al., 2018; Shavitt & Segal, 2018), they mostly do not compare with the properly tuned GBDT implementations, which are the most appropriate baselines. The recent preprint (Ke et al., 2018) reports the marginal improvement over GBDT with default parameters, but in our experiments, the baseline performance is much higher. To the best of our knowledge, our approach is the first to consistently outperform the tuned GBDTs over a large number of datasets.
+
+# 3 NEURAL OBLIVIOUS DECISION ENSEMBLES
+
+We introduce the Neural Oblivious Decision Ensemble (NODE) architecture with a layer-wise structure similar to existing deep learning models. In a nutshell, our architecture consists of differentiable oblivious decision trees (ODT) that are trained end-to-end by backpropagation. We describe our implementation of the differentiable NODE layer in Section 3.1, the full model architecture in Section 3.2, and the training and inference procedures in section 3.3.
+
+# 3.1 DIFFERENTIABLE OBLIVIOUS DECISION TREES
+
+The core building block of our model is a Neural Oblivious Decision Ensemble (NODE) layer. The layer is composed of $m$ differentiable oblivious decision trees (ODTs) of equal depth $d$ . As an input, all $m$ trees get a common vector $x \in \mathbb { R } ^ { n }$ , containing $n$ numeric features. Below we describe a design of a single differentiable ODT.
+
+In its essence, an ODT is a decision table that splits the data along $d$ splitting features and compares each feature to a learned threshold. Then, the tree returns one of the $2 ^ { d }$ possible responses, corresponding to the comparisons result. Therefore, each ODT is completely determined by its splitting $2 \times 2 \times 2$ features $f \in \mathbb { R } ^ { d }$ , splitting thresholds $b \in \mathbb { R } ^ { d }$ and a $d$ -dimensional tensor of responses $R \in \mathbb { R } ^ { -  }$ In this notation, the tree output is defined as:
+
+$$
+h ( \boldsymbol { x } ) = R [ \mathbb { 1 } ( f _ { 1 } ( \boldsymbol { x } ) - b _ { 1 } ) , \dots , \mathbb { 1 } ( f _ { d } ( \boldsymbol { x } ) - b _ { d } ) ] ,
+$$
+
+where $\mathbb { 1 } ( \cdot )$ denotes the Heaviside function.
+
+![](images/737b77b3bfdeeef216ef864f7167d710d7b5f1fe32211a4126e6d2a45ee460a8.jpg)  
+Figure 1: The single ODT inside the NODE layer. The splitting features and the splitting thresholds are shared across all the internal nodes of the same depth. The output is a sum of leaf responses scaled by the choice weights.
+
+To make the tree output (1) differentiable, we replace the splitting feature choice $f _ { i }$ and the comparison operator $\mathbb { 1 } ( f _ { i } ( x ) - b _ { i } )$ by their continuous counterparts. There are several existing approaches that can be used for modelling differentiable choice functions in decision trees (Yang et al., 2018), for instance, REINFORCE (Williams, 1992) or Gumbel-softmax (Jang et al., 2016). However, these approaches typically require long training time, which can be crucial in practice.
+
+Instead, we propose to use the $\alpha$ -entmax function (Peters et al., 2019) as it is able to learn sparse choices, depending only on a few features, via standard gradient descent. This function is a generalization of softmax in its variational form: $s o f t m a x ( x ) = a r g m a x _ { p \in \Delta } [ \langle p , x \rangle + H ( p ) ]$ where $H ( p )$ is Shannon entropy. We can define $\alpha$ -entmax by replacing $H ( p )$ with Tsallis $\alpha$ -entropy2.
+
+The choice function is hence replaced by a weighted sum of features, with weights computed as $\alpha$ -entmax $( \alpha { = } 1 . 5$ ) over the learnable feature selection matrix $F \in \mathbb { R } ^ { d \times n }$ :
+
+$$
+\hat { f } _ { i } ( x ) = \sum _ { j = 1 } ^ { n } x _ { j } \cdot e n t m a x _ { \alpha } ( F _ { i j } )
+$$
+
+Similarly, we relax the Heaviside function $\mathbb { 1 } ( f _ { i } ( x ) - b _ { i } )$ as a two-class entmax, which we denote as $\sigma _ { \alpha } ( x ) { = } e n t m a x _ { \alpha } ( [ x , 0 ] )$ . As different features can have different characteristic scales, we use the scaled version $\begin{array} { r } { c _ { i } ( x ) = \sigma _ { \alpha } \left( \frac { f _ { i } ( x ) - b _ { i } } { \tau _ { i } } \right) } \end{array}$ , where $b _ { i }$ and $\tau _ { i }$ are learnable parameters for thresholds and scales respectively.
+
+Based on the $c _ { i } ( x )$ values, we define a ”choice” tensor $C \in \mathbb { R } ^ { \frac { 2 \times 2 \times 2 } { d } }$ of the same size as the response tensor $R$ by computing the outer product of all $c _ { i }$ :
+
+$$
+C ( x ) = { \Big [ } { \begin{array} { c } { c _ { 1 } ( x ) } \\ { 1 - c _ { 1 } ( x ) { \Big ] } \otimes { \Big [ } 1 - c _ { 2 } ( x ) { \Big ] } \otimes \cdots \otimes { \Big [ } 1 - c _ { d } ( x ) { \Big ] } } \end{array} }
+$$
+
+The final prediction is then computed as a weighted linear combination of response tensor entries $R$ with weights from the entries of choice tensor $C$ :
+
+$$
+\hat { h } ( x ) = \sum _ { \substack { i _ { 1 } , \ldots i _ { d } \in \{ 0 , 1 \} ^ { d } } } R _ { i _ { 1 } , \ldots , i _ { d } } \cdot C _ { i _ { 1 } , \ldots , i _ { d } } ( x )
+$$
+
+Note, that this relaxation equals to the classic non-differentiable ODT $h ( x ) ( 1 )$ iff both feature selection and threshold functions reach one-hot state, i.e. entmax always returns non-zero weights for a single feature and $c _ { i }$ always return exactly zeros or ones.
+
+Finally, the output of the NODE layer is composed as a concatenation of the outputs of $m$ individual trees $\left[ \hat { h } _ { 1 } ( x ) , \ldots , \hat { h } _ { m } ( x ) \right]$ .
+
+Multidimensional tree outputs. In the description above, we assumed that tree outputs are onedimensional $\hat { h } ( x ) \in \mathbb { R }$ . For classification problems, where NODE predicts probabilities of each class, we use multidimensional tree outputs $\hat { h } ( x ) \in \mathbb { R } ^ { | C | }$ , where $| C |$ is a number of classes.
+
+# 3.2 GOING DEEPER WITH THE NODE ARCHITECTURE
+
+The NODE layer, described above, can be trained alone or within a complex structure, like fullyconnected layers that can be organized into the multi-layer architectures. In this work, we introduce a new architecture, following the popular DenseNet (Huang et al., 2017) model and train it end-toend via backpropagation.
+
+![](images/8831390659b0e81c1a123e6ab71a5d88d05e86d42f60168fe8727ad070880f3d.jpg)  
+Figure 2: The NODE architecture, consisting of densely connected NODE layers. Each layer contains several trees whose outputs are concatenated and serve as input for the subsequent layer. The final prediction is obtained by averaging the outputs of all trees from all the layers.
+
+Similar to DenseNet, our architecture is a sequence of $k$ NODE layers (see Section 3.1), where each layer uses a concatenation of all previous layers as its input. The input layer 0 of this architecture corresponds to the input features $x$ , accessible by all successor layers. Due to such a design, our architecture is capable to learn both shallow and deep decision rules. A single tree on $i$ -th layer can rely on chains of up to $i - 1$ layer outputs as features, allowing it to capture complex dependencies. The resulting prediction is a simple average of all decision trees from all layers.
+
+Note, in the multi-layer architecture described above, tree outputs $\hat { h } ( x )$ from early layers are used as inputs for subsequent layers. Therefore, we do not restrict the dimensionality of $\hat { h } ( x )$ to be equal to the number of classes, and allow it to have an arbitrary dimensionality $l$ , which correspond to $2 \times 2 \times 2 \times l$ the $( d + 1 )$ -dimensional response tensor $R \in \mathbb { R } ^ { \sum _ { d } ^ { \cdots } }$ . When averaging the predictions from all layers, only first $| C |$ coordinates of $\hat { h } ( x )$ are used for classification problems and the first one for regression problems. Overall, $l$ is an additional hyperparameter with typical values in [1, 3].
+
+# 3.3 TRAINING
+
+Here we summarize the details of our training protocol.
+
+Data preprocessing. First, we transform each data feature to follow a normal distribution via quantile transform3. In experiments, we observed that this step was important for stable training and faster convergence.
+
+Initialization. Before training, we perform the data-aware initialization (Mishkin & Matas, 2016) to obtain a good initial parameter values. In particular, we initialize the feature selection matrix uniformly $F _ { i j } \sim U ( 0 , 1 )$ , while the thresholds $b$ are initialized with random feature values $f _ { i } ( x )$ observed in the first data batch. The scales $\tau _ { i }$ are initialized in such a way that all the samples in the first batch belong to the linear region of $\sigma _ { \alpha }$ , and hence receive nonzero gradients. Finally, the response tensor entries are initialized with the standard normal distribution ${ \cal R } [ \bar { i } _ { 1 } , \dots , i _ { d } ] \sim { \cal N } ( 0 , 1 )$ .
+
+Training. As for existing DNN architectures, NODE is trained end-to-end via mini-batch SGD. We jointly optimize all model parameters: $F , b , R$ . In this work, we experimented with traditional objective functions (cross-entropy for classification and mean squared error for regression), but any differentiable objective can be used as well. As an optimization method, we use the recent QuasiHyperbolic Adam with parameters recommended in the original paper (Ma & Yarats, 2018). We also average the model parameters over $c = 5$ consecutive checkpoints (Izmailov et al., 2018) and pick the optimal stopping point on the hold-out validation dataset.
+
+Inference. During training, a significant fraction of time is spent computing the entmax function and multiplying the choice tensor. Once the model is trained, one can pre-compute entmax feature selectors and store them as a sparse vector (e.g., in coordinate (coo) format), making inference more efficient.
+
+# 4 EXPERIMENTS
+
+In this section, we report the results of a comparison between our approach and the leading GBDT packages. We also provide several ablation studies that demonstrate the influence of each design choice in the proposed NODE architecture.
+
+# 4.1 COMPARISON TO THE STATE-OF-THE-ART.
+
+As our main experiments, we compare the proposed NODE architecture with two state-of-the-art GBDT implementations on a large number of datasets. In all the experiments we set $\alpha$ parameter in the entmax transformation to 1.5. All other details of the comparison protocol are described below.
+
+Datasets. We perform most of the experiments on six open-source tabular datasets from different domains: Epsilon, YearPrediction, Higgs, Microsoft, Yahoo, Click. The detailed description of the datasets is available in appendix. All the datasets provide train/test splits, and we used $20 \%$ samples from the train set as a validation set to tune the hyperparameters. For each dataset, we fix the train/val/test splits for a fair comparison. For the classification datasets (Epsilon, Higgs, Click), we minimize cross-entropy loss and report the classification error. For the regression and ranking datasets (YearPrediction, Microsoft, Yahoo), we minimize and report mean squared error (which corresponds to the pointwise approach to learning-to-rank).
+
+Methods. We compare the proposed NODE architecture to the following baselines:
+
+• Catboost. The recent GBDT implementation (Prokhorenkova et al., 2018) that uses oblivious decision trees as weak learners. We use the open-source implementation, provided by the authors. • XGBoost. The most popular GBDT implementation widely used in machine learning competitions (Chen & Guestrin, 2016). We use the open-source implementation, provided by the authors. • FCNN. Deep neural network, consisting of several fully-connected layers with ReLU nonlinearity layers (Nair & Hinton, 2010).
+
+Regimes. We perform comparison in two following regimes that are the most important in practice:
+
+• Default hyperparameters. In this regime, we compare the methods as easy-to-tune toolkits that could be used by a non-professional audience. Namely, here we do not tune hyperparameters and use the default ones provided by the GBDT packages. The only tunable parameter here is a number of trees (up to 2048) in CatBoost/XGBoost, which is set based on the validation set. We do not compare with FCNN in this regime, as it typically requires much tuning, and we did not find the set of parameters, appropriate for all datasets. The default architecture in our model contains only a single layer with 2048 decision trees of depth six. Both of these hyperparameters were inherited from the CatBoost package settings for oblivious decision trees. With these parameters, the NODE architecture is shallow, but it still benefits from end-to-end training via back-propagation.
+
+Table 1: The comparison of NODE with the shallow state-of-the-art counterparts with default hyperparameters. The results are computed over ten runs with different random seeds.   
+
+<table><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>Epsilon</td><td rowspan=1 colspan=1>YearPrediction</td><td rowspan=1 colspan=1>Higgs</td><td rowspan=1 colspan=1>Microsoft</td><td rowspan=1 colspan=1>Yahoo</td><td rowspan=1 colspan=1>Click</td></tr><tr><td rowspan=1 colspan=7>Default hyperparameters</td></tr><tr><td rowspan=1 colspan=1>CatBoost</td><td rowspan=1 colspan=1>0.1119±2e-4</td><td rowspan=1 colspan=1>80.68±0.04</td><td rowspan=1 colspan=1>0.2434±2e-4</td><td rowspan=1 colspan=1>0.5587±2e-4</td><td rowspan=1 colspan=1>0.5781±3e-4</td><td rowspan=1 colspan=1>0.3438±1e-3</td></tr><tr><td rowspan=1 colspan=1>XGBoost</td><td rowspan=1 colspan=1>0.1144</td><td rowspan=1 colspan=1>81.11</td><td rowspan=1 colspan=1>0.2600</td><td rowspan=1 colspan=1>0.5637</td><td rowspan=1 colspan=1>0.5756</td><td rowspan=1 colspan=1>0.3461</td></tr><tr><td rowspan=1 colspan=1>NODE</td><td rowspan=1 colspan=1>0.1043±4e-4</td><td rowspan=1 colspan=1>77.43±0.09</td><td rowspan=1 colspan=1>0.2412±5e-4</td><td rowspan=1 colspan=1>10.5584±3e-40.5666±5e-4</td><td rowspan=1 colspan=1>10.5584±3e-40.5666±5e-4</td><td rowspan=1 colspan=1>10.3309±3e--4</td></tr></table>
+
+<table><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>Epsilon</td><td rowspan=1 colspan=1>YearPrediction</td><td rowspan=1 colspan=1>Higgs</td><td rowspan=1 colspan=1>Microsoft</td><td rowspan=1 colspan=1>Yahoo</td><td rowspan=1 colspan=1>Click</td></tr><tr><td rowspan=1 colspan=7>Tuned hyperparameters</td></tr><tr><td rowspan=1 colspan=1>CatBoost</td><td rowspan=1 colspan=1>0.1113±4e-4</td><td rowspan=1 colspan=1>79.67±0.12</td><td rowspan=1 colspan=1>0.2378±1e-4</td><td rowspan=1 colspan=1>0.5565±2e-4</td><td rowspan=1 colspan=1>0.5632±3e-4</td><td rowspan=1 colspan=1>0.3401±2e-3</td></tr><tr><td rowspan=1 colspan=1>XGBoost</td><td rowspan=1 colspan=1>0.1112±6e-4</td><td rowspan=1 colspan=1>78.53±0.09</td><td rowspan=1 colspan=1>0.2328±3e-4</td><td rowspan=1 colspan=1>0.5544±1e-4</td><td rowspan=1 colspan=1>10.5420±4e-4</td><td rowspan=1 colspan=1>0.3334±2e-3</td></tr><tr><td rowspan=1 colspan=1>FCNN</td><td rowspan=1 colspan=1>0.1058±1e-3</td><td rowspan=1 colspan=1>81.17±0.81</td><td rowspan=1 colspan=1>0.2139±4e-4</td><td rowspan=1 colspan=1>0.5595±2e-4</td><td rowspan=1 colspan=1>0.5691±7e-4</td><td rowspan=1 colspan=1>0.3324±6e-5</td></tr><tr><td rowspan=1 colspan=1>NODE</td><td rowspan=1 colspan=1>0.1034±3e-4</td><td rowspan=1 colspan=1>76.21±0.12</td><td rowspan=1 colspan=1>0.2101±5e-4</td><td rowspan=1 colspan=1>0.5570±2e-4</td><td rowspan=1 colspan=1>0.5692±2e-4</td><td rowspan=1 colspan=1>0.3312±2e-3</td></tr><tr><td rowspan=1 colspan=1>mGBDT</td><td rowspan=1 colspan=1>00M</td><td rowspan=1 colspan=1>80.67</td><td rowspan=1 colspan=1>00M</td><td rowspan=1 colspan=1>0OM</td><td rowspan=1 colspan=1>00M</td><td rowspan=1 colspan=1>0OM</td></tr><tr><td rowspan=1 colspan=1>DeepForest</td><td rowspan=1 colspan=1>0.1179</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>0.2391</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>丨</td><td rowspan=1 colspan=1>0.3333</td></tr></table>
+
+Table 2: The comparison of NODE with both shallow and deep counterparts with hyperparameters tuned for optimal performance. The results are computed over ten runs with different random seeds.
+
+• Tuned hyperparameters. In this regime, we tune the hyperparameters for both NODE and the competitors on the validation subsets. The optimal configuration for NODE contains between two and eight NODE layers, while the total number of trees across all the layers does not exceed 2048. The details of hyperparameter optimization are provided in appendix.
+
+The results of the comparison are summarized in Table 1 and Table 2. For all methods, we report mean performance and standard deviations computed over ten runs with different random seeds. Several key observations are highlighted below:
+
+1. With default hyperparameters, the proposed NODE architecture consistently outperforms both CatBoost and XGBoost on all datasets. The results advocate the usage of NODE as a handy tool for machine learning on tabular problems.   
+2. With tuned hyperparameters, NODE also outperforms the competitors on most of the tasks. Two exceptions are the Yahoo and Microsoft datasets, where tuned XGBoost provides the highest performance. Given the large advantage of XGBoost over CatBoost on Yahoo, we speculate that the usage of oblivious decision trees is an inappropriate inductive bias for this dataset. This implies that NODE should be extended to non-oblivious trees, which we leave for future work.   
+3. In the regime with tuned hyperparameters on some datasets FCNN outperforms GBDT, while on others GBDT is superior. Meanwhile, the proposed NODE architecture appears to be a universal instrument, providing the highest performance on most of the tasks.
+
+For completeness we also aimed to compare to previously proposed architectures for deep learning on tabular data. Unfortunately, many works did not publish the source code. We were only able to perform a partial comparison with mGBDT (Feng et al., 2018) and DeepForest (Zhou & Feng, 2017), which source code is available. For both baselines, we use the implementations, provided by the authors, and tune the parameters on the validation set. Note, that the DeepForest implementation is available only for classification problems. Moreover, both implementations do not scale well, and for many datasets, we obtained Out-Of-Memory error (OOM). On datasets in our experiments it turns out that properly tuned GBDTs outperform both (Feng et al., 2018) and (Zhou & Feng, 2017).
+
+# 4.2 ABLATIVE ANALYSIS
+
+In this section, we analyze the key architecture components that define our model.
+
+Choice functions. Constructing differentiable decision trees requires a function that selects items from a set. Such function is required for both splitting feature selection and decision tree routing. We experimented with four possible options, each having different implications:
+
+<table><tr><td rowspan="2">Dataset Function</td><td colspan="4">YearPrediction</td><td colspan="4">Epsilon</td></tr><tr><td>softmax</td><td>Gumbel</td><td>sparsemax</td><td>entmax</td><td>softmax</td><td>Gumbel</td><td>sparsemax</td><td>entmax</td></tr><tr><td>1 layer</td><td>78.41</td><td>79.39</td><td>78.13</td><td>77.43</td><td>0.1045</td><td>0.1979</td><td>0.1083</td><td>0.1043</td></tr><tr><td>2 layers</td><td>77.61</td><td>79.31</td><td>76.81</td><td>77.05</td><td>0.1041</td><td>0.2884</td><td>0.1052</td><td>0.1031</td></tr><tr><td>4 layers</td><td>77.58</td><td>79.69</td><td>76.60</td><td>76.21</td><td>0.1034</td><td>0.2908</td><td>0.1058</td><td>0.1033</td></tr><tr><td>8 layers</td><td>77.47</td><td>80.49</td><td>76.31</td><td>76.17</td><td>0.1036</td><td>0.3081</td><td>0.1058</td><td>0.1036</td></tr></table>
+
+Table 3: The experimental comparison of various choice functions and architecture depths. The values represent mean squared error for YearPrediction and classification error rate for Epsilon.
+
+![](images/95a7f08422ead456e42a50f6e2277283ffbea43872d472162268379ca8c0ca2d.jpg)  
+Figure 3: NODE on UCI Higgs dataset: Left-Top: individual feature importance distributions for both original and learned features. Left-Bottom: mean absolute contribution of individual trees to the final response. Right: responses dependence on feature importances. See details in the text.
+
+• Softmax learns dense decision rules where all items have nonzero weights;   
+• Gumbel-Softmax (Jang et al., 2016) learns to stochastically sample a single element from a set;   
+• Sparsemax (Martins $\pmb { \& }$ Astudillo, 2016) learns sparse decision rules, where only a few items have nonzero weights;   
+• Entmax (Peters et al., 2019) generalizes both sparsemax and softmax; it is able to learn sparse decision rules, but is smoother than sparsemax, being more appropriate for gradient-based optimization. In comparison $\alpha$ parameter was set to 1.5.
+
+We experimentally compare the four options above with both shallow and deep architectures in Table 3. We use the same choice function for both feature selection and tree routing across all experiments. In Gumbel-Softmax, we replaced it with hard argmax one-hot during inference. The results clearly show that Entmax with $\alpha { = } 1 . 5$ outperforms the competitors across all experiments. First, Table 3 demonstrates that sparsemax and softmax are not universal choice functions. For instance, on the YearPrediction dataset, sparsemax outperforms softmax, while on the Epsilon dataset softmax is superior. In turn, entmax provides great empirical performance across all datasets. Another observation is that Gumbel-Softmax is unable to learn deep architectures with both constant and annealed temperature schedules. This behavior is probably caused by the stochasticity of Gumbel-Softmax and the responses on the former layers are too noisy to produce useful features for the latter layers.
+
+Feature importance. In this series of experiments, we analyze the internal representations, learned by the NODE architecture. We begin by estimating the feature importances from different layers of a multi-layer ensemble via permutation feature importance, initially introduced in (Breiman, 2001). Namely, for 10.000 objects from the Higgs dataset we randomly shuffle the values of each feature (original or learnt on some NODE layer) and compute the increase in the classification error. Then for each layer, we split feature importance values into seven equal bins and calculate the total feature importance of each bin, shown on Figure 3 (left-top). We discovered that the features from the first layer are used the most, with feature importances decreasing with depth. This figure shows that deep layers are able to produce important features, even though earlier layers have an advantage because of the DenseNet architecture. Next, we estimated the mean absolute contribution of individual trees to the final response, reported on Figure 3 (left-bottom). One can see the reverse trend, deep trees tend to contribute more to the final response. Figure 3 (right) clearly shows that there is anticorrelation of feature importances and contributions in the final response, which implies that the main role of ealier layers is to produce informative features, while the latter layers mostly use them for accurate prediction.
+
+Training/Inference runtime. Finally, we compare the NODE runtime to the timings of the stateof-the-art GBDT implementations. In Table 4 we report the training and inference time for million of objects from the YearPrediction dataset. In this experiment, we evaluate ensembles of 1024 trees of depth six with all other parameters set to their default values. Our GPU setup has a single 1080Ti GPU and 2 CPU cores. In turn, our CPU setup has a 28-core Xeon E5-2660 v4 processor (which costs almost twice as much as the GPU). We use CatBoost v0.15 and XGBoost v0.90 as baselines, while NODE inference runs on PyTorch v1.1.0. Overall, NODE inference time is on par with heavily optimized GBDT libraries despite being implemented in pure PyTorch (i.e. no custom kernels).
+
+<table><tr><td>Method</td><td>NODE 8 layers 1080Ti</td><td>XGBoost Xeon</td><td>XGBoost 1080Ti</td><td>CatBoost Xeon</td></tr><tr><td>Training</td><td>7min 42s</td><td>5min 39s</td><td>1min 13s</td><td>41s</td></tr><tr><td>Inference</td><td>8.56s</td><td>5.94s</td><td>4.45s</td><td>4.62s</td></tr></table>
+
+Table 4: Training and inference runtime for models with 1024 trees of depth six on the YearPrediction dataset, averaged over five runs. Both training and inference of eight-layer NODE architecture on GPU are on par with shallow counterparts of the same total number of trees in an ensemble.
+
+# 5 CONCLUSION
+
+In this paper, we introduce a new DNN architecture for deep learning on heterogeneous tabular data. The architecture is differentiable deep GBDTs, trained end-to-end via backpropagation. In extensive experiments, we demonstrate the advantages of our architecture over existing competitors with the default and tuned hyperparameters. A promising research direction is incorporating the NODE layer into complex pipelines trained via back-propagation. For instance, in multi-modal problems, the NODE layer could be employed as a way to incorporate the tabular data, as CNNs are currently used for images, or RNNs are used for sequences.
+
+# REFERENCES
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+Andre Martins and Ramon Astudillo. From softmax to sparsemax: A sparse model of attention and multi-label classification. In International Conference on Machine Learning, 2016.
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+Vlad Niculae and Mathieu Blondel. A regularized framework for sparse and structured neural attention. In Advances in Neural Information Processing Systems, 2017.
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+Vlad Niculae, Andre FT Martins, Mathieu Blondel, and Claire Cardie. Sparsemap: Differentiable ´ sparse structured inference. arXiv preprint arXiv:1802.04223, 2018.
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+Ben Peters, Vlad Niculae, and Andre F. T. Martins. Sparse sequence-to-sequence models. In ´ ACL, 2019, pp. 1504–1519, 2019.
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+Ira Shavitt and Eran Segal. Regularization learning networks: Deep learning for tabular datasets. In Advances in Neural Information Processing Systems, pp. 1379–1389, 2018.
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+
+Table 5: The datasets used in our experiments.   
+
+<table><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>Train</td><td rowspan=1 colspan=1>Test</td><td rowspan=1 colspan=1>Features</td><td rowspan=1 colspan=1>Task</td><td rowspan=1 colspan=1>Metric</td><td rowspan=1 colspan=1>Description</td></tr><tr><td rowspan=1 colspan=1>Epsilon5</td><td rowspan=1 colspan=1>400K</td><td rowspan=1 colspan=1>100K</td><td rowspan=1 colspan=1>2000</td><td rowspan=1 colspan=1>Classification</td><td rowspan=1 colspan=1>Error</td><td rowspan=1 colspan=1>PASCAL Challenge 2008</td></tr><tr><td rowspan=1 colspan=1>YearPrediction6</td><td rowspan=1 colspan=1>463K</td><td rowspan=1 colspan=1>51.6K</td><td rowspan=1 colspan=1>90</td><td rowspan=1 colspan=1>Regression</td><td rowspan=1 colspan=1>MSE</td><td rowspan=1 colspan=1>Million Song Dataset</td></tr><tr><td rowspan=1 colspan=1>Higgs7</td><td rowspan=1 colspan=1>10.5M</td><td rowspan=1 colspan=1>500K</td><td rowspan=1 colspan=1>28</td><td rowspan=1 colspan=1>Classification</td><td rowspan=1 colspan=1>Error</td><td rowspan=1 colspan=1>UCIML Higgs</td></tr><tr><td rowspan=1 colspan=1>Microsoft8</td><td rowspan=1 colspan=1>723K</td><td rowspan=1 colspan=1>241K</td><td rowspan=1 colspan=1>136</td><td rowspan=1 colspan=1>Regression</td><td rowspan=1 colspan=1>MSE</td><td rowspan=1 colspan=1>MSLR-WEB10K</td></tr><tr><td rowspan=1 colspan=1>Yahoo9</td><td rowspan=1 colspan=1>544K</td><td rowspan=1 colspan=1>165K</td><td rowspan=1 colspan=1>699</td><td rowspan=1 colspan=1>Regression</td><td rowspan=1 colspan=1>MSE</td><td rowspan=1 colspan=1>Yahoo LETOR dataset</td></tr><tr><td rowspan=1 colspan=1>Click10</td><td rowspan=1 colspan=1>800K</td><td rowspan=1 colspan=1>200K</td><td rowspan=1 colspan=1>11</td><td rowspan=1 colspan=1>Classification</td><td rowspan=1 colspan=1>Error</td><td rowspan=1 colspan=1>2012 KDD Cup</td></tr></table>
+
+# A APPENDIX
+
+# A.1 DESCRIPTION OF THE DATASETS
+
+In our experiments, we used six tabular datasets, described in Table 5. (1) Epsilon is high dimensional dataset from the PASCAL Large Scale Learning Challenge 2008. The problem is a binary classification. (2) YearPrediction is a subset of Million Song Dataset. It is regression dataset, and the task is to predict the release year of the song by using the audio features. It contains tracks from 1922 to 2011. (3) Higgs is a dataset from the UCI ML Repository. The problem is to predict whether the given event produces Higgs bosons or not. (4) Microsoft is a Learning to Rank Dataset. It consists of 136-dimensional feature vectors extracted from query-url pairs. Each pair has relevance judgment labels, which take values from 0 (irrelevant) to 4 (perfectly relevant) (5) Yahoo is very similar ranking dataset with query-url pairs labeled from 0 to 4. We treat both ranking problems as regression (which corresponds to the pointwise approach to learning-to-rank) (6) Click is a subset of data from the 2012 KDD Cup. For the subset construction, we randomly sample 500.000 objects of a positive class and 500.000 objects of a negative class. The categorical features were converted to numerical ones via Leave-One-Out encoder from category encoders package of the scikit-learn library.
+
+# A.2 OPTIMIZATION OF HYPERPARAMETERS
+
+In order to tune the hyperparameters, we performed a random stratified split of full training data into train set $( 8 0 \% )$ and validation set $( 2 0 \% )$ for the Epsilon, YearPrediction, Higgs, Microsoft, and Click datasets. For Yahoo, we use train/val/test split provided by the dataset authors. We use the Hyperopt4 library to optimize Catboost, XGBoost, and FCNN hyperparameters. For each method, we perform 50 steps of Tree-structured Parzen Estimator (TPE) optimization algorithm. As a final configuration, we choose the set of hyperparameters, corresponding to the smallest loss on the validation set.
+
+# A.2.1 CATBOOST AND XGBOOST
+
+On each iteration of Hyperopt, the number of trees was set based on the validation set, with maximal trees count set to 2048. Below is the list of hyperparameters and their search spaces for Catboost.
+
+• learning rate: Log-Uniform distribution $[ e ^ { - 5 } , 1 ]$ • random strength: Discrete uniform distribution [1, 20] • one hot max size: Discrete uniform distribution [0, 25] • l2 leaf reg: Log-Uniform distribution [1, 10] • bagging temperature: Uniform distribution [0, 1] • leaf estimation iterations: Discrete uniform distribution [1, 10]
+
+XGBoost tuned parameters and their search spaces:
+
+• eta: Log-Uniform distribution $[ e ^ { - 7 } , 1 ]$   
+• max depth: Discrete uniform distribution [2, 10]   
+• subsample: Uniform distribution [0.5, 1]   
+• colsample bytree: Uniform distribution [0.5, 1]   
+• colsample bylevel: Uniform distribution [0.5, 1]   
+• min child weight: Log-Uniform distribution $[ e ^ { - 1 6 } , e ^ { 5 } ]$   
+• alpha: Uniform choice $\{ 0 \}$ , Log-Uniform distribution $[ e ^ { - 1 6 } , e ^ { 2 } ] \}$   
+• lambda: Uniform choice $\{ 0 \}$ , Log-Uniform distribution $[ e ^ { - 1 6 } , e ^ { 2 } ] \}$   
+• gamma: Uniform choice $\{ 0$ , Log-Uniform distribution $[ e ^ { - 1 6 } , e ^ { 2 } ] \}$
+
+# A.2.2 FCNN
+
+Fully connected neural networks were tuned using Hyperas 11 library, which is a Keras wrapper for Hyperopt. We consider FCNN constructed from the following blocks: Dense-ReLU-Dropout. The number of units in each layer is independent of each other, and dropout value is the same for the whole network. The networks are trained with the Adam optimizer with averaging the model parameters over $c { = } 5$ consecutive checkpoints (Izmailov et al., 2018) and early stopping on validation. Batch size is fixed to 1024 for all datasets. Below is the list of tuned hyperparameters.
+
+• Architecture: either Sequential (each layer is receives previous layer activations) or DenseNet (each layer receives activations from all previous layers   
+• Number of layers: Discrete uniform distribution [2, 7]   
+• Number of units: Dicrete uniform distribution over a set $\{ 1 2 8 , 2 5 6 , 5 1 2 , 1 0 2 4 \}$   
+• Learning rate: Uniform distribution $[ 1 e - 4 , 1 e - 2 ]$   
+• Dropout: Uniform distribution [0, 0.5]
+
+# A.2.3 NODE
+
+Neural Oblivious Decision Ensembles were tuned by grid search over the following hyperparameter values. In the multi-layer NODE, we use the same architecture for all layers, i.e., the same number of trees of the same depth. total tree count here denotes the total number of trees on all layers. For each dataset, we use the maximal batch size, which fits in the GPU memory. We always use learning rate $1 0 ^ { - 3 }$ .
+
+• num layers: {2, 4, 8} • total tree count: {1024, 2048} • tree depth: $\{ 6 , 8 \}$ • tree output dim: $\{ 2 , 3 \}$

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+        "type": "text",
+        "text": "NEURAL OBLIVIOUS DECISION ENSEMBLES FOR DEEP LEARNING ON TABULAR DATA ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Sergei Popov   \nYandex   \nsapopov@yandex-team.ru Stanislav Morozov   \nYandex   \nLomonosov Moscow State University stanis-morozov@yandex.ru ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Artem Babenko ",
+        "text_level": 1,
+        "bbox": [
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+            261
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Yandex National Research University Higher School of Economics artem.babenko@phystech.edu ",
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+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
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+    },
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+        "text": "Nowadays, deep neural networks (DNNs) have become the main instrument for machine learning tasks within a wide range of domains, including vision, NLP, and speech. Meanwhile, in an important case of heterogenous tabular data, the advantage of DNNs over shallow counterparts remains questionable. In particular, there is no sufficient evidence that deep learning machinery allows constructing methods that outperform gradient boosting decision trees (GBDT), which are often the top choice for tabular problems. In this paper, we introduce Neural Oblivious Decision Ensembles (NODE), a new deep learning architecture, designed to work with any tabular data. In a nutshell, the proposed NODE architecture generalizes ensembles of oblivious decision trees, but benefits from both end-to-end gradient-based optimization and the power of multi-layer hierarchical representation learning. With an extensive experimental comparison to the leading GBDT packages on a large number of tabular datasets, we demonstrate the advantage of the proposed NODE architecture, which outperforms the competitors on most of the tasks. We open-source the PyTorch implementation of NODE and believe that it will become a universal framework for machine learning on tabular data. ",
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+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
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+        "page_idx": 0
+    },
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+        "type": "text",
+        "text": "The recent rise of deep neural networks (DNN) resulted in a substantial breakthrough for a large number of machine learning tasks in computer vision, natural language processing, speech recognition, reinforcement learning (Goodfellow et al., 2016). Both gradient-based optimization via backpropagation (Rumelhart et al., 1985) and hierarchical representation learning appear to be crucial in increasing the performance of machine learning for these problems by a large margin. ",
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+        "text": "While the superiority of deep architectures in these domains is undoubtful, machine learning for tabular data still did not fully benefit from the DNN power. Namely, the state-of-the-art performance in problems with tabular heterogeneous data is often achieved by “shallow” models, such as gradient boosted decision trees (GBDT) (Friedman, 2001; Chen & Guestrin, 2016; Ke et al., 2017; Prokhorenkova et al., 2018). While the importance of deep learning on tabular data is recognized by the ML community, and many works address this problem (Zhou & Feng, 2017; Yang et al., 2018; Miller et al., 2017; Lay et al., 2018; Feng et al., 2018; Ke et al., 2018), the proposed DNN approaches do not consistently outperform the state-of-the-art shallow models by a notable margin. In particular, to the best of our knowledge, there is still no universal DNN approach that was shown to systematically outperform the leading GBDT packages (e.g., XGBoost (Chen & Guestrin, 2016)). As additional evidence, a large number of Kaggle ML competitions with tabular data are still won by the shallow GBDT methods (Harasymiv, 2015). Overall, at the moment, there is no dominant deep learning solution for tabular data problems, and we aim to reduce this gap by our paper. ",
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+        "text": "We introduce Neural Oblivious Decision Ensembles (NODE), a new DNN architecture, designed to work with tabular problems. The NODE architecture is partially inspired by the recent CatBoost package (Prokhorenkova et al., 2018), which was shown to provide state-of-the-art performance on a large number of tabular datasets. In a nutshell, CatBoost performs gradient boosting on oblivious decision trees (decision tables) (Kohavi, 1994; Lou & Obukhov, 2017), which makes inference very efficient, and the method is quite resistant to overfitting. In its essence, the proposed NODE architecture generalizes CatBoost, making the splitting feature choice and decision tree routing differentiable. As a result, the NODE architecture is fully differentiable and could be incorporated in any computational graph of existing DL packages, such as TensorFlow or PyTorch. Furthermore, NODE allows constructing multi-layer architectures, which resembles ”deep” GBDT that is trained end-to-end, which was never proposed before. Besides the usage of oblivious decision tables, another important design choice is the recent entmax transformation (Peters et al., 2019), which effectively performs a ”soft” splitting feature choice in decision trees inside the NODE architecture. As discussed in the following sections, these design choices are critical to obtain state-of-the-art performance. In a large number of experiments, we compare the proposed approach with the leading GBDT implementations with tuned hyperparameters and demonstrate that NODE outperforms competitors consistently on most of the datasets. ",
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+        "text": "Overall, the main contributions of our paper can be summarized as follows: ",
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+        "text": "1. We introduce a new DNN architecture for machine learning on tabular data. To the best of our knowledge, our method is the first successful example of deep architectures that substantially outperforms leading GBDT packages on tabular data.   \n2. Via an extensive experimental evaluation on a large number of datasets, we show that the proposed NODE architecture outperforms existing GBDT implementations.   \n3. The PyTorch implementation of NODE is available online1. ",
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+        "type": "text",
+        "text": "The rest of the paper is organized as follows. In Section 2 we review prior work relevant to our method. The proposed Neural Oblivious Decision Ensembles architecture is described in Section 3 and experimentally evaluated in Section 4. Section 5 concludes the paper. ",
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+    {
+        "type": "text",
+        "text": "2 RELATED WORK ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In this section, we briefly review the main ideas from prior work that are relevant to our method. ",
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+        "text": "The state-of-the-art for tabular data. Ensembles of decision trees, such as GBDT (Friedman, 2001) or random forests (Barandiaran, 1998), are currently the top choice for tabular data problems. Currently, there are several leading GBDT packages, such as XGBoost (Chen & Guestrin, 2016), LightGBM (Ke et al., 2017), CatBoost (Prokhorenkova et al., 2018), which are widely used by both academicians and ML practitioners. While these implementations vary in details, on most of the tasks their performances do not differ much (Prokhorenkova et al., 2018; Anghel et al.). The most important distinction of CatBoost is that it uses oblivious decision trees (ODTs) as weak learners. As ODTs are also an important ingredient of our NODE architecture, we discuss them below. ",
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+    {
+        "type": "text",
+        "text": "Oblivious Decision Trees. An oblivious decision tree is a regular tree of depth $d$ that is constrained to use the same splitting feature and splitting threshold in all internal nodes of the same depth. This constraint essentially allows representing an ODT as a table with $2 ^ { d }$ entries, corresponding to all possible combinations of $d$ splits (Lou & Obukhov, 2017). Of course, due to the constraints above, ODTs are significantly weaker learners compared to unconstrained decision trees. However, when used in an ensemble, such trees are less prone to overfitting, which was shown to synergize well with gradient boosting (Prokhorenkova et al., 2018). Furthermore, the inference in ODTs is very efficient: one can compute $d$ independent binary splits in parallel and return the appropriate table entry. In contrast, non-oblivious decision trees require evaluating $d$ splits sequentially. ",
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+    {
+        "type": "text",
+        "text": "Differentiable trees. The significant drawback of tree-based approaches is that they usually do not allow end-to-end optimization and employ greedy, local optimization procedures for tree construction. Thus, they cannot be used as a component for pipelines, trained in an end-to-end fashion. To address this issue, several works (Kontschieder et al., 2015; Yang et al., 2018; Lay et al., 2018) ",
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+    {
+        "type": "text",
+        "text": "propose to ”soften” decision functions in the internal tree nodes to make the overall tree function and tree routing differentiable. In our work, we advocate the usage of the recent entmax transformation (Peters et al., 2019) to ”soften” decision trees. We confirm its advantages over the previously proposed approaches in the experimental section. ",
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+    {
+        "type": "text",
+        "text": "Entmax. The key building block of our model is the entmax transformation (Peters et al., 2019), which maps a vector of real-valued scores to a discrete probability distribution. This transformation generalizes the traditional softmax and its sparsity-enforcing alternative sparsemax (Martins & Astudillo, 2016), which has already received significant attention in a wide range of applications: probabilistic inference, topic modeling, neural attention (Niculae & Blondel, 2017; Niculae et al., 2018; Lin et al., 2019). The entmax is capable to produce sparse probability distributions, where the majority of probabilities are exactly equal to 0. In this work, we argue that entmax is also an appropriate inductive bias in our model, which allows differentiable split decision construction in the internal tree nodes. Intuitively, entmax can learn splitting decisions based on a small subset of data features (up to one, as in classical decision trees), avoiding undesired influence from others. As an additional advantage, using entmax for feature selection allows for computationally efficient inference using the sparse pre-computed choice vectors as described below in Section 3. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Multi-layer non-differentiable architectures. Another line of work (Miller et al., 2017; Zhou & Feng, 2017; Feng et al., 2018) promotes the construction of multi-layer architectures from nondifferentiable blocks, such as random forests or GBDT ensembles. For instance, (Zhou & Feng, 2017; Miller et al., 2017) propose to use stacking of several random forests, which are trained separately. In recent work, (Feng et al., 2018) introduces the multi-layer GBDTs and proposes a training procedure that does not require each layer component to be differentiable. While these works report marginal improvements over shallow counterparts, they lack the capability for end-to-end training, which could result in inferior performance. In contrast, we argue that end-to-end training is crucial and confirm this claim in the experimental section. ",
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+    {
+        "type": "text",
+        "text": "Specific DNN for tabular data. While a number of prior works propose architectures designed for tabular data (Ke et al., 2018; Shavitt & Segal, 2018), they mostly do not compare with the properly tuned GBDT implementations, which are the most appropriate baselines. The recent preprint (Ke et al., 2018) reports the marginal improvement over GBDT with default parameters, but in our experiments, the baseline performance is much higher. To the best of our knowledge, our approach is the first to consistently outperform the tuned GBDTs over a large number of datasets. ",
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "3 NEURAL OBLIVIOUS DECISION ENSEMBLES ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We introduce the Neural Oblivious Decision Ensemble (NODE) architecture with a layer-wise structure similar to existing deep learning models. In a nutshell, our architecture consists of differentiable oblivious decision trees (ODT) that are trained end-to-end by backpropagation. We describe our implementation of the differentiable NODE layer in Section 3.1, the full model architecture in Section 3.2, and the training and inference procedures in section 3.3. ",
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+    {
+        "type": "text",
+        "text": "3.1 DIFFERENTIABLE OBLIVIOUS DECISION TREES ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "The core building block of our model is a Neural Oblivious Decision Ensemble (NODE) layer. The layer is composed of $m$ differentiable oblivious decision trees (ODTs) of equal depth $d$ . As an input, all $m$ trees get a common vector $x \\in \\mathbb { R } ^ { n }$ , containing $n$ numeric features. Below we describe a design of a single differentiable ODT. ",
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+    {
+        "type": "text",
+        "text": "In its essence, an ODT is a decision table that splits the data along $d$ splitting features and compares each feature to a learned threshold. Then, the tree returns one of the $2 ^ { d }$ possible responses, corresponding to the comparisons result. Therefore, each ODT is completely determined by its splitting $2 \\times 2 \\times 2$ features $f \\in \\mathbb { R } ^ { d }$ , splitting thresholds $b \\in \\mathbb { R } ^ { d }$ and a $d$ -dimensional tensor of responses $R \\in \\mathbb { R } ^ { -  }$ In this notation, the tree output is defined as: ",
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/01422b6472286c70262bd758dbbfcea0af2ca4bd7191b2052f7b7d342bc9cd6a.jpg",
+        "text": "$$\nh ( \\boldsymbol { x } ) = R [ \\mathbb { 1 } ( f _ { 1 } ( \\boldsymbol { x } ) - b _ { 1 } ) , \\dots , \\mathbb { 1 } ( f _ { d } ( \\boldsymbol { x } ) - b _ { d } ) ] ,\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where $\\mathbb { 1 } ( \\cdot )$ denotes the Heaviside function. ",
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/737b77b3bfdeeef216ef864f7167d710d7b5f1fe32211a4126e6d2a45ee460a8.jpg",
+        "image_caption": [
+            "Figure 1: The single ODT inside the NODE layer. The splitting features and the splitting thresholds are shared across all the internal nodes of the same depth. The output is a sum of leaf responses scaled by the choice weights. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "To make the tree output (1) differentiable, we replace the splitting feature choice $f _ { i }$ and the comparison operator $\\mathbb { 1 } ( f _ { i } ( x ) - b _ { i } )$ by their continuous counterparts. There are several existing approaches that can be used for modelling differentiable choice functions in decision trees (Yang et al., 2018), for instance, REINFORCE (Williams, 1992) or Gumbel-softmax (Jang et al., 2016). However, these approaches typically require long training time, which can be crucial in practice. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Instead, we propose to use the $\\alpha$ -entmax function (Peters et al., 2019) as it is able to learn sparse choices, depending only on a few features, via standard gradient descent. This function is a generalization of softmax in its variational form: $s o f t m a x ( x ) = a r g m a x _ { p \\in \\Delta } [ \\langle p , x \\rangle + H ( p ) ]$ where $H ( p )$ is Shannon entropy. We can define $\\alpha$ -entmax by replacing $H ( p )$ with Tsallis $\\alpha$ -entropy2. ",
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+        "type": "text",
+        "text": "The choice function is hence replaced by a weighted sum of features, with weights computed as $\\alpha$ -entmax $( \\alpha { = } 1 . 5$ ) over the learnable feature selection matrix $F \\in \\mathbb { R } ^ { d \\times n }$ : ",
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "equation",
+        "img_path": "images/ffbbf15870109e67d718f72ee80e0602a153c63ae0c375d2da9bee899090b542.jpg",
+        "text": "$$\n\\hat { f } _ { i } ( x ) = \\sum _ { j = 1 } ^ { n } x _ { j } \\cdot e n t m a x _ { \\alpha } ( F _ { i j } )\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "Similarly, we relax the Heaviside function $\\mathbb { 1 } ( f _ { i } ( x ) - b _ { i } )$ as a two-class entmax, which we denote as $\\sigma _ { \\alpha } ( x ) { = } e n t m a x _ { \\alpha } ( [ x , 0 ] )$ . As different features can have different characteristic scales, we use the scaled version $\\begin{array} { r } { c _ { i } ( x ) = \\sigma _ { \\alpha } \\left( \\frac { f _ { i } ( x ) - b _ { i } } { \\tau _ { i } } \\right) } \\end{array}$ , where $b _ { i }$ and $\\tau _ { i }$ are learnable parameters for thresholds and scales respectively. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Based on the $c _ { i } ( x )$ values, we define a ”choice” tensor $C \\in \\mathbb { R } ^ { \\frac { 2 \\times 2 \\times 2 } { d } }$ of the same size as the response tensor $R$ by computing the outer product of all $c _ { i }$ : ",
+        "bbox": [
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+    {
+        "type": "equation",
+        "img_path": "images/c5f4a4f06c7fed05c4c81a539aeb317710c3b5556546b719d04b4a0efc2164e1.jpg",
+        "text": "$$\nC ( x ) = { \\Big [ } { \\begin{array} { c } { c _ { 1 } ( x ) } \\\\ { 1 - c _ { 1 } ( x ) { \\Big ] } \\otimes { \\Big [ } 1 - c _ { 2 } ( x ) { \\Big ] } \\otimes \\cdots \\otimes { \\Big [ } 1 - c _ { d } ( x ) { \\Big ] } } \\end{array} }\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The final prediction is then computed as a weighted linear combination of response tensor entries $R$ with weights from the entries of choice tensor $C$ : ",
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+    {
+        "type": "equation",
+        "img_path": "images/8ad968214f3ae1a76b6a75e0ac42f03b79b4f103a271ebf668a68499ee5d634d.jpg",
+        "text": "$$\n\\hat { h } ( x ) = \\sum _ { \\substack { i _ { 1 } , \\ldots i _ { d } \\in \\{ 0 , 1 \\} ^ { d } } } R _ { i _ { 1 } , \\ldots , i _ { d } } \\cdot C _ { i _ { 1 } , \\ldots , i _ { d } } ( x )\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "Note, that this relaxation equals to the classic non-differentiable ODT $h ( x ) ( 1 )$ iff both feature selection and threshold functions reach one-hot state, i.e. entmax always returns non-zero weights for a single feature and $c _ { i }$ always return exactly zeros or ones. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Finally, the output of the NODE layer is composed as a concatenation of the outputs of $m$ individual trees $\\left[ \\hat { h } _ { 1 } ( x ) , \\ldots , \\hat { h } _ { m } ( x ) \\right]$ . ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Multidimensional tree outputs. In the description above, we assumed that tree outputs are onedimensional $\\hat { h } ( x ) \\in \\mathbb { R }$ . For classification problems, where NODE predicts probabilities of each class, we use multidimensional tree outputs $\\hat { h } ( x ) \\in \\mathbb { R } ^ { | C | }$ , where $| C |$ is a number of classes. ",
+        "bbox": [
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+        "page_idx": 4
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+    {
+        "type": "text",
+        "text": "3.2 GOING DEEPER WITH THE NODE ARCHITECTURE ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The NODE layer, described above, can be trained alone or within a complex structure, like fullyconnected layers that can be organized into the multi-layer architectures. In this work, we introduce a new architecture, following the popular DenseNet (Huang et al., 2017) model and train it end-toend via backpropagation. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/8831390659b0e81c1a123e6ab71a5d88d05e86d42f60168fe8727ad070880f3d.jpg",
+        "image_caption": [
+            "Figure 2: The NODE architecture, consisting of densely connected NODE layers. Each layer contains several trees whose outputs are concatenated and serve as input for the subsequent layer. The final prediction is obtained by averaging the outputs of all trees from all the layers. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 4
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+    {
+        "type": "text",
+        "text": "Similar to DenseNet, our architecture is a sequence of $k$ NODE layers (see Section 3.1), where each layer uses a concatenation of all previous layers as its input. The input layer 0 of this architecture corresponds to the input features $x$ , accessible by all successor layers. Due to such a design, our architecture is capable to learn both shallow and deep decision rules. A single tree on $i$ -th layer can rely on chains of up to $i - 1$ layer outputs as features, allowing it to capture complex dependencies. The resulting prediction is a simple average of all decision trees from all layers. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Note, in the multi-layer architecture described above, tree outputs $\\hat { h } ( x )$ from early layers are used as inputs for subsequent layers. Therefore, we do not restrict the dimensionality of $\\hat { h } ( x )$ to be equal to the number of classes, and allow it to have an arbitrary dimensionality $l$ , which correspond to $2 \\times 2 \\times 2 \\times l$ the $( d + 1 )$ -dimensional response tensor $R \\in \\mathbb { R } ^ { \\sum _ { d } ^ { \\cdots } }$ . When averaging the predictions from all layers, only first $| C |$ coordinates of $\\hat { h } ( x )$ are used for classification problems and the first one for regression problems. Overall, $l$ is an additional hyperparameter with typical values in [1, 3]. ",
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+    {
+        "type": "text",
+        "text": "3.3 TRAINING ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Here we summarize the details of our training protocol. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Data preprocessing. First, we transform each data feature to follow a normal distribution via quantile transform3. In experiments, we observed that this step was important for stable training and faster convergence. ",
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+    {
+        "type": "text",
+        "text": "Initialization. Before training, we perform the data-aware initialization (Mishkin & Matas, 2016) to obtain a good initial parameter values. In particular, we initialize the feature selection matrix uniformly $F _ { i j } \\sim U ( 0 , 1 )$ , while the thresholds $b$ are initialized with random feature values $f _ { i } ( x )$ observed in the first data batch. The scales $\\tau _ { i }$ are initialized in such a way that all the samples in the first batch belong to the linear region of $\\sigma _ { \\alpha }$ , and hence receive nonzero gradients. Finally, the response tensor entries are initialized with the standard normal distribution ${ \\cal R } [ \\bar { i } _ { 1 } , \\dots , i _ { d } ] \\sim { \\cal N } ( 0 , 1 )$ . ",
+        "bbox": [
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+        "page_idx": 4
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Training. As for existing DNN architectures, NODE is trained end-to-end via mini-batch SGD. We jointly optimize all model parameters: $F , b , R$ . In this work, we experimented with traditional objective functions (cross-entropy for classification and mean squared error for regression), but any differentiable objective can be used as well. As an optimization method, we use the recent QuasiHyperbolic Adam with parameters recommended in the original paper (Ma & Yarats, 2018). We also average the model parameters over $c = 5$ consecutive checkpoints (Izmailov et al., 2018) and pick the optimal stopping point on the hold-out validation dataset. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Inference. During training, a significant fraction of time is spent computing the entmax function and multiplying the choice tensor. Once the model is trained, one can pre-compute entmax feature selectors and store them as a sparse vector (e.g., in coordinate (coo) format), making inference more efficient. ",
+        "bbox": [
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+        "page_idx": 5
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+    {
+        "type": "text",
+        "text": "4 EXPERIMENTS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In this section, we report the results of a comparison between our approach and the leading GBDT packages. We also provide several ablation studies that demonstrate the influence of each design choice in the proposed NODE architecture. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "4.1 COMPARISON TO THE STATE-OF-THE-ART. ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "As our main experiments, we compare the proposed NODE architecture with two state-of-the-art GBDT implementations on a large number of datasets. In all the experiments we set $\\alpha$ parameter in the entmax transformation to 1.5. All other details of the comparison protocol are described below. ",
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+    {
+        "type": "text",
+        "text": "Datasets. We perform most of the experiments on six open-source tabular datasets from different domains: Epsilon, YearPrediction, Higgs, Microsoft, Yahoo, Click. The detailed description of the datasets is available in appendix. All the datasets provide train/test splits, and we used $20 \\%$ samples from the train set as a validation set to tune the hyperparameters. For each dataset, we fix the train/val/test splits for a fair comparison. For the classification datasets (Epsilon, Higgs, Click), we minimize cross-entropy loss and report the classification error. For the regression and ranking datasets (YearPrediction, Microsoft, Yahoo), we minimize and report mean squared error (which corresponds to the pointwise approach to learning-to-rank). ",
+        "bbox": [
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+        "page_idx": 5
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+    {
+        "type": "text",
+        "text": "Methods. We compare the proposed NODE architecture to the following baselines: ",
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+        "text": "• Catboost. The recent GBDT implementation (Prokhorenkova et al., 2018) that uses oblivious decision trees as weak learners. We use the open-source implementation, provided by the authors. • XGBoost. The most popular GBDT implementation widely used in machine learning competitions (Chen & Guestrin, 2016). We use the open-source implementation, provided by the authors. • FCNN. Deep neural network, consisting of several fully-connected layers with ReLU nonlinearity layers (Nair & Hinton, 2010). ",
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+    {
+        "type": "text",
+        "text": "Regimes. We perform comparison in two following regimes that are the most important in practice: ",
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+        "type": "text",
+        "text": "• Default hyperparameters. In this regime, we compare the methods as easy-to-tune toolkits that could be used by a non-professional audience. Namely, here we do not tune hyperparameters and use the default ones provided by the GBDT packages. The only tunable parameter here is a number of trees (up to 2048) in CatBoost/XGBoost, which is set based on the validation set. We do not compare with FCNN in this regime, as it typically requires much tuning, and we did not find the set of parameters, appropriate for all datasets. The default architecture in our model contains only a single layer with 2048 decision trees of depth six. Both of these hyperparameters were inherited from the CatBoost package settings for oblivious decision trees. With these parameters, the NODE architecture is shallow, but it still benefits from end-to-end training via back-propagation. ",
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+        "type": "table",
+        "img_path": "images/56f13a00d48b546531842b58f04b5217f59242b8828c466762573b4ae4bb70e2.jpg",
+        "table_caption": [
+            "Table 1: The comparison of NODE with the shallow state-of-the-art counterparts with default hyperparameters. The results are computed over ten runs with different random seeds. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>Epsilon</td><td rowspan=1 colspan=1>YearPrediction</td><td rowspan=1 colspan=1>Higgs</td><td rowspan=1 colspan=1>Microsoft</td><td rowspan=1 colspan=1>Yahoo</td><td rowspan=1 colspan=1>Click</td></tr><tr><td rowspan=1 colspan=7>Default hyperparameters</td></tr><tr><td rowspan=1 colspan=1>CatBoost</td><td rowspan=1 colspan=1>0.1119±2e-4</td><td rowspan=1 colspan=1>80.68±0.04</td><td rowspan=1 colspan=1>0.2434±2e-4</td><td rowspan=1 colspan=1>0.5587±2e-4</td><td rowspan=1 colspan=1>0.5781±3e-4</td><td rowspan=1 colspan=1>0.3438±1e-3</td></tr><tr><td rowspan=1 colspan=1>XGBoost</td><td rowspan=1 colspan=1>0.1144</td><td rowspan=1 colspan=1>81.11</td><td rowspan=1 colspan=1>0.2600</td><td rowspan=1 colspan=1>0.5637</td><td rowspan=1 colspan=1>0.5756</td><td rowspan=1 colspan=1>0.3461</td></tr><tr><td rowspan=1 colspan=1>NODE</td><td rowspan=1 colspan=1>0.1043±4e-4</td><td rowspan=1 colspan=1>77.43±0.09</td><td rowspan=1 colspan=1>0.2412±5e-4</td><td rowspan=1 colspan=1>10.5584±3e-40.5666±5e-4</td><td rowspan=1 colspan=1>10.5584±3e-40.5666±5e-4</td><td rowspan=1 colspan=1>10.3309±3e--4</td></tr></table>",
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+    },
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+        "type": "table",
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+        "table_caption": [],
+        "table_footnote": [
+            "Table 2: The comparison of NODE with both shallow and deep counterparts with hyperparameters tuned for optimal performance. The results are computed over ten runs with different random seeds. "
+        ],
+        "table_body": "<table><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>Epsilon</td><td rowspan=1 colspan=1>YearPrediction</td><td rowspan=1 colspan=1>Higgs</td><td rowspan=1 colspan=1>Microsoft</td><td rowspan=1 colspan=1>Yahoo</td><td rowspan=1 colspan=1>Click</td></tr><tr><td rowspan=1 colspan=7>Tuned hyperparameters</td></tr><tr><td rowspan=1 colspan=1>CatBoost</td><td rowspan=1 colspan=1>0.1113±4e-4</td><td rowspan=1 colspan=1>79.67±0.12</td><td rowspan=1 colspan=1>0.2378±1e-4</td><td rowspan=1 colspan=1>0.5565±2e-4</td><td rowspan=1 colspan=1>0.5632±3e-4</td><td rowspan=1 colspan=1>0.3401±2e-3</td></tr><tr><td rowspan=1 colspan=1>XGBoost</td><td rowspan=1 colspan=1>0.1112±6e-4</td><td rowspan=1 colspan=1>78.53±0.09</td><td rowspan=1 colspan=1>0.2328±3e-4</td><td rowspan=1 colspan=1>0.5544±1e-4</td><td rowspan=1 colspan=1>10.5420±4e-4</td><td rowspan=1 colspan=1>0.3334±2e-3</td></tr><tr><td rowspan=1 colspan=1>FCNN</td><td rowspan=1 colspan=1>0.1058±1e-3</td><td rowspan=1 colspan=1>81.17±0.81</td><td rowspan=1 colspan=1>0.2139±4e-4</td><td rowspan=1 colspan=1>0.5595±2e-4</td><td rowspan=1 colspan=1>0.5691±7e-4</td><td rowspan=1 colspan=1>0.3324±6e-5</td></tr><tr><td rowspan=1 colspan=1>NODE</td><td rowspan=1 colspan=1>0.1034±3e-4</td><td rowspan=1 colspan=1>76.21±0.12</td><td rowspan=1 colspan=1>0.2101±5e-4</td><td rowspan=1 colspan=1>0.5570±2e-4</td><td rowspan=1 colspan=1>0.5692±2e-4</td><td rowspan=1 colspan=1>0.3312±2e-3</td></tr><tr><td rowspan=1 colspan=1>mGBDT</td><td rowspan=1 colspan=1>00M</td><td rowspan=1 colspan=1>80.67</td><td rowspan=1 colspan=1>00M</td><td rowspan=1 colspan=1>0OM</td><td rowspan=1 colspan=1>00M</td><td rowspan=1 colspan=1>0OM</td></tr><tr><td rowspan=1 colspan=1>DeepForest</td><td rowspan=1 colspan=1>0.1179</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>0.2391</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>丨</td><td rowspan=1 colspan=1>0.3333</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "• Tuned hyperparameters. In this regime, we tune the hyperparameters for both NODE and the competitors on the validation subsets. The optimal configuration for NODE contains between two and eight NODE layers, while the total number of trees across all the layers does not exceed 2048. The details of hyperparameter optimization are provided in appendix. ",
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+        "type": "text",
+        "text": "The results of the comparison are summarized in Table 1 and Table 2. For all methods, we report mean performance and standard deviations computed over ten runs with different random seeds. Several key observations are highlighted below: ",
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+        "type": "text",
+        "text": "1. With default hyperparameters, the proposed NODE architecture consistently outperforms both CatBoost and XGBoost on all datasets. The results advocate the usage of NODE as a handy tool for machine learning on tabular problems.   \n2. With tuned hyperparameters, NODE also outperforms the competitors on most of the tasks. Two exceptions are the Yahoo and Microsoft datasets, where tuned XGBoost provides the highest performance. Given the large advantage of XGBoost over CatBoost on Yahoo, we speculate that the usage of oblivious decision trees is an inappropriate inductive bias for this dataset. This implies that NODE should be extended to non-oblivious trees, which we leave for future work.   \n3. In the regime with tuned hyperparameters on some datasets FCNN outperforms GBDT, while on others GBDT is superior. Meanwhile, the proposed NODE architecture appears to be a universal instrument, providing the highest performance on most of the tasks. ",
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+        "type": "text",
+        "text": "For completeness we also aimed to compare to previously proposed architectures for deep learning on tabular data. Unfortunately, many works did not publish the source code. We were only able to perform a partial comparison with mGBDT (Feng et al., 2018) and DeepForest (Zhou & Feng, 2017), which source code is available. For both baselines, we use the implementations, provided by the authors, and tune the parameters on the validation set. Note, that the DeepForest implementation is available only for classification problems. Moreover, both implementations do not scale well, and for many datasets, we obtained Out-Of-Memory error (OOM). On datasets in our experiments it turns out that properly tuned GBDTs outperform both (Feng et al., 2018) and (Zhou & Feng, 2017). ",
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+    {
+        "type": "text",
+        "text": "4.2 ABLATIVE ANALYSIS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In this section, we analyze the key architecture components that define our model. ",
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+        "type": "text",
+        "text": "Choice functions. Constructing differentiable decision trees requires a function that selects items from a set. Such function is required for both splitting feature selection and decision tree routing. We experimented with four possible options, each having different implications: ",
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+        "img_path": "images/82057d76b71466b18511a12bfa7a2a9265863a8a3e31903431a94f260bd849a2.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Dataset Function</td><td colspan=\"4\">YearPrediction</td><td colspan=\"4\">Epsilon</td></tr><tr><td>softmax</td><td>Gumbel</td><td>sparsemax</td><td>entmax</td><td>softmax</td><td>Gumbel</td><td>sparsemax</td><td>entmax</td></tr><tr><td>1 layer</td><td>78.41</td><td>79.39</td><td>78.13</td><td>77.43</td><td>0.1045</td><td>0.1979</td><td>0.1083</td><td>0.1043</td></tr><tr><td>2 layers</td><td>77.61</td><td>79.31</td><td>76.81</td><td>77.05</td><td>0.1041</td><td>0.2884</td><td>0.1052</td><td>0.1031</td></tr><tr><td>4 layers</td><td>77.58</td><td>79.69</td><td>76.60</td><td>76.21</td><td>0.1034</td><td>0.2908</td><td>0.1058</td><td>0.1033</td></tr><tr><td>8 layers</td><td>77.47</td><td>80.49</td><td>76.31</td><td>76.17</td><td>0.1036</td><td>0.3081</td><td>0.1058</td><td>0.1036</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 3: The experimental comparison of various choice functions and architecture depths. The values represent mean squared error for YearPrediction and classification error rate for Epsilon. ",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/95a7f08422ead456e42a50f6e2277283ffbea43872d472162268379ca8c0ca2d.jpg",
+        "image_caption": [
+            "Figure 3: NODE on UCI Higgs dataset: Left-Top: individual feature importance distributions for both original and learned features. Left-Bottom: mean absolute contribution of individual trees to the final response. Right: responses dependence on feature importances. See details in the text. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "• Softmax learns dense decision rules where all items have nonzero weights;   \n• Gumbel-Softmax (Jang et al., 2016) learns to stochastically sample a single element from a set;   \n• Sparsemax (Martins $\\pmb { \\& }$ Astudillo, 2016) learns sparse decision rules, where only a few items have nonzero weights;   \n• Entmax (Peters et al., 2019) generalizes both sparsemax and softmax; it is able to learn sparse decision rules, but is smoother than sparsemax, being more appropriate for gradient-based optimization. In comparison $\\alpha$ parameter was set to 1.5. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We experimentally compare the four options above with both shallow and deep architectures in Table 3. We use the same choice function for both feature selection and tree routing across all experiments. In Gumbel-Softmax, we replaced it with hard argmax one-hot during inference. The results clearly show that Entmax with $\\alpha { = } 1 . 5$ outperforms the competitors across all experiments. First, Table 3 demonstrates that sparsemax and softmax are not universal choice functions. For instance, on the YearPrediction dataset, sparsemax outperforms softmax, while on the Epsilon dataset softmax is superior. In turn, entmax provides great empirical performance across all datasets. Another observation is that Gumbel-Softmax is unable to learn deep architectures with both constant and annealed temperature schedules. This behavior is probably caused by the stochasticity of Gumbel-Softmax and the responses on the former layers are too noisy to produce useful features for the latter layers. ",
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+    {
+        "type": "text",
+        "text": "Feature importance. In this series of experiments, we analyze the internal representations, learned by the NODE architecture. We begin by estimating the feature importances from different layers of a multi-layer ensemble via permutation feature importance, initially introduced in (Breiman, 2001). Namely, for 10.000 objects from the Higgs dataset we randomly shuffle the values of each feature (original or learnt on some NODE layer) and compute the increase in the classification error. Then for each layer, we split feature importance values into seven equal bins and calculate the total feature importance of each bin, shown on Figure 3 (left-top). We discovered that the features from the first layer are used the most, with feature importances decreasing with depth. This figure shows that deep layers are able to produce important features, even though earlier layers have an advantage because of the DenseNet architecture. Next, we estimated the mean absolute contribution of individual trees to the final response, reported on Figure 3 (left-bottom). One can see the reverse trend, deep trees tend to contribute more to the final response. Figure 3 (right) clearly shows that there is anticorrelation of feature importances and contributions in the final response, which implies that the main role of ealier layers is to produce informative features, while the latter layers mostly use them for accurate prediction. ",
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+    {
+        "type": "text",
+        "text": "Training/Inference runtime. Finally, we compare the NODE runtime to the timings of the stateof-the-art GBDT implementations. In Table 4 we report the training and inference time for million of objects from the YearPrediction dataset. In this experiment, we evaluate ensembles of 1024 trees of depth six with all other parameters set to their default values. Our GPU setup has a single 1080Ti GPU and 2 CPU cores. In turn, our CPU setup has a 28-core Xeon E5-2660 v4 processor (which costs almost twice as much as the GPU). We use CatBoost v0.15 and XGBoost v0.90 as baselines, while NODE inference runs on PyTorch v1.1.0. Overall, NODE inference time is on par with heavily optimized GBDT libraries despite being implemented in pure PyTorch (i.e. no custom kernels). ",
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/28e1fb924c6270491ec84d6ef84effeb53c6b0e44989deb360a5b6bd6388e20d.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>NODE 8 layers 1080Ti</td><td>XGBoost Xeon</td><td>XGBoost 1080Ti</td><td>CatBoost Xeon</td></tr><tr><td>Training</td><td>7min 42s</td><td>5min 39s</td><td>1min 13s</td><td>41s</td></tr><tr><td>Inference</td><td>8.56s</td><td>5.94s</td><td>4.45s</td><td>4.62s</td></tr></table>",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Table 4: Training and inference runtime for models with 1024 trees of depth six on the YearPrediction dataset, averaged over five runs. Both training and inference of eight-layer NODE architecture on GPU are on par with shallow counterparts of the same total number of trees in an ensemble. ",
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+    {
+        "type": "text",
+        "text": "5 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In this paper, we introduce a new DNN architecture for deep learning on heterogeneous tabular data. The architecture is differentiable deep GBDTs, trained end-to-end via backpropagation. In extensive experiments, we demonstrate the advantages of our architecture over existing competitors with the default and tuned hyperparameters. A promising research direction is incorporating the NODE layer into complex pipelines trained via back-propagation. For instance, in multi-modal problems, the NODE layer could be employed as a way to incorporate the tabular data, as CNNs are currently used for images, or RNNs are used for sequences. ",
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+    {
+        "type": "text",
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+        "table_caption": [
+            "Table 5: The datasets used in our experiments. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>Train</td><td rowspan=1 colspan=1>Test</td><td rowspan=1 colspan=1>Features</td><td rowspan=1 colspan=1>Task</td><td rowspan=1 colspan=1>Metric</td><td rowspan=1 colspan=1>Description</td></tr><tr><td rowspan=1 colspan=1>Epsilon5</td><td rowspan=1 colspan=1>400K</td><td rowspan=1 colspan=1>100K</td><td rowspan=1 colspan=1>2000</td><td rowspan=1 colspan=1>Classification</td><td rowspan=1 colspan=1>Error</td><td rowspan=1 colspan=1>PASCAL Challenge 2008</td></tr><tr><td rowspan=1 colspan=1>YearPrediction6</td><td rowspan=1 colspan=1>463K</td><td rowspan=1 colspan=1>51.6K</td><td rowspan=1 colspan=1>90</td><td rowspan=1 colspan=1>Regression</td><td rowspan=1 colspan=1>MSE</td><td rowspan=1 colspan=1>Million Song Dataset</td></tr><tr><td rowspan=1 colspan=1>Higgs7</td><td rowspan=1 colspan=1>10.5M</td><td rowspan=1 colspan=1>500K</td><td rowspan=1 colspan=1>28</td><td rowspan=1 colspan=1>Classification</td><td rowspan=1 colspan=1>Error</td><td rowspan=1 colspan=1>UCIML Higgs</td></tr><tr><td rowspan=1 colspan=1>Microsoft8</td><td rowspan=1 colspan=1>723K</td><td rowspan=1 colspan=1>241K</td><td rowspan=1 colspan=1>136</td><td rowspan=1 colspan=1>Regression</td><td rowspan=1 colspan=1>MSE</td><td rowspan=1 colspan=1>MSLR-WEB10K</td></tr><tr><td rowspan=1 colspan=1>Yahoo9</td><td rowspan=1 colspan=1>544K</td><td rowspan=1 colspan=1>165K</td><td rowspan=1 colspan=1>699</td><td rowspan=1 colspan=1>Regression</td><td rowspan=1 colspan=1>MSE</td><td rowspan=1 colspan=1>Yahoo LETOR dataset</td></tr><tr><td rowspan=1 colspan=1>Click10</td><td rowspan=1 colspan=1>800K</td><td rowspan=1 colspan=1>200K</td><td rowspan=1 colspan=1>11</td><td rowspan=1 colspan=1>Classification</td><td rowspan=1 colspan=1>Error</td><td rowspan=1 colspan=1>2012 KDD Cup</td></tr></table>",
+        "bbox": [
+            173,
+            101,
+            856,
+            223
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "A APPENDIX ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            276,
+            299,
+            292
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "A.1 DESCRIPTION OF THE DATASETS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            310,
+            441,
+            324
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "In our experiments, we used six tabular datasets, described in Table 5. (1) Epsilon is high dimensional dataset from the PASCAL Large Scale Learning Challenge 2008. The problem is a binary classification. (2) YearPrediction is a subset of Million Song Dataset. It is regression dataset, and the task is to predict the release year of the song by using the audio features. It contains tracks from 1922 to 2011. (3) Higgs is a dataset from the UCI ML Repository. The problem is to predict whether the given event produces Higgs bosons or not. (4) Microsoft is a Learning to Rank Dataset. It consists of 136-dimensional feature vectors extracted from query-url pairs. Each pair has relevance judgment labels, which take values from 0 (irrelevant) to 4 (perfectly relevant) (5) Yahoo is very similar ranking dataset with query-url pairs labeled from 0 to 4. We treat both ranking problems as regression (which corresponds to the pointwise approach to learning-to-rank) (6) Click is a subset of data from the 2012 KDD Cup. For the subset construction, we randomly sample 500.000 objects of a positive class and 500.000 objects of a negative class. The categorical features were converted to numerical ones via Leave-One-Out encoder from category encoders package of the scikit-learn library. ",
+        "bbox": [
+            174,
+            338,
+            825,
+            532
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "A.2 OPTIMIZATION OF HYPERPARAMETERS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            554,
+            488,
+            568
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "In order to tune the hyperparameters, we performed a random stratified split of full training data into train set $( 8 0 \\% )$ and validation set $( 2 0 \\% )$ for the Epsilon, YearPrediction, Higgs, Microsoft, and Click datasets. For Yahoo, we use train/val/test split provided by the dataset authors. We use the Hyperopt4 library to optimize Catboost, XGBoost, and FCNN hyperparameters. For each method, we perform 50 steps of Tree-structured Parzen Estimator (TPE) optimization algorithm. As a final configuration, we choose the set of hyperparameters, corresponding to the smallest loss on the validation set. ",
+        "bbox": [
+            174,
+            582,
+            825,
+            665
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "A.2.1 CATBOOST AND XGBOOST ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            684,
+            419,
+            699
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "On each iteration of Hyperopt, the number of trees was set based on the validation set, with maximal trees count set to 2048. Below is the list of hyperparameters and their search spaces for Catboost. ",
+        "bbox": [
+            174,
+            710,
+            825,
+            739
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "• learning rate: Log-Uniform distribution $[ e ^ { - 5 } , 1 ]$ • random strength: Discrete uniform distribution [1, 20] • one hot max size: Discrete uniform distribution [0, 25] • l2 leaf reg: Log-Uniform distribution [1, 10] • bagging temperature: Uniform distribution [0, 1] • leaf estimation iterations: Discrete uniform distribution [1, 10] ",
+        "bbox": [
+            215,
+            753,
+            647,
+            885
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "XGBoost tuned parameters and their search spaces: ",
+        "bbox": [
+            176,
+            103,
+            511,
+            118
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "• eta: Log-Uniform distribution $[ e ^ { - 7 } , 1 ]$   \n• max depth: Discrete uniform distribution [2, 10]   \n• subsample: Uniform distribution [0.5, 1]   \n• colsample bytree: Uniform distribution [0.5, 1]   \n• colsample bylevel: Uniform distribution [0.5, 1]   \n• min child weight: Log-Uniform distribution $[ e ^ { - 1 6 } , e ^ { 5 } ]$   \n• alpha: Uniform choice $\\{ 0 \\}$ , Log-Uniform distribution $[ e ^ { - 1 6 } , e ^ { 2 } ] \\}$   \n• lambda: Uniform choice $\\{ 0 \\}$ , Log-Uniform distribution $[ e ^ { - 1 6 } , e ^ { 2 } ] \\}$   \n• gamma: Uniform choice $\\{ 0$ , Log-Uniform distribution $[ e ^ { - 1 6 } , e ^ { 2 } ] \\}$ ",
+        "bbox": [
+            215,
+            128,
+            666,
+            276
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "A.2.2 FCNN ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            290,
+            281,
+            305
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Fully connected neural networks were tuned using Hyperas 11 library, which is a Keras wrapper for Hyperopt. We consider FCNN constructed from the following blocks: Dense-ReLU-Dropout. The number of units in each layer is independent of each other, and dropout value is the same for the whole network. The networks are trained with the Adam optimizer with averaging the model parameters over $c { = } 5$ consecutive checkpoints (Izmailov et al., 2018) and early stopping on validation. Batch size is fixed to 1024 for all datasets. Below is the list of tuned hyperparameters. ",
+        "bbox": [
+            173,
+            314,
+            825,
+            398
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "• Architecture: either Sequential (each layer is receives previous layer activations) or DenseNet (each layer receives activations from all previous layers   \n• Number of layers: Discrete uniform distribution [2, 7]   \n• Number of units: Dicrete uniform distribution over a set $\\{ 1 2 8 , 2 5 6 , 5 1 2 , 1 0 2 4 \\}$   \n• Learning rate: Uniform distribution $[ 1 e - 4 , 1 e - 2 ]$   \n• Dropout: Uniform distribution [0, 0.5] ",
+        "bbox": [
+            215,
+            411,
+            825,
+            507
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "A.2.3 NODE ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            520,
+            282,
+            535
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Neural Oblivious Decision Ensembles were tuned by grid search over the following hyperparameter values. In the multi-layer NODE, we use the same architecture for all layers, i.e., the same number of trees of the same depth. total tree count here denotes the total number of trees on all layers. For each dataset, we use the maximal batch size, which fits in the GPU memory. We always use learning rate $1 0 ^ { - 3 }$ . ",
+        "bbox": [
+            173,
+            545,
+            825,
+            614
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "• num layers: {2, 4, 8} • total tree count: {1024, 2048} • tree depth: $\\{ 6 , 8 \\}$ • tree output dim: $\\{ 2 , 3 \\}$ ",
+        "bbox": [
+            215,
+            627,
+            436,
+            693
+        ],
+        "page_idx": 11
+    }
+]