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+# POLICY GRADIENT WITH EXPECTED QUADRATICUTILITY MAXIMIZATION: A NEW MEAN-VARIANCEAPPROACH IN REINFORCEMENT LEARNING
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+In real-world decision-making problems, risk management is critical. Among various risk management approaches, the mean-variance criterion is one of the most widely used in practice. In this paper, we suggest expected quadratic utility maximization (EQUM) as a new framework for policy gradient style reinforcement learning (RL) algorithms with mean-variance control. The quadratic utility function is a common objective of risk management in finance and economics. The proposed EQUM has several interpretations, such as reward-constrained variance minimization and regularization, as well as agent utility maximization. In addition, the computation of the EQUM is easier than that of existing mean-variance RL methods, which require double sampling. In experiments, we demonstrate the effectiveness of the EQUM in benchmark setting of RL and financial data.
+
+# 1 INTRODUCTION
+
+Reinforcement learning (RL) with Markov decision processes (MDPs) is one type of dynamic decision-making problem (Puterman, 1994; Sutton & Barto, 1998). While the typical objective is the expected cumulative reward maximization, risk-aware decision-making has attracted great attention in real-world applications, such as finance and robotics (Geibel & Wysotzki, 2005; García & Fernández, 2015). The notion of risk is related to the fact that even an optimal policy may perform poorly owing to the stochastic nature of the problem. To capture the risk, various criteria have been proposed, such as Value at Risk (Luenberger, 1998; Chow & Ghavamzadeh, 2014; Chow et al., 2017) and variance (Markowitz, 1952; Markowitz et al., 2000; Tamar et al., 2012; Prashanth & Ghavamzadeh, 2013). Among them, we focus on the mean-variance trade-off.
+
+Typical mean-variance RL (MVRL) methods attempt to maximize the expected cumulative reward while maintaining the variance threshold (Tamar et al., 2012; Prashanth & Ghavamzadeh, 2013; 2016; Xie et al., 2018; Bisi et al., 2020; Zhang et al., 2020). However, most existing MVRL methods suffer from high computational costs owing to the double sampling issue when approximating the gradient of the variance term (Tamar et al., 2012; Prashanth & Ghavamzadeh, 2013; 2016). To avoid the double sampling issue, Xie et al. (2018) proposed a method based on the Legendre-Fenchel duality (Boyd & Vandenberghe, 2004). Although the method does not suffer from the double sampling issue, we cannot apply a standard policy gradient method and must use a coordinate descent algorithm. In addition, the method cannot control risk at a certain desirable level.
+
+From an economics perspective, the difference in the RL objectives arises from the forms of utility functions. When the objective of an agent is expected cumulative reward maximization, the utility function is risk-neutral; when an agent attempts to control the risk based on an expected reward, the utility function is risk-averse (Mas-Colell et al., 1995). In economics, there have been several risk-averse utility functions proposed. The quadratic utility function is one such functions and is frequently used in financial economics (Luenberger, 1998). Under the quadratic utility function, the mean-variance portfolio maximizes the utility of the investor. In addition, other various financial theories are also based on the quadratic utility maximization (Markowitz, 1952; Sharpe, 1964; Lintner, 1965; Mossin, 1966). For more details, see Appendix A. In this study, as one of the MVRL approaches, we consider the expected quadratic utility maximization (EQUM) based on the policy gradient method (Williams, 1988; 1992; Sutton et al., 1999; Baxter & Bartlett, 2001).
+
+The EQUM has the following advantages: (i) low computational cost; (ii) numerous interpretations, and (iii) direct connections to real-world applications. In this study, as interpretations of EQUM, we propose the minimization of the variance under the constraint of the expected cumulative reward, reward-targeting optimization, and regularization. Thus, this study contributes to the context of riskaverse RL and MVRL. In the following sections, we first formulate the problem setting in Section 2 and review the existing methods in Section 3. Then, we propose the main algorithms in Section 4. Finally, we investigate the empirical effectiveness of the EQUM in Section 5.
+
+# 2 PROBLEM SETTING
+
+We consider the standard RL framework, where a learning agent interacts with an unfamiliar, dynamic, and stochastic environment modeled by a Markov decision process (MDP) in discrete time. We define the MDP as the tuple $( S , { \mathcal { A } } , r , P , P _ { 0 } )$ , where $s$ is a set of states, $\mathcal { A }$ is a set of actions, $r : \mathcal { S } \times \mathcal { A } \to \mathbb { R }$ is a reward function, $P : \mathcal { S } \times \mathcal { S } \times \mathcal { A }  [ 0 , 1 ]$ is the transition kernel, and $P _ { 0 } : { \mathcal { S } }  [ 0 , 1 ]$ is an initial state distribution. The initial state $S _ { 1 }$ is sampled from $P _ { 0 }$ . Let $\pi _ { \theta } : \mathcal { A } \times \mathcal { S }  [ 0 , 1 ]$ be a parameterized stochastic policy mapping states to actions, where $\theta$ is the tunable parameter. At time step $t$ , an agent chooses an action $A _ { t }$ according to a policy $\pi _ { \boldsymbol { \theta } } ( \cdot \mid S _ { t } )$ . We assume that the policy $\pi _ { \theta }$ is a differentiable function with respect to $\theta$ ; that is, $\frac { \partial \pi _ { \theta } ( a , s ) } { \partial \theta }$ exists.
+
+mulative reward from time step There are several performance measures for a policy $t$ to $u$ defined as $\mathbb { E } _ { \pi _ { \theta } } [ R _ { t : u } ]$ $\pi _ { \theta }$ . One popular measure is the expected cu- , where $\begin{array} { r } { R _ { t : u } = \sum _ { i = 0 } ^ { u } \gamma ^ { i } r ( S _ { t + i } , A _ { t + i } ) } \end{array}$ $\gamma \in ( 0 , 1 )$ is a discount factor and $\mathbb { E } _ { \pi _ { \theta } }$ denotes the expectation operator over a policy $\pi _ { \theta }$ , and $S _ { 1 }$ is generated from $P _ { 0 }$ . When $\gamma = 1$ , to ensure the cumulative reward well defined, it is usually assumed that all policies are proper (Bertsekas & Tsitsiklis, 1996); that is, for any policy $\pi _ { \theta }$ , the agent goes to a recurrent state $S ^ { * }$ with probability 1. After the agent passes the recurrent state $S ^ { * }$ at a time $\tau$ , the rewards are always 0. Such a finite horizon case is called episodic MDPs (Puterman, 1994). For brevity, we denote $R _ { t : u }$ as $R$ when the meaning is obvious. Under these criteria, the agent may attempt to obtain a higher cumulative reward while taking higher risks. In real-world applications, such as portfolio management in finance (Markowitz, 1952; Markowitz et al., 2000), such risky decision-making is not always desired, and we, therefore, consider the trade-off between the expected cumulative reward and the variance. Thus, while the goal of the risk-neutral MDP problem is to find the parameter $\theta$ that maximizes the total reward, we consider the mean-variance trade-off between the cumulative expected reward and the variance of the cumulative reward $R$ in the MVRL problem. Note that even when the reward $r$ is deterministic, the cumulative reward is a random variable owing to the stochastic policy, and there exists the mean-variance trade-off. In addition, even if the optimal policy is deterministic, the proposed method empirically has the potential to improves the stability of the training from the observations in the experiments of Section 5.3.
+
+# 3 EXISTING MVRL METHODS
+
+In this section, we introduce existing studies of MVRL.
+
+# 3.1 CONSTRAINED TRAJECTORY-VARIANCE PROBLEM
+
+Tamar et al. (2012), Prashanth & Ghavamzadeh (2013), and Xie et al. (2018) formulated MVRL by a constrained optimization problem defined as $\begin{array} { r l } { \operatorname* { m a x } _ { \theta \in \Theta } } & { { } \mathbb { E } _ { \pi _ { \theta } } [ R ] } \end{array}$ s.t. $\operatorname { V a r } _ { \pi _ { \theta } } ( R ) ~ \leq ~ \eta$ . In their formulation, the goal is to maximize the expected cumulative reward with controlling the trajectory-variance at a certain level. To solve this problem, Tamar et al. (2012), Prashanth & Ghavamzadeh (2013), and Xie et al. (2018) consider a penalized method defined as $\begin{array} { r } { \operatorname* { m a x } _ { \theta \in \Theta } \mathbb { E } _ { \pi _ { \theta } } [ R ] - \delta g \big ( \mathrm { V a r } _ { \pi _ { \theta } } ( R ) - \eta \big ) } \end{array}$ , where $\delta > 0$ is a constant and $g : \mathbb { R }  \mathbb { R }$ is a penalty function, such as $g ( x ) = x$ or $g ( x ) = x ^ { 2 }$ .
+
+# 3.1.1 DOUBLE SAMPLING ISSUE
+
+Tamar et al. (2012), Prashanth & Ghavamzadeh (2013), and Xie et al. (2018) report the double sampling issue in MVRL, which requires sampling from two different trajectories for estimating the policy gradient. For instance, in an episodic MDP with the discount factor $\gamma = 1$ and the stopping time $\tau = \operatorname* { m i n } \{ t \mid S _ { t } = S ^ { * } \}$ , the gradients of $\mathbb { E } _ { \pi _ { \theta } } [ R ]$ , $\mathbb { E } _ { \pi _ { \theta } } \left[ R ^ { 2 } \right]$ , and $\left( \mathbb { E } _ { \pi _ { \theta } } [ R ] \right) ^ { 2 }$ are given as $\begin{array} { r } { \nabla _ { \theta } \mathbb { E } _ { \pi _ { \theta } } [ R ] = \mathbb { E } _ { \pi _ { \theta } } [ R \sum _ { t = 1 } ^ { \tau } \nabla _ { \theta } \log \pi _ { \theta } ( S _ { t } , A _ { t } ) ] . } \end{array}$ , $\begin{array} { r } { \nabla _ { \theta } \mathbb { E } _ { \pi _ { \theta } } \big [ R ^ { 2 } \big ] = \mathbb { E } \left[ R ^ { 2 } \sum _ { t = 1 } ^ { \tau } \nabla _ { \theta } \log \pi _ { \theta } ( S _ { t } , A _ { t } ) \right] } \end{array}$ , and $\nabla _ { \theta } \bigl ( \mathbb { E } _ { \pi _ { \theta } } [ R ] \bigr ) ^ { 2 } \ = \ 2 \mathbb { E } _ { \pi _ { \theta } } [ R ] \nabla _ { \theta } \mathbb { E } _ { \pi _ { \theta } } [ R ]$ (Tamar et al., 2012). Besides, the gradient of the variance is given as $\begin{array} { r } { \mathbb { E } _ { \pi _ { \theta } } \left[ R ^ { 2 } \sum _ { t = 1 } ^ { \tau } \nabla _ { \theta } \log \pi _ { \theta } ( S _ { t } , A _ { t } ) \right] - 2 \mathbb { E } _ { \pi _ { \theta } } [ R ] \nabla _ { \theta } \mathbb { E } _ { \pi _ { \theta } } [ R ] } \end{array}$ . Because optimizing the policy $\pi _ { \theta }$ using the gradients directly is computationally intractable, we replace them with . Supp, where e that there is a simulator generating a trajectory is the stopping time of the trajectory. Then, we can $k$ withaively $\{ ( S _ { t } ^ { k } , A _ { t } ^ { k } , r ( S _ { t } ^ { k } , A _ { t } ^ { k } ) ) \} _ { t = 1 } ^ { \tau ^ { k } }$ $\tau ^ { k }$ construct unbiased estimators of $\mathbb { E } _ { \pi _ { \theta } } [ R ]$ and $\mathbb { E } _ { \pi _ { \theta } } \left[ R ^ { 2 } \right]$ as $\begin{array} { r } { \widehat { \nabla } _ { \theta } \mathbb { E } _ { \pi _ { \theta } } [ R ] = \widehat { R } ^ { k } \sum _ { t = 1 } ^ { \tau ^ { k } } \nabla _ { \theta } \log \pi _ { \theta } ( S _ { t } ^ { k } , A _ { t } ^ { k } ) } \end{array}$ and $\begin{array} { r l r } { \widehat { \nabla } _ { \theta } \mathbb { E } _ { \pi _ { \theta } } \big [ R ^ { 2 } \big ] } & { = } & { \Big ( \widehat { R } ^ { k } \Big ) ^ { 2 } \sum _ { t = 1 } ^ { \tau ^ { k } } \nabla _ { \theta } \log \pi _ { \theta } \big ( S _ { t } ^ { k } , A _ { t } ^ { k } \big ) } \end{array}$ , where $\widehat { R } ^ { k }$ is a sample approximation of $\mathbb { E } _ { \pi _ { \theta } } [ R ]$ at the episode $k$ . However, obtaining an unbiased estimator of $\begin{array} { r l } { \small } & { { } \nabla _ { \theta } \left( \mathbb { E } _ { \pi _ { \theta } } [ R ] \right) ^ { 2 } ~ = } \end{array}$ $2 \mathbb { E } _ { \pi _ { \theta } } [ R ] \nabla _ { \theta } \mathbb { E } _ { \pi _ { \theta } } [ R ]$ is difficult because it requires sampling from two different trajectories for approximating $\mathbb { E } _ { \pi _ { \theta } } [ R ]$ and $\nabla _ { \boldsymbol { \theta } } \mathbb { E } _ { \pi _ { \boldsymbol { \theta } } } [ R ]$ . This issue makes the optimization problem difficult.
+
+# 3.1.2 EXISTING SOLUTIONS TO DOUBLE SAMPLING ISSUE
+
+For the double sampling issue, Tamar et al. (2012), Prashanth & Ghavamzadeh (2013), and Xie et al.   
+(2018) presented the following solutions.
+
+Multi-time-scale stochastic optimization: The proposed methods of Tamar et al. (2012) and Prashanth & Ghavamzadeh (2013) are based on stochastic approximation to find an equilibrium point of an ordinary differential equation and saddle point of the objective, respectively.
+
+Coordinate descent optimization: Xie et al. (2018) proposed using the Legendre-Fenchel dual transformation with coordinate descent algorithm. First, based on Lagrangian relaxation, Xie et al. (2018) set an objective function as $\mathrm { m a x } _ { \theta \in \Theta } \mathbb { E } _ { \pi _ { \theta } } [ R ] - \delta \left( \mathrm { V a r } _ { \pi _ { \theta } } ( R ) - \eta \right)$ . Then, Xie et al. (2018) transformed the objective function as $\begin{array} { r } { \operatorname* { m a x } _ { \theta \in \Theta , y \in \mathbb { R } } 2 y \left( \mathbb { E } _ { \pi _ { \theta } } [ R ] + \frac { 1 } { 2 \delta } \right) - y ^ { 2 } - \mathbb { E } _ { \pi _ { \theta _ { * } } } \left[ R ^ { 2 } \right] } \end{array}$ and estimated a parameter by solving the optimization problem via a coordinate descent algorithm.
+
+Weakness of existing approaches: The multi-time-scale approaches by Tamar et al. (2012) and Prashanth & Ghavamzadeh (2013) are known to be sensitive to the choice of the step-size schedules, which are not easy to be controlled (Xie et al., 2018). The method by Xie et al. (2018) does not reflect the constraint condition $\eta$ as shown above; that is, in the objective function of Xie et al. (2018), there exits penalty coefficient $\delta$ , but does not exist the constraint condition $\eta$ . Note that the problem of Xie et al. (2018) is owing to their objective function based on the penalty function $g ( x ) = x$ $) = x \colon \operatorname { \mathbb { E } } _ { \pi _ { \theta } } [ R ] - \delta \left( \operatorname { V a r } _ { \pi _ { \theta } } ( R ) - \eta \right)$ , in which the first derivative does not include $\eta$ . In addition, when using quadratic function as $g ( \overset { \cdot } { x } ) = x ^ { 2 }$ to consider $\eta$ , we cannot remove $\mathbb { E } [ R ^ { 2 } ]$ even with Legendre-Fenchel dual; that is, the method also suffers the double sampling issue.
+
+# 3.2 CONSTRAINED PER-STEP VARIANCE PROBLEM
+
+Bisi et al. (2020) and Zhang et al. (2020) proposed solving a constrained per-step variance problem for MVRL. Bisi et al. (2020) showed that the per-step variance $\begin{array} { r } { \operatorname { V a r } _ { \pi _ { \theta } } \dot { ( } R ) \le \frac { \operatorname { V a r } _ { \pi _ { \theta } } ( r ( S _ { t } , \dot { } A _ { t } ) ) } { ( 1 - \gamma ) ^ { 2 } } } \end{array}$ , which implies that the minimization of the per-step variance $\mathrm { V a r } ( r ( S _ { t } , A _ { t } ) )$ also minimizes trajectory-variance $\operatorname { V a r } _ { \pi _ { \theta } } ( R )$ . Therefore, they train a policy $\pi _ { \theta }$ by maximizing $\mathbb { E } _ { \pi _ { \theta } } [ r ( S _ { t } , A _ { t } ) ] -$ $\kappa \bar { \mathsf { V a r } } _ { \pi _ { \theta } } ( r ( S _ { t } , A _ { t } ) )$ , where $\kappa > 0$ is a parameter of the penalty function. The methods of Bisi et al. (2020) and Zhang et al. (2020) are based on the trust region policy optimization (Schulman et al., 2015) and coordinate descent with Legendre-Fenchel duality (Xie et al., 2018), respectively.
+
+# 3.3 CONSTRAINED CUMULATIVE EXPECTED REWARD PROBLEM
+
+While existing MVRL studies mainly focus on a constrained trajectory-variance problem, a constrained cumulative expected reward optimization is also frequently used in practical situations, such as finance (Markowitz, 1952; Markowitz et al., 2000). In the constrained cumulative expected
+
+reward problem, we solve the following problem:
+
+$$
+\operatorname* { m i n } _ { \theta \in \Theta } \operatorname { V a r } _ { \pi _ { \theta } } ( R ) \mathrm { s . t . } \mathbb { E } _ { \pi _ { \theta } } [ R ] = \xi .
+$$
+
+Our proposed EQUM framework is based on this motivation; that is, variance minimization. As shown in the following section, from a computational perspective, there is a critical difference between the constrained cumulative expected reward and trajectory-variance problems.
+
+# 4 EQUM FRAMEWORK
+
+In this paper, as a novel approach for MVRL, we propose a Expected Quadratic Utility maximization RL (EQUM). In economic model, by using two parameters $\alpha > 0$ and $\beta > 0$ , the quadratic utility function for the cumulative return $R$ is defined as $\begin{array} { r } { U ( R ; \alpha , \beta ) = \alpha R - \frac { 1 } { 2 } \beta R ^ { 2 } } \end{array}$ for $\alpha > 0 , \beta \ge 0$ (Luenberger, 1998). The quadratic utility function captures the preference of a risk-averse agent over the cumulative return $R$ . Let us consider the expected quadratic utility function defined as
+
+$$
+\begin{array} { l } { { \displaystyle { \mathbb E } _ { \pi _ { \theta } } \left[ U ( R ; \alpha , \beta ) \right] = \alpha { \mathbb E } _ { \pi _ { \theta } } \left[ R \right] - \frac 1 2 \beta { \mathbb E } _ { \pi _ { \theta } } \left[ R ^ { 2 } \right] } } \\ { ~ = \alpha { \mathbb E } _ { \pi _ { \theta } } \left[ R \right] - \frac 1 2 \beta { \big ( } { \mathbb E } _ { \pi _ { \theta } } [ R ] { \big ) } ^ { 2 } - \frac 1 2 \beta { \mathbb E } _ { \pi _ { \theta } } \left[ { \big ( } { \mathbb E } _ { \pi _ { \theta } } [ R ] - R { \big ) } ^ { 2 } \right] . } \end{array}
+$$
+
+In the EQUM framework, we train a policy by maximizing the expected quadratic utility function.
+
+# 4.1 INTERPRETATIONS
+
+Here, we introduce four interpretations of EQUM. We can interpret the EQUM as an approach for (i) an expected utility maximization, (ii) a targeting optimization problem to achieve an expected cumulative reward $\zeta$ , (iii) a constrained trajectory-reward problem with a quadratic penalized function, and (iv) an expected cumulative reward maximization with regularization.
+
+First, we discuss the connection with respect to training an agent to achieve a predefined return (Berger, 1985). Let $\zeta$ be a target return that the algorithm aims to achieve. Then, we consider the mean squared error (MSE) minimization between the expected deviation of the return and $\zeta$ :
+
+$$
+\underset { \theta \in \Theta } { \arg \operatorname* { m i n } } J ( \theta ; \zeta ) = \underset { \theta \in \Theta } { \arg \operatorname* { m i n } } \mathbb { E } _ { \pi _ { \theta } } \left[ \left( \zeta - R \right) ^ { 2 } \right]
+$$
+
+We can decompose the MSE into the bias and variance as follows:
+
+$$
+\begin{array} { r l } & { \mathbb { E } _ { \pi _ { \theta } } \left[ \left( \zeta - R \right) ^ { 2 } \right] } \\ & { = \underbrace { \left( \zeta - \mathbb { E } _ { \pi _ { \theta } } [ R ] \right) ^ { 2 } } _ { \mathrm { B i a s } } + \underbrace { 2 \mathbb { E } _ { \pi _ { \theta } } \left[ \left( \zeta - \mathbb { E } _ { \pi _ { \theta } } [ R ] \right) \left( \mathbb { E } _ { \pi _ { \theta } } [ R ] - R \right) \right] } _ { 0 } + \underbrace { \mathbb { E } _ { \pi _ { \theta } } \left[ \left( \mathbb { E } _ { \pi _ { \theta } } [ R ] - R \right) ^ { 2 } \right] } _ { \mathrm { V a r i a n c e } } } \\ & { = \zeta ^ { 2 } - 2 \zeta \mathbb { E } _ { \pi _ { \theta } } [ R ] + \left( \mathbb { E } _ { \pi _ { \theta } } [ R ] \right) ^ { 2 } + \mathbb { E } _ { \pi _ { \theta } } \left[ \left( \mathbb { E } _ { \pi _ { \theta } } [ R ] - R \right) ^ { 2 } \right] . } \end{array}
+$$
+
+Thus, the minimization problem (3) trains the policy $\pi _ { \theta }$ to consider the trade-off between the bias $\begin{array} { r } { \left( \zeta - \mathbb { E } _ { \pi _ { \theta } } [ R ] \right) ^ { 2 } } \end{array}$ and variance $\mathbb { E } _ { \pi _ { \theta } } \left[ \left( \mathbb { E } _ { \pi _ { \theta } } [ R ] - R \right) ^ { 2 } \right]$ (Section 9.5 of Luenberger (1998)). Moreover, we find that the EQUM is equivalent to the reward-targeting optimization when $\begin{array} { r } { \zeta = \frac { \alpha } { \beta } } \end{array}$ ; that is,
+
+$$
+\begin{array} { r l } & { \underset { \theta \in \Theta } { \arg \operatorname* { m i n } } J \left( \theta ; \frac { \alpha } { \beta } \right) = \underset { \theta \in \Theta } { \arg \operatorname* { m i n } } \left( \frac { \alpha } { \beta } \right) ^ { 2 } - 2 \frac { \alpha } { \beta } \mathbb { E } _ { \pi _ { \theta } } [ R ] + \left( \mathbb { E } _ { \pi _ { \theta } } [ R ] \right) ^ { 2 } + \mathbb { E } _ { \pi _ { \theta } } \left[ \left( \mathbb { E } _ { \pi _ { \theta } } [ R ] - R \right) ^ { 2 } \right] } \\ & { \quad \quad \quad = \underset { \theta \in \Theta } { \arg \operatorname* { m a x } } \mathbb { E } _ { \pi _ { \theta } } \left[ U ( R ; \alpha , \beta ) \right] . } \end{array}
+$$
+
+Second, the bias-variance trade-off heuristically provides a solution to a constraint optimization problem (1) with the constraint $\begin{array} { r } { \xi = \zeta = \frac { \alpha } { \beta } } \end{array}$ by solving the following penalized problem:
+
+$$
+\operatorname* { m i n } _ { \theta \in \Theta } \mathrm { V a r } _ { \pi _ { \theta } } ( R ) + \big ( \mathbb { E } _ { \pi _ { \theta } } [ R ] - \xi \big ) ^ { 2 } .
+$$
+
+Third, we can regard the quadratic utility function as an expected cumulative reward maximization with a regularization term defined as $\mathbb { E } \big [ \dot { R } ^ { 2 } \big ]$ ; that is, minimization of the risk $\mathcal { R } ( \pi _ { \theta } )$ :
+
+$$
+\begin{array} { r } { \mathcal { R } ( \theta ) = \underbrace { - \mathbb { E } _ { \pi _ { \theta } } [ R ] } _ { \substack { \mathrm { R i s k ~ o f ~ e x r e f e d ~ c u m u l a t i v e ~ r e w a r d ~ m a v i m i z a t i o n } } } + \underbrace { \psi \mathbb { E } _ { \pi _ { \theta } } \big [ R ^ { 2 } \big ] } _ { \substack { \mathrm { D e a s u m i a r i z a t i o n ~ t o ~ r e g u a r i z e } } } } \end{array}
+$$
+
+where $\psi > 0$ is a regulation parameter and $\begin{array} { r } { \psi = \frac { \beta } { 2 \alpha } = \frac { 1 } { 2 \zeta } } \end{array}$ . As $\zeta  \infty$ , $\mathcal { R } ( \pi _ { \theta } )  - \mathbb { E } _ { \pi _ { \theta } } [ R ]$
+
+# 4.2 MERITS OF THE EQUM FRAMEWORK
+
+In this section, we present two advantages of the EQUM framework. The first advantage is in computation. The EQUM framework is an MVRL method. However, compared with existing MVRL methods, which involve the double sampling issue, the computation of the EQUM framework is much simpler because we transform the MVRL problem (4) into the optimization problem without the term $\left( \mathbb { E } _ { \pi _ { \theta } } [ R ] \right) ^ { 2 }$ (see (2) and (5)). The second advantage is that it provides a variety of interpretations. Because the EQUM framework can interpret economic theory, it is applicable for modeling economic dynamics. In addition, as one of the MVRL methods, it is suitable for various real-world applications, such as finance (Deng et al., 2016) and playing games. By regarding the proposed EQUM as a regularization framework, we can combine it with existing RL methods.
+
+# 4.3 IMPLEMENTATIONS OF THE EQUM FRAMEWORK
+
+Here, we discuss the implementations of the EQUM framework.
+
+Simplest policy gradient with EQUM With the EQUM framework, we introduce a main algorithm with simplest policy gradient (SPG) algorithm (Brockman et al., 2016), which is also called the REINFORCE algorithm (Williams, 1992). For an episode $k$ with length $n$ , the method replaces the expectations $\mathbb { E } _ { \pi _ { \theta } } ^ { { \mathrm { ~ \tiny ~ - ~ } } } [ R ]$ and $\mathbb { E } _ { \pi _ { \theta } } \left[ R ^ { 2 } \right]$ with the sample approximations $\scriptstyle \sum _ { t = 1 } ^ { n } \gamma ^ { t - 1 } r ( S _ { t } , { \bar { A _ { t } } } )$ and $\begin{array} { r } { \left( \sum _ { t = 1 } ^ { n } \gamma ^ { t - 1 } r ( S _ { t } , A _ { t } ) \right) ^ { 2 } } \end{array}$ , respectively (Brockman et al., 2016). Then, the unbiased gradients are
+
+$$
+\widehat { \nabla } _ { \theta } \mathbb { E } _ { \pi _ { \theta } } [ R ] = \widehat { R } ^ { k } \sum _ { t = 1 } ^ { n } \nabla _ { \theta } \log \pi _ { \theta } ( S _ { t } ^ { k } , A _ { t } ^ { k } ) \mathrm { ~ a n d ~ } \widehat { \nabla } _ { \theta } \mathbb { E } _ { \pi _ { \theta } } \big [ R ^ { 2 } \big ] = \Big ( \widehat { R } ^ { k } \Big ) ^ { 2 } \sum _ { t = 1 } ^ { n } \nabla _ { \theta } \log \pi _ { \theta } ( S _ { t } ^ { k } , A _ { t } ^ { k } ) .
+$$
+
+Therefore, for a sample approximation $\widehat { R } ^ { k }$ of $\mathbb { E } _ { \pi _ { \theta } } \left[ R ^ { 2 } \right]$ at the episode $k$ , we optimize the policy with ascending the following gradient: $\begin{array} { r } { \bigg ( \alpha \widehat { R } ^ { k } - \frac { 1 } { 2 } \beta \left( \widehat { R } ^ { k } \right) ^ { 2 } \bigg ) \sum _ { t = 1 } ^ { n } \nabla _ { \theta } \log \pi _ { \theta } ( S _ { t } ^ { k } , A _ { t } ^ { k } ) . } \end{array}$
+
+Actor-critic with EQUM: For another combination with the EQUM framework, we apply an actor-critic (AC) based algorithms, which is also refereed to as the advantage actor-critic (A2C) algorithm (Williams & Peng, 1991; Mnih et al., 2016). Extending the AC algorithm, for an episode $k$ with the length $n$ , we train the policy by a gradient defined as
+
+$$
+\nabla _ { \theta } \log \pi _ { \theta } ( S _ { t } ^ { k } , A _ { t } ^ { k } ) \left\{ \left( \alpha \widetilde { R } _ { t : t + n - 1 } ^ { k } - \frac { 1 } { 2 } \beta \widetilde { R } _ { t : t + n - 1 } ^ { k , 2 } \right) - \left( \alpha M _ { \hat { \omega } _ { k } ^ { ( 1 ) } } ^ { ( 1 ) } ( S _ { t } ^ { k } ) - \frac { 1 } { 2 } \beta M _ { \hat { \omega } _ { k } ^ { ( 2 ) } } ^ { ( 2 ) } ( S _ { t } ^ { k } ) \right) \right\} ,
+$$
+
+where $\widetilde { R } _ { t : t + n - 1 } ^ { k } = { \widehat { R } _ { t : t + n - 1 } ^ { k } } + \gamma ^ { n } M _ { \hat { \omega } _ { k } ^ { ( 1 ) } } ^ { ( 1 ) } ( S _ { t + n } ^ { k } )$ nM (1)ωˆ(1)k (Skt+n), and Rek,2t:t+n−1 = $\widetilde { R } _ { t : t + n - 1 } ^ { k , 2 } = \bigg ( \widehat { R } _ { t : t + n - 1 } ^ { k } + \gamma ^ { n } M _ { \hat { \omega } _ { k } ^ { ( 1 ) } } ^ { ( 1 ) } ( S _ { t + n } ^ { k } ) \bigg ) ^ { 2 }$ and M (1)(1) $M _ { \hat { \omega } _ { k } ^ { ( 1 ) } } ^ { ( 1 ) } ( S _ { t } ^ { k } )$ and $M _ { \hat { \omega } _ { k } ^ { ( 2 ) } } ^ { ( 2 ) } ( S _ { t } ^ { k } )$ are value functions approximating $\mathbb { E } [ R _ { t + 1 : \infty } ]$ and $\mathbb { E } [ R _ { t + 1 : \infty } ^ { 2 } ]$ with parameters $\hat { \omega } _ { k } ^ { ( 1 ) }$ ) and ωˆk ωˆ k(2) , respectively.
+
+For other RL algorithms, we can heuristically extend our proposed framework EQUM to accept the other RL algorithms by adding $\mathbb { E } [ R ^ { 2 } ]$ as regularization term.
+
+Determining $\alpha$ and $\beta$ : Next, we discuss the parameter tuning of $\alpha$ and $\beta$ , which are equivalent to $\zeta , \xi$ , and $\psi$ ). As explained, the parameter $\psi$ has several meanings based on the interpretations of the EQUM, such as the quadratic utility function, targeting optimization, and constrained optimization. In addition, from the regularization perspective, we can adjust the parameter to maximize the expected cumulative reward in the validation data. Thus, we propose the following four directions for the parameter tuning. First, in economic applications, such as finance, we choose ${ \frac { \beta } { 2 \alpha } } = \psi$ based on the theoretical economic assumptions and economic empirical studies (Ziemba et al., 1974; Kallberg & Ziemba, 1983) (Appendix A). For instance, Capital Asset Pricing Model (CAPM), which is one of the most popular economic models, is also base on the quadratic utility function (Sharpe, 1964; Lintner, 1965; Mossin, 1966). Second, we set $\begin{array} { r } { \zeta = \frac { 1 } { 2 \psi } } \end{array}$ as the targeted reward to achieve. Third, we regard the parameter $\psi$ as the constrained problem (1). Fourth, through cross-validation, we optimize the regularization parameter $\psi$ .
+
+![](images/6c9ee4bb13dab434c96baab6fdf4c87e694e9a2e9d0855722b82b9d7eac7c5ff.jpg)  
+Figure 1: The ARs and SDs in the training process of the experiment using the synthetic dataset.
+
+# 5 EXPERIMENTS
+
+This section investigates the empirical performance of the proposed EQUM with synthetic and realworld financial datasets. The goal of these experiments is to construct a portfolio with a wellcontrolled mean and variance through algorithms. In addition, we also show experimental results using CartPole and Atari games. Note that the per-step rewards of portfolio selection are stochastic variables and those of CartPole and Atari games are deterministic variables. However, even when the reward is deterministic, the cumulative reward has randomness owing to the stochastic policy.
+
+# 5.1 EXPERIMENTS WITH SYNTHETIC PORTFOLIO SELECTION DATASETS
+
+Following Tamar et al. (2012) and Xie et al. (2018), we artificially generate a portfolio dataset. Let us consider a portfolio composed of two types of assets: a liquid asset, which has a fixed interest rate $r _ { 1 } = 1 . 0 0 1$ , and a non-liquid asset, which has a time-dependent interest rate $r _ { \mathrm { n l } } ( t ) \in \{ 1 . 1 , 2 \}$ . While we can sell the liquid asset at every time step $t = 1 , 2 , \dots , T$ , we can sell the non-liquid asset only after a maturity period of $N$ steps; that is, when holding 1 liquid asset, we obtain 1.001 per period; when holding 1 non-liquid asset at the $t { \cdot }$ -th period, we obtain 1.1 or 2 at the $t + N$ -th periods. In addition, the non-liquid asset has some risk of not being paid with a probability $p _ { \mathrm { r i s k } }$ ; that is, if the non-liquid asset defaulted during the $N$ periods, we cannot obtain any profits by having the asset. In this setup, a typical investment strategy is to construct a portfolio using both liquid and non-liquid assets to control the mean and variance. In our model, the investor may change his portfolio by investing a fixed fraction $\alpha = 0 . 2$ to the non-liquid asset at each time step. As a performance metric of the portfolio, we focus on the mean and variance of the cumulative reward when having the cash 1 at the first period and investing the cash for 50 periods following an algorithm.
+
+In particular, we aim to investigate the sensitivity of the EQUM against the parameter $\psi ~ = ~ 2 / \zeta$ and compare the EQUM with the standard SPG and AC algorithms. We apply the SPG algorithm with the EQUM (Section 4.3) to the synthetic datasets. For $\zeta$ , we use $\zeta = 1 , 2 , 3 , 4 , 5 , 6$ . Note that from the regularization perspective with a parameter $\psi$ , EQUM with $\psi = 0 . 1$ is equal to minimize the MSE between the cumulative reward and $\zeta = 5 = 1 / ( 2 \times 0 . 1 )$ . We train the model with 500 episodes. In Figure 1, we calculate the average reward and standard deviation at each episode of the training process over 1, 000 trials. In Table 1, using the trained model for the test environment, we show the average reward (AR) and standard deviation (SD) by conducting 1, 000 trials.
+
+![](images/cbc355b3843eb705c8032338e7f393d23daa94702a7de204250f9153d67d4c09.jpg)  
+Figure 2: Higher AR and lower Var methods are Pareto efficient.
+
+For each trial, we compute the AR and SD over 100 trial and compute the average of each AR and SD over 1, 000 trials. From Figure 1 and Table 1, we can clearly confirm that the EQUM framework realize the control of the mean-variance trade-off. As shown in the results, we can reduce the variance by increasing $\zeta$ . The MSE from target $\zeta$ is shown in Table 2. In Figure 2, for the EQUM with various $\zeta$ and the method of Tamar et al. (2012) (Tamar) with various variance constraints (var), we plot the AR and variance (Var) computed on the train environment over $1 , 0 0 0$ trials. We show the Var instead of the SD because the Tamar controls the variance. Compared with Tamar, the EQUM returns Pareto efficient portfolios; that is, higher AR and lower Var. We consider unlike the direct optimization of the EQUM, the Tamar suffers from the complicated optimization mechanism. Figure 3 in Appendix B.1 corresponds to the test environment version of Figure 2.
+
+Table 1: The experimental results of the synthetic dataset with the ARs and SDs over 1, 000 trials.   
+
+<table><tr><td rowspan="2"></td><td rowspan="2">Standard SPG =0</td><td colspan="6">SPG with EQUM</td></tr><tr><td>(=1</td><td>=2</td><td>（=3</td><td>(=4</td><td>=5</td><td>(=6</td></tr><tr><td>AR</td><td>6.767</td><td>-0.774</td><td>2.028</td><td>4.779</td><td>5.952</td><td>6.253</td><td>6.412</td></tr><tr><td>SD</td><td>5.324</td><td>1.977</td><td>3.971</td><td>4.832</td><td>5.037</td><td>5.089</td><td>5.080</td></tr></table>
+
+Table 2: The experimental results of the synthetic dataset with the MSEs for $\zeta$ over 1000 trials.   
+
+<table><tr><td rowspan="2">Target Value</td><td rowspan="2">Standard SPG =0</td><td colspan="6">SPG with EQUM</td></tr><tr><td>=1</td><td>=2</td><td>=3</td><td>=4</td><td>=5</td><td>=6</td></tr><tr><td>MSE from（ = 1</td><td>41.054</td><td>5.465</td><td>7.564</td><td>22.961</td><td>33.400</td><td>36.479</td><td>38.569</td></tr><tr><td>= 2</td><td>30.519</td><td>10.014</td><td>6.509</td><td>16.404</td><td>24.496</td><td>26.973</td><td>28.745</td></tr><tr><td>= 3</td><td>21.984</td><td>16.562</td><td>7.454</td><td>11.846</td><td>17.593</td><td>19.466</td><td>20.921</td></tr><tr><td>SSSSS = 4</td><td>15.450</td><td>25.111</td><td>10.399</td><td>9.289</td><td>12.689</td><td>13.960</td><td>15.096</td></tr><tr><td>=5</td><td>10.915</td><td>35.659</td><td>15.343</td><td>8.732</td><td>9.785</td><td>10.454</td><td>11.272</td></tr><tr><td>=6</td><td>8.381</td><td>48.208</td><td>22.288</td><td>10.174</td><td>8.882</td><td>8.948</td><td>9.448</td></tr></table>
+
+In Appendix B.2, we also show experimental results using another synthetic dataset of Americanstyle option following Tamar et al. (2014) and Xie et al. (2018).
+
+# 5.2 EXPERIMENTS WITH REAL-WORLD DATASET
+
+We use well-known benchmarks called Fama & French (1992) (FF) datasets to ensure the reproducibility of the experiment. We use the FF25, FF48 and FF100 datasets. The FF25 and FF 100 dataset includes 25 and 100 portfolios formed based on size and book-to-market ratio; the FF48 dataset contains 48 portfolios representing different industrial sectors. We formulate the problem by an episodic MDP. We use all datasets covering monthly data from July 1980 to June 2020. The state is past 12 months returns of each asset and the action is defined as portfolio weight; that is, the number of actions is equal to that of assets. The reward is obtained as the portfolio return. Here, the portfolio return at time $1 \leq t \leq T$ is defined as $\begin{array} { r } { y _ { t } = \sum _ { j = 1 } ^ { m } y _ { j , t } w _ { j , t - 1 } } \end{array}$ , where $y _ { j , t }$ is the return of $j$ asset at time $t$ , $w _ { j , t - 1 }$ is the weight of $j$ asset in the portfolio at time $t - 1$ , and $m$ is the number of assets. The length of the episode is 1 years (12 months). For the stochastic policy, we adopt a three-layer feed-forward neural network with the ReLU activation function where the number of units in each respective layer is equal to the number of assets, 100, 50, and the number of actions. We use the softmax function for the output layer.
+
+Portfolio models: We use the following portfolio models. An equally-weighted portfolio (EW) weights the financial assets equally (DeMiguel et al., 2007). A mean-variance portfolio (MV) computes the optimal variance under a mean constraint (Markowitz, 1952). For computing the mean vector and covariance matrix, we use the latest 10 years (120 months) data. An Kelly growth optimal portfolio with ensemble learning (EGO) is proposed by Shen et al. (2019). We set the number of resamples as $m _ { 1 } = 5 0$ , the size of each resample $m _ { 2 } = 5 \tau$ , the number of periods of return data $\tau = 6 0$ , the number of resampled subsets $m _ { 3 } = 5 0$ , and the size of each subset ${ m _ { 4 } } = n ^ { 0 . 7 }$ , where $m$ is number of assets; that is, $m = 2 5$ in FF25, $m = 4 8$ in FF48 and $m = 1 0 0$ in FF100. A portfolio blending via Thompson sampling (BLD) is proposed by Shen & Wang (2016). We use the latest 10 years (120 months) data to compute for the sample covariance matrix and blending parameters. A policy gradients with variance related risk criteria (Tamar) is proposed by Tamar et al. (2012). We set the target variance terms $\eta$ as 250,500,1000. A block coordinate ascent algorithm proposed by Xie et al. (2018), which is referred to as Mean-Variance Portfolio (MVP). We set the regularization parameters $\delta$ as 10,100,1000. Then, let us denote the SPG with the EQUM framework as EQUM. The parameter $\psi$ is chosen from $1 / 3 , 2 / 3$ , and 1. For optimizing Tamar, MVP and EQUM, we set the Adam optimizer with learning rate 0.01 and weight decay parameter 0.1. We train the neural networks for 10 episodes. Each portfolio is updated by sliding one-month-ahead.
+
+Performance metrics: The following measures widely used in finance to evaluate portfolio strategies (Brandt, 2010) are chosen. The cumulative return (CR), annualized risk as the standard de
+
+Table 3: The performance of each portfolio models during out-of-sample period (from July 2000 to June 2020) for FF25 dataset (upper table) , FF48 (middle table) and FF100 (lower table). For each dataset, the best performance is highlighted in bold.   
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">EW</td><td rowspan="2">MV</td><td rowspan="2">EGO</td><td rowspan="2">BLD n=250</td><td colspan="3">Tamar</td><td colspan="3">MVP</td><td colspan="3">EQUM</td></tr><tr><td>n=500</td><td>=1000</td><td>δ=10</td><td>δ=100</td><td>δ=1000</td><td>=1/3</td><td>=2/3</td><td>= 1</td></tr><tr><td colspan="10">FF25</td><td></td><td></td><td></td><td></td></tr><tr><td>CR↑</td><td>191.35</td><td>25.62 209.76</td><td>134.21</td><td></td><td>231.02 286.34</td><td>286.89</td><td>215.95</td><td></td><td>215.95</td><td>243.88</td><td>300.18</td><td>194.12</td><td>243.93</td></tr><tr><td>RISK↓</td><td>18.53</td><td>25.36 19.17</td><td></td><td>12.00</td><td>24.22</td><td>20.21</td><td>20.20</td><td>19.28</td><td>19.28</td><td>13.96</td><td>13.42</td><td>12.19</td><td>14.95</td></tr><tr><td>RR↑</td><td>0.52</td><td>0.05</td><td>0.55</td><td>0.56</td><td>0.48</td><td>0.71</td><td>0.71</td><td>0.56</td><td>0.56</td><td>0.87</td><td>1.12</td><td>0.80</td><td>0.82</td></tr><tr><td>MaxDD↓</td><td>0.54</td><td>0.75 0.57</td><td></td><td>0.37</td><td>0.64</td><td>0.58</td><td>0.58</td><td>0.57</td><td>0.57</td><td>0.30</td><td>0.31</td><td>0.30</td><td>0.36</td></tr><tr><td colspan="10">FF48</td><td colspan="3"></td></tr><tr><td>CR↑</td><td>194.73</td><td>34.81</td><td>249.14</td><td>124.45</td><td>120.96</td><td>188.10</td><td>150.65</td><td>344.72</td><td>333.66</td><td>210.99</td><td>226.39</td><td>246.61</td><td>236.43</td></tr><tr><td>RISK↓</td><td>16.58</td><td>30.38</td><td>19.56</td><td>10.76</td><td>13.20</td><td>14.96</td><td>14.73</td><td>23.98</td><td>21.87</td><td>20.25</td><td>19.81</td><td>15.38</td><td>11.75</td></tr><tr><td>RR↑</td><td>0.59</td><td>0.06</td><td>0.64</td><td>0.58</td><td>0.46</td><td>0.63</td><td>0.51</td><td>0.72</td><td>0.76</td><td>0.52</td><td>0.57</td><td>0.80</td><td>1.01</td></tr><tr><td>MaxDD↓</td><td>0.53</td><td>0.84</td><td>0.53</td><td>0.38</td><td>0.58</td><td>0.54</td><td>0.45</td><td>0.56</td><td>0.52</td><td>0.65</td><td>0.45</td><td>0.45</td><td>0.29</td></tr><tr><td colspan="10">FF100</td><td colspan="3"></td></tr><tr><td>CR↑</td><td>193.91</td><td>34.26</td><td>207.37</td><td>127.92</td><td>314.77</td><td>238.27</td><td>272.11</td><td>294.07</td><td>228.53</td><td>318.90</td><td>262.54</td><td>227.04</td><td>327.16</td></tr><tr><td>RISK↓</td><td>18.77</td><td>26.36</td><td>19.72</td><td>11.89</td><td>19.80</td><td>14.35</td><td>20.09</td><td>22.89</td><td>31.36</td><td>22.89</td><td>13.33</td><td>13.64</td><td>15.51</td></tr><tr><td>RR↑</td><td>0.52</td><td>0.06</td><td>0.53</td><td>0.54</td><td>0.79</td><td>0.83</td><td>0.68</td><td>0.64</td><td>0.36</td><td>0.70</td><td>0.98</td><td>0.83</td><td>1.05</td></tr><tr><td>MaxDD↓</td><td>0.55</td><td>0.72</td><td>0.58</td><td>0.36</td><td>0.39</td><td>0.49</td><td>0.38</td><td>0.52</td><td>0.65</td><td>0.46</td><td>0.24</td><td>0.31</td><td>0.39</td></tr></table>
+
+viation of return (RISK) and risk-adjusted return (R/R) are defined as follows: $\begin{array} { r } { \mathrm { C R } = \sum _ { t = 1 } ^ { T } y _ { t } . } \end{array}$   
+$\begin{array} { r } { \mathrm { R I S K } = \sqrt { \frac { 1 2 } { T - 1 } \sum _ { t = 1 } ^ { T } ( y _ { t } - \mathrm { C R } / T ) ^ { 2 } } } \end{array}$ , and $\begin{array} { r } { \mathrm { R } / \mathrm { R } = { \frac { 1 2 } { T } } \times \mathrm { C R } / \mathrm { R I S K . ~ R } / \mathrm { R } } \end{array}$ is the most important mea  
+sure for a portfolio strategy. We also evaluate the maximum draw-down (MaxDD), which is another   
+MaxD the largest drop from a peak d $\&$ ned as $\begin{array} { r } { \mathrm { M a x D D } = \operatorname* { m i n } _ { t \in [ 1 , T ] } \left( 0 , \frac { W _ { t } } { \operatorname* { m a x } _ { \tau \in [ 1 , t ] } W _ { \tau } } - 1 \right) } \end{array}$ $W _ { k }$ $k$ $\begin{array} { r } { W _ { t } = \prod _ { t ^ { \prime } = 1 } ^ { t } ( 1 + y _ { t ^ { \prime } } ) } \end{array}$
+
+Table 3 reports the performances of the portfolios. In almost all cases, the EQUM portfolio achieves the highest R/R and the lowest MaxDD. Therefore, we can confirm that the EQUM portfolio has a high $\operatorname { R } / \operatorname { R }$ , and avoids a large drawdown. The real objective (minimizing variance with a penalty on return targeting) for Tamar, MVP, and EQUM is shown in Appendix B.3. Except for FF48’s MVP, the objective itself is smaller than EQUM’s. Since the values of the objective is the same as the RR, we can empirically confirm that the better optimization, the better performance.
+
+# 5.3 EXPERIMENTS WITH CARTPOLE AND ATARI GAMES
+
+We also conduct experiments using CartPole and Atari games, where the reward is given as deterministic, and the randomness of the cumulative reward depends only on the stochastic policy. We investigate the sensitivity of $\psi = 1 / ( 2 \zeta )$ with CartPole and the compared the performance of the EQUM framework with that of Tamar et al. (2012) and Xie et al. (2018). The results are shown in Appendix B.4. In many experimental results, contrary to our expectations, we observed that the EQUM also improves the expected cumulative reward, not only the variance. We hypothesize that this is because there is often a limit on the cumulative rewards achieved by the standard expected cumulative reward maximizing algorithms. For instance, when the reward at each period is 1, and the discount factor is 0.99, the infinite sum is 100. In such a case, instead of naive reward maximization, MSE minimization against the target reward 100 may result in a more stable performance empirically. We also hypothesize that even if an optimal policy is deterministic, the EQUM can improve the stability of the training process by reducing the variance. This observation is an open problem related to exploration and exploitation trade-off. Therefore, unless we could increase the cumulative reward infinitely, the proposed EQUM framework can stabilize the performance. From this aspect, we can confirm that the EQUM provides a regularization effect.
+
+# 6 CONCLUSION
+
+In this paper, we proposed an EQUM framework as a variant of MVRL. Compared with existing MVRL methods, the EQUM framework is computationally friendly. The proposed EQUM framework also includes various interpretations, such as targeting optimization and regularization and is suitable for many real-world applications, such as finance and playing games. We investigated the effectiveness of the EQUM framework compared with the standard RL and existing MVRL methods through the experiments. In the results, the proposed method successfully controls the mean-variance trade-off. As an open problem, we also observed that even when an optimal policy is deterministic, the proposed method improves performance. We hypothesize that the proposed method affects the stabilization of the training process.
+
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+Aviv Tamar, Shie Mannor, and Huan Xu. Scaling up robust mdps using function approximation. In ICML, 2014.
+
+J. Tobin. Liquidity Preference as Behavior Towards Risk. Review of Economic Studies, 1958.
+
+R.J. Williams. Toward a Theory of Reinforcement-learning Connectionist Systems. 1988.
+
+Ronald Williams and Jing Peng. Function optimization using connectionist reinforcement learning algorithms. Connection Science, 1991.
+
+Ronald J. Williams. Simple statistical gradient-following algorithms for connectionist reinforcement learning. Machine Learning, 1992.
+
+Tengyang Xie, Bo Liu, Yangyang Xu, Mohammad Ghavamzadeh, Yinlam Chow, Daoming Lyu, and Daesub Yoon. A block coordinate ascent algorithm for mean-variance optimization. In NeurIPS. 2018.
+
+Shangtong Zhang, Bo Liu, and Shimon Whiteson. Mean-variance policy iteration for risk-averse reinforcement learning, 2020.
+
+W. T. Ziemba, C. Parkan, and R. Brooks-Hill. Calculation of investment portfolios with risk free borrowing and lending. Management Science, 1974.
+
+# A ECONOMIC THEORY AND QUADRATIC UTILITY FUNCTION
+
+Considering the mean-variance trade-off in a portfolio and economic activity is an essential task in economics as Tamar et al. (2012) and Xie et al. (2018) pointed out. The mean-variance trade-off is justified by assuming either quadratic utility function to the economic agent or multivariate normal distribution to the financial assets. By assuming the quadratic utility function or the normal distribution, we can assume that the expected utility function of the agent is maximized by maximizing the expected reward and minimizing the variance. Based on this observation, Markowitz (1952) proposed the following steps for providing a portfolio to an economic agent (Also see Markowitz (1959), page 288, and Luenberger (1998)):
+
+• Constructing portfolios minimizing the variance under several reward constraint; • Among the portfolios constructed in the first step, the economic agent chooses a portfolio maximizing the utility function.
+
+Therefore, the goal of Markowitz’s portfolio is not only to construct the portfolio itself but also to maximize the expected utility function of the agent. In traditional economics, this two-step is adopted because directly predicting the reward and variance to maximize the expected utility function is difficult; therefore, first gathering information based on analyses of an economist, then we construct the portfolio using the information and provide the set of the portfolios to an economic agent. However, owing to the recent development of machine learning, we can directly represent the complicated economic dynamics using flexible models, such as deep neural networks. In addition, as Tamar et al. (2012) and Xie et al. (2018) reported, when constructing the mean-variance portfolio in RL, we suffer the double sampling issue. Therefore, in this paper, we aim to achieve the original goal of the mean-variance approach; that is, the expected utility maximization. Note that this idea is not restricted to financial applications but can be applied to applications where the agent utility can be represented only by the mean and variance. In the following subsection, we review the existing studies of finance and quadratic utility function.
+
+# A.1 MARKOWITZ’S PORTFOLIO AND CAPITAL ASSET PRICING MODEL
+
+Markowitz’s portfolio is known as the mean-variance portfolio (Markowitz, 1952; Markowitz et al., 2000). Constructing the mean-variance portfolio is motivated by the agent’s expected utility maximization. When the utility function is given as the quadratic utility function, or the financial asset follows the multivariate normal distribution, a portfolio maximizing the agent’s expected utility function is given as a portfolio with minimum variance under a certain standard expected reward.
+
+The Capital Asset Pricing Model (CAPM) theory is a concept which is closely related to Markowitz’s portfolio (Sharpe, 1964; Mossin, 1966; Lintner, 1965). This theory theoretically explains the expected return of investors when the investor invests in a financial asset; that is, it derives the optimal price of the financial asset. To derive this theory, as well as Markowitz’s portfolio, we assume the quadratic utility function to the investors or the multivariate normal distribution to the financial assets.
+
+Merton (1969) extended the static portfolio selection problem to a dynamic case. Fishburn & Porter (1976) studied the sensitivity of the portfolio proportion when the safe and risky asset distributions change under the quadratic utility function. Thus, there are various studies investigating relationship between the utility function and risk-averse optimization (Tobin, 1958; Kroll et al., 1984; Bulmu¸s & Özekici, 2014; Bodnar et al., 2015).
+
+# A.2 EMPIRICAL STUDIES ON THE UTILITY FUNCTIONS
+
+The standard financial theory is built on the assumption that the economic agent has the quadratic utility function. For supporting this theory, there are several empirical studies to estimate the parameters of the quadratic utility function. Ziemba et al. (1974) investigated the change of the portfolio proportion when the parameter of the quadratic utility function changes using the Canadian financial dataset. Recently, Bodnar et al. (2018) investigate the risk parameter ( $\scriptstyle { \alpha }$ and $\beta$ in our formulation of the quadratic utility function) using the markets indexes in the world. They found that the utility function parameter depends on the market data model.
+
+![](images/74ad0b5e542099599c240748f8604c480f6c23f0ec0fcd58ad4987205970380f.jpg)  
+Figure 3: The AR and Var on the test environment. Higher AR and lower Var methods are Pareto efficient.
+
+# A.3 CRITICISM
+
+For the simple form of the quadratic utility function, the financial models based on the utility are widely accepted in practice. However, there is also criticism that the simple form cannot capture the real-world complicated utility function. For instance, Kallberg & Ziemba (1983) criticized the use of the quadratic utility function and proposed using a utility function, including higher moments. This study also provided empirical studies using U.S. financial dataset for investigating the properties of the alternative utility functions. However, to the best of our knowledge, financial practitioners still use financial models based on the quadratic utility function. We consider this is because the simple form gains the interpretability of the financial models.
+
+# B DETAILS OF EXPERIMENTS
+
+In this section, we show the additional experiments and describe the details of the experiments. To implement SPG and AC algorithms, we mainly follow the Pytorch example1.
+
+B.1 PARETO EFFICIENCY ON THE TEST ENVIRONMENT OF THE SYNTHETIC PORTFOLIO SELECTION DATASET
+
+For investigating the Pareto efficiency, we show the AR and Var of the train environment in Figure 2 of Section 5.1. Here, we also show the AR and Var of the test environment in Figure 3.
+
+# B.2 EXPERIMENTS USING THE SYNTHETIC AMERICAN-STYLE OPTION DATASET
+
+Among various options in finance, an American-style option refers to a contract that we can execute an option right at any time before the maturity time $\tau$ ; that is, a buyer who bought a call option has a right to buy the asset with the call option strike price $W _ { \mathrm { c a l l } }$ at any time; a buyer who bought a put option has a right to sell the with the call option strike price $W _ { \mathrm { p u t } }$ at any time.
+
+In the setting of Tamar et al. (2014) and Xie et al. (2018), the buyer simultaneously buy call and put options, which have the strike price $W _ { \mathrm { c a l l } } =$ and $W _ { \mathrm { p u t } } =$ , respectively. The maturity time is set as $\tau =$ . If the buyer executes the option at time $t$ , the buyer obtains a reward $r _ { t } = \mathrm { { \dot { m a x } } } ( 0 , W _ { \mathrm { { p u t } } } -$ ${ x } _ { t } ) + \operatorname* { m a x } ( 0 , { x } _ { t } - { W } _ { \mathrm { c a l l } } )$ , where $x _ { t }$ is an asset price. We set $x _ { 0 } = 1$ and define the stochastic process as follows: $x _ { t } = x _ { t - 1 } f _ { u }$ with probability 1 and $x _ { t } = x _ { t - 1 } f _ { d }$ with probability 1, where $f _ { u }$ and $f _ { d }$ . These parameters follows Xie et al. (2018). Under this setting, we investigate the performance of our EQUM. For the EQUM, we use $\zeta = 0 . 1 , 0 . 3 , 0 . 5 , 0 . 7 , 1 , 1 . 3$ . For the other settings, we follow the previous experiment for portfolio management.
+
+![](images/438ed18f4520292cff6d150b6798884961b9cac665dd068aa3299619687c602d.jpg)  
+Figure 4: The ARs and SDs in the training process of the experiment using the synthetic dataset.
+
+Table 4: The experimental results of the synthetic dataset with the ARs and SDs over 1000 trials.   
+Table 5: The experimental results of the synthetic dataset with the MSEs for $\zeta$ over 1000 trials.   
+
+<table><tr><td rowspan="2"></td><td rowspan="2">Standard s=0</td><td colspan="6">EQUM</td></tr><tr><td>S=0.1</td><td>=0.3</td><td>=0.5</td><td>=0.7</td><td>=1.0</td><td> = 1.3</td></tr><tr><td>AR</td><td>0.367</td><td>0.301</td><td>0.321</td><td>0.356</td><td>0.372</td><td>0.377</td><td>0.377</td></tr><tr><td>SD</td><td>0.307</td><td>0.275</td><td>0.285</td><td>0.306</td><td>0.317</td><td>0.318</td><td>0.320</td></tr></table>
+
+<table><tr><td rowspan="2"></td><td rowspan="2">Target Value</td><td rowspan="2">Standard =0</td><td colspan="6">EQUM</td></tr><tr><td>=0.1</td><td>=0.3</td><td>=0.5</td><td>=0.7</td><td>= 1.0</td><td>= 1.3</td></tr><tr><td rowspan="7">SPG</td><td>MSE from=0.1</td><td>0.072</td><td>0.041</td><td>0.050</td><td>0.067</td><td>0.076</td><td>0.078</td><td>0.078</td></tr><tr><td>=0.3</td><td>0.006</td><td>0.001</td><td>0.002</td><td>0.005</td><td>0.007</td><td>0.007</td><td>0.007</td></tr><tr><td>=0.5</td><td>0.019</td><td>0.040</td><td>0.033</td><td>0.022</td><td>0.018</td><td>0.017</td><td>0.017</td></tr><tr><td>S =0.7</td><td>0.112</td><td>0.160</td><td>0.145</td><td>0.120</td><td>0.109</td><td>0.106</td><td>0.106</td></tr><tr><td>S = 1.0</td><td>0.402</td><td>0.489</td><td>0.462</td><td>0.416</td><td>0.395</td><td>0.390</td><td>0.390</td></tr><tr><td>=1.3</td><td>0.872</td><td>0.999</td><td>0.960</td><td>0.893</td><td>0.862</td><td>0.854</td><td>0.853</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></table>
+
+In Figure 4, we calculate the average reward and standard deviation at each episode of the training process by conducting 1, 000 trials. In Table 4, using the trained model for the test environment, we show the average reward (AR) and standard deviation (SD) by conducting 1, 000 trials. We show the MSE between the realized reward and the target reward $\zeta$ in Table 5, where the lowest MSE method is highlighted in bold. As well as the experimental results with the synthetic portfolio dataset, we can confirm that the EQUM can control the risk well. In addition, as well as the experiments with CartPole and Atari games, we can observe that the EQUM also increases the expected reward contrary to our expectation.
+
+# B.3 DETAILS OF EXPERIMENTS OF PORTFOLIO OPTIMIZATION
+
+The real objective (minimizing variance with a penalty on return targeting) for Tamar, MVP and EQUM is shown in Table 6. Except for FF48’s MVP, the objective itself is smaller than EQUM’s. Since the values of objective is the same as the RR, we can empirically confirm that the better optimization, the better performance.
+
+We also divide the performance period into two for robustness checks. Table 7 shows the first-half results from July 2000 to June 2010 and the second-half results from July 2010 to June 2020. In almost all cases, the EQUM portfolio achieves the highest R/R.
+
+Table 6: The real objective (minimizing variance with a penalty on return targeting) for Tamar, MVP and EQUM for FF25 dataset (upper panel) , FF48 (middle panel) and FF100 (lower panel). Among the comparisons of the various portfolios, the best performance within each dataset is highlighted in bold.
+
+<table><tr><td rowspan=2 colspan=1></td><td rowspan=1 colspan=3>Tamar</td><td rowspan=1 colspan=3>MVP</td><td rowspan=1 colspan=3>EQUM</td></tr><tr><td rowspan=1 colspan=1>250</td><td rowspan=1 colspan=1>500</td><td rowspan=1 colspan=1>1000</td><td rowspan=1 colspan=1>10</td><td rowspan=1 colspan=1>100</td><td rowspan=1 colspan=1>1000</td><td rowspan=1 colspan=1>1/3</td><td rowspan=1 colspan=1>2/3</td><td rowspan=1 colspan=1>1</td></tr><tr><td rowspan=1 colspan=1>FF25</td><td rowspan=1 colspan=1>-5,359</td><td rowspan=1 colspan=1>-7,346</td><td rowspan=1 colspan=1>-7,444</td><td rowspan=1 colspan=1>-6,206</td><td rowspan=1 colspan=1>-6,206</td><td rowspan=1 colspan=1>-7,496</td><td rowspan=1 colspan=1>-8,857</td><td rowspan=1 colspan=1>-7,521</td><td rowspan=1 colspan=1>-7,620</td></tr><tr><td rowspan=1 colspan=1>FF48</td><td rowspan=1 colspan=1>-5,265</td><td rowspan=1 colspan=1>-7,252</td><td rowspan=1 colspan=1>-7,345</td><td rowspan=1 colspan=1>-6,384</td><td rowspan=1 colspan=1>-9,616</td><td rowspan=1 colspan=1>-7,369</td><td rowspan=1 colspan=1>-7,514</td><td rowspan=1 colspan=1>-8,343</td><td rowspan=1 colspan=1>-8,772</td></tr><tr><td rowspan=1 colspan=1>FF100</td><td rowspan=1 colspan=1>-6,600</td><td rowspan=1 colspan=1>-7,158</td><td rowspan=1 colspan=1>-6,042</td><td rowspan=1 colspan=1>-6,148</td><td rowspan=1 colspan=1>-5,327</td><td rowspan=1 colspan=1>-6,913</td><td rowspan=1 colspan=1>-8,269</td><td rowspan=1 colspan=1>-7,270</td><td rowspan=1 colspan=1>-9,650</td></tr></table>
+
+Table 7: The performance of each portfolio during first half out-of-sample period (from July 2000 to June 2010) and second half out-of-sample period (from July 2010 to June 2020) for FF25 dataset (upper panel) , FF48 (middle panel) and FF100 (lower panel). Among the comparisons of the various portfolios, the best performance within each dataset is highlighted in bold.   
+
+<table><tr><td rowspan=2 colspan=1>FF25</td><td rowspan=2 colspan=1>EW</td><td rowspan=2 colspan=1>MV</td><td rowspan=2 colspan=1>EGO</td><td rowspan=2 colspan=1>BLD</td><td rowspan=1 colspan=3>Tamar</td><td rowspan=1 colspan=3>MVP</td><td rowspan=1 colspan=3>EQUM</td></tr><tr><td rowspan=1 colspan=1>250</td><td rowspan=1 colspan=1>500</td><td rowspan=1 colspan=1>1000</td><td rowspan=1 colspan=1>10</td><td rowspan=1 colspan=1>100</td><td rowspan=1 colspan=1>1000</td><td rowspan=1 colspan=1>1/3</td><td rowspan=1 colspan=1>2/3</td><td rowspan=1 colspan=1>1</td></tr><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>First</td><td rowspan=1 colspan=1>HalfPeri</td><td rowspan=1 colspan=1>od(from</td><td rowspan=1 colspan=1>uly2000</td><td rowspan=1 colspan=1>toJune20</td><td rowspan=1 colspan=1>10）</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td></tr><tr><td rowspan=1 colspan=1>CR↑</td><td rowspan=1 colspan=1>69.36</td><td rowspan=1 colspan=1>-50.09</td><td rowspan=1 colspan=1>86.53</td><td rowspan=1 colspan=1>49.76</td><td rowspan=1 colspan=1>79.06</td><td rowspan=1 colspan=1>159.61</td><td rowspan=1 colspan=1>159.56</td><td rowspan=1 colspan=1>132.79</td><td rowspan=1 colspan=1>132.79</td><td rowspan=1 colspan=1>146.45</td><td rowspan=1 colspan=1>186.21</td><td rowspan=1 colspan=1>141.17</td><td rowspan=1 colspan=1>158.23</td></tr><tr><td rowspan=1 colspan=1>RISK↓</td><td rowspan=1 colspan=1>19.35</td><td rowspan=1 colspan=1>28.85</td><td rowspan=1 colspan=1>19.99</td><td rowspan=1 colspan=1>12.25</td><td rowspan=1 colspan=1>21.32</td><td rowspan=1 colspan=1>15.95</td><td rowspan=1 colspan=1>15.95</td><td rowspan=1 colspan=1>13.91</td><td rowspan=1 colspan=1>13.91</td><td rowspan=1 colspan=1>14.33</td><td rowspan=1 colspan=1>11.58</td><td rowspan=1 colspan=1>11.61</td><td rowspan=1 colspan=1>11.69</td></tr><tr><td rowspan=1 colspan=1>RR个</td><td rowspan=1 colspan=1>0.36</td><td rowspan=1 colspan=1>-0.17</td><td rowspan=1 colspan=1>0.43</td><td rowspan=1 colspan=1>0.41</td><td rowspan=1 colspan=1>0.37</td><td rowspan=1 colspan=1>1.00</td><td rowspan=1 colspan=1>1.00</td><td rowspan=1 colspan=1>0.95</td><td rowspan=1 colspan=1>0.95</td><td rowspan=1 colspan=1>1.02</td><td rowspan=1 colspan=1>1.61</td><td rowspan=1 colspan=1>1.22</td><td rowspan=1 colspan=1>1.35</td></tr><tr><td rowspan=1 colspan=1>MaxDD↓</td><td rowspan=1 colspan=1>0.54</td><td rowspan=1 colspan=1>0.75</td><td rowspan=1 colspan=1>0.57</td><td rowspan=1 colspan=1>0.37</td><td rowspan=1 colspan=1>0.33</td><td rowspan=1 colspan=1>0.31</td><td rowspan=1 colspan=1>0.31</td><td rowspan=1 colspan=1>0.22</td><td rowspan=1 colspan=1>0.22</td><td rowspan=1 colspan=1>0.21</td><td rowspan=1 colspan=1>0.13</td><td rowspan=1 colspan=1>0.14</td><td rowspan=1 colspan=1>0.18</td></tr><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>Secon</td><td rowspan=1 colspan=1>d-HalfPe</td><td rowspan=1 colspan=1>riod(from</td><td rowspan=1 colspan=1>July200</td><td rowspan=1 colspan=1>toJune</td><td rowspan=1 colspan=1>010）</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td></tr><tr><td rowspan=1 colspan=1>CR↑</td><td rowspan=1 colspan=1>121.99</td><td rowspan=1 colspan=1>75.71</td><td rowspan=1 colspan=1>123.23</td><td rowspan=1 colspan=1>84.45</td><td rowspan=1 colspan=1>151.96</td><td rowspan=1 colspan=1>126.73</td><td rowspan=1 colspan=1>127.33</td><td rowspan=1 colspan=1>83.16</td><td rowspan=1 colspan=1>83.16</td><td rowspan=1 colspan=1>97.43</td><td rowspan=1 colspan=1>113.97</td><td rowspan=1 colspan=1>52.96</td><td rowspan=1 colspan=1>85.70</td></tr><tr><td rowspan=1 colspan=1>RISK↓</td><td rowspan=1 colspan=1>17.64</td><td rowspan=1 colspan=1>21.14</td><td rowspan=1 colspan=1>18.30</td><td rowspan=1 colspan=1>11.73</td><td rowspan=1 colspan=1>26.76</td><td rowspan=1 colspan=1>23.71</td><td rowspan=1 colspan=1>23.70</td><td rowspan=1 colspan=1>23.43</td><td rowspan=1 colspan=1>23.43</td><td rowspan=1 colspan=1>13.56</td><td rowspan=1 colspan=1>14.97</td><td rowspan=1 colspan=1>12.62</td><td rowspan=1 colspan=1>17.56</td></tr><tr><td rowspan=1 colspan=1>RR↑</td><td rowspan=1 colspan=1>0.69</td><td rowspan=1 colspan=1>0.36</td><td rowspan=1 colspan=1>0.67</td><td rowspan=1 colspan=1>0.72</td><td rowspan=1 colspan=1>0.57</td><td rowspan=1 colspan=1>0.53</td><td rowspan=1 colspan=1>0.54</td><td rowspan=1 colspan=1>0.35</td><td rowspan=1 colspan=1>0.35</td><td rowspan=1 colspan=1>0.72</td><td rowspan=1 colspan=1>0.76</td><td rowspan=1 colspan=1>0.42</td><td rowspan=1 colspan=1>0.49</td></tr><tr><td rowspan=1 colspan=1>MaxDD↓</td><td rowspan=1 colspan=1>0.31</td><td rowspan=1 colspan=1>0.50</td><td rowspan=1 colspan=1>0.31</td><td rowspan=1 colspan=1>0.22</td><td rowspan=1 colspan=1>0.64</td><td rowspan=1 colspan=1>0.58</td><td rowspan=1 colspan=1>0.58</td><td rowspan=1 colspan=1>0.57</td><td rowspan=1 colspan=1>0.57</td><td rowspan=1 colspan=1>0.30</td><td rowspan=1 colspan=1>0.31</td><td rowspan=1 colspan=1>0.30</td><td rowspan=1 colspan=1>0.36</td></tr><tr><td rowspan=2 colspan=1>FF48</td><td rowspan=2 colspan=1>EW</td><td rowspan=2 colspan=1>MV</td><td rowspan=2 colspan=1>EGO</td><td rowspan=2 colspan=1>BLD</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>Tamar</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>MVP</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>EQUM</td><td rowspan=1 colspan=1></td></tr><tr><td rowspan=1 colspan=1>250</td><td rowspan=1 colspan=1>500</td><td rowspan=1 colspan=1>1000</td><td rowspan=1 colspan=1>10</td><td rowspan=1 colspan=1>100</td><td rowspan=1 colspan=1>1000</td><td rowspan=1 colspan=1>1/3</td><td rowspan=1 colspan=1>2/3</td><td rowspan=1 colspan=1>1</td></tr><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>First</td><td rowspan=1 colspan=1>HalfPeri</td><td rowspan=1 colspan=1>od(from</td><td rowspan=1 colspan=1>uly2000</td><td rowspan=1 colspan=1>toJune20</td><td rowspan=1 colspan=1>10）</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td></tr><tr><td rowspan=1 colspan=1>CR↑</td><td rowspan=1 colspan=1>72.02</td><td rowspan=1 colspan=1>49.11</td><td rowspan=1 colspan=1>89.90</td><td rowspan=1 colspan=1>41.26</td><td rowspan=1 colspan=1>119.64</td><td rowspan=1 colspan=1>64.99</td><td rowspan=1 colspan=1>78.38</td><td rowspan=1 colspan=1>209.60</td><td rowspan=1 colspan=1>185.42</td><td rowspan=1 colspan=1>195.13</td><td rowspan=1 colspan=1>118.40</td><td rowspan=1 colspan=1>127.62</td><td rowspan=1 colspan=1>163.23</td></tr><tr><td rowspan=1 colspan=1>RISK↓</td><td rowspan=1 colspan=1>17.61</td><td rowspan=1 colspan=1>26.27</td><td rowspan=1 colspan=1>21.72</td><td rowspan=1 colspan=1>11.48</td><td rowspan=1 colspan=1>8.48</td><td rowspan=1 colspan=1>9.03</td><td rowspan=1 colspan=1>6.61</td><td rowspan=1 colspan=1>19.73</td><td rowspan=1 colspan=1>17.21</td><td rowspan=1 colspan=1>18.11</td><td rowspan=1 colspan=1>21.49</td><td rowspan=1 colspan=1>8.83</td><td rowspan=1 colspan=1>8.96</td></tr><tr><td rowspan=1 colspan=1>RR↑</td><td rowspan=1 colspan=1>0.41</td><td rowspan=1 colspan=1>0.19</td><td rowspan=1 colspan=1>0.41</td><td rowspan=1 colspan=1>0.36</td><td rowspan=1 colspan=1>1.41</td><td rowspan=1 colspan=1>0.72</td><td rowspan=1 colspan=1>1.19</td><td rowspan=1 colspan=1>1.06</td><td rowspan=1 colspan=1>1.08</td><td rowspan=1 colspan=1>1.08</td><td rowspan=1 colspan=1>0.55</td><td rowspan=1 colspan=1>1.45</td><td rowspan=1 colspan=1>1.82</td></tr><tr><td rowspan=1 colspan=1>MaxDD↓</td><td rowspan=1 colspan=1>0.53</td><td rowspan=1 colspan=1>0.58</td><td rowspan=1 colspan=1>0.53</td><td rowspan=1 colspan=1>0.38</td><td rowspan=1 colspan=1>0.05</td><td rowspan=1 colspan=1>0.15</td><td rowspan=1 colspan=1>0.04</td><td rowspan=1 colspan=1>0.25</td><td rowspan=1 colspan=1>0.24</td><td rowspan=1 colspan=1>0.21</td><td rowspan=1 colspan=1>0.45</td><td rowspan=1 colspan=1>0.15</td><td rowspan=1 colspan=1>0.05</td></tr><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>Secor</td><td rowspan=1 colspan=1>d-HalfPe</td><td rowspan=1 colspan=1>riod(from</td><td rowspan=1 colspan=1>July200</td><td rowspan=1 colspan=1>toJune</td><td rowspan=1 colspan=1>2010)</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td></tr><tr><td rowspan=1 colspan=1>CR↑</td><td rowspan=1 colspan=1>122.71</td><td rowspan=1 colspan=1>-14.30</td><td rowspan=1 colspan=1>159.25</td><td rowspan=1 colspan=1>83.19</td><td rowspan=1 colspan=1>1.32</td><td rowspan=1 colspan=1>123.11</td><td rowspan=1 colspan=1>72.27</td><td rowspan=1 colspan=1>135.12</td><td rowspan=1 colspan=1>148.24</td><td rowspan=1 colspan=1>15.86</td><td rowspan=1 colspan=1>107.99</td><td rowspan=1 colspan=1>118.99</td><td rowspan=1 colspan=1>73.20</td></tr><tr><td rowspan=1 colspan=1>RISK↓</td><td rowspan=1 colspan=1>15.45</td><td rowspan=1 colspan=1>33.97</td><td rowspan=1 colspan=1>17.06</td><td rowspan=1 colspan=1>9.96</td><td rowspan=1 colspan=1>16.46</td><td rowspan=1 colspan=1>19.10</td><td rowspan=1 colspan=1>19.75</td><td rowspan=1 colspan=1>27.53</td><td rowspan=1 colspan=1>25.70</td><td rowspan=1 colspan=1>21.88</td><td rowspan=1 colspan=1>17.97</td><td rowspan=1 colspan=1>19.88</td><td rowspan=1 colspan=1>13.87</td></tr><tr><td rowspan=1 colspan=1>RR↑</td><td rowspan=1 colspan=1>0.79</td><td rowspan=1 colspan=1>-0.04</td><td rowspan=1 colspan=1>0.93</td><td rowspan=1 colspan=1>0.84</td><td rowspan=1 colspan=1>0.01</td><td rowspan=1 colspan=1>0.64</td><td rowspan=1 colspan=1>0.37</td><td rowspan=1 colspan=1>0.49</td><td rowspan=1 colspan=1>0.58</td><td rowspan=1 colspan=1>0.07</td><td rowspan=1 colspan=1>0.60</td><td rowspan=1 colspan=1>0.60</td><td rowspan=1 colspan=1>0.53</td></tr><tr><td rowspan=1 colspan=1>MaxDD↓</td><td rowspan=1 colspan=1>0.26</td><td rowspan=1 colspan=1>0.84</td><td rowspan=1 colspan=1>0.28</td><td rowspan=1 colspan=1>0.17</td><td rowspan=1 colspan=1>0.58</td><td rowspan=1 colspan=1>0.54</td><td rowspan=1 colspan=1>0.45</td><td rowspan=1 colspan=1>0.56</td><td rowspan=1 colspan=1>0.52</td><td rowspan=1 colspan=1>0.65</td><td rowspan=1 colspan=1>0.32</td><td rowspan=1 colspan=1>0.45</td><td rowspan=1 colspan=1>0.29</td></tr><tr><td rowspan=2 colspan=1>FF100</td><td rowspan=2 colspan=1>EW</td><td rowspan=2 colspan=1>MV</td><td rowspan=2 colspan=1>EGO</td><td rowspan=2 colspan=1>BLD</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>Tamar</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>MVP</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>EQUM</td><td rowspan=1 colspan=1></td></tr><tr><td rowspan=1 colspan=1>250</td><td rowspan=1 colspan=1>500</td><td rowspan=1 colspan=1>1000</td><td rowspan=1 colspan=1>10</td><td rowspan=1 colspan=1>100</td><td rowspan=1 colspan=1>1000</td><td rowspan=1 colspan=1>1/3</td><td rowspan=1 colspan=1>2/3</td><td rowspan=1 colspan=1>1</td></tr><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>First</td><td rowspan=1 colspan=1>HalfPeri</td><td rowspan=1 colspan=1>od(from</td><td rowspan=1 colspan=1>uly2000</td><td rowspan=1 colspan=1>toJune20</td><td rowspan=1 colspan=1>10）</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td></tr><tr><td rowspan=1 colspan=1>CR↑</td><td rowspan=1 colspan=1>73.25</td><td rowspan=1 colspan=1>-44.84</td><td rowspan=1 colspan=1>87.78</td><td rowspan=1 colspan=1>48.85</td><td rowspan=1 colspan=1>143.26</td><td rowspan=1 colspan=1>146.59</td><td rowspan=1 colspan=1>166.74</td><td rowspan=1 colspan=1>218.62</td><td rowspan=1 colspan=1>55.87</td><td rowspan=1 colspan=1>170.36</td><td rowspan=1 colspan=1>215.59</td><td rowspan=1 colspan=1>142.66</td><td rowspan=1 colspan=1>199.92</td></tr><tr><td rowspan=1 colspan=1>RISK↓</td><td rowspan=1 colspan=1>19.60</td><td rowspan=1 colspan=1>30.86</td><td rowspan=1 colspan=1>20.53</td><td rowspan=1 colspan=1>12.21</td><td rowspan=1 colspan=1>16.99</td><td rowspan=1 colspan=1>11.21</td><td rowspan=1 colspan=1>18.45</td><td rowspan=1 colspan=1>20.52</td><td rowspan=1 colspan=1>31.72</td><td rowspan=1 colspan=1>22.13</td><td rowspan=1 colspan=1>13.03</td><td rowspan=1 colspan=1>12.69</td><td rowspan=1 colspan=1>13.11</td></tr><tr><td rowspan=1 colspan=1>RR↑</td><td rowspan=1 colspan=1>0.37</td><td rowspan=1 colspan=1>-0.15</td><td rowspan=1 colspan=1>0.43</td><td rowspan=1 colspan=1>0.40</td><td rowspan=1 colspan=1>0.84</td><td rowspan=1 colspan=1>1.31</td><td rowspan=1 colspan=1>0.90</td><td rowspan=1 colspan=1>1.07</td><td rowspan=1 colspan=1>0.18</td><td rowspan=1 colspan=1>0.77</td><td rowspan=1 colspan=1>1.65</td><td rowspan=1 colspan=1>1.12</td><td rowspan=1 colspan=1>1.52</td></tr><tr><td rowspan=1 colspan=1>MaxDD↓</td><td rowspan=1 colspan=1>0.55</td><td rowspan=1 colspan=1>0.72</td><td rowspan=1 colspan=1>0.58</td><td rowspan=1 colspan=1>0.36</td><td rowspan=1 colspan=1>0.39</td><td rowspan=1 colspan=1>0.18</td><td rowspan=1 colspan=1>0.27</td><td rowspan=1 colspan=1>0.46</td><td rowspan=1 colspan=1>0.46</td><td rowspan=1 colspan=1>0.31</td><td rowspan=1 colspan=1>0.11</td><td rowspan=1 colspan=1>0.15</td><td rowspan=1 colspan=1>0.16</td></tr><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>Secor</td><td rowspan=1 colspan=1>d-HalfPe</td><td rowspan=1 colspan=1>iod(from</td><td rowspan=1 colspan=1>July 200</td><td rowspan=1 colspan=1>toJune</td><td rowspan=1 colspan=1>2010)</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td></tr><tr><td rowspan=1 colspan=1>CR↑</td><td rowspan=1 colspan=1>120.66</td><td rowspan=1 colspan=1>79.10</td><td rowspan=1 colspan=1>119.59</td><td rowspan=1 colspan=1>79.07</td><td rowspan=1 colspan=1>171.50</td><td rowspan=1 colspan=1>91.69</td><td rowspan=1 colspan=1>105.37</td><td rowspan=1 colspan=1>75.45</td><td rowspan=1 colspan=1>172.66</td><td rowspan=1 colspan=1>148.55</td><td rowspan=1 colspan=1>46.95</td><td rowspan=1 colspan=1>84.39</td><td rowspan=1 colspan=1>127.25</td></tr><tr><td rowspan=1 colspan=1>RISK↓</td><td rowspan=1 colspan=1>17.87</td><td rowspan=1 colspan=1>20.76</td><td rowspan=1 colspan=1>18.86</td><td rowspan=1 colspan=1>11.55</td><td rowspan=1 colspan=1>22.25</td><td rowspan=1 colspan=1>16.88</td><td rowspan=1 colspan=1>21.56</td><td rowspan=1 colspan=1>24.87</td><td rowspan=1 colspan=1>30.91</td><td rowspan=1 colspan=1>23.62</td><td rowspan=1 colspan=1>13.18</td><td rowspan=1 colspan=1>14.47</td><td rowspan=1 colspan=1>17.52</td></tr><tr><td rowspan=1 colspan=1>RR↑</td><td rowspan=1 colspan=1>0.68</td><td rowspan=1 colspan=1>0.38</td><td rowspan=1 colspan=1>0.63</td><td rowspan=1 colspan=1>0.68</td><td rowspan=1 colspan=1>0.77</td><td rowspan=1 colspan=1>0.54</td><td rowspan=1 colspan=1>0.49</td><td rowspan=1 colspan=1>0.30</td><td rowspan=1 colspan=1>0.56</td><td rowspan=1 colspan=1>0.63</td><td rowspan=1 colspan=1>0.36</td><td rowspan=1 colspan=1>0.58</td><td rowspan=1 colspan=1>0.73</td></tr><tr><td rowspan=1 colspan=1>MaxDD↓</td><td rowspan=1 colspan=1>0.32</td><td rowspan=1 colspan=1>0.35</td><td rowspan=1 colspan=1>0.31</td><td rowspan=1 colspan=1>0.22</td><td rowspan=1 colspan=1>0.38</td><td rowspan=1 colspan=1>0.49</td><td rowspan=1 colspan=1>0.38</td><td rowspan=1 colspan=1>0.50</td><td rowspan=1 colspan=1>0.65</td><td rowspan=1 colspan=1>0.46</td><td rowspan=1 colspan=1>0.24</td><td rowspan=1 colspan=1>0.31</td><td rowspan=1 colspan=1>0.39</td></tr></table>
+
+# B.4 DETAILS OF EXPERIMENTS WITH CARPOLE AND ATARI GAMES
+
+In this section, we report the experimental performances of the proposed EQUM framework with well-known benchmarks. We investigate how the behaviors of existing RL methods are changed by adding the additional $\mathbb { E } [ R ^ { 2 } ]$ term. We use a simple two-layer perceptron for modeling the policy following the Pytorch example (Paszke et al., 2019). For the SPG-based algorithms, we define the cumulative reward as finite sum with $\gamma = 1$ following (Tamar et al., 2012). For the AC-based algorithms, we define the cumulative reward as infinite sum with $\gamma = 0 . 9 9$ following (Prashanth & Ghavamzadeh, 2013). For the SPG-based algorithms, we define the cumulative reward as finite sum with $\gamma = 1$ following (Tamar et al., 2012). For the AC-based algorithms, we define the cumulative reward as infinite sum with $\gamma = 0 . 9 9$ following (Prashanth & Ghavamzadeh, 2013).
+
+# B.4.1 SENSITIVITY ANALYSIS ON $\psi$
+
+First, we investigate the sensitivity of the EQUM framework to the parameter $\psi$ using the CartPole. We apply the SPG and AC methods (Section 4.3) with the EQUM framework to the Cartpole problem, which is a classic control problem. We use $\psi = 0 . 0 0 1 , 0 . 0 0 2 , 0 . 0 0 3 , 0 . 0 0 5 , 0 . 0 1 , 0 . 1$ and compare the results with the standard SPG and AC methods. For instance, from the targeting optimization perspective, EQUM with $\psi = 0 . 0 0 1$ is equal to minimize the MSE between the cumulative reward and $\zeta ^ { \circ } = 5 0 0 = 1 / ( 2 * 0 . 0 0 1 )$ . We train the model by 300 episodes. We calculate the average reward and standard deviation at each period by conducting 300 trials. The results are shown in Figure 5. In the SPG results, we can confirm the mean-variance trade-off. In contrast, in the SPG with $\psi = 0 . 0 0 1$ and all AC results, the EQUM framework improves the expected cumulative reward. These results are contrary to our expectations because MVRL methods typically decrease the expected cumulative return to decrease the variance. We discuss this topic in more detail in Section 5.3.
+
+![](images/523890089189957b9fa29fa5c234056bb7d7b18322e3bd33037d0e1e7ee7f348.jpg)  
+Figure 5: Sensitivity analysis regarding $\psi$ . The upper two graphs are the results using the SPG-based method and the lower two graphs are the results using the AC-based algorithms. The average reward of the SPG result with $\psi = 0 . 1$ is lower than 80, and we do not show the result here.
+
+# B.4.2 EXPERIMENTS OF ATARI GAMES
+
+When playing games, we often consider risk-control while maintaining a certain level of reward. Under this motivation, we benchmark the proposed EQUM framework on four Atari game tasks from the OpenAI gym (Brockman et al., 2016). Among the games, we choose BeamRider, Seaquest, Qbert, and SpaceInvaders in which SPG and AC methods work well. We use simplified environments in which the observations are the RAM of the Atari machine, consisting of only 128 bytes. We compare our methods with the standard SPG, and MVLR methods of Tamar et al. (2012) and Xie et al. (2018). We calculate the average reward (AR) at the last episode over 5 trials and the standard deviation (SD). In Table 8, we show the results of the SPG algorithm with the standard setting and EQUM framework, where $\psi$ is chosen from 0.001, 0.003, 0.005, 0.01, 0.03, and 0.3. Note that when using $\psi = 0 . 0 0 5$ , it is equal to minimize the MSE between the expected cumulative reward and the target 100. In almost all cases, the EQUM framework shows the better AR than the standard methods. As well as the previous sensitivity experiment, this result is contrary to our expectation. Among the games, we choose simplified BeamRider, Seaquest, Qbert, and SpaceInvaders in which the SPG algorithm work well, and the observations are the RAM of the Atari machine, consisting of only 128 bytes. We compare our methods with the standard SPG algorithms, and MVRL methods of Tamar et al. (2012) and Xie et al. (2018). We denote the SPG-based methods proposed by Tamar et al. (2012) and Xie et al. (2018) as Tamar and MVP, respectively. We calculate the average reward (AR) at the last episode over 5 trials and the standard deviation (SD). We choose the parameter of Tamar from 200 and 2000, which is denoted as $b$ in Tamar et al. (2012). We choose the parameter of MVP from 1 and 10, which is denoted as $\lambda$ in Tamar et al. (2012). The parameters are denoted as param in Table 8.
+
+Table 8: The results on Atari games with SPG-based methods.. The highest ARs and lowest SDs are highlighted in bold.   
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">SPG</td><td colspan="10">EQUMwith SPG =0.003</td><td colspan="6">Tamar param: 2000</td><td colspan="4">MVP</td></tr><tr><td></td><td></td><td>ψ= 0.001</td><td></td><td></td><td></td><td></td><td>ψ=0.005</td><td></td><td>ψ=0.01</td><td></td><td>ψ=0.03</td><td></td><td>=0.3</td><td></td><td></td><td></td><td></td><td>param: 20000</td><td>param: 1</td><td></td><td>param: 10</td><td></td></tr><tr><td>Game</td><td>AR</td><td>SD</td><td>AR</td><td>SD</td><td>AR</td><td>SD</td><td>AR</td><td>SD</td><td>AR</td><td>SD</td><td>AR</td><td>SD</td><td></td><td>AR</td><td>SD</td><td>AR</td><td>SD</td><td>AR</td><td>SD</td><td>AR</td><td>SD</td><td>AR</td><td>SD</td></tr><tr><td>BeamRider</td><td>99.6</td><td>315.0</td><td>165.6</td><td>358.0</td><td>136.8</td><td>288.6</td><td>265.2</td><td>436.7</td><td>397.2</td><td>436.3</td><td>165.6</td><td>358.0</td><td>136.8</td><td></td><td>288.6</td><td>189.6</td><td>400.4</td><td>99.6</td><td>315.0</td><td>4.4</td><td>13.9</td><td>180.0</td><td>379.5</td></tr><tr><td>Seaquest</td><td>26.0</td><td>59.7</td><td>26.0</td><td>59.7</td><td>26.0</td><td>59.7</td><td>34.0</td><td>61.1</td><td>50.0</td><td>60.6</td><td>16.0</td><td>33.7</td><td></td><td>26.0</td><td>42.2</td><td>32.0</td><td>41.3</td><td>26.0</td><td>59.7</td><td>42.0</td><td>61.4</td><td>42.0</td><td>61.4</td></tr><tr><td>Qbert</td><td>40.0</td><td>64.8</td><td>15.0</td><td>47.4</td><td>55.0</td><td>71.5</td><td>40.0</td><td>64.8</td><td>27.5</td><td>58.3</td><td>15.0</td><td>47.4</td><td></td><td>0.0</td><td>0.0</td><td>40.0</td><td>64.8</td><td>15.0</td><td>47.4</td><td>50.0</td><td>64.5</td><td>50.0</td><td>64.5</td></tr><tr><td>SpaceInvaders</td><td>169.5</td><td>146.0</td><td>168.0</td><td>144.7</td><td>171.0</td><td>147.2</td><td>109.5</td><td>141.4</td><td>139.5</td><td>147.1</td><td>165.0</td><td>142.1</td><td>139.5</td><td></td><td>147.1</td><td>169.5</td><td>146.0</td><td>169.5</td><td>146.0</td><td>169.5</td><td>146.0</td><td>169.5</td><td>146.0</td></tr></table>

parse/train/Hyg_X2C5FX/Hyg_X2C5FX.md

@@ -0,0 +1,369 @@
+# GAN DISSECTION: VISUALIZING AND UNDERSTANDING GENERATIVE ADVERSARIAL NETWORKS
+
+David $\mathbf { B a u } ^ { 1 , 2 }$ , Jun-Yan $\mathbf { Z } \mathbf { h } \mathbf { u } ^ { \mathbf { 1 } }$ , Hendrik Strobelt2,3, Bolei Zhou4, Joshua B. Tenenbaum1, William T. Freeman1, Antonio Torralba1,2 1Massachusetts Institute of Technology, 2MIT-IBM Watson AI Lab, 3IBM Research, 4The Chinese University of Hong Kong
+
+# ABSTRACT
+
+Generative Adversarial Networks (GANs) have recently achieved impressive results for many real-world applications, and many GAN variants have emerged with improvements in sample quality and training stability. However, they have not been well visualized or understood. How does a GAN represent our visual world internally? What causes the artifacts in GAN results? How do architectural choices affect GAN learning? Answering such questions could enable us to develop new insights and better models.
+
+In this work, we present an analytic framework to visualize and understand GANs at the unit-, object-, and scene-level. We first identify a group of interpretable units that are closely related to object concepts using a segmentation-based network dissection method. Then, we quantify the causal effect of interpretable units by measuring the ability of interventions to control objects in the output. We examine the contextual relationship between these units and their surroundings by inserting the discovered object concepts into new images. We show several practical applications enabled by our framework, from comparing internal representations across different layers, models, and datasets, to improving GANs by locating and removing artifact-causing units, to interactively manipulating objects in a scene. We provide open source interpretation tools to help researchers and practitioners better understand their GAN models.
+
+# 1 INTRODUCTION
+
+Generative Adversarial Networks (GANs) (Goodfellow et al., 2014) have been able to produce photorealistic images, often indistinguishable from real images. This remarkable ability has powered many real-world applications ranging from visual recognition (Wang et al., 2017), to image manipulation (Isola et al., 2017; Zhu et al., 2017), to video prediction (Mathieu et al., 2016). Since their invention in 2014, many GAN variants have been proposed (Radford et al., 2016; Zhang et al., 2018a), often producing more realistic and diverse samples with better training stability.
+
+Despite this tremendous success, many questions remain to be answered. For example, to produce a church image (Figure 1a), what knowledge does a GAN need to learn? Alternatively, when a GAN sometimes produces terribly unrealistic images (Figure 1f), what causes the mistakes? Why does one GAN variant work better than another? What fundamental differences are encoded in their weights?
+
+In this work, we study the internal representations of GANs. To a human observer, a well-trained GAN appears to have learned facts about the objects in the image: for example, a door can appear on a building but not on a tree. We wish to understand how a GAN represents such structure. Do the objects emerge as pure pixel patterns without any explicit representation of objects such as doors and trees, or does the GAN contain internal variables that correspond to the objects that humans perceive? If the GAN does contain variables for doors and trees, do those variables cause the generation of those objects, or do they merely correlate? How are relationships between objects represented?
+
+![](images/3464bf4447b0d8bd276280c2e276dc1e7cdef1a0bf23e3968844ab35d3d7c5f1.jpg)  
+Figure 1: Overview: (a) Realistic outdoor church images generated by Progressive GANs (Karras et al., 2018). (b) Given a pre-trained GAN model, we identify a set of interpretable units whose featuremap is correlated to an object class across different images. For example, one unit in layer4 localizes tree regions with diverse visual appearance. (c) We force the activation of the units to be zero and quantify the average casual effect of the ablation. Here we successfully remove trees from church images. (d) We activate tree causal units in other locations. These same units synthesize new trees, visually compatible with their surrounding context. In addition, our method can diagnose and improve GANs by identifying artifact-causing units (e). We can remove the artifacts that appear (f) and significantly improve the results by ablating the “artifact” units (g). Please see our demo video.
+
+We present a general method for visualizing and understanding GANs at different levels of abstraction, from each neuron, to each object, to the contextual relationship between different objects. We first identify a group of interpretable units that are related to object concepts (Figure 1b). These units’ featuremaps closely match the semantic segmentation of a particular object class (e.g., trees). Second, we directly intervene within the network to identify sets of units that cause a type of objects to disappear (Figure 1c) or appear (Figure 1d). We quantify the causal effect of these units using a standard causality metric. Finally, we examine the contextual relationship between these causal object units and the background. We study where we can insert object concepts in new images and how this intervention interacts with other objects in the image (Figure 1d). To our knowledge, our work provides the first systematic analysis for understanding the internal representations of GANs.
+
+Finally, we show several practical applications enabled by this analytic framework, from comparing internal representations across different layers, GAN variants and datasets; to debugging and improving GANs by locating and ablating “artifact” units (Figure 1e); to understanding contextual relationships between objects in scenes; to manipulating images with interactive object-level control.
+
+# 2 RELATED WORK
+
+Generative Adversarial Networks. The quality and diversity of results from GANs (Goodfellow et al., 2014) has continued to improve, from generating simple digits and faces (Goodfellow et al., 2014), to synthesizing natural scene images (Radford et al., 2016; Denton et al., 2015), to generating 1k photorealistic portraits (Karras et al., 2018), to producing one thousand object classes (Miyato et al., 2018; Zhang et al., 2018a). GANs have also enabled applications such as visual recognition (Wang et al., 2017; Hoffman et al., 2018), image manipulation (Isola et al., 2017; Zhu et al., 2017), and video generation (Mathieu et al., 2016; Wang et al., 2018). Despite the successes, little work has been done to visualize what GANs have learned. Prior work (Radford et al., 2016; Zhu et al., 2016; Brock et al., 2017) manipulates latent vectors and observes how the results change accordingly.
+
+![](images/cb9a6b5396be6a88518313ffff2657b31f04a5a62fed33f50532c978fb4c526d.jpg)  
+Figure 2: Measuring the relationship between representation units and trees in the output using (a) dissection and (b) intervention. Dissection measures agreement between a unit $u$ and a concept $c$ by comparing its thresholded upsampled heatmap with a semantic segmentation of the generated image $s _ { c } ( x )$ . Intervention measures the causal effect of a set of units $U$ on a concept $c$ by comparing the effect of forcing these units on (unit insertion) and off (unit ablation). The segmentation $s _ { c }$ reveals that trees increase after insertion and decrease after ablation. The average difference in the tree pixels measures the average causal effect. In this figure, interventions are applied to the entire featuremap $\mathbb { P }$ , but insertions and ablations can also apply to any subset of pixels $\mathrm { \bf P } \subset \mathbb { P }$ .
+
+Visualizing deep neural networks. A CNN can be visualized by reconstructing salient image features (Simonyan et al., 2014; Mahendran & Vedaldi, 2015) or by mining patches that maximize hidden layers’ activations (Zeiler & Fergus, 2014); or we can synthesize input images to invert a feature layer (Dosovitskiy & Brox, 2016). Alternately, we can identify the semantics of each unit (Zhou et al., 2015; Bau et al., 2017; Zhou et al., 2018a) by measuring agreement between unit activations and object segmentation masks, or by training a network to increase interpretability of such units (Zhang et al., 2018b). Visualization of an RNN has also revealed interpretable units that track long-range dependencies (Karpathy et al., 2016; Strobelt et al., 2018). Most previous work on network visualization has focused on networks trained for classification; our work explores deep generative models trained for image generation.
+
+Understanding neural representation in biology. Studies of biological neural networks find evidence of both local representations in which individual neurons are selective for meaningful concepts (Quiroga, 2012), as well as distributed representations in which individual neurons are essentially meaningless (Yuste, 2015). Computational models of biological learning (Bowers et al., 2016; Dasgupta et al., 2018) find sparse and local representations can aid generalization to novel stimuli.
+
+Explaining the decisions of deep neural networks. Individual network decisions can be explained using informative heatmaps (Zhou et al., 2018b; 2016; Selvaraju et al., 2017) or by scoring salience (Simonyan et al., 2014; Bach et al., 2015; Sundararajan et al., 2017; Lundberg & Lee, 2017). Such analyses reveals which inputs contribute most to a categorical prediction by a network. Recent work has also studied the contribution of feature vectors (Kim et al., 2017; Zhou et al., 2018b) or individual channels (Olah et al., 2018) to a final prediction, and Morcos et al. (2018) has examined the effect of individual units by ablating them. Those methods explain discriminative classifiers. Our method aims to explain how an image can be generated by a network, which is much less explored.
+
+# 3 METHOD
+
+Our goal is to analyze how objects such as trees are encoded by the internal representations of a GAN generator $G \colon { \mathbf { z } }  { \mathbf { x } }$ . Here $\mathbf { z } \in \mathbb { R } ^ { | z | }$ denotes a latent vector sampled from a low-dimensional distribution, and $\mathbf { x } \in \mathbb { R } ^ { H \times W \times 3 }$ denotes an $H \times W$ generated image. We use representation to
+
+![](images/c336fa265ed423129426a5cb9cdb5a33d82cc0eb3bec4a42642967fd0a8ffcf7.jpg)
+
+Thresholding unit #65 layer 3 of a dining room generator matches ‘table’ segmentations with $\mathrm { I o U } { = } 0 . 3 4$ .
+
+![](images/6eca35238c9ed4fa28c21db3105eaa38efe24c43cd3e1ee9e20fd974ef3a322c.jpg)  
+Thresholding unit #37 layer 4 of a living room generator matches ‘sofa’ segmentations with $\mathrm { I o U } { = } 0 . 2 9$ .   
+Figure 3: Visualizing the activations of individual units in two GANs. Top ten activating images are shown, and IoU is measured over a sample of 1000 images. In each image, the unit feature is upsampled and thresholded as described in Eqn. 2.
+
+describe the tensor r output from a particular layer of the generator $G$ , where the generator creates an image x from random $\mathbf { z }$ through a composition of layers: $\mathbf { r } = h ( \mathbf { z } )$ and $\mathbf { x } = f ( \mathbf { r } ) \bar { = } f ( h ( \mathbf { z } ) ) = G ( \mathbf { z } )$
+
+Since r has all the data necessary to produce the image $\mathbf { x } = f ( \mathbf { r } )$ , r certainly contains the information to deduce the presence of any visible class $c$ in the image. Therefore the question we ask is not whether information about $c$ is present in $\mathbf { r }$ — it is — but how such information is encoded in r. In particular, for any class from a universe of concepts $c \in \mathbb { C }$ , we seek to understand whether r explicitly represents $c$ in some way where it is possible to factor $\mathbf { r }$ at locations $\mathrm { \bf P }$ into two components
+
+$$
+{ \bf r } _ { \mathbb { U } , \mathrm { P } } = ( { \bf r } _ { \mathrm { U } , \mathrm { P } } , { \bf r } _ { \overline { { \mathrm { U } } } , \mathrm { P } } ) ,
+$$
+
+where the generation of the object $c$ at locations $\mathrm { \bf P }$ depends mainly on the units $\mathbf { r } _ { \mathrm { U , P } }$ , and is insensitive to the other units $\mathbf { r } _ { \overline { { \mathbf { U } } } , \mathbf { P } }$ . Here we refer to each channel of the featuremap as a unit: U denotes the set of unit indices of interest and $\overline { { \mathrm { ~ U ~ } } }$ is its complement; we will write $\mathbb { U }$ and $\mathbb { P }$ to refer to the entire set of units and featuremap pixels in $r$ . We study the structure of $\mathbf { r }$ in two phases:
+
+• Dissection: starting with a large dictionary of object classes, we identify the classes that have an explicit representation in $\mathbf { r }$ by measuring the agreement between individual units of $\mathbf { r }$ and every class $c$ (Figure 1b).   
+• Intervention: for the represented classes identified through dissection, we identify causal sets of units and measure causal effects between units and object classes by forcing sets of units on and off (Figure 1c,d).
+
+# 3.1 CHARACTERIZING UNITS BY DISSECTION
+
+We first focus on individual units of the representation. Recall that $\mathbf { r } _ { u , \mathbb { P } }$ is the one-channel $h \times w$ featuremap of unit $u$ in a convolutional generator, where $h \times w$ is typically smaller than the image size. We want to know if a specific unit $\mathbf { r } _ { u , \mathbb { P } }$ encodes a semantic class such as a “tree”. For image classification networks, Bau et al. (2017) has observed that many units can approximately locate emergent object classes when the units are upsampled and thresholded. In that spirit, we select a universe of concepts $c \in \mathbb { C }$ for which we have a semantic segmentation ${ \bf s } _ { c } ( { \bf x } )$ for each class. Then we quantify the spatial agreement between the unit $u$ ’s thresholded featuremap and a concept $c$ ’s segmentation with the following intersection-over-union (IoU) measure:
+
+$$
+\mathrm { I o U } _ { u , c } \equiv \frac { \mathbb { E } _ { \mathbf { z } } \left| ( \mathbf { r } _ { u , \mathbb { P } } ^ { \uparrow } > t _ { u , c } ) \wedge \mathbf { s } _ { c } ( \mathbf { x } ) \right| } { \mathbb { E } _ { \mathbf { z } } \left| ( \mathbf { r } _ { u , \mathbb { P } } ^ { \uparrow } > t _ { u , c } ) \vee \mathbf { s } _ { c } ( \mathbf { x } ) \right| } , \mathrm { w h e r e ~ } t _ { u , c } = \arg \operatorname* { m a x } _ { t } \frac { \mathrm { I } ( \mathbf { r } _ { u , \mathbb { P } } ^ { \uparrow } > t ; \mathbf { s } _ { c } ( \mathbf { x } ) ) } { \mathrm { H } ( \mathbf { r } _ { u , \mathbb { P } } ^ { \uparrow } > t , \mathbf { s } _ { c } ( \mathbf { x } ) ) } ,
+$$
+
+where $\wedge$ and $\vee$ denote intersection and union operations, and $\mathbf { x } = G ( \mathbf { z } )$ denotes the image generated from $\mathbf { z }$ . The one-channel feature map $\mathbf { r } _ { u , \mathbb { P } }$ slices the entire featuremap $\mathbf { \hat { r } } = h ( \mathbf { z } )$ at unit $u$ . As shown in Figure 2a, we upsample $\mathbf { r } _ { u , \mathbb { P } }$ to the output image resolution as $\mathbf { r } _ { u , \mathbb { P } } ^ { \uparrow }$ P. (r↑u,P > tu,c) produces a binary mask by thresholding the $\mathbf { r } _ { u , \mathbb { P } } ^ { \uparrow }$ at a fixed level $t _ { u , c }$ . ${ \bf s } _ { c } ( { \bf x } )$ is a binary mask where each pixel indicates the presence of class $c$ in the generated image $\mathbf { x }$ . The threshold $t _ { u , c }$ is chosen to be informative as possible by maximizing the information quality ratio $\mathrm { I / H }$ (using a separate validation set), that is, it maximizes the portion of the joint entropy $_ \mathrm { H }$ which is mutual information I (Wijaya et al., 2017).
+
+We can use $\mathrm { I o U } _ { u , c }$ to rank the concepts related to each unit and label each unit with the concept that matches it best. Figure 3 shows examples of interpretable units with high $\mathrm { I o U } _ { u , c }$ . They are not the only units to match tables and sofas: layer3 of the dining room generator has 31 units (of 512) that match tables and table parts, and layer4 of the living room generator has 65 (of 512) sofa units.
+
+![](images/780ef8f97ca06fc19fbda82fc54bce0e7414e4eeadbec64d32ea873d6d7729de.jpg)  
+Figure 4: Ablating successively larger sets of tree-causal units from a GAN trained on LSUN outdoor church images, showing that the more units are removed, the more trees are reduced, while buildings remain. The choice of units to ablate is specific to the tree class and does not depend on the image. At right, the causal effect of removing successively more tree units is plotted, comparing units chosen to optimize the average causal effect (ACE) and units chosen with the highest IoU for trees.
+
+Once we have identified an object class that a set of units match closely, we next ask: which units are responsible for triggering the rendering of that object? A unit that correlates highly with an output object might not actually cause that output. Furthermore, any output will jointly depend on several parts of the representation. We need a way to identify combinations of units that cause an object.
+
+# 3.2 MEASURING CAUSAL RELATIONSHIPS USING INTERVENTION
+
+To answer the above question about causality, we probe the network using interventions: we test whether a set of units U in $\mathbf { r }$ cause the generation of $c$ by forcing the units of $\mathrm { U }$ on and off.
+
+Recall that $\mathbf { r } _ { \mathrm { U , P } }$ denotes the featuremap $\mathbf { r }$ at units $\mathrm { U }$ and locations P. We ablate those units by forcing $\mathbf { r } _ { \mathrm { U , P } } = \mathbf { 0 }$ . Similarly, we insert those units by forcing ${ \bf r } _ { \mathrm { U , P } } = { \bf k }$ , where $\mathbf { k }$ is a per-class constant, as described in Section S-6.4. We decompose the featuremap $\mathbf { r }$ into two parts $( \mathbf { r } _ { \mathrm { U , P } } , \mathbf { r } _ { \overline { { \mathrm { U , P } } } } )$ , where $\mathbf { r } _ { \overline { { \mathbf { U } , \mathbf { P } } } }$ are unforced components of $\mathbf { r }$ :
+
+$$
+\begin{array} { r l r } & { \mathrm { O r i g i n a l i m a g e : } } & { \qquad \mathbf { x } = G ( \mathbf { z } ) \equiv f ( \mathbf { r } ) \equiv f ( \mathbf { r } _ { \mathrm { U , P } } , \mathbf { r } _ { \mathrm { U , P } } ) } \\ & { \mathrm { I m a g e ~ w i t h ~ U ~ a b l a t e d ~ a t ~ p i x e l s ~ P : } } & { \qquad \mathbf { x } _ { a } = f ( \mathbf { 0 } , \mathbf { r } _ { \overline { { \mathrm { U , P } } } } ) } \\ & { \mathrm { I m a g e ~ w i t h ~ U ~ i n s e r t e d ~ a t ~ p i x e l s ~ P : } } & { \qquad \mathbf { x } _ { i } = f ( \mathbf { k } , \mathbf { r } _ { \overline { { \mathrm { U , P } } } } ) } \end{array}
+$$
+
+An object is caused by U if the object appears in $\mathbf { x } _ { i }$ and disappears from $\mathbf { x } _ { a }$ . Figure 1c demonstrates the ablation of units that remove trees, and Figure 1d demonstrates insertion of units at specific locations to make trees appear. This causality can be quantified by comparing the presence of trees in $\mathbf { x } _ { i }$ and $\mathbf { x } _ { a }$ and averaging effects over all locations and images. Following prior work (Holland, 1988; Pearl, 2009), we define the average causal effect (ACE) of units $\mathrm { U }$ on the generation of on class $c$ as:
+
+$$
+\delta _ { \mathrm { U }  c } \equiv \mathbb { E } _ { \mathbf { z } , \mathrm { P } } [ \mathbf { s } _ { c } ( \mathbf { x } _ { i } ) ] - \mathbb { E } _ { \mathbf { z } , \mathrm { P } } [ \mathbf { s } _ { c } ( \mathbf { x } _ { a } ) ] ,
+$$
+
+where ${ \bf s } _ { c } ( { \bf x } )$ denotes a segmentation indicating the presence of class $c$ in the image $\mathbf { x }$ at $\mathrm { \bf P }$ . To permit comparisons of $\delta _ { \mathrm { U }  c }$ between classes $c$ which are rare, we normalize our segmentation $\mathbf { s } _ { c }$ by $\mathbb { E } _ { \mathbf { z } , \mathrm { P } } [ \mathbf { s } _ { c } ( x ) ]$ . While these measures can be applied to a single unit, we have found that objects tend to depend on more than one unit. Thus we wish to identify a set of units U that maximize the average causal effect $\delta _ { \mathrm { U }  c }$ for an object class $c$ .
+
+Finding sets of units with high ACE. Given a representation $\mathbf { r }$ with $d$ units, exhaustively searching for a fixed-size set U with high $\delta _ { \mathrm { U }  c }$ is prohibitive as it has $\binom { d } { | \mathrm { U } | }$ subsets. Instead, we optimize a continuous intervention $\alpha \in [ 0 , 1 ] ^ { d }$ , where each dimension $\pmb { \alpha } _ { u }$ indicates the degree of intervention for a unit $u$ . We maximize the following average causal effect formulation $\delta _ { \alpha  c }$ :
+
+$$
+\begin{array} { r l r l } & { \mathrm { I m a g e ~ w i t h ~ p a r t i a l ~ a b l a t i o n ~ a t ~ p i x e l s ~ P : } \quad } & & { \mathbf { x } _ { a } ^ { \prime } = f \big ( ( \mathbf { 1 } - \boldsymbol { \alpha } ) \odot \mathbf { r } _ { \mathbb { U } , \mathrm { P } } , \ \mathbf { r } _ { \mathbb { U } , \overline { { P } } } \big ) } \\ & { \mathrm { I m a g e ~ w i t h ~ p a r t i a l ~ i n s e r t i o n ~ a t ~ p i x e l s ~ P : } \quad } & & { \mathbf { x } _ { i } ^ { \prime } = f \big ( { \boldsymbol \alpha } \odot \mathbf { k } + ( \mathbf { 1 } - { \boldsymbol \alpha } ) \odot \mathbf { r } _ { \mathbb { U } , \mathrm { P } } , \ \mathbf { r } _ { \mathbb { U } , \overline { { P } } } \big ) } \\ & { \mathrm { O b j e c t i v e : } \quad } & & { \delta _ { { \boldsymbol \alpha }  c } = \mathbb { E } _ { \mathbf { z } , \mathrm { P } } \big [ \mathbf { s } _ { c } \big ( \mathbf { x } _ { i } ^ { \prime } \big ) \big ] - \mathbb { E } _ { \mathbf { z } , \mathrm { P } } \big [ \mathbf { s } _ { c } \big ( \mathbf { x } _ { a } ^ { \prime } \big ) \big ] , } \end{array}
+$$
+
+where $\mathbf { r } _ { \mathbb { U } , \mathrm { P } }$ denotes the all-channel featuremap at locations $\mathrm { \bf P }$ , $\mathbf { r } _ { \mathbb { U } , \overline { { \mathrm { P } } } }$ denotes the all-channel featuremap at other locations $\overline { { \mathsf { P } } }$ , and $\odot$ applies a per-channel scaling vector $_ \alpha$ to the featuremap $\mathbf { r } _ { \mathbb { U } , \mathrm { P } }$ . We optimize
+
+$_ { \pmb { \alpha } }$ over the following loss with an L2 regularization:
+
+$$
+\pmb { \alpha } ^ { * } = \arg \operatorname* { m i n } _ { \pmb { \alpha } } ( - \delta _ { \pmb { \alpha }  c } + \lambda | | \pmb { \alpha } | | _ { 2 } ) ,
+$$
+
+where $\lambda$ controls the relative importance of each term. We add the L2 loss as we seek a minimal set of casual units. We optimize using stochastic gradient descent, sampling over both $\mathbf { z }$ and featuremap locations $\mathrm { \bf P }$ and clamping the coefficient $_ { \pmb { \alpha } }$ within the range $[ 0 , 1 ] ^ { d }$ at each step (d is the total number of units). More details of this optimization are discussed in Section S-6.4. Finally, we can rank units by $\alpha _ { u } ^ { * }$ and achieve a stronger causal effect (i.e., removing trees) when ablating successively larger sets of tree-causing units as shown in Figure 4.
+
+# 4 RESULTS
+
+We study three variants of Progressive GANs (Karras et al., 2018) trained on LSUN scene datasets (Yu et al., 2015). To segment the generated images, we use a recent model (Xiao et al., 2018) trained on the ADE20K scene dataset (Zhou et al., 2017). The model can segment the input image into 336 object classes, 29 parts of large objects, and 25 materials. To further identify units that specialize in object parts, we expand each object class $c$ into additional object part classes c-t, c-b, c-l, and $c { - } r$ , which denote the top, bottom, left, or right half of the bounding box of a connected component.
+
+Below, we use dissection for analyzing and comparing units across datasets, layers, and models (Section 4.1), and locating artifact units (Section 4.2). Then, we start with a set of dominant object classes and use intervention to locate causal units that can remove and insert objects in different images (Section 4.3 and 4.4). In addition, our video demonstrates our interactive tool.
+
+# .1 COMPARING UNITS ACROSS DATASETS, LAYERS, AND MODELS
+
+Emergence of individual unit object detectors We are particularly interested in any units that are correlated with instances of an object class with diverse visual appearances; these would suggest that GANs generate those objects using similar abstractions as humans. Figure 3 illustrates two such units. In the dining room dataset, a unit emerges to match dining table regions. More interestingly, the matched tables have different colors, materials, geometry, viewpoints, and levels of clutter: the only obvious commonality among these regions is the concept of a table. This unit’s featuremap correlates to the fully supervised segmentation model (Xiao et al., 2018) with a high IoU of 0.34.
+
+Interpretable units for different scene categories The set of all object classes matched by the units of a GAN provides a map of what a GAN has learned about the data. Figure 5 examines units from GANs trained on four LSUN scene categories (Yu et al., 2015). The units that emerge are object classes appropriate to the scene type: for example, when we examine a GAN trained on kitchen scenes, we find units that match stoves, cabinets, and the legs of tall kitchen stools. Another striking phenomenon is that many units represent parts of objects: for example, the conference room GAN contains separate units for the body and head of a person.
+
+Interpretable units for different network layers. In classifier networks, the type of information explicitly represented changes from layer to layer (Zeiler & Fergus, 2014). We find a similar phenomenon in a GAN. Figure 6 compares early, middle, and late layers of a progressive GAN with 14 internal convolutional layers. The output of the first convolutional layer, one step away from the input $z$ , remains entangled: individual units do not correlate well with any object classes except for two units that are biased towards the ceiling of the room. Mid-level layers 4 to 7 have many units that match semantic objects and object parts. Units in layers 10 and beyond match local pixel patterns such as materials, edges and colors. All layers are shown in Section S-6.7.
+
+Interpretable units for different GAN models. Interpretable units can provide insights about how GAN architecture choices affect the structures learned inside a GAN. Figure 7 compares three models from Karras et al. (2018): a baseline Progressive GANs, a modification that introduces minibatch stddev statistics, and a further modification that adds pixelwise normalization. By examining unit semantics, we confirm that providing minibatch stddev statistics to the discriminator increases not only the realism of results, but also the diversity of concepts represented by units: the number of types of objects, parts, and materials matching units increases by more than $4 0 \%$ . The pixelwise normalization increases the number of units that match semantic classes by $1 9 \%$ .
+
+![](images/48f2e3ea25bf071cb331ec43d80250119dbe47c1c838b43856bc6609d385e2fb.jpg)  
+Figure 5: Comparing representations learned by progressive GANs trained on different scene types. The units that emerge match objects that commonly appear in the scene type: seats in conference rooms and stoves in kitchens. Units from layer4 are shown. A unit is counted as a class predictor if it matches a supervised segmentation class with pixel accuracy $> 0 . 7 5$ and $\mathrm { I o U } > 0 . 0 5$ when upsampled and thresholded. The distribution of units over classes is shown in the right column.
+
+![](images/fcc6015500695ddaf505c4301a73be86169c016401324290b6861658a5db5c8b.jpg)  
+Figure 6: Comparing layers of a progressive GAN trained to generate LSUN living room images. The output of the first convolutional layer has almost no units that match semantic objects, but many objects emerge at layers 4-7. Later layers are dominated by low-level materials, edges and colors.
+
+# 4.2 DIAGNOSING AND IMPROVING GANS
+
+While our framework can reveal how GANs succeed in producing realistic images, it can also analyze the causes of failures in their results. Figure 8a shows several annotated units that are responsible for typical artifacts consistently appearing across different images. We can identify these units efficiently by human annotation: out of a sample of 1000 images, we visualize the top ten highest activating images for each unit, and we manually identify units with noticeable artifacts in this set. It typically takes 10 minutes to locate 20 artifact-causing units out of 512 units in layer4.
+
+More importantly, we can fix these errors by ablating the above 20 artifact-causing units. Figure 8b shows that artifacts are successfully removed, and the artifact-free pixels stay the same, improving the generated results. In Table 1 we report two standard metrics, comparing our improved images to both the original artifact images and a simple baseline that ablates 20 randomly chosen units. First, we compute the widely used Frechet Inception Distance ( ´ Heusel et al., 2017) between the generated images and real images. We use 50, 000 real images and generate 10, 000 images with high activations on these units. Second, we score 1, 000 images per method on Amazon MTurk, collecting 20, 000 human annotations regarding whether the modified image looks more realistic compared to the original. Both metrics show significant improvements. Strikingly, this simple manual change to a network beats state-of-the-art GANs models. The manual identification of “artifact” units can be approximated by an automatic scoring of the realism of each unit, as detailed in Section S-6.1.
+
+![](images/b3b9639f2a5d71f35ac700815ea50208d06bf7aa6b36eeb5b0c2aae1ce01a2a8.jpg)  
+Figure 7: Comparing layer4 representations learned by different training variations. Sliced Wasserstein Distance (SWD) is a GAN quality metric suggested by Karras et al. (2018): lower SWD indicates more realistic image statistics. Note that as the quality of the model improves, the number of interpretable units also rises. Progressive GANs apply several innovations including making the discriminator aware of minibatch statistics, and pixelwise normalization at each layer. We can see batch awareness increases the number of object classes matched by units, and pixel norm (applied in addition to batch stddev) increases the number of units matching objects.
+
+![](images/c54400d708578b42a3e0abe37a55e0de7c23e5ece4be6e8badac38d4717ed88c.jpg)  
+Figure 8: (a) We show two example units that are responsible for visual artifacts in GAN results. There are 20 units in total. By ablating these units, we can fix the artifacts in (b) and significantly improve the visual quality as shown in (c).
+
+# 4.3 LOCATING CAUSAL UNITS WITH ABLATION
+
+Errors are not the only type of output that can be affected by directly intervening in a GAN. A variety of specific object types can also be removed from GAN output by ablating a set of units in a GAN. In Figure 9 we apply the method in Section 3.2 to identify sets of 20 units that have causal effects on common object classes in conference rooms scenes. We find that, by turning off these small sets of units, most of the output of people, curtains, and windows can be removed from the generated scenes. However, not every object can be erased: tables and chairs cannot be removed. Ablating those units will reduce the size and density of these objects, but will rarely eliminate them.
+
+The ease of object removal depends on the scene type. Figure 10 shows that, while windows can be removed well from conference rooms, they are more difficult to remove from other scenes. In particular, windows are just as difficult to remove from a bedroom as tables and chairs from a conference room. We hypothesize that the difficulty of removal reflects the level of choice that a GAN has learned for a concept: a conference room is defined by the presence of chairs, so they cannot be altered. And modern building codes mandate that all bedrooms must have windows; the GAN seems to have caught on to that pattern.
+
+Table 1: We compare generated images before and after ablating 20 “artifacts” units. We also report a simple baseline that ablates 20 randomly chosen units.   
+
+<table><tr><td colspan="2">Fréchet Inception Distance (FID)</td></tr><tr><td>original images</td><td>43.16</td></tr><tr><td>“artifacts”units ablated (ours)</td><td>27.14</td></tr><tr><td>random units ablated</td><td>43.17</td></tr></table>
+
+<table><tr><td>Human preference score</td><td>original images</td></tr><tr><td>“artifacts”units ablated (ours)</td><td>72.4%</td></tr><tr><td>random units ablated</td><td>49.9%</td></tr></table>
+
+![](images/1f533220533042bd5692e3238ab6e9f3c0a844aeef4cfe076277d9e6c2db7c58.jpg)  
+Figure 9: Measuring the effect of ablating units in a GAN trained on conference room images. Five different sets of units have been ablated related to a specific object class. In each case, 20 (out of 512) units are ablated from the same GAN model. The 20 units are specific to the object class and independent of the image. The average causal effect is reported as the portion of pixels that are removed in 1 000 randomly generated images. We observe that some object classes are easier to remove cleanly than others: a small ablation can erase most pixels for people, curtains, and windows, whereas a similar ablation for tables and chairs only reduces object sizes without deleting them.
+
+# 4.4 CHARACTERIZING CONTEXTUAL RELATIONSHIPS VIA INSERTION
+
+We can also learn about the operation of a GAN by forcing units on and inserting these features into specific locations in scenes. Figure 11 shows the effect of inserting 20 layer4 causal door units in church scenes. In this experiment, we insert these units by setting their activation to the fixed mean value for doors (further details in Section S-6.4). Although this intervention is the same in each case, the effects vary widely depending on the objects’ surrounding context. For example, the doors added to the five buildings in Figure 11 appear with a diversity of visual attributes, each with an orientation, size, material, and style that matches the building.
+
+We also observe that doors cannot be added in most locations. The locations where a door can be added are highlighted by a yellow box. The bar chart in Figure 11 shows average causal effects of insertions of door units, conditioned on the background object class at the location of the intervention. We find that the GAN allows doors to be added in buildings, particularly in plausible locations such as where a window is present, or where bricks are present. Conversely, it is not possible to trigger a door in the sky or on trees. Interventions provide insight on how a GAN enforces relationships between objects. Even if we try to add a door in $\mathtt { 1 a y e r 4 }$ , that choice can be vetoed later if the object is not appropriate for the context. These downstream effects are further explored in Section S-6.5.
+
+# 5 DISCUSSION
+
+By carefully examining representation units, we have found that many parts of GAN representations can be interpreted, not only as signals that correlate with object concepts but as variables that have a causal effect on the synthesis of objects in the output. These interpretable effects can be used to compare, debug, modify, and reason about a GAN model. Our method can be potentially applied to other generative models such as VAEs (Kingma & Welling, 2014) and RealNVP (Dinh et al., 2017).
+
+We have focused on the generator rather than the discriminator (as did in Radford et al. (2016)) because the generator must represent all the information necessary to approximate the target distribution, while the discriminator only learns to capture the difference between real and fake images. Alternatively, we can train an encoder to invert the generator (Donahue et al., 2017; Dumoulin et al., 2017). However, this incurs additional complexity and errors. Many GANs also do not have an encoder.
+
+![](images/d95b40f694e777817012acbb1836b521080507c9ee55b98c11b00a753c506e47.jpg)  
+Figure 10: Comparing the effect of ablating 20 window-causal units in GANs trained on five scene categories. In each case, the 20 ablated units are specific to the class and the generator and independent of the image. In some scenes, windows are reduced in size or number rather than eliminated, or replaced by visually similar objects such as paintings.
+
+![](images/8e0ead3e20c733b4df79af8ad4c1a424a5be42cb9259e8c4ac8ed79b99044229.jpg)  
+Figure 11: Inserting door units by setting 20 causal units to a fixed high value at one pixel in the representation. Whether the door units can cause the generation of doors is dependent on its local context: we highlight every location that is responsive to insertions of door units on top of the original image, including two separate locations in (b) (we intervene at left). The same units are inserted in every case, but the door that appears has a size, alignment, and color appropriate to the location. Emphasizing a door that is already present results in a larger door (d). The chart summarizes the causal effect of inserting door units at one pixel with different contexts.
+
+Our method is not designed to compare the quality of GANs to one another, and it is not intended as a replacement for well-studied GAN metrics such as FID, which estimate realism by measuring the distance between the generated distribution of images and the true distribution (Borji (2018) surveys these methods). Instead, our goal has been to identify the interpretable structure and provide a window into the internal mechanisms of a GAN.
+
+Prior visualization methods (Zeiler & Fergus, 2014; Bau et al., 2017; Karpathy et al., 2016) have brought new insights into CNN and RNN research. Motivated by that, in this work we have taken a small step towards understanding the internal representations of a GAN, and we have uncovered many questions that we cannot yet answer with the current method. For example: why can a door not be inserted in the sky? How does the GAN suppress the signal in the later layers? Further work will be needed to understand the relationships between layers of a GAN. Nevertheless, we hope that our work can help researchers and practitioners better analyze and develop their own GANs.
+
+# REFERENCES
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+Ishaan Gulrajani, Faruk Ahmed, Martin Arjovsky, Vincent Dumoulin, and Aaron C Courville. Improved training of wasserstein gans. In NIPS, 2017. 16
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+Judea Pearl. Causality. Cambridge university press, 2009. 5
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+Rodrigo Quian Quiroga. Concept cells: the building blocks of declarative memory functions. Nature Reviews Neuroscience, 13(8):587, 2012. 3
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+Karen Simonyan, Andrea Vedaldi, and Andrew Zisserman. Deep inside convolutional networks: Visualising image classification models and saliency maps. In ICLR Workshop, 2014. 3
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+Tete Xiao, Yingcheng Liu, Bolei Zhou, Yuning Jiang, and Jian Sun. Unified perceptual parsing for scene understanding. In ECCV, 2018. 6
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+Fisher Yu, Ari Seff, Yinda Zhang, Shuran Song, Thomas Funkhouser, and Jianxiong Xiao. Lsun: Construction of a large-scale image dataset using deep learning with humans in the loop. arXiv preprint arXiv:1506.03365, 2015. 6
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+Rafael Yuste. From the neuron doctrine to neural networks. Nature reviews neuroscience, 16(8):487, 2015. 3
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+Matthew D Zeiler and Rob Fergus. Visualizing and understanding convolutional networks. In ECCV, 2014. 3, 6, 10
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+Han Zhang, Ian Goodfellow, Dimitris Metaxas, and Augustus Odena. Self-attention generative adversarial networks. arXiv preprint arXiv:1805.08318, 2018a. 1, 2   
+Quanshi Zhang, Ying Nian Wu, and Song-Chun Zhu. Interpretable convolutional neural networks. In CVPR, 2018b. 3   
+Bolei Zhou, Aditya Khosla, Agata Lapedriza, Aude Oliva, and Antonio Torralba. Object detectors emerge in deep scene cnns. In ICLR, 2015. 3   
+Bolei Zhou, Hang Zhao, Xavier Puig, Sanja Fidler, Adela Barriuso, and Antonio Torralba. Scene parsing through ade20k dataset. In CVPR, 2017. 6   
+Bolei Zhou, David Bau, Aude Oliva, and Antonio Torralba. Interpreting deep visual representations via network dissection. PAMI, 2018a. 3   
+Bolei Zhou, Yiyou Sun, David Bau, and Antonio Torralba. Interpretable basis decomposition for visual explanation. In ECCV, pp. 119–134, 2018b. 3   
+Tinghui Zhou, Philipp Krahenbuhl, Mathieu Aubry, Qixing Huang, and Alexei A Efros. Learning dense correspondence via 3d-guided cycle consistency. In CVPR, 2016. 3   
+Jun-Yan Zhu, Philipp Krahenb ¨ uhl, Eli Shechtman, and Alexei A. Efros. Generative visual manipula- ¨ tion on the natural image manifold. In ECCV, 2016. 2   
+Jun-Yan Zhu, Taesung Park, Phillip Isola, and Alexei A Efros. Unpaired image-to-image translation using cycle-consistent adversarial networks. In ICCV, 2017. 1, 2
+
+![](images/9c0c48fce58fcbadd90dc49d6f6c145a4ea921ac7088b48cceb7e69f7ce5d18d.jpg)  
+Figure 12: At left, visualizations of the highest-activating image patches (from a sample of 1000) for three units. (a) the lowest-FID unit that is manually flagged as showing artifacts (b) the highest-FID unit that is not manually flagged (c) the highest-FID unit overall, which is also manually flagged. At right, the precision-recall curve for unit FID as a predictor of the manually flagged artifact units. A FID threshold selecting the top 20 FID units will identify 10 (of 20) of the manually flagged units.
+
+![](images/3d2e591cc9c5daff993fc6a880075352656fa4bca866aa3441dbd66ef068bccf.jpg)  
+  
+Figure 13: The effects of ablating high-FID units compared to manually-flagged units: (a) generated images with artifacts, without intervention; (b) those images generated after ablating the 20-highest FID units; (c) those images generated after ablating the 20 manually-chosen artifact units.
+
+# S-6 SUPPLEMENTARY MATERIAL
+
+# S-6.1 AUTOMATIC IDENTIFICATION OF ARTIFACT UNITS
+
+In Section 4.2, we have improved GANs by manually identifying and ablating artifact-causing units.   
+Now we describe an automatic procedure to identify artifact units using unit-specific FID scores.
+
+To compute the FID score (Heusel et al., 2017) for a unit $u$ , we generate 200, 000 images and select the 10, 000 images that maximize the activation of unit $u$ , and this subset of 10, 000 images is compared to the true distribution (50, 000 real images) using FID. Although every such unit-maximizing subset of images represents a skewed distribution, we find that the per-unit FID scores fall in a wide range, with most units scoring well in FID while a few units stand out with bad FID scores: many of them were also manually flagged by humans, as they tend to activate on images with clear visible artifacts.
+
+Figure 12 shows the performance of FID scores as a predictor of manually flagged artifact units. The per-unit FID scores can achieve $50 \%$ precision and $50 \%$ recall. That is, of the 20 worst-FID units, 10 are also among the 20 units manually judged to have the most noticeable artifacts. Furthermore, repairing the model by ablating the highest-FID units works: qualitative results are shown in Figure 13 and quantitative results are shown in Table 2.
+
+Table 2: We compare generated images before and after ablating “artifact” units. The “artifacts” units are found either manually, automatically, or both. We also report a simple baseline that ablates 20 randomly chosen units.   
+
+<table><tr><td colspan="2">Fréchet Inception Distance (FID)</td></tr><tr><td>original images</td><td>43.16</td></tr><tr><td>manually chosen “artifact”units ablated (as in Section 4.2)</td><td>27.14</td></tr><tr><td>highest-20 FIDunitsablated</td><td>27.6</td></tr><tr><td>union of manual and highest FID (3O total) units ablated</td><td>26.1</td></tr><tr><td>20 random units ablated</td><td>43.17</td></tr></table>
+
+![](images/0a4639748e857ee3a693a712cb5764413ec84cf29c8e285bdaedc1612797bcee.jpg)  
+Figure 14: Two examples of generator units that our dissection method labels differently from humans. Both units are taken from layer4 of a Progressive GAN of living room model. In (a), human label the unit as ‘sofa’ based on viewing the top-20 activating images, and our method labels as ‘ceiling’. In this case, our method counts many ceiling activations in a sample of 1000 images beyond the top 20. In (b), the dissection method has no confident label prediction even though the unit consistently triggers on white letterbox shapes at the top and bottom of the image. The segmentation model we use has no label for such abstract shapes.
+
+# S-6.2 HUMAN EVALUATION OF DISSECTION
+
+As a sanity check, we evaluate the gap between human labeling of object concepts correlated with units and our automatic segmentation-based labeling, for one model, as follows.
+
+For each of 512 units of layer4 of a “living room” Progressive GAN, 5 to 9 human annotations were collected (3728 labels in total). In each case, an AMT worker is asked to provide one or two words describing the highlighted patches in a set of top-activating images for a unit. Of the 512 units, 201 units were described by the same consistent word (such as ”sofa”, ”fireplace” or ”wicker”) in $50 \%$ or more of the human labels. These units are interpretable to humans.
+
+Applying our segmentation-based dissection method, 154/201 of these units are also labeled with a confident label with $\mathrm { I o U } > 0 . 0 5$ by dissection. In 104/154 cases, the segmentation-based model gave the same label word as the human annotators, and most others are slight shifts in specificity. For example, the segmentation labels “ottoman” or “curtain” or “painting” when a person labels “sofa” or “window” or “picture,” respectively. A second AMT evaluation was done to rate the accuracy of both segmentation-derived and human-derived labels. Human-derived labels scored $100 \%$ (of the 201 human-labeled units, all of the labels were rated as consistent by most raters). Of the 154 segmentation-generated labels, 149 $( 9 6 \% )$ were rated by most AMT raters as accurate as well.
+
+The five failure cases (where the segmentation is confident but rated as inaccurate by humans) arise from situations in which human evaluators saw one concept after observing only 20 top-activating images, while the algorithm, in evaluating 1000 images, counted a different concept as dominant. Figure 14a shows one example: in the top images, mostly sofas are highlighted and few ceilings, whereas in the larger sample, mostly ceilings are triggered.
+
+There are also 47/201 cases where the segmenter is not confident while humans have consensus. Some of these are due to missing concepts in the segmenter. Figure 14b shows a typical example, where a unit is devoted to letterboxing (white stripes at the top and bottom of images), but the segmentation has no confident label to assign to these. We expect that as future semantic segmentation models are developed to be able to identify more concepts such as abstract shapes, more of these units can be automatically identified.
+
+![](images/5857bfcb842ad3a357424d60048d2db92561ce52395dd56f84934a0f2fb73ffa.jpg)  
+(b) Unit 371, FID 58.3, "Swimming Pool" with IoU 0.02.
+
+![](images/2b14f0c0d79f5c6183c78f46720439480f4387bf63d19dd693330cee931e324d.jpg)  
+Figure 15: Two examples of units that correlate with unrealistic images that confuse a semantic segmentation network. Both units are taken from a WGAN-GP for LSUN bedrooms.   
+Figure 16: Comparing a dissection of units for a WGAN-GP trained on LSUN bedrooms, considering all units (at left) and considering only “realistic” units with $\mathrm { F I D } < 5 5$ (at right). Filtering units by FID scores removes spurious detected concepts such as ‘sky’, ‘ground’, and ‘building’.
+
+# S-6.3 PROTECTING SEGMENTATION MODEL AGAINST UNREALISTIC IMAGES
+
+Our method relies on having a segmentation function $s _ { c } ( \mathbf { x } )$ that identifies pixels of class $c$ in the output x. However, the segmentation model $s _ { c }$ can perform poorly in the cases where $\mathbf { x }$ does not resemble the original training set of $s _ { c }$ . This phenomenon is visible when analyzing earlier GAN models. For example, Figure 15 visualizes two units from a WGAN-GP model (Gulrajani et al., 2017) for LSUN bedrooms (this model was trained by Karras et al. (2018) as a baseline in the original paper). For these two units, the segmentation network seems to be confused by the distorted images.
+
+To protect against such spurious segmentation labels, we can use a technique similar to that described in Section S-6.1: automatically identify units that produce unrealistic images, and omit those “unrealistic” units from semantic segmentation. An appropriate threshold to apply will depend on the distribution being modeled: in Figure 16, we show how applying a filter, ignoring segmentation on units with FID 55 or higher, affects the analysis of this base WGAN model. In general, fewer irrelevant labels are associated with units.
+
+# S-6.4 COMPUTING CAUSAL UNITS
+
+In this section we provide more details about the ACE optimization described in Section 3.2.
+
+Specifying the per-class positive intervention constant k. In Eqn. 3, the negative intervention is defined as zeroing the intervened units, and a positive intervention is defined as setting the intervened units to some big class-specific constant $\mathbf { k }$ . For interventions for class $c$ , we set $\mathbf { k }$ to be mean featuremap activation conditioned on the presence of class $c$ at that location in the output, with each pixel weighted by the portion of the featuremap locations that are covered by the class $c$ . Setting all units at a pixel to $\mathbf { k }$ will tend to strongly cause the target class. The goal of the optimization is to find the subset of units that is causal for $c$ .
+
+Sampling $c$ -relevant locations $\mathbf { P }$ . When optimizing the causal objective (Eqn. 5), the intervention locations $\mathrm { \bf P }$ are sampled from individual featuremap locations. When the class $c$ is rare, most featuremap locations are uninformative: for example, when class $c$ is a door in church scenes, most regions of the sky, grass, and trees are locations where doors will not appear. Therefore, we focus the optimization as follows: during training, minibatches are formed by sampling locations $\mathrm { \bf P }$ that are relevant to class $c$ by including locations where the class $c$ is present in the output (and are therefore candidates for removal by ablating a subset of units), and an equal portion of locations where class $c$ is not present at $\mathrm { \bf P }$ , but it would be present if all the units are set to the constant $\mathbf { k }$ (candidate locations for insertion with a subset of units). During the evaluation, causal effects are evaluated using uniform samples: the region $\mathrm { \bf P }$ is set to the entire image when measuring ablations, and to uniformly sampled pixels $\mathrm { \bf P }$ when measuring single-pixel insertions.
+
+![](images/bc240744718c3c6cda1eee4018008630bf1f641d462f4cd5cc686228ba4d1ea9.jpg)  
+Figure 17: Tracing the effect of inserting door units on downstream layers. An identical ”door” intervention at layer4 of each pixel in the featuremap has a different effect on later feature layers, depending on the location of the intervention. In the heatmap, brighter colors indicate a stronger effect on the layer14 feature. A request for a door has a larger effect in locations of a building, and a smaller effect near trees and sky. At right, the magnitude of feature effects at every layer is shown, measured by the changes of mean-normalized features. In the line plot, feature changes for interventions that result in human-visible changes are separated from interventions that do not result in noticeable changes in the output.
+
+Initializing $_ { \pmb { \alpha } }$ with IoU. When optimizing causal $_ \alpha$ for class $c$ , we initialize with
+
+$$
+\alpha _ { u } = \frac { \mathrm { I o U } _ { u , c } } { \operatorname* { m a x } _ { v } \mathrm { I o U } _ { v , c } }
+$$
+
+That is, we set the initial $\alpha$ so that the largest component corresponds to the unit with the largest IoU for class $c$ , and we normalize the components so that this largest component is 1.
+
+Applying a learned intervention $_ \alpha$ When applying the interventions, we clip $_ \alpha$ by keeping only its top $n$ components and zeroing the remainder. To compare the interventions of different classes an different models on an equal basis, we examine interventions where we set $n = 2 0$ .
+
+# S-6.5 TRACING THE EFFECT OF AN INTERVENTION
+
+To investigate the mechanism for suppressing the visible effects of some interventions seen in Section 4.4, in this section we insert 20 door-causal units on a sample of individual featuremap locations at $\mathtt { 1 a y e r 4 }$ and measure the changes caused in later layers.
+
+To quantify effects on downstream features, the change in each feature channel is normalized by that channel’s mean L1 magnitude, and we examine the mean change in these normalized featuremaps at each layer. In Figure 17, these effects that propagate to layer14 are visualized as a heatmap: brighter colors indicate a stronger effect on the final feature layer when the door intervention is in the neighborhood of a building instead of trees or sky. Furthermore, we plot the average effect on every layer at right in Figure 17, separating interventions that have a visible effect from those that do not. A small identical intervention at layer4 is amplified to larger changes up to a peak at layer12.
+
+# S-6.6 MONITORING GAN UNITS DURING TRAINING
+
+Dissection can also be used to monitor the progress of training by quantifying the emergence, diversity, and quality of interpretable units. For example, in Figure 18 we show dissections of layer4 representations of a Progressive GAN model trained on bedrooms, captured at a sequence of checkpoints during training. As training proceeds, the number of units matching objects increases, as does the number of object classes with matching units, and the quality of object detectors as measured by average IoU over units increases. During this successful training, dissection suggests that the model is gradually learning the structure of a bedroom, as increasingly units converge to meaningful bedroom concepts.
+
+![](images/cad93eb9cc9ec0daa9de61c15ec2baff405ad2e89f5afeca9902c057ef0565ec.jpg)  
+Figure 18: The evolution of $\mathtt { l a y e r 4 }$ of a Progressive GAN bedroom generator as training proceeds. The number and quality of interpretable units increases during training. Note that in early iterations, Progressive GAN generates images at a low resolution. The top-activating images for the same four selected units is shown for each iteration, along with the IoU and the matched concept for each unit at that checkpoint.
+
+# S-6.7 ALL LAYERS OF A GAN
+
+In Section 4.1 we show a small selection of layers of a GAN; in Figure 19 we show a complete listing of all the internal convolutional layers of that model (a Progressive GAN trained on LSUN living room images). As can be seen, the diversity of units matching high-level object concepts peaks at layer4-layer6, then declines in later layers, with the later layers dominated by textures, colors, and shapes.
+
+![](images/be3d8f590ea85f23160f14a695d85d37b582b2681518c60587d22589ea9ebadd.jpg)  
+Figure 19: All layers of a Progressive GAN trained to generate LSUN living room images.

parse/train/Hyg_X2C5FX/Hyg_X2C5FX_content_list.json

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+    {
+        "type": "text",
+        "text": "GAN DISSECTION: VISUALIZING AND UNDERSTANDING GENERATIVE ADVERSARIAL NETWORKS ",
+        "text_level": 1,
+        "bbox": [
+            174,
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+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "David $\\mathbf { B a u } ^ { 1 , 2 }$ , Jun-Yan $\\mathbf { Z } \\mathbf { h } \\mathbf { u } ^ { \\mathbf { 1 } }$ , Hendrik Strobelt2,3, Bolei Zhou4, Joshua B. Tenenbaum1, William T. Freeman1, Antonio Torralba1,2 1Massachusetts Institute of Technology, 2MIT-IBM Watson AI Lab, 3IBM Research, 4The Chinese University of Hong Kong ",
+        "bbox": [
+            183,
+            193,
+            645,
+            253
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            290,
+            544,
+            306
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Generative Adversarial Networks (GANs) have recently achieved impressive results for many real-world applications, and many GAN variants have emerged with improvements in sample quality and training stability. However, they have not been well visualized or understood. How does a GAN represent our visual world internally? What causes the artifacts in GAN results? How do architectural choices affect GAN learning? Answering such questions could enable us to develop new insights and better models. ",
+        "bbox": [
+            233,
+            327,
+            764,
+            424
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In this work, we present an analytic framework to visualize and understand GANs at the unit-, object-, and scene-level. We first identify a group of interpretable units that are closely related to object concepts using a segmentation-based network dissection method. Then, we quantify the causal effect of interpretable units by measuring the ability of interventions to control objects in the output. We examine the contextual relationship between these units and their surroundings by inserting the discovered object concepts into new images. We show several practical applications enabled by our framework, from comparing internal representations across different layers, models, and datasets, to improving GANs by locating and removing artifact-causing units, to interactively manipulating objects in a scene. We provide open source interpretation tools to help researchers and practitioners better understand their GAN models. ",
+        "bbox": [
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+            431,
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            636,
+            336,
+            651
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Generative Adversarial Networks (GANs) (Goodfellow et al., 2014) have been able to produce photorealistic images, often indistinguishable from real images. This remarkable ability has powered many real-world applications ranging from visual recognition (Wang et al., 2017), to image manipulation (Isola et al., 2017; Zhu et al., 2017), to video prediction (Mathieu et al., 2016). Since their invention in 2014, many GAN variants have been proposed (Radford et al., 2016; Zhang et al., 2018a), often producing more realistic and diverse samples with better training stability. ",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Despite this tremendous success, many questions remain to be answered. For example, to produce a church image (Figure 1a), what knowledge does a GAN need to learn? Alternatively, when a GAN sometimes produces terribly unrealistic images (Figure 1f), what causes the mistakes? Why does one GAN variant work better than another? What fundamental differences are encoded in their weights? ",
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In this work, we study the internal representations of GANs. To a human observer, a well-trained GAN appears to have learned facts about the objects in the image: for example, a door can appear on a building but not on a tree. We wish to understand how a GAN represents such structure. Do the objects emerge as pure pixel patterns without any explicit representation of objects such as doors and trees, or does the GAN contain internal variables that correspond to the objects that humans perceive? If the GAN does contain variables for doors and trees, do those variables cause the generation of those objects, or do they merely correlate? How are relationships between objects represented? ",
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+            "Figure 1: Overview: (a) Realistic outdoor church images generated by Progressive GANs (Karras et al., 2018). (b) Given a pre-trained GAN model, we identify a set of interpretable units whose featuremap is correlated to an object class across different images. For example, one unit in layer4 localizes tree regions with diverse visual appearance. (c) We force the activation of the units to be zero and quantify the average casual effect of the ablation. Here we successfully remove trees from church images. (d) We activate tree causal units in other locations. These same units synthesize new trees, visually compatible with their surrounding context. In addition, our method can diagnose and improve GANs by identifying artifact-causing units (e). We can remove the artifacts that appear (f) and significantly improve the results by ablating the “artifact” units (g). Please see our demo video. "
+        ],
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+        "type": "text",
+        "text": "We present a general method for visualizing and understanding GANs at different levels of abstraction, from each neuron, to each object, to the contextual relationship between different objects. We first identify a group of interpretable units that are related to object concepts (Figure 1b). These units’ featuremaps closely match the semantic segmentation of a particular object class (e.g., trees). Second, we directly intervene within the network to identify sets of units that cause a type of objects to disappear (Figure 1c) or appear (Figure 1d). We quantify the causal effect of these units using a standard causality metric. Finally, we examine the contextual relationship between these causal object units and the background. We study where we can insert object concepts in new images and how this intervention interacts with other objects in the image (Figure 1d). To our knowledge, our work provides the first systematic analysis for understanding the internal representations of GANs. ",
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+        "text": "Finally, we show several practical applications enabled by this analytic framework, from comparing internal representations across different layers, GAN variants and datasets; to debugging and improving GANs by locating and ablating “artifact” units (Figure 1e); to understanding contextual relationships between objects in scenes; to manipulating images with interactive object-level control. ",
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+        "type": "text",
+        "text": "2 RELATED WORK ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Generative Adversarial Networks. The quality and diversity of results from GANs (Goodfellow et al., 2014) has continued to improve, from generating simple digits and faces (Goodfellow et al., 2014), to synthesizing natural scene images (Radford et al., 2016; Denton et al., 2015), to generating 1k photorealistic portraits (Karras et al., 2018), to producing one thousand object classes (Miyato et al., 2018; Zhang et al., 2018a). GANs have also enabled applications such as visual recognition (Wang et al., 2017; Hoffman et al., 2018), image manipulation (Isola et al., 2017; Zhu et al., 2017), and video generation (Mathieu et al., 2016; Wang et al., 2018). Despite the successes, little work has been done to visualize what GANs have learned. Prior work (Radford et al., 2016; Zhu et al., 2016; Brock et al., 2017) manipulates latent vectors and observes how the results change accordingly. ",
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+            "Figure 2: Measuring the relationship between representation units and trees in the output using (a) dissection and (b) intervention. Dissection measures agreement between a unit $u$ and a concept $c$ by comparing its thresholded upsampled heatmap with a semantic segmentation of the generated image $s _ { c } ( x )$ . Intervention measures the causal effect of a set of units $U$ on a concept $c$ by comparing the effect of forcing these units on (unit insertion) and off (unit ablation). The segmentation $s _ { c }$ reveals that trees increase after insertion and decrease after ablation. The average difference in the tree pixels measures the average causal effect. In this figure, interventions are applied to the entire featuremap $\\mathbb { P }$ , but insertions and ablations can also apply to any subset of pixels $\\mathrm { \\bf P } \\subset \\mathbb { P }$ . "
+        ],
+        "image_footnote": [],
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Visualizing deep neural networks. A CNN can be visualized by reconstructing salient image features (Simonyan et al., 2014; Mahendran & Vedaldi, 2015) or by mining patches that maximize hidden layers’ activations (Zeiler & Fergus, 2014); or we can synthesize input images to invert a feature layer (Dosovitskiy & Brox, 2016). Alternately, we can identify the semantics of each unit (Zhou et al., 2015; Bau et al., 2017; Zhou et al., 2018a) by measuring agreement between unit activations and object segmentation masks, or by training a network to increase interpretability of such units (Zhang et al., 2018b). Visualization of an RNN has also revealed interpretable units that track long-range dependencies (Karpathy et al., 2016; Strobelt et al., 2018). Most previous work on network visualization has focused on networks trained for classification; our work explores deep generative models trained for image generation. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Understanding neural representation in biology. Studies of biological neural networks find evidence of both local representations in which individual neurons are selective for meaningful concepts (Quiroga, 2012), as well as distributed representations in which individual neurons are essentially meaningless (Yuste, 2015). Computational models of biological learning (Bowers et al., 2016; Dasgupta et al., 2018) find sparse and local representations can aid generalization to novel stimuli. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Explaining the decisions of deep neural networks. Individual network decisions can be explained using informative heatmaps (Zhou et al., 2018b; 2016; Selvaraju et al., 2017) or by scoring salience (Simonyan et al., 2014; Bach et al., 2015; Sundararajan et al., 2017; Lundberg & Lee, 2017). Such analyses reveals which inputs contribute most to a categorical prediction by a network. Recent work has also studied the contribution of feature vectors (Kim et al., 2017; Zhou et al., 2018b) or individual channels (Olah et al., 2018) to a final prediction, and Morcos et al. (2018) has examined the effect of individual units by ablating them. Those methods explain discriminative classifiers. Our method aims to explain how an image can be generated by a network, which is much less explored. ",
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+    {
+        "type": "text",
+        "text": "3 METHOD ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Our goal is to analyze how objects such as trees are encoded by the internal representations of a GAN generator $G \\colon { \\mathbf { z } }  { \\mathbf { x } }$ . Here $\\mathbf { z } \\in \\mathbb { R } ^ { | z | }$ denotes a latent vector sampled from a low-dimensional distribution, and $\\mathbf { x } \\in \\mathbb { R } ^ { H \\times W \\times 3 }$ denotes an $H \\times W$ generated image. We use representation to ",
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+    {
+        "type": "image",
+        "img_path": "images/c336fa265ed423129426a5cb9cdb5a33d82cc0eb3bec4a42642967fd0a8ffcf7.jpg",
+        "image_caption": [],
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+    {
+        "type": "text",
+        "text": "Thresholding unit #65 layer 3 of a dining room generator matches ‘table’ segmentations with $\\mathrm { I o U } { = } 0 . 3 4$ . ",
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+    {
+        "type": "image",
+        "img_path": "images/6eca35238c9ed4fa28c21db3105eaa38efe24c43cd3e1ee9e20fd974ef3a322c.jpg",
+        "image_caption": [
+            "Thresholding unit #37 layer 4 of a living room generator matches ‘sofa’ segmentations with $\\mathrm { I o U } { = } 0 . 2 9$ . ",
+            "Figure 3: Visualizing the activations of individual units in two GANs. Top ten activating images are shown, and IoU is measured over a sample of 1000 images. In each image, the unit feature is upsampled and thresholded as described in Eqn. 2. "
+        ],
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+    {
+        "type": "text",
+        "text": "describe the tensor r output from a particular layer of the generator $G$ , where the generator creates an image x from random $\\mathbf { z }$ through a composition of layers: $\\mathbf { r } = h ( \\mathbf { z } )$ and $\\mathbf { x } = f ( \\mathbf { r } ) \\bar { = } f ( h ( \\mathbf { z } ) ) = G ( \\mathbf { z } )$ ",
+        "bbox": [
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+        "type": "text",
+        "text": "Since r has all the data necessary to produce the image $\\mathbf { x } = f ( \\mathbf { r } )$ , r certainly contains the information to deduce the presence of any visible class $c$ in the image. Therefore the question we ask is not whether information about $c$ is present in $\\mathbf { r }$ — it is — but how such information is encoded in r. In particular, for any class from a universe of concepts $c \\in \\mathbb { C }$ , we seek to understand whether r explicitly represents $c$ in some way where it is possible to factor $\\mathbf { r }$ at locations $\\mathrm { \\bf P }$ into two components ",
+        "bbox": [
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+    {
+        "type": "equation",
+        "img_path": "images/8a6ce09c19ad83f1ebe81c2d3bac77664b0ba7cc9eb5e36337b04f5b5665c21c.jpg",
+        "text": "$$\n{ \\bf r } _ { \\mathbb { U } , \\mathrm { P } } = ( { \\bf r } _ { \\mathrm { U } , \\mathrm { P } } , { \\bf r } _ { \\overline { { \\mathrm { U } } } , \\mathrm { P } } ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "where the generation of the object $c$ at locations $\\mathrm { \\bf P }$ depends mainly on the units $\\mathbf { r } _ { \\mathrm { U , P } }$ , and is insensitive to the other units $\\mathbf { r } _ { \\overline { { \\mathbf { U } } } , \\mathbf { P } }$ . Here we refer to each channel of the featuremap as a unit: U denotes the set of unit indices of interest and $\\overline { { \\mathrm { ~ U ~ } } }$ is its complement; we will write $\\mathbb { U }$ and $\\mathbb { P }$ to refer to the entire set of units and featuremap pixels in $r$ . We study the structure of $\\mathbf { r }$ in two phases: ",
+        "bbox": [
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+        "type": "text",
+        "text": "• Dissection: starting with a large dictionary of object classes, we identify the classes that have an explicit representation in $\\mathbf { r }$ by measuring the agreement between individual units of $\\mathbf { r }$ and every class $c$ (Figure 1b).   \n• Intervention: for the represented classes identified through dissection, we identify causal sets of units and measure causal effects between units and object classes by forcing sets of units on and off (Figure 1c,d). ",
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+    {
+        "type": "text",
+        "text": "3.1 CHARACTERIZING UNITS BY DISSECTION ",
+        "text_level": 1,
+        "bbox": [
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+        "type": "text",
+        "text": "We first focus on individual units of the representation. Recall that $\\mathbf { r } _ { u , \\mathbb { P } }$ is the one-channel $h \\times w$ featuremap of unit $u$ in a convolutional generator, where $h \\times w$ is typically smaller than the image size. We want to know if a specific unit $\\mathbf { r } _ { u , \\mathbb { P } }$ encodes a semantic class such as a “tree”. For image classification networks, Bau et al. (2017) has observed that many units can approximately locate emergent object classes when the units are upsampled and thresholded. In that spirit, we select a universe of concepts $c \\in \\mathbb { C }$ for which we have a semantic segmentation ${ \\bf s } _ { c } ( { \\bf x } )$ for each class. Then we quantify the spatial agreement between the unit $u$ ’s thresholded featuremap and a concept $c$ ’s segmentation with the following intersection-over-union (IoU) measure: ",
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+    {
+        "type": "equation",
+        "img_path": "images/a7b6a5b2bb1735678f0c60fcc5917e57524a4eedf98724122026d35a268bf9ec.jpg",
+        "text": "$$\n\\mathrm { I o U } _ { u , c } \\equiv \\frac { \\mathbb { E } _ { \\mathbf { z } } \\left| ( \\mathbf { r } _ { u , \\mathbb { P } } ^ { \\uparrow } > t _ { u , c } ) \\wedge \\mathbf { s } _ { c } ( \\mathbf { x } ) \\right| } { \\mathbb { E } _ { \\mathbf { z } } \\left| ( \\mathbf { r } _ { u , \\mathbb { P } } ^ { \\uparrow } > t _ { u , c } ) \\vee \\mathbf { s } _ { c } ( \\mathbf { x } ) \\right| } , \\mathrm { w h e r e ~ } t _ { u , c } = \\arg \\operatorname* { m a x } _ { t } \\frac { \\mathrm { I } ( \\mathbf { r } _ { u , \\mathbb { P } } ^ { \\uparrow } > t ; \\mathbf { s } _ { c } ( \\mathbf { x } ) ) } { \\mathrm { H } ( \\mathbf { r } _ { u , \\mathbb { P } } ^ { \\uparrow } > t , \\mathbf { s } _ { c } ( \\mathbf { x } ) ) } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $\\wedge$ and $\\vee$ denote intersection and union operations, and $\\mathbf { x } = G ( \\mathbf { z } )$ denotes the image generated from $\\mathbf { z }$ . The one-channel feature map $\\mathbf { r } _ { u , \\mathbb { P } }$ slices the entire featuremap $\\mathbf { \\hat { r } } = h ( \\mathbf { z } )$ at unit $u$ . As shown in Figure 2a, we upsample $\\mathbf { r } _ { u , \\mathbb { P } }$ to the output image resolution as $\\mathbf { r } _ { u , \\mathbb { P } } ^ { \\uparrow }$ P. (r↑u,P > tu,c) produces a binary mask by thresholding the $\\mathbf { r } _ { u , \\mathbb { P } } ^ { \\uparrow }$ at a fixed level $t _ { u , c }$ . ${ \\bf s } _ { c } ( { \\bf x } )$ is a binary mask where each pixel indicates the presence of class $c$ in the generated image $\\mathbf { x }$ . The threshold $t _ { u , c }$ is chosen to be informative as possible by maximizing the information quality ratio $\\mathrm { I / H }$ (using a separate validation set), that is, it maximizes the portion of the joint entropy $_ \\mathrm { H }$ which is mutual information I (Wijaya et al., 2017). ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We can use $\\mathrm { I o U } _ { u , c }$ to rank the concepts related to each unit and label each unit with the concept that matches it best. Figure 3 shows examples of interpretable units with high $\\mathrm { I o U } _ { u , c }$ . They are not the only units to match tables and sofas: layer3 of the dining room generator has 31 units (of 512) that match tables and table parts, and layer4 of the living room generator has 65 (of 512) sofa units. ",
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+        "type": "image",
+        "img_path": "images/780ef8f97ca06fc19fbda82fc54bce0e7414e4eeadbec64d32ea873d6d7729de.jpg",
+        "image_caption": [
+            "Figure 4: Ablating successively larger sets of tree-causal units from a GAN trained on LSUN outdoor church images, showing that the more units are removed, the more trees are reduced, while buildings remain. The choice of units to ablate is specific to the tree class and does not depend on the image. At right, the causal effect of removing successively more tree units is plotted, comparing units chosen to optimize the average causal effect (ACE) and units chosen with the highest IoU for trees. "
+        ],
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+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "Once we have identified an object class that a set of units match closely, we next ask: which units are responsible for triggering the rendering of that object? A unit that correlates highly with an output object might not actually cause that output. Furthermore, any output will jointly depend on several parts of the representation. We need a way to identify combinations of units that cause an object. ",
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+    {
+        "type": "text",
+        "text": "3.2 MEASURING CAUSAL RELATIONSHIPS USING INTERVENTION ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "To answer the above question about causality, we probe the network using interventions: we test whether a set of units U in $\\mathbf { r }$ cause the generation of $c$ by forcing the units of $\\mathrm { U }$ on and off. ",
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+    {
+        "type": "text",
+        "text": "Recall that $\\mathbf { r } _ { \\mathrm { U , P } }$ denotes the featuremap $\\mathbf { r }$ at units $\\mathrm { U }$ and locations P. We ablate those units by forcing $\\mathbf { r } _ { \\mathrm { U , P } } = \\mathbf { 0 }$ . Similarly, we insert those units by forcing ${ \\bf r } _ { \\mathrm { U , P } } = { \\bf k }$ , where $\\mathbf { k }$ is a per-class constant, as described in Section S-6.4. We decompose the featuremap $\\mathbf { r }$ into two parts $( \\mathbf { r } _ { \\mathrm { U , P } } , \\mathbf { r } _ { \\overline { { \\mathrm { U , P } } } } )$ , where $\\mathbf { r } _ { \\overline { { \\mathbf { U } , \\mathbf { P } } } }$ are unforced components of $\\mathbf { r }$ : ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/57560ed54fe53b67a0840cf84a7d2beeb6ea46da48b184363f060d9323fd324d.jpg",
+        "text": "$$\n\\begin{array} { r l r } & { \\mathrm { O r i g i n a l i m a g e : } } & { \\qquad \\mathbf { x } = G ( \\mathbf { z } ) \\equiv f ( \\mathbf { r } ) \\equiv f ( \\mathbf { r } _ { \\mathrm { U , P } } , \\mathbf { r } _ { \\mathrm { U , P } } ) } \\\\ & { \\mathrm { I m a g e ~ w i t h ~ U ~ a b l a t e d ~ a t ~ p i x e l s ~ P : } } & { \\qquad \\mathbf { x } _ { a } = f ( \\mathbf { 0 } , \\mathbf { r } _ { \\overline { { \\mathrm { U , P } } } } ) } \\\\ & { \\mathrm { I m a g e ~ w i t h ~ U ~ i n s e r t e d ~ a t ~ p i x e l s ~ P : } } & { \\qquad \\mathbf { x } _ { i } = f ( \\mathbf { k } , \\mathbf { r } _ { \\overline { { \\mathrm { U , P } } } } ) } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "An object is caused by U if the object appears in $\\mathbf { x } _ { i }$ and disappears from $\\mathbf { x } _ { a }$ . Figure 1c demonstrates the ablation of units that remove trees, and Figure 1d demonstrates insertion of units at specific locations to make trees appear. This causality can be quantified by comparing the presence of trees in $\\mathbf { x } _ { i }$ and $\\mathbf { x } _ { a }$ and averaging effects over all locations and images. Following prior work (Holland, 1988; Pearl, 2009), we define the average causal effect (ACE) of units $\\mathrm { U }$ on the generation of on class $c$ as: ",
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+    {
+        "type": "equation",
+        "img_path": "images/9ecf6ef55e9d6aba59f8fe766401a58ebf31e7394870abb568179e65fb1a1de7.jpg",
+        "text": "$$\n\\delta _ { \\mathrm { U }  c } \\equiv \\mathbb { E } _ { \\mathbf { z } , \\mathrm { P } } [ \\mathbf { s } _ { c } ( \\mathbf { x } _ { i } ) ] - \\mathbb { E } _ { \\mathbf { z } , \\mathrm { P } } [ \\mathbf { s } _ { c } ( \\mathbf { x } _ { a } ) ] ,\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where ${ \\bf s } _ { c } ( { \\bf x } )$ denotes a segmentation indicating the presence of class $c$ in the image $\\mathbf { x }$ at $\\mathrm { \\bf P }$ . To permit comparisons of $\\delta _ { \\mathrm { U }  c }$ between classes $c$ which are rare, we normalize our segmentation $\\mathbf { s } _ { c }$ by $\\mathbb { E } _ { \\mathbf { z } , \\mathrm { P } } [ \\mathbf { s } _ { c } ( x ) ]$ . While these measures can be applied to a single unit, we have found that objects tend to depend on more than one unit. Thus we wish to identify a set of units U that maximize the average causal effect $\\delta _ { \\mathrm { U }  c }$ for an object class $c$ . ",
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+    {
+        "type": "text",
+        "text": "Finding sets of units with high ACE. Given a representation $\\mathbf { r }$ with $d$ units, exhaustively searching for a fixed-size set U with high $\\delta _ { \\mathrm { U }  c }$ is prohibitive as it has $\\binom { d } { | \\mathrm { U } | }$ subsets. Instead, we optimize a continuous intervention $\\alpha \\in [ 0 , 1 ] ^ { d }$ , where each dimension $\\pmb { \\alpha } _ { u }$ indicates the degree of intervention for a unit $u$ . We maximize the following average causal effect formulation $\\delta _ { \\alpha  c }$ : ",
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+        "img_path": "images/e7ed29dadfe2232f95e9b510b770c8f9ed4cf4f06ebf7e5582fddb7dd3c2ed48.jpg",
+        "text": "$$\n\\begin{array} { r l r l } & { \\mathrm { I m a g e ~ w i t h ~ p a r t i a l ~ a b l a t i o n ~ a t ~ p i x e l s ~ P : } \\quad } & & { \\mathbf { x } _ { a } ^ { \\prime } = f \\big ( ( \\mathbf { 1 } - \\boldsymbol { \\alpha } ) \\odot \\mathbf { r } _ { \\mathbb { U } , \\mathrm { P } } , \\ \\mathbf { r } _ { \\mathbb { U } , \\overline { { P } } } \\big ) } \\\\ & { \\mathrm { I m a g e ~ w i t h ~ p a r t i a l ~ i n s e r t i o n ~ a t ~ p i x e l s ~ P : } \\quad } & & { \\mathbf { x } _ { i } ^ { \\prime } = f \\big ( { \\boldsymbol \\alpha } \\odot \\mathbf { k } + ( \\mathbf { 1 } - { \\boldsymbol \\alpha } ) \\odot \\mathbf { r } _ { \\mathbb { U } , \\mathrm { P } } , \\ \\mathbf { r } _ { \\mathbb { U } , \\overline { { P } } } \\big ) } \\\\ & { \\mathrm { O b j e c t i v e : } \\quad } & & { \\delta _ { { \\boldsymbol \\alpha }  c } = \\mathbb { E } _ { \\mathbf { z } , \\mathrm { P } } \\big [ \\mathbf { s } _ { c } \\big ( \\mathbf { x } _ { i } ^ { \\prime } \\big ) \\big ] - \\mathbb { E } _ { \\mathbf { z } , \\mathrm { P } } \\big [ \\mathbf { s } _ { c } \\big ( \\mathbf { x } _ { a } ^ { \\prime } \\big ) \\big ] , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $\\mathbf { r } _ { \\mathbb { U } , \\mathrm { P } }$ denotes the all-channel featuremap at locations $\\mathrm { \\bf P }$ , $\\mathbf { r } _ { \\mathbb { U } , \\overline { { \\mathrm { P } } } }$ denotes the all-channel featuremap at other locations $\\overline { { \\mathsf { P } } }$ , and $\\odot$ applies a per-channel scaling vector $_ \\alpha$ to the featuremap $\\mathbf { r } _ { \\mathbb { U } , \\mathrm { P } }$ . We optimize ",
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+    {
+        "type": "text",
+        "text": "$_ { \\pmb { \\alpha } }$ over the following loss with an L2 regularization: ",
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/4d9fb9f3bc4433a4004a6485b7037421843ec064387e42d19ffbb3b5f2ae188c.jpg",
+        "text": "$$\n\\pmb { \\alpha } ^ { * } = \\arg \\operatorname* { m i n } _ { \\pmb { \\alpha } } ( - \\delta _ { \\pmb { \\alpha }  c } + \\lambda | | \\pmb { \\alpha } | | _ { 2 } ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where $\\lambda$ controls the relative importance of each term. We add the L2 loss as we seek a minimal set of casual units. We optimize using stochastic gradient descent, sampling over both $\\mathbf { z }$ and featuremap locations $\\mathrm { \\bf P }$ and clamping the coefficient $_ { \\pmb { \\alpha } }$ within the range $[ 0 , 1 ] ^ { d }$ at each step (d is the total number of units). More details of this optimization are discussed in Section S-6.4. Finally, we can rank units by $\\alpha _ { u } ^ { * }$ and achieve a stronger causal effect (i.e., removing trees) when ablating successively larger sets of tree-causing units as shown in Figure 4. ",
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+    {
+        "type": "text",
+        "text": "4 RESULTS ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "We study three variants of Progressive GANs (Karras et al., 2018) trained on LSUN scene datasets (Yu et al., 2015). To segment the generated images, we use a recent model (Xiao et al., 2018) trained on the ADE20K scene dataset (Zhou et al., 2017). The model can segment the input image into 336 object classes, 29 parts of large objects, and 25 materials. To further identify units that specialize in object parts, we expand each object class $c$ into additional object part classes c-t, c-b, c-l, and $c { - } r$ , which denote the top, bottom, left, or right half of the bounding box of a connected component. ",
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+        "type": "text",
+        "text": "Below, we use dissection for analyzing and comparing units across datasets, layers, and models (Section 4.1), and locating artifact units (Section 4.2). Then, we start with a set of dominant object classes and use intervention to locate causal units that can remove and insert objects in different images (Section 4.3 and 4.4). In addition, our video demonstrates our interactive tool. ",
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+        "type": "text",
+        "text": ".1 COMPARING UNITS ACROSS DATASETS, LAYERS, AND MODELS ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Emergence of individual unit object detectors We are particularly interested in any units that are correlated with instances of an object class with diverse visual appearances; these would suggest that GANs generate those objects using similar abstractions as humans. Figure 3 illustrates two such units. In the dining room dataset, a unit emerges to match dining table regions. More interestingly, the matched tables have different colors, materials, geometry, viewpoints, and levels of clutter: the only obvious commonality among these regions is the concept of a table. This unit’s featuremap correlates to the fully supervised segmentation model (Xiao et al., 2018) with a high IoU of 0.34. ",
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+    {
+        "type": "text",
+        "text": "Interpretable units for different scene categories The set of all object classes matched by the units of a GAN provides a map of what a GAN has learned about the data. Figure 5 examines units from GANs trained on four LSUN scene categories (Yu et al., 2015). The units that emerge are object classes appropriate to the scene type: for example, when we examine a GAN trained on kitchen scenes, we find units that match stoves, cabinets, and the legs of tall kitchen stools. Another striking phenomenon is that many units represent parts of objects: for example, the conference room GAN contains separate units for the body and head of a person. ",
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+        "type": "text",
+        "text": "Interpretable units for different network layers. In classifier networks, the type of information explicitly represented changes from layer to layer (Zeiler & Fergus, 2014). We find a similar phenomenon in a GAN. Figure 6 compares early, middle, and late layers of a progressive GAN with 14 internal convolutional layers. The output of the first convolutional layer, one step away from the input $z$ , remains entangled: individual units do not correlate well with any object classes except for two units that are biased towards the ceiling of the room. Mid-level layers 4 to 7 have many units that match semantic objects and object parts. Units in layers 10 and beyond match local pixel patterns such as materials, edges and colors. All layers are shown in Section S-6.7. ",
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+    {
+        "type": "text",
+        "text": "Interpretable units for different GAN models. Interpretable units can provide insights about how GAN architecture choices affect the structures learned inside a GAN. Figure 7 compares three models from Karras et al. (2018): a baseline Progressive GANs, a modification that introduces minibatch stddev statistics, and a further modification that adds pixelwise normalization. By examining unit semantics, we confirm that providing minibatch stddev statistics to the discriminator increases not only the realism of results, but also the diversity of concepts represented by units: the number of types of objects, parts, and materials matching units increases by more than $4 0 \\%$ . The pixelwise normalization increases the number of units that match semantic classes by $1 9 \\%$ . ",
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+    {
+        "type": "image",
+        "img_path": "images/48f2e3ea25bf071cb331ec43d80250119dbe47c1c838b43856bc6609d385e2fb.jpg",
+        "image_caption": [
+            "Figure 5: Comparing representations learned by progressive GANs trained on different scene types. The units that emerge match objects that commonly appear in the scene type: seats in conference rooms and stoves in kitchens. Units from layer4 are shown. A unit is counted as a class predictor if it matches a supervised segmentation class with pixel accuracy $> 0 . 7 5$ and $\\mathrm { I o U } > 0 . 0 5$ when upsampled and thresholded. The distribution of units over classes is shown in the right column. "
+        ],
+        "image_footnote": [],
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+    {
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+        "img_path": "images/fcc6015500695ddaf505c4301a73be86169c016401324290b6861658a5db5c8b.jpg",
+        "image_caption": [
+            "Figure 6: Comparing layers of a progressive GAN trained to generate LSUN living room images. The output of the first convolutional layer has almost no units that match semantic objects, but many objects emerge at layers 4-7. Later layers are dominated by low-level materials, edges and colors. "
+        ],
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+    {
+        "type": "text",
+        "text": "4.2 DIAGNOSING AND IMPROVING GANS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "While our framework can reveal how GANs succeed in producing realistic images, it can also analyze the causes of failures in their results. Figure 8a shows several annotated units that are responsible for typical artifacts consistently appearing across different images. We can identify these units efficiently by human annotation: out of a sample of 1000 images, we visualize the top ten highest activating images for each unit, and we manually identify units with noticeable artifacts in this set. It typically takes 10 minutes to locate 20 artifact-causing units out of 512 units in layer4. ",
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+        "type": "text",
+        "text": "More importantly, we can fix these errors by ablating the above 20 artifact-causing units. Figure 8b shows that artifacts are successfully removed, and the artifact-free pixels stay the same, improving the generated results. In Table 1 we report two standard metrics, comparing our improved images to both the original artifact images and a simple baseline that ablates 20 randomly chosen units. First, we compute the widely used Frechet Inception Distance ( ´ Heusel et al., 2017) between the generated images and real images. We use 50, 000 real images and generate 10, 000 images with high activations on these units. Second, we score 1, 000 images per method on Amazon MTurk, collecting 20, 000 human annotations regarding whether the modified image looks more realistic compared to the original. Both metrics show significant improvements. Strikingly, this simple manual change to a network beats state-of-the-art GANs models. The manual identification of “artifact” units can be approximated by an automatic scoring of the realism of each unit, as detailed in Section S-6.1. ",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/b3b9639f2a5d71f35ac700815ea50208d06bf7aa6b36eeb5b0c2aae1ce01a2a8.jpg",
+        "image_caption": [
+            "Figure 7: Comparing layer4 representations learned by different training variations. Sliced Wasserstein Distance (SWD) is a GAN quality metric suggested by Karras et al. (2018): lower SWD indicates more realistic image statistics. Note that as the quality of the model improves, the number of interpretable units also rises. Progressive GANs apply several innovations including making the discriminator aware of minibatch statistics, and pixelwise normalization at each layer. We can see batch awareness increases the number of object classes matched by units, and pixel norm (applied in addition to batch stddev) increases the number of units matching objects. "
+        ],
+        "image_footnote": [],
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+    },
+    {
+        "type": "image",
+        "img_path": "images/c54400d708578b42a3e0abe37a55e0de7c23e5ece4be6e8badac38d4717ed88c.jpg",
+        "image_caption": [
+            "Figure 8: (a) We show two example units that are responsible for visual artifacts in GAN results. There are 20 units in total. By ablating these units, we can fix the artifacts in (b) and significantly improve the visual quality as shown in (c). "
+        ],
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+        "text": "",
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+    {
+        "type": "text",
+        "text": "4.3 LOCATING CAUSAL UNITS WITH ABLATION ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Errors are not the only type of output that can be affected by directly intervening in a GAN. A variety of specific object types can also be removed from GAN output by ablating a set of units in a GAN. In Figure 9 we apply the method in Section 3.2 to identify sets of 20 units that have causal effects on common object classes in conference rooms scenes. We find that, by turning off these small sets of units, most of the output of people, curtains, and windows can be removed from the generated scenes. However, not every object can be erased: tables and chairs cannot be removed. Ablating those units will reduce the size and density of these objects, but will rarely eliminate them. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The ease of object removal depends on the scene type. Figure 10 shows that, while windows can be removed well from conference rooms, they are more difficult to remove from other scenes. In particular, windows are just as difficult to remove from a bedroom as tables and chairs from a conference room. We hypothesize that the difficulty of removal reflects the level of choice that a GAN has learned for a concept: a conference room is defined by the presence of chairs, so they cannot be altered. And modern building codes mandate that all bedrooms must have windows; the GAN seems to have caught on to that pattern. ",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/f9a187e59a9b8d40a530ca7e71eae6196863eb69239395fa39ea14e2b85bbc67.jpg",
+        "table_caption": [
+            "Table 1: We compare generated images before and after ablating 20 “artifacts” units. We also report a simple baseline that ablates 20 randomly chosen units. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"2\">Fréchet Inception Distance (FID)</td></tr><tr><td>original images</td><td>43.16</td></tr><tr><td>“artifacts”units ablated (ours)</td><td>27.14</td></tr><tr><td>random units ablated</td><td>43.17</td></tr></table>",
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+    {
+        "type": "table",
+        "img_path": "images/4e8d363fabcb453499d11c878a9fb2bbe817e93f83f43cc64d3631ba92371149.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Human preference score</td><td>original images</td></tr><tr><td>“artifacts”units ablated (ours)</td><td>72.4%</td></tr><tr><td>random units ablated</td><td>49.9%</td></tr></table>",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/1f533220533042bd5692e3238ab6e9f3c0a844aeef4cfe076277d9e6c2db7c58.jpg",
+        "image_caption": [
+            "Figure 9: Measuring the effect of ablating units in a GAN trained on conference room images. Five different sets of units have been ablated related to a specific object class. In each case, 20 (out of 512) units are ablated from the same GAN model. The 20 units are specific to the object class and independent of the image. The average causal effect is reported as the portion of pixels that are removed in 1 000 randomly generated images. We observe that some object classes are easier to remove cleanly than others: a small ablation can erase most pixels for people, curtains, and windows, whereas a similar ablation for tables and chairs only reduces object sizes without deleting them. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "4.4 CHARACTERIZING CONTEXTUAL RELATIONSHIPS VIA INSERTION ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We can also learn about the operation of a GAN by forcing units on and inserting these features into specific locations in scenes. Figure 11 shows the effect of inserting 20 layer4 causal door units in church scenes. In this experiment, we insert these units by setting their activation to the fixed mean value for doors (further details in Section S-6.4). Although this intervention is the same in each case, the effects vary widely depending on the objects’ surrounding context. For example, the doors added to the five buildings in Figure 11 appear with a diversity of visual attributes, each with an orientation, size, material, and style that matches the building. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We also observe that doors cannot be added in most locations. The locations where a door can be added are highlighted by a yellow box. The bar chart in Figure 11 shows average causal effects of insertions of door units, conditioned on the background object class at the location of the intervention. We find that the GAN allows doors to be added in buildings, particularly in plausible locations such as where a window is present, or where bricks are present. Conversely, it is not possible to trigger a door in the sky or on trees. Interventions provide insight on how a GAN enforces relationships between objects. Even if we try to add a door in $\\mathtt { 1 a y e r 4 }$ , that choice can be vetoed later if the object is not appropriate for the context. These downstream effects are further explored in Section S-6.5. ",
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+    {
+        "type": "text",
+        "text": "5 DISCUSSION ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "By carefully examining representation units, we have found that many parts of GAN representations can be interpreted, not only as signals that correlate with object concepts but as variables that have a causal effect on the synthesis of objects in the output. These interpretable effects can be used to compare, debug, modify, and reason about a GAN model. Our method can be potentially applied to other generative models such as VAEs (Kingma & Welling, 2014) and RealNVP (Dinh et al., 2017). ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We have focused on the generator rather than the discriminator (as did in Radford et al. (2016)) because the generator must represent all the information necessary to approximate the target distribution, while the discriminator only learns to capture the difference between real and fake images. Alternatively, we can train an encoder to invert the generator (Donahue et al., 2017; Dumoulin et al., 2017). However, this incurs additional complexity and errors. Many GANs also do not have an encoder. ",
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+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/d95b40f694e777817012acbb1836b521080507c9ee55b98c11b00a753c506e47.jpg",
+        "image_caption": [
+            "Figure 10: Comparing the effect of ablating 20 window-causal units in GANs trained on five scene categories. In each case, the 20 ablated units are specific to the class and the generator and independent of the image. In some scenes, windows are reduced in size or number rather than eliminated, or replaced by visually similar objects such as paintings. "
+        ],
+        "image_footnote": [],
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+        "page_idx": 9
+    },
+    {
+        "type": "image",
+        "img_path": "images/8e0ead3e20c733b4df79af8ad4c1a424a5be42cb9259e8c4ac8ed79b99044229.jpg",
+        "image_caption": [
+            "Figure 11: Inserting door units by setting 20 causal units to a fixed high value at one pixel in the representation. Whether the door units can cause the generation of doors is dependent on its local context: we highlight every location that is responsive to insertions of door units on top of the original image, including two separate locations in (b) (we intervene at left). The same units are inserted in every case, but the door that appears has a size, alignment, and color appropriate to the location. Emphasizing a door that is already present results in a larger door (d). The chart summarizes the causal effect of inserting door units at one pixel with different contexts. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Our method is not designed to compare the quality of GANs to one another, and it is not intended as a replacement for well-studied GAN metrics such as FID, which estimate realism by measuring the distance between the generated distribution of images and the true distribution (Borji (2018) surveys these methods). Instead, our goal has been to identify the interpretable structure and provide a window into the internal mechanisms of a GAN. ",
+        "bbox": [
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Prior visualization methods (Zeiler & Fergus, 2014; Bau et al., 2017; Karpathy et al., 2016) have brought new insights into CNN and RNN research. Motivated by that, in this work we have taken a small step towards understanding the internal representations of a GAN, and we have uncovered many questions that we cannot yet answer with the current method. For example: why can a door not be inserted in the sky? How does the GAN suppress the signal in the later layers? Further work will be needed to understand the relationships between layers of a GAN. Nevertheless, we hope that our work can help researchers and practitioners better analyze and develop their own GANs. ",
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "REFERENCES ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            102,
+            287,
+            118
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Sebastian Bach, Alexander Binder, Gregoire Montavon, Frederick Klauschen, Klaus-Robert M ´ uller, ¨ and Wojciech Samek. On pixel-wise explanations for non-linear classifier decisions by layer-wise relevance propagation. PloS one, 10(7), 2015. 3 ",
+        "bbox": [
+            174,
+            133,
+            826,
+            176
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "David Bau, Bolei Zhou, Aditya Khosla, Aude Oliva, and Antonio Torralba. Network dissection: Quantifying interpretability of deep visual representations. In CVPR, 2017. 3, 4, 10 ",
+        "bbox": [
+            176,
+            185,
+            821,
+            214
+        ],
+        "page_idx": 10
+    },
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+        "bbox": [
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+    {
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+        "img_path": "images/9c0c48fce58fcbadd90dc49d6f6c145a4ea921ac7088b48cceb7e69f7ce5d18d.jpg",
+        "image_caption": [
+            "Figure 12: At left, visualizations of the highest-activating image patches (from a sample of 1000) for three units. (a) the lowest-FID unit that is manually flagged as showing artifacts (b) the highest-FID unit that is not manually flagged (c) the highest-FID unit overall, which is also manually flagged. At right, the precision-recall curve for unit FID as a predictor of the manually flagged artifact units. A FID threshold selecting the top 20 FID units will identify 10 (of 20) of the manually flagged units. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/3d2e591cc9c5daff993fc6a880075352656fa4bca866aa3441dbd66ef068bccf.jpg",
+        "image_caption": [
+            "",
+            "Figure 13: The effects of ablating high-FID units compared to manually-flagged units: (a) generated images with artifacts, without intervention; (b) those images generated after ablating the 20-highest FID units; (c) those images generated after ablating the 20 manually-chosen artifact units. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            174,
+            316,
+            825,
+            585
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "S-6 SUPPLEMENTARY MATERIAL ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            665,
+            465,
+            680
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "S-6.1 AUTOMATIC IDENTIFICATION OF ARTIFACT UNITS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            702,
+            575,
+            715
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "In Section 4.2, we have improved GANs by manually identifying and ablating artifact-causing units.   \nNow we describe an automatic procedure to identify artifact units using unit-specific FID scores. ",
+        "bbox": [
+            171,
+            728,
+            825,
+            756
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "To compute the FID score (Heusel et al., 2017) for a unit $u$ , we generate 200, 000 images and select the 10, 000 images that maximize the activation of unit $u$ , and this subset of 10, 000 images is compared to the true distribution (50, 000 real images) using FID. Although every such unit-maximizing subset of images represents a skewed distribution, we find that the per-unit FID scores fall in a wide range, with most units scoring well in FID while a few units stand out with bad FID scores: many of them were also manually flagged by humans, as they tend to activate on images with clear visible artifacts. ",
+        "bbox": [
+            173,
+            762,
+            825,
+            847
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "Figure 12 shows the performance of FID scores as a predictor of manually flagged artifact units. The per-unit FID scores can achieve $50 \\%$ precision and $50 \\%$ recall. That is, of the 20 worst-FID units, 10 are also among the 20 units manually judged to have the most noticeable artifacts. Furthermore, repairing the model by ablating the highest-FID units works: qualitative results are shown in Figure 13 and quantitative results are shown in Table 2. ",
+        "bbox": [
+            174,
+            853,
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+            922
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "table",
+        "img_path": "images/5e8ceb2456e270c9ace2f26f5f36677c34deaebdbed2e0fad36ce72dee4acb2f.jpg",
+        "table_caption": [
+            "Table 2: We compare generated images before and after ablating “artifact” units. The “artifacts” units are found either manually, automatically, or both. We also report a simple baseline that ablates 20 randomly chosen units. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"2\">Fréchet Inception Distance (FID)</td></tr><tr><td>original images</td><td>43.16</td></tr><tr><td>manually chosen “artifact”units ablated (as in Section 4.2)</td><td>27.14</td></tr><tr><td>highest-20 FIDunitsablated</td><td>27.6</td></tr><tr><td>union of manual and highest FID (3O total) units ablated</td><td>26.1</td></tr><tr><td>20 random units ablated</td><td>43.17</td></tr></table>",
+        "bbox": [
+            289,
+            148,
+            705,
+            239
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "image",
+        "img_path": "images/0a4639748e857ee3a693a712cb5764413ec84cf29c8e285bdaedc1612797bcee.jpg",
+        "image_caption": [
+            "Figure 14: Two examples of generator units that our dissection method labels differently from humans. Both units are taken from layer4 of a Progressive GAN of living room model. In (a), human label the unit as ‘sofa’ based on viewing the top-20 activating images, and our method labels as ‘ceiling’. In this case, our method counts many ceiling activations in a sample of 1000 images beyond the top 20. In (b), the dissection method has no confident label prediction even though the unit consistently triggers on white letterbox shapes at the top and bottom of the image. The segmentation model we use has no label for such abstract shapes. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            189,
+            253,
+            808,
+            387
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "S-6.2 HUMAN EVALUATION OF DISSECTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            507,
+            490,
+            521
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "As a sanity check, we evaluate the gap between human labeling of object concepts correlated with units and our automatic segmentation-based labeling, for one model, as follows. ",
+        "bbox": [
+            176,
+            532,
+            823,
+            561
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "For each of 512 units of layer4 of a “living room” Progressive GAN, 5 to 9 human annotations were collected (3728 labels in total). In each case, an AMT worker is asked to provide one or two words describing the highlighted patches in a set of top-activating images for a unit. Of the 512 units, 201 units were described by the same consistent word (such as ”sofa”, ”fireplace” or ”wicker”) in $50 \\%$ or more of the human labels. These units are interpretable to humans. ",
+        "bbox": [
+            174,
+            568,
+            825,
+            637
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Applying our segmentation-based dissection method, 154/201 of these units are also labeled with a confident label with $\\mathrm { I o U } > 0 . 0 5$ by dissection. In 104/154 cases, the segmentation-based model gave the same label word as the human annotators, and most others are slight shifts in specificity. For example, the segmentation labels “ottoman” or “curtain” or “painting” when a person labels “sofa” or “window” or “picture,” respectively. A second AMT evaluation was done to rate the accuracy of both segmentation-derived and human-derived labels. Human-derived labels scored $100 \\%$ (of the 201 human-labeled units, all of the labels were rated as consistent by most raters). Of the 154 segmentation-generated labels, 149 $( 9 6 \\% )$ were rated by most AMT raters as accurate as well. ",
+        "bbox": [
+            174,
+            645,
+            825,
+            756
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "The five failure cases (where the segmentation is confident but rated as inaccurate by humans) arise from situations in which human evaluators saw one concept after observing only 20 top-activating images, while the algorithm, in evaluating 1000 images, counted a different concept as dominant. Figure 14a shows one example: in the top images, mostly sofas are highlighted and few ceilings, whereas in the larger sample, mostly ceilings are triggered. ",
+        "bbox": [
+            174,
+            763,
+            825,
+            833
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "There are also 47/201 cases where the segmenter is not confident while humans have consensus. Some of these are due to missing concepts in the segmenter. Figure 14b shows a typical example, where a unit is devoted to letterboxing (white stripes at the top and bottom of images), but the segmentation has no confident label to assign to these. We expect that as future semantic segmentation models are developed to be able to identify more concepts such as abstract shapes, more of these units can be automatically identified. ",
+        "bbox": [
+            174,
+            840,
+            825,
+            924
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "image",
+        "img_path": "images/5857bfcb842ad3a357424d60048d2db92561ce52395dd56f84934a0f2fb73ffa.jpg",
+        "image_caption": [
+            "(b) Unit 371, FID 58.3, \"Swimming Pool\" with IoU 0.02. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            174,
+            102,
+            823,
+            284
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "image",
+        "img_path": "images/2b14f0c0d79f5c6183c78f46720439480f4387bf63d19dd693330cee931e324d.jpg",
+        "image_caption": [
+            "Figure 15: Two examples of units that correlate with unrealistic images that confuse a semantic segmentation network. Both units are taken from a WGAN-GP for LSUN bedrooms. ",
+            "Figure 16: Comparing a dissection of units for a WGAN-GP trained on LSUN bedrooms, considering all units (at left) and considering only “realistic” units with $\\mathrm { F I D } < 5 5$ (at right). Filtering units by FID scores removes spurious detected concepts such as ‘sky’, ‘ground’, and ‘building’. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            178,
+            335,
+            818,
+            410
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "S-6.3 PROTECTING SEGMENTATION MODEL AGAINST UNREALISTIC IMAGES",
+        "text_level": 1,
+        "bbox": [
+            176,
+            484,
+            710,
+            497
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "Our method relies on having a segmentation function $s _ { c } ( \\mathbf { x } )$ that identifies pixels of class $c$ in the output x. However, the segmentation model $s _ { c }$ can perform poorly in the cases where $\\mathbf { x }$ does not resemble the original training set of $s _ { c }$ . This phenomenon is visible when analyzing earlier GAN models. For example, Figure 15 visualizes two units from a WGAN-GP model (Gulrajani et al., 2017) for LSUN bedrooms (this model was trained by Karras et al. (2018) as a baseline in the original paper). For these two units, the segmentation network seems to be confused by the distorted images. ",
+        "bbox": [
+            174,
+            508,
+            825,
+            592
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "To protect against such spurious segmentation labels, we can use a technique similar to that described in Section S-6.1: automatically identify units that produce unrealistic images, and omit those “unrealistic” units from semantic segmentation. An appropriate threshold to apply will depend on the distribution being modeled: in Figure 16, we show how applying a filter, ignoring segmentation on units with FID 55 or higher, affects the analysis of this base WGAN model. In general, fewer irrelevant labels are associated with units. ",
+        "bbox": [
+            173,
+            599,
+            825,
+            683
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "S-6.4 COMPUTING CAUSAL UNITS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            699,
+            423,
+            713
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "In this section we provide more details about the ACE optimization described in Section 3.2. ",
+        "bbox": [
+            171,
+            724,
+            776,
+            739
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "Specifying the per-class positive intervention constant k. In Eqn. 3, the negative intervention is defined as zeroing the intervened units, and a positive intervention is defined as setting the intervened units to some big class-specific constant $\\mathbf { k }$ . For interventions for class $c$ , we set $\\mathbf { k }$ to be mean featuremap activation conditioned on the presence of class $c$ at that location in the output, with each pixel weighted by the portion of the featuremap locations that are covered by the class $c$ . Setting all units at a pixel to $\\mathbf { k }$ will tend to strongly cause the target class. The goal of the optimization is to find the subset of units that is causal for $c$ . ",
+        "bbox": [
+            174,
+            747,
+            825,
+            844
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "Sampling $c$ -relevant locations $\\mathbf { P }$ . When optimizing the causal objective (Eqn. 5), the intervention locations $\\mathrm { \\bf P }$ are sampled from individual featuremap locations. When the class $c$ is rare, most featuremap locations are uninformative: for example, when class $c$ is a door in church scenes, most regions of the sky, grass, and trees are locations where doors will not appear. Therefore, we focus the optimization as follows: during training, minibatches are formed by sampling locations $\\mathrm { \\bf P }$ that are relevant to class $c$ by including locations where the class $c$ is present in the output (and are therefore candidates for removal by ablating a subset of units), and an equal portion of locations where class $c$ is not present at $\\mathrm { \\bf P }$ , but it would be present if all the units are set to the constant $\\mathbf { k }$ (candidate locations for insertion with a subset of units). During the evaluation, causal effects are evaluated using uniform samples: the region $\\mathrm { \\bf P }$ is set to the entire image when measuring ablations, and to uniformly sampled pixels $\\mathrm { \\bf P }$ when measuring single-pixel insertions. ",
+        "bbox": [
+            174,
+            854,
+            823,
+            924
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "image",
+        "img_path": "images/bc240744718c3c6cda1eee4018008630bf1f641d462f4cd5cc686228ba4d1ea9.jpg",
+        "image_caption": [
+            "Figure 17: Tracing the effect of inserting door units on downstream layers. An identical ”door” intervention at layer4 of each pixel in the featuremap has a different effect on later feature layers, depending on the location of the intervention. In the heatmap, brighter colors indicate a stronger effect on the layer14 feature. A request for a door has a larger effect in locations of a building, and a smaller effect near trees and sky. At right, the magnitude of feature effects at every layer is shown, measured by the changes of mean-normalized features. In the line plot, feature changes for interventions that result in human-visible changes are separated from interventions that do not result in noticeable changes in the output. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            178,
+            107,
+            810,
+            258
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            174,
+            395,
+            825,
+            478
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "Initializing $_ { \\pmb { \\alpha } }$ with IoU. When optimizing causal $_ \\alpha$ for class $c$ , we initialize with ",
+        "bbox": [
+            174,
+            486,
+            720,
+            501
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "equation",
+        "img_path": "images/3c44f254cab4c29d1300ba63dab4b42f8362110f361313f59c1c085fffde7bcf.jpg",
+        "text": "$$\n\\alpha _ { u } = \\frac { \\mathrm { I o U } _ { u , c } } { \\operatorname* { m a x } _ { v } \\mathrm { I o U } _ { v , c } }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            433,
+            506,
+            565,
+            540
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "That is, we set the initial $\\alpha$ so that the largest component corresponds to the unit with the largest IoU for class $c$ , and we normalize the components so that this largest component is 1. ",
+        "bbox": [
+            173,
+            544,
+            825,
+            573
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "Applying a learned intervention $_ \\alpha$ When applying the interventions, we clip $_ \\alpha$ by keeping only its top $n$ components and zeroing the remainder. To compare the interventions of different classes an different models on an equal basis, we examine interventions where we set $n = 2 0$ . ",
+        "bbox": [
+            174,
+            580,
+            825,
+            623
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "S-6.5 TRACING THE EFFECT OF AN INTERVENTION ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            640,
+            539,
+            654
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "To investigate the mechanism for suppressing the visible effects of some interventions seen in Section 4.4, in this section we insert 20 door-causal units on a sample of individual featuremap locations at $\\mathtt { 1 a y e r 4 }$ and measure the changes caused in later layers. ",
+        "bbox": [
+            176,
+            665,
+            823,
+            707
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "To quantify effects on downstream features, the change in each feature channel is normalized by that channel’s mean L1 magnitude, and we examine the mean change in these normalized featuremaps at each layer. In Figure 17, these effects that propagate to layer14 are visualized as a heatmap: brighter colors indicate a stronger effect on the final feature layer when the door intervention is in the neighborhood of a building instead of trees or sky. Furthermore, we plot the average effect on every layer at right in Figure 17, separating interventions that have a visible effect from those that do not. A small identical intervention at layer4 is amplified to larger changes up to a peak at layer12. ",
+        "bbox": [
+            174,
+            714,
+            825,
+            813
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "S-6.6 MONITORING GAN UNITS DURING TRAINING ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            828,
+            547,
+            843
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "Dissection can also be used to monitor the progress of training by quantifying the emergence, diversity, and quality of interpretable units. For example, in Figure 18 we show dissections of layer4 representations of a Progressive GAN model trained on bedrooms, captured at a sequence of checkpoints during training. As training proceeds, the number of units matching objects increases, as does the number of object classes with matching units, and the quality of object detectors as measured by average IoU over units increases. During this successful training, dissection suggests that the model is gradually learning the structure of a bedroom, as increasingly units converge to meaningful bedroom concepts. ",
+        "bbox": [
+            174,
+            853,
+            825,
+            924
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "image",
+        "img_path": "images/cad93eb9cc9ec0daa9de61c15ec2baff405ad2e89f5afeca9902c057ef0565ec.jpg",
+        "image_caption": [
+            "Figure 18: The evolution of $\\mathtt { l a y e r 4 }$ of a Progressive GAN bedroom generator as training proceeds. The number and quality of interpretable units increases during training. Note that in early iterations, Progressive GAN generates images at a low resolution. The top-activating images for the same four selected units is shown for each iteration, along with the IoU and the matched concept for each unit at that checkpoint. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            171,
+            97,
+            826,
+            571
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            174,
+            664,
+            825,
+            707
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "S-6.7 ALL LAYERS OF A GAN ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            723,
+            398,
+            738
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "In Section 4.1 we show a small selection of layers of a GAN; in Figure 19 we show a complete listing of all the internal convolutional layers of that model (a Progressive GAN trained on LSUN living room images). As can be seen, the diversity of units matching high-level object concepts peaks at layer4-layer6, then declines in later layers, with the later layers dominated by textures, colors, and shapes. ",
+        "bbox": [
+            174,
+            748,
+            826,
+            819
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "image",
+        "img_path": "images/be3d8f590ea85f23160f14a695d85d37b582b2681518c60587d22589ea9ebadd.jpg",
+        "image_caption": [
+            "Figure 19: All layers of a Progressive GAN trained to generate LSUN living room images. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            173,
+            82,
+            826,
+            895
+        ],
+        "page_idx": 18
+    }
+]

parse/train/JCodE7xOcc5/JCodE7xOcc5.md

@@ -0,0 +1,264 @@
+# HSVA: Hierarchical Semantic-Visual Adaptation for Zero-Shot Learning
+
+Shiming Chen†, Guo-Sen Xie‡, Yang $\mathbf { L i u ^ { \ S } }$ , Qinmu Peng†, Baigui $\mathbf { S u n ^ { \ S } }$ , Hao $\mathbf { L i } ^ { \ S }$ , Xinge $\mathbf { V o u } ^ { \dagger }$ , Ling Shao‡]
+
+†Huazhong University of Science and Technology (HUST), China §Alibaba Group, Hangzhou, China ‡Mohamed bin Zayed University of AI (MBZUAI), UAE ]Inception Institute of Artificial Intelligence (IIAI), UAE {shimingchen,youxg}@hust.edu.cn ling.shao@ieee.org
+
+# Abstract
+
+Zero-shot learning (ZSL) tackles the unseen class recognition problem, transferring semantic knowledge from seen classes to unseen ones. Typically, to guarantee desirable knowledge transfer, a common (latent) space is adopted for associating the visual and semantic domains in ZSL. However, existing common space learning methods align the semantic and visual domains by merely mitigating distribution disagreement through one-step adaptation. This strategy is usually ineffective due to the heterogeneous nature of the feature representations in the two domains, which intrinsically contain both distribution and structure variations. To address this and advance ZSL, we propose a novel hierarchical semantic-visual adaptation (HSVA) framework. Specifically, HSVA aligns the semantic and visual domains by adopting a hierarchical two-step adaptation, i.e., structure adaptation and distribution adaptation. In the structure adaptation step, we take two task-specific encoders to encode the source data (visual domain) and the target data (semantic domain) into a structure-aligned common space. To this end, a supervised adversarial discrepancy (SAD) learning is proposed to adversarially minimize the discrepancy between the predictions of two task-specific classifiers, thus making the visual and semantic feature manifolds more closely aligned. In the distribution adaptation step, we directly minimize the Wasserstein distance between the latent multivariate Gaussian distributions to align the visual and semantic distributions using a common encoder. Finally, the structure and distribution adaptation are derived in a unified framework under two partially-aligned variational autoencoders. Extensive experiments on four benchmark datasets demonstrate that HSVA achieves superior performance on both conventional and generalized ZSL. The code is available at https://github.com/shiming-chen/HSVA .
+
+# 1 Introduction
+
+Over the past decade, significant progress has been made in zero-shot learning (ZSL), which aims to recognize new classes during learning by exploiting the intrinsic semantic relatedness between seen and unseen categories [1, 2, 3]. Inspired by the way humans learn unknown concepts, sideinformation (e.g., attributes [4], word vectors [5], and sentences [6]) related to seen/unseen classes is employed to guarantee knowledge transfer between the seen/unseen data. Common space learning is one typical method for representing the relationship between the visual and semantic domains for ZSL, which is key to dealing with the knowledge transfer [7]. However, existing common space learning methods align the distributions of the semantic and visual domains with one-step adaptation [8, 9, 7, 10, 11, 12, 13], while neglecting the fact that the heterogeneous feature representations of distinct semantic and visual domains have both distribution and structure variations. Thus, their performance is limited. In this work, we propose a novel common space learning formulation that leverages a hierarchical semantic-visual adaptation to learn an intrinsic common space for a better alignment of the two heterogeneous representation domains.
+
+![](images/dc999e1d7892af3d10757148783beb12428b11ffc6dae40cc3e7298f6d9e759d.jpg)  
+Figure 1: Illustration of HSVA. Common space learning methods learn domain-aligned feature representations for semantic and visual domains in latent embedding space with semantic-visual adaptation. However, the heterogeneous feature representations of the semantic and visual domains vary in both distribution and structure. (a) One-step adaptation focuses on distribution alignment between visual and semantic domains, neglecting structure variation. This causes the semantic and visual distributions to be located in different manifolds, resulting in the misclassification of some samples. (b) Hierarchical adaptation, in contrast, can learn an intrinsic and discriminative common space for semantic and visual feature representations by adopting sequential structure adaptation and distribution adaptation. We provide t-SNE visualizations [14] of features learned by (c) CADA-VAE [11] and (d) our HSVA on 10 classes from AWA2 (the "o" and $" \mathbf { X } "$ indicate visual and semantic features, respectively, and different colors denote different classes). Best viewed in color.
+
+The heterogeneous feature representations of the semantic and visual domains are distinct [15, 16]. Although one-step adaptation learns distribution-aligned feature representations for the semantic and visual domains using two different mapping models (e.g., encoders) and distribution alignment constraints (e.g., maximum mean discrepancy (MMD)), the two distributions are located in different manifolds since the one-step adaptation does not consider the manifold structure relationship between visual and semantic representations, as shown in Figure 1 (a) and (c). If we take the Euclidean distance or manifold distance [17, 18] to measure the relationship between different classes, the classifier inevitably misclassifies some samples, thus leading to inferior ZSL performance. As such, mapping the semantic and visual domains into an intrinsic and desirable common space for conducting an effective ZSL is highly necessary.
+
+To learn structure- and distribution-aligned feature representations for distinct visual and semantic domains, we propose a hierarchical semantic-visual adaptation (HSVA) framework to learn an intrinsic common space that contains the essential multi-modal information associated with unseen classes (Figure 1 (b) and (d)). HSVA aligns the semantic and visual domains with structure adaptation (SA) and distribution adaptation (DA) in a unified framework, under two partially-aligned variational autoencoders. In the SA, we use two task-specific encoders to encode source data (visual domain) and target data (semantic domain), respectively, into a structure-aligned space, which is learned through supervised adversarial discrepancy (SAD) learning to minimize the discrepancy between the predictions of the two task-specific classifiers. This encourages the visual and semantic feature manifolds to be closer to each other, thus aligning the manifold structure variation. In the DA, we map the structure-aligned features into a distribution-aligned common space using a common encoder, which is optimized by minimizing the Wasserstein distance between the latent multivariate Gaussian distributions of the visual and semantic domains. The common encoder preserves the structure-aligned representations in the DA. Thus, HSVA can learn a structure and distributionaligned common space for visual and semantic feature representations, which is better than the distribution-aligned feature representations learned by existing common space learning methods [8, 9, 7, 10, 11, 19]. To the best of our knowledge, this is the first work that leverages hierarchical semantic-visual adaptation to address heterogeneous feature alignment in ZSL. Following [11], we conduct extensive experiments on four challenging benchmark datasets, i.e., CUB, SUN, AWA1, and AWA2, under both conventional and generalized ZSL settings. The proposed HSVA achieves consistent improvement over the existing common space learning methods on all datasets. We show qualitatively that the structural variation is important for the interaction between visual and semantic domains. Moreover, we show significantly better common space for visual and semantic feature representations than the existing common space learning methods, e.g., CADA-VAE [11].
+
+# 2 Related Work
+
+Zero-Shot Learning. In practice, the relationship between visual and semantic domains is determined by learning an embedding space where semantic vectors and visual features interact [20, 21, 22, 23, 24, 25, 26, 19]. There are three mapping methods for learning such an embedding space, including direct mapping, model parameter transfer, and common space learning [7]. Direct mapping learns a mapping function from visual features to semantic representations [4, 20, 27]. However, its generalization is limited by the high intra-class variability of the visual domain. Meanwhile, the lower-dimensional semantic space shrinks the variance of the projected data points, resulting in the hubness problem [28]. Model parameter transfer, in contrast, takes place in the visual space, where the model parameters for unseen classes are usually obtained [29, 30]. In essence, generative ZSL follows this methodology, simultaneously learning semantic visual mapping and data augmentation [22, 31, 32, 22, 33]. However, since the inter-class relationships among unseen classes are not taken into account, model parameter transfer is often limited [7]. Finally, common space learning learns a common representation space into which both visual features and semantic representations are projected for effective knowledge transfer [34, 9, 7, 10, 11]. By calibrating the common space using bidirectionally aligned knowledge of the visual and semantic representations, it can simultaneously avoid the issues of direct mapping and model parameter transfer. As such, common space learning is a promising methodology for ZSL. However, existing common space learning methods align the semantic and visual distributions with one-step adaptation, which neglects the distinct heterogeneous feature representations of the semantic and visual domains that are characterized by structure and distribution variations. This causes the distribution-aligned common space to be located in a different manifold, and samples to thus inevitably misclassified. In contrast, we propose an effective framework with both structure adaptation and distribution adaptation to address these challenges.
+
+Domain Adaptation. Domain adaptation aims to learn domain-invariant representations by minimizing the discrepancy between the distributions of source and target via distribution alignment, domain adversarial learning, or task-specific methods. It can be divided into homogeneous and heterogeneous domain adaptation according to the characteristics of the source and target data. In the homogeneous domain adaptation setting, the feature spaces of the source and target domains are identical, with the same dimensions. Thus, one-step adaptation can be employed [35, 36, 37]. In contrast, in the heterogeneous setting, the feature spaces of the source and target domains are distant, and their dimensions also typically differ. Since there is little overlap between the two domains, one-step domain adaptation is not effective in the heterogeneous domain adaptation [38, 39]. Thus, multi-step (or transitive) domain adaptation methods are used for heterogeneous domain adaptation. However, these methods cannot be directly used in ZSL. Since ZSL has four domains (i.e., seen, unseen, semantic, and visual), knowledge cannot be transferred between two domains only, i.e., the distributions of the source and target domains cannot be aligned. We argue that the structure variation should also be taken into account when aligning the visual and semantic domains in ZSL.
+
+![](images/e0e5b6841996583a69ec502360589336056faa42cb1c0ad7e385dee66ed23bfe.jpg)  
+Figure 2: The framework of the proposed hierarchical semantic-visual adaptation (HSVA). HSVA consists of two partially-aligned variational autoencoders, which simultaneously perform structure adaptation and distribution adaptation with various constraints. Our two-step adaptation formulation helps HSVA learn structure and distribution-aligned feature representations for visual and semantic in an unified framework, which avoids the adverse effects of heterogeneous feature representations between distinct visual and semantic domains.
+
+# 3 Hierarchical Semantic-Visual Adaptation
+
+The task of ZSL is formulated as follows. Let $S = \{ ( x ^ { s } , y ^ { s } , a ^ { s } ) ~ | ~ x ^ { s } \in X , y ^ { s } \in Y ^ { s } , a ^ { s } \in A \}$ be a training set consisting of image features $x$ extracted by a convolutional neural network (CNN) Backbone (e.g., ResNet-101), where seen class embeddings $a ^ { s }$ are learned by a language model and seen class labels $y ^ { s }$ . In addition, an auxiliary training set $U = \{ ( y ^ { u } , a ^ { u } ) ~ | ~ y ^ { u } \in Y ^ { u } \}$ from unseen classes is used, where $y ^ { u }$ denotes unseen classes from a set $Y ^ { u }$ , which is disjoint from $Y ^ { S }$ . $x ^ { u } \in X$ are the unseen visual features in the test set. Note that $x = x ^ { s } \cup x ^ { u }$ and $a = a ^ { s } \cup a ^ { u }$ . The goal of conventional ZSL (CZSL) is to learn a classifier for unseen visual features, i.e., $f _ { C Z S L } : X \stackrel { \textstyle - } { \to } Y ^ { U }$ , while for generalized ZSL (GZSL) the goal is to learn a classifier for seen and unseen visual features, i.e., $f _ { G Z S L } : X \to Y ^ { U } \cup Y ^ { S }$ .
+
+In the following, we introduce our HSVA, which learns an intrinsic common space for semantic and visual feature representations to conduct ZSL. As shown in Figure 2, our framework consists of two partially-aligned autoencoders, which conduct structure adaptation (SA) and distribution adaptation (DA). In the end of this section, we demonstrate how we perform zero-shot learning using the feature representations extracted from the intrinsic common manifold space.
+
+# 3.1 Partially-Aligned Variational Autoencoders
+
+Our HSVA model consists of two partially-aligned variational autoencoders. The first includes two feature encoders (visual encoder $E ^ { x }$ and common encoder $E ^ { z }$ ) and one decoder (visual decoder $D ^ { x }$ ). $E ^ { x }$ and $E ^ { z }$ are used to learn structure and distribution-aligned visual embeddings, respectively, which share two common spaces (i.e., structure and distribution-aligned spaces) with the semantic embeddings. $D ^ { x }$ aims to decode the distribution-aligned embeddings from the visual and semantic features to be similar to the visual features. Analogously, the second variational autoencoder has a similar structure to the first (i.e., it includes a semantic encoder $E ^ { a }$ , the $E ^ { z }$ , and a semantic decoder $D ^ { a }$ ), but it is employed to learn semantic embeddings. The partially-aligned variational autoencoders are first optimized by two variational autoencoders (VAE) losses:
+
+$$
+\begin{array} { r l } & { \mathcal { L } _ { V A E } ^ { x } ( E ^ { x } , E ^ { z } ) = \mathbb { E } [ \log D ^ { x } ( z ^ { x ^ { s } } ) ] - \gamma \mathrm { K L } ( E ^ { z } ( E ^ { x } ( x ^ { s } ) ) ) \| p ( z ^ { x ^ { s } } | x ^ { s } ) ) , } \\ & { \mathcal { L } _ { V A E } ^ { a } ( E ^ { a } , E ^ { z } ) = \mathbb { E } [ \log D ^ { a } ( z ^ { a ^ { s } } ) ] - \gamma \mathrm { K L } ( E ^ { z } ( E ^ { a } ( a ^ { s } ) ) ) \| p ( z ^ { a ^ { s } } | a ^ { s } ) ) , } \end{array}
+$$
+
+where $z ^ { x ^ { s } }$ and $z ^ { a ^ { s } }$ are the visual and semantic embeddings in the distribution-aligned space, $\gamma$ is the weight of the KL-divergence, and $p ( z ^ { a ^ { s } } | a ^ { s } )$ and $p ( z ^ { x ^ { s } } | x ^ { s } )$ are the prior distributions assumed to be $\mathcal { N } ( 0 , 1 )$ . To make the visual and semantic embeddings in the structure- and distribution-aligned spaces more consistent, we then use a cross reconstruction loss to constrain the two partially-aligned
+
+variational autoencoders:
+
+$$
+\mathcal { L } _ { R E C } ( E ^ { x } , E ^ { a } , E ^ { z } , D ^ { x } , D ^ { a } ) = \mathcal { L } _ { R E C } ^ { x } ( E ^ { x } , E ^ { z } , D ^ { x } ) + \mathcal { L } _ { R E C } ^ { a } ( E ^ { a } , E ^ { z } , D ^ { a } )
+$$
+
+where
+
+$$
+\begin{array} { r } { \mathcal { L } _ { R E C } ^ { x } ( E ^ { x } , E ^ { z } , D ^ { x } ) = \Big \lVert x ^ { s } - D ^ { x } ( z ^ { a ^ { s } } ) \Big \rVert _ { 1 } , } \\ { \mathcal { L } _ { R E C } ^ { a } ( E ^ { a } , E ^ { z } , D ^ { a } ) = \Big \lVert a ^ { s } - D ^ { a } ( z ^ { x ^ { s } } ) \Big \rVert _ { 1 } . } \end{array}
+$$
+
+Finally, the two partially-aligned variational autoencoders conduct structure and distribution adaptation for the visual and semantic features, which will be introduced in the following.
+
+# 3.2 Structure Adaptation
+
+Structure adaptation (SA) is used to guide the encoder $E ^ { x }$ and $E ^ { a }$ to learn a structure-aligned space for the visual and semantic features. Previous methods [7, 11] directly align the semantic and visual features with distribution distance constraints (e.g., MMD), which neglects the structure variation between the heterogeneous feature representations of the two domains. Furthermore, these methods fail to learn discriminative features as they do not take category relationships into account, as shown in Figure 1 (a). Motivated by task-specific unsupervised domain adaptation [36, 37], we propose a supervised adversarial discrepancy (SAD) learning to minimize the discrepancy between the outputs of two task-specific classifiers $( \dot { C } L \dot { S } ^ { 1 } , \dot { C } L S ^ { 2 } )$ . This enables us to learn a class decision boundary and embed semantic and visual features into a structure-aligned common space for SA. Thus, SA can learn discriminative structure-aligned representations for semantic and visual features. Different from [36, 37], which only detect the target samples (e.g., semantic embeddings $E ^ { a } ( a ) )$ ) to learn a single encoder (generator), SAD simultaneously detects the source samples (e.g., visual embeddings $E ^ { x } ( x ) _ { , }$ ) and target samples (e.g., semantic embeddings $E ^ { a } ( a ) )$ ) to learn a good structure-aligned common space with two task-specific encoders. Specifically, SAD includes three steps for optimization: 1) semantic and visual embedding classification for $E ^ { x }$ , $E ^ { a }$ , $C L S ^ { 1 }$ and $\boldsymbol { C } \boldsymbol { \dot { L } } \boldsymbol { S } ^ { 2 }$ ; 2) discrepancy maximization for $C L S ^ { 1 }$ and $C L S ^ { \overline { { 2 } } }$ ; and 3) discrepancy minimization for $E ^ { x }$ and $E ^ { a }$ .
+
+Semantic and Visual Embedding Classification. We train $E ^ { x }$ , $E ^ { a }$ , $C L S ^ { 1 }$ and $C L S ^ { 2 }$ by minimizing the softmax cross-entropy to collectly classify the structure-aligned semantic and visual embeddings. This is crucial for enabling classifiers and encoders $( E ^ { x } , E ^ { a } )$ to obtain task-specific discriminative features. The visual and semantic classification loss is formulated as:
+
+$$
+\begin{array} { r l r } & { } & { \mathcal { L } _ { C L S } ( E ^ { x } , E ^ { a } , C L S ^ { 1 } , C L S ^ { 2 } ) = \mathcal { L } _ { C L S ^ { 1 } } ( E ^ { x } ( x ^ { s } ) , y ^ { s } ) + \mathcal { L } _ { C L S ^ { 2 } } ( E ^ { x } ( x ^ { s } ) , y ^ { s } ) } \\ & { } & { + \mathcal { L } _ { C L S ^ { 1 } } ( E ^ { a } ( a ^ { s } ) , y ^ { s } ) + \mathcal { L } _ { C L S ^ { 2 } } ( E ^ { a } ( a ^ { s } ) , y ^ { s } ) , } \end{array}
+$$
+
+where
+
+$$
+\mathcal { L } _ { C L S ^ { 1 } } ( \mathbf { x } , \mathbf { y } ) = \mathcal { L } _ { C L S ^ { 2 } } ( \mathbf { x } , \mathbf { y } ) = - \mathbb { E } \sum _ { k = 1 } ^ { K } \mathbb { I } _ { [ k = \mathbf { y } ] } \log p \left( y \mid \mathbf { x } \right) .
+$$
+
+Here K is the number of seen classes, $\mathbb { I } _ { [ k = \mathbf { y } ] }$ is an indicator function (i.e., it is one when $k = \mathbf { y }$ , otherwise zero), and $p \left( y | \mathbf { x } \right)$ is the prediction of $\mathbf { x }$ . We use two classifiers to simultaneously classify the visual and semantic embeddings to initialize the classifiers, which are used for discrepancy learning later.
+
+Discrepancy Maximization for Classifiers. In this step, we freeze the parameters of the encoders $( E ^ { x } , E ^ { a } )$ and update the classifiers $( C L S ^ { 1 } , C L S ^ { 2 } )$ to maximize the discrepancy between the outputs of the two classifiers on the visual and semantic embeddings. Thus, the source and target samples outside the support of task-specific decisions are identified, providing the positive signals to separate the class decision boundaries. Since sliced Wasserstein discrepancy (SWD) [37] provides geometrically meaningful guidance for capturing the natural notion of dissimilarity, we use it to measure the discrepancy between two classifier predictions for visual embeddings $\dot { ( p _ { 1 } ( y ^ { s } | E ^ { x } ( x ^ { s } ) ) }$ , $p _ { 2 } ( y ^ { s } | E ^ { x } ( x ^ { s } ) ) \rangle$ and semantic embeddings $( p _ { 1 } ( y ^ { \bar { s } } | E ^ { a } ( a ^ { s } ) )$ , $p _ { 2 } ( y ^ { s } | E ^ { a } ( a ^ { s } ) ) _ { , } ^ { }$ ):
+
+$$
+\begin{array} { r l r } {  { \mathcal { L } _ { D I S ^ { 1 } } ( C L S ^ { 1 } , C L S ^ { 2 } ) = - \mathcal { L } _ { S W D } ( E ^ { x } ( x ^ { s } ) ) - \mathcal { L } _ { S W D } ( E ^ { a } ( a ^ { s } ) ) , } } \\ & { \mathcal { L } _ { S W D } ( \mathbf { x } ) = \displaystyle \sum _ { m } ( \mathcal { R } _ { \theta _ { m } } p _ { 1 } ( y | \mathbf { x } ) , \mathcal { R } _ { \theta _ { m } } p _ { 2 } ( y | \mathbf { x } ) ) , } \end{array}
+$$
+
+where $\mathcal { R } _ { \theta _ { m } }$ is the mth one-dimensional linear projection operation, and $\theta$ is a uniform measure on the unit sphere $S ^ { ( d - 1 ) }$ in $\mathbb { R } ^ { d }$ . The larger the $\mathcal { L } _ { D I S }$ , the larger the discrepancy.
+
+Discrepancy Minimization for Encoders. To encourage the visual embedding $( E ^ { x } ( x ^ { s } ) )$ and semantic embedding $( E ^ { a } ( a ^ { s } ) )$ to be aligned well in the structure-aligned space, we freeze the parameters of the two classifiers and update the two encoders $( E ^ { x } , E ^ { a } )$ to minimize the discrepancy between the outputs of the two classifiers on $E ^ { x } ( x ^ { s } )$ and $E ^ { a } ( a ^ { s } )$ :
+
+$$
+\mathcal { L } _ { D I S ^ { 2 } } ( E ^ { x } , E ^ { a } ) = \mathcal { L } _ { S W D } ( E ^ { x } ( x ^ { s } ) ) + \mathcal { L } _ { S W D } ( E ^ { a } ( a ^ { s } ) ) .
+$$
+
+This encourages the visual and semantic feature manifolds to be closer to each other, and thus the manifold structure variation is circumvented.
+
+# 3.3 Distribution Adaptation
+
+After structure adaptation, HSVA can learn a structure-aligned common space to avoid manifold structure difference between visual and semantic embeddings. However, the structure-aligned common space is still limited by distribution variation. To further learn a distribution-aligned common space for visual and semantic feature representations, we propose distribution adaptation. Existing common space learning methods [8, 9, 7, 10, 11] employ two different mapping functions (encoders) to align the visual and semantic distributions to learn distribution-aligned embedding. In contrast, our main idea is to protect the structure-aligned visual and semantic embeddings in a distribution-aligned space using a common encoder $E ^ { z }$ , which preserves the structure-aligned representations in the DA. Our DA is first optimized by minimizing the Wasserstein distance between the latent multivariate Gaussian distributions, formulated as follows:
+
+$$
+\begin{array} { r } { \mathcal { L } _ { D A } ( E ^ { x } , E ^ { a } , E ^ { z } ) = \left( \left. \mu ^ { x ^ { s } } - \mu ^ { a ^ { s } } \right. _ { 2 } ^ { 2 } + \left. ( \delta ^ { x ^ { s } } ) ^ { \frac { 1 } { 2 } } - ( \delta ^ { a ^ { s } } ) ^ { \frac { 1 } { 2 } } \right. _ { \mathrm { F } } ^ { 2 } \right) ^ { \frac { 1 } { 2 } } , } \end{array}
+$$
+
+where $\| \cdot \| _ { F } ^ { 2 }$ denotes the squared matrix Frobenius norm.
+
+In essence, our HSVA is also a generative model, which is different to the GAN/VAE based methods [40, 31, 33] (i.e., learning mechanism and optimization). Due to the bias problem that arises when using generative models for ZSL, the synthesized unseen samples $( E ^ { z } ( E ^ { a } ( a ^ { u } ) ) )$ in the distributionaligned common space might be unexpectedly close to the seen ones. We propose to explicitly tackle this seen-unseen bias problem by preventing the encoded unseen samples $( E ^ { z } ( E ^ { a } ( a ^ { u } ) ) )$ from colliding with the encoded seen ones $( \bar { E } ^ { z } ( E ^ { x } ( x ^ { \bar { s } } ) ) ) ^ { 2 }$ . Since correlation alignment (CORAL) [41] has been shown effective for asymmetric transformations in domain adaptation, we take the CORALbased metric to measure the discrepancy between seen and unseen class samples. Different from [41], which takes CORAL to decrease the discrepancy between two domains, we aim to increase the discrepancy. Hence, we employ the inverse CORAL (iCORAL), defined upon the numerical negation of CORAL:
+
+$$
+\mathcal { L } _ { i C O R A L } ( E ^ { x } , E ^ { a } , E ^ { z } ) = - C O R A L ( E ^ { z } ( E ^ { x } ( x ^ { s } ) ) , E ^ { z } ( E ^ { a } ( a ^ { u } ) ) ) .
+$$
+
+# 3.4 Optimization
+
+Our full model optimizes the partially-aligned variational autoencoders, DA and SA, simultaneously with the following objective function:
+
+$$
+\begin{array} { r l } & { \mathcal { L } _ { H S V A } ( E ^ { x } , E ^ { a } , C L S ^ { 1 } , C L S ^ { 2 } , E ^ { z } , D ^ { x } , D ^ { a } ) = \mathcal { L } _ { V A E } ^ { x } + \mathcal { L } _ { V A E } ^ { a } + \lambda _ { 1 } \mathcal { L } _ { R E C } + \mathcal { L } _ { C L S } } \\ & { \phantom { \mathcal { L } _ { H S V A } } + \lambda _ { 2 } ( \mathcal { L } _ { D I S ^ { 1 } } + \mathcal { L } _ { D I S ^ { 2 } } ) + \lambda _ { 3 } ( \mathcal { L } _ { i C O R A L } + \mathcal { L } _ { D A } ) , } \end{array}
+$$
+
+where $\lambda _ { 1 } , \lambda _ { 2 } ,$ $\lambda _ { 3 }$ are the weights that control the importance of the related loss terms. Similar to the alternative updating policy for generative adversarial networks (GANs), we alternately train $E ^ { x }$ , $E ^ { a }$ , $C L S ^ { 1 }$ , $C L \bar { S } ^ { 2 }$ when optimizing SA. Although, HSVA has three components in total, the whole training process are simultaneous and loss weights of all terms in Eq. 13 are the same for all datasets. The consistently significant results on all datasets show that our model is robust and easy to train.
+
+# 3.5 Classification
+
+Once our HSVA model is learned, the visual and semantic features are encoded as new feature representations in a distribution-aligned common space, where structure variation is aslo considered for classification. Using the reparametrization trick [42], we take $E ^ { x }$ and $E ^ { z }$ to encode the visual features of seen classes $( x ^ { s } )$ and unseen classes $( x ^ { u } )$ into structure- and distribution-aligned feature representations, i.e., $z ^ { x ^ { s } } = E ^ { z } ( E ^ { x } ( x ^ { s } ) )$ and $z ^ { x ^ { u } } = E ^ { z } ( E ^ { x } ( x ^ { u } ) )$ . Analogously, we take $E ^ { a }$ and $E ^ { z }$ to encode the semantic embeddings $a$ as $z ^ { a } = E ^ { z } ( E ^ { a } ( a ) )$ , where $z ^ { a } = \bar { z } ^ { a ^ { s } } \cup \bar { z } ^ { a ^ { u } }$ . We employ $z ^ { x ^ { s } }$ $x ^ { s }$ from the training set) and $z ^ { a ^ { u } }$ to train a supervised classifier (e.g., softmax). Once the classifier is trained, we use $z ^ { \bar { x } ^ { s } }$ $x ^ { s }$ from the test set) and $z ^ { x ^ { u } }$ to test the model. Note that our HSVA is an inductive method as we do not use the visual features of unseen classes for training.
+
+# 4 Experiments
+
+Datasets. We conduct extensive experiments on four well-known ZSL benchmark datasets, including fine-grained datasets (e.g., CUB [43] and SUN [44]) and coarse-grained datasets (e.g., AWA1 [4] and AWA2 [45]). CUB includes 11,788 images of 200 bird classes (seen/unseen classes $= 1 5 0 / 5 0 $ ) with 312 attributes. SUN contains 14,340 images from 717 scene classes (seen/unseen classes $=$ 645/72) with 102 attributes. AWA1 and AWA2 contain 30,475 and 37,322 images from 50 animal classes (seen/unseen classes $= 4 0 / 1 0$ ) with 85 attributes.
+
+Implementation Details. We use the training splits proposed in [46]. Meanwhile, the visual features are extracted from the 2048-dimensional top-layer pooling units of a CNN backbone (i.e., ResNet-101) pre-trained on ImageNet. The encoders and decoders are multilayer perceptrons (MLPs). We employ the Adam optimizer [47] with $\beta _ { 1 } = 0 . 5$ and $\beta _ { 2 } = 0 . 9 9 9$ . We use an annealing scheme [48] to increase the weights $\gamma$ , $\lambda _ { 1 }$ , $\lambda _ { 2 }$ , $\lambda _ { 3 }$ with same setting for all datasets. Specifically, $\gamma$ is increased by a rate of 0.0026 per epoch until epoch 90, $\lambda _ { 1 }$ is increased from epoch 21 to 75 by 0.044 per epoch, and $\lambda _ { 2 }$ , $\lambda _ { 3 }$ are increased from epoch 0 to epoch 22 by a rate of 0.54 per epoch. In the CZSL setting, we synthesize 800, 400 and 200 features per unseen class to train the classifier for AWA1, CUB and SUN datasets, respectively. In the GZSL setting, we take 400 synthesized features per unseen class and 200 synthesized features per seen class to train the classifier for all datasets. The dimensions of the structure-aligned and distribution-aligned spaces are set to 2048 and 64 for three datasets (i.e., CUB, AWA1, AWA2), respectively, and 2048 and 128 for SUN benchmark.
+
+Evaluation Protocols. During testing, we follow the unified evaluation protocols proposed in [45]. Specifically, we measure the top-1 accuracy of unseen class $( A c c )$ for the CZSL setting. In the GZSL setting, we take the top-1 accuracy on seen classes $( S )$ and unseen classes $( U )$ , as well as their harmonic mean (defined as $H = ( 2 \times S \times U ) / ( S + U ) )$ .
+
+<table><tr><td>Method</td><td>AWA1 Acc</td><td>CUB Acc</td><td>SUN Acc</td></tr><tr><td>DeViSE(NeurIPS&#x27;13) [34]</td><td>54.2</td><td>52.0</td><td>56.5</td></tr><tr><td>DCN(NeurIPS&#x27;18)[10] CADA-VAE(CVPR&#x27;19)[11]</td><td>65.3 63.0</td><td>56.2 59.8</td><td>61.8 61.7</td></tr><tr><td></td><td></td><td></td><td></td></tr><tr><td>Our HSVA</td><td>70.6</td><td>62.8</td><td>63.8</td></tr></table>
+
+Table 1: Results of common space learning methods under the CZSL setting on three datasets.
+
+# 4.1 Experimental Results
+
+Results of Conventional Zero-Shot Learning. Table 1 presents the results of CZSL on various datasets. Our HSVA, with a softmax classifier, significantly outperforms other common space learning methods [34, 10, 11] by at least $5 . 3 \%$ , $3 . 0 \%$ and $2 . 0 \%$ on AWA1, CUB and SUN, respectively. Our significant performance improvements demonstrate that hierarchical semantic-visual adaptation can effectively learn an intrinsic common space to represent visual and semantic features. This space is structure- and distribution-aligned and alleviates the gap between heterogeneous feature representations.
+
+Table 2: State-of-the-art comparison under the GZSL setting on four datasets. The best and secondbest results are marked in red and blue, respectively. The "Common space" and "Non-common space" denote common space learning and non-common space learning methods, respectively. Meanwhile, the non-common space learning methods include the non-generative methods and generative methods.   
+
+<table><tr><td rowspan="2"></td><td rowspan="2">Method</td><td rowspan="2"></td><td colspan="3">AWA1 S</td><td colspan="3">AWA2 S</td><td colspan="3">CUB</td><td colspan="3">SUN</td></tr><tr><td>U</td><td></td><td>H</td><td>U</td><td></td><td>H</td><td>U</td><td>S</td><td>H</td><td>U</td><td>S</td><td>H</td></tr><tr><td rowspan="10">onns cooorcee</td><td>CRnet(ICML&#x27;19)[49]</td><td>58.1</td><td>74.7</td><td>65.4</td><td>- 31.7</td><td>- 70.9</td><td>- 43.8</td><td>45.5 43.2</td><td>56.8</td><td>50.5</td><td>34.1</td><td></td><td>36.5</td><td>35.3</td></tr><tr><td>PQZSL(CVPR&#x27;19)[50]</td><td>-</td><td>-</td><td></td><td></td><td></td><td></td><td></td><td></td><td>51.4</td><td>46.9</td><td>35.1</td><td>35.3</td><td>35.2</td></tr><tr><td>TCN(ICCV&#x27;19) [51]</td><td>49.4</td><td>76.5</td><td>60.0</td><td>61.2</td><td>65.8</td><td>63.4</td><td>52.6</td><td></td><td>52.0</td><td>52.3</td><td>31.2</td><td>37.3</td><td>34.0</td></tr><tr><td>SGMA(NeurIPS&#x27;19) [52]</td><td>37.6</td><td>87.1</td><td>52.5</td><td>-</td><td></td><td>-</td><td>36.7</td><td>71.3</td><td></td><td>48.5</td><td>-</td><td></td><td>-</td></tr><tr><td>DVBE(CVPR&#x27;20)[53]</td><td>-</td><td>-</td><td>-</td><td>63.6</td><td>70.8</td><td>67.0</td><td>53.2</td><td></td><td>60.2</td><td>56.5</td><td>45.0</td><td>37.2</td><td>40.7</td></tr><tr><td>DAZLE(CVPR&#x27;20) [54]</td><td>-</td><td></td><td>-</td><td>60.3</td><td>75.7</td><td>67.1</td><td>59.6</td><td></td><td>56.7</td><td>58.1</td><td>52.3</td><td>24.3</td><td>33.2</td></tr><tr><td>RGEN(ECCV&#x27;20)[55]</td><td>-</td><td></td><td>=</td><td>67.1</td><td>76.5</td><td>71.5</td><td>60.0</td><td></td><td>73.5</td><td>66.1</td><td>44.0</td><td>31.7</td><td>36.8</td></tr><tr><td>Composer(NeurIPS&#x27;20)[23]</td><td>-</td><td>-</td><td>-</td><td></td><td>62.1</td><td>77.3 68.8</td><td></td><td>63.8</td><td>56.4</td><td>59.9</td><td>55.1</td><td>22.0</td><td>31.4</td></tr><tr><td>APN(NeurIPS&#x27;20)[25]</td><td>-</td><td>-</td><td>-</td><td></td><td>56.5</td><td>78.0 65.5</td><td></td><td>65.3</td><td>69.3</td><td>67.2</td><td>41.9</td><td>34.0</td><td>37.6</td></tr><tr><td>f-CLSWGAN(CVPR&#x27;18) [46]</td><td>57.9</td><td>61.4</td><td></td><td>59.6</td><td>-</td><td></td><td>-</td><td>43.7</td><td>57.7</td><td>49.7</td><td>42.6</td><td>36.6</td><td>39.4</td></tr><tr><td>f-VAEGAN(CVPR&#x27;19) [31]</td><td></td><td>52.6</td><td>76.3</td><td>-</td><td>57.6</td><td>70.6</td><td>63.5</td><td>48.4</td><td>60.1</td><td>53.6</td><td>45.1</td><td>38.0</td><td>41.3</td></tr><tr><td>LisGAN(CVPR&#x27;19) [56]</td><td></td><td></td><td></td><td>62.3</td><td>-</td><td>- -</td><td>-</td><td>46.5</td><td>57.9</td><td>51.6</td><td>42.9</td><td>37.8</td><td>40.2</td></tr><tr><td>LsrGAN(ECCV&#x27;20) [22] AGZSL(ICLR&#x27;21) [26]</td><td>54.6 -</td><td>74.6 -</td><td></td><td>63.0</td><td></td><td></td><td></td><td>48.1 41.4</td><td>59.1</td><td>53.0</td><td>44.8</td><td>37.7</td><td>40.9</td></tr><tr><td></td><td></td><td></td><td></td><td>1</td><td>65.1</td><td>78.9</td><td>71.3</td><td></td><td>49.7</td><td>45.2</td><td>29.9</td><td>40.2</td><td>34.3</td></tr><tr><td rowspan="6">eords noonea</td><td>DeViSE(NeurIPS&#x27;13) [34]</td><td>13.4</td><td>68.7</td><td>22.4</td><td>17.1</td><td>74.7</td><td>27.8</td><td>23.8</td><td>53.0</td><td>32.8</td><td>16.9</td><td>27.4</td><td>20.9</td></tr><tr><td>ReViSE(ICCV&#x27;17)[9]</td><td>46.1</td><td>37.1</td><td>41.1</td><td>46.4</td><td>39.7</td><td>42.8</td><td>37.6</td><td>28.3</td><td>32.3</td><td>24.3</td><td>20.1</td><td>22.0</td></tr><tr><td>DCN(NeurIPS&#x27;18)[10]</td><td>25.5</td><td>84.2</td><td>39.1</td><td>-</td><td>=</td><td>-</td><td>28.4</td><td>60.7</td><td>38.7</td><td>25.5</td><td>37.0</td><td>30.2</td></tr><tr><td>CADA-VAE(CVPR&#x27;19)[11]</td><td>57.3</td><td>72.8</td><td>64.1</td><td>55.8</td><td>75.0</td><td>63.9</td><td>51.6</td><td>53.5</td><td>52.4</td><td>47.2</td><td>35.7</td><td>40.6</td></tr><tr><td>SGAL(NeurIPS&#x27;19)[19]</td><td>52.7</td><td>74.0</td><td>61.5</td><td>52.5</td><td>86.3</td><td>65.3</td><td>40.9</td><td>55.3</td><td>47.0</td><td>35.5</td><td>34.4</td><td>34.9</td></tr><tr><td>Our HSVA</td><td>59.3</td><td>76.6</td><td>66.8</td><td>56.7</td><td>79.8</td><td>66.3</td><td>52.7</td><td>58.3</td><td>55.3</td><td>48.6</td><td>39.0</td><td>43.3</td></tr></table>
+
+Table 3: Ablation study of HSVA under the GZSL setting on four datasets. "HSVA w/o $\mathcal { L } _ { S A }$ " denotes HSVA without the constraints in SA, "HSVA w/o $\mathcal { L } _ { D A }$ and $ { \mathcal { L } } _ { i C O R A L } "$ denotes HSVA without the constraints in DA, "HSVA w/o $ { \mathcal { L } } _ { i C O R A L } "$ denotes HSVA without $ { \mathcal { L } } _ { i C O R A L }$ , and "HSVA (full)" denotes our full model HSVA.   
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">AWA1</td><td colspan="3">AWA2</td><td colspan="3">CUB</td><td colspan="3">SUN</td></tr><tr><td>U</td><td>S</td><td>H</td><td>U</td><td>S</td><td>H</td><td>U</td><td>S</td><td>H</td><td>U</td><td>S</td><td>H</td></tr><tr><td>HSVA w/o LsA</td><td>55.2</td><td>71.5</td><td>62.3</td><td>53.9</td><td>77.2</td><td>63.5</td><td>49.3</td><td>57.9</td><td>53.2</td><td>49.7</td><td>37.2</td><td>42.6</td></tr><tr><td>HSVA w/o LDA and LiCORAL</td><td>31.3</td><td>70.6</td><td>43.4</td><td>26.3</td><td>78.4</td><td>39.3</td><td>41.9</td><td>56.1</td><td>47.9</td><td>42.2</td><td>35.5</td><td>38.6</td></tr><tr><td>HSVA w/oLiCORAL</td><td>54.3</td><td>73.5</td><td>62.4</td><td>51.3</td><td>82.6</td><td>63.3</td><td>51.1</td><td>57.0</td><td>53.9</td><td>45.1</td><td>38.9</td><td>41.8</td></tr><tr><td>HSVA (full)</td><td>59.3</td><td>76.6</td><td>66.8</td><td>56.7</td><td>79.8</td><td>66.3</td><td>52.7</td><td>58.3</td><td>55.3</td><td>48.6</td><td>39.0</td><td>43.3</td></tr></table>
+
+Results of Generalized Zero-Shot Learning. Table 2 shows the GZSL performances of various methods, including non-generative methods (direct mapping and model parameter transfer), generative methods, and common space learning methods. Compared to other common space learning models [34, 9, 10, 11, 19], our HSVA achieves significant improvements of at least $2 . 7 \%$ , $1 . 0 \%$ , $2 . 9 \%$ and $2 . 7 \%$ in harmonic mean on AWA1, AWA2, CUB and SUN, respectively. Especially, our HSVA outperforms the latest common space learning method (i.e., SGAL [19]) by a large margin, resulting in harmonic mean improvements of $5 . 3 \%$ , $1 . 0 \%$ , $8 . 3 \%$ and $8 . 4 \%$ on AWA1, AWA2, CUB and SUN, respectively. Since our method can also act as a generative method, we compare it with other state-ofthe-art generative methods. The results show that our method performs significantly better on AWA1, CUB and SUN datasets. Our model also achieves competitive results compared to non-generative methods. For example, HSVA performs best results (e.g., the harmonic mean of 43.3) on SUN that is the most challenging benchmark in ZSL. These results consistently demonstrate the superiority and great potential of hierarchical semantic-visual adaptation.
+
+Ablation Study. We conduct ablation studies to evaluate the effectiveness of our HSVA in terms of the structure adaptation constraints (denoted as $\mathcal { L } _ { S A }$ ), distribution adaptation constraints (i.e., $\mathcal { L } _ { D A } + \mathcal { L } _ { i C O R A L } )$ , and only inverse CORAL $ { \mathcal { L } } _ { i C O R A L }$ . Our results are shown in Table 3. HSVA performs poorer than its full model when no constraints are used during structure adaptation, i.e., the harmonic mean drops by $4 . 5 \%$ on AWA1 and $2 . 1 \%$ on CUB. If constraints are not used during distribution adaptation, HSVA achieves very poor results compared to its full model, i.e., the harmonic mean drops by more than $2 3 . 4 \%$ on coarse-grained datasets and $4 . 7 \%$ on fine-grained datasets. These results show that distribution alignment is essential for common space learning, while structure adaptation is necessary for semantic-visual adaptation. This is typically neglected by distribution alignment methods with one-step adaptation [8, 9, 7, 10, 11, 19]. Moreover, $ { \mathcal { L } } _ { i C O R A L }$ pushes unseen classes away from seen classes, which explicitly tackles the seen-unseen bias problem. HSVA cooperates with iCORAL to improve the accuracy of classification using softmax, achieving harmonic mean improvement of $4 . 4 \%$ , $3 . 0 \%$ , $1 . 4 \%$ , and $1 . 5 \%$ on AWA1, AWA2, CUB, and SUN, respectively.
+
+![](images/b00593c55106182e94de61030b2afbbc3c4d862c87db2fc8045211e8e8477366.jpg)  
+Figure 3: t-SNE visualization [14] of visual/semantic features learned by our HSVA and CADA-VAE [11] for the same seen and unseen classes. Different colors denote different classes. The "o" and "x" indicate visual and semantic features, respectively. We conduct experiments on 10 classes of (a) CUB and (b) AWA1. CADA-VAE clearly maps the visual and semantic features into various manifolds focusing on distribution alignment, while HSVA learns an intrinsic common space for discriminative feature representations by adopting sequential structure and distribution adaptation.
+
+Qualitative Results. We first qualitatively investigate the difference between our HSVA and onestep adaptation methods (e.g., CADA-VAE [11]) for common space learning. We conduct t-SNE visualization [14] of visual/semantic features mapped by our HSVA and CADA-VAE on 10 classes from (a) CUB and (b) AWA1. As shown in Figure 3, CADA-VAE maps semantic and visual features into different manifolds, which confuses the visual and semantic features of various categories, resulting in misclassification for some samples. This intuitively shows that the existing common space learning methods neglect the different structures of the heterogeneous feature representations in the visual and semantic domains. In contrast, HSVA learns an intrinsic common space that better bridges the gap between the heterogeneous feature representations for effective knowledge transfer, using structure and distribution adaptation. Thus, hierarchical semantic-visual adaptation is an effective solution for common space learning in ZSL.
+
+In addition, unlike other methods [8, 9, 7, 10, 11] that can only align visual and semantic distributions, our HSVA can take class relationships into account to learn discriminatively aligned feature representations. As shown in Figure 3, CADA-VAE maps visual and semantic features into compact manifolds, resulting in confused class relationships. In contrast, HSVA learns discriminative structureand distribution-aligned features for the visual and semantic feature representations, which enables HSVA to achieve better ZSL classification.
+
+# 5 Conclusion
+
+In this work, we develop a zero-shot learning framework, i.e. hierarchical semantic-visual adaptation (HSVA), to learn an intrinsic common space for visual and semantic feature representations. By conducting structure and distribution adaptation using two partially-aligned variational autoencoders, our model effectively tackles the problem of heterogeneous feature representations and bridges the gap between the visual and semantic domains. We demonstrate that HSVA achieves consistent improvement over the current state-of-the-art methods on four ZSL benchmarks. We qualitatively verify that our hierarchical semantic-visual adaptation framework can align the visual and semantic domains in terms of both structure and distribution, while other common space learning methods only take distribution alignment into account. This intuitively shows that the learned feature representations of HSVA are more discriminative and accurate than other methods. To the best of our knowledge, we are the first to investigate the different structural characteristics of the visual and semantic domains in ZSL. We believe that our work will facilitate the development of stronger visual-and-language learning systems, including zero-shot learning, visual question answering [57], image captioning [58], natural language for visual reasoning [59], heterogeneous domain adaptation [60].
+
+# Acknowledgements
+
+This work is partially supported by NSFC (61772220), Special projects for technological innovation in Hubei Province (2018ACA135) and Key R&D Plan of Hubei Province (2020BAB027).
+
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+
+# Checklist
+
+1. For all authors...
+
+• Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? [Yes] See the abstract and introduction.   
+• Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes]   
+• Did you discuss any potential negative societal impacts of your work? [Yes]   
+• Did you describe the limitations of your work? [No]
+
+2. If you are including theoretical results...
+
+• Did you state the full set of assumptions of all theoretical results? [No] • Did you include complete proofs of all theoretical results? [No]
+
+3. If you ran experiments...
+
+• 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] We anonymously released our pre-trained models and test code at https://github.com/anonymou-ssubmition/ HSVA-NeurIPS-21.   
+• Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [Yes]   
+• Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? [No]   
+• Did you include the amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)? [Yes]
+
+4. If you are using existing assets (e.g., code, data, models) or curating/releasing new assets...
+
+• If your work uses existing assets, did you cite the creators? [Yes]   
+• Did you mention the license of the assets? [No]   
+• Did you include any new assets either in the supplemental material or as a URL? [Yes] We provided more experimental analyses in the supplemental material. We also anonymously released our pre-trained models and test code at https://github.com/ anonymou-ssubmition/HSVA-NeurIPS-21.   
+• Did you discuss whether and how consent was obtained from people whose data you’re using/curating? [No]   
+• Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content? [No]
+
+5. If you used crowdsourcing or conducted research with human subjects...
+
+• Did you include the full text of instructions given to participants and screenshots, if applicable? [No]   
+• Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable? [No]   
+• Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? [No]   
+• Did you discuss whether and how consent was obtained from people whose data you’re using/curating? [No]

parse/train/rJvJXZb0W/rJvJXZb0W.md

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+# AN EFFICIENT FRAMEWORK FOR LEARNING SENTENCE REPRESENTATIONS
+
+Lajanugen Logeswaran∗ & Honglak Lee†∗ ∗University of Michigan, Ann Arbor, MI, USA †Google Brain, Mountain View, CA, USA {llajan,honglak}@umich.edu,honglak@google.com
+
+# ABSTRACT
+
+In this work we propose a simple and efficient framework for learning sentence representations from unlabelled data. Drawing inspiration from the distributional hypothesis and recent work on learning sentence representations, we reformulate the problem of predicting the context in which a sentence appears as a classification problem. Given a sentence and the context in which it appears, a classifier distinguishes context sentences from other contrastive sentences based on their vector representations. This allows us to efficiently learn different types of encoding functions, and we show that the model learns high-quality sentence representations. We demonstrate that our sentence representations outperform stateof-the-art unsupervised and supervised representation learning methods on several downstream NLP tasks that involve understanding sentence semantics while achieving an order of magnitude speedup in training time.
+
+# 1 INTRODUCTION
+
+Methods for learning meaningful representations of data have received widespread attention in recent years. It has become common practice to exploit these representations trained on large corpora for downstream tasks since they capture a lot of prior knowlege about the domain of interest and lead to improved performance. This is especially attractive in a transfer learning setting where only a small amount of labelled data is available for supervision.
+
+Unsupervised learning allows us to learn useful representations from large unlabelled corpora. The idea of self-supervision has recently become popular where representations are learned by designing learning objectives that exploit labels that are freely available with the data. Tasks such as predicting the relative spatial location of nearby image patches (Doersch et al., 2015), inpainting (Pathak et al., 2016) and solving image jigsaw puzzles (Noroozi & Favaro, 2016) have been successfully used for learning visual feature representations. In the language domain, the distributional hypothesis has been integral in the development of learning methods for obtaining semantic vector representations of words (Mikolov et al., 2013b). This is the assumption that the meaning of a word is characterized by the word-contexts in which it appears. Neural approaches based on this assumption have been successful at learning high quality representations from large text corpora.
+
+Recent methods have applied similar ideas for learning sentence representations (Kiros et al., 2015; Hill et al., 2016; Gan et al., 2016). These are encoder-decoder models that learn to predict/reconstruct the context sentences of a given sentence. Despite their success, several modelling issues exist in these methods. There are numerous ways of expressing an idea in the form of a sentence. The ideal semantic representation is insensitive to the form in which meaning is expressed. Existing models are trained to reconstruct the surface form of a sentence, which forces the model to not only predict its semantics, but aspects that are irrelevant to the meaning of the sentence as well.
+
+The other problem associated with these models is computational cost. These methods have a word level reconstruction objective that involves sequentially decoding the words of target sentences. Training with an output softmax layer over the entire vocabulary is a significant source of slowdown in the training process. This further limits the size of the vocabulary and the model (Variations of the softmax layer such as hierarchical softmax (Mnih & Hinton, 2009), sampling based softmax (Jean et al., 2014) and sub-word representations (Sennrich et al., 2015) can help alleviate this issue).
+
+We circumvent these problems by proposing an objective that operates directly in the space of sentence embeddings. The generation objective is replaced by a discriminative approximation where the model attempts to identify the embedding of a correct target sentence given a set of sentence candidates. In this context, we interpret the ‘meaning’ of a sentence as the information in a sentence that allows it to predict and be predictable from the information in context sentences. We name our approach quick thoughts (QT), to mean efficient learning of thought vectors.
+
+Our key contributions in this work are the following:
+
+• We propose a simple and general framework for learning sentence representations efficiently. We train widely used encoder architectures an order of magnitude faster than previous methods, achieving better performance at the same time. • We establish a new state-of-the-art for unsupervised sentence representation learning methods across several downstream tasks that involve understanding sentence semantics.
+
+The pre-trained encoders will be made publicly available.
+
+# 2 RELATED WORK
+
+We discuss prior approaches to learning sentence representations from labelled and unlabelled data.
+
+Learning from Unlabelled corpora. Le & Mikolov (2014) proposed the paragraph vector (PV) model to embed variable-length text. Models are trained to predict a word given it’s context or words appearing in a small window based on a vector representation of the source document. Unlike most other methods, in this work sentences are considered as atomic units instead of as a compositional function of its words.
+
+Encoder-decoder models have been successful at learning semantic representations. Kiros et al. (2015) proposed the skip-thought vectors model, which consists of an encoder RNN that produces a vector representation of the source sentence and a decoder RNN that sequentially predicts the words of adjacent sentences. Drawing inspiration from this model, Gan et al. (2016) explore the use of convolutional neural network (CNN) encoders. The base model uses a CNN encoder and reconstructs the input sentence as well as neighboring sentences using an RNN. They also consider a hierarchical version of the model which sequentially reconstructs sentences within a larger context.
+
+Autoencoder models have been explored for representation learning in a wide variety of data domains. An advantage of autoencoders over context prediction models is that they do not require ordered sentences for learning. Socher et al. (2011) proposed recursive autoencoders which encode an input sentence using a recursive encoder and a decoder reconstructs the hidden states of the encoder. Hill et al. (2016) considered a de-noising autoencoder model (SDAE) where noise is introduced in a sentence by deleting words and swapping bigrams and the decoder is required to reconstruct the original sentence. Bowman et al. (2015) proposed a generative model of sentences based on a variational autoencoder.
+
+Kenter et al. (2016) learn bag-of-words (BoW) representations of sentences by considering a conceptually similar task of identifying context sentences from candidates and evaluate their representations on sentence similarity tasks. Hill et al. (2016) introduced the FastSent model which uses a BoW representation of the input sentence and predicts the words appearing in context (and optionally, the source) sentences. The model is trained to predict whether a word appears in the target sentences. Arora et al. (2016) consider a weighted BoW model followed by simple post-processing and show that it performs better than BoW models trained on paraphrase data.
+
+Jernite et al. (2017) use paragraph level coherence as a learning signal to learn representations. The following related task is considered in their work. Given the first three sentences of a paragraph, choose the next sentence from five sentences later in the paragraph. Related to our objective is the local coherence model of Li & Hovy (2014) where a binary classifier is trained to identify coherent/incoherent sentence windows. In contrast, we only encourage observed contexts to be more plausible than contrastive ones and formulate it as a multi-class classification problem. We experimentally found that this relaxed constraint helps learn better representations.
+
+Encoder-decoder based sequence models are known to work well, but they are slow to train on large amounts of data. On the other hand, bag-of-words models train efficiently by ignoring word order.
+
+![](images/21cae2b04f4edf179da8352b7975508a6f751e122cb715b1751db7461b777c89.jpg)  
+Figure 1: Overview. (a) The approach adopted by most prior work where given an input sentence the model attempts to generate a context sentence. (b) Our approach replaces the decoder with a classifier which chooses the target sentence from a set of candidate sentences.
+
+We incorporate the best of both worlds by retaining flexibility of the encoder architecture, while still being able to to train efficiently.
+
+Structured Resources. There have been attempts to use labeled/structured data to learn sentence representations. Hill et al. (2016) learn to map words to their dictionary definitions using a max margin loss that encourages the encoded representation of a definition to be similar to the corresponding word. Wieting et al. (2015) and Wieting & Gimpel (2017) use paraphrase data to learn an encoder that maps synonymous phrases to similar embeddings using a margin loss. Hermann & Blunsom (2013) consider a similar objective of minimizing the inner product between paired sentences in different languages. Wieting et al. (2017) explore the use of machine translation to obtain more paraphrase data via back-translation and use it for learning paraphrastic embeddings.
+
+Conneau et al. (2017) consider the supervised task of Natural language inference (NLI) as a means of learning generic sentence representations. The task involves identifying one of three relationships between two given sentences - entailment, neutral and contradiction. The training strategy consists of learning a classifier on top of the embeddings of the input pair of sentences. The authors show that sentence encoders trained for this task perform strongly on downstream transfer tasks.
+
+# 3 PROPOSED FRAMEWORK
+
+The distributional hypothesis has been operationalized by prior work in different ways. A common approach is illustrated in Figure 1(a), where an encoding function computes a vector representation of an input sentence, and then a decoding function attempts to generate the words of a target sentence conditioned on this representation. In the skip-thought model, the target sentences are those that appear in the neighborhood of the input sentence. There have been variations on the decoder such as autoencoder models which predict the input sentence instead of neighboring sentences (Hill et al., 2016) and predicting properties of a window of words in the input sentence (Le & Mikolov, 2014).
+
+Instead of training a model to reconstruct the surface form of the input sentence or its neighbors, we take the following approach. Use the meaning of the current sentence to predict the meanings of adjacent sentences, where meaning is represented by an embedding of the sentence computed from an encoding function. Despite the simplicity of the modeling approach, we show that it facilitates learning rich representations.
+
+Our approach is illustrated in figure 1(b). Given an input sentence, it is encoded as before using some function. But instead of generating the target sentence, the model chooses the correct target sentence from a set of candidate sentences. Viewing generation as choosing a sentence from all possible sentences, this can be seen as a discriminative approximation to the generation problem.
+
+A key difference between these two approaches is that in figure 1(b), the model can choose to ignore aspects of the sentence that are irrelevant in constructing a semantic embedding space. Loss functions defined in a feature space as opposed to the raw data space have been found to be more attractive in recent work for similar reasons (Larsen et al., 2015; Pathak et al., 2017).
+
+Formally described, let $f$ and $g$ be parametrized functions that take a sentence as input and encode it into a fixed length vector. Let $s$ be a given sentence. Let $S _ { \mathrm { c t x t } }$ be the set of sentences appearing in the context of $s$ (for a particular context size) in the training data. Let $S _ { \mathrm { c a n d } }$ be the set of candidate sentences considered for a given context sentence $s _ { \mathrm { c t x t } } \in \ S _ { \mathrm { c t x t } }$ . In other words, $S _ { \mathrm { c a n d } }$ contains a valid context sentence $s _ { \mathrm { c t x t } }$ (ground truth) and many other non-context sentences, and is used for the classification objective as described below.
+
+For a given sentence position in the context of $s$ (e.g., the next sentence), the probability that a candidate sentence $s _ { \mathrm { c a n d } } \in S _ { \mathrm { c a n d } }$ is the correct sentence (i.e., appearing in the context of $s$ ) for that position is given by
+
+$$
+p ( s _ { \mathrm { c a n d } } | s , S _ { \mathrm { c a n d } } ) = \frac { \exp [ c ( f ( s ) , g ( s _ { \mathrm { c a n d } } ) ) ] } { \sum _ { s ^ { \prime } \in S _ { \mathrm { c a n d } } } \exp [ c ( f ( s ) , g ( s ^ { \prime } ) ) ] }
+$$
+
+where $c$ is a scoring function/classifier.
+
+The training objective maximizes the probability of identifying the correct context sentences for each sentence in the training data $D$ .
+
+$$
+\sum _ { s \in D } \sum _ { s _ { \mathrm { c t x t } } \in S _ { \mathrm { c t x t } } } \log p ( s _ { \mathrm { c t x t } } | s , S _ { \mathrm { c a n d } } )
+$$
+
+The modeling approach encapsulates the Skip-gram approach of Mikolov et al. (2013b) when words play the role of sentences. In this case the encoding functions are simple lookup tables considering words to be atomic units, and the training objective maximizes the similarity between the source word and a target word in its context given a set of negative samples.
+
+Alternatively, we considered an objective function similar to the negative sampling approach of Mikolov et al. (2013b). This takes the form of a binary classifier which takes a sentence window as input and classifies them as plausible and implausible context windows. We found objective (2) to work better, presumably due to the relaxed constraint it imposes. Instead of requiring context windows to be classified as positive/negative, it only requires ground-truth contexts to be more plausible than contrastive contexts. This objective also performed empirically better than a maxmargin loss.
+
+In our experiments, $c$ is simply defined to be an inner product $c ( u , v ) = u ^ { T } v$ . This was motivated by considering pathological solutions where the model learns poor sentence encoders and a rich classifier to compensate for it. This is undesirable since the classifier will be discarded and only the sentence encoders will be used to extract features for downstream tasks. Minimizing the number of parameters in the classifier encourages the encoders to learn disentangled and useful representations.
+
+We consider $f , g$ to have different parameters, although they were motivated from the perspective of modeling sentence meaning. Another motivation comes from word representation learning methods which use different sets of input and output parameters. Parameter sharing is further not a significant concern since these models are trained on large corpora. At test time, for a given sentence $s$ we consider its representation to be the concatenation of the outputs of the two encoders $\left[ f ( s ) \ g ( s ) \right]$ .
+
+Our framework allows flexible encoding functions to be used. We use RNNs as $f$ and $g$ as they have been widely used in recent sentence representation learning methods. The words of the sentence are sequentially fed as input to the RNN and the final hidden state is interpreted as a representation of the sentence. We use gated recurrent units (GRU) (Chung et al., 2015) as the RNN cell similar to Kiros et al. (2015).
+
+# 4 EXPERIMENTAL RESULTS
+
+# 4.1 EVALUATING SENTENCE EMBEDDINGS
+
+We evaluate our sentence representations by using them as feature representations for downstream NLP tasks. Alternative fine-grained evaluation tasks such as identifying word appearance and word order were proposed in Adi et al. (2017). Although this provides some useful insight about the representations, these tasks focus on the syntactic aspects of a sentence. We are more interested in assessing how well representations capture sentence semantics. Although limitations of these evaluations have been pointed out, we stick to the traditional approach of evaluating using downstream tasks.
+
+# 4.2 DATA
+
+Models were trained on the 7000 novels of the BookCorpus dataset (Kiros et al., 2015). The dataset consists of about 45M ordered sentences. We also consider a larger corpus for training: the UMBC corpus (Han et al., 2013), a dataset of 100M web pages crawled from the internet, preprocessed and tokenized into paragraphs. The dataset has 129M sentences, about three times larger than BookCorpus. For models trained from scratch, we used case-sensitive vocabularies of sizes $5 0 \mathrm { k }$ and $1 0 0 \mathrm { k }$ for the two datasets respectively.
+
+# 4.3 TRAINING
+
+A minibatch is constructed using a contiguous sets of sentences in the corpus. For each sentence, all the sentences in the minibatch are considered to be the candidate pool $S _ { \mathbf { c a n d } }$ of sentences for classification. This simple scheme for picking contrastive sentences performed as well as other schemes such as random sampling and picking nearest neighbors of the input sentence. Hyperparameters including batch size, learning rate, prediction context size were obtained using prediction accuracies (accuracy of predicting context sentences) on the validation set. A context size of 3 was used, i.e., predicting the previous and next sentences given the current sentence. We used a batch size of 400 and learning rate of 5e-4 with the Adam optimizer for all experiments. All our RNN-based models are single-layered and use GRU cells. Weights of the GRU are initialized using uniform Xavier initialization and gate biases are initialized to 1. Word embeddings are initialized from $U [ - 0 . 1 , 0 . 1 ]$ .
+
+# 4.4 EVALUATION
+
+Tasks We evaluate the sentence representations on tasks that require understanding sentence semantics. The following classification benchmarks are commonly used: movie review sentiment (MR) (Pang & Lee, 2005), product reviews (CR) (Hu & Liu, 2004), subjectivity classification (SUBJ) (Pang & Lee, 2004), opinion polarity (MPQA) (Wiebe et al., 2005), question type classification (TREC) (Voorhees & Buckland, 2003) and paraphrase identification (MSRP) (Dolan et al., 2004). The semantic relatedness task on the SICK dataset (Marelli et al., 2014) involves predicting relatedness scores for a given pair of sentences that correlate well with human judgements.
+
+The MR, CR, SUBJ, MPQA tasks are binary classification tasks. 10-fold cross validation is used in reporting test performance for these tasks. The other tasks come with train/dev/test splits and the dev set is used for choosing the regularization parameter. We follow the evaluation scheme of Kiros et al. (2015) where feature representations of sentences are obtained from the trained encoders and a logistic/softmax classifier is trained on top of the embeddings for each task while keeping the sentence embeddings fixed. Kiros et al.’s scripts are used for evaluation.
+
+# 4.4.1 COMPARISON AGAINST UNSUPERVISED METHODS
+
+Table 1 compares our work against representations from prior methods that learn from unlabelled data. The dimensionality of sentence representations and training time are also indicated. For our RNN based encoder we consider variations that are analogous to the skip-thought model. The uniQT model uses uni-directional RNNs as the sentence encoders $f$ and $g$ . In the bi-QT model, the concatenation of the final hidden states of two RNNs represent $f$ and $g$ , each processing the sentence in a different (forward/backward) direction. The combine-QT model concatenates the representations (at test time) learned by the uni-QT and bi-QT models.
+
+Models trained from scratch on BookCorpus. While the FastSent model is efficient to train (training time of 2h), this efficiency stems from using a bag-of-words encoder. Bag of words provides a strong baseline because of its ability to preserves word identity information. However, the model performs poorly compared to most of the other methods. Bag-of-words is also conceptually less attractive as a representation scheme since it ignores word order, which is a key aspect of meaning.
+
+The de-noising autoencoder (SDAE) performs strongly on the paraphrase detection task (MSRP). This is attributable to the reconstruction (autoencoding) loss which encourages word identity and
+
+<table><tr><td rowspan="2">Model</td><td rowspan="2">Dim</td><td rowspan="2">Training time (h)</td><td rowspan="2">MR</td><td rowspan="2">CR</td><td rowspan="2">SUBJ</td><td rowspan="2">MPQA TREC</td><td colspan="2">MSRP</td><td rowspan="2"></td><td colspan="3">SICK</td></tr><tr><td>(Acc)</td><td>(F1)</td><td>r</td><td>p</td><td>MSE</td></tr><tr><td>GloVeBoW</td><td>300</td><td>-</td><td>78.1</td><td>80.4</td><td>91.9</td><td>87.8</td><td>85.2</td><td>72.5</td><td>81.1</td><td>0.764</td><td>0.687</td><td>0.425</td></tr><tr><td colspan="11">Trained from scratch on BookCorpus data</td></tr><tr><td>SDAE FastSent ParagraphVec</td><td>2400 &lt;500</td><td>192 2* 4*</td><td>67.6 71.8</td><td>74.0 78.4</td><td>89.3 88.7</td><td>81.3 81.5</td><td>77.6 76.8</td><td>76.4 72.2</td><td>83.4 80.3</td><td>N/A N/A</td><td>N/A N/A</td><td>N/A N/A</td></tr><tr><td></td><td>&lt;500</td><td></td><td>61.5</td><td>68.6</td><td>76.4</td><td>78.1</td><td>55.8</td><td>73.6</td><td>81.9</td><td>N/A</td><td>N/A</td><td>N/A</td></tr><tr><td>uni-skip bi-skip</td><td>2400</td><td>336</td><td>75.5</td><td>79.3</td><td>92.1</td><td>86.9</td><td>91.4</td><td>73.0</td><td>81.9</td><td>0.848</td><td>0.778</td><td>0.287</td></tr><tr><td>combine-skip</td><td>2400</td><td>336</td><td>73.9</td><td>77.9</td><td>92.5</td><td>83.3</td><td>89.4</td><td>71.2</td><td>81.2</td><td>0.841</td><td>0.770</td><td>0.300</td></tr><tr><td>combine-cnn</td><td>4800</td><td>336t</td><td>76.5</td><td>80.1</td><td>93.6</td><td>87.1</td><td>92.2</td><td>73.0</td><td>82.0</td><td>0.858</td><td>0.792</td><td>0.269</td></tr><tr><td>uni-QT</td><td>4800</td><td>-</td><td>77.2</td><td>80.9</td><td>93.1</td><td>89.1</td><td>91.8</td><td>75.5</td><td>82.6</td><td>0.853</td><td>0.789</td><td>0.279</td></tr><tr><td>bi-QT</td><td>2400</td><td>11</td><td>77.2</td><td>82.8</td><td>92.4</td><td>87.2</td><td>90.6</td><td>74.7</td><td>82.7</td><td>0.844</td><td>0.778</td><td>0.293</td></tr><tr><td></td><td>2400</td><td>9</td><td>77.0</td><td>83.5</td><td>92.3</td><td>87.5</td><td>89.4</td><td>74.8</td><td>82.9</td><td>0.855</td><td>0.787</td><td>0.274</td></tr><tr><td>combine-QT</td><td>4800</td><td>11</td><td>78.2</td><td>84.4</td><td>93.3</td><td>88.0</td><td>90.8</td><td>76.2</td><td>83.5</td><td>0.860</td><td>0.796</td><td>0.267</td></tr><tr><td colspan="14">Trained on BookCorpus, ,pre-trained word vectors are used</td></tr><tr><td>combine-cnn MC-QT</td><td>4800 4800</td><td>1 11</td><td>77.8 80.4</td><td>82.1</td><td>93.6</td><td>89.4</td><td>92.6</td><td>76.5</td><td>83.8</td><td>0.862</td><td>0.798</td><td>0.267</td></tr><tr><td></td><td></td><td></td><td></td><td>85.2</td><td>93.9</td><td>89.4</td><td>92.8</td><td>76.9</td><td>84.0</td><td>0.868</td><td>0.801</td><td>0.256</td></tr><tr><td colspan="14"> Trained on (BookCorpus + UMBC) data, from scratch and using pre-trained word vectors</td></tr><tr><td>combine-QT</td><td>4800</td><td>28</td><td>81.3</td><td>84.5</td><td>94.6</td><td>89.5</td><td>92.4</td><td></td><td></td><td>0.871</td><td></td><td></td></tr><tr><td>MC-QT</td><td>4800</td><td>28</td><td>82.4</td><td>86.0</td><td>94.8</td><td>90.2</td><td>92.4</td><td>75.9 76.9</td><td>83.3 84.0</td><td>0.874</td><td>0.807 0.811</td><td>0.247 0.243</td></tr></table>
+
+Table 1: Comparison of sentence representations on downstream tasks. The baseline methods are GloVe bag-of-words representation, De-noising auto-encoders and FastSent from Hill et al. (2016), the paragraph vector distributed memory model (Le & Mikolov, 2014), skip-thought vectors (Kiros et al., 2015) and the CNN model of Gan et al. (2016). Training times indicated using \* refers to CPU trained models and † assumes concatenated representations are trained independently. Performance figures for SDAE, FastSent and ParagraphVec were obtained from Hill et al. (2016). Higher numbers are better in all columns except for the last (MSE). The table is divided into different sections. The bold-face numbers indicate the best performance values among models in the current and all previous sections. Best overall values in each column are underlined.
+
+order information to be encoded in the representation. However, it fails to perform well in other tasks that require higher level sentence understanding and is also inefficient to train.
+
+Our uni/bi/combine-QT variations perform comparably (and in most cases, better) to the skipthought model and the CNN-based variation of Gan et al. (2016) in all tasks despite requiring much less training time. Since these models were trained from scratch, this also shows that the model learns good word representations as well.
+
+MultiChannel-QT. Next, we consider using pre-trained word vectors to train the model. The MultiChannel-QT model (MC-QT) is defined as the concatenation of two bi-directional RNNs. One of these uses fixed pre-trained word embeddings coming from a large vocabulary $( \sim 3 \mathbf { M } )$ as input. While the other uses tunable word embeddings trained from scratch (from a smaller vocabulary $\sim$ 50k). This model was inspired by the multi-channel CNN model of Kim (2014) which considered two sets of embeddings. With different input representations, the two models discover less redundant features, as opposed to the uni and bi variations suggested in Kiros et al. (2015). We use GloVe vectors (Pennington et al., 2014) as pre-trained word embeddings. The MC-QT model outperforms all previous methods, including the variation of Gan et al. (2016) which uses pre-trained word embeddings.
+
+UMBC data. Because our framework is efficient to train, we also experimented on a larger dataset of documents. Results for models trained on BookCorpus and UMBC corpus pooled together ( $\sim$ 174M sentences) are shown at the bottom of the table. We observe strict improvements on a majority of the tasks compared to our BookCorpus models. This shows that we can exploit huge corpora to obtain better models while keeping the training time practically feasible.
+
+Computational efficiency. Our models are implemented in Tensorflow. Experiments were performed using cuda 8.0 and cuDNN 6.0 libraries on a GTX Titan X GPU. Our best BookCorpus model (MC-QT) trains in just under 11hrs (On both the Titan X and GTX 1080). Training time for the skip-thoughts model is mentioned as 2 weeks in Kiros et al. (2015) and a more recent Tensorflow implementation1 reports a training time of 9 days on a GTX 1080. On the augmented dataset our models take about a day to train, and we observe monotonic improvements in all tasks except the TREC task. Our framework allows training with much larger vocabulary sizes than most previous models. Our approach is also memory efficient. The paragraph vector model has a big memory footprint since it has to store vectors of documents used for training. Softmax computations over the vocabulary in the skip-thought and other models with word-level reconstruction objectives incur heavy memory consumption. Our RNN based implementation (with the indicated hyperparamters and batch size) fits within 3GB of GPU memory, a majority of it consumed by the word embeddings.
+
+4.4.2 COMPARISON AGAINST SUPERVISED METHODS   
+
+<table><tr><td>Model</td><td>MR</td><td>CR</td><td>SUBJ</td><td>MPQA</td><td>SST</td><td>TREC</td><td>MSRP</td><td></td><td>SICK</td></tr><tr><td>CaptionRep</td><td>61.9</td><td>69.3</td><td>77.4</td><td>70.8</td><td>1</td><td>72.2</td><td>1</td><td>-</td><td>-</td></tr><tr><td>DictRep</td><td>76.7</td><td>78.7</td><td>90.7</td><td>87.2</td><td></td><td>81.0</td><td>68.4</td><td>76.8</td><td>-</td></tr><tr><td>NMTEn-to-Fr</td><td>64.7</td><td>70.1</td><td>84.9</td><td>81.5</td><td>■</td><td>82.8</td><td>=</td><td>-</td><td>1</td></tr><tr><td>InferSent</td><td>81.1</td><td>86.3</td><td>92.4</td><td>90.2</td><td>84.6</td><td>88.2</td><td>76.2</td><td>83.1</td><td>0.884</td></tr><tr><td>MC-QT</td><td>82.4</td><td>86.0</td><td>94.8</td><td>90.2</td><td>87.6</td><td>92.4</td><td>76.9</td><td>84.0</td><td>0.874</td></tr></table>
+
+Table 2: Comparison against supervised representation learning methods on downstream tasks.   
+
+<table><tr><td>Model</td><td>MR</td><td>CR</td><td>SUBJ</td><td>MPQA</td><td>SST</td><td>TREC</td><td>MSRP</td><td></td><td>SICK</td></tr><tr><td>Ensemble</td><td>82.7</td><td>86.7</td><td>95.5</td><td>90.3</td><td>88.2</td><td>93.4</td><td>78.5</td><td>85.1</td><td>0.881</td></tr><tr><td colspan="10">Task specific methods</td></tr><tr><td>AdaSent</td><td>83.1</td><td>86.3</td><td>95.5</td><td>93.3</td><td>1</td><td>92.4</td><td></td><td></td><td>1</td></tr><tr><td>CNN</td><td>81.5</td><td>85.0</td><td>93.4</td><td>89.6</td><td>88.1</td><td>93.6</td><td>1</td><td>1</td><td></td></tr><tr><td>TF-KLD</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>80.4</td><td>85.9</td><td>1</td></tr><tr><td>DT-LSTM</td><td>-</td><td>■</td><td>1</td><td>=</td><td>1</td><td>■</td><td>1</td><td>-</td><td>0.868</td></tr></table>
+
+Table 3: Comparison against task-specific supervised models. The models are AdaSent (Zhao et al., 2015), CNN (Kim, 2014), TF-KLD (Ji & Eisenstein, 2013) and Dependency-Tree LSTM (Tai et al., 2015). Note that our performance values correspond to a linear classifier trained on fixed pre-trained embeddings, while the task-specific methods are tuned end-to-end.
+
+Table 2 compares our approach against methods that learn from labelled/structured data. The CaptionRep, DictRep and NMT models are from Hill et al. (2016) which are trained respectively on the tasks of matching images and captions, mapping words to their dictionary definitions and machine translation. The InferSent model of Conneau et al. (2017) is trained on the NLI task. In addition to the benchmarks considered before, we additionally also include the sentiment analysis binary classification task on Stanford Sentiment Treebank (SST) (Socher et al., 2013).
+
+The Infersent model has strong performance on the tasks. Our multichannel model trained on the (BookCorpus $^ +$ UMBC) data outperforms InferSent in most of the tasks, with most significant margins in the SST and TREC tasks. Infersent is strong in the SICK task presumably due to the following reasons. The model gets to observes near paraphrases (entailment relationship) and sentences that are not-paraphrases (contradiction relationship) at training time. Furthermore, it considers difference features $( | u - v | )$ and multiplicative features $( u * v )$ of the input pair of sentences $u , v$ during training. This is identical to the feature transformations used in the SICK evaluation as well.
+
+Ensemble We consider ensembling to exploit the strengths of different types of encoders. Since our models are efficient to train, we are able to feasibly train many models. We consider a subset of the following model variations for the ensemble.
+
+• Model type - Uni/Bi-directional RNN • Word embeddings - Trained from scratch/Pre-trained • Dataset - BookCorpus/UMBC
+
+<table><tr><td colspan="8">COCORetrieval</td></tr><tr><td>Model</td><td>Image</td><td colspan="3">Annotation</td><td></td><td>Image Search</td><td></td></tr><tr><td></td><td>R@1</td><td>R@5</td><td>R@10</td><td>Med r</td><td>R@1</td><td>R@5 R@10</td><td>Med r</td></tr><tr><td colspan="8">Pre-trained unsupervised sentence representations</td></tr><tr><td>Combine-skip</td><td>33.8</td><td>67.7 82.1</td><td>3</td><td>25.9</td><td>60.0</td><td>74.6</td><td>4</td></tr><tr><td>Combine-cnn</td><td>34.4</td><td>1</td><td>3 1</td><td>26.6</td><td>1</td><td>1</td><td>4</td></tr><tr><td>MC-QT</td><td>37.1</td><td>72.0</td><td>84.7</td><td>2</td><td>27.9 63.3</td><td>78.3</td><td>3</td></tr><tr><td colspan="8">Direct supervision of sentence representations</td></tr><tr><td>DVSA</td><td>38.4</td><td>69.6 80.5</td><td>1</td><td>27.4</td><td>60.2</td><td>74.8</td><td>3</td></tr><tr><td>GMM+HGLMM</td><td>39.4</td><td>67.9</td><td>80.9</td><td>2</td><td>25.1 59.8</td><td>76.6</td><td>4</td></tr><tr><td>m-RNN</td><td>41.0</td><td>73.0</td><td>83.5</td><td>2 29.0</td><td>42.2</td><td>77.0</td><td>3</td></tr><tr><td>Order</td><td>46.7</td><td>88.9</td><td>1 2</td><td>37.9</td><td>85.9</td><td>1</td><td>2</td></tr></table>
+
+Table 4: Image-caption retrieval. The purely supervised models are respectively from (Karpathy & Fei-Fei, 2015), (Klein et al., 2015), (Mao et al., 2014) and (Vendrov et al., 2015). Best pre-trained representations and best task-specific methods are highlighted.
+
+Models are combined using a weighted average of the predicted log-probabilities of individual models, the weights being normalized validation set performance scores. Results are presented in table 3. Performance of the best purely supervised task-specific methods are shown at the bottom for reference. Note that these numbers are not directly comparable with the unsupervised methods since the sentence embeddings are not fine-tuned. We observe that the ensemble model closely approaches the performance of the best supervised task-specific methods, outperforming them in 3 out of the 8 tasks.
+
+# 4.4.3 IMAGE-SENTENCE RANKING
+
+The image-to-caption and caption-to-image retrieval tasks have been commonly used to evaluate sentence representations in a multi-modal setting. The task requires retrieving an image matching a given text description and vice versa. The evaluation setting is identical to Kiros et al. (2015). Images and captions are represented as vectors. Given a matching image-caption pair $( I , C )$ a scoring function $f$ determines the compatibility of the corresponding vector representations $v _ { I } , v _ { C }$ . The scoring function is trained using a margin loss which encourages matching pairs to have higher compatibility than mismatching pairs.
+
+$$
+\sum _ { ( I , C ) } \sum _ { I ^ { \prime } } \operatorname* { m a x } \{ 0 , \alpha - f ( v _ { I } , v _ { C } ) + f ( v _ { I } , v _ { C ^ { \prime } } ) \} + \sum _ { ( I , C ) } \sum _ { C ^ { \prime } } \operatorname* { m a x } \{ 0 , \alpha - f ( v _ { I } , v _ { C } ) + f ( v _ { I ^ { \prime } } , v _ { C } ) \}
+$$
+
+As in prior work, we use VGG-Net features (4096-dimensional) as the image representation. Sentences are represented as vectors using the representation learning method to be evaluated. These representations are held fixed during training. The scoring function used in prior work is $f ( x , y ) \stackrel { \cdot } { = } ( U x ) ^ { T } ( V y )$ where $U , V$ are projection matrices which project down the image and sentence vectors to the same dimensionality.
+
+The MSCOCO dataset (Lin et al., 2014) has been traditionally used for this task. We use the train/val/test split proposed in Karpathy & Fei-Fei (2015). The training, validation and test sets respectively consist of 113,287, 5000, 5000 images, each annotated with 5 captions. Performance is reported as an average over 5 splits of 1000 image-caption pairs each from the test set. Results are presented in table 3. We outperform previous unsupervised pre-training methods by a significant margin, strictly improving the median retrieval rank for both the annotation and search tasks. We also outperform some of the purely supervised task specific methods by some metrics.
+
+# 4.4.4 NEAREST NEIGHBORS
+
+Our model and the skip-thought model have conceptually similar objective functions. This suggests examining properties of the embedding spaces to better understand how they encode semantics. We consider a nearest neighbor retrieval experiment to compare the embedding spaces. We use a pool of 1M sentences from a Wikipedia dump for this experiment. For a given query sentence, the best neighbor determined by cosine distance in the embedding space is retrieved.
+
+Table 5 shows a random sample of query sentences from the dataset and the corresponding retrieved sentences. These examples show that our retrievals are often more related to the query sentence compared to the skip-thought model. It is interesting to see in the first example that the model identifies a sentence with similar meaning even though the main clause and conditional clause are in a different order. This is in line with our goal of learning representations that are less sensitive to the form in which meaning is expressed.
+
+Table 5: Nearest neighbors retrieved by the skip-thought model (ST) and our model (QT).   
+
+<table><tr><td colspan="2"></td></tr><tr><td>Query ST</td><td>Seizures may occur as the glucose falls further . It may also occur during an excessively rapid entry into autorotation .</td></tr><tr><td>QT</td><td>When brain glucose levels are suffciently low , seizures may result .</td></tr><tr><td>Query ST QT</td><td>This evidence was only made public after both enquiries were completed . This visa was provided for under Republic Act No. These evidence were made public by the United States but concealed the names of</td></tr><tr><td>Query ST</td><td>sources . He kept both medals in a biscuit tin . He kept wicket for Middlesex in two first-class cricket matches during the 1891 County</td></tr><tr><td>QT</td><td>Championship . He won a three medals at four Winter Olympics .</td></tr><tr><td>Query ST</td><td>The American alligator is the only known natural predator of the panther . Their mascot is the panther . The American alligator is a fairly large species of crocodilian .</td></tr><tr><td>QT Query</td><td>Several of them died prematurely : Carmen and Toms very young ，while Carlos and Pablo both died .</td></tr><tr><td>ST QT</td><td>At the age of 13,Ahmed Sher died . Many of them died in prison</td></tr><tr><td>Query ST</td><td>Music for“ Expo 2O68 ” originated from the same studio session . His 1994 work“ Dialogue ” was premiered at the Merkin Concert Hall in New York</td></tr><tr><td>QT</td><td>City : Music from“ Korra ”and“ Avatar” was also played in concert at the PlayFest festival</td></tr><tr><td>Query</td><td>in Mlaga, Spain in September 2014. Mohammad Ali Jinnah yielded to the demands of refugees from the Indian states of</td></tr><tr><td>ST</td><td>Bihar and Uttar Pradesh ,who insisted that Urdu be Pakistan &#x27;s official language . Georges Charachidz ,a historian and linguist of Georgian origin under Dumzil &#x27;s tute- lage ，became a noted specialist of the Caucasian cultures and aided Dumzil in the re-</td></tr><tr><td>QT</td><td>construction of the Ubykh language . Wali Mohammed Wali &#x27;s visit thus stimulated the growth and development of Urdu</td></tr><tr><td>Query ST</td><td>Ghazal in Delhi . The PCC, together with the retrosplenial cortex , forms the retrosplenial gyrus . The Macro domain from human , macroH2A1.1,binds an NAD metabolite O-acetyl-</td></tr><tr><td>QT</td><td>ADP-ribose . The PCC forms a part of the posteromedial cortex ,along with the retrosplenial cortex (</td></tr><tr><td>Query</td><td>Brodmann areas 29 and 30 ） and precuneus （located posterior and superior to the PCC ） With the exception of what are known as the Douglas Treaties , negotiated by Sir James</td></tr><tr><td></td><td>Douglas with the native people of the Victoria area , no treaties were signed in British Columbia until 1998 .</td></tr><tr><td>ST</td><td>All the assets of the Natal Railway Company ,including its locomotive fleet of three , were purchased for the sum of 4O,OoO by the Natal Colonial Government in 1876</td></tr><tr><td>QT</td><td>With few exceptions （ the Douglas Treaties of Fort Rupert and southern Vancouver Is- land ） no treaties were signed .</td></tr></table>
+
+# 5 CONCLUSION
+
+We proposed a framework to learn generic sentence representations efficiently from large unlabelled text corpora. Our simple approach learns richer representations than prior unsupervised and supervised methods, consuming an order of magnitude less training time. We establish a new state-of
+
+the-art for unsupervised sentence representation learning methods on several downstream tasks. We believe that exploring scalable approaches to learn data representations is key to exploit unlabelled data available in abundance.
+
+# ACKNOWLEDGMENTS
+
+This material is based in part upon work supported by IBM 4915012629, NSF CAREER IIS1453651, and Sloan Research Fellowship. We thank Jongwook Choi, Junhyuk Oh, Kibok Lee, Ruben Villegas, Seunghoon Hong, Xinchen Yan, Yijie Guo and Yuting Zhang for helpful comments and discussions.
+
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+
+# A ANALOGY MAKING
+
+In this experiment we compare the ability of our model and skip-thought vectors to reason about analogies in the sentence embedding space. The analogy task has been widely used for evaluating word representations. The task involves answering questions of the type $A : B : : C : ?$ where the answer word shares a relationship to word $C$ that is identical to the relationship between words $A$ and $B$ . We consider an analogous task at the sentence level and formulate it as a retrieval task where the query vector $v ( C ) + v ( B ) - v ( A )$ is used to identify the closest sentence vector $v ( \hat { D } )$ from a pool of candidates. This evaluation favors models that produce meaningful dimensions.
+
+Guu et al. (2017) exploit word analogy datasets to construct sentence tuples with analogical relationships. They mine sentence pairs $\left( { { s _ { 1 } } , { s _ { 2 } } } \right)$ from the Yelp dataset (Yelp, 2017) which approximately differ by a single word, and use these pairs to construct sentence analogy tuples based on known word analogy tuples. The dataset has 1300 tuples of sentences collected in this fashion. For each sentence tuple we derive 4 questions by considering three of the sentences to form the query vector. The candidate pool for sentence retrieval consists of all sentences in this dataset and 1M other sentences from the Yelp dataset.
+
+Table 6 compares the retrieval performance of our representations and skip-thought vectors on the above task. Results are classified under word-pair categories in the Google and Microsoft word analogy datasets (Mikolov et al., 2013a;c). Our model outperforms skip-thoughts across several categories and has good performance in the family and verb transformation categories .
+
+Table 6: Analogy task - Retrieval performance.   
+
+<table><tr><td>Method</td><td colspan="3">Google</td><td colspan="6">Microsoft</td></tr><tr><td></td><td>gram4-</td><td>gram3- superlative comparative</td><td>family</td><td>JJR_JJS</td><td>VB_VBD</td><td>VBD_VBZ NN_NNS</td><td></td><td>JJ_JJS</td><td>JJ_JJR</td></tr><tr><td>Combine-skip</td><td>0.00</td><td>0.00</td><td>0.04</td><td>0.12</td><td>0.38</td><td>0.44</td><td>0.00</td><td>0.00</td><td>0.00</td></tr><tr><td>MC-QT</td><td>0.04</td><td>0.06</td><td>0.34</td><td>0.18</td><td>0.34</td><td>0.52</td><td>0.06</td><td>0.06</td><td>0.08</td></tr></table>
+
+<table><tr><td>A</td><td>dr.&lt;person&gt;and his staff are simply amazing ! dr.&lt;person&gt;and her staff are simply amazing ！！! i had the chicken and my husband had the pulled pork sandwich . i had the pulled pork sandwich and my wife had the pulled chicken sandwich. √</td></tr><tr><td>A</td><td>place looks great inside. place looked great inside . the complimentary valet is also a nice touch . the complimentary valet was also a nice touch .√</td></tr><tr><td>Q A</td><td>i liked the beef better than the chicken. i like the chicken better than the beef . i wanted to like this place so badly ！ i want so badly to like this place ！！√</td></tr><tr><td>Q A</td><td>the egg drop soup is the best . the egg drop soup is good . horrible food and worst customer service. horrible food and worst customer service .X</td></tr></table>
+
+Table 7: Analogy task - Qualitative results. In each table cell the first three sentences form the query and the last sentence is the answer retrieved by the model.
+
+Table 7 shows some qualitative retrieval results. Each row of the table shows three sentences that form the query and the answer identified by the model. The last row shows an example where the model fails. This is a common failure case of both methods where the model assumes that $A$ and $B$ are identical in a question $A : B : : C : ?$ and retrieves sentence $C$ as the answer.
+
+These experiments show that the our representations possess better linearity properties. The transformations evaluated here are mostly syntactic transformations involving a few words. It would be interesting to explore other high-level transformations such as switching sentiment polarity and analogical relationships that involve several words in future work.
+
+# B SEMANTIC TEXTUAL SIMILARITY
+
+In this section we assess the representations learned by our encoders on semantic similarity tasks. The STS14 datasets (Agirre et al., 2014) consist of pairs of sentences annotated by humans with similarity scores. Representations are evaluated by measuring the correlation between human judgments and the cosine similarity of vector representations for a given pair of sentences.
+
+We consider two types of encoders trained using our objective - RNN encoders and BoW encoders. Models were trained from scratch on the BookCorpus data. The RNN version is the same as the combine-QT model in Table 1. We describe the BoW encoder training below.
+
+We train a BoW encoder using our training objective. Hyperparameter choices for the embedding size $\langle 1 0 0 , 3 0 0 , 5 0 0 \} \rangle$ , number of contrastive sentences $\{ 5 0 0 , 1 0 0 0 , \mathbf { 1 5 0 0 } , 2 0 0 0 \}$ ) and context size $( \{ 3 , 5 , 7 \} )$ were made based on the validation set (optimal choices highlighted in bold). Training this model on the BookCorpus dataset takes 2 hours on a Titan X GPU. Similar to the RNN encoders, the representation of a sentence is obtained by concatenating the outputs of the input and output sentence encoders.
+
+Table 8 compares different unsupervised representation learning methods trained on the BookCorpus data from scratch. Methods are categorized as sequence models and bag-of-words models. Our RNN-based encoder performs strongly compared to other sequence encoders. Bag-of-words models are known to perform strongly in this task as they are better able to encode word identity information. Our BoW variation performs comparably to prior BoW based models.
+
+Table 8: Comparison (Pearson score) of sentence representations on Semantic Textual Similarity (STS14) tasks. SDAE, CBOW, Skipgram and FastSent are from Hill et al. (2016). The other baselines are Skip-Thoughts (Kiros et al., 2015) and Siamese CBOW (Kenter et al., 2016). QT (RNN) and QT (BoW) are our models trained with RNN and BoW encoders, respectively.   
+
+<table><tr><td>Model</td><td>News</td><td>Forum</td><td>WordNet</td><td>Tweets</td><td>Images</td><td>Headlines</td><td>Overall</td></tr><tr><td colspan="8">Sequence Models</td></tr><tr><td>SDAE</td><td>0.04</td><td>0.13</td><td>0.24</td><td>0.42</td><td>0.38</td><td>0.36</td><td>0.15</td></tr><tr><td>Skip-Thoughts</td><td>0.45</td><td>0.12</td><td>0.35</td><td>0.36</td><td>0.62</td><td>0.36</td><td>0.39</td></tr><tr><td>QT(RNN)</td><td>0.48</td><td>0.15</td><td>0.53</td><td>0.62</td><td>0.53</td><td>0.48</td><td>0.49</td></tr><tr><td colspan="8">BoW Models</td></tr><tr><td>CBOW</td><td>0.61</td><td>0.44</td><td>0.69</td><td>0.75</td><td>0.73</td><td>0.59</td><td>0.65</td></tr><tr><td>Skipgram</td><td>0.59</td><td>0.42</td><td>0.70</td><td>0.74</td><td>0.67</td><td>0.58</td><td>0.63</td></tr><tr><td>FastSent</td><td>0.59</td><td>0.36</td><td>0.70</td><td>0.66</td><td>0.78</td><td>0.59</td><td>0.64</td></tr><tr><td>Siamese CBOW</td><td>0.59</td><td>0.41</td><td>0.61</td><td>0.73</td><td>0.65</td><td>0.64</td><td>0.62</td></tr><tr><td>QT (BoW)</td><td>0.62</td><td>0.37</td><td>0.76</td><td>0.67</td><td>0.76</td><td>0.60</td><td>0.65</td></tr></table>
+
+# C TRAINING EFFICIENCY
+
+To better assess the training efficiency of our models, we perform the following experiment. We train the same encoder architecture using our objective and the skip-thought (ST) objective and compare the performance after a certain number of hours of training. Since training the ST objective with large embedding sizes takes many days, we consider a lower dimensional sentence encoder for this experiment. We chose the encoder architecture to be a single-layer GRU Recurrent neural net with hidden state size $H = 1 0 0 0$ . The word embedding size was set to $W = 3 0 0$ and a vocabulary size of $V = 2 0 , 0 0 0$ words was used. Both models are initialized randomly from the same distribution. The models are trained on the same data for 1 epoch using the Adam optimizer with learning rate 5e-4 and batch size 400. For the low dimensional model considered, the model trained with our objective and ST objective take 6.5 hrs and 31 hrs, respectively.
+
+The number of parameters for the two objectives are
+
+Only the input side encoder parameters $\approx 9 . 9 M$ parameters) are used for the evaluation.
+
+The 1000-dimensional sentence embeddings are used for evaluation. Evaluation follows the same protocol as in section 4.4. Figure 2 compares the performance of the two models on downstream tasks after $x$ number of training hours. The speed benefits of our training objective is apparent from these comparisons.
+
+![](images/4acf7be5fec05dcb2c6ca8065b11ece42c388bd130814ea3a667673cb6ec10de.jpg)  
+Figure 2: Same encoder architecture trained using our objective and Skip-thought (ST) objective and performance on downstream tasks is compared after a given number of hours.
+
+The overall training speedup observed for our objective is $4 . 8 \times$ . Note that the output encoder was discarded for our model, unlike the experiments in the main text where the representations from the input and output encoders are concatenated. Further speedups can be achieved by training with encoders half the size and concatenating them (This is also parameter efficient).
+
+We explore the trade-off between training efficiency and the quality of representations by varying the representation size. We trained models with different representation sizes and evaluate them on the downstream tasks. The multi-channel model (MC-QT) was used for these experiments. Models were trained on the BookCorpus dataset.
+
+Table 9 shows the training time and the performance corresponding to different embedding sizes. The training times listed here assume that the two component models in MC-QT are trained in parallel. The reported performance is an average over all the classification benchmarks (MSRP, TREC, MR, CR, SUBJ, MPQA). We note that the classifiers trained on top of the embeddings for downstream tasks differ in size for each embedding size. So it is difficult to make any strong conclusions about the quality of embeddings for the different sizes. However, we are able to reduce the embedding size and train the models more efficiently, at the expense of marginal loss in performance in most cases.
+
+The 4800-dimensional Skip-thought model (Kiros et al., 2015) and Combine-CNN model (Gan et al., 2016) achieve mean accuracies of 83.75 and 85.33 respectively. We note that our 1600- dimensional model and 3200-dimensional model are respectively better than these models, in terms of the mean performance across the benchmarks (We acknowledge that the Skip-thought model did not use pre-trained word embeddings). This suggests that high-quality models can be obtained even more efficiently by training lower-dimensional models on large amounts of data using our objective.
+
+<table><tr><td>Embedding size</td><td>Training time (h)</td><td>Performance</td></tr><tr><td>1600</td><td>4</td><td>84.57</td></tr><tr><td>2400</td><td>4.7</td><td>85.12</td></tr><tr><td>3200</td><td>6</td><td>85.74</td></tr><tr><td>4000</td><td>7.15</td><td>86.09</td></tr><tr><td>4800</td><td>8.5</td><td>86.43</td></tr><tr><td>5600</td><td>10.15</td><td>86.72</td></tr></table>
+
+Table 9: Training time and performance for different embedding sizes. The reported performance is the mean accuracy over the classification benchmarks (MSRP, TREC, MR, CR, SUBJ, MPQA).

parse/train/rJvJXZb0W/rJvJXZb0W_content_list.json

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+    {
+        "type": "text",
+        "text": "AN EFFICIENT FRAMEWORK FOR LEARNING SENTENCE REPRESENTATIONS ",
+        "text_level": 1,
+        "bbox": [
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+        "type": "text",
+        "text": "Lajanugen Logeswaran∗ & Honglak Lee†∗ ∗University of Michigan, Ann Arbor, MI, USA †Google Brain, Mountain View, CA, USA {llajan,honglak}@umich.edu,honglak@google.com ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "ABSTRACT ",
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+        ],
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+        "text": "In this work we propose a simple and efficient framework for learning sentence representations from unlabelled data. Drawing inspiration from the distributional hypothesis and recent work on learning sentence representations, we reformulate the problem of predicting the context in which a sentence appears as a classification problem. Given a sentence and the context in which it appears, a classifier distinguishes context sentences from other contrastive sentences based on their vector representations. This allows us to efficiently learn different types of encoding functions, and we show that the model learns high-quality sentence representations. We demonstrate that our sentence representations outperform stateof-the-art unsupervised and supervised representation learning methods on several downstream NLP tasks that involve understanding sentence semantics while achieving an order of magnitude speedup in training time. ",
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+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
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+    },
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+        "text": "Methods for learning meaningful representations of data have received widespread attention in recent years. It has become common practice to exploit these representations trained on large corpora for downstream tasks since they capture a lot of prior knowlege about the domain of interest and lead to improved performance. This is especially attractive in a transfer learning setting where only a small amount of labelled data is available for supervision. ",
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+        "text": "Unsupervised learning allows us to learn useful representations from large unlabelled corpora. The idea of self-supervision has recently become popular where representations are learned by designing learning objectives that exploit labels that are freely available with the data. Tasks such as predicting the relative spatial location of nearby image patches (Doersch et al., 2015), inpainting (Pathak et al., 2016) and solving image jigsaw puzzles (Noroozi & Favaro, 2016) have been successfully used for learning visual feature representations. In the language domain, the distributional hypothesis has been integral in the development of learning methods for obtaining semantic vector representations of words (Mikolov et al., 2013b). This is the assumption that the meaning of a word is characterized by the word-contexts in which it appears. Neural approaches based on this assumption have been successful at learning high quality representations from large text corpora. ",
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+        "text": "Recent methods have applied similar ideas for learning sentence representations (Kiros et al., 2015; Hill et al., 2016; Gan et al., 2016). These are encoder-decoder models that learn to predict/reconstruct the context sentences of a given sentence. Despite their success, several modelling issues exist in these methods. There are numerous ways of expressing an idea in the form of a sentence. The ideal semantic representation is insensitive to the form in which meaning is expressed. Existing models are trained to reconstruct the surface form of a sentence, which forces the model to not only predict its semantics, but aspects that are irrelevant to the meaning of the sentence as well. ",
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+        "type": "text",
+        "text": "The other problem associated with these models is computational cost. These methods have a word level reconstruction objective that involves sequentially decoding the words of target sentences. Training with an output softmax layer over the entire vocabulary is a significant source of slowdown in the training process. This further limits the size of the vocabulary and the model (Variations of the softmax layer such as hierarchical softmax (Mnih & Hinton, 2009), sampling based softmax (Jean et al., 2014) and sub-word representations (Sennrich et al., 2015) can help alleviate this issue). ",
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+        "type": "text",
+        "text": "We circumvent these problems by proposing an objective that operates directly in the space of sentence embeddings. The generation objective is replaced by a discriminative approximation where the model attempts to identify the embedding of a correct target sentence given a set of sentence candidates. In this context, we interpret the ‘meaning’ of a sentence as the information in a sentence that allows it to predict and be predictable from the information in context sentences. We name our approach quick thoughts (QT), to mean efficient learning of thought vectors. ",
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+        "type": "text",
+        "text": "Our key contributions in this work are the following: ",
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+        "text": "• We propose a simple and general framework for learning sentence representations efficiently. We train widely used encoder architectures an order of magnitude faster than previous methods, achieving better performance at the same time. • We establish a new state-of-the-art for unsupervised sentence representation learning methods across several downstream tasks that involve understanding sentence semantics. ",
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+    {
+        "type": "text",
+        "text": "The pre-trained encoders will be made publicly available. ",
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+    {
+        "type": "text",
+        "text": "2 RELATED WORK ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We discuss prior approaches to learning sentence representations from labelled and unlabelled data. ",
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+    {
+        "type": "text",
+        "text": "Learning from Unlabelled corpora. Le & Mikolov (2014) proposed the paragraph vector (PV) model to embed variable-length text. Models are trained to predict a word given it’s context or words appearing in a small window based on a vector representation of the source document. Unlike most other methods, in this work sentences are considered as atomic units instead of as a compositional function of its words. ",
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+    {
+        "type": "text",
+        "text": "Encoder-decoder models have been successful at learning semantic representations. Kiros et al. (2015) proposed the skip-thought vectors model, which consists of an encoder RNN that produces a vector representation of the source sentence and a decoder RNN that sequentially predicts the words of adjacent sentences. Drawing inspiration from this model, Gan et al. (2016) explore the use of convolutional neural network (CNN) encoders. The base model uses a CNN encoder and reconstructs the input sentence as well as neighboring sentences using an RNN. They also consider a hierarchical version of the model which sequentially reconstructs sentences within a larger context. ",
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+    {
+        "type": "text",
+        "text": "Autoencoder models have been explored for representation learning in a wide variety of data domains. An advantage of autoencoders over context prediction models is that they do not require ordered sentences for learning. Socher et al. (2011) proposed recursive autoencoders which encode an input sentence using a recursive encoder and a decoder reconstructs the hidden states of the encoder. Hill et al. (2016) considered a de-noising autoencoder model (SDAE) where noise is introduced in a sentence by deleting words and swapping bigrams and the decoder is required to reconstruct the original sentence. Bowman et al. (2015) proposed a generative model of sentences based on a variational autoencoder. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Kenter et al. (2016) learn bag-of-words (BoW) representations of sentences by considering a conceptually similar task of identifying context sentences from candidates and evaluate their representations on sentence similarity tasks. Hill et al. (2016) introduced the FastSent model which uses a BoW representation of the input sentence and predicts the words appearing in context (and optionally, the source) sentences. The model is trained to predict whether a word appears in the target sentences. Arora et al. (2016) consider a weighted BoW model followed by simple post-processing and show that it performs better than BoW models trained on paraphrase data. ",
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+    {
+        "type": "text",
+        "text": "Jernite et al. (2017) use paragraph level coherence as a learning signal to learn representations. The following related task is considered in their work. Given the first three sentences of a paragraph, choose the next sentence from five sentences later in the paragraph. Related to our objective is the local coherence model of Li & Hovy (2014) where a binary classifier is trained to identify coherent/incoherent sentence windows. In contrast, we only encourage observed contexts to be more plausible than contrastive ones and formulate it as a multi-class classification problem. We experimentally found that this relaxed constraint helps learn better representations. ",
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+    {
+        "type": "text",
+        "text": "Encoder-decoder based sequence models are known to work well, but they are slow to train on large amounts of data. On the other hand, bag-of-words models train efficiently by ignoring word order. ",
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+    },
+    {
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+        "img_path": "images/21cae2b04f4edf179da8352b7975508a6f751e122cb715b1751db7461b777c89.jpg",
+        "image_caption": [
+            "Figure 1: Overview. (a) The approach adopted by most prior work where given an input sentence the model attempts to generate a context sentence. (b) Our approach replaces the decoder with a classifier which chooses the target sentence from a set of candidate sentences. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We incorporate the best of both worlds by retaining flexibility of the encoder architecture, while still being able to to train efficiently. ",
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+    {
+        "type": "text",
+        "text": "Structured Resources. There have been attempts to use labeled/structured data to learn sentence representations. Hill et al. (2016) learn to map words to their dictionary definitions using a max margin loss that encourages the encoded representation of a definition to be similar to the corresponding word. Wieting et al. (2015) and Wieting & Gimpel (2017) use paraphrase data to learn an encoder that maps synonymous phrases to similar embeddings using a margin loss. Hermann & Blunsom (2013) consider a similar objective of minimizing the inner product between paired sentences in different languages. Wieting et al. (2017) explore the use of machine translation to obtain more paraphrase data via back-translation and use it for learning paraphrastic embeddings. ",
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+    {
+        "type": "text",
+        "text": "Conneau et al. (2017) consider the supervised task of Natural language inference (NLI) as a means of learning generic sentence representations. The task involves identifying one of three relationships between two given sentences - entailment, neutral and contradiction. The training strategy consists of learning a classifier on top of the embeddings of the input pair of sentences. The authors show that sentence encoders trained for this task perform strongly on downstream transfer tasks. ",
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+    {
+        "type": "text",
+        "text": "3 PROPOSED FRAMEWORK ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "The distributional hypothesis has been operationalized by prior work in different ways. A common approach is illustrated in Figure 1(a), where an encoding function computes a vector representation of an input sentence, and then a decoding function attempts to generate the words of a target sentence conditioned on this representation. In the skip-thought model, the target sentences are those that appear in the neighborhood of the input sentence. There have been variations on the decoder such as autoencoder models which predict the input sentence instead of neighboring sentences (Hill et al., 2016) and predicting properties of a window of words in the input sentence (Le & Mikolov, 2014). ",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Instead of training a model to reconstruct the surface form of the input sentence or its neighbors, we take the following approach. Use the meaning of the current sentence to predict the meanings of adjacent sentences, where meaning is represented by an embedding of the sentence computed from an encoding function. Despite the simplicity of the modeling approach, we show that it facilitates learning rich representations. ",
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+    {
+        "type": "text",
+        "text": "Our approach is illustrated in figure 1(b). Given an input sentence, it is encoded as before using some function. But instead of generating the target sentence, the model chooses the correct target sentence from a set of candidate sentences. Viewing generation as choosing a sentence from all possible sentences, this can be seen as a discriminative approximation to the generation problem. ",
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+    {
+        "type": "text",
+        "text": "A key difference between these two approaches is that in figure 1(b), the model can choose to ignore aspects of the sentence that are irrelevant in constructing a semantic embedding space. Loss functions defined in a feature space as opposed to the raw data space have been found to be more attractive in recent work for similar reasons (Larsen et al., 2015; Pathak et al., 2017). ",
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "Formally described, let $f$ and $g$ be parametrized functions that take a sentence as input and encode it into a fixed length vector. Let $s$ be a given sentence. Let $S _ { \\mathrm { c t x t } }$ be the set of sentences appearing in the context of $s$ (for a particular context size) in the training data. Let $S _ { \\mathrm { c a n d } }$ be the set of candidate sentences considered for a given context sentence $s _ { \\mathrm { c t x t } } \\in \\ S _ { \\mathrm { c t x t } }$ . In other words, $S _ { \\mathrm { c a n d } }$ contains a valid context sentence $s _ { \\mathrm { c t x t } }$ (ground truth) and many other non-context sentences, and is used for the classification objective as described below. ",
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+    {
+        "type": "text",
+        "text": "For a given sentence position in the context of $s$ (e.g., the next sentence), the probability that a candidate sentence $s _ { \\mathrm { c a n d } } \\in S _ { \\mathrm { c a n d } }$ is the correct sentence (i.e., appearing in the context of $s$ ) for that position is given by ",
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+    {
+        "type": "equation",
+        "img_path": "images/2f2bec4168004efd93b9ca7d68816d058c4c078e5c847c7e80f45fbca616b9f0.jpg",
+        "text": "$$\np ( s _ { \\mathrm { c a n d } } | s , S _ { \\mathrm { c a n d } } ) = \\frac { \\exp [ c ( f ( s ) , g ( s _ { \\mathrm { c a n d } } ) ) ] } { \\sum _ { s ^ { \\prime } \\in S _ { \\mathrm { c a n d } } } \\exp [ c ( f ( s ) , g ( s ^ { \\prime } ) ) ] }\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where $c$ is a scoring function/classifier. ",
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+    {
+        "type": "text",
+        "text": "The training objective maximizes the probability of identifying the correct context sentences for each sentence in the training data $D$ . ",
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+        "type": "equation",
+        "img_path": "images/ba85f881580c4ff406c19f4d2fd8ac9ed6a20b7a94eb94b03670a5ff9566fd5c.jpg",
+        "text": "$$\n\\sum _ { s \\in D } \\sum _ { s _ { \\mathrm { c t x t } } \\in S _ { \\mathrm { c t x t } } } \\log p ( s _ { \\mathrm { c t x t } } | s , S _ { \\mathrm { c a n d } } )\n$$",
+        "text_format": "latex",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The modeling approach encapsulates the Skip-gram approach of Mikolov et al. (2013b) when words play the role of sentences. In this case the encoding functions are simple lookup tables considering words to be atomic units, and the training objective maximizes the similarity between the source word and a target word in its context given a set of negative samples. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Alternatively, we considered an objective function similar to the negative sampling approach of Mikolov et al. (2013b). This takes the form of a binary classifier which takes a sentence window as input and classifies them as plausible and implausible context windows. We found objective (2) to work better, presumably due to the relaxed constraint it imposes. Instead of requiring context windows to be classified as positive/negative, it only requires ground-truth contexts to be more plausible than contrastive contexts. This objective also performed empirically better than a maxmargin loss. ",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In our experiments, $c$ is simply defined to be an inner product $c ( u , v ) = u ^ { T } v$ . This was motivated by considering pathological solutions where the model learns poor sentence encoders and a rich classifier to compensate for it. This is undesirable since the classifier will be discarded and only the sentence encoders will be used to extract features for downstream tasks. Minimizing the number of parameters in the classifier encourages the encoders to learn disentangled and useful representations. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We consider $f , g$ to have different parameters, although they were motivated from the perspective of modeling sentence meaning. Another motivation comes from word representation learning methods which use different sets of input and output parameters. Parameter sharing is further not a significant concern since these models are trained on large corpora. At test time, for a given sentence $s$ we consider its representation to be the concatenation of the outputs of the two encoders $\\left[ f ( s ) \\ g ( s ) \\right]$ . ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Our framework allows flexible encoding functions to be used. We use RNNs as $f$ and $g$ as they have been widely used in recent sentence representation learning methods. The words of the sentence are sequentially fed as input to the RNN and the final hidden state is interpreted as a representation of the sentence. We use gated recurrent units (GRU) (Chung et al., 2015) as the RNN cell similar to Kiros et al. (2015). ",
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+    {
+        "type": "text",
+        "text": "4 EXPERIMENTAL RESULTS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "4.1 EVALUATING SENTENCE EMBEDDINGS ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "We evaluate our sentence representations by using them as feature representations for downstream NLP tasks. Alternative fine-grained evaluation tasks such as identifying word appearance and word order were proposed in Adi et al. (2017). Although this provides some useful insight about the representations, these tasks focus on the syntactic aspects of a sentence. We are more interested in assessing how well representations capture sentence semantics. Although limitations of these evaluations have been pointed out, we stick to the traditional approach of evaluating using downstream tasks. ",
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+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "4.2 DATA ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Models were trained on the 7000 novels of the BookCorpus dataset (Kiros et al., 2015). The dataset consists of about 45M ordered sentences. We also consider a larger corpus for training: the UMBC corpus (Han et al., 2013), a dataset of 100M web pages crawled from the internet, preprocessed and tokenized into paragraphs. The dataset has 129M sentences, about three times larger than BookCorpus. For models trained from scratch, we used case-sensitive vocabularies of sizes $5 0 \\mathrm { k }$ and $1 0 0 \\mathrm { k }$ for the two datasets respectively. ",
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+    {
+        "type": "text",
+        "text": "4.3 TRAINING ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "A minibatch is constructed using a contiguous sets of sentences in the corpus. For each sentence, all the sentences in the minibatch are considered to be the candidate pool $S _ { \\mathbf { c a n d } }$ of sentences for classification. This simple scheme for picking contrastive sentences performed as well as other schemes such as random sampling and picking nearest neighbors of the input sentence. Hyperparameters including batch size, learning rate, prediction context size were obtained using prediction accuracies (accuracy of predicting context sentences) on the validation set. A context size of 3 was used, i.e., predicting the previous and next sentences given the current sentence. We used a batch size of 400 and learning rate of 5e-4 with the Adam optimizer for all experiments. All our RNN-based models are single-layered and use GRU cells. Weights of the GRU are initialized using uniform Xavier initialization and gate biases are initialized to 1. Word embeddings are initialized from $U [ - 0 . 1 , 0 . 1 ]$ . ",
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+    {
+        "type": "text",
+        "text": "4.4 EVALUATION ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Tasks We evaluate the sentence representations on tasks that require understanding sentence semantics. The following classification benchmarks are commonly used: movie review sentiment (MR) (Pang & Lee, 2005), product reviews (CR) (Hu & Liu, 2004), subjectivity classification (SUBJ) (Pang & Lee, 2004), opinion polarity (MPQA) (Wiebe et al., 2005), question type classification (TREC) (Voorhees & Buckland, 2003) and paraphrase identification (MSRP) (Dolan et al., 2004). The semantic relatedness task on the SICK dataset (Marelli et al., 2014) involves predicting relatedness scores for a given pair of sentences that correlate well with human judgements. ",
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The MR, CR, SUBJ, MPQA tasks are binary classification tasks. 10-fold cross validation is used in reporting test performance for these tasks. The other tasks come with train/dev/test splits and the dev set is used for choosing the regularization parameter. We follow the evaluation scheme of Kiros et al. (2015) where feature representations of sentences are obtained from the trained encoders and a logistic/softmax classifier is trained on top of the embeddings for each task while keeping the sentence embeddings fixed. Kiros et al.’s scripts are used for evaluation. ",
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+    {
+        "type": "text",
+        "text": "4.4.1 COMPARISON AGAINST UNSUPERVISED METHODS ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Table 1 compares our work against representations from prior methods that learn from unlabelled data. The dimensionality of sentence representations and training time are also indicated. For our RNN based encoder we consider variations that are analogous to the skip-thought model. The uniQT model uses uni-directional RNNs as the sentence encoders $f$ and $g$ . In the bi-QT model, the concatenation of the final hidden states of two RNNs represent $f$ and $g$ , each processing the sentence in a different (forward/backward) direction. The combine-QT model concatenates the representations (at test time) learned by the uni-QT and bi-QT models. ",
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Models trained from scratch on BookCorpus. While the FastSent model is efficient to train (training time of 2h), this efficiency stems from using a bag-of-words encoder. Bag of words provides a strong baseline because of its ability to preserves word identity information. However, the model performs poorly compared to most of the other methods. Bag-of-words is also conceptually less attractive as a representation scheme since it ignores word order, which is a key aspect of meaning. ",
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The de-noising autoencoder (SDAE) performs strongly on the paraphrase detection task (MSRP). This is attributable to the reconstruction (autoencoding) loss which encourages word identity and ",
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+        "type": "table",
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+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Model</td><td rowspan=\"2\">Dim</td><td rowspan=\"2\">Training time (h)</td><td rowspan=\"2\">MR</td><td rowspan=\"2\">CR</td><td rowspan=\"2\">SUBJ</td><td rowspan=\"2\">MPQA TREC</td><td colspan=\"2\">MSRP</td><td rowspan=\"2\"></td><td colspan=\"3\">SICK</td></tr><tr><td>(Acc)</td><td>(F1)</td><td>r</td><td>p</td><td>MSE</td></tr><tr><td>GloVeBoW</td><td>300</td><td>-</td><td>78.1</td><td>80.4</td><td>91.9</td><td>87.8</td><td>85.2</td><td>72.5</td><td>81.1</td><td>0.764</td><td>0.687</td><td>0.425</td></tr><tr><td colspan=\"11\">Trained from scratch on BookCorpus data</td></tr><tr><td>SDAE FastSent ParagraphVec</td><td>2400 &lt;500</td><td>192 2* 4*</td><td>67.6 71.8</td><td>74.0 78.4</td><td>89.3 88.7</td><td>81.3 81.5</td><td>77.6 76.8</td><td>76.4 72.2</td><td>83.4 80.3</td><td>N/A N/A</td><td>N/A N/A</td><td>N/A N/A</td></tr><tr><td></td><td>&lt;500</td><td></td><td>61.5</td><td>68.6</td><td>76.4</td><td>78.1</td><td>55.8</td><td>73.6</td><td>81.9</td><td>N/A</td><td>N/A</td><td>N/A</td></tr><tr><td>uni-skip bi-skip</td><td>2400</td><td>336</td><td>75.5</td><td>79.3</td><td>92.1</td><td>86.9</td><td>91.4</td><td>73.0</td><td>81.9</td><td>0.848</td><td>0.778</td><td>0.287</td></tr><tr><td>combine-skip</td><td>2400</td><td>336</td><td>73.9</td><td>77.9</td><td>92.5</td><td>83.3</td><td>89.4</td><td>71.2</td><td>81.2</td><td>0.841</td><td>0.770</td><td>0.300</td></tr><tr><td>combine-cnn</td><td>4800</td><td>336t</td><td>76.5</td><td>80.1</td><td>93.6</td><td>87.1</td><td>92.2</td><td>73.0</td><td>82.0</td><td>0.858</td><td>0.792</td><td>0.269</td></tr><tr><td>uni-QT</td><td>4800</td><td>-</td><td>77.2</td><td>80.9</td><td>93.1</td><td>89.1</td><td>91.8</td><td>75.5</td><td>82.6</td><td>0.853</td><td>0.789</td><td>0.279</td></tr><tr><td>bi-QT</td><td>2400</td><td>11</td><td>77.2</td><td>82.8</td><td>92.4</td><td>87.2</td><td>90.6</td><td>74.7</td><td>82.7</td><td>0.844</td><td>0.778</td><td>0.293</td></tr><tr><td></td><td>2400</td><td>9</td><td>77.0</td><td>83.5</td><td>92.3</td><td>87.5</td><td>89.4</td><td>74.8</td><td>82.9</td><td>0.855</td><td>0.787</td><td>0.274</td></tr><tr><td>combine-QT</td><td>4800</td><td>11</td><td>78.2</td><td>84.4</td><td>93.3</td><td>88.0</td><td>90.8</td><td>76.2</td><td>83.5</td><td>0.860</td><td>0.796</td><td>0.267</td></tr><tr><td colspan=\"14\">Trained on BookCorpus, ,pre-trained word vectors are used</td></tr><tr><td>combine-cnn MC-QT</td><td>4800 4800</td><td>1 11</td><td>77.8 80.4</td><td>82.1</td><td>93.6</td><td>89.4</td><td>92.6</td><td>76.5</td><td>83.8</td><td>0.862</td><td>0.798</td><td>0.267</td></tr><tr><td></td><td></td><td></td><td></td><td>85.2</td><td>93.9</td><td>89.4</td><td>92.8</td><td>76.9</td><td>84.0</td><td>0.868</td><td>0.801</td><td>0.256</td></tr><tr><td colspan=\"14\"> Trained on (BookCorpus + UMBC) data, from scratch and using pre-trained word vectors</td></tr><tr><td>combine-QT</td><td>4800</td><td>28</td><td>81.3</td><td>84.5</td><td>94.6</td><td>89.5</td><td>92.4</td><td></td><td></td><td>0.871</td><td></td><td></td></tr><tr><td>MC-QT</td><td>4800</td><td>28</td><td>82.4</td><td>86.0</td><td>94.8</td><td>90.2</td><td>92.4</td><td>75.9 76.9</td><td>83.3 84.0</td><td>0.874</td><td>0.807 0.811</td><td>0.247 0.243</td></tr></table>",
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+        "type": "text",
+        "text": "Table 1: Comparison of sentence representations on downstream tasks. The baseline methods are GloVe bag-of-words representation, De-noising auto-encoders and FastSent from Hill et al. (2016), the paragraph vector distributed memory model (Le & Mikolov, 2014), skip-thought vectors (Kiros et al., 2015) and the CNN model of Gan et al. (2016). Training times indicated using \\* refers to CPU trained models and † assumes concatenated representations are trained independently. Performance figures for SDAE, FastSent and ParagraphVec were obtained from Hill et al. (2016). Higher numbers are better in all columns except for the last (MSE). The table is divided into different sections. The bold-face numbers indicate the best performance values among models in the current and all previous sections. Best overall values in each column are underlined. ",
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+    {
+        "type": "text",
+        "text": "order information to be encoded in the representation. However, it fails to perform well in other tasks that require higher level sentence understanding and is also inefficient to train. ",
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+        "type": "text",
+        "text": "Our uni/bi/combine-QT variations perform comparably (and in most cases, better) to the skipthought model and the CNN-based variation of Gan et al. (2016) in all tasks despite requiring much less training time. Since these models were trained from scratch, this also shows that the model learns good word representations as well. ",
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+    {
+        "type": "text",
+        "text": "MultiChannel-QT. Next, we consider using pre-trained word vectors to train the model. The MultiChannel-QT model (MC-QT) is defined as the concatenation of two bi-directional RNNs. One of these uses fixed pre-trained word embeddings coming from a large vocabulary $( \\sim 3 \\mathbf { M } )$ as input. While the other uses tunable word embeddings trained from scratch (from a smaller vocabulary $\\sim$ 50k). This model was inspired by the multi-channel CNN model of Kim (2014) which considered two sets of embeddings. With different input representations, the two models discover less redundant features, as opposed to the uni and bi variations suggested in Kiros et al. (2015). We use GloVe vectors (Pennington et al., 2014) as pre-trained word embeddings. The MC-QT model outperforms all previous methods, including the variation of Gan et al. (2016) which uses pre-trained word embeddings. ",
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+        "type": "text",
+        "text": "UMBC data. Because our framework is efficient to train, we also experimented on a larger dataset of documents. Results for models trained on BookCorpus and UMBC corpus pooled together ( $\\sim$ 174M sentences) are shown at the bottom of the table. We observe strict improvements on a majority of the tasks compared to our BookCorpus models. This shows that we can exploit huge corpora to obtain better models while keeping the training time practically feasible. ",
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+        "type": "text",
+        "text": "Computational efficiency. Our models are implemented in Tensorflow. Experiments were performed using cuda 8.0 and cuDNN 6.0 libraries on a GTX Titan X GPU. Our best BookCorpus model (MC-QT) trains in just under 11hrs (On both the Titan X and GTX 1080). Training time for the skip-thoughts model is mentioned as 2 weeks in Kiros et al. (2015) and a more recent Tensorflow implementation1 reports a training time of 9 days on a GTX 1080. On the augmented dataset our models take about a day to train, and we observe monotonic improvements in all tasks except the TREC task. Our framework allows training with much larger vocabulary sizes than most previous models. Our approach is also memory efficient. The paragraph vector model has a big memory footprint since it has to store vectors of documents used for training. Softmax computations over the vocabulary in the skip-thought and other models with word-level reconstruction objectives incur heavy memory consumption. Our RNN based implementation (with the indicated hyperparamters and batch size) fits within 3GB of GPU memory, a majority of it consumed by the word embeddings. ",
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+        "type": "text",
+        "text": "",
+        "bbox": [
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+    {
+        "type": "table",
+        "img_path": "images/7856636fe73d43d0e2f6c8d19220ab6084fa02bb492f719ff70465e025830e83.jpg",
+        "table_caption": [
+            "4.4.2 COMPARISON AGAINST SUPERVISED METHODS "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>MR</td><td>CR</td><td>SUBJ</td><td>MPQA</td><td>SST</td><td>TREC</td><td>MSRP</td><td></td><td>SICK</td></tr><tr><td>CaptionRep</td><td>61.9</td><td>69.3</td><td>77.4</td><td>70.8</td><td>1</td><td>72.2</td><td>1</td><td>-</td><td>-</td></tr><tr><td>DictRep</td><td>76.7</td><td>78.7</td><td>90.7</td><td>87.2</td><td></td><td>81.0</td><td>68.4</td><td>76.8</td><td>-</td></tr><tr><td>NMTEn-to-Fr</td><td>64.7</td><td>70.1</td><td>84.9</td><td>81.5</td><td>■</td><td>82.8</td><td>=</td><td>-</td><td>1</td></tr><tr><td>InferSent</td><td>81.1</td><td>86.3</td><td>92.4</td><td>90.2</td><td>84.6</td><td>88.2</td><td>76.2</td><td>83.1</td><td>0.884</td></tr><tr><td>MC-QT</td><td>82.4</td><td>86.0</td><td>94.8</td><td>90.2</td><td>87.6</td><td>92.4</td><td>76.9</td><td>84.0</td><td>0.874</td></tr></table>",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/597d6efe27163df515d9144aa01d21c68b8e03e87e0fc3f0458e84b774cdb758.jpg",
+        "table_caption": [
+            "Table 2: Comparison against supervised representation learning methods on downstream tasks. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>MR</td><td>CR</td><td>SUBJ</td><td>MPQA</td><td>SST</td><td>TREC</td><td>MSRP</td><td></td><td>SICK</td></tr><tr><td>Ensemble</td><td>82.7</td><td>86.7</td><td>95.5</td><td>90.3</td><td>88.2</td><td>93.4</td><td>78.5</td><td>85.1</td><td>0.881</td></tr><tr><td colspan=\"10\">Task specific methods</td></tr><tr><td>AdaSent</td><td>83.1</td><td>86.3</td><td>95.5</td><td>93.3</td><td>1</td><td>92.4</td><td></td><td></td><td>1</td></tr><tr><td>CNN</td><td>81.5</td><td>85.0</td><td>93.4</td><td>89.6</td><td>88.1</td><td>93.6</td><td>1</td><td>1</td><td></td></tr><tr><td>TF-KLD</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>80.4</td><td>85.9</td><td>1</td></tr><tr><td>DT-LSTM</td><td>-</td><td>■</td><td>1</td><td>=</td><td>1</td><td>■</td><td>1</td><td>-</td><td>0.868</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 3: Comparison against task-specific supervised models. The models are AdaSent (Zhao et al., 2015), CNN (Kim, 2014), TF-KLD (Ji & Eisenstein, 2013) and Dependency-Tree LSTM (Tai et al., 2015). Note that our performance values correspond to a linear classifier trained on fixed pre-trained embeddings, while the task-specific methods are tuned end-to-end. ",
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+    {
+        "type": "text",
+        "text": "Table 2 compares our approach against methods that learn from labelled/structured data. The CaptionRep, DictRep and NMT models are from Hill et al. (2016) which are trained respectively on the tasks of matching images and captions, mapping words to their dictionary definitions and machine translation. The InferSent model of Conneau et al. (2017) is trained on the NLI task. In addition to the benchmarks considered before, we additionally also include the sentiment analysis binary classification task on Stanford Sentiment Treebank (SST) (Socher et al., 2013). ",
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+    {
+        "type": "text",
+        "text": "The Infersent model has strong performance on the tasks. Our multichannel model trained on the (BookCorpus $^ +$ UMBC) data outperforms InferSent in most of the tasks, with most significant margins in the SST and TREC tasks. Infersent is strong in the SICK task presumably due to the following reasons. The model gets to observes near paraphrases (entailment relationship) and sentences that are not-paraphrases (contradiction relationship) at training time. Furthermore, it considers difference features $( | u - v | )$ and multiplicative features $( u * v )$ of the input pair of sentences $u , v$ during training. This is identical to the feature transformations used in the SICK evaluation as well. ",
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+        "type": "text",
+        "text": "Ensemble We consider ensembling to exploit the strengths of different types of encoders. Since our models are efficient to train, we are able to feasibly train many models. We consider a subset of the following model variations for the ensemble. ",
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+    {
+        "type": "text",
+        "text": "• Model type - Uni/Bi-directional RNN • Word embeddings - Trained from scratch/Pre-trained • Dataset - BookCorpus/UMBC ",
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+        "type": "table",
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+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"8\">COCORetrieval</td></tr><tr><td>Model</td><td>Image</td><td colspan=\"3\">Annotation</td><td></td><td>Image Search</td><td></td></tr><tr><td></td><td>R@1</td><td>R@5</td><td>R@10</td><td>Med r</td><td>R@1</td><td>R@5 R@10</td><td>Med r</td></tr><tr><td colspan=\"8\">Pre-trained unsupervised sentence representations</td></tr><tr><td>Combine-skip</td><td>33.8</td><td>67.7 82.1</td><td>3</td><td>25.9</td><td>60.0</td><td>74.6</td><td>4</td></tr><tr><td>Combine-cnn</td><td>34.4</td><td>1</td><td>3 1</td><td>26.6</td><td>1</td><td>1</td><td>4</td></tr><tr><td>MC-QT</td><td>37.1</td><td>72.0</td><td>84.7</td><td>2</td><td>27.9 63.3</td><td>78.3</td><td>3</td></tr><tr><td colspan=\"8\">Direct supervision of sentence representations</td></tr><tr><td>DVSA</td><td>38.4</td><td>69.6 80.5</td><td>1</td><td>27.4</td><td>60.2</td><td>74.8</td><td>3</td></tr><tr><td>GMM+HGLMM</td><td>39.4</td><td>67.9</td><td>80.9</td><td>2</td><td>25.1 59.8</td><td>76.6</td><td>4</td></tr><tr><td>m-RNN</td><td>41.0</td><td>73.0</td><td>83.5</td><td>2 29.0</td><td>42.2</td><td>77.0</td><td>3</td></tr><tr><td>Order</td><td>46.7</td><td>88.9</td><td>1 2</td><td>37.9</td><td>85.9</td><td>1</td><td>2</td></tr></table>",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 4: Image-caption retrieval. The purely supervised models are respectively from (Karpathy & Fei-Fei, 2015), (Klein et al., 2015), (Mao et al., 2014) and (Vendrov et al., 2015). Best pre-trained representations and best task-specific methods are highlighted. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Models are combined using a weighted average of the predicted log-probabilities of individual models, the weights being normalized validation set performance scores. Results are presented in table 3. Performance of the best purely supervised task-specific methods are shown at the bottom for reference. Note that these numbers are not directly comparable with the unsupervised methods since the sentence embeddings are not fine-tuned. We observe that the ensemble model closely approaches the performance of the best supervised task-specific methods, outperforming them in 3 out of the 8 tasks. ",
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.4.3 IMAGE-SENTENCE RANKING",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The image-to-caption and caption-to-image retrieval tasks have been commonly used to evaluate sentence representations in a multi-modal setting. The task requires retrieving an image matching a given text description and vice versa. The evaluation setting is identical to Kiros et al. (2015). Images and captions are represented as vectors. Given a matching image-caption pair $( I , C )$ a scoring function $f$ determines the compatibility of the corresponding vector representations $v _ { I } , v _ { C }$ . The scoring function is trained using a margin loss which encourages matching pairs to have higher compatibility than mismatching pairs. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "equation",
+        "img_path": "images/5dc3d8d881df8de43bd973c25b09cacd69d523bae05423ac6acfaf9e7016dfb8.jpg",
+        "text": "$$\n\\sum _ { ( I , C ) } \\sum _ { I ^ { \\prime } } \\operatorname* { m a x } \\{ 0 , \\alpha - f ( v _ { I } , v _ { C } ) + f ( v _ { I } , v _ { C ^ { \\prime } } ) \\} + \\sum _ { ( I , C ) } \\sum _ { C ^ { \\prime } } \\operatorname* { m a x } \\{ 0 , \\alpha - f ( v _ { I } , v _ { C } ) + f ( v _ { I ^ { \\prime } } , v _ { C } ) \\}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "As in prior work, we use VGG-Net features (4096-dimensional) as the image representation. Sentences are represented as vectors using the representation learning method to be evaluated. These representations are held fixed during training. The scoring function used in prior work is $f ( x , y ) \\stackrel { \\cdot } { = } ( U x ) ^ { T } ( V y )$ where $U , V$ are projection matrices which project down the image and sentence vectors to the same dimensionality. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The MSCOCO dataset (Lin et al., 2014) has been traditionally used for this task. We use the train/val/test split proposed in Karpathy & Fei-Fei (2015). The training, validation and test sets respectively consist of 113,287, 5000, 5000 images, each annotated with 5 captions. Performance is reported as an average over 5 splits of 1000 image-caption pairs each from the test set. Results are presented in table 3. We outperform previous unsupervised pre-training methods by a significant margin, strictly improving the median retrieval rank for both the annotation and search tasks. We also outperform some of the purely supervised task specific methods by some metrics. ",
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+    {
+        "type": "text",
+        "text": "4.4.4 NEAREST NEIGHBORS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Our model and the skip-thought model have conceptually similar objective functions. This suggests examining properties of the embedding spaces to better understand how they encode semantics. We consider a nearest neighbor retrieval experiment to compare the embedding spaces. We use a pool of 1M sentences from a Wikipedia dump for this experiment. For a given query sentence, the best neighbor determined by cosine distance in the embedding space is retrieved. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 5 shows a random sample of query sentences from the dataset and the corresponding retrieved sentences. These examples show that our retrievals are often more related to the query sentence compared to the skip-thought model. It is interesting to see in the first example that the model identifies a sentence with similar meaning even though the main clause and conditional clause are in a different order. This is in line with our goal of learning representations that are less sensitive to the form in which meaning is expressed. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/2db9f8012853e8748c371dd1b99175962983a3387fadcdf570e428fdbf47209a.jpg",
+        "table_caption": [
+            "Table 5: Nearest neighbors retrieved by the skip-thought model (ST) and our model (QT). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"2\"></td></tr><tr><td>Query ST</td><td>Seizures may occur as the glucose falls further . It may also occur during an excessively rapid entry into autorotation .</td></tr><tr><td>QT</td><td>When brain glucose levels are suffciently low , seizures may result .</td></tr><tr><td>Query ST QT</td><td>This evidence was only made public after both enquiries were completed . This visa was provided for under Republic Act No. These evidence were made public by the United States but concealed the names of</td></tr><tr><td>Query ST</td><td>sources . He kept both medals in a biscuit tin . He kept wicket for Middlesex in two first-class cricket matches during the 1891 County</td></tr><tr><td>QT</td><td>Championship . He won a three medals at four Winter Olympics .</td></tr><tr><td>Query ST</td><td>The American alligator is the only known natural predator of the panther . Their mascot is the panther . The American alligator is a fairly large species of crocodilian .</td></tr><tr><td>QT Query</td><td>Several of them died prematurely : Carmen and Toms very young ，while Carlos and Pablo both died .</td></tr><tr><td>ST QT</td><td>At the age of 13,Ahmed Sher died . Many of them died in prison</td></tr><tr><td>Query ST</td><td>Music for“ Expo 2O68 ” originated from the same studio session . His 1994 work“ Dialogue ” was premiered at the Merkin Concert Hall in New York</td></tr><tr><td>QT</td><td>City : Music from“ Korra ”and“ Avatar” was also played in concert at the PlayFest festival</td></tr><tr><td>Query</td><td>in Mlaga, Spain in September 2014. Mohammad Ali Jinnah yielded to the demands of refugees from the Indian states of</td></tr><tr><td>ST</td><td>Bihar and Uttar Pradesh ,who insisted that Urdu be Pakistan &#x27;s official language . Georges Charachidz ,a historian and linguist of Georgian origin under Dumzil &#x27;s tute- lage ，became a noted specialist of the Caucasian cultures and aided Dumzil in the re-</td></tr><tr><td>QT</td><td>construction of the Ubykh language . Wali Mohammed Wali &#x27;s visit thus stimulated the growth and development of Urdu</td></tr><tr><td>Query ST</td><td>Ghazal in Delhi . The PCC, together with the retrosplenial cortex , forms the retrosplenial gyrus . The Macro domain from human , macroH2A1.1,binds an NAD metabolite O-acetyl-</td></tr><tr><td>QT</td><td>ADP-ribose . The PCC forms a part of the posteromedial cortex ,along with the retrosplenial cortex (</td></tr><tr><td>Query</td><td>Brodmann areas 29 and 30 ） and precuneus （located posterior and superior to the PCC ） With the exception of what are known as the Douglas Treaties , negotiated by Sir James</td></tr><tr><td></td><td>Douglas with the native people of the Victoria area , no treaties were signed in British Columbia until 1998 .</td></tr><tr><td>ST</td><td>All the assets of the Natal Railway Company ,including its locomotive fleet of three , were purchased for the sum of 4O,OoO by the Natal Colonial Government in 1876</td></tr><tr><td>QT</td><td>With few exceptions （ the Douglas Treaties of Fort Rupert and southern Vancouver Is- land ） no treaties were signed .</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "5 CONCLUSION ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We proposed a framework to learn generic sentence representations efficiently from large unlabelled text corpora. Our simple approach learns richer representations than prior unsupervised and supervised methods, consuming an order of magnitude less training time. We establish a new state-of",
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+    {
+        "type": "text",
+        "text": "the-art for unsupervised sentence representation learning methods on several downstream tasks. We believe that exploring scalable approaches to learn data representations is key to exploit unlabelled data available in abundance. ",
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+    {
+        "type": "text",
+        "text": "ACKNOWLEDGMENTS ",
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+        "text": "This material is based in part upon work supported by IBM 4915012629, NSF CAREER IIS1453651, and Sloan Research Fellowship. We thank Jongwook Choi, Junhyuk Oh, Kibok Lee, Ruben Villegas, Seunghoon Hong, Xinchen Yan, Yijie Guo and Yuting Zhang for helpful comments and discussions. ",
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+    {
+        "type": "text",
+        "text": "In this experiment we compare the ability of our model and skip-thought vectors to reason about analogies in the sentence embedding space. The analogy task has been widely used for evaluating word representations. The task involves answering questions of the type $A : B : : C : ?$ where the answer word shares a relationship to word $C$ that is identical to the relationship between words $A$ and $B$ . We consider an analogous task at the sentence level and formulate it as a retrieval task where the query vector $v ( C ) + v ( B ) - v ( A )$ is used to identify the closest sentence vector $v ( \\hat { D } )$ from a pool of candidates. This evaluation favors models that produce meaningful dimensions. ",
+        "bbox": [
+            174,
+            113,
+            825,
+            213
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Guu et al. (2017) exploit word analogy datasets to construct sentence tuples with analogical relationships. They mine sentence pairs $\\left( { { s _ { 1 } } , { s _ { 2 } } } \\right)$ from the Yelp dataset (Yelp, 2017) which approximately differ by a single word, and use these pairs to construct sentence analogy tuples based on known word analogy tuples. The dataset has 1300 tuples of sentences collected in this fashion. For each sentence tuple we derive 4 questions by considering three of the sentences to form the query vector. The candidate pool for sentence retrieval consists of all sentences in this dataset and 1M other sentences from the Yelp dataset. ",
+        "bbox": [
+            173,
+            219,
+            825,
+            318
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Table 6 compares the retrieval performance of our representations and skip-thought vectors on the above task. Results are classified under word-pair categories in the Google and Microsoft word analogy datasets (Mikolov et al., 2013a;c). Our model outperforms skip-thoughts across several categories and has good performance in the family and verb transformation categories . ",
+        "bbox": [
+            173,
+            324,
+            825,
+            381
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "table",
+        "img_path": "images/491d3adada29a4b718a2ed736e3f539fed61bcfada8072774263ef775035fc21.jpg",
+        "table_caption": [
+            "Table 6: Analogy task - Retrieval performance. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td colspan=\"3\">Google</td><td colspan=\"6\">Microsoft</td></tr><tr><td></td><td>gram4-</td><td>gram3- superlative comparative</td><td>family</td><td>JJR_JJS</td><td>VB_VBD</td><td>VBD_VBZ NN_NNS</td><td></td><td>JJ_JJS</td><td>JJ_JJR</td></tr><tr><td>Combine-skip</td><td>0.00</td><td>0.00</td><td>0.04</td><td>0.12</td><td>0.38</td><td>0.44</td><td>0.00</td><td>0.00</td><td>0.00</td></tr><tr><td>MC-QT</td><td>0.04</td><td>0.06</td><td>0.34</td><td>0.18</td><td>0.34</td><td>0.52</td><td>0.06</td><td>0.06</td><td>0.08</td></tr></table>",
+        "bbox": [
+            174,
+            392,
+            823,
+            467
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "table",
+        "img_path": "images/62588ab513791cbda2ff33472de60961c8d2a4e2341d732c5f53666e74be977f.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>A</td><td>dr.&lt;person&gt;and his staff are simply amazing ! dr.&lt;person&gt;and her staff are simply amazing ！！! i had the chicken and my husband had the pulled pork sandwich . i had the pulled pork sandwich and my wife had the pulled chicken sandwich. √</td></tr><tr><td>A</td><td>place looks great inside. place looked great inside . the complimentary valet is also a nice touch . the complimentary valet was also a nice touch .√</td></tr><tr><td>Q A</td><td>i liked the beef better than the chicken. i like the chicken better than the beef . i wanted to like this place so badly ！ i want so badly to like this place ！！√</td></tr><tr><td>Q A</td><td>the egg drop soup is the best . the egg drop soup is good . horrible food and worst customer service. horrible food and worst customer service .X</td></tr></table>",
+        "bbox": [
+            209,
+            506,
+            789,
+            732
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Table 7: Analogy task - Qualitative results. In each table cell the first three sentences form the query and the last sentence is the answer retrieved by the model. ",
+        "bbox": [
+            173,
+            742,
+            823,
+            771
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Table 7 shows some qualitative retrieval results. Each row of the table shows three sentences that form the query and the answer identified by the model. The last row shows an example where the model fails. This is a common failure case of both methods where the model assumes that $A$ and $B$ are identical in a question $A : B : : C : ?$ and retrieves sentence $C$ as the answer. ",
+        "bbox": [
+            174,
+            786,
+            825,
+            842
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "These experiments show that the our representations possess better linearity properties. The transformations evaluated here are mostly syntactic transformations involving a few words. It would be interesting to explore other high-level transformations such as switching sentiment polarity and analogical relationships that involve several words in future work. ",
+        "bbox": [
+            174,
+            849,
+            823,
+            905
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "B SEMANTIC TEXTUAL SIMILARITY ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            84,
+            491,
+            99
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "In this section we assess the representations learned by our encoders on semantic similarity tasks. The STS14 datasets (Agirre et al., 2014) consist of pairs of sentences annotated by humans with similarity scores. Representations are evaluated by measuring the correlation between human judgments and the cosine similarity of vector representations for a given pair of sentences. ",
+        "bbox": [
+            174,
+            113,
+            825,
+            170
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "We consider two types of encoders trained using our objective - RNN encoders and BoW encoders. Models were trained from scratch on the BookCorpus data. The RNN version is the same as the combine-QT model in Table 1. We describe the BoW encoder training below. ",
+        "bbox": [
+            176,
+            176,
+            821,
+            218
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "We train a BoW encoder using our training objective. Hyperparameter choices for the embedding size $\\langle 1 0 0 , 3 0 0 , 5 0 0 \\} \\rangle$ , number of contrastive sentences $\\{ 5 0 0 , 1 0 0 0 , \\mathbf { 1 5 0 0 } , 2 0 0 0 \\}$ ) and context size $( \\{ 3 , 5 , 7 \\} )$ were made based on the validation set (optimal choices highlighted in bold). Training this model on the BookCorpus dataset takes 2 hours on a Titan X GPU. Similar to the RNN encoders, the representation of a sentence is obtained by concatenating the outputs of the input and output sentence encoders. ",
+        "bbox": [
+            173,
+            224,
+            825,
+            309
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "Table 8 compares different unsupervised representation learning methods trained on the BookCorpus data from scratch. Methods are categorized as sequence models and bag-of-words models. Our RNN-based encoder performs strongly compared to other sequence encoders. Bag-of-words models are known to perform strongly in this task as they are better able to encode word identity information. Our BoW variation performs comparably to prior BoW based models. ",
+        "bbox": [
+            173,
+            315,
+            825,
+            386
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "table",
+        "img_path": "images/5d65f68fd6d23f528a754d9aa8a3a66da634bf958173d3fd5bef16d6d7d088cb.jpg",
+        "table_caption": [
+            "Table 8: Comparison (Pearson score) of sentence representations on Semantic Textual Similarity (STS14) tasks. SDAE, CBOW, Skipgram and FastSent are from Hill et al. (2016). The other baselines are Skip-Thoughts (Kiros et al., 2015) and Siamese CBOW (Kenter et al., 2016). QT (RNN) and QT (BoW) are our models trained with RNN and BoW encoders, respectively. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>News</td><td>Forum</td><td>WordNet</td><td>Tweets</td><td>Images</td><td>Headlines</td><td>Overall</td></tr><tr><td colspan=\"8\">Sequence Models</td></tr><tr><td>SDAE</td><td>0.04</td><td>0.13</td><td>0.24</td><td>0.42</td><td>0.38</td><td>0.36</td><td>0.15</td></tr><tr><td>Skip-Thoughts</td><td>0.45</td><td>0.12</td><td>0.35</td><td>0.36</td><td>0.62</td><td>0.36</td><td>0.39</td></tr><tr><td>QT(RNN)</td><td>0.48</td><td>0.15</td><td>0.53</td><td>0.62</td><td>0.53</td><td>0.48</td><td>0.49</td></tr><tr><td colspan=\"8\">BoW Models</td></tr><tr><td>CBOW</td><td>0.61</td><td>0.44</td><td>0.69</td><td>0.75</td><td>0.73</td><td>0.59</td><td>0.65</td></tr><tr><td>Skipgram</td><td>0.59</td><td>0.42</td><td>0.70</td><td>0.74</td><td>0.67</td><td>0.58</td><td>0.63</td></tr><tr><td>FastSent</td><td>0.59</td><td>0.36</td><td>0.70</td><td>0.66</td><td>0.78</td><td>0.59</td><td>0.64</td></tr><tr><td>Siamese CBOW</td><td>0.59</td><td>0.41</td><td>0.61</td><td>0.73</td><td>0.65</td><td>0.64</td><td>0.62</td></tr><tr><td>QT (BoW)</td><td>0.62</td><td>0.37</td><td>0.76</td><td>0.67</td><td>0.76</td><td>0.60</td><td>0.65</td></tr></table>",
+        "bbox": [
+            173,
+            397,
+            825,
+            558
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "C TRAINING EFFICIENCY ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            83,
+            400,
+            99
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "To better assess the training efficiency of our models, we perform the following experiment. We train the same encoder architecture using our objective and the skip-thought (ST) objective and compare the performance after a certain number of hours of training. Since training the ST objective with large embedding sizes takes many days, we consider a lower dimensional sentence encoder for this experiment. We chose the encoder architecture to be a single-layer GRU Recurrent neural net with hidden state size $H = 1 0 0 0$ . The word embedding size was set to $W = 3 0 0$ and a vocabulary size of $V = 2 0 , 0 0 0$ words was used. Both models are initialized randomly from the same distribution. The models are trained on the same data for 1 epoch using the Adam optimizer with learning rate 5e-4 and batch size 400. For the low dimensional model considered, the model trained with our objective and ST objective take 6.5 hrs and 31 hrs, respectively. ",
+        "bbox": [
+            173,
+            113,
+            825,
+            253
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "The number of parameters for the two objectives are ",
+        "bbox": [
+            176,
+            260,
+            517,
+            273
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Only the input side encoder parameters $\\approx 9 . 9 M$ parameters) are used for the evaluation. ",
+        "bbox": [
+            171,
+            319,
+            756,
+            333
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "The 1000-dimensional sentence embeddings are used for evaluation. Evaluation follows the same protocol as in section 4.4. Figure 2 compares the performance of the two models on downstream tasks after $x$ number of training hours. The speed benefits of our training objective is apparent from these comparisons. ",
+        "bbox": [
+            174,
+            340,
+            825,
+            396
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "image",
+        "img_path": "images/4acf7be5fec05dcb2c6ca8065b11ece42c388bd130814ea3a667673cb6ec10de.jpg",
+        "image_caption": [
+            "Figure 2: Same encoder architecture trained using our objective and Skip-thought (ST) objective and performance on downstream tasks is compared after a given number of hours. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            191,
+            410,
+            813,
+            722
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "The overall training speedup observed for our objective is $4 . 8 \\times$ . Note that the output encoder was discarded for our model, unlike the experiments in the main text where the representations from the input and output encoders are concatenated. Further speedups can be achieved by training with encoders half the size and concatenating them (This is also parameter efficient). ",
+        "bbox": [
+            174,
+            780,
+            825,
+            837
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "We explore the trade-off between training efficiency and the quality of representations by varying the representation size. We trained models with different representation sizes and evaluate them on the downstream tasks. The multi-channel model (MC-QT) was used for these experiments. Models were trained on the BookCorpus dataset. ",
+        "bbox": [
+            174,
+            113,
+            825,
+            169
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "Table 9 shows the training time and the performance corresponding to different embedding sizes. The training times listed here assume that the two component models in MC-QT are trained in parallel. The reported performance is an average over all the classification benchmarks (MSRP, TREC, MR, CR, SUBJ, MPQA). We note that the classifiers trained on top of the embeddings for downstream tasks differ in size for each embedding size. So it is difficult to make any strong conclusions about the quality of embeddings for the different sizes. However, we are able to reduce the embedding size and train the models more efficiently, at the expense of marginal loss in performance in most cases. ",
+        "bbox": [
+            173,
+            176,
+            825,
+            287
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "The 4800-dimensional Skip-thought model (Kiros et al., 2015) and Combine-CNN model (Gan et al., 2016) achieve mean accuracies of 83.75 and 85.33 respectively. We note that our 1600- dimensional model and 3200-dimensional model are respectively better than these models, in terms of the mean performance across the benchmarks (We acknowledge that the Skip-thought model did not use pre-trained word embeddings). This suggests that high-quality models can be obtained even more efficiently by training lower-dimensional models on large amounts of data using our objective. ",
+        "bbox": [
+            173,
+            294,
+            825,
+            378
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "table",
+        "img_path": "images/8b7d2724d0b979843be6a6903cd72f21f5108345a3821f5e5693b46125eb8b96.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Embedding size</td><td>Training time (h)</td><td>Performance</td></tr><tr><td>1600</td><td>4</td><td>84.57</td></tr><tr><td>2400</td><td>4.7</td><td>85.12</td></tr><tr><td>3200</td><td>6</td><td>85.74</td></tr><tr><td>4000</td><td>7.15</td><td>86.09</td></tr><tr><td>4800</td><td>8.5</td><td>86.43</td></tr><tr><td>5600</td><td>10.15</td><td>86.72</td></tr></table>",
+        "bbox": [
+            318,
+            391,
+            681,
+            492
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "Table 9: Training time and performance for different embedding sizes. The reported performance is the mean accuracy over the classification benchmarks (MSRP, TREC, MR, CR, SUBJ, MPQA). ",
+        "bbox": [
+            169,
+            502,
+            825,
+            530
+        ],
+        "page_idx": 15
+    }
+]

parse/train/rkaSvlnoG/rkaSvlnoG.md

@@ -0,0 +1,211 @@
+# Unsupervised learning of the brain connectivity dynamic using residual D-net
+
+Youngjoo $\mathbf { S e o ^ { 1 } }$ , Manuel Morante2,3, Yannis Kopsinis4,3 and Sergios Theodoridis5,2,3 1Signal Processing Laboratory 2, EPFL (Switzerland) 2Dept. of Informatics and Telecommunications, University of Athens (Greece) 3Computer Technology Institute & Press “Diophantus” (CTI), Patras (Greece) 4LIBRA MLI Ltd, Edinburgh (UK) 5IAASARS, National Observatory of Athens, GR-15236, Penteli (Greece) youngjoo.seo@epfl.ch, morante@cti.gr, kopsinis@ieee.org, stheodor@di.uoa.gr
+
+# Abstract
+
+In this paper, we propose a novel unsupervised learning method to learn the brain dynamics using a deep learning architecture named residual D-net. As it is often the case in medical research, in contrast to typical deep learning tasks, the size of the resting-state functional Magnetic Resonance Image (rs-fMRI) datasets for training is limited. Thus, the available data should be very efficiently used to learn the complex patterns underneath the brain connectivity dynamics. To address this issue, we use residual connections to alleviate the training complexity through recurrent multi-scale representation. We conduct two classification tasks to differentiate early and late stage Mild Cognitive Impairment (MCI) from Normal healthy Control (NC) subjects. The experiments verify that our proposed residual D-net indeed learns the brain connectivity dynamics, leading to significantly higher classification accuracy compared to previously published techniques.
+
+# 1 Introduction
+
+Alzheimer’s Disease (AD) is the most common degenerative brain disease associated with dementia in elder people [1], and it is characterized by a progressive decline of memory, language and cognitive skills. The transition from cognitive health to dementia flows throw different stages, and it may require decades until the damage is noticeable [2].
+
+Unfortunately, the precise biological mechanisms behind the AD remain unknown, to a large extent, and this makes the development of an effective treatment difficult. Moreover, the costs of Alzheimer’s care constitutes a substantial burden on families, which exacerbates through the evolution of the disease [3]. For these reasons, early detection is crucial to prevent, slow down and, hopefully, stop the development of the AD.
+
+Towards this goal, several studies point out that an intermediate stage of cognitive brain dysfunction, referred as Mild Cognitive Impairment (MCI), is a potential precursor of AD [3] (especially with respect to memory problems, referred as amnesic MCI). Although the final transition from MCI to AD varies per individual, a recent systematic review of 32 available studies reported that at least 3 out 10 patients with MCI developed the AD over the period of five or more years.
+
+During the early stages of the AD and MCI, the brain operates so that to allow the individuals to function normally by inducing abnormal neuronal activity, that compensates for the progressive loss of neurons. These fluctuations can be measured using rs-fMRI, which is a powerful non-invasive technique to examine the brain behavior. Therefore, the rs-fMRI provides valuable information that allows to study the brain connectivity dynamics and, potentially, to detect individuals with AD or MCI from healthy subjects.
+
+Table 1: Demographics of the healthy control subjects (NC), patients with eMCI and patients with LMCI   
+
+<table><tr><td></td><td>NC</td><td>eMCI</td><td>LMCI</td></tr><tr><td>Number of Subjects</td><td>36</td><td>31</td><td>26</td></tr><tr><td>Male/Female</td><td>14/22</td><td>15/16</td><td>15/11</td></tr><tr><td>Number of Scans</td><td>100</td><td>100</td><td>77</td></tr><tr><td>Male/Female</td><td>37/63</td><td>58/42</td><td>41/36</td></tr><tr><td>Age (mean±SD)</td><td>72.7±4.5</td><td>72.4±3.8</td><td>74.3±3.4</td></tr></table>
+
+Nowadays, several methods have been proposed to classify subjects with MCI from healthy subjects using fMRI data [4]. The most basic approach consists of a direct study of the mean Functional Connectivity (FC). For example, features from the FC matrix [5] or graph theoretical approach [6] are proposed to perform the classification task. However, two practical limitations restrict these approaches: first, the manual feature designing requires an extensive domain knowledge of the brain connectivity dynamics and, second, the limited number of the available data samples makes it difficult to find a proper model that will generalize in different datasets.
+
+On the other hand, a more sophisticated approach is proposed in [7] to address these two problems: this method automatically learns the features from the data using a Deep Auto-Encoder (DAE) by avoiding potential human biases. Nevertheless, the DAE does not consider any information regarding the brain connectivity dynamics, which is crucial to understand the AD.
+
+Accordingly, any alternative deep learning method must simultaneously consider the structure and the dynamics of the brain functional connectivity, for automatically extracting significant features from the data. However, since complex deep learning architectures usually require a large number of training samples, the lack of sufficient data constitutes the major practical limitation of such methods.
+
+For all these reasons, in this paper, we introduce a recurrent multi-scale deep neuronal network, named residual D-net, to analyze the brain behavior. The main novelty of the presented architecture is that it allows us to unravel the brain connectivity dynamics, but, efficiently learning with a limited number of samples, which constitutes the most common scenario in practice.
+
+Therefore, we applied our proposed residual D-net to learn the brain connectivity dynamics of our subjects. Then, we feed the learned brain dynamic features into a classifier to distinguish subjects with MCI from healthy individuals.
+
+# 2 Materials and Preprocessing
+
+In this study, we use a public rs-fMRI cohort from the Clinical Core of Alzheimer’s Disease Neuroimaging Initiative (ADNI)1, which has established a competitive collaboration among academia and industry investigation focused on the early identification and intervention of AD [8].
+
+Among the different datasets of ADNI (including the latest studies ADNI go and ADNI 2), there are data sets referring to patient with early stage of Mild Cognitive Impairment (eMCI), and patients with an advanced stage of the condition referred as Late stage Mild Cognitive Impairment (LMCI). In this paper, we report studies for both datasets separately.
+
+# 2.1 ADNI Cohorts
+
+The final used cohort comprises 277 scans from 36 Normal healthy Control (NC) subjects, 31 patients with eMCI and 26 patients with LMCI (see Table (1)). We distinguish between scans and subjects because some subjects have several scans at different points; the same person has undergone the scan at different times. This consideration is crucial: otherwise, we can introduce potential bias that affects the accuracy of the method.
+
+With respect to the data acquisition, all the rs-fMRI scans were collected at different medical centers using a 3 Tesla Philips scanners following the same acquisition protocol [9]: Repetition Time $\mathrm { ( T R ) = }$ $3 0 0 0 \mathrm { m s }$ , Echo Time $\mathrm { ( T E ) } = 3 0 ~ \mathrm { m s }$ , flip angle $= 8 0 ^ { \circ }$ , matrix size $6 4 \times 6 4$ , number of slices $= 4 8$ and voxel thickness $= 3 . 3 1 3 \ \mathrm { m m }$ . Each scan was performed during 7 minutes producing a total number of 140 brain volumes.
+
+# 2.2 Preprocessing
+
+The functional images were preprocessed using the Data Processing Assistant for Resting-State fMRI (DPARSF) toolbox2 and the SPM 12 package3 following standard preprocessing steps:
+
+– First, we discarded the first 10 volumes of each scan to avoid T1 equilibrium effects and we applied a slice-timing correction to the slice collected at TR/2 to minimize T1 equilibrium errors across each TR.
+
+– After correcting the acquisition time, we realigned each time-series using a six-parameter rigid-body spatial transformation to compensate for head movements [10]. During this step, we excluded any scanner that exhibited a movement or rotation in any direction bigger than $3 \mathrm { m m }$ or $3 ^ { \circ }$ respectively.
+
+– Then, we normalized the corrected images over the Montreal Neurological Institute (MNI) space and resampled to $3 \mathrm { m m }$ isotropic voxels. The resulted images were detrended in time through a linear approximation and spatially smoothed using a Gaussian filtering with $\mathrm { F W H M } = 4 \mathrm { m m }$ .
+
+– Finally, we removed the nuisance covariates of the white matter and the cerebrospinal fluid to avoid further effects and focused on the signal of the grey matter, and we band-pass filtered $( 0 . 0 1 { - } 0 . 0 8 \mathrm { H z } )$ the remaining signals to reduce the effects of motion and non-neuronal activity fluctuations.
+
+# 2.3 Brain network analysis
+
+In order to investigate the behavior of the brain functional connectivity, we labeled each brain volume into 116 Regions of Interest (ROIs), using the Automated Anatomical Labeling (AAL) atlas4. This atlas divides the brain into macroscopic brain structures: 45 ROIs for each hemisphere and 26 cerebellar ROIs. In this study, we excluded the 26 cerebellar ROIs, because theses areas are mainly related to motor and cognitive functional networks [11].
+
+Then, we estimated a representative time course by averaging the intensity of all the voxel within each ROI, and we normalized the values in the range -1 to 1. Finally, we folded all the time courses into a matrix $\mathbf { R } \in \mathbb { R } ^ { 9 0 \times 1 3 0 }$ , where each row contains the time evolution of one specific ROI.
+
+# 3 Proposed methods
+
+In this paper, we propose a novel residual D-net framework to model the brain connectivity dynamics. First, the selective brain functional connectivity dynamics, used as input for the residual D-net is presented. Then, the details of residual D-net will be described.
+
+# 3.1 Selective Brain Functional Connectivity Dynamics
+
+In order to capture the brain connective dynamics in the rs-fMRI, we examine the time-varying functional connectivity (FC) variability via windowing correlation matrices [12], which provides a fair estimate of the natural dynamics of the functional brain connectivity.
+
+However, our goal is to identify individuals that will potentially develop AD. Consequently, we restricted our study of the whole-brain dynamics to just a few areas that may suffer damage due to the AD, which, also, reduces the pattern complexity of the brain functional connectivity.
+
+![](images/bd40ed3a2d4bf9f3a8380761c629f7784f5475f226bb2706427516b46c5bb831.jpg)  
+Figure 1: Residual D-net architecture
+
+In this way, severals studies have pointed that certain brain areas are more likely to be affected by the AD. These areas are localized in the Frontal Lobe [13], the Hypocampus [14] and the Temporal Lobe [14], [15] . Therefore, we limited our study of the brain connectivity dynamics to 28 ROIs that are vulnerable to AD.
+
+Thus, using this specific set of ROIs and following the method described in [12], for each scan $( \mathbf { R } _ { i } )$ , with $i = 1 , 2 , \dots , N$ , where $N$ is the total number of analyzed scans, we estimated the dynamic FC through a sliding window approach, and we computed each covariance matrix from a windowed segment of $\mathbf { R } _ { i }$ . We applied a tapered window created by convolving a rectangle ( $\mathrm { w i t h } = 1 0 \mathrm { T R s } { = } 3 0 )$ ) with a Gaussian $\sigma = 4 \mathrm { T R s } )$ ) and a sliding window in steps of 2 TRs, resulting in a total number of 56 windows.
+
+Accordingly, the result of each scan contains a sequence of 56 covariance matrices that encode the connectivity dynamics of the studied ROIs. These sequential matrices comprise the FC dynamics of the $2 8 ~ \mathrm { R O I s }$ , and we will use them as an input to the proposed method. Figure (4.a) shows examples of input sequences of these covariance matrices.
+
+# 3.2 Residual D-net
+
+The proposed model needs to understand the dynamics of brain FC; that is, how the pattern within the covariance matrix changes along time. Furthermore, the model should be very efficient to learn the dynamics given a limited number of training data.
+
+To address these issues, the proposed residual D-net has three major properties that allow the model to learn with relatively few training samples, while retaining its capacity to learn complex dynamics. Figure (1) shows the main architecture of the proposed residual D-net, which is formed by three main components: up residual block, down residual block (RES_U/D_Block) and a residual convolutional long short-term memory block (RES_cLSTM).
+
+RES_U/D_Block: The residual network (resNet) [16] is a competitive deep architecture capable to produce a detailed decomposition of the input data. The residual connection in the resNet constrains the network to learn a residual representation, so that to facilitate the training. We exploit this property to learn complex patterns in the input, while keeping the training to be simple. In addition, we add an “average pooling” layer and “up convolution” layer, to express the multi-scale representation. The formulations of each down/up residual block can be expressed as follows:
+
+![](images/27888626740e87ea3c594e6a2d8c0e58a43cab4e8b0acc988578b90be3c10215.jpg)  
+Figure 2: Major component of the residual D-net: Donw/up Residual Block and Residual convLSTM Block
+
+$$
+\begin{array} { r l } & { x _ { t } ^ { l + 1 } = \mathrm { a v g p o o l } ( F _ { d } ^ { l } ( x _ { t } ^ { l } ) + x _ { t } ^ { l } ) , } \\ & { y _ { t } ^ { l + 1 } = F _ { u } ^ { l } ( [ \hat { y } _ { t } ^ { l } , z _ { t } ^ { l } ] ) + y _ { t } ^ { l } , } \end{array}
+$$
+
+where $\boldsymbol { x } _ { t } ^ { l }$ and $y _ { t } ^ { l }$ are the inputs of the $l _ { t h }$ RES_D/U_Block, respectively. Each block has a bypass identity connection to fit the residual mapping from the input. We denote each convolutional layer in the block as $F _ { d } ^ { l } ( x _ { t } ^ { l } )$ and $F _ { u } ^ { l } ( y _ { t } ^ { l } )$ in Figure (2), which are composed of two $3 \times 3$ convolutional layers and we employ the exponential linear units (ELUs) [17] as the nonlinear activation function. The major difference lies in in their “up/down sampling" layer. In the RES_D_BLOCK, a average pooling layer is attached to down sample the input. In the RES_U_BLOCK, we use a up-conv layer for up-sampling $( \hat { y } _ { t } ^ { l } )$ the input and it is concatenated with $z _ { t } ^ { l }$ , which comes from the high resolution feature map in the upper RES_cLSTM Block.
+
+RES_cLSTM Block: The convolutional LSTM [18] is a well-known Recurrent Neural Network (RNN) model, capable of capturing spatial-temporal features in a video sequence. As we described above, the brain dynamics is represented as a sequence of images. Thus, the use of a convolutional LSTM is fully justified by the nature of our task. Moreover, the use of the residual connection, together with the convolutional LSTM, facilitates the training, while retaining the spatial-temporal information. The connection was designed in a way similar to existing residual LSTM models [19, 20, 21] with two concatenated LSTM blocks with identity connection as shown in Figure (2). The formulation of the Residual Convolutional LSTM block can be expressed as follows:
+
+$$
+\begin{array} { r l } & { z _ { t } ^ { l + 1 } = h _ { t } ^ { l _ { 2 } } + z _ { t } ^ { l } , } \\ & { ~ h _ { t } ^ { l _ { 2 } } = G ^ { l } ( z _ { t } ^ { l } , h _ { t - 1 } ^ { l _ { 1 } } , h _ { t - 1 } ^ { l _ { 2 } } ) . } \end{array}
+$$
+
+Here, $z _ { t } ^ { l }$ is the input of the $l _ { t h }$ RES_cLSTM Block and $h _ { t - 1 } ^ { l _ { 1 } } , h _ { t - 1 } ^ { l _ { 2 } }$ represents hidden states of the convolutional LSTM layer from previous $t - 1$ time step. The function $G ^ { l } ( z _ { t } ^ { l } , h _ { t - 1 } ^ { l _ { 1 } } , h _ { t - 1 } ^ { l _ { 2 } } )$ represents the $l _ { t h }$ two-layered convolutional LSTM that maps dynamics of the input pattern into the current hidden states $( \dot { H } _ { t } ^ { l } : [ h _ { t } ^ { l _ { 1 } } , h _ { t } ^ { l _ { 2 } } ] )$ . Similarly to the residual block, all convolutional layer uses $3 \times 3$ size filter.
+
+Structure of residual D-net: Using the residual blocks as components, we build a 2-depth U-net architecture for multi-scale representation. The U-net framework [22] was developed for dealing with deep representative learning tasks with few training samples. We adopt the same framework to take advantage of the rich feature representation and the efficient learning scheme. In addition, we add a recurrent flow to capture the dynamic behavior, so that the architecture forms D-shape.
+
+As shown in Figure (1), The input $x _ { t } ^ { l = 0 }$ comprises $2 8 \times 2 8$ images of the correlation map at $t$ time step. RES_D_Block decreases the input size by half and increases the feature map by two starting from the initial 16-feature map size. The feature maps are contracting until they reach the last RES_cLSTM block. These abstract embeddings $( z _ { t } ^ { l a s t } )$ are finally used later on for the classification. During the expansion path, the feature map from the middle-depth layer, $z _ { t } ^ { m i d d l e }$ , is concatenated via a skip-connection. This multi-scale way of training allows to learn the complex patterns of the input sequences and to capture the dynamic changes in the hidden state of the convolutional LSTM.
+
+![](images/87929d1b22b9d85b22fc4506f73bcd31f5103dd03645e74031cea3cd0388e69b.jpg)  
+Figure 3: Training scheme of the (a) unsupervised pre-training and (b) supervised fine-tuning using the residual D-net.
+
+# 3.3 Unsupervised pre-training and fine-tuning
+
+First, we train our residual D-net with sequences of correlation maps by predicting a few steps ahead of the sequences. Given $T$ -time step input sequences, residual D-net predicts the output until next $2 T$ time points $( \tilde { x } _ { T + 1 , \dots , 2 T } )$ . By predicting the future steps, model can be trained unsupervised way [23], see Figure (3). We use mean square error $( M S E )$ of prediction as the loss, and the adam [24] optimizer for updating the parameter with learning rate 0.0005. In Figure (4.b), we can see an example of the predicted sequences, and it shows that unsupervised learning of the residual D-net learns the dynamic behavior of the human brain.
+
+After unsupervised training, we take all the output of the last layer of RES_cLSTM block $( z _ { t } ^ { l a s t } )$ for classification task. During the classification learning, the parameters in the contracting path $( 2 \times ( \mathrm { R E S \_ D \_ B L O C K + R E S \_ c L S T M } ) )$ can be fine-tuned with concatenated softmax-classifier such as Figure (3.b). And the final decision will be made by averaging the result from classifier as follows:
+
+$$
+l o g i t = \frac { 1 } { T } \sum _ { t = 1 } ^ { N } \mathrm { s o f t m a x } ( w _ { c l } \times z _ { t } ^ { l a s t } + b _ { c l } ) .
+$$
+
+Here, $w _ { c l }$ and $b _ { c l }$ are the softmax-classifier projection weights and bias, respectively. We use the binary cross-entropy as a loss function to fine-tune the architecture with a learning rate 0.00001. We found that involving unsupervised pre-training is crucial, in order to avoid over-fitting during the training of the networks, see Figure (5). After the fine-tuning, the classifier learns the differences between the two dynamic pattern in each class.
+
+![](images/95d713640d515f35cbb13496e4fec8280944443c9fd826a6bf5fc80f9ce81711.jpg)  
+Figure 4: (a) shows the sequences of the dynamic functional connectivity that used for input, and (b) shows the target sequences to be predicted and (c) represents the sequences of the predictions from residual D-net.
+
+# 4 Performance Evaluation
+
+We conducted two classification experiments (NC vs. eMCI and NC vs. LMCI) to evaluate the proposed residual D-net and compare it with three baselines techniques. For this, we performed a five-fold subject-wise cross-validation to avoid using the same subject. Each validation set was used for selecting the optimal hyper-parameters for the classification model. The performance was measured by the total accuracy, precision, and recall on the test set.
+
+Table 2: Values of the Accuracy (Acc), Precision (Pre) and Recall (Rec) for each five-fold subject-wise cross-validation for the eMCI dataset.   
+
+<table><tr><td></td><td colspan="3">SFC+SVM</td><td colspan="3">DFC+SVM</td><td colspan="3">DAE+HMM</td><td colspan="3">Res. D-net</td></tr><tr><td>CV</td><td>Acc</td><td>Pre</td><td>Rec</td><td>Acc</td><td>Pre</td><td>Rec</td><td>Acc</td><td>Pre</td><td>Rec</td><td>Acc</td><td>Pre</td><td>Rec</td></tr><tr><td>1</td><td>57.1</td><td>52.0</td><td>68.4</td><td>50.0</td><td>46.2</td><td>63.2</td><td>59.5</td><td>54.5</td><td>63.2</td><td>71.4</td><td>62.1</td><td>94.7</td></tr><tr><td>2</td><td>52.5</td><td>61.1</td><td>47.8</td><td>42.5</td><td>50.0</td><td>30.4</td><td>45.0</td><td>53.8</td><td>30.4</td><td>70.0</td><td>66.7</td><td>95.7</td></tr><tr><td>3</td><td>27.8</td><td>36.8</td><td>33.3</td><td>63.9</td><td>78.6</td><td>52.4</td><td>63.9</td><td>65.4</td><td>81.0</td><td>72.2</td><td>72.0</td><td>85.7</td></tr><tr><td>4</td><td>50.0</td><td>48.0</td><td>57.1</td><td>43.2</td><td>40.0</td><td>38.1</td><td>43.2</td><td>41.7</td><td>47.6</td><td>72.7</td><td>66.7</td><td>85.7</td></tr><tr><td>5</td><td>36.8</td><td>33.3</td><td>50.0</td><td>42.1</td><td>38.5</td><td>62.5</td><td>52.6</td><td>45.5</td><td>62.5</td><td>65.8</td><td>56.0</td><td>87.5</td></tr><tr><td>Total</td><td>45.5</td><td>45.9</td><td>51.0</td><td>48.0</td><td>48.0</td><td>48.0</td><td>52.5</td><td>52.3</td><td>56.0</td><td>70.5</td><td>64.7</td><td>90.0</td></tr></table>
+
+Table 3: Values of the Accuracy (Acc), Precision (Pre) and Recall (Rec) for each five-fold subject-wise cross-validation for the LMCI dataset.   
+
+<table><tr><td></td><td colspan="3">SFC+SVM</td><td colspan="3">DFC+SVM</td><td colspan="3">DAE+HMM</td><td colspan="3">Res. D-net</td></tr><tr><td>CV</td><td>Acc</td><td>Pre</td><td>Rec</td><td>Acc</td><td>Pre</td><td>Rec</td><td>Acc</td><td>Pre</td><td>Rec</td><td>Acc</td><td>Pre</td><td>Rec</td></tr><tr><td>1</td><td>50.0</td><td>44.4</td><td>42.1</td><td>50.0</td><td>41.7</td><td>26.3</td><td>38.1</td><td>37.9</td><td>57.9</td><td>73.8</td><td>68.2</td><td>78.9</td></tr><tr><td>2</td><td>48.5</td><td>44.4</td><td>25.0</td><td>54.5</td><td>55.6</td><td>31.3</td><td>60.6</td><td>80.0</td><td>25.0</td><td>75.8</td><td>75.0</td><td>75.0</td></tr><tr><td>3</td><td>74.1</td><td>85.7</td><td>50.0</td><td>33.3</td><td>25.0</td><td>25.0</td><td>51.9</td><td>46.7</td><td>58.3</td><td>66.7</td><td>60.0</td><td>75.0</td></tr><tr><td>4</td><td>61.1</td><td>47.1</td><td>61.5</td><td>50.0</td><td>27.3</td><td>23.1</td><td>61.1</td><td>46.7</td><td>53.8</td><td>72.2</td><td>61.5</td><td>61.5</td></tr><tr><td>5</td><td>48.7</td><td>40.0</td><td>35.3</td><td>61.5</td><td>57.1</td><td>47.1</td><td>56.4</td><td>50.0</td><td>52.9</td><td>64.1</td><td>55.6</td><td>88.2</td></tr><tr><td>Total</td><td>55.4</td><td>48.5</td><td>41.6</td><td>50.8</td><td>41.4</td><td>31.2</td><td>53.1</td><td>46.3</td><td>49.4</td><td>70.6</td><td>63.4</td><td>76.6</td></tr></table>
+
+# 4.1 Baselines
+
+Static Functional Connectivity $( \mathbf { S F C } ) + \mathbf { S V M }$ : Zhang et al. [5] suggest five specific pairs of the Pearson’s correlation coefficients on each raw dataset $( \breve { \mathbf { R } } \in \mathbb { R } ^ { 9 0 \times 1 3 0 } ,$ ), assuming that the FC can be used to distinguish the MCI subjects from the NC. The authors explicitly selected these features after applying a two-sample T-test on 40 subjects.
+
+In this paper, we further investigated twenty alternative coefficients using Fisher feature selection [25], and we fed the selected features to a linear Support Vector Machine (SVM) classifier to perform the classification task.
+
+Dynamic Functional Connectivity $\mathbf { ( D F C ) } + \mathbf { S V M }$ : In this experiment, in order to consider the brain dynamics, we used a sliding rectangular window (width: 30 TRs) and a 5 TRs stride to estimate the functional connectivity maps $\Sigma ( w ) \breve { \in } \mathbb { R } ^ { 9 0 \times 9 0 }$ in each window $\mathbf { \chi } ^ { \prime } w = 1 , \dots , 2 0 )$ . Then, according to [26], we project our data into a $K \times 2 0$ -dimensional feature map and then, we selected the best 100 features using Fisher feature selection, and we measured the performance with a linear SVM classifier.
+
+Deep Auto-Encoder $\mathbf { ( D A E ) } + \mathbf { H M M }$ : Suk et al. [7] propose an unsupervised feature learning using a DAE. First, they trained a four-layer DAE (hidden layers: 200-100-50-2) using as an input all the ROIs directly. Afterward, for each specific time instance, they converted the information of all the ROIs (a 116 real vector) into a 2-dimensional feature map. Then, they fit these 2-dimensional feature maps into two Hidden Markov Models (HMM) to model the NC and the MCI classes. Similarly, we implemented this method but using 6 hidden states with 2-mixtures of Gaussian HMM via the Baum-Welch algorithm.
+
+# 4.2 Discussion and Results
+
+As we discussed during the description of the experiment, we adopted a five-fold subject-wise crossvalidation, in order to ensure the reliability of the different methods. Table (2) and Table (3) show the results associated with the accuracy, precision and recall obtained for the different methods, for the eMCI and LMCI dataset respectively.
+
+![](images/c93c6fafb03003cc4ca200483da54e93c4087b4f15b1f54ea05c72f218aabdfe.jpg)  
+Figure 5: Cross-entropy errors on the LMCI dataset obtained by the proposed method without pre-training (a) and with pre-training (b). The dot lines represent the actual loss errors obtained for each specific cross-validation sets, and the continuous line represents the mean value among all the cross-validation datasets.
+
+The main conclusion is that all the baseline techniques turned out significantly inferior results. First, the inferior performance of $\mathrm { S F C } { + } \mathrm { S V M }$ is expected because it does not consider any brain dynamics. Moreover, a further analysis turned out that this method performed well on the training set, in contrast to the test set. This observation evidences that the method fails to generalize among different datasets.
+
+On the other hand, although the $\mathrm { D F C + S V M }$ takes into account the time evolution of the FC, the method does not learn the relationships within the brain dynamics and, consequently, fails to perform the classification task.
+
+Regarding to the $\mathrm { D A E + H M M }$ , the major limitation of this approach is that is not an end-to-end learning method. That is, although it incorporates an HMM that tries to model the dynamics, the DAE does not capture any information from the brain connectivity dynamics. Leading to a inferior performance.
+
+In contrast, further analysis during the training and the pre-training have shown that our proposed method effectively learns the brain dynamics. Thus, Figure (4) shows the original and the predicted covariance matrices, which assembles the FC brain dynamics. Observe that our proposed approach captures and reproduces the true dynamics of the brain behavior.
+
+This explains why the proposed method exhibits the best performance and it properly generalizes among the different cross-validation sets.
+
+# Pre-training vs. Overfitting
+
+Considering the limited number of samples of the studied datasets, the primary risk of our proposed method is that of overfitting. However, we faced this challenge by introducing the residual D-net architecture, and also by pre-training the model prior to the classification task.
+
+Although we have already discussed the advantages the residual D-net architecture, we illustrate the benefits of the pre-training in Figure (5), where we plotted the loss errors for the LMCI dataset with and without pre-training.
+
+Observe that the model overfits without pre-training (see Figure (5.a)); that is, we can not guarantee that the method had generalized correctly, making it impossible to establish any proper stopping criterion.
+
+However, the behavior of the loss curves radically changes after pre-training the model (see Figure (5.b)). Now, the method has converged and we can define a proper stopping criterion.
+
+Figure (5) only shows the results for the LMCI dataset, but we have observed the same effects in the eMCI dataset as well.
+
+# 5 Conclusions
+
+In this paper, we presented a new method named residual D-net to identify MCI from NC subjects. In contrast to the previous methods, proposed residual D-net can be efficiently trained with few number of training samples, while unravels the brain connectivity dynamics in unsupervised learning. Furthermore, the proposed pre-training approach robustifies the generalization performance of the proposed method and offers an adequate selection of a stopping criterion in practice.
+
+# References
+
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+[2] Robert S. Wilson, Eisuke Segawa, Patricia A. Boyle, Sophia E. Anagnos, Loren P. Hizel, and David A. Bennett. The natural history of cognitive decline in Alzheimer’s disease. Psychology and Aging, 27(4):1008–1017, 2012.   
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+        "text": "In this paper, we propose a novel unsupervised learning method to learn the brain dynamics using a deep learning architecture named residual D-net. As it is often the case in medical research, in contrast to typical deep learning tasks, the size of the resting-state functional Magnetic Resonance Image (rs-fMRI) datasets for training is limited. Thus, the available data should be very efficiently used to learn the complex patterns underneath the brain connectivity dynamics. To address this issue, we use residual connections to alleviate the training complexity through recurrent multi-scale representation. We conduct two classification tasks to differentiate early and late stage Mild Cognitive Impairment (MCI) from Normal healthy Control (NC) subjects. The experiments verify that our proposed residual D-net indeed learns the brain connectivity dynamics, leading to significantly higher classification accuracy compared to previously published techniques. ",
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+        "type": "text",
+        "text": "1 Introduction ",
+        "text_level": 1,
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+        "text": "Alzheimer’s Disease (AD) is the most common degenerative brain disease associated with dementia in elder people [1], and it is characterized by a progressive decline of memory, language and cognitive skills. The transition from cognitive health to dementia flows throw different stages, and it may require decades until the damage is noticeable [2]. ",
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+        "text": "Unfortunately, the precise biological mechanisms behind the AD remain unknown, to a large extent, and this makes the development of an effective treatment difficult. Moreover, the costs of Alzheimer’s care constitutes a substantial burden on families, which exacerbates through the evolution of the disease [3]. For these reasons, early detection is crucial to prevent, slow down and, hopefully, stop the development of the AD. ",
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+        "text": "Towards this goal, several studies point out that an intermediate stage of cognitive brain dysfunction, referred as Mild Cognitive Impairment (MCI), is a potential precursor of AD [3] (especially with respect to memory problems, referred as amnesic MCI). Although the final transition from MCI to AD varies per individual, a recent systematic review of 32 available studies reported that at least 3 out 10 patients with MCI developed the AD over the period of five or more years. ",
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+        "text": "During the early stages of the AD and MCI, the brain operates so that to allow the individuals to function normally by inducing abnormal neuronal activity, that compensates for the progressive loss of neurons. These fluctuations can be measured using rs-fMRI, which is a powerful non-invasive technique to examine the brain behavior. Therefore, the rs-fMRI provides valuable information that allows to study the brain connectivity dynamics and, potentially, to detect individuals with AD or MCI from healthy subjects. ",
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+        "table_caption": [
+            "Table 1: Demographics of the healthy control subjects (NC), patients with eMCI and patients with LMCI "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>NC</td><td>eMCI</td><td>LMCI</td></tr><tr><td>Number of Subjects</td><td>36</td><td>31</td><td>26</td></tr><tr><td>Male/Female</td><td>14/22</td><td>15/16</td><td>15/11</td></tr><tr><td>Number of Scans</td><td>100</td><td>100</td><td>77</td></tr><tr><td>Male/Female</td><td>37/63</td><td>58/42</td><td>41/36</td></tr><tr><td>Age (mean±SD)</td><td>72.7±4.5</td><td>72.4±3.8</td><td>74.3±3.4</td></tr></table>",
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+        "text": "Nowadays, several methods have been proposed to classify subjects with MCI from healthy subjects using fMRI data [4]. The most basic approach consists of a direct study of the mean Functional Connectivity (FC). For example, features from the FC matrix [5] or graph theoretical approach [6] are proposed to perform the classification task. However, two practical limitations restrict these approaches: first, the manual feature designing requires an extensive domain knowledge of the brain connectivity dynamics and, second, the limited number of the available data samples makes it difficult to find a proper model that will generalize in different datasets. ",
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+        "text": "On the other hand, a more sophisticated approach is proposed in [7] to address these two problems: this method automatically learns the features from the data using a Deep Auto-Encoder (DAE) by avoiding potential human biases. Nevertheless, the DAE does not consider any information regarding the brain connectivity dynamics, which is crucial to understand the AD. ",
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+        "text": "Accordingly, any alternative deep learning method must simultaneously consider the structure and the dynamics of the brain functional connectivity, for automatically extracting significant features from the data. However, since complex deep learning architectures usually require a large number of training samples, the lack of sufficient data constitutes the major practical limitation of such methods. ",
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+        "text": "For all these reasons, in this paper, we introduce a recurrent multi-scale deep neuronal network, named residual D-net, to analyze the brain behavior. The main novelty of the presented architecture is that it allows us to unravel the brain connectivity dynamics, but, efficiently learning with a limited number of samples, which constitutes the most common scenario in practice. ",
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+        "text": "Therefore, we applied our proposed residual D-net to learn the brain connectivity dynamics of our subjects. Then, we feed the learned brain dynamic features into a classifier to distinguish subjects with MCI from healthy individuals. ",
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+        "text": "2 Materials and Preprocessing ",
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+        "text": "In this study, we use a public rs-fMRI cohort from the Clinical Core of Alzheimer’s Disease Neuroimaging Initiative (ADNI)1, which has established a competitive collaboration among academia and industry investigation focused on the early identification and intervention of AD [8]. ",
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+        "text": "Among the different datasets of ADNI (including the latest studies ADNI go and ADNI 2), there are data sets referring to patient with early stage of Mild Cognitive Impairment (eMCI), and patients with an advanced stage of the condition referred as Late stage Mild Cognitive Impairment (LMCI). In this paper, we report studies for both datasets separately. ",
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+        "type": "text",
+        "text": "2.1 ADNI Cohorts ",
+        "text_level": 1,
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+        "text": "The final used cohort comprises 277 scans from 36 Normal healthy Control (NC) subjects, 31 patients with eMCI and 26 patients with LMCI (see Table (1)). We distinguish between scans and subjects because some subjects have several scans at different points; the same person has undergone the scan at different times. This consideration is crucial: otherwise, we can introduce potential bias that affects the accuracy of the method. ",
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+        "text": "With respect to the data acquisition, all the rs-fMRI scans were collected at different medical centers using a 3 Tesla Philips scanners following the same acquisition protocol [9]: Repetition Time $\\mathrm { ( T R ) = }$ $3 0 0 0 \\mathrm { m s }$ , Echo Time $\\mathrm { ( T E ) } = 3 0 ~ \\mathrm { m s }$ , flip angle $= 8 0 ^ { \\circ }$ , matrix size $6 4 \\times 6 4$ , number of slices $= 4 8$ and voxel thickness $= 3 . 3 1 3 \\ \\mathrm { m m }$ . Each scan was performed during 7 minutes producing a total number of 140 brain volumes. ",
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+        "text": "2.2 Preprocessing ",
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+        "text": "The functional images were preprocessed using the Data Processing Assistant for Resting-State fMRI (DPARSF) toolbox2 and the SPM 12 package3 following standard preprocessing steps: ",
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+        "text": "– First, we discarded the first 10 volumes of each scan to avoid T1 equilibrium effects and we applied a slice-timing correction to the slice collected at TR/2 to minimize T1 equilibrium errors across each TR. ",
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+        "text": "– After correcting the acquisition time, we realigned each time-series using a six-parameter rigid-body spatial transformation to compensate for head movements [10]. During this step, we excluded any scanner that exhibited a movement or rotation in any direction bigger than $3 \\mathrm { m m }$ or $3 ^ { \\circ }$ respectively. ",
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+        "text": "– Then, we normalized the corrected images over the Montreal Neurological Institute (MNI) space and resampled to $3 \\mathrm { m m }$ isotropic voxels. The resulted images were detrended in time through a linear approximation and spatially smoothed using a Gaussian filtering with $\\mathrm { F W H M } = 4 \\mathrm { m m }$ . ",
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+        "type": "text",
+        "text": "– Finally, we removed the nuisance covariates of the white matter and the cerebrospinal fluid to avoid further effects and focused on the signal of the grey matter, and we band-pass filtered $( 0 . 0 1 { - } 0 . 0 8 \\mathrm { H z } )$ the remaining signals to reduce the effects of motion and non-neuronal activity fluctuations. ",
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+        "text": "2.3 Brain network analysis ",
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+        "type": "text",
+        "text": "In order to investigate the behavior of the brain functional connectivity, we labeled each brain volume into 116 Regions of Interest (ROIs), using the Automated Anatomical Labeling (AAL) atlas4. This atlas divides the brain into macroscopic brain structures: 45 ROIs for each hemisphere and 26 cerebellar ROIs. In this study, we excluded the 26 cerebellar ROIs, because theses areas are mainly related to motor and cognitive functional networks [11]. ",
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+        "text": "Then, we estimated a representative time course by averaging the intensity of all the voxel within each ROI, and we normalized the values in the range -1 to 1. Finally, we folded all the time courses into a matrix $\\mathbf { R } \\in \\mathbb { R } ^ { 9 0 \\times 1 3 0 }$ , where each row contains the time evolution of one specific ROI. ",
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+        "type": "text",
+        "text": "3 Proposed methods ",
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+        "text": "In this paper, we propose a novel residual D-net framework to model the brain connectivity dynamics. First, the selective brain functional connectivity dynamics, used as input for the residual D-net is presented. Then, the details of residual D-net will be described. ",
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+        "type": "text",
+        "text": "3.1 Selective Brain Functional Connectivity Dynamics ",
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+        "type": "text",
+        "text": "In order to capture the brain connective dynamics in the rs-fMRI, we examine the time-varying functional connectivity (FC) variability via windowing correlation matrices [12], which provides a fair estimate of the natural dynamics of the functional brain connectivity. ",
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+        "text": "However, our goal is to identify individuals that will potentially develop AD. Consequently, we restricted our study of the whole-brain dynamics to just a few areas that may suffer damage due to the AD, which, also, reduces the pattern complexity of the brain functional connectivity. ",
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+        "image_caption": [
+            "Figure 1: Residual D-net architecture "
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+        "text": "In this way, severals studies have pointed that certain brain areas are more likely to be affected by the AD. These areas are localized in the Frontal Lobe [13], the Hypocampus [14] and the Temporal Lobe [14], [15] . Therefore, we limited our study of the brain connectivity dynamics to 28 ROIs that are vulnerable to AD. ",
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+        "text": "Thus, using this specific set of ROIs and following the method described in [12], for each scan $( \\mathbf { R } _ { i } )$ , with $i = 1 , 2 , \\dots , N$ , where $N$ is the total number of analyzed scans, we estimated the dynamic FC through a sliding window approach, and we computed each covariance matrix from a windowed segment of $\\mathbf { R } _ { i }$ . We applied a tapered window created by convolving a rectangle ( $\\mathrm { w i t h } = 1 0 \\mathrm { T R s } { = } 3 0 )$ ) with a Gaussian $\\sigma = 4 \\mathrm { T R s } )$ ) and a sliding window in steps of 2 TRs, resulting in a total number of 56 windows. ",
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+        "text": "Accordingly, the result of each scan contains a sequence of 56 covariance matrices that encode the connectivity dynamics of the studied ROIs. These sequential matrices comprise the FC dynamics of the $2 8 ~ \\mathrm { R O I s }$ , and we will use them as an input to the proposed method. Figure (4.a) shows examples of input sequences of these covariance matrices. ",
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+        "text": "3.2 Residual D-net ",
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+        "text": "The proposed model needs to understand the dynamics of brain FC; that is, how the pattern within the covariance matrix changes along time. Furthermore, the model should be very efficient to learn the dynamics given a limited number of training data. ",
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+        "text": "To address these issues, the proposed residual D-net has three major properties that allow the model to learn with relatively few training samples, while retaining its capacity to learn complex dynamics. Figure (1) shows the main architecture of the proposed residual D-net, which is formed by three main components: up residual block, down residual block (RES_U/D_Block) and a residual convolutional long short-term memory block (RES_cLSTM). ",
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+        "text": "RES_U/D_Block: The residual network (resNet) [16] is a competitive deep architecture capable to produce a detailed decomposition of the input data. The residual connection in the resNet constrains the network to learn a residual representation, so that to facilitate the training. We exploit this property to learn complex patterns in the input, while keeping the training to be simple. In addition, we add an “average pooling” layer and “up convolution” layer, to express the multi-scale representation. The formulations of each down/up residual block can be expressed as follows: ",
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+        "image_caption": [
+            "Figure 2: Major component of the residual D-net: Donw/up Residual Block and Residual convLSTM Block "
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+        "img_path": "images/1e948d5b71490ddad026d8ba29615c649b9eea2d0d2c5679bf02d3ed69c079a6.jpg",
+        "text": "$$\n\\begin{array} { r l } & { x _ { t } ^ { l + 1 } = \\mathrm { a v g p o o l } ( F _ { d } ^ { l } ( x _ { t } ^ { l } ) + x _ { t } ^ { l } ) , } \\\\ & { y _ { t } ^ { l + 1 } = F _ { u } ^ { l } ( [ \\hat { y } _ { t } ^ { l } , z _ { t } ^ { l } ] ) + y _ { t } ^ { l } , } \\end{array}\n$$",
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+        "type": "text",
+        "text": "where $\\boldsymbol { x } _ { t } ^ { l }$ and $y _ { t } ^ { l }$ are the inputs of the $l _ { t h }$ RES_D/U_Block, respectively. Each block has a bypass identity connection to fit the residual mapping from the input. We denote each convolutional layer in the block as $F _ { d } ^ { l } ( x _ { t } ^ { l } )$ and $F _ { u } ^ { l } ( y _ { t } ^ { l } )$ in Figure (2), which are composed of two $3 \\times 3$ convolutional layers and we employ the exponential linear units (ELUs) [17] as the nonlinear activation function. The major difference lies in in their “up/down sampling\" layer. In the RES_D_BLOCK, a average pooling layer is attached to down sample the input. In the RES_U_BLOCK, we use a up-conv layer for up-sampling $( \\hat { y } _ { t } ^ { l } )$ the input and it is concatenated with $z _ { t } ^ { l }$ , which comes from the high resolution feature map in the upper RES_cLSTM Block. ",
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+        "text": "RES_cLSTM Block: The convolutional LSTM [18] is a well-known Recurrent Neural Network (RNN) model, capable of capturing spatial-temporal features in a video sequence. As we described above, the brain dynamics is represented as a sequence of images. Thus, the use of a convolutional LSTM is fully justified by the nature of our task. Moreover, the use of the residual connection, together with the convolutional LSTM, facilitates the training, while retaining the spatial-temporal information. The connection was designed in a way similar to existing residual LSTM models [19, 20, 21] with two concatenated LSTM blocks with identity connection as shown in Figure (2). The formulation of the Residual Convolutional LSTM block can be expressed as follows: ",
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+        "text": "$$\n\\begin{array} { r l } & { z _ { t } ^ { l + 1 } = h _ { t } ^ { l _ { 2 } } + z _ { t } ^ { l } , } \\\\ & { ~ h _ { t } ^ { l _ { 2 } } = G ^ { l } ( z _ { t } ^ { l } , h _ { t - 1 } ^ { l _ { 1 } } , h _ { t - 1 } ^ { l _ { 2 } } ) . } \\end{array}\n$$",
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+        "type": "text",
+        "text": "Here, $z _ { t } ^ { l }$ is the input of the $l _ { t h }$ RES_cLSTM Block and $h _ { t - 1 } ^ { l _ { 1 } } , h _ { t - 1 } ^ { l _ { 2 } }$ represents hidden states of the convolutional LSTM layer from previous $t - 1$ time step. The function $G ^ { l } ( z _ { t } ^ { l } , h _ { t - 1 } ^ { l _ { 1 } } , h _ { t - 1 } ^ { l _ { 2 } } )$ represents the $l _ { t h }$ two-layered convolutional LSTM that maps dynamics of the input pattern into the current hidden states $( \\dot { H } _ { t } ^ { l } : [ h _ { t } ^ { l _ { 1 } } , h _ { t } ^ { l _ { 2 } } ] )$ . Similarly to the residual block, all convolutional layer uses $3 \\times 3$ size filter. ",
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+        "text": "Structure of residual D-net: Using the residual blocks as components, we build a 2-depth U-net architecture for multi-scale representation. The U-net framework [22] was developed for dealing with deep representative learning tasks with few training samples. We adopt the same framework to take advantage of the rich feature representation and the efficient learning scheme. In addition, we add a recurrent flow to capture the dynamic behavior, so that the architecture forms D-shape. ",
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+        "text": "As shown in Figure (1), The input $x _ { t } ^ { l = 0 }$ comprises $2 8 \\times 2 8$ images of the correlation map at $t$ time step. RES_D_Block decreases the input size by half and increases the feature map by two starting from the initial 16-feature map size. The feature maps are contracting until they reach the last RES_cLSTM block. These abstract embeddings $( z _ { t } ^ { l a s t } )$ are finally used later on for the classification. During the expansion path, the feature map from the middle-depth layer, $z _ { t } ^ { m i d d l e }$ , is concatenated via a skip-connection. This multi-scale way of training allows to learn the complex patterns of the input sequences and to capture the dynamic changes in the hidden state of the convolutional LSTM. ",
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+    {
+        "type": "image",
+        "img_path": "images/87929d1b22b9d85b22fc4506f73bcd31f5103dd03645e74031cea3cd0388e69b.jpg",
+        "image_caption": [
+            "Figure 3: Training scheme of the (a) unsupervised pre-training and (b) supervised fine-tuning using the residual D-net. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "3.3 Unsupervised pre-training and fine-tuning ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "First, we train our residual D-net with sequences of correlation maps by predicting a few steps ahead of the sequences. Given $T$ -time step input sequences, residual D-net predicts the output until next $2 T$ time points $( \\tilde { x } _ { T + 1 , \\dots , 2 T } )$ . By predicting the future steps, model can be trained unsupervised way [23], see Figure (3). We use mean square error $( M S E )$ of prediction as the loss, and the adam [24] optimizer for updating the parameter with learning rate 0.0005. In Figure (4.b), we can see an example of the predicted sequences, and it shows that unsupervised learning of the residual D-net learns the dynamic behavior of the human brain. ",
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+        "type": "text",
+        "text": "After unsupervised training, we take all the output of the last layer of RES_cLSTM block $( z _ { t } ^ { l a s t } )$ for classification task. During the classification learning, the parameters in the contracting path $( 2 \\times ( \\mathrm { R E S \\_ D \\_ B L O C K + R E S \\_ c L S T M } ) )$ can be fine-tuned with concatenated softmax-classifier such as Figure (3.b). And the final decision will be made by averaging the result from classifier as follows: ",
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+    {
+        "type": "equation",
+        "img_path": "images/fbe58d6974bec4cf2020c400c3539896e126a3eb5ba41be674ec18692b0b95a4.jpg",
+        "text": "$$\nl o g i t = \\frac { 1 } { T } \\sum _ { t = 1 } ^ { N } \\mathrm { s o f t m a x } ( w _ { c l } \\times z _ { t } ^ { l a s t } + b _ { c l } ) .\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "Here, $w _ { c l }$ and $b _ { c l }$ are the softmax-classifier projection weights and bias, respectively. We use the binary cross-entropy as a loss function to fine-tune the architecture with a learning rate 0.00001. We found that involving unsupervised pre-training is crucial, in order to avoid over-fitting during the training of the networks, see Figure (5). After the fine-tuning, the classifier learns the differences between the two dynamic pattern in each class. ",
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+    {
+        "type": "image",
+        "img_path": "images/95d713640d515f35cbb13496e4fec8280944443c9fd826a6bf5fc80f9ce81711.jpg",
+        "image_caption": [
+            "Figure 4: (a) shows the sequences of the dynamic functional connectivity that used for input, and (b) shows the target sequences to be predicted and (c) represents the sequences of the predictions from residual D-net. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "4 Performance Evaluation ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We conducted two classification experiments (NC vs. eMCI and NC vs. LMCI) to evaluate the proposed residual D-net and compare it with three baselines techniques. For this, we performed a five-fold subject-wise cross-validation to avoid using the same subject. Each validation set was used for selecting the optimal hyper-parameters for the classification model. The performance was measured by the total accuracy, precision, and recall on the test set. ",
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+    {
+        "type": "table",
+        "img_path": "images/f35d1490bd6a0c1d1a41b93817f336d27833b3835ffc8aa4335f02e32842e341.jpg",
+        "table_caption": [
+            "Table 2: Values of the Accuracy (Acc), Precision (Pre) and Recall (Rec) for each five-fold subject-wise cross-validation for the eMCI dataset. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td colspan=\"3\">SFC+SVM</td><td colspan=\"3\">DFC+SVM</td><td colspan=\"3\">DAE+HMM</td><td colspan=\"3\">Res. D-net</td></tr><tr><td>CV</td><td>Acc</td><td>Pre</td><td>Rec</td><td>Acc</td><td>Pre</td><td>Rec</td><td>Acc</td><td>Pre</td><td>Rec</td><td>Acc</td><td>Pre</td><td>Rec</td></tr><tr><td>1</td><td>57.1</td><td>52.0</td><td>68.4</td><td>50.0</td><td>46.2</td><td>63.2</td><td>59.5</td><td>54.5</td><td>63.2</td><td>71.4</td><td>62.1</td><td>94.7</td></tr><tr><td>2</td><td>52.5</td><td>61.1</td><td>47.8</td><td>42.5</td><td>50.0</td><td>30.4</td><td>45.0</td><td>53.8</td><td>30.4</td><td>70.0</td><td>66.7</td><td>95.7</td></tr><tr><td>3</td><td>27.8</td><td>36.8</td><td>33.3</td><td>63.9</td><td>78.6</td><td>52.4</td><td>63.9</td><td>65.4</td><td>81.0</td><td>72.2</td><td>72.0</td><td>85.7</td></tr><tr><td>4</td><td>50.0</td><td>48.0</td><td>57.1</td><td>43.2</td><td>40.0</td><td>38.1</td><td>43.2</td><td>41.7</td><td>47.6</td><td>72.7</td><td>66.7</td><td>85.7</td></tr><tr><td>5</td><td>36.8</td><td>33.3</td><td>50.0</td><td>42.1</td><td>38.5</td><td>62.5</td><td>52.6</td><td>45.5</td><td>62.5</td><td>65.8</td><td>56.0</td><td>87.5</td></tr><tr><td>Total</td><td>45.5</td><td>45.9</td><td>51.0</td><td>48.0</td><td>48.0</td><td>48.0</td><td>52.5</td><td>52.3</td><td>56.0</td><td>70.5</td><td>64.7</td><td>90.0</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/64d2050ea53a428e30a18914ebb15eede139efe9c1f2a2893e26805e938e269f.jpg",
+        "table_caption": [
+            "Table 3: Values of the Accuracy (Acc), Precision (Pre) and Recall (Rec) for each five-fold subject-wise cross-validation for the LMCI dataset. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td colspan=\"3\">SFC+SVM</td><td colspan=\"3\">DFC+SVM</td><td colspan=\"3\">DAE+HMM</td><td colspan=\"3\">Res. D-net</td></tr><tr><td>CV</td><td>Acc</td><td>Pre</td><td>Rec</td><td>Acc</td><td>Pre</td><td>Rec</td><td>Acc</td><td>Pre</td><td>Rec</td><td>Acc</td><td>Pre</td><td>Rec</td></tr><tr><td>1</td><td>50.0</td><td>44.4</td><td>42.1</td><td>50.0</td><td>41.7</td><td>26.3</td><td>38.1</td><td>37.9</td><td>57.9</td><td>73.8</td><td>68.2</td><td>78.9</td></tr><tr><td>2</td><td>48.5</td><td>44.4</td><td>25.0</td><td>54.5</td><td>55.6</td><td>31.3</td><td>60.6</td><td>80.0</td><td>25.0</td><td>75.8</td><td>75.0</td><td>75.0</td></tr><tr><td>3</td><td>74.1</td><td>85.7</td><td>50.0</td><td>33.3</td><td>25.0</td><td>25.0</td><td>51.9</td><td>46.7</td><td>58.3</td><td>66.7</td><td>60.0</td><td>75.0</td></tr><tr><td>4</td><td>61.1</td><td>47.1</td><td>61.5</td><td>50.0</td><td>27.3</td><td>23.1</td><td>61.1</td><td>46.7</td><td>53.8</td><td>72.2</td><td>61.5</td><td>61.5</td></tr><tr><td>5</td><td>48.7</td><td>40.0</td><td>35.3</td><td>61.5</td><td>57.1</td><td>47.1</td><td>56.4</td><td>50.0</td><td>52.9</td><td>64.1</td><td>55.6</td><td>88.2</td></tr><tr><td>Total</td><td>55.4</td><td>48.5</td><td>41.6</td><td>50.8</td><td>41.4</td><td>31.2</td><td>53.1</td><td>46.3</td><td>49.4</td><td>70.6</td><td>63.4</td><td>76.6</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "4.1 Baselines ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Static Functional Connectivity $( \\mathbf { S F C } ) + \\mathbf { S V M }$ : Zhang et al. [5] suggest five specific pairs of the Pearson’s correlation coefficients on each raw dataset $( \\breve { \\mathbf { R } } \\in \\mathbb { R } ^ { 9 0 \\times 1 3 0 } ,$ ), assuming that the FC can be used to distinguish the MCI subjects from the NC. The authors explicitly selected these features after applying a two-sample T-test on 40 subjects. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this paper, we further investigated twenty alternative coefficients using Fisher feature selection [25], and we fed the selected features to a linear Support Vector Machine (SVM) classifier to perform the classification task. ",
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+    {
+        "type": "text",
+        "text": "Dynamic Functional Connectivity $\\mathbf { ( D F C ) } + \\mathbf { S V M }$ : In this experiment, in order to consider the brain dynamics, we used a sliding rectangular window (width: 30 TRs) and a 5 TRs stride to estimate the functional connectivity maps $\\Sigma ( w ) \\breve { \\in } \\mathbb { R } ^ { 9 0 \\times 9 0 }$ in each window $\\mathbf { \\chi } ^ { \\prime } w = 1 , \\dots , 2 0 )$ . Then, according to [26], we project our data into a $K \\times 2 0$ -dimensional feature map and then, we selected the best 100 features using Fisher feature selection, and we measured the performance with a linear SVM classifier. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Deep Auto-Encoder $\\mathbf { ( D A E ) } + \\mathbf { H M M }$ : Suk et al. [7] propose an unsupervised feature learning using a DAE. First, they trained a four-layer DAE (hidden layers: 200-100-50-2) using as an input all the ROIs directly. Afterward, for each specific time instance, they converted the information of all the ROIs (a 116 real vector) into a 2-dimensional feature map. Then, they fit these 2-dimensional feature maps into two Hidden Markov Models (HMM) to model the NC and the MCI classes. Similarly, we implemented this method but using 6 hidden states with 2-mixtures of Gaussian HMM via the Baum-Welch algorithm. ",
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+    {
+        "type": "text",
+        "text": "4.2 Discussion and Results ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "As we discussed during the description of the experiment, we adopted a five-fold subject-wise crossvalidation, in order to ensure the reliability of the different methods. Table (2) and Table (3) show the results associated with the accuracy, precision and recall obtained for the different methods, for the eMCI and LMCI dataset respectively. ",
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+    {
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+        "img_path": "images/c93c6fafb03003cc4ca200483da54e93c4087b4f15b1f54ea05c72f218aabdfe.jpg",
+        "image_caption": [
+            "Figure 5: Cross-entropy errors on the LMCI dataset obtained by the proposed method without pre-training (a) and with pre-training (b). The dot lines represent the actual loss errors obtained for each specific cross-validation sets, and the continuous line represents the mean value among all the cross-validation datasets. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "The main conclusion is that all the baseline techniques turned out significantly inferior results. First, the inferior performance of $\\mathrm { S F C } { + } \\mathrm { S V M }$ is expected because it does not consider any brain dynamics. Moreover, a further analysis turned out that this method performed well on the training set, in contrast to the test set. This observation evidences that the method fails to generalize among different datasets. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "On the other hand, although the $\\mathrm { D F C + S V M }$ takes into account the time evolution of the FC, the method does not learn the relationships within the brain dynamics and, consequently, fails to perform the classification task. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Regarding to the $\\mathrm { D A E + H M M }$ , the major limitation of this approach is that is not an end-to-end learning method. That is, although it incorporates an HMM that tries to model the dynamics, the DAE does not capture any information from the brain connectivity dynamics. Leading to a inferior performance. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In contrast, further analysis during the training and the pre-training have shown that our proposed method effectively learns the brain dynamics. Thus, Figure (4) shows the original and the predicted covariance matrices, which assembles the FC brain dynamics. Observe that our proposed approach captures and reproduces the true dynamics of the brain behavior. ",
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+    {
+        "type": "text",
+        "text": "This explains why the proposed method exhibits the best performance and it properly generalizes among the different cross-validation sets. ",
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+    {
+        "type": "text",
+        "text": "Pre-training vs. Overfitting ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Considering the limited number of samples of the studied datasets, the primary risk of our proposed method is that of overfitting. However, we faced this challenge by introducing the residual D-net architecture, and also by pre-training the model prior to the classification task. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Although we have already discussed the advantages the residual D-net architecture, we illustrate the benefits of the pre-training in Figure (5), where we plotted the loss errors for the LMCI dataset with and without pre-training. ",
+        "bbox": [
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+        "page_idx": 7
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+    {
+        "type": "text",
+        "text": "Observe that the model overfits without pre-training (see Figure (5.a)); that is, we can not guarantee that the method had generalized correctly, making it impossible to establish any proper stopping criterion. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "However, the behavior of the loss curves radically changes after pre-training the model (see Figure (5.b)). Now, the method has converged and we can define a proper stopping criterion. ",
+        "bbox": [
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+        "page_idx": 7
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+    {
+        "type": "text",
+        "text": "Figure (5) only shows the results for the LMCI dataset, but we have observed the same effects in the eMCI dataset as well. ",
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+    {
+        "type": "text",
+        "text": "5 Conclusions ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we presented a new method named residual D-net to identify MCI from NC subjects. In contrast to the previous methods, proposed residual D-net can be efficiently trained with few number of training samples, while unravels the brain connectivity dynamics in unsupervised learning. Furthermore, the proposed pre-training approach robustifies the generalization performance of the proposed method and offers an adequate selection of a stopping criterion in practice. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "References ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            209,
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+    },
+    {
+        "type": "text",
+        "text": "[1] Warren W. Barker, Cheryl A. Luis, Alice Kashuba, Mercy Luis, Dylan G. Harwood, David Loewenstein, Carol Waters, Pat Jimison, Eugene Shepherd, and Steven Sevush. Relative frequencies of Alzheimer disease, Lewy body, vascular and frontotemporal dementia, and hippocampal sclerosis in the State of Florida Brain Bank. Alzheimer Disease & Associated Disorders, 16(4):203–212, 2002.   \n[2] Robert S. Wilson, Eisuke Segawa, Patricia A. Boyle, Sophia E. Anagnos, Loren P. Hizel, and David A. Bennett. The natural history of cognitive decline in Alzheimer’s disease. Psychology and Aging, 27(4):1008–1017, 2012.   \n[3] Alzheimer’s Association. 2016 Alzheimer’s disease facts and figures. Alzheimer’s & Dementia, 12(4):459–509, 2016.   \n[4] Colin J Brown and Ghassan Hamarneh. Machine learning on human connectome data from mri. arXiv preprint arXiv:1611.08699, 2016.   \n[5] Xiaowei Zhang, Bin Hu, Xu Ma, and Linxin Xu. 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