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+# Beyond Pinball Loss: Quantile Methods for Calibrated Uncertainty Quantification
+
+# Youngseog Chung
+
+Machine Learning Department Carnegie Mellon University Pittsburgh, PA 15213 youngsec@cs.cmu.edu
+
+Willie Neiswanger   
+Department of Computer Science   
+Stanford University   
+Stanford, CA 94305   
+neiswanger@cs.stanford.edu
+
+# Ian Char
+
+# Jeff Schneider
+
+Machine Learning Department   
+Carnegie Mellon University Pittsburgh, PA 15213 ichar@cs.cmu.edu
+
+Robotics Institute Carnegie Mellon University Pittsburgh, PA 15213 schneide@cs.cmu.edu
+
+# Abstract
+
+Among the many ways of quantifying uncertainty in a regression setting, specifying the full quantile function is attractive, as quantiles are amenable to interpretation and evaluation. A model that predicts the true conditional quantiles for each input, at all quantile levels, presents a correct and efficient representation of the underlying uncertainty. To achieve this, many current quantile-based methods focus on optimizing the pinball loss. However, this loss restricts the scope of applicable regression models, limits the ability to target many desirable properties (e.g. calibration, sharpness, centered intervals), and may produce poor conditional quantiles. In this work, we develop new quantile methods that address these shortcomings. In particular, we propose methods that can apply to any class of regression model, select an explicit balance between calibration and sharpness, optimize for calibration of centered intervals, and produce more accurate conditional quantiles. We provide a thorough experimental evaluation of our methods, which includes a high dimensional uncertainty quantification task in nuclear fusion.
+
+# 1 Introduction
+
+Uncertainty quantification (UQ) in machine learning typically refers to the task of quantifying the confidence of a given prediction. This measure of certainty can be crucial in a variety of downstream applications, including Bayesian optimization [36, 45, 54], model-based reinforcement learning [64, 42, 10, 18], and in high-stakes predictions where mistakes incur large costs [52, 61].
+
+While the common goal of UQ is to describe predictive distributions over outputs for given inputs, the representation of the distributional prediction varies across methods. For example, some methods assume a parametric distribution and return parameter estimates [65, 14, 37], while others return density function estimates, as is common in Bayesian methods [41, 38, 24, 3, 33, 50]. Alternatively, many methods represent predictive uncertainty with quantile estimates [15, 53, 58, 49, 27].
+
+Quantiles provide an attractive representation for uncertainty because they can be used to model complex distributions without parametric assumptions, are interpretable with units in the target output space, allow for easy construction of prediction intervals, and can be used to efficiently sample from the predictive distribution via inverse transform sampling [22, 32]. Learning the quantile for a single quantile level is a well studied problem in quantile regression (QR) [30, 32], which typically involves optimizing the so-called pinball loss, a tilted transformation of the absolute value function. Given a target $y$ , a prediction $\hat { y }$ , and quantile level $\tau \in ( 0 , 1 )$ , the pinball loss $\rho _ { \tau }$ is defined as
+
+$$
+\rho _ { \tau } ( y , \hat { y } ) = ( \hat { y } - y ) ( \mathbb { I } \{ y \leq \hat { y } \} - \tau ) .
+$$
+
+By training for all quantiles simultaneously, recent works have made concrete steps in incorporating QR methods to form competitive UQ methods which output the full predictive distribution [51, 58].
+
+In this work, we highlight some limitations of the pinball loss and propose several methods to address these shortcomings. Specifically, we explore the following:
+
+• Model agnostic QR. Optimizing the pinball loss often restricts the choice of model family for which we can provide UQ. We propose an algorithm to learn all quantiles simultaneously by utilizing methods from conditional density estimation. This algorithm is agnostic to model class and can be applied to any regression model.   
+• Explicitly balancing calibration and sharpness. While the pinball loss, as a proper scoring rule, targets both calibration and sharpness, the balance between these two quantities is made implicitly, which may result in a poor optimization objective. We propose a tunable loss function that targets calibration and sharpness separately, and allows the end-user to set an explicit balance.   
+• Centered intervals. In practice, we often desire uncertainty predictions made with centered intervals, which are not targeted via the pinball loss. We propose an alternative loss function that is better suited for this goal.   
+• Encouraging individual calibration. Perfect quantile forecasts will satisfy individual calibration (Eq. 2), which is a much stricter condition than the more-commonly used notion of average calibration (Eq. 3). We introduce a training procedure that aims to improve quantile predictions beyond average calibration, and demonstrate its efficacy via adversarial group calibration (Eq. 4).
+
+We proceed by first describing methods of assessing the quality of predictive UQ and the pitfalls of optimizing the pinball loss in Section 2. Drawing motivation from this, we then present our proposed methods in Section 3. In Section 4, we demonstrate our methods experimentally, where we model predictive uncertainty on benchmark datasets, and on a high-dimensional, real-world uncertainty estimation task in the area of nuclear fusion.
+
+# 2 Preliminaries and Background
+
+We first lay out the notation, terminology, and class of models considered in this paper. Then we provide an overview of evaluation metrics in UQ and demonstrate how the pinball loss may be inadequate both as an evaluation metric and as an optimization objective.
+
+# 2.1 Notation
+
+Bold upper case letters $\mathbf { X }$ , $\mathbf { Y }$ denote random variables, lower case letters $x , y$ , denote their values, and calligraphic upper case letters $\mathcal { X } , \mathcal { y }$ denote sets of possible values. We use $x \in \mathcal { X }$ to denote the input feature vector and $y \in \mathcal { V }$ to denote the corresponding target. Additionally, we consider the regression setting where $\mathcal { V } \subset \mathbb { R }$ and $\mathcal { X } \subset \mathbb { R } ^ { n }$ . We use $\mathbb { F } _ { \mathbf { X } } , \mathbb { F } _ { \mathbf { Y | } x } , \mathbb { F } _ { \mathbf { Y } }$ to denote the true cumulative distribution of the subscript random variable. For any $x \in \mathcal { X }$ , we assume there exists a true conditional distribution $\mathbb { F } _ { \mathbf { Y } \mid x }$ over $\mathcal { V }$ , and we assume $\mathbb { Q } _ { p } ( x )$ denotes the true $p ^ { \mathrm { t h } }$ quantile of this distribution, i.e. $\mathbb { F } _ { \mathbf { Y } | x } ( \mathbb { Q } _ { p } ( x ) ) = p$ . Any estimates of the true functions $\mathbb { F } , \mathbb { Q } _ { p }$ will be denoted with a hat, $\hat { \mathbb { F } } , \hat { \mathbb { Q } } _ { p }$ . We will specifically refer to any family of estimates for $\mathbb { Q } _ { p }$ , with $p \in ( 0 , 1 )$ , as a “quantile model”, denoted $\hat { \mathbb { Q } } : \mathcal { X } \times ( 0 , 1 )  \mathcal { Y }$ . Unless otherwise noted, we will always consider the conditional problem of estimating quantities in the target space $\mathcal { V }$ , conditioned on a value $x \in \mathcal { X }$ .
+
+# 2.2 Assessing the Quality of Predictive UQ
+
+While various metrics have been proposed to assess the quality of UQ, there has been a great deal of recent focus on the notions of calibration and sharpness [15, 13, 65, 60, 55, 35, 21, 20]. We introduce calibration here, but for a more thorough treatment, see Zhao et al. [65]. Broadly speaking, calibration in the regression setting requires that the probability of observing the target random variable below a predicted $p ^ { \mathrm { t h } }$ quantile is equal to the expected probability $p$ , for all $p \in ( 0 , 1 )$ . We refer to the former quantity as the observed probability and denote it $p ^ { \mathrm { o b s } } ( p )$ , for an expected probability $p$ , which we will write as $p ^ { \mathrm { o b s } }$ when it is clear from context. Calibration requires $p ^ { \mathrm { o b s } } ( p ) = p$ , $\forall p \in ( 0 , 1 )$ . From this generic statement, we can describe different notions of calibration based on how $p ^ { \mathrm { o b s } }$ is defined.
+
+![](images/7372c433b9bf3bf4fad46c06b83fa479629c7afcfb557c6a470fb9749ab1f6cd.jpg)  
+Figure 1: (a) Test loss continues to decrease until the validated epoch. (b-c) At the validated epoch, $S Q R$ (optimizes pinball loss) is highly miscalibrated while sharper than the true sharpness level. Cali (optimizes proposed calibration loss) is better calibrated while less sharp than the true sharpness.
+
+A model is individually calibrated if it outputs the true conditional quantiles, i.e. $\hat { \mathbb { Q } } _ { p } ( x ) = \mathbb { Q } _ { p } ( x )$ In this case, we define the observed probability to be
+
+$$
+p _ { i n d v } ^ { \mathrm { o b s } } ( p , x ) : = \mathbb { F } _ { \mathbf { Y } | x } ( \hat { \mathbb { Q } } _ { p } ( x ) ) , \forall x \in \mathcal { X } , \forall p \in ( 0 , 1 ) .
+$$
+
+In words, this requires that the probability of observing $y$ below the quantile prediction is equal to $p$ , at each point $x \in \mathcal { X }$ , individually. If we can verify this property for all $x \in \mathcal { X }$ , then by definition, we will know the quantile output is correct and precisely the true conditional quantile. However, individual calibration is typically unverifiable with finite datasets in the assumption-less case [65].
+
+A relaxed condition is average calibration. In this case, we define the observed probability to be
+
+$$
+p _ { a v g } ^ { \mathrm { o b s } } ( p ) : = \mathbb { E } _ { x \sim \mathbb { F } _ { \mathbf { X } } } [ \mathbb { F } _ { \mathbf { Y } \mid x } ( \hat { \mathbb { Q } } _ { p } ( x ) ) ] , \forall p \in ( 0 , 1 ) ,
+$$
+
+i.e. the probability of observing the target below the quantile prediction, averaged over $\mathbb { F } _ { X }$ , is equal to $D = \{ ( x _ { i } , y _ { i } ) \} _ { i = 1 } ^ { N }$ $p$ . Average calibration is often referred to simply as “calibration” [13, 35]. Given a dataset , we can estimate $p _ { a v g } ^ { \mathrm { o b s } } ( p )$ with $\begin{array} { r } { \hat { p } _ { a v g } ^ { \mathrm { o b s } } ( D , p ) = \frac { 1 } { N } \sum _ { i = 1 } ^ { N } \mathbb { I } \{ y _ { i } \leq \hat { \mathbb { Q } } _ { p } ( x _ { i } ) \} } \end{array}$ . Note that if our quantile estimate achieves average calibration then $\hat { p } _ { a v g } ^ { \mathrm { o b s } }  p$ as $N  \infty$ , $\forall p \in ( 0 , 1 )$ The degree of error in average calibration is commonly measured by expected calibration error [60, 13, 21], $\begin{array} { r } { \mathrm { E C E } ( D , \hat { \mathbb { Q } } ) = \frac { 1 } { m } \sum _ { j = 1 } ^ { m } \left| \hat { p } _ { a v g } ^ { \mathrm { o b s } } \left( D , p _ { j } \right) - p _ { j } \right| } \end{array}$ , where $p _ { j } \sim \mathrm { U n i f } ( 0 , 1 )$ .
+
+It may be possible to have an uninformative, yet average calibrated model. For example, quantile predictions that match the true marginal quantiles of $\mathbb { F } _ { \mathbf { Y } }$ will be average calibrated, but will hardly be useful since they do not depend on the input $x$ . Therefore, the notion of sharpness is also considered, which quantifies the concentration of distributional predictions [20]. For example, for non-parametric predictions, the width of a centered $9 5 \%$ prediction interval is often used as a measure of sharpness. There generally exists a tradeoff between average calibration and sharpness [20, 46].
+
+Recent works have suggested a notion of calibration stronger than average calibration, called adversarial group calibration [65]. This stems from the notion of group calibration [23, 29], which prescribes measurable subsets $s _ { i } \subset \mathcal { X }$ s.t. $P _ { x \sim \mathbb { F } _ { \mathbf { X } } } ( x \in S _ { i } ) > 0$ , $i = 1 , \ldots , k$ , and requires the predictions to be average calibrated within each subset. Adversarial group calibration then requires average calibration for any subset of $\mathcal { X }$ with non-zero measure. Denote $\mathbf { X } _ { \mathcal { S } }$ as a random variable that is conditioned on being in the set $s$ . For adversarial group calibration, the observed probability is
+
+$$
+p _ { a d v } ^ { \mathsf { o b s } } ( p ) : = \mathbb { E } _ { x \sim \mathbb { F } _ { \mathbf { X } _ { S } } } [ \mathbb { F } _ { \mathbf { Y } | x } ( \hat { \mathbb { Q } } _ { p } ( x ) ) ] , \forall p \in ( 0 , 1 ) , \forall S \subset \mathcal { K } \mathrm { ~ s . t . ~ } P _ { x \sim \mathbb { F } _ { \mathbf { X } } } ( x \in S ) > 0 .
+$$
+
+With a finite dataset, we can measure a proxy of adversarial group calibration by measuring the average calibration within all subsets of the dataset with sufficiently many points.
+
+Intuitively, individual calibration inspects the discrepancy between $p ^ { \mathrm { o b s } }$ and $p$ for individual inputs $x \in \mathcal { X }$ , adversarial group calibration relaxes this by inspecting any subset of $\mathcal { X }$ with non-zero measure, and average calibration relaxes this further by considering the full distribution of $\mathbf { X }$ .
+
+One alternative family of evaluation metrics is proper scoring rules [19]. Proper scoring rules are summary statistics of overall performance of a distributional prediction and consider both calibration and sharpness jointly [20]. For example, negative log-likelihood (NLL) is a proper scoring rule that is commonly used with density predictions [14, 48, 37]. For quantile predictions, one proper score is the check score, which is identical to the pinball loss. Since proper scoring rules consider both calibration and sharpness together in a single value, they can serve as optimization objectives for UQ. For example, optimizing the pinball loss is the traditional method in quantile regression [31], and many recent quantile-based UQ methods focus on optimizing this objective [51, 58, 8, 63].
+
+In this work, however, we note that the balance between calibration and sharpness implied by the pinball loss is arbitrary and depends on the expressivity of the model class—and with highly expressive models, this balance can be heavily skewed towards sharpness. In their seminal work on probabilistic forecasts, Gneiting and Raftery [19] contend that the goal of probabilistic forecasting is to “maximize the sharpness of the predictive distribution subject to calibration”, i.e. calibration should be first achieved and then sharpness optimized. We show that common machine learning methods that use the pinball loss objective may in fact lead to an arbitrary and miscalibrated UQ.
+
+Proposition 1. Consider a finite dataset $D$ , the pinball loss $\rho _ { \tau }$ (Eq. 1) and a quantile model $f : \mathcal { X } \times ( 0 , 1 )  \mathcal { Y }$ that is average calibrated on $D$ , i.e. $E C E ( D , f ) = 0$ . Then there always exists another quantile modlower pinball loss than $f$ $g : \mathcal { X } \times ( 0 , 1 )  \mathcal { Y }$ $D$ $\begin{array} { r } { \sum _ { i = 1 } ^ { N } \rho _ { \tau } ( y _ { i } , g _ { \tau } ( x _ { i } ) ) < \sum _ { i = 1 } ^ { N } \rho _ { \tau } ( y _ { i } , f _ { \tau } ( x _ { i } ) ) } \end{array}$ l , $\tau \in ( 0 , 1 )$ , g hasaverage calibration than $f _ { i }$ , i.e. $E C E ( D , g ) \stackrel { } { > } E \dot { C } E ( D , f )$ .
+
+Proof: The proof is given in Appendix A.1.
+
+This proposition essentially states how the pinball loss can become detached from calibration, and we show its practical ramifications via a synthetic example in Figure 1 (experiment details in Appendix E.1). We first note in Figure 1 (a) and (b) that even while the pinball loss decreases on the test set, test calibration worsens (while sharpness improves). Further, at the best validation epoch, optimizing the pinball loss converges to a solution that is sharper than the true noise level. Note that a UQ that is sharper than the true noise level will never be calibrated (meanwhile, a less sharp prediction can still be calibrated, e.g. the marginal distribution $\mathbb { F } _ { \mathbf { Y } }$ ). While this may seem like an issue that can simply be addressed with regularization, we demonstrate in Appendix E.2 how that is not the case. These pitfalls motivate our methods in Section 3.
+
+# 3 Methods
+
+We propose four methods that aim to produce an improved quantile model. The first is a modelagnostic procedure that relies on conditional density estimation (Section 3.1). To address settings where density estimation may be difficult, we then propose two loss functions to optimize with differentiable models: the combined calibration loss (Section 3.2), which directly optimizes calibration and sharpness, and the interval score (Section 3.3), which is a proper scoring rule for centered intervals. Finally, we propose a group batching method (Section 3.4) that can be applied to the batch optimization procedure for any loss function (e.g. combined calibration loss, interval score, and even pinball loss) to induce better convergence towards adversarial group calibration.
+
+# 3.1 Utilizing Conditional Density Estimation for Model Agnostic QR
+
+One drawback of many existing quantile-based UQ methods is that their training procedure requires differentiable models. In fact, most UQ methods require a specific class of models because of their modeling structure or their loss objective (e.g. Gaussian processes [50], dropout [17], latent variable models [33], simultaneous pinball loss [58], and NLL-based losses [37]). This model restriction can be especially unfavorable in practical settings. A domain expert with an established point prediction model and compute infrastructure may want to add UQ without much additional overhead.
+
+To address these issues, we can consider the following model-agnostic procedure. Instead of optimizing a designated loss function, we can consider splitting the given problem into two parts: estimate conditional quantiles directly from data, then regress onto these estimates. The benefit of this method is that, granted we can estimate the conditional quantiles accurately, we can use any regression model to regress onto these quantile estimates. Further, this regression task directly targets the goal of producing the true conditional quantiles (i.e. individual calibration). This procedure, which we refer to as Model Agnostic QR (MAQR), is outlined in Algorithm 1.
+
+# Algorithm 1 MAQR
+
+1: Input: Train data $\{ x _ { i } , y _ { i } \} _ { i = 1 } ^ { N }$ , trained regression model $\hat { f } ( x )$   
+2: Calculate residuals $\epsilon _ { i } = y _ { i } - \hat { f } ( x _ { i } ) ,$ $i \in$ $[ N ]$ , and denote the residual dataset $R =$ $\mathbf { \bar { \{ } }  x _ { i } , \epsilon _ { i } \} _ { i = 1 } ^ { N }$   
+3: Initialize $D  \emptyset$   
+4: for $i = 1$ to $N$ do   
+5: $D _ { i }$ ← CONDQUANTILESESTIMATORS $( R , i )$ (Algorithm 2)   
+6: $D  D \cup D _ { i }$   
+7: end for   
+8: Use $D$ to fit a regression model $\hat { g }$ $\widehat { g } : ( x , p ) \mapsto \overline { { \epsilon } }$   
+9: Output: $\hat { f } + \hat { g }$
+
+1: Input: Dataset $\{ x _ { i } , \epsilon _ { i } \} _ { i = 1 } ^ { N }$ , point index $k \in$   
+$[ N ]$   
+2 $: \stackrel { \cdot } { E } _ { k , d _ { N } } ^ { \enspace \enspace } \gets \enspace \{ \epsilon _ { i } \enspace : \enspace \mathrm { d i s t } ( x _ { k } , x _ { i } ) \enspace \le \enspace d _ { N } , i \enspace \in$   
+3: Construct an empirical CDF with $E _ { k , d _ { N } }$ to   
+produce $\hat { \mathbb { F } } _ { \mathbf { E } | x _ { k } } : \epsilon \mapsto p \in [ 0 , 1 ]$   
+4: Initialize $D  \varnothing$   
+5: for each $\epsilon _ { j }$ in $E _ { k , d _ { N } }$ do   
+6: pˆk,j ← FˆE|xk (j )   
+7: $D \gets D \cup \{ x _ { k } , \hat { p } _ { k , j } , \epsilon _ { j } \}$   
+8: end for   
+9: Output: D
+
+MAQR is based on the key assumption that nearby points in $\mathcal { X }$ will have similar conditional distributions, i.e. if $x _ { j } \approx x _ { k }$ then $\mathbb { F } _ { \mathbf { Y } | x _ { j } } \approx \mathbb { F } _ { \mathbf { Y } | x _ { k } }$ . Given this smoothness assumption, we can group neighboring points to estimate the conditional density at each locality over $\mathcal { X }$ , with locality determined by the hyperparameter $d _ { N }$ (Algorithm 2, line 2). We then construct an empirical CDF with the group of neighboring points, and conditional quantile estimates are produced with this empirical CDF. These estimates are collected into $D$ (Algorithm 1, line 6), which is ultimately used as the training set for the quantile model $\hat { g }$ .
+
+In practice, we perform these steps with residuals, by first estimating a mean function $\hat { f }$ (Algorithm 1, line 1). This practical choice stems from existing works in conditional density estimation, which suggests that having 0 conditional mean in the data provides benefits in terms of lower asymptotic mean squared error in the conditional density predictions [26]. Further, this demonstrates how MAQR can be readily applied in the application setting where an accurate point prediction model often already exist.
+
+Algorithm 1 is a specific implementation of a more general model-agnostic algorithm, in which we directly estimate conditional quantiles from the data with tools from conditional density estimation. We note that using KDEs for conditional density estimation is a well studied problem with theoretical guarantees [25, 26, 57]. In the case the distance in $\mathcal { X }$ is measured using a uniform kernel with mild assumptions on the bandwidth, Algorithm 1 falls under the guarantees stated by Stute et al. [57].
+
+Theorem 1 [57]. Assume $\mathcal { V } \subset \mathbb { R } ,$ , $\mathcal { X } \subset \mathbb { R } ^ { n }$ , $d i s t ( x _ { i } , x _ { j } ) : = | x _ { i } - x _ { j } | _ { \infty }$ , and that $\hat { \mathbb { F } } _ { \mathbf { E } | x }$ is constructed using the procedure given in line 5 of Algorithm $I$ (i.e. $x _ { i } = x$ ). Further assume that, as $N \to \infty$ , $d _ { N }  0$ and that $\begin{array} { r } { \sum _ { N \ge 1 } \exp ( - \rho N d _ { N } ^ { n } ) < \infty } \end{array}$ , $\forall \rho > 0$ . Then, as $N  \infty$ , for almost all $x \in \mathcal { X }$ $\operatorname* { s u p } _ { \epsilon } [ \hat { \mathbb { F } } _ { \mathbf { E } | x } ( \epsilon ) - \mathbb { F } _ { \mathbf { E } | x } ( \epsilon ) ]  0$ with probability $^ { l }$ .
+
+This theorem states that in the limit of data, for almost all $x \in \mathcal { X }$ , the CDF estimate $\hat { \mathbb { F } } _ { \mathbf { E } | x }$ will converge uniformly to the true CDF $\mathbb { F } _ { \mathbf { E } | x }$ with probability 1. The dataset, $D$ , will therefore be populated with good estimates of the conditional quantile and quantile level pair for $x$ . In Appendix B, we state the general form of Algorithm 1 and also demonstrate how the algorithm is model agnostic. Through our experiments in Section 4, we will show empirically that utilizing these density estimates sidesteps the issues inherent to the pinball loss and produces much higher quality quantile predictions.
+
+# 3.2 Explicitly balancing calibration and sharpness with the combined calibration loss
+
+While MAQR can produce strong results, its performance can suffer in high-dimensional settings, where nonparametric conditional density estimation methods falter. Neural networks (NNs) have shown good performance in high dimensional settings, given their high capacity to approximate complex functions and recent advances in fast gradient-based optimization. We therefore propose a loss-based approach to estimating conditional quantiles for NNs and other differentiable models.
+
+Drawing motivation from the arbitrary balance between calibration and sharpness that pinball loss implicitly provides, we propose objectives separately for calibration and sharpness, Then, we combine the two objectives into a single loss function that provides an explicit balance between calibration and sharpness that can be chosen by the end user.
+
+We first consider calibration of a quantile prediction, $\hat { \mathbb { Q } } _ { p } \in \mathcal { V }$ for quantile level $p \in ( 0 , 1 )$ . Here, we omit conditioning on $x$ for clarity. For this prediction to be average calibrated, exactly a $p$ proportion of the true density should lie below $\hat { \mathbb { Q } } _ { p }$ , i.e. $p _ { a \nu g } ^ { \mathrm { o b s } } = P ( Y \leq \hat { \mathbb { Q } } _ { p } ) = p$ . While calibration (e.g. $| p _ { a \nu g } ^ { \mathrm { o b s } } - p | )$ is a non-differentiable objective, by inducing a truncated distribution based on the currentlibration, we can construct the following calibration objective, which is minimized if and only if the prediction is average calibrated:
+
+$$
+\begin{array} { r } { \mathcal { C } ( \hat { \mathbb { Q } } _ { p } , p ) = \mathbb { I } \{ \hat { p } _ { p } < p \} * \mathbb { E } [ Y - \hat { \mathbb { Q } } _ { p } | Y > \hat { \mathbb { Q } } _ { p } ] * P ( Y > \hat { \mathbb { Q } } _ { p } ) } \\ { + \mathbb { I } \{ \hat { p } _ { p } > p \} * \mathbb { E } [ \hat { \mathbb { Q } } _ { p } - Y | \hat { \mathbb { Q } } _ { p } > Y ] * P ( \hat { \mathbb { Q } } _ { p } > Y ) } \end{array}
+$$
+
+The empirical calibration objective, $\mathcal { C } ( D , \hat { \mathbb { Q } } _ { p } , p )$ , is then defined as follows:
+
+$$
+\begin{array} { r l r } {  { \mathcal { C } ( D , \hat { \mathbb { Q } } , p ) = \mathbb { I } \{ \hat { p } _ { a v g } ^ { \mathrm { o b s } } < p \} * \frac { 1 } { N } \sum _ { i = 1 } ^ { N } \Big [ ( y _ { i } - \hat { \mathbb { Q } } _ { p } ( x _ { i } ) ) \mathbb { I } \{ y _ { i } > \hat { \mathbb { Q } } _ { p } ( x _ { i } ) \} \Big ] } } \\ & { } & { \quad + \mathbb { I } \{ \hat { p } _ { a v g } ^ { \mathrm { o b s } } > p \} * \frac { 1 } { N } \sum _ { i = 1 } ^ { N } \Big [ ( \hat { \mathbb { Q } } _ { p } ( x _ { i } ) - y _ { i } ) \mathbb { I } \{ \hat { \mathbb { Q } } _ { p } ( x _ { i } ) > y _ { i } \} \Big ] . } \end{array}
+$$
+
+Note $\pmb { I }$ : Intuition of the calibration objective. For any given $p$ , consider the case when the quantile estimate $\hat { \mathbb { Q } } _ { p }$ is below the true $p ^ { \mathrm { t h } }$ quantile $\mathbb { Q } _ { p }$ . Since $\hat { \mathbb { Q } } _ { p } < \mathbb { Q } _ { p } \Longrightarrow \hat { p } _ { p } < p$ , this implies that too much data density lies above $\hat { \mathbb { Q } } _ { p }$ . In this case, ${ \mathcal { C } } ( { \hat { \mathbb { Q } } } _ { p } , p )$ reduces to $\mathbb { E } [ Y - \hat { \mathbb { Q } } _ { p } | Y > \hat { \mathbb { Q } } _ { p } ] * P ( Y > \hat { \mathbb { Q } } _ { p } )$ . $\hat { \mathbb { Q } } _ { p }$ is pulled higher with the expectation of the truncated distribution that places $\hat { \mathbb { Q } } _ { p }$ at the lower bound of the support. In the opposite case, when $\hat { \mathbb { Q } } _ { p } > \mathbb { Q } _ { p }$ , $\hat { \mathbb { Q } } _ { p }$ is pulled lower by the same logic.
+
+Note 2: Is the proposed calibration objective a proper scoring rule? Strictly speaking, the calibration objective is a non-decomposable function, hence deviates from the standard convention of proper scoring rules [19], which can be “decomposed” into scores for individual examples $( x _ { i } , y _ { i } )$ . This simply arises from the fact that measuring average calibration (i.e. $\hat { p } _ { a \nu g } ^ { \mathrm { o b s } }$ ) is non-decomposable. Proper scoring rules are defined such that an optimum of the expected score (or risk, if we consider the score as a loss function) occurs at the true distribution quantity. While an example level loss or score does not exist due to non-decomposability, we can still show the (expectation-level) score (i.e. $\mathcal { C } ( \hat { \mathbb { Q } } _ { p } , p ) )$ ) is minimized by the true distribution and hence enjoys the optimum property of proper scoring rules.
+
+Proposition 2. For any quantile level $p \in \mathsf { \Gamma } ( 0 , 1 )$ , the true quantile function $\mathbb { Q } _ { p }$ minimizes the calibration objective, ${ \mathcal { C } } ( { \hat { \mathbb { Q } } } _ { p } , p )$ . Further, on a finite dataset $D$ , the empirical calibration objective, $\mathcal { C } ( D , \hat { \mathbb { Q } } _ { p } , p )$ , is minimized by an average calibrated solution on $D$ , i.e. when $\hat { p } _ { a \nu g } ^ { o b s } ( D , p ) = p$ .
+
+Proof: The proof is given in Appendix A.2.
+
+Note 3: Non-zero gradients for miscalibrated predictions $\hat { \mathbb { Q } } _ { p }$ . We can further show that for a miscalibrated quantile prediction, the gradients of $\mathcal { C }$ are always non-zero. When $\hat { p } _ { p } < p$ , $\partial \mathcal { C } ( \hat { \mathbb { Q } } _ { p } , p ) / \partial \hat { \mathbb { Q } } _ { p }$ $= - P ( Y > \hat { \mathbb { Q } } _ { p } ) < 0$ . Thus increasing $\hat { \mathbb { Q } } _ { p }$ decreases the objective $\mathcal { C }$ . Similarly, when $\hat { p } _ { p } > p$ , $\partial \mathcal { C } ( \hat { \mathbb { Q } } _ { p } , p ) / \partial \hat { \mathbb { Q } } _ { p } = P ( Y < \hat { \mathbb { Q } } _ { p } ) > 0$ , and an analogous argument follows (proof in Appendix A.3).
+
+As discussed in Section 2.2, average calibration by itself is not a sufficient condition for meaningful UQ, hence we also desire sharp quantile models, with more-concentrated (less dispersed) distributions. We can induce this property in quantile predictions by predicting the $( 1 - p ) ^ { \mathrm { t h } }$ quantile $\hat { \mathbb { Q } } _ { 1 - p } ( x _ { i } )$ alongside each prediction $\hat { \mathbb { Q } } _ { p } ( x _ { i } )$ and penalizing the width between the quantile predictions:
+
+$$
+\mathcal { P } ( \hat { \mathbb { Q } } _ { p } , p ) = \mathbb { E } \left[ \left| \hat { \mathbb { Q } } _ { p } - \hat { \mathbb { Q } } _ { 1 - p } \right| \right] .
+$$
+
+The empirical sharpness objective, $\mathcal { P } ( D , \hat { \mathbb { Q } } _ { p } , p )$ , is then defined as follows:
+
+$$
+\mathcal { P } ( D , \hat { \mathbb { Q } } , p ) = \frac { 1 } { N } \sum _ { i = 1 } ^ { N } \left\{ \hat { \mathbb { Q } } _ { 1 - p } ( x _ { i } ) - \hat { \mathbb { Q } } _ { p } ( x _ { i } ) \ ( p \leq 0 . 5 ) \right.
+$$
+
+It is important to note that the true underlying distribution will not have 0 sharpness if there is significant noise, and sharpness should be optimized subject to calibration. Therefore, we should only penalize sharpness when the data suggests our quantiles are too dispersed, i.e. when $\left| p _ { a v g } ^ { \mathrm { o b s } } ( p ) - p _ { a v g } ^ { \mathrm { o b s } } ( 1 - p ) \right|$ , the observed coverage between the pair of quantiles $\hat { \mathbb { Q } } _ { p } ( x _ { i } )$ and $\hat { \mathbb { Q } } _ { 1 - p } ( x _ { i } )$ is greater than $| 2 p - 1 |$ , the expected coverage.
+
+Combining the calibration and sharpness terms, we have the combined calibration loss
+
+$$
+\mathcal { L } ( D , \hat { \mathbb { Q } } _ { p } , p ) = ( 1 - \lambda ) \mathcal { C } ( D , \hat { \mathbb { Q } } _ { p } , p ) + \lambda \mathcal { P } ( D , \hat { \mathbb { Q } } _ { p } , p ) .
+$$
+
+The hyperparameter $\lambda \in [ 0 , 1 ]$ sets the explicit balance between calibration and sharpness. Note that setting $\lambda = 0$ may not always be desirable, since optimizing $\mathcal { C } ( D , \hat { \mathbb { Q } } _ { p } , p )$ alone may converge to quantiles of the marginal distribution, $\mathbb { F } _ { \mathbf { Y } }$ . Further, in certain downstream applications that utilize UQ, a sharper prediction, even at the cost of worse calibration, may result in higher utility, and $\lambda$ can be tuned according to the utility function of the application. In our experiments, we tune $\lambda$ by cross-validating with adversarial group calibration as it is the strictest notion of calibration that can be estimated with a finite dataset. Since we learn a quantile model that outputs the conditional quantile estimates for all probabilities, our training objective is $\mathbb { E } _ { p \sim \mathrm { U n i f } ( 0 , 1 ) } \mathcal { L } ( D , \hat { \mathbb { Q } } _ { p } , p )$ .
+
+# 3.3 Encouraging calibration of centered intervals with the interval score
+
+The combined calibration loss (Eq. 9) optimizes average calibration, which targets observed probabilities below a quantile. In many applications, however, we may desire a centered prediction interval (PI) which requires a pair of quantile predictions. A centered $9 5 \%$ PI, for example, is a pair of quantile predictions at quantile levels 0.025 and 0.975. Hence, for the average calibration of the $p ^ { \mathrm { t h } }$ centered interval, we want interval coverage $\big [ \hat { p } _ { a \nu g } ^ { \mathrm { o b s } } ( 0 . 5 + { \textstyle \frac { p } { 2 } } ) - \hat { p } _ { a \nu g } ^ { \mathrm { o b s } } ( 0 . 5 - { \textstyle \frac { p } { 2 } } ) \big ]$ (the PI’s observed probability, a.k.a. p to be equal to the expected probability diction. While $p$ we can modify the objective in Eq. 9 to adhere to this altered goal, here we propose simultaneously optimizing the interval score (or Winkler score) [19, 62] for all expected probabilities $p \in ( 0 , 1 )$ , and bring to light a proper scoring rule that has largely been neglected for the purpose of learning quantiles. While some previous works utilize the interval score to evaluate interval predictions [7, 4, 1, 40], to the best of our knowledge, no previous work has focused on simultaneously optimizing it and shown a thorough experimental evaluation as we provide in Section 4.
+
+For a point $( x , y )$ , if we denote a $( 1 - \alpha )$ centered PI as $\hat { l } , \hat { u }$ , i.e. $\hat { l } = \hat { \mathbb { Q } } _ { \mathit { \Pi } _ { 2 } ^ { \alpha } } ( x )$ and $\hat { u } = \hat { \mathbb { Q } } _ { 1 - \frac { \alpha } { 2 } } ( x )$ , the interval score is defined as $\begin{array} { r } { S _ { \alpha } ( \widehat { l } , \widehat { u } ; y ) = ( \widehat { u } - \widehat { l } ) + \frac { 2 } { \alpha } ( \widehat { l } - y ) \mathbb { I } \{ y < \widehat { l } \} + \frac { 2 } { \alpha } ( y - \widehat { u } ) \mathbb { I } \{ y > \widehat { u } \} } \end{array}$ . We show in Appendix A.4 that the minimum of the expectation of the interval score is attained at the true conditional quantiles, $\hat { l } = \mathbb { Q } _ { \frac { \alpha } { 2 } } ( \cdot )$ , $\hat { u } = \mathbb { Q } _ { 1 - \frac { \alpha } { 2 } } ( \cdot )$ . We train our quantile model for all centered intervals (and hence all quantile levels) simultaneously by setting our loss as ${ \mathbb E } _ { \alpha \sim \mathrm { U n i f } ( 0 , 1 ) } S _ { \alpha }$ .
+
+# 3.4 Inducing adversarial group calibration with group batching
+
+The calibration loss (Section 3.2) and the interval score (Section 3.3) optimize for the average calibration of quantiles and centered intervals, respectively. To get closer to individual calibration, one condition we can additionally require is adversarial group calibration. Since adversarial group calibration requires average calibration over any subset of non-zero measure over the domain, this is not fully observable with finite datasets $D$ for all subset sizes. However, for any subset in $D$ with enough datapoints, we can still estimate average calibration over the subset. Hence, we can apply our optimization objectives onto appropriately large subsets to induce adversarial group calibration.
+
+In practice, this involves constructing subsets within the domain and taking gradient steps based on the loss over each subset. In naive implementations of stochastic gradient descent, a random batch is drawn uniformly from the training dataset $D$ , and a gradient step is taken according to the loss over this batch. This is also the case in SQR [58]. The uniform draw of the batch will tend to preserve $\mathbb { F } _ { \mathbf { X } }$ (the marginal distribution of $\mathbf { X }$ ), hence optimizing average calibration over this batch will only induce average calibration of the model.
+
+Instead, deliberately grouping the datapoints based on input features, and then batching and taking gradient steps based on these batches, induces better adversarial group calibration. We find in our experiments that adversarial group calibration improves significantly with simple implementations of group batching, and in Section 4.2, we show through an ablation study that group batching can improve average calibration and adversarial group calibration of SQR as well.
+
+![](images/bd4e6a74d9ec6ee06ad76783f821645f1e3ef8b5e5e28b8a1f678cfa4430b6f2.jpg)  
+Figure 2: UCI Experiments. (Top Table): Average calibration (measured by ECE) and sharpness in parentheses. The best mean ECE for each dataset has been bolded and the best mean sharpness has been underlined (all values multiplied by 100 for readability). (Bottom Figure): Adversarial group calibration for the first 5 UCI datasets (full set of results in Appendix D.1). Group size refers to proportion of test dataset size.
+
+<table><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>SQR</td><td rowspan=1 colspan=1>mPAIC</td><td rowspan=1 colspan=1>Interval</td><td rowspan=1 colspan=1>Cali</td></tr><tr><td rowspan=10 colspan=1>uoisn</td><td rowspan=1 colspan=1>aminor</td><td rowspan=1 colspan=1>5.8 ± 0.9(1.6± 0.0)</td><td rowspan=1 colspan=1>13.5 ± 0.0(5.3 ± 0.0)</td><td rowspan=1 colspan=1>3.6 ±0.7(3.7± 0.1)</td><td rowspan=1 colspan=1>2.9±0.2(2.2 ± 0.0)</td></tr><tr><td rowspan=1 colspan=1>betan</td><td rowspan=1 colspan=1>3.1 ±0.4(2.8 ± 0.1)</td><td rowspan=1 colspan=1>9.2 ± 0.4(5.5 ± 0.1)</td><td rowspan=1 colspan=1>5.1 ± 0.4(5.7± 0.3)</td><td rowspan=1 colspan=1>3.4± 0.5(3.3± 0.2)</td></tr><tr><td rowspan=1 colspan=1>dssdenest</td><td rowspan=1 colspan=1>4.4± 0.5(7.2± 0.2)</td><td rowspan=1 colspan=1>8.4±0.1(13.7± 0.1)</td><td rowspan=1 colspan=1>2.9 ± 0.3(13.3± 0.4)</td><td rowspan=1 colspan=1>4.1±0.5(8.9±0.3)</td></tr><tr><td rowspan=1 colspan=1>ip</td><td rowspan=1 colspan=1>3.2 ± 0.3(2.4 ± 0.1)</td><td rowspan=1 colspan=1>13.5 ± 0.2(9.0 ± 0.2)</td><td rowspan=1 colspan=1>4.4± 0.3(5.4± 0.1)</td><td rowspan=1 colspan=1>2.3± 0.2(3.8 ± 0.1)</td></tr><tr><td rowspan=1 colspan=1>kappa</td><td rowspan=1 colspan=1>4.4± 0.6(2.5± 0.1)</td><td rowspan=1 colspan=1>14.8 ±0.5(9.0±0.4)</td><td rowspan=1 colspan=1>4.2 ±0.4(6.1 ± 0.2)</td><td rowspan=1 colspan=1>3.6±0.2(3.4± 0.1)</td></tr><tr><td rowspan=1 colspan=1>li</td><td rowspan=1 colspan=1>4.4±0.6(1.0±0.1)</td><td rowspan=1 colspan=1>12.6± 0.6(2.7±0.1)</td><td rowspan=1 colspan=1>3.7 ± 0.6(2.2 ± 0.1)</td><td rowspan=1 colspan=1>2.9 ±0.4(1.3± 0.1)</td></tr><tr><td rowspan=1 colspan=1>R0</td><td rowspan=1 colspan=1>5.3 ± 0.8(3.3 ± 0.1)</td><td rowspan=1 colspan=1>8.7±0.4(7.2±0.3)</td><td rowspan=1 colspan=1>3.4±0.2(6.2±0.1)</td><td rowspan=1 colspan=1>3.6±0.2(4.0±0.3)</td></tr><tr><td rowspan=1 colspan=1>tribot</td><td rowspan=1 colspan=1>4.6± 0.4(2.4 ± 0.1)</td><td rowspan=1 colspan=1>15.1 ± 0.7(8.8± 0.7)</td><td rowspan=1 colspan=1>3.9 ± 0.5(6.0 ±0.2)</td><td rowspan=1 colspan=1>4.6 ± 0.5(3.0 ± 0.2)</td></tr><tr><td rowspan=1 colspan=1>tritop</td><td rowspan=1 colspan=1>5.6±0.7(2.7±0.1)</td><td rowspan=1 colspan=1>12.9±0.7(7.2 ±0.7)</td><td rowspan=1 colspan=1>3.7 ± 0.8(6.5 ± 0.4)</td><td rowspan=1 colspan=1>2.5 ± 0.3(4.4 ± 0.1)</td></tr><tr><td rowspan=1 colspan=1>volume</td><td rowspan=1 colspan=1>5.8±1.2(0.9±0.0)</td><td rowspan=1 colspan=1>16.9 ± 1.1(3.9 ± 0.4)</td><td rowspan=1 colspan=1>3.6 ± 0.3(2.0± 0.1)</td><td rowspan=1 colspan=1>2.8 ±0.1(1.2 ±0.0)</td></tr></table>
+
+![](images/da3c2dff2329190ace15eacd3307983a5b037c4488ed0574640b3caf980496c6.jpg)  
+Figure 3: Fusion Experiments. (Top Table): Average calibration (measured by ECE) and sharpness in parentheses. The best mean ECE for each dataset has been bolded and the best mean sharpness has been underlined (all values multiplied by 100 for readability). (Bottom Figure): Adversarial group calibration for the first 5 fusion datasets (full set of results in Appendix D.2). Group size refers to proportion of test dataset size.
+
+To summarize, the main idea we introduce here with group batching is that, only taking uniform batches from the training set (thus only drawing batches which preserve $\mathbb { F } _ { \mathbf { X } }$ ) can be detrimental when optimizing for calibration. Thus, additionally drawing batches based on deliberate groupings within the training set (thus, batches which do not preserve $\mathbb { F } _ { \mathbf { X } }$ ) can help to induce a stronger notion of calibration (i.e. adversarial group calibration) in the model than average calibration. This concept is quite general and allows for variations in implementations when constructing the groups. In Appendix C.3 we provide details on how we implemented group batching for our experiments and ablation study.
+
+# 4 Experiments
+
+We demonstrate the performances of our proposed methods on the standard 8 UCI datasets [2], and on a real-world problem in nuclear fusion. To assess the predictions, we use all metrics from Section 2.2 that can be estimated with a finite test dataset: 1) average calibration vs sharpness, 2) adversarial group calibration, 3) centered interval calibration, 4) check score, and 5) interval score. The results for the first two of these metrics are displayed in the main body of the paper, and the results for the other three metrics are shown in Appendix D due to space restrictions. We describe how each of these evaluation metrics are calculated in Appendix C.4.
+
+Figure 4: Group Batching Ablation: Average Calibration and Sharpness. The table shows mean ECE and sharpness (in parentheses) and their standard error with and without group batching. The best mean ECE for each dataset has been bolded and the best mean sharpness has been underlined for Cali and SQR separately. All values have been multiplied by 100 for readability.   
+
+<table><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=2>Cali</td><td rowspan=1 colspan=2>SQR</td></tr><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>RandomBatch</td><td rowspan=1 colspan=1>Group Batch</td><td rowspan=1 colspan=1>RandomBatch</td><td rowspan=1 colspan=1>Group Batch</td></tr><tr><td rowspan=1 colspan=1>Boston</td><td rowspan=1 colspan=1>9.7 ± 1.3(10.2 ± 0.7)</td><td rowspan=1 colspan=1>8.5 ± 1.5(10.9 ± 0.6)</td><td rowspan=1 colspan=1>10.9 ± 1.0(8.8 ± 1.1)</td><td rowspan=1 colspan=1>9.8 ± 1.2(9.5 ± 0.9)</td></tr><tr><td rowspan=1 colspan=1>Concrete</td><td rowspan=1 colspan=1>6.6± 0.9(17.6 ± 2.3)</td><td rowspan=1 colspan=1>5.6 ± 0.8(17.3 ± 1.5)</td><td rowspan=1 colspan=1>9.8 ± 1.3(7.0± 0.6)</td><td rowspan=1 colspan=1>7.1 ± 0.9(8.5 ± 0.6)</td></tr><tr><td rowspan=1 colspan=1>Energy</td><td rowspan=1 colspan=1>9.2± 0.3(2.8± 0.1)</td><td rowspan=1 colspan=1>5.8± 0.4(3.6±0.3)</td><td rowspan=1 colspan=1>10.2 ± 0.8(1.8 ± 0.1)</td><td rowspan=1 colspan=1>6.9±1.1(2.4±0.2)</td></tr><tr><td rowspan=1 colspan=1>Kin8nm</td><td rowspan=1 colspan=1>3.4±0.3(13.7± 0.4)</td><td rowspan=1 colspan=1>3.5±0.3(13.7±0.7)</td><td rowspan=1 colspan=1>4.7± 0.3(11.1± 0.1)</td><td rowspan=1 colspan=1>3.9±0.4(11.3± 0.2)</td></tr><tr><td rowspan=1 colspan=1>Wine</td><td rowspan=1 colspan=1>4.4± 0.5(25.6± 0.8)</td><td rowspan=1 colspan=1>4.2 ±0.4(26.0±0.8)</td><td rowspan=1 colspan=1>4.5± 0.4(29.7 ± 0.5)</td><td rowspan=1 colspan=1>4.0± 0.4(28.5 ± 0.8)</td></tr><tr><td rowspan=1 colspan=1>Yacht</td><td rowspan=1 colspan=1>11.1 ± 1.8(1.8 ± 0.1)</td><td rowspan=1 colspan=1>8.3±0.6(2.0± 0.4)</td><td rowspan=1 colspan=1>9.0 ± 0.9(0.9 ± 0.1)</td><td rowspan=1 colspan=1>8.9±0.9(2.3 ± 0.2)</td></tr><tr><td rowspan=1 colspan=1>Power</td><td rowspan=1 colspan=1>1.7 ± 0.2(14.2 ± 0.3)</td><td rowspan=1 colspan=1>2.0± 0.1(13.1± 0.1)</td><td rowspan=1 colspan=1>2.5± 0.3(14.0± 0.5)</td><td rowspan=1 colspan=1>2.9 ± 0.5(13.6± 0.8)</td></tr><tr><td rowspan=1 colspan=1>Naval</td><td rowspan=1 colspan=1>2.8± 0.2(12.1 ± 3.1)</td><td rowspan=1 colspan=1>2.4± 0.3(50.6± 8.6)</td><td rowspan=1 colspan=1>8.6 ±1.6(3.6± 0.1)</td><td rowspan=1 colspan=1>5.3± 0.8(6.0± 0.5)</td></tr></table>
+
+We provide comparisons against current state-of-the-art UQ methods for which computing the above metrics is tractable. SQR [58] is an NN model that optimizes the pinball loss for a batch of random quantile levels $p \sim \mathrm { U n i f } ( 0 , 1 )$ . mPAIC [65] is an extension of probabilistic neural networks [37, 47] that optimizes a combination of the standard Gaussian NLL and a loss that induces individual calibration. While additional quantile and PI based UQ methods exist, they are mostly designed to output a single quantile level or interval coverage level, which makes measuring calibration extremely expensive (training up to 100 models separately). For these methods, we provide a comparison on a simplified task of predicting the $9 5 \%$ PI in Appendix E.3. Lastly, we could also consider the recalibration algorithm of Kuleshov et al. [35], which is not a standalone UQ method, but a post-hoc refinement step that can be applied on top of other methods. We discuss recalibration results in Appendix E.4. All results report the mean and error across 5 trials. Error bars and shaded bands in plots indicate $\pm 1$ standard error.
+
+# 4.1 UCI and Fusion Experiments
+
+UCI datasets: We evaluate 5 methods on the 8 UCI benchmark datasets: three proposed algorithms— MAQR, Cali (combined calibration loss), and Interval (interval score)—and 2 alternative algorithms— SQR and mPAIC. Appendix C.1 includes more details on the experiment setup and hyperparameters.
+
+Fusion datasets: We further evaluate the methods on a high-dimensional task from nuclear fusion: quantifying uncertainty in plasma dynamics. Recently, there has been increasing interest in applying machine learning to prediction and control tasks in the area of nuclear fusion [11, 9, 43]. The plasma data in this paper was recorded from the DIII-D tokamak, a nuclear fusion device operated by General Atomics [39]. Plasma dynamics during fusion reactions are highly stochastic and running live fusion experiments is costly. Hence, practitioners use this dataset to learn a dynamics model of the system for various purposes, such as controller learning to optimize reaction efficiency and stability [16, 5, 6]. There are 10 scalar target signals to model in this dataset (full list in Appendix C.2), each describing a particular aspect of the current state of plasma. For each signal, the input features are 468 dimensional. We do not apply MAQR on this dataset because of the high computational costs and statistical challenge associated with nonparametric density estimation in high dimensions. Appendix C.2 provides more details on the dataset, experiment setup, and hyperparameters.
+
+Analysis of Results: Figure 2 displays average calibration-sharpness for all 8 UCI datasets and adversarial group calibration for the first 5 UCI datasets (alphabetical order). MAQR produces the best average calibrated models on 7 of the 8 UCI datasets, and adversarial group calibration also indicates that MAQR tends to achieve the lowest calibration error across any random subgroup of any size with more than one point (6 out of 8 datasets). Excluding MAQR, Interval and Cali achieve competitive average calibration and adversarial group calibration on 7 out of 8 UCI datasets. Notably, SQR tends to produce the sharpest predictions across all datasets (often at the cost of worse calibration), which is not surprising following the discussion in Section 2.2. Lastly, we also note that Interval and Cali tend to be less brittle compared to SQR and mPAIC, which incur major failures in some cases (e.g. mPAIC in Kin8nm, SQR in Naval).
+
+The fusion experiment results display a similar pattern (Figure 3). Interval and Cali achieve competitive average calibration and adversarial group calibration on 9 out of 10 fusion datasets, and SQR produces the sharpest UQ at the cost worse average and adversarial group calibration (except on betan). We also observe that mPAIC performs the poorest on the fusion datasets, with least calibrated and least sharp predictions. It is generally known that plasma dynamics display complex stochasticity [16, 34], and hence we suspect mPAIC’s performance degrades significantly because it assumes a Gaussian output and is trained according to the Gaussian likelihood.
+
+Only a subset of the plots and metrics are shown in the main paper due to space restrictions. Readers are encouraged to see the full set of results in Appendix D, but we summarize the main findings here. The check score, interval score, and centered interval calibration in the tables in Appendix D.1 also rank MAQR’s prediction as best on the UCI datasets. This is surprising since SQR and Interval train NNs of the same capacity to explicitly minimize the check and interval scores, respectively. This indicates the distribution predicted by MAQR is fundamentally different as it utilizes direct estimates of the conditional distribution, while the other methods all optimize a specific loss function. The centered interval calibration metric on the fusion datasets (Appendix D.2) indicates that Cali and Interval both produce competitive centered PI’s (9 out of 10 fusion datasets), suggesting that both methods have generally estimated the conditional quantiles better than the alternative algorithms.
+
+# 4.2 Ablation Study: Effect of Group Batching
+
+We provide an ablation study on the effect of group batching (experiment details in Appendix F.1). Figure 4 displays how group batching affects average calibration-sharpness of Cali and SQR on all 8 UCI datasets. Average calibration improved on 6 out of 8 datasets for Cali, and on 7 out of 8 datasets on SQR. While sharpness tends to worsen with group batching, it’s important to note that less sharp (i.e. more dispersed) predictions are desirable if there is high noise in the true data distribution. In Appendix F.2, we show that group batching also improves adversarial group calibration, suggesting that the underlying data distribution truly does have high noise. This study indicates that deliberately taking batches during training that do not follow $\mathbb { F } _ { \mathbf { X } }$ can improve UQ performance.
+
+# 5 Discussion
+
+In this paper, we have proposed four methods to improve quantile estimates for calibrated uncertainty quantification in regression. We assert that the pinball loss may not be an adequate objective to optimize in order to achieve calibration, and that our proposed methods provide better means of learning calibrated conditional quantiles. We have also extended the scope of regression models on which quantile-based UQ can be applied by developing a model-agnostic method. This can be of practical interest to users that have specific training infrastructure or preexisting regression procedures, since these procedures can be leveraged to quantify uncertainty without much additional overhead.
+
+By providing an extensive evaluation with a suite of metrics, we also aim to show that there is not one single metric that captures full information about the performance of a UQ procedure. Rather, a holistic review of multiple types of metrics sheds light on different aspects of performance. This point has motivated us to additionally develop and make publicly available Uncertainty Toolbox [12], a Python library for evaluation, visualization and recalibration of predictive uncertainty, which includes the full suite of metrics discussed in this work.
+
+In certain applications, users may also be concerned with modeling epistemic uncertainty. This is somewhat orthogonal to the goals of this paper; nevertheless, we provide a discussion on how bootstrapped ensembles of our methods can incorporate epistemic uncertainty in Appendix G.
+
+# Acknowledgments
+
+This work was funded in part by DOE grant number DE-SC0021414 and DE-AC02-76SF00515.
+
+Willie Neiswanger was supported in part by NSF (#1651565), ONR (N000141912145), AFOSR (FA95501910024), ARO (W911NF-21-1-0125), DOE (DE-AC02-76SF00515) and Sloan Fellowship.
+
+Ian Char was also supported by NSF grant DGE1745016. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
+
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parse/train/S1lhbnRqF7/S1lhbnRqF7.md

@@ -0,0 +1,261 @@
+# BUILDING DYNAMIC KNOWLEDGE GRAPHS FROM TEXT USING MACHINE READING COMPREHENSION
+
+Rajarshi Das∗1, Tsendsuren Munkhdalai2, Xingdi Yuan2, Adam Trischler2, Andrew McCallum
+
+1College of Information and Computer Sciences   
+University of Massachusetts, Amherst   
+{rajarshi, mccallum}@cs.umass.edu   
+2Microsoft Research Montreal ´   
+Montreal, Qu ´ ebec, Canada ´   
+{tsendsuren.munkhdalai,eric.yuan, adam.trischler}@microsoft.com
+
+# ABSTRACT
+
+We propose a neural machine reading model that constructs dynamic knowledge graphs from procedural text. It builds these graphs recurrently for each step of the described procedure, and uses them to track the evolving states of participant entities. We harness and extend a recently proposed machine reading comprehension (MRC) model to query for entity states, since these states are generally communicated in spans of text and MRC models perform well in extracting entity-centric spans. The explicit, structured, and evolving knowledge graph representations that our model constructs can be used in downstream question answering tasks to improve machine comprehension of text, as we demonstrate empirically. On two comprehension tasks from the recently proposed PROPARA dataset (Dalvi et al., 2018), our model achieves state-of-the-art results. The model also outperforms previous approaches on the RECIPES dataset (Kiddon et al., 2015), which suggests it may apply broadly to procedural text. Finally, we present some evidence that the model’s graphical representations help it to impose commonsense constraints on its predictions.
+
+# 1 INTRODUCTION
+
+Automatically building knowledge graphs (KGs) from text is a long-standing goal in artificial intelligence research. KGs organize raw information in a structured form, capturing relationships (labeled edges) between entities (nodes). They enable automated reasoning, e.g., the ability to infer unobserved facts from observed evidence and to make logical “hops,” and render data amenable to decades of work in graph analysis.
+
+There exists a profusion of text that describes complex, dynamic worlds in which entities’ relationships evolve through time. This includes news articles, scientific manuals, and procedural text (e.g., recipes, how-to guides, and so on). Building KGs from this data would not only help us to study the changing relations among participant entities, but also to make implicit information more explicit. For example, the graphs at each step in Figure 1 help us to infer that the new entity mixture is created in the leaf, since the previous location of its participant entities (light, $C O _ { 2 }$ , water) was leaf – even though this is never stated in the text.
+
+This paper introduces a neural machine-reading model, KG-MRC, that (i) explicitly constructs dynamic knowledge graphs to track state changes in procedural text and (ii) conditions on its own constructed knowledge graphs to improve downstream question answering on the text. Our dynamic graph model is recurrent, that is, the graph at each time step depends on the state of the graph at the previous time step. The constructed graphs are parameterized by real-valued embeddings for each node that change through time.
+
+In text, entities and their states (e.g., their locations) are given by spans of words. Because of the variety of natural language, the same entity/state may be described with several surface forms. To
+
+Chloroplast in leaf of the plant trap light from the sun. The root absorbs minerals from the soil. This combination of water and minerals flows from the stem into the leaf. Carbon dioxide enters the leaf. Light, water and minerals, and the carbon dioxide all combine into a mixture. This mixture forms sugar (glucose) which is what the plant eats.
+
+![](images/f75f36db041dfe1a0ac8b779a083af6c2880f85c4d21e93bff636bc407f60c51.jpg)  
+Figure 1: Snapshot of the knowledge graphs created by our model before and after reading the sentence in boldface. Since the KG explicitly stores the current location of light, $C O _ { 2 }$ , and water as leaf, the model can infer that mixture is formed in the leaf even though this is not explicitly stated. The three participant entities also get destroyed in the process, which is captured in the graph by pointing to a special Nowhere node.
+
+address the challenge of entity/state recognition, our model uses a machine reading comprehension (MRC) mechanism (Seo et al., 2017a; Xiong et al., 2017; Chen et al., 2017; Yu et al., 2018, inter alia), which queries for entities and their states at each time step. We leverage MRC mechanisms because they have proven adept at extracting text spans that answer entity-centric questions (Levy et al., 2017). However, such models are static by design, returning the same answer for the same query and context. Since we expect answers about entity states to change over the course of the text, our model’s MRC component conditions on the evolving graph at the current time step (this graph captures the instantaneous states of entities).
+
+To address the challenge of aliased text mentions, our model performs soft co-reference as it updates the graph. Instead of adding an alias node, like the leaf or leaves as aliases for leaf, the graph update procedure soft-attends (Bahdanau et al., 2014) over all nodes at the previous time step and performs a gated update (Cho et al., 2014; Chung et al., 2014) of the current embeddings with the previous ones. This ensures that state information is preserved and propagated across time steps. Soft coreference can also handle the case that entity states do not change across time steps, by applying a near-null update to the existing state node rather than duplicating it.
+
+At each time step, after the graph has been updated with the (possibly) new states of all entities, our model updates each entity representation with information about its state. The updated information about each individual entity is further propagated to all other entities $( \ S 4 . 4 )$ . This enables the model to recognize, for example, that entities are present in the same location (e.g., light, $C O _ { 2 }$ and water in Figure 1). Thus, our model can use the information encoded in its internal knowledge graphs for a more comprehensive understanding of the text. We will demonstrate this experimentally by tackling comprehension tasks from the the recently released PROPARA and RECIPES datasets.
+
+Our complete machine reading model, which both builds and leverages dynamic knowledge graphs, can be trained end-to-end using only the loss from its MRC component; i.e., the negative loglikelihood that the MRC component assigns to the span that correctly describes each entity’s queried state. We evaluate our model (KG-MRC) on the above two PROPARA tasks and find that the same model significantly outperforms the previous state of the art. For example, KG-MRC obtains a $9 . 9 2 \%$ relative improvement on the hard task of predicting at which time-step an entity moves. Similarly on the latter task, KG-MRC obtains a $5 . 7 \%$ relative improvement over PROSTRUCT and $41 \%$ relative improvement over other entity-centric models such as ENTNET (Henaff et al., 2017). The same model also obtains state-of-the-art performance on the RECIPES dataset.
+
+# 2 RELATED WORK
+
+There are few datasets that address the challenging problem of tracking entity state changes. The bAbI dataset (Weston et al., 2015) includes questions about movement of entities; however, its language is generated synthetically over a small lexicon, and hence models trained on bAbI often do not generalize well when tested on real-world data. For example, state-of-the-art models like ENTNET (Henaff et al., 2017) and Query Reduction Networks (Seo et al., 2017b) fail to perform well on PROPARA.
+
+PROREAD (Berant et al., 2014) introduced the PROCESSBANK dataset, which contains paragraphs of procedural text as in PROPARA. However, this earlier task involves mining arguments and relations from events, not tracking the dynamic state changes of entities. The model that Berant et al. (2014) propose builds small knowledge graphs from the text, but they are not dynamic in nature. The model also relies on densely annotated process structure for training, demanding curation by domain experts. On the other hand, our model, KG-MRC, learns to build dynamic KGs just from annotations of text spans, which are much easier to collect.
+
+For the sentence-level PROPARA task they propose, Dalvi et al. (2018) introduce two models: PROLOCAL and PROGLOBAL. PROLOCAL makes local predictions about entities by considering just the current sentence. This is followed by some heuristic/rule-based answer propagation. PROGLOBAL considers a broader context (previous sentences) and also includes the previous state of entities by considering the probability distribution over paragraph tokens in the previous step. Tandon et al. (2018) recently proposed a neural structured-prediction model, (PROSTRUCT), where hard and soft common-sense constraints are injected to steer their model away from globally incoherent predictions. We evaluate KG-MRC on the two PROPARA tasks proposed by Dalvi et al. (2018) and Tandon et al. (2018), respectively, and find that our single model outperforms each of the above models on their respective tasks of focus.
+
+ENTNET (Henaff et al., 2017) and query reduction networks (QRN) (Seo et al., 2017b) are two state-of-the-art entity-centric models for the bAbI dataset. ENTNET maintains a dynamic memory of hidden states with a gated update to the memory slots at each step. Memory slots can be tied to specific entities, but unlike our model, ENTNET does not maintain separate embeddings of individual states (e.g., current locations); it also does not perform explicit co-reference updates. QRN refines the query vector as it processes each subsequent sentence until the query points to the answer, but does not maintain explicit representations of entity states. Neural Process Networks (NPN) (Bosselut et al., 2018) learn to understand procedural text by explicitly parameterizing actions and composing them with entities. These three models return an answer by predicting a vocabulary item in a multi-class classification setup, while in our work we predict spans of text directly from the paragraph.
+
+MRC models have been used previously for extracting the argument of knowledge base (KB) relations, by associating one or more natural language questions with each relation (querification). These models have been shown to perform well in a zero-shot setting, i.e., for a previously unseen relation type (Levy et al., 2017), and for extracting entities that belong to non-standard types (Roth et al., 2018). These recent positive results motivate our use of an MRC component in KG-MRC.
+
+# 3 DATA & TASKS
+
+We evaluate KG-MRC on the recently released PROPARA dataset (Dalvi et al., 2018), which comprises procedural text about scientific processes. The location states of participant entities at each time step (sentence) in these processes are labeled by human annotators, and the names of participant entities are given. As an example, for a process describing photosynthesis, the participant entities provided are: light, $C O _ { 2 }$ , water, mixture and glucose. Although participant entities are thus known a priori, the location of an entity could be any arbitrary span in the process text. This makes the task of determining and tracking an entity’s changing location quite challenging.
+
+It should also be noted that the dataset does not provide information on whether a particular entity is an input to or output of a process. Not all entities exist from the beginning of the process (e.g. glucose) and not all exist at the end (e.g. water). Table 1 shows statistics of PROPARA. As can be seen, the training set is small, which makes learning challenging.
+
+Table 1: Statistics of PROPARA.   
+
+<table><tr><td># para</td><td>488</td></tr><tr><td># train/#dev/#test</td><td>391/43/54</td></tr><tr><td>avg.#entities</td><td>4.17</td></tr><tr><td>avg. # sentences</td><td>6.7</td></tr><tr><td># sentences</td><td>3.3K</td></tr></table>
+
+Along with the dataset, Dalvi et al. (2018) introduce the task of tracking state changes at a fine-grained sentence level. To solve this task, a model must answer three categories of questions (10 questions in total) about an entity $E$ : (1) Is $E$ created, (destroyed, moved) in the process? (2) When (step #) is $E$ created, (destroyed, moved)? (3) Where is $E$ created, (destroyed, moved from/to)? Cat. 1 asks boolean questions about the existence and movement of entities. Cat. 2 and 3 are harder tasks, as the model must correctly predict the step number at which a state changes as well as the correct locations (text spans) of entities at each step.
+
+Tandon et al. (2018) introduce a second task on the PROPARA dataset that measures state changes at a coarser process level. To solve this task, a model must correctly answer the following four types of questions: (1) What are the inputs to the process? (2) What are the outputs of the process? (3) What conversions occur, when and where? (4) What movements occur, when and where? Inputs to a process are defined as entities that exist at the start of the process but not at the end and outputs are entities that exist at the end of the process and were created during it. A conversion is when some entities are created and others destroyed, while movements refer to changes in location. Dalvi et al. (2018) and Tandon et al. (2018) propose different models to solve each of these tasks separately, whereas we evaluate the same model, KG-MRC, on both tasks.
+
+Bosselut et al. (2018) recently released the RECIPES dataset, which has various annotated states (e.g. shape, composition, location, etc.) for ingredients in cooking recipes. We further test KG-MRC on the location task to align with our PROPARA experiments. This is arguably the dataset’s hardest task, since it requires classification over more than 260 classes while the others have a much smaller label space (maximum of 4). Note that rather than treating this problem as classification over a fixed lexicon as in previous models, our model aims to find the location-describing span of text in the recipe paragraph.
+
+# 4 MODEL
+
+KG-MRC tracks the temporal state change of entities in procedural text. Naturally, the model is entity-centric (Henaff et al., 2017; Bansal et al., 2017): it associates each participant entity of the procedural text with a unique node and embedding in its internal graph. KG-MRC is also equipped with a neural machine reading comprehension model which is queried about the current location of each entity.
+
+At a high level, the model operates as follows. We summarize some important notation in Table 2. KG-MRC takes as input a paragraph $p = \{ w _ { j } \} _ { j = 1 } ^ { P } = \{ s _ { t } \} _ { t = 1 } ^ { T }$ , consisting of $P$ tokens spread across $T$ sentences. The model reads this paragraph incrementally. Specifically, at each time step (sentence) $t$ , the model reads the paragraph prefix comprising all sentences up to and including $s _ { t }$ . We then engage the MRC module to query for the state of each participant entity (these participants are known in PROPARA a priori and we index them with $i$ ). The querying process conditions on both the input text and the constructed knowledge graph from the previous time step. In response to a query, the MRC module returns a span from the text that describes the ith entity’s location at $t$ . We encode this into a vector representation. Finally, conditioning on the span vectors for all entities, the model constructs the graph $G _ { t }$ by updating graph $G _ { t - 1 }$ from the previous time step.
+
+The model’s knowledge graphs $G _ { t }$ are bipartite, having two sets of nodes with implied connections between them: $G _ { t } = \{ \bar { e } _ { i , t } , \bar { \lambda } _ { i , t } \}$ . Each node denotes either an entity $( e _ { i , t } )$ or that entity’s corresponding location $( \lambda _ { i , t } )$ , and is associated with a real-valued vector. We use $e _ { i , t }$ and $\lambda _ { i , t }$ to denote nodes in the graph and their vector representations interchangeably. The bipartite graphs $G _ { t }$ have only one (implicit) relation type, the current location, though we plan to extend this in future work. To derive $G _ { t }$ from its previous iterate $G _ { t - 1 }$ , we combine both hard and soft graph updates. The update to an entity’s node representation with new location information arises from a hard decision made by the MRC model, whereas co-reference between entities across time steps is resolved with soft attention. We now describe all components of the model in detail.
+
+# 4.1 ENTITY AND SPAN REPRESENTATIONS
+
+In the PROPARA dataset, entities appear in the paragraph text.1 Therefore, we derive the initial entity representations from contextualized hidden vectors by encoding the paragraph with a bi-directional LSTM (Hochreiter & Schmidhuber, 1997). This choice has the added advantage that initial entity representations share information through context, unlike in previous models (Henaff et al., 2017; Das et al., 2017; Bansal et al., 2017). Entities in the dataset can be multi-word expressions (e.g., electric oven). To obtain a single representation, we concatenate the contextualized hidden vectors corresponding to the start and end span tokens and take a linear projection. i.e., if the mention of entity $i$ occurs between the $j$ -th and $j + k$ -th position, then the initial entity representation $\nu _ { i }$ is computed as $\mathbf { v } _ { i } = W _ { e } [ c _ { j } ; c _ { j + k } ] + b _ { e }$ . We use $i$ to index an entity and its corresponding location, while $c _ { j }$ represents the contextualized hidden vectors for token $j$ and $[ ; ]$ represents the concatenate operation. An entity may occur multiple times within a paragraph. We give equal importance to all occurrences by summing the representations for each.
+
+Table 2: Symbols used in Section 4. The text-based representations of entities and locations are derived from the hidden representations of the context-RNN $( \ S 4 . 1 )$ . The node representations are added to the graph $G _ { t }$ at the end of time step t (§ 4.4).   
+
+<table><tr><td>Notation</td><td>Meaning</td></tr><tr><td>NEN</td><td>Number of participant entities in the process.</td></tr><tr><td>Vi∈Rd</td><td>Initial entity representation,derived from the text,for the i-th entity at time t = O(§ 4.1)</td></tr><tr><td>ei,tERd</td><td>Entity node representation for the i-th entity at time t,in the graph Gt (§ 4.4)</td></tr><tr><td>YitERd</td><td>Location representation derived from the text for the i-th entity at time t (§ 4.1)</td></tr><tr><td>2iERd</td><td>Location node representation for the i-th entity at time t,in the graph Gt (8 4.3,4.4)</td></tr><tr><td>A∈RNxd</td><td>Matrix of all location node representations at time t. (Essentially all λi,t stacked row-wise at t)</td></tr><tr><td>UERNXN</td><td>Soft co-reference matrix at time step t (§ 4.3)</td></tr></table>
+
+When queried about the current location of an entity, the MRC module $( \ S 4 . 2 )$ returns a span of text as the answer, whose representation is later used to update the appropriate node vector in the graph. We obtain this answer-span representation analogously as above, and denote it with $\Psi _ { i , t }$ .
+
+# 4.2 MACHINE READING COMPREHENSION MODEL
+
+Rather than design a specialized MRC architecture, we make simple extensions to a widely used model – DRQA (Chen et al., 2017) – to adapt it to query about the evolving states of entities. In summary, our modified DRQA implementation operates on prefixes of sentences rather than the full paragraph (like PROGLOBAL), and at each sentence (time step) it conditions on both the current sentence representation $s _ { t }$ and the dynamic entity representations in $G _ { t - 1 }$ .
+
+For complete details of the DRQA model, we refer readers to the original publication (Chen et al., 2017). Broadly, it uses a multi-layer recurrent neural network (RNN) architecture for encoding both the passage and question text and uses self-attention to match these two encodings. For each token $j$ in the text, it outputs a score indicating its likelihood of being the start or end of the span that answers the question. We reuse all of these operations in our model, modified as described below.
+
+We query the DRQA model about the state of each participant entity at each time step $t$ . This involves reading the paragraph up to and including sentence $s _ { t }$ . To query, we generate simple natural language questions for an entity, $E$ , such as “Where is $E$ located?” This is motivated by the work of Levy et al. (2017). Our DRQA component also conditions on entities. Recall that vector $e _ { i , t - 1 }$ denotes the entity’s representation in the knowledge graph $G _ { t - 1 }$ . The module conditions on $e _ { i , t - 1 }$ in its output layer, basically the same way as the question representation is used in the output alignment step in Chen et al. (2017). However, instead of taking a bi-linear map between the question and passage representations as in that work, we first concatenate the question representation with $e _ { i , t - 1 }$ and pass the concatenation through a 2-layer MLP. This yields an entity-dependent question representation. We use this to compute the output start and end scores for each token position, taking the argmax to obtain the most likely span. As mentioned, we encode this span as vector $\Psi _ { i , t }$ $( \ S 4 . 1 )$ .
+
+The PROPARA dataset includes two special locations that don’t appear as text spans: nowhere and somewhere. The current location of an entity is nowhere when the entity does not exist yet or has been destroyed, whereas it is somewhere when the entity exists but its location is unknown from the text. Since these locations don’t appear as tokens in the text, the span-predictive MRC module cannot extract them. Following Dalvi et al. (2018), we address this with a separate classifier that predicts, given a graph entity node and the text, whether the entity represented by the node is nowhere, somewhere, or its location is stated. We learn the location-node representations for nowhere and somewhere during training.
+
+# 4.3 SOFT CO-REFERENCE
+
+To handle cases when entity states do not change and when states are referred to with different surface forms (either of which could lead to undesired node duplication), our model uses soft co
+
+![](images/4b16542539584ac4ac3986a665ab29d520ceb59df28c94712d538115a8660dc2.jpg)  
+Knowledge graph at time (t-1)   
+Figure 2: Soft co-reference across time steps. The sentence at the current time step is highlighted. When the MRC model predicts a span (leaf ) present in the graph at the previous time step, KG-MRC does soft attention and a gated update to preserve information across time steps $( \ S 4 . 3 )$ . The thicker arrow shows higher attention weight between the old and new node.
+
+reference mechanisms (Figure 2) both across and within time steps. Disambiguation across time steps is accomplished by attention and a gated update, using the incoming location vector $\Psi _ { i , t }$ and the location node representations from the previous time step:
+
+$$
+\begin{array} { r l } & { a _ { i , t } = \operatorname { s o f t m a x } ( \Lambda _ { t - 1 } \Psi _ { i , t } ) } \\ & { \Psi _ { i , t } ^ { \prime } = \Lambda _ { t - 1 } ^ { \top } a _ { i , t } } \\ & { g _ { i } = \operatorname { s i g m o i d } ( W _ { i } [ \Psi _ { i , t } ^ { \prime } ; \Psi _ { i , t } ] + b _ { i } ) } \\ & { \lambda _ { i , t } ^ { \prime } = g _ { i } \Psi _ { i , t } + ( 1 - g _ { i } ) \Psi _ { i , t } ^ { \prime } , } \end{array}
+$$
+
+where $\Lambda _ { t - 1 } = [ \lambda _ { i , t } ] _ { i = 1 } ^ { N } \in \mathbb { R } ^ { N \times d }$ is a matrix of location node representations from the previous time step (stacked row-wise) and $\Psi _ { i , t }$ is the location span vector output by the MRC module. The result vector $\lambda _ { i , t } ^ { \prime }$ is a disambiguated intermediate node representation.
+
+This process only partially addresses node de-duplication. Since different instances of the same location can be predicted for multiple entities, we also perform a co-reference disambiguation within each time step using a self-attention mechanism:
+
+$$
+\begin{array} { r l } & { u _ { i , t } = \mathrm { s o f t m a x } ( \Lambda _ { t } ^ { \prime } \lambda _ { i , t } ^ { \prime } ) } \\ & { { \lambda _ { i , t } } = { \Lambda _ { t } ^ { \prime } } ^ { \top } u _ { i , t } , } \end{array}
+$$
+
+where $\Lambda _ { t } ^ { \prime } = [ \lambda _ { i , t } ^ { \prime } ] _ { i = 1 } ^ { N } \in \mathbb { R } ^ { N \times d }$ is a matrix of intermediate node representations (stacked row-wise) and $U _ { t } = [ u _ { i , t } ] _ { i = 1 } ^ { N } \in \mathbb { R } ^ { N \times N }$ is a co-reference adjacency matrix. We calculate this adjacency matrix at the beginning of each time step to track related nodes within $t$ , and re-use it in the graph update step.
+
+# 4.4 GRAPH UPDATE
+
+The graph update proceeds according to the following set of equations for each update layer $l$
+
+$$
+\begin{array} { r l } & { { h } _ { i , t } ^ { l } = \mathrm { L S T M } ( [ e _ { i , t } ^ { l - 1 } ; \lambda _ { i , t } ^ { l - 1 } ; h _ { i , t - 1 } ^ { l } ] ) } \\ & { e _ { i , t } ^ { l } = e _ { i , t } ^ { l - 1 } + h _ { i , t } ^ { l } } \\ & { \tilde { \lambda } _ { i , t } ^ { l } = \lambda _ { i , t } ^ { l - 1 } + h _ { i , t } ^ { l } } \\ & { \lambda _ { i , t } ^ { l } = \tilde { \Lambda } _ { t } ^ { l \top } u _ { i , t } . } \end{array}
+$$
+
+We first compose all connected entity and location nodes with their history summary, $h _ { i , t - 1 } ^ { l }$ , using an LSTM unit. Next, the updated node information is attached to the entity and location representations through two residual updates (He et al., 2016). These propagate information between the entity and location representations; i.e., if two entities are at the same location, then the corresponding entity representations will receive a similar update. Likewise, location representations are updated with pertinent entity information. Last, we perform another co-reference pooling operation for the location nodes. After the recurrent and residual graph updates, information propagation may yield different, diverging representations for nodes that belong to the same location. This final pooling operation corrects for this, by tying the co-referent representations in a soft way. It uses the previously computed adjacency matrix $U _ { t }$ and $\tilde { \Lambda } _ { t } ^ { l }$ , which is a row-wise stacked matrix of the $\tilde { \lambda } _ { i , t } ^ { l }$ .
+
+The recurrent graph module stacks $L$ such layers to propagate node information along the graph’s edges. The resulting node representations are $\dot { e } _ { i , t } ^ { L }$ and $\bar { \lambda } _ { i , t } ^ { L }$ for each participant entity and its location. We use $e _ { i , t } = e _ { i , t } ^ { L }$ to condition the MRC model, as described in $\ S 4 . 2$ . We make use of this particular graph module structure, rather than adopting an existing model like GraphCNNs (Edwards & Xie, 2016; Kipf & Welling, 2017), because recurrent networks are designed to propagate information through time.
+
+# 4.5 TRAINING
+
+The full KG-MRC model is trained end-to-end by minimizing the negative log-likelihood of the correct span tokens under the MRC module’s output distribution and the textual entailment model. This is a fairly soft supervision signal, since we do not train the graph construction modules directly. We teacher-force the model at training time by updating the location-node representations with the encoding of the correct span. We do not pretrain the MRC module, but we represent paragraph tokens with pretrained FastText embeddings (Joulin et al., 2016). See the appendix A for full implementation and training details.
+
+# 5 EXPERIMENTS AND DISCUSSION
+
+We evaluate our model on three different tasks. We also provide an ablation study along with quantitative and qualitative analyses to highlight the performance contributions of each module.
+
+# 5.1 RESULTS ON PROCEDURAL TEXT
+
+We benchmarked our model on two PROPARA comprehension tasks introduced respectively in Dalvi et al. (2018) and Tandon et al. (2018). Refer to Section 3 for a detailed description about the data and tasks. Dalvi et al. (2018) and Tandon et al. (2018) respectively introduce a specific model for each task, whereas we test KG-MRC on both tasks. A primary motivation for building KGs is because they can be queried for salient knowledge in downstream applications. We evaluate KG-MRC on the above two tasks by querying the KGs it builds at each time-step; we use the official evaluation pipeline2 for each task. In results below, we report an average score of three runs of our model with different hyperparameter settings.
+
+# 5.1.1 TASK 1: SENTENCE-LEVEL EVALUATION
+
+Table 3 shows our main results on the first task. Following the original task evaluation, we report model accuracy on each subtask category and macro and micro averages over the subtasks.
+
+Human performance is $7 9 . 6 9 \%$ , micro-average. A state-of-the-art memory augmented network, ENTNET (Henaff et al., 2017), which is built to track entities but lacks an explicit graph structure, achieves $2 5 . 9 6 \%$ . The previous best performing model is PROGLOBAL, which achieves $4 5 . 3 7 \%$ . Our KG-MRC improves over this result by $1 . 2 5 \%$ absolute score in terms of micro-averaged accuracy. Comparing various models for each subtask category, PROGLOBAL leads in Category 1 by a small margin of around $0 . 1 \%$ . For the more challenging Categories 2 and 3, KG-MRC outperforms PROGLOBAL by a large margin. These questions require fine-grained predictions of state changes.
+
+Table 3: Task 1 results (accuracy).   
+
+<table><tr><td></td><td>Cat1</td><td>Cat2</td><td>Cat 3</td><td>Macro-avg</td><td>Micro-avg</td></tr><tr><td>Human upper bound</td><td>91.67</td><td>87.66</td><td>62.96</td><td>80.76</td><td>79.69</td></tr><tr><td>Majority</td><td>51.01</td><td>1</td><td>1</td><td>1</td><td>1</td></tr><tr><td>Rule based</td><td>57.14</td><td>20.33</td><td>2.40</td><td>26.62</td><td>26.24</td></tr><tr><td>Feature based</td><td>58.64</td><td>20.82</td><td>9.66</td><td>29.7</td><td>29.64</td></tr><tr><td>EntNet (Henaff et al.(2017))</td><td>51.62</td><td>18.83</td><td>7.77</td><td>26.07</td><td>25.96</td></tr><tr><td>Pro-Local (Dalvi et al. (2018))</td><td>62.65</td><td>30.50</td><td>10.35</td><td>34.50</td><td>33.96</td></tr><tr><td>Pro-Global (Dalvi et al.(2018))</td><td>62.95</td><td>36.39</td><td>35.90</td><td>45.08</td><td>45.37</td></tr><tr><td>KG-MRC (ours)</td><td>62.86</td><td>40.00</td><td>38.23</td><td>47.03</td><td>46.62</td></tr></table>
+
+# 5.1.2 TASK 2: DOCUMENT-LEVEL EVALUATION
+
+We report the performance of our model on the document-level task, along with previously published results, in Table 4. The same KG-MRC model achieves $3 . 0 2 \%$ absolute improvement in $\mathrm { F } _ { 1 }$ over the previous best result of PROSTRUCT. PROSTRUCT incorporates a set of commonsense constraints for globally consistent predictions. We analyzed KG-MRC’s outputs and were surprised to discover that our model learns these commonsense constraints from the data in an end-to-end fashion, as we show quantitatively in $\ S 5 . 4$ .
+
+Table 4: Task 2 results.   
+
+<table><tr><td></td><td>Precision</td><td>Recall</td><td>F1</td></tr><tr><td>Pro-Local (Dalvi et al.(2018))</td><td>77.4</td><td>22.9</td><td>35.3</td></tr><tr><td>QRN (Seo et al. (2017b))</td><td>55.5</td><td>31.3</td><td>40.0</td></tr><tr><td>EntNet (Henaff et al. (2017))</td><td>50.2</td><td>33.5</td><td>40.2</td></tr><tr><td>Pro-Global (Dalvi et al.(2018))</td><td>46.7</td><td>52.4</td><td>49.4</td></tr><tr><td>Pro-Struct (Tandon et al. (2018))</td><td>74.2</td><td>42.1</td><td>53.75</td></tr><tr><td>KG-MRC (ours)</td><td>64.52</td><td>50.68</td><td>56.77</td></tr></table>
+
+# 5.2 RECIPE DESCRIPTION EXPERIMENTS
+
+We also evaluate our model on the RECIPES dataset, for which we predict the evolving locations of cooking ingredients. In the original work of Bosselut et al. (2018), they treat this problem as classification over a fixed lexicon of locations. KG-MRC searches for the correct location span in the text. On this task, our model outperforms the baseline NPN model by a significant margin, achieving a score of $5 4 . 2 7 \%$ $\mathrm { F } _ { 1 }$ compared to NPN’s $5 1 . 2 8 \% \mathrm { F } _ { 1 }$ . On further analysis of the results, we found several cases where our model was wrongly penalized, e.g., for predicting the span “saucepan” when the ground truth class label was “pan.” We believe that our results would improve further if we mapped our predicted spans to the ground truth class labels.
+
+# 5.3 ABLATION STUDY
+
+We performed an ablation study to evaluate different model variations on PROPARA Task 1. The main results are reported in Table 5. Removing the soft co-reference disambiguation within time steps (Equations 2) from KG-MRC resulted in around $1 \%$ performance drop. The drop is more significant when the co-reference disambiguation across time steps (Equations 1) is removed.
+
+We also replaced the recurrent graph module with the standard LSTM unit and used the LSTM hidden state for the entity representation. Because this model variant does not propagate information across graph nodes (the final step in Equations 3), we observed a large performance decrease.
+
+For the last two variations, we simply train the MRC model in isolation and predict location spans from the current sentence or paragraph prefix text (i.e., the current and all previous sentences). These models construct no internal knowledge graphs. We can see that training the MRC model on paragraph prefixes already provides a good starting performance of $4 0 . 8 3 \%$ micro-average, which is significantly boosted by the recurrent graph module and graph conditioning up to $4 7 . 6 4 \%$ .
+
+Table 5: Ablation experiment results   
+
+<table><tr><td></td><td>Cat1</td><td>Cat2</td><td>Cat 3</td><td>Macro-avg</td><td>Micro-avg</td></tr><tr><td>KG-MRC</td><td>58.55</td><td>38.52</td><td>42.22</td><td>46.43</td><td>47.64</td></tr><tr><td>- Coref across time steps</td><td>61.07</td><td>37.38</td><td>35.58</td><td>44.68</td><td>46.32</td></tr><tr><td>-Coref within time step</td><td>57.88</td><td>38.09</td><td>40.19</td><td>45.39</td><td>46.63</td></tr><tr><td>- Coref in the graph-update step</td><td>60.91</td><td>34.71</td><td>32.34</td><td>42.65</td><td>44.48</td></tr><tr><td>Standard LSTM as graph unit</td><td>56.84</td><td>13.15</td><td>10.95</td><td>26.98</td><td>29.97</td></tr><tr><td>MRC on entire paragraph</td><td>58.85</td><td>21.82</td><td>26.52</td><td>35.73</td><td>35.98</td></tr><tr><td>MRC on prefix</td><td>61.28</td><td>32.58</td><td>29.48</td><td>41.11</td><td>40.83</td></tr></table>
+
+# 5.4 COMMONSENSE CONSTRAINTS
+
+For accurate, globally consistent predictions on the second PROPARA task, Tandon et al. (2018) introduced a set of commonsense constraints that they impose on their model in a pruning stage. Stated in natural language, these constraints are: 1) An entity must exist before it can be moved or destroyed; 2) An entity cannot be created if it already exists; 3) An entity cannot change until it is mentioned in the paragraph.
+
+To analyze whether our model can learn these constraints directly from data, we count the number of model predictions that violate constraints on the test set. To our surprise, this demonstrates that KGMRC learns to violate fewer constraints (proportionally) than PROSTRUCT, even without explicitly training it to do so. In more detail, we find that KG-MRC, like PROSTRUCT, does not violate any Type 1 or Type 2 constraints. In Table 6 we compare several models in terms of Type 3 constraint violations. Note that we only count instances where a model predicts an entity state change.
+
+Table 6: Commonsense constraint violations.   
+
+<table><tr><td>Model</td><td>State Change Predictions</td><td>Violations</td><td>Violation Proportion (%)</td></tr><tr><td>PROSTRUCT (Tandon et al. (2018))</td><td>270</td><td>17</td><td>6.30</td></tr><tr><td>MRC on entire paragraph</td><td>381</td><td>104</td><td>27.30</td></tr><tr><td>MRC on prefix</td><td>703</td><td>154</td><td>21.93</td></tr><tr><td>Standard LSTM as graph unit</td><td>447</td><td>20</td><td>4.47</td></tr><tr><td>KG-MRC</td><td>466</td><td>19</td><td>4.08</td></tr></table>
+
+As shown, KG-MRC makes fewer Type 3 violations that PROSTRUCT. Furthermore, MRC models without recurrent graph modules perform worse in terms of constraint violations than both KGMRC and a model using a standard LSTM as its graph unit. This suggests that recurrent graphical representations play an important role in helping the model to learn and adhere to the constraints.
+
+# 5.5 QUALITATIVE ANALYSIS
+
+We picked an example from the test data and took a closer look at the model outputs to investigate how KG-MRC dynamically adjusts its decisions via the dynamic graph module and finds accurate spans with the conditional MRC model. The step-by-step output of both PROGLOBAL (Dalvi et al. (2018)) and KG-MRC is shown in Table 7, where we track the state of entity blood across six sentences. KG-MRC outputs smoother and more accurate predictions.
+
+<table><tr><td>Sentences</td><td colspan="2">Location of entities after each sentence</td></tr><tr><td>(Before first sentence)</td><td>somewhere</td><td>somewhere</td></tr><tr><td>Blood enters the right side of your heart.</td><td>heart</td><td>right side of your heart</td></tr><tr><td>Blood travels to the lungs.</td><td>lung</td><td>lungs</td></tr><tr><td>Carbon dioxide is removed from the blood.</td><td>blood</td><td>lungs</td></tr><tr><td>Oxygen is added to your blood.</td><td>lung</td><td>lungs</td></tr><tr><td>Blood returns to left side of your heart.</td><td>blood</td><td>heart</td></tr><tr><td>The blood travels through the body.</td><td>body</td><td>body</td></tr></table>
+
+Table 7: Two models’ predictions of entity locations, on randomly selected paragraph about blood circulation. In this example the entity is blood. Predicted results from Pro-Local (Dalvi et al. (2018)) are in orange, results from KG-MRC are in red, important locations in paragraph are in blue.
+
+# 6 CONCLUSION
+
+We proposed a neural machine-reading model that constructs dynamic knowledge graphs from text to track locations of participant entities in procedural text. It further uses these graphical representations to improve its downstream comprehension of text. Our model, KG-MRC, achieves state-of-theart results on two question-answering tasks from the PROPARA dataset and one from the RECIPES dataset. In future work, we will extend the model to construct more general knowledge graphs with multiple relation types.
+
+# REFERENCES
+
+Dzmitry Bahdanau, Kyunghyun Cho, and Yoshua Bengio. Neural machine translation by jointly learning to align and translate. arXiv preprint arXiv:1409.0473, 2014.
+
+Trapit Bansal, Arvind Neelakantan, and Andrew McCallum. Relnet: End-to-end modeling of entities & relations. In AKBC, NIPS, 2017.
+
+Jonathan Berant, Vivek Srikumar, Pei-Chun Chen, Abby Vander Linden, Brittany Harding, Brad Huang, Peter Clark, and Christopher D Manning. Modeling biological processes for reading comprehension. In EMNLP, 2014.
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+Antoine Bosselut, Omer Levy, Ari Holtzman, Corin Ennis, Dieter Fox, and Yejin Choi. Simulating action dynamics with neural process networks. In ICLR, 2018.
+
+Danqi Chen, Adam Fisch, Jason Weston, and Antoine Bordes. Reading wikipedia to answer opendomain questions. In ACL, 2017.
+
+Kyunghyun Cho, Bart Van Merrienboer, Caglar Gulcehre, Dzmitry Bahdanau, Fethi Bougares, Hol- ¨ ger Schwenk, and Yoshua Bengio. Learning phrase representations using rnn encoder-decoder for statistical machine translation. arXiv preprint arXiv:1406.1078, 2014.
+
+Junyoung Chung, Caglar Gulcehre, KyungHyun Cho, and Yoshua Bengio. Empirical evaluation of gated recurrent neural networks on sequence modeling. arXiv preprint arXiv:1412.3555, 2014.
+
+Bhavana Dalvi, Lifu Huang, Niket Tandon, Wen-tau Yih, and Peter Clark. Tracking state changes in procedural text: a challenge dataset and models for process paragraph comprehension. In NAACL, 2018.
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+Rajarshi Das, Manzil Zaheer, Siva Reddy, and Andrew McCallum. Question answering on knowledge bases and text using universal schema and memory networks. In ACL, 2017.
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+Michael Edwards and Xianghua Xie. Graph based convolutional neural network. arXiv preprint arXiv:1609.08965, 2016.
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+Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 770–778, 2016.
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+Mikael Henaff, Jason Weston, Arthur Szlam, Antoine Bordes, and Yann LeCun. Tracking the world state with recurrent entity networks. In ICLR, 2017.
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+Sepp Hochreiter and Jurgen Schmidhuber. Long short-term memory. ¨ Neural computation, 1997.
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+Armand Joulin, Edouard Grave, Piotr Bojanowski, Matthijs Douze, Herve J ´ egou, and Tomas ´ Mikolov. Fasttext.zip: Compressing text classification models. arXiv preprint arXiv:1612.03651, 2016.
+
+Chloe Kiddon, Ganesa Thandavam Ponnuraj, Luke Zettlemoyer, and Yejin Choi. Mise en place:´ Unsupervised interpretation of instructional recipes. In EMNLP, 2015.
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+Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014.
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+Thomas N Kipf and Max Welling. Semi-supervised classification with graph convolutional networks. In ICLR, 2017.
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+Omer Levy, Minjoon Seo, Eunsol Choi, and Luke S. Zettlemoyer. Zero-shot relation extraction via reading comprehension. In CoNLL, 2017.
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+Adam Paszke, Sam Gross, Soumith Chintala, Gregory Chanan, Edward Yang, Zachary DeVito, Zeming Lin, Alban Desmaison, Luca Antiga, and Adam Lerer. Automatic differentiation in pytorch. In NIPS-W, 2017.
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+Benjamin Roth, Costanza Conforti, Nina Poerner, Sanjeev Karn, and Hinrich Schutze. Neural ar- ¨ chitectures for open-type relation argument extraction. arXiv preprint arXiv:1803.01707, 2018.
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+Niket Tandon, Bhavana Dalvi Mishra, Joel Grus, Wen-tau Yih, Antoine Bosselut, and Peter Clark. Reasoning about actions and state changes by injecting commonsense knowledge. In EMNLP, 2018.
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+
+# A IMPLEMENTATION DETAILS
+
+Implementation details of KG-MRC are as follows.
+
+In all experiments, the word embeddings are initialized with FastText embeddings (Joulin et al., 2016); we use a document LSTM with two layers, the number of hidden units in each layer is 64. We apply dropout rate of 0.4 in all recurrent layers, and 0.3 in all other layers. The number of recurrent graph layers were set to $( L = 2$ ). The hidden unit size for the recurrent graph component was set to 64.
+
+During training, the mini-batch size is 8. We use adam (Kingma & Ba, 2014) as the step rule for optimization, The learning rate is set to 0.002. The model is implemented using PyTorch (Paszke et al., 2017).

parse/train/S1lhbnRqF7/S1lhbnRqF7_content_list.json

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+    {
+        "type": "text",
+        "text": "BUILDING DYNAMIC KNOWLEDGE GRAPHS FROM TEXT USING MACHINE READING COMPREHENSION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            98,
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+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "Rajarshi Das∗1, Tsendsuren Munkhdalai2, Xingdi Yuan2, Adam Trischler2, Andrew McCallum ",
+        "bbox": [
+            187,
+            169,
+            844,
+            185
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1College of Information and Computer Sciences   \nUniversity of Massachusetts, Amherst   \n{rajarshi, mccallum}@cs.umass.edu   \n2Microsoft Research Montreal ´   \nMontreal, Qu ´ ebec, Canada ´   \n{tsendsuren.munkhdalai,eric.yuan, adam.trischler}@microsoft.com ",
+        "bbox": [
+            184,
+            186,
+            709,
+            270
+        ],
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+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
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+            454,
+            306,
+            544,
+            321
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "We propose a neural machine reading model that constructs dynamic knowledge graphs from procedural text. It builds these graphs recurrently for each step of the described procedure, and uses them to track the evolving states of participant entities. We harness and extend a recently proposed machine reading comprehension (MRC) model to query for entity states, since these states are generally communicated in spans of text and MRC models perform well in extracting entity-centric spans. The explicit, structured, and evolving knowledge graph representations that our model constructs can be used in downstream question answering tasks to improve machine comprehension of text, as we demonstrate empirically. On two comprehension tasks from the recently proposed PROPARA dataset (Dalvi et al., 2018), our model achieves state-of-the-art results. The model also outperforms previous approaches on the RECIPES dataset (Kiddon et al., 2015), which suggests it may apply broadly to procedural text. Finally, we present some evidence that the model’s graphical representations help it to impose commonsense constraints on its predictions. ",
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+            337,
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+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
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+            176,
+            570,
+            336,
+            587
+        ],
+        "page_idx": 0
+    },
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+        "text": "Automatically building knowledge graphs (KGs) from text is a long-standing goal in artificial intelligence research. KGs organize raw information in a structured form, capturing relationships (labeled edges) between entities (nodes). They enable automated reasoning, e.g., the ability to infer unobserved facts from observed evidence and to make logical “hops,” and render data amenable to decades of work in graph analysis. ",
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+        "type": "text",
+        "text": "There exists a profusion of text that describes complex, dynamic worlds in which entities’ relationships evolve through time. This includes news articles, scientific manuals, and procedural text (e.g., recipes, how-to guides, and so on). Building KGs from this data would not only help us to study the changing relations among participant entities, but also to make implicit information more explicit. For example, the graphs at each step in Figure 1 help us to infer that the new entity mixture is created in the leaf, since the previous location of its participant entities (light, $C O _ { 2 }$ , water) was leaf – even though this is never stated in the text. ",
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+        "text": "This paper introduces a neural machine-reading model, KG-MRC, that (i) explicitly constructs dynamic knowledge graphs to track state changes in procedural text and (ii) conditions on its own constructed knowledge graphs to improve downstream question answering on the text. Our dynamic graph model is recurrent, that is, the graph at each time step depends on the state of the graph at the previous time step. The constructed graphs are parameterized by real-valued embeddings for each node that change through time. ",
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+        "type": "text",
+        "text": "In text, entities and their states (e.g., their locations) are given by spans of words. Because of the variety of natural language, the same entity/state may be described with several surface forms. To ",
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+        "type": "text",
+        "text": "Chloroplast in leaf of the plant trap light from the sun. The root absorbs minerals from the soil. This combination of water and minerals flows from the stem into the leaf. Carbon dioxide enters the leaf. Light, water and minerals, and the carbon dioxide all combine into a mixture. This mixture forms sugar (glucose) which is what the plant eats. ",
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+        "img_path": "images/f75f36db041dfe1a0ac8b779a083af6c2880f85c4d21e93bff636bc407f60c51.jpg",
+        "image_caption": [
+            "Figure 1: Snapshot of the knowledge graphs created by our model before and after reading the sentence in boldface. Since the KG explicitly stores the current location of light, $C O _ { 2 }$ , and water as leaf, the model can infer that mixture is formed in the leaf even though this is not explicitly stated. The three participant entities also get destroyed in the process, which is captured in the graph by pointing to a special Nowhere node. "
+        ],
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+        "type": "text",
+        "text": "address the challenge of entity/state recognition, our model uses a machine reading comprehension (MRC) mechanism (Seo et al., 2017a; Xiong et al., 2017; Chen et al., 2017; Yu et al., 2018, inter alia), which queries for entities and their states at each time step. We leverage MRC mechanisms because they have proven adept at extracting text spans that answer entity-centric questions (Levy et al., 2017). However, such models are static by design, returning the same answer for the same query and context. Since we expect answers about entity states to change over the course of the text, our model’s MRC component conditions on the evolving graph at the current time step (this graph captures the instantaneous states of entities). ",
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+        "type": "text",
+        "text": "To address the challenge of aliased text mentions, our model performs soft co-reference as it updates the graph. Instead of adding an alias node, like the leaf or leaves as aliases for leaf, the graph update procedure soft-attends (Bahdanau et al., 2014) over all nodes at the previous time step and performs a gated update (Cho et al., 2014; Chung et al., 2014) of the current embeddings with the previous ones. This ensures that state information is preserved and propagated across time steps. Soft coreference can also handle the case that entity states do not change across time steps, by applying a near-null update to the existing state node rather than duplicating it. ",
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+        "type": "text",
+        "text": "At each time step, after the graph has been updated with the (possibly) new states of all entities, our model updates each entity representation with information about its state. The updated information about each individual entity is further propagated to all other entities $( \\ S 4 . 4 )$ . This enables the model to recognize, for example, that entities are present in the same location (e.g., light, $C O _ { 2 }$ and water in Figure 1). Thus, our model can use the information encoded in its internal knowledge graphs for a more comprehensive understanding of the text. We will demonstrate this experimentally by tackling comprehension tasks from the the recently released PROPARA and RECIPES datasets. ",
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+        "type": "text",
+        "text": "Our complete machine reading model, which both builds and leverages dynamic knowledge graphs, can be trained end-to-end using only the loss from its MRC component; i.e., the negative loglikelihood that the MRC component assigns to the span that correctly describes each entity’s queried state. We evaluate our model (KG-MRC) on the above two PROPARA tasks and find that the same model significantly outperforms the previous state of the art. For example, KG-MRC obtains a $9 . 9 2 \\%$ relative improvement on the hard task of predicting at which time-step an entity moves. Similarly on the latter task, KG-MRC obtains a $5 . 7 \\%$ relative improvement over PROSTRUCT and $41 \\%$ relative improvement over other entity-centric models such as ENTNET (Henaff et al., 2017). The same model also obtains state-of-the-art performance on the RECIPES dataset. ",
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+    {
+        "type": "text",
+        "text": "2 RELATED WORK ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "There are few datasets that address the challenging problem of tracking entity state changes. The bAbI dataset (Weston et al., 2015) includes questions about movement of entities; however, its language is generated synthetically over a small lexicon, and hence models trained on bAbI often do not generalize well when tested on real-world data. For example, state-of-the-art models like ENTNET (Henaff et al., 2017) and Query Reduction Networks (Seo et al., 2017b) fail to perform well on PROPARA. ",
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+    {
+        "type": "text",
+        "text": "PROREAD (Berant et al., 2014) introduced the PROCESSBANK dataset, which contains paragraphs of procedural text as in PROPARA. However, this earlier task involves mining arguments and relations from events, not tracking the dynamic state changes of entities. The model that Berant et al. (2014) propose builds small knowledge graphs from the text, but they are not dynamic in nature. The model also relies on densely annotated process structure for training, demanding curation by domain experts. On the other hand, our model, KG-MRC, learns to build dynamic KGs just from annotations of text spans, which are much easier to collect. ",
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+    {
+        "type": "text",
+        "text": "For the sentence-level PROPARA task they propose, Dalvi et al. (2018) introduce two models: PROLOCAL and PROGLOBAL. PROLOCAL makes local predictions about entities by considering just the current sentence. This is followed by some heuristic/rule-based answer propagation. PROGLOBAL considers a broader context (previous sentences) and also includes the previous state of entities by considering the probability distribution over paragraph tokens in the previous step. Tandon et al. (2018) recently proposed a neural structured-prediction model, (PROSTRUCT), where hard and soft common-sense constraints are injected to steer their model away from globally incoherent predictions. We evaluate KG-MRC on the two PROPARA tasks proposed by Dalvi et al. (2018) and Tandon et al. (2018), respectively, and find that our single model outperforms each of the above models on their respective tasks of focus. ",
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+    {
+        "type": "text",
+        "text": "ENTNET (Henaff et al., 2017) and query reduction networks (QRN) (Seo et al., 2017b) are two state-of-the-art entity-centric models for the bAbI dataset. ENTNET maintains a dynamic memory of hidden states with a gated update to the memory slots at each step. Memory slots can be tied to specific entities, but unlike our model, ENTNET does not maintain separate embeddings of individual states (e.g., current locations); it also does not perform explicit co-reference updates. QRN refines the query vector as it processes each subsequent sentence until the query points to the answer, but does not maintain explicit representations of entity states. Neural Process Networks (NPN) (Bosselut et al., 2018) learn to understand procedural text by explicitly parameterizing actions and composing them with entities. These three models return an answer by predicting a vocabulary item in a multi-class classification setup, while in our work we predict spans of text directly from the paragraph. ",
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+    {
+        "type": "text",
+        "text": "MRC models have been used previously for extracting the argument of knowledge base (KB) relations, by associating one or more natural language questions with each relation (querification). These models have been shown to perform well in a zero-shot setting, i.e., for a previously unseen relation type (Levy et al., 2017), and for extracting entities that belong to non-standard types (Roth et al., 2018). These recent positive results motivate our use of an MRC component in KG-MRC. ",
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+    {
+        "type": "text",
+        "text": "3 DATA & TASKS ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We evaluate KG-MRC on the recently released PROPARA dataset (Dalvi et al., 2018), which comprises procedural text about scientific processes. The location states of participant entities at each time step (sentence) in these processes are labeled by human annotators, and the names of participant entities are given. As an example, for a process describing photosynthesis, the participant entities provided are: light, $C O _ { 2 }$ , water, mixture and glucose. Although participant entities are thus known a priori, the location of an entity could be any arbitrary span in the process text. This makes the task of determining and tracking an entity’s changing location quite challenging. ",
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+        "type": "text",
+        "text": "It should also be noted that the dataset does not provide information on whether a particular entity is an input to or output of a process. Not all entities exist from the beginning of the process (e.g. glucose) and not all exist at the end (e.g. water). Table 1 shows statistics of PROPARA. As can be seen, the training set is small, which makes learning challenging. ",
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+    {
+        "type": "table",
+        "img_path": "images/643f83e993d501d7de6ad19b25af24f327e9a8c0a41c767c5a56ddae1f7b0cfb.jpg",
+        "table_caption": [
+            "Table 1: Statistics of PROPARA. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td># para</td><td>488</td></tr><tr><td># train/#dev/#test</td><td>391/43/54</td></tr><tr><td>avg.#entities</td><td>4.17</td></tr><tr><td>avg. # sentences</td><td>6.7</td></tr><tr><td># sentences</td><td>3.3K</td></tr></table>",
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "Along with the dataset, Dalvi et al. (2018) introduce the task of tracking state changes at a fine-grained sentence level. To solve this task, a model must answer three categories of questions (10 questions in total) about an entity $E$ : (1) Is $E$ created, (destroyed, moved) in the process? (2) When (step #) is $E$ created, (destroyed, moved)? (3) Where is $E$ created, (destroyed, moved from/to)? Cat. 1 asks boolean questions about the existence and movement of entities. Cat. 2 and 3 are harder tasks, as the model must correctly predict the step number at which a state changes as well as the correct locations (text spans) of entities at each step. ",
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+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "Tandon et al. (2018) introduce a second task on the PROPARA dataset that measures state changes at a coarser process level. To solve this task, a model must correctly answer the following four types of questions: (1) What are the inputs to the process? (2) What are the outputs of the process? (3) What conversions occur, when and where? (4) What movements occur, when and where? Inputs to a process are defined as entities that exist at the start of the process but not at the end and outputs are entities that exist at the end of the process and were created during it. A conversion is when some entities are created and others destroyed, while movements refer to changes in location. Dalvi et al. (2018) and Tandon et al. (2018) propose different models to solve each of these tasks separately, whereas we evaluate the same model, KG-MRC, on both tasks. ",
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+    {
+        "type": "text",
+        "text": "Bosselut et al. (2018) recently released the RECIPES dataset, which has various annotated states (e.g. shape, composition, location, etc.) for ingredients in cooking recipes. We further test KG-MRC on the location task to align with our PROPARA experiments. This is arguably the dataset’s hardest task, since it requires classification over more than 260 classes while the others have a much smaller label space (maximum of 4). Note that rather than treating this problem as classification over a fixed lexicon as in previous models, our model aims to find the location-describing span of text in the recipe paragraph. ",
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+    {
+        "type": "text",
+        "text": "4 MODEL ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "KG-MRC tracks the temporal state change of entities in procedural text. Naturally, the model is entity-centric (Henaff et al., 2017; Bansal et al., 2017): it associates each participant entity of the procedural text with a unique node and embedding in its internal graph. KG-MRC is also equipped with a neural machine reading comprehension model which is queried about the current location of each entity. ",
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+        "type": "text",
+        "text": "At a high level, the model operates as follows. We summarize some important notation in Table 2. KG-MRC takes as input a paragraph $p = \\{ w _ { j } \\} _ { j = 1 } ^ { P } = \\{ s _ { t } \\} _ { t = 1 } ^ { T }$ , consisting of $P$ tokens spread across $T$ sentences. The model reads this paragraph incrementally. Specifically, at each time step (sentence) $t$ , the model reads the paragraph prefix comprising all sentences up to and including $s _ { t }$ . We then engage the MRC module to query for the state of each participant entity (these participants are known in PROPARA a priori and we index them with $i$ ). The querying process conditions on both the input text and the constructed knowledge graph from the previous time step. In response to a query, the MRC module returns a span from the text that describes the ith entity’s location at $t$ . We encode this into a vector representation. Finally, conditioning on the span vectors for all entities, the model constructs the graph $G _ { t }$ by updating graph $G _ { t - 1 }$ from the previous time step. ",
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+        "type": "text",
+        "text": "The model’s knowledge graphs $G _ { t }$ are bipartite, having two sets of nodes with implied connections between them: $G _ { t } = \\{ \\bar { e } _ { i , t } , \\bar { \\lambda } _ { i , t } \\}$ . Each node denotes either an entity $( e _ { i , t } )$ or that entity’s corresponding location $( \\lambda _ { i , t } )$ , and is associated with a real-valued vector. We use $e _ { i , t }$ and $\\lambda _ { i , t }$ to denote nodes in the graph and their vector representations interchangeably. The bipartite graphs $G _ { t }$ have only one (implicit) relation type, the current location, though we plan to extend this in future work. To derive $G _ { t }$ from its previous iterate $G _ { t - 1 }$ , we combine both hard and soft graph updates. The update to an entity’s node representation with new location information arises from a hard decision made by the MRC model, whereas co-reference between entities across time steps is resolved with soft attention. We now describe all components of the model in detail. ",
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+    {
+        "type": "text",
+        "text": "4.1 ENTITY AND SPAN REPRESENTATIONS ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In the PROPARA dataset, entities appear in the paragraph text.1 Therefore, we derive the initial entity representations from contextualized hidden vectors by encoding the paragraph with a bi-directional LSTM (Hochreiter & Schmidhuber, 1997). This choice has the added advantage that initial entity representations share information through context, unlike in previous models (Henaff et al., 2017; Das et al., 2017; Bansal et al., 2017). Entities in the dataset can be multi-word expressions (e.g., electric oven). To obtain a single representation, we concatenate the contextualized hidden vectors corresponding to the start and end span tokens and take a linear projection. i.e., if the mention of entity $i$ occurs between the $j$ -th and $j + k$ -th position, then the initial entity representation $\\nu _ { i }$ is computed as $\\mathbf { v } _ { i } = W _ { e } [ c _ { j } ; c _ { j + k } ] + b _ { e }$ . We use $i$ to index an entity and its corresponding location, while $c _ { j }$ represents the contextualized hidden vectors for token $j$ and $[ ; ]$ represents the concatenate operation. An entity may occur multiple times within a paragraph. We give equal importance to all occurrences by summing the representations for each. ",
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+    {
+        "type": "table",
+        "img_path": "images/727ef41a6fbb33bebf38531df716dfccf47dfa820badfd48e847065951c1c14d.jpg",
+        "table_caption": [
+            "Table 2: Symbols used in Section 4. The text-based representations of entities and locations are derived from the hidden representations of the context-RNN $( \\ S 4 . 1 )$ . The node representations are added to the graph $G _ { t }$ at the end of time step t (§ 4.4). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Notation</td><td>Meaning</td></tr><tr><td>NEN</td><td>Number of participant entities in the process.</td></tr><tr><td>Vi∈Rd</td><td>Initial entity representation,derived from the text,for the i-th entity at time t = O(§ 4.1)</td></tr><tr><td>ei,tERd</td><td>Entity node representation for the i-th entity at time t,in the graph Gt (§ 4.4)</td></tr><tr><td>YitERd</td><td>Location representation derived from the text for the i-th entity at time t (§ 4.1)</td></tr><tr><td>2iERd</td><td>Location node representation for the i-th entity at time t,in the graph Gt (8 4.3,4.4)</td></tr><tr><td>A∈RNxd</td><td>Matrix of all location node representations at time t. (Essentially all λi,t stacked row-wise at t)</td></tr><tr><td>UERNXN</td><td>Soft co-reference matrix at time step t (§ 4.3)</td></tr></table>",
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+        "text": "",
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+        "type": "text",
+        "text": "When queried about the current location of an entity, the MRC module $( \\ S 4 . 2 )$ returns a span of text as the answer, whose representation is later used to update the appropriate node vector in the graph. We obtain this answer-span representation analogously as above, and denote it with $\\Psi _ { i , t }$ . ",
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+    {
+        "type": "text",
+        "text": "4.2 MACHINE READING COMPREHENSION MODEL ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Rather than design a specialized MRC architecture, we make simple extensions to a widely used model – DRQA (Chen et al., 2017) – to adapt it to query about the evolving states of entities. In summary, our modified DRQA implementation operates on prefixes of sentences rather than the full paragraph (like PROGLOBAL), and at each sentence (time step) it conditions on both the current sentence representation $s _ { t }$ and the dynamic entity representations in $G _ { t - 1 }$ . ",
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+    {
+        "type": "text",
+        "text": "For complete details of the DRQA model, we refer readers to the original publication (Chen et al., 2017). Broadly, it uses a multi-layer recurrent neural network (RNN) architecture for encoding both the passage and question text and uses self-attention to match these two encodings. For each token $j$ in the text, it outputs a score indicating its likelihood of being the start or end of the span that answers the question. We reuse all of these operations in our model, modified as described below. ",
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+    {
+        "type": "text",
+        "text": "We query the DRQA model about the state of each participant entity at each time step $t$ . This involves reading the paragraph up to and including sentence $s _ { t }$ . To query, we generate simple natural language questions for an entity, $E$ , such as “Where is $E$ located?” This is motivated by the work of Levy et al. (2017). Our DRQA component also conditions on entities. Recall that vector $e _ { i , t - 1 }$ denotes the entity’s representation in the knowledge graph $G _ { t - 1 }$ . The module conditions on $e _ { i , t - 1 }$ in its output layer, basically the same way as the question representation is used in the output alignment step in Chen et al. (2017). However, instead of taking a bi-linear map between the question and passage representations as in that work, we first concatenate the question representation with $e _ { i , t - 1 }$ and pass the concatenation through a 2-layer MLP. This yields an entity-dependent question representation. We use this to compute the output start and end scores for each token position, taking the argmax to obtain the most likely span. As mentioned, we encode this span as vector $\\Psi _ { i , t }$ $( \\ S 4 . 1 )$ . ",
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+    {
+        "type": "text",
+        "text": "The PROPARA dataset includes two special locations that don’t appear as text spans: nowhere and somewhere. The current location of an entity is nowhere when the entity does not exist yet or has been destroyed, whereas it is somewhere when the entity exists but its location is unknown from the text. Since these locations don’t appear as tokens in the text, the span-predictive MRC module cannot extract them. Following Dalvi et al. (2018), we address this with a separate classifier that predicts, given a graph entity node and the text, whether the entity represented by the node is nowhere, somewhere, or its location is stated. We learn the location-node representations for nowhere and somewhere during training. ",
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+    {
+        "type": "text",
+        "text": "4.3 SOFT CO-REFERENCE ",
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+        "text": "To handle cases when entity states do not change and when states are referred to with different surface forms (either of which could lead to undesired node duplication), our model uses soft co",
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+        "img_path": "images/4b16542539584ac4ac3986a665ab29d520ceb59df28c94712d538115a8660dc2.jpg",
+        "image_caption": [
+            "Knowledge graph at time (t-1) ",
+            "Figure 2: Soft co-reference across time steps. The sentence at the current time step is highlighted. When the MRC model predicts a span (leaf ) present in the graph at the previous time step, KG-MRC does soft attention and a gated update to preserve information across time steps $( \\ S 4 . 3 )$ . The thicker arrow shows higher attention weight between the old and new node. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "reference mechanisms (Figure 2) both across and within time steps. Disambiguation across time steps is accomplished by attention and a gated update, using the incoming location vector $\\Psi _ { i , t }$ and the location node representations from the previous time step: ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/0efdb42c0becb62a98fdfcde8e46795ff155b2a4133fcc4680d6a72fe06ae132.jpg",
+        "text": "$$\n\\begin{array} { r l } & { a _ { i , t } = \\operatorname { s o f t m a x } ( \\Lambda _ { t - 1 } \\Psi _ { i , t } ) } \\\\ & { \\Psi _ { i , t } ^ { \\prime } = \\Lambda _ { t - 1 } ^ { \\top } a _ { i , t } } \\\\ & { g _ { i } = \\operatorname { s i g m o i d } ( W _ { i } [ \\Psi _ { i , t } ^ { \\prime } ; \\Psi _ { i , t } ] + b _ { i } ) } \\\\ & { \\lambda _ { i , t } ^ { \\prime } = g _ { i } \\Psi _ { i , t } + ( 1 - g _ { i } ) \\Psi _ { i , t } ^ { \\prime } , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            393,
+            395,
+            602,
+            478
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where $\\Lambda _ { t - 1 } = [ \\lambda _ { i , t } ] _ { i = 1 } ^ { N } \\in \\mathbb { R } ^ { N \\times d }$ is a matrix of location node representations from the previous time step (stacked row-wise) and $\\Psi _ { i , t }$ is the location span vector output by the MRC module. The result vector $\\lambda _ { i , t } ^ { \\prime }$ is a disambiguated intermediate node representation. ",
+        "bbox": [
+            173,
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "This process only partially addresses node de-duplication. Since different instances of the same location can be predicted for multiple entities, we also perform a co-reference disambiguation within each time step using a self-attention mechanism: ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/1fea52473c88359d66e8a15726b1afd66e29a22c30de0b6e01413480624a1540.jpg",
+        "text": "$$\n\\begin{array} { r l } & { u _ { i , t } = \\mathrm { s o f t m a x } ( \\Lambda _ { t } ^ { \\prime } \\lambda _ { i , t } ^ { \\prime } ) } \\\\ & { { \\lambda _ { i , t } } = { \\Lambda _ { t } ^ { \\prime } } ^ { \\top } u _ { i , t } , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            424,
+            583,
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+            626
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where $\\Lambda _ { t } ^ { \\prime } = [ \\lambda _ { i , t } ^ { \\prime } ] _ { i = 1 } ^ { N } \\in \\mathbb { R } ^ { N \\times d }$ is a matrix of intermediate node representations (stacked row-wise) and $U _ { t } = [ u _ { i , t } ] _ { i = 1 } ^ { N } \\in \\mathbb { R } ^ { N \\times N }$ is a co-reference adjacency matrix. We calculate this adjacency matrix at the beginning of each time step to track related nodes within $t$ , and re-use it in the graph update step. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.4 GRAPH UPDATE ",
+        "text_level": 1,
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The graph update proceeds according to the following set of equations for each update layer $l$ ",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/2fc1c2a3a1f17065b9809e337d3fc7ea033b5f5f679673325f10258a0b561c77.jpg",
+        "text": "$$\n\\begin{array} { r l } & { { h } _ { i , t } ^ { l } = \\mathrm { L S T M } ( [ e _ { i , t } ^ { l - 1 } ; \\lambda _ { i , t } ^ { l - 1 } ; h _ { i , t - 1 } ^ { l } ] ) } \\\\ & { e _ { i , t } ^ { l } = e _ { i , t } ^ { l - 1 } + h _ { i , t } ^ { l } } \\\\ & { \\tilde { \\lambda } _ { i , t } ^ { l } = \\lambda _ { i , t } ^ { l - 1 } + h _ { i , t } ^ { l } } \\\\ & { \\lambda _ { i , t } ^ { l } = \\tilde { \\Lambda } _ { t } ^ { l \\top } u _ { i , t } . } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            392,
+            742,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We first compose all connected entity and location nodes with their history summary, $h _ { i , t - 1 } ^ { l }$ , using an LSTM unit. Next, the updated node information is attached to the entity and location representations through two residual updates (He et al., 2016). These propagate information between the entity and location representations; i.e., if two entities are at the same location, then the corresponding entity representations will receive a similar update. Likewise, location representations are updated with pertinent entity information. Last, we perform another co-reference pooling operation for the location nodes. After the recurrent and residual graph updates, information propagation may yield different, diverging representations for nodes that belong to the same location. This final pooling operation corrects for this, by tying the co-referent representations in a soft way. It uses the previously computed adjacency matrix $U _ { t }$ and $\\tilde { \\Lambda } _ { t } ^ { l }$ , which is a row-wise stacked matrix of the $\\tilde { \\lambda } _ { i , t } ^ { l }$ . ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The recurrent graph module stacks $L$ such layers to propagate node information along the graph’s edges. The resulting node representations are $\\dot { e } _ { i , t } ^ { L }$ and $\\bar { \\lambda } _ { i , t } ^ { L }$ for each participant entity and its location. We use $e _ { i , t } = e _ { i , t } ^ { L }$ to condition the MRC model, as described in $\\ S 4 . 2$ . We make use of this particular graph module structure, rather than adopting an existing model like GraphCNNs (Edwards & Xie, 2016; Kipf & Welling, 2017), because recurrent networks are designed to propagate information through time. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.5 TRAINING ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The full KG-MRC model is trained end-to-end by minimizing the negative log-likelihood of the correct span tokens under the MRC module’s output distribution and the textual entailment model. This is a fairly soft supervision signal, since we do not train the graph construction modules directly. We teacher-force the model at training time by updating the location-node representations with the encoding of the correct span. We do not pretrain the MRC module, but we represent paragraph tokens with pretrained FastText embeddings (Joulin et al., 2016). See the appendix A for full implementation and training details. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5 EXPERIMENTS AND DISCUSSION ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We evaluate our model on three different tasks. We also provide an ablation study along with quantitative and qualitative analyses to highlight the performance contributions of each module. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "5.1 RESULTS ON PROCEDURAL TEXT ",
+        "text_level": 1,
+        "bbox": [
+            176,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We benchmarked our model on two PROPARA comprehension tasks introduced respectively in Dalvi et al. (2018) and Tandon et al. (2018). Refer to Section 3 for a detailed description about the data and tasks. Dalvi et al. (2018) and Tandon et al. (2018) respectively introduce a specific model for each task, whereas we test KG-MRC on both tasks. A primary motivation for building KGs is because they can be queried for salient knowledge in downstream applications. We evaluate KG-MRC on the above two tasks by querying the KGs it builds at each time-step; we use the official evaluation pipeline2 for each task. In results below, we report an average score of three runs of our model with different hyperparameter settings. ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.1.1 TASK 1: SENTENCE-LEVEL EVALUATION ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            712,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 3 shows our main results on the first task. Following the original task evaluation, we report model accuracy on each subtask category and macro and micro averages over the subtasks. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Human performance is $7 9 . 6 9 \\%$ , micro-average. A state-of-the-art memory augmented network, ENTNET (Henaff et al., 2017), which is built to track entities but lacks an explicit graph structure, achieves $2 5 . 9 6 \\%$ . The previous best performing model is PROGLOBAL, which achieves $4 5 . 3 7 \\%$ . Our KG-MRC improves over this result by $1 . 2 5 \\%$ absolute score in terms of micro-averaged accuracy. Comparing various models for each subtask category, PROGLOBAL leads in Category 1 by a small margin of around $0 . 1 \\%$ . For the more challenging Categories 2 and 3, KG-MRC outperforms PROGLOBAL by a large margin. These questions require fine-grained predictions of state changes. ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/2ede4501aecc5ac203c07e40f59c75a4a9290f3233c51ddfa233e1f00cbbef9e.jpg",
+        "table_caption": [
+            "Table 3: Task 1 results (accuracy). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Cat1</td><td>Cat2</td><td>Cat 3</td><td>Macro-avg</td><td>Micro-avg</td></tr><tr><td>Human upper bound</td><td>91.67</td><td>87.66</td><td>62.96</td><td>80.76</td><td>79.69</td></tr><tr><td>Majority</td><td>51.01</td><td>1</td><td>1</td><td>1</td><td>1</td></tr><tr><td>Rule based</td><td>57.14</td><td>20.33</td><td>2.40</td><td>26.62</td><td>26.24</td></tr><tr><td>Feature based</td><td>58.64</td><td>20.82</td><td>9.66</td><td>29.7</td><td>29.64</td></tr><tr><td>EntNet (Henaff et al.(2017))</td><td>51.62</td><td>18.83</td><td>7.77</td><td>26.07</td><td>25.96</td></tr><tr><td>Pro-Local (Dalvi et al. (2018))</td><td>62.65</td><td>30.50</td><td>10.35</td><td>34.50</td><td>33.96</td></tr><tr><td>Pro-Global (Dalvi et al.(2018))</td><td>62.95</td><td>36.39</td><td>35.90</td><td>45.08</td><td>45.37</td></tr><tr><td>KG-MRC (ours)</td><td>62.86</td><td>40.00</td><td>38.23</td><td>47.03</td><td>46.62</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.1.2 TASK 2: DOCUMENT-LEVEL EVALUATION ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            275,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We report the performance of our model on the document-level task, along with previously published results, in Table 4. The same KG-MRC model achieves $3 . 0 2 \\%$ absolute improvement in $\\mathrm { F } _ { 1 }$ over the previous best result of PROSTRUCT. PROSTRUCT incorporates a set of commonsense constraints for globally consistent predictions. We analyzed KG-MRC’s outputs and were surprised to discover that our model learns these commonsense constraints from the data in an end-to-end fashion, as we show quantitatively in $\\ S 5 . 4$ . ",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/361d48b9046435821e980ba64ccb71443b7480efaf80a9c119370a5722ce57ac.jpg",
+        "table_caption": [
+            "Table 4: Task 2 results. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Precision</td><td>Recall</td><td>F1</td></tr><tr><td>Pro-Local (Dalvi et al.(2018))</td><td>77.4</td><td>22.9</td><td>35.3</td></tr><tr><td>QRN (Seo et al. (2017b))</td><td>55.5</td><td>31.3</td><td>40.0</td></tr><tr><td>EntNet (Henaff et al. (2017))</td><td>50.2</td><td>33.5</td><td>40.2</td></tr><tr><td>Pro-Global (Dalvi et al.(2018))</td><td>46.7</td><td>52.4</td><td>49.4</td></tr><tr><td>Pro-Struct (Tandon et al. (2018))</td><td>74.2</td><td>42.1</td><td>53.75</td></tr><tr><td>KG-MRC (ours)</td><td>64.52</td><td>50.68</td><td>56.77</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.2 RECIPE DESCRIPTION EXPERIMENTS ",
+        "text_level": 1,
+        "bbox": [
+            176,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We also evaluate our model on the RECIPES dataset, for which we predict the evolving locations of cooking ingredients. In the original work of Bosselut et al. (2018), they treat this problem as classification over a fixed lexicon of locations. KG-MRC searches for the correct location span in the text. On this task, our model outperforms the baseline NPN model by a significant margin, achieving a score of $5 4 . 2 7 \\%$ $\\mathrm { F } _ { 1 }$ compared to NPN’s $5 1 . 2 8 \\% \\mathrm { F } _ { 1 }$ . On further analysis of the results, we found several cases where our model was wrongly penalized, e.g., for predicting the span “saucepan” when the ground truth class label was “pan.” We believe that our results would improve further if we mapped our predicted spans to the ground truth class labels. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.3 ABLATION STUDY ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            718,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We performed an ablation study to evaluate different model variations on PROPARA Task 1. The main results are reported in Table 5. Removing the soft co-reference disambiguation within time steps (Equations 2) from KG-MRC resulted in around $1 \\%$ performance drop. The drop is more significant when the co-reference disambiguation across time steps (Equations 1) is removed. ",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We also replaced the recurrent graph module with the standard LSTM unit and used the LSTM hidden state for the entity representation. Because this model variant does not propagate information across graph nodes (the final step in Equations 3), we observed a large performance decrease. ",
+        "bbox": [
+            176,
+            805,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "For the last two variations, we simply train the MRC model in isolation and predict location spans from the current sentence or paragraph prefix text (i.e., the current and all previous sentences). These models construct no internal knowledge graphs. We can see that training the MRC model on paragraph prefixes already provides a good starting performance of $4 0 . 8 3 \\%$ micro-average, which is significantly boosted by the recurrent graph module and graph conditioning up to $4 7 . 6 4 \\%$ . ",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/392a8913b9f97c8c4038ca662e42cf78273d9b1b3bd407fd328319adfe90f385.jpg",
+        "table_caption": [
+            "Table 5: Ablation experiment results "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Cat1</td><td>Cat2</td><td>Cat 3</td><td>Macro-avg</td><td>Micro-avg</td></tr><tr><td>KG-MRC</td><td>58.55</td><td>38.52</td><td>42.22</td><td>46.43</td><td>47.64</td></tr><tr><td>- Coref across time steps</td><td>61.07</td><td>37.38</td><td>35.58</td><td>44.68</td><td>46.32</td></tr><tr><td>-Coref within time step</td><td>57.88</td><td>38.09</td><td>40.19</td><td>45.39</td><td>46.63</td></tr><tr><td>- Coref in the graph-update step</td><td>60.91</td><td>34.71</td><td>32.34</td><td>42.65</td><td>44.48</td></tr><tr><td>Standard LSTM as graph unit</td><td>56.84</td><td>13.15</td><td>10.95</td><td>26.98</td><td>29.97</td></tr><tr><td>MRC on entire paragraph</td><td>58.85</td><td>21.82</td><td>26.52</td><td>35.73</td><td>35.98</td></tr><tr><td>MRC on prefix</td><td>61.28</td><td>32.58</td><td>29.48</td><td>41.11</td><td>40.83</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "5.4 COMMONSENSE CONSTRAINTS ",
+        "text_level": 1,
+        "bbox": [
+            176,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "For accurate, globally consistent predictions on the second PROPARA task, Tandon et al. (2018) introduced a set of commonsense constraints that they impose on their model in a pruning stage. Stated in natural language, these constraints are: 1) An entity must exist before it can be moved or destroyed; 2) An entity cannot be created if it already exists; 3) An entity cannot change until it is mentioned in the paragraph. ",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "To analyze whether our model can learn these constraints directly from data, we count the number of model predictions that violate constraints on the test set. To our surprise, this demonstrates that KGMRC learns to violate fewer constraints (proportionally) than PROSTRUCT, even without explicitly training it to do so. In more detail, we find that KG-MRC, like PROSTRUCT, does not violate any Type 1 or Type 2 constraints. In Table 6 we compare several models in terms of Type 3 constraint violations. Note that we only count instances where a model predicts an entity state change. ",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/1d42ade21bbcb2e1b467e08fbbffcfb3971085c6f1cc80c017a97d25372b5a5e.jpg",
+        "table_caption": [
+            "Table 6: Commonsense constraint violations. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>State Change Predictions</td><td>Violations</td><td>Violation Proportion (%)</td></tr><tr><td>PROSTRUCT (Tandon et al. (2018))</td><td>270</td><td>17</td><td>6.30</td></tr><tr><td>MRC on entire paragraph</td><td>381</td><td>104</td><td>27.30</td></tr><tr><td>MRC on prefix</td><td>703</td><td>154</td><td>21.93</td></tr><tr><td>Standard LSTM as graph unit</td><td>447</td><td>20</td><td>4.47</td></tr><tr><td>KG-MRC</td><td>466</td><td>19</td><td>4.08</td></tr></table>",
+        "bbox": [
+            238,
+            462,
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+            539
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "As shown, KG-MRC makes fewer Type 3 violations that PROSTRUCT. Furthermore, MRC models without recurrent graph modules perform worse in terms of constraint violations than both KGMRC and a model using a standard LSTM as its graph unit. This suggests that recurrent graphical representations play an important role in helping the model to learn and adhere to the constraints. ",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "5.5 QUALITATIVE ANALYSIS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            666,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We picked an example from the test data and took a closer look at the model outputs to investigate how KG-MRC dynamically adjusts its decisions via the dynamic graph module and finds accurate spans with the conditional MRC model. The step-by-step output of both PROGLOBAL (Dalvi et al. (2018)) and KG-MRC is shown in Table 7, where we track the state of entity blood across six sentences. KG-MRC outputs smoother and more accurate predictions. ",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/7adfbc524c59b1427a95eb67f6a6164bdc02656932787c2a1b857a00e03b0dd9.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Sentences</td><td colspan=\"2\">Location of entities after each sentence</td></tr><tr><td>(Before first sentence)</td><td>somewhere</td><td>somewhere</td></tr><tr><td>Blood enters the right side of your heart.</td><td>heart</td><td>right side of your heart</td></tr><tr><td>Blood travels to the lungs.</td><td>lung</td><td>lungs</td></tr><tr><td>Carbon dioxide is removed from the blood.</td><td>blood</td><td>lungs</td></tr><tr><td>Oxygen is added to your blood.</td><td>lung</td><td>lungs</td></tr><tr><td>Blood returns to left side of your heart.</td><td>blood</td><td>heart</td></tr><tr><td>The blood travels through the body.</td><td>body</td><td>body</td></tr></table>",
+        "bbox": [
+            289,
+            773,
+            709,
+            871
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Table 7: Two models’ predictions of entity locations, on randomly selected paragraph about blood circulation. In this example the entity is blood. Predicted results from Pro-Local (Dalvi et al. (2018)) are in orange, results from KG-MRC are in red, important locations in paragraph are in blue. ",
+        "bbox": [
+            173,
+            882,
+            821,
+            920
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "6 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
+            174,
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+            318,
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "We proposed a neural machine-reading model that constructs dynamic knowledge graphs from text to track locations of participant entities in procedural text. It further uses these graphical representations to improve its downstream comprehension of text. Our model, KG-MRC, achieves state-of-theart results on two question-answering tasks from the PROPARA dataset and one from the RECIPES dataset. In future work, we will extend the model to construct more general knowledge graphs with multiple relation types. ",
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+    {
+        "type": "text",
+        "text": "A IMPLEMENTATION DETAILS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            102,
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Implementation details of KG-MRC are as follows. ",
+        "bbox": [
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+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "In all experiments, the word embeddings are initialized with FastText embeddings (Joulin et al., 2016); we use a document LSTM with two layers, the number of hidden units in each layer is 64. We apply dropout rate of 0.4 in all recurrent layers, and 0.3 in all other layers. The number of recurrent graph layers were set to $( L = 2$ ). The hidden unit size for the recurrent graph component was set to 64. ",
+        "bbox": [
+            174,
+            147,
+            825,
+            217
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "During training, the mini-batch size is 8. We use adam (Kingma & Ba, 2014) as the step rule for optimization, The learning rate is set to 0.002. The model is implemented using PyTorch (Paszke et al., 2017). ",
+        "bbox": [
+            174,
+            224,
+            825,
+            266
+        ],
+        "page_idx": 11
+    }
+]

parse/train/SkfTIj0cKX/SkfTIj0cKX.md

@@ -0,0 +1,210 @@
+# PURCHASE AS REWARD: SESSION-BASED RECOM-MENDATION BY IMAGINATION RECONSTRUCTION
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+One of the key challenges of session-based recommender systems is to enhance users’ purchase intentions. In this paper, we formulate the sequential interactions between user sessions and a recommender agent as a Markov Decision Process (MDP). In practice, the purchase reward is delayed and sparse, and may be buried by clicks, making it an impoverished signal for policy learning. Inspired by the prediction error minimization (PEM) and embodied cognition, we propose a simple architecture to augment reward, namely Imagination Reconstruction Network (IRN). Specifically, IRN enables the agent to explore its environment and learn predictive representations via three key components. The imagination core generates predicted trajectories, i.e., imagined items that users may purchase. The trajectory manager controls the granularity of imagined trajectories using the planning strategies, which balances the long-term rewards and short-term rewards. To optimize the action policy, the imagination-augmented executor minimizes the intrinsic imagination error of simulated trajectories by self-supervised reconstruction, while maximizing the extrinsic reward using model-free algorithms. Empirically, IRN promotes quicker adaptation to user interest, and shows improved robustness to the cold-start scenario and ultimately higher purchase performance compared to several baselines. Somewhat surprisingly, IRN using only the purchase reward achieves excellent next-click prediction performance, demonstrating that the agent can "guess what you like" via internal planning.
+
+# 1 INTRODUCTION
+
+A good recommender system can enhance both satisfaction for users and profit for content providers (Gomez-Uribe & Hunt, 2016). In many real-world scenarios, the recommender systems make recommendations based only on the current browsing session, given the absence of user profiles (because the user is new or not tracked or not logged in, till the final purchase step). A session is a group of sequential interactions between a user and the system within a short period of time. To model this phenomenon, Recurrent Neural Networks (RNNs) were recently employed as session-based recommenders (Hidasi et al., 2016; Jannach & Ludewig, 2017). For instance, GRU4Rec (Hidasi et al., 2016) utilizes the session-parallel mini-batch training to handle the variable lengths of sessions, and predicts the next action given the sequence of items in the current session. However, these approaches primarily focus on next-click prediction and model the session data via sequential classification, and thus cannot distinguish the different effects of user clicks and purchases.
+
+In this paper, we consider the session-based recommendation as a Markov Decision Process (MDP), which can take into account both the click reward and the purchase reward (see Figure 1), and leverage Reinforcement Learning (RL) to learn the recommendation strategy. In practice, several challenges need to be addressed. First, the recommender systems involve large numbers of discrete actions (i.e., items), making current RL algorithms difficult to apply (Dulac-Arnold et al., 2015; Sunehag et al., 2015). This requires the agent to explore its environment for action feature learning and develop an ability to generalize over unseen actions. Second, we found it difficult to specify the click reward and the purchase reward; the policy may be biased by long sessions that contain many user clicks, as RL algorithms maximize the accumulated reward. Besides, real-world recommender systems require quick adaptation to user interest and robustness to the cold-start scenario (i.e., enhancing the purchase performance of short sessions). Therefore, we will be particularly interested in a case where only the purchase is used as reward (click sequences are used as inputs of the imagination core for exploration).1 However, the purchase reward is delayed and sparse (one session may contain only one purchase), making it a difficult signal for policy learning.
+
+To augment reward and encourage exploration, we present the Imagination Reconstruction Network (IRN), which is inspired by the prediction error minimization (PEM) (Hohwy, 2016; Friston, 2010; Lotter et al., 2017) and embodied cognition (Clark, 2013; Burr & Jones, 2016; Seth, 2014; de Bruin & Michael, 2017) from the neuroscience literature. The PEM is an increasingly influential theory that stresses the importance of brain-body-world interactions in cognitive processes, involving perception, action and learning. In particular, IRN can be regarded as a proof-of-concept for the PEM from the recommendation perspective, following the ideas in Burr & Jones (2016) and Seth (2014) — the brain utilizes active sensorimotor predictions (or counterfactual predictions) to represent states of affairs in the world in an action-oriented manner. Specifically, the imagination core of IRN that predicts the future trajectories (i.e., a set of imagined items that user may purchase) conditioned on actions sampled from the imagination policy, can be considered as the generative model of the brain that simulates sensorimotor predictions. To update the action policy, the imagination-augmented executor minimizes the intrinsic imagination error of predicted trajectories by self-supervised reconstruction, while maximizing the extrinsic reward using RL, with shared input state or output action representations for predictive learning. This simulates the active perception (a key aspect of embodied cognition) of the body under the PEM framework, which adapts the agent to possible changes that arise from the ongoing exploratory action. Note that the imagination policy imitates the action policy through distillation or a delayed target network, and thus IRN constructs a loop between brain and body, encouraging the agent to perform actions that can reduce the error in the agent’s ability to predict the future events (Pathak et al., 2017). IRN equips the agent with a planning module, trajectory manager, that controls the granularity of imagined trajectories using the planning strategies (e.g., breadth- $\mathbf { \nabla } \cdot n$ and depth- $\mathbf { \nabla } m$ ). Besides, IRN is a combination of model-based planning and self-supervised RL, as the imagined trajectories provide dense training signals for auxiliary task learning (see section 2).
+
+The key contributions of this paper are summarized as follows:
+
+• We formulate the session-based recommendation as a MDP, and leverage deep RL to learn the optimal recommendation policy, and also discuss several challenges when RL is applied. We consider a special case where only the purchase is used as reward, and then propose the IRN architecture to optimize the sparser but more business-critical purchase signals, which draws inspiration from the theories of cognition science. We present a self-supervised reconstruction method for predictive learning, which minimizes the imagination error of simulated trajectories over time. IRN achieves excellent click and purchase performance even without any external reward (predictive perception (Seth, 2014)). We conduct a comprehensive set of experiments to demonstrate the effectiveness of IRN. Compared to several baselines, IRN improves data efficiency, promotes quicker adaptation to user interest, and shows improved robustness to the cold-start scenario and ultimately higher purchase performance. These are highly valuable properties in an industrial context.
+
+# 2 RELATED WORK
+
+Session-based Recommenders Classical latent factor models (e.g., matrix factorization) break down in the session-based setting, given the absence of user profiles. A natural solution is the neighborhood approach like item-to-item recommendation (Mirowski et al., 2016). In this setting, an item similarity matrix can be precomputed based on co-occurrences of clicked items in sessions. However, this method only considers the last clicked item of the browsing session for recommendations, ignoring the sequential information of the previous events. Previous works also attempt to apply MDPs in the recommendation systems (Shani et al., 2002; Tavakol & Brefeld, 2014). The main issue is that the state space quickly becomes unmanageable due to the large number of items (IRN employs deep learning to overcome this problem and thus generalizes well to unseen states). Recently, RNNs have been used with success in this area (Hidasi et al., 2016; Hidasi & Karatzoglou, 2017; Jannach & Ludewig, 2017). GRU4Rec (Hidasi et al., 2016) is the first application of RNNs to model the session data, which can provide recommendations after each click for new sessions.
+
+![](images/7c0479c96ae8d2260faae1dbd823d4c79eda8ec9cf8e5608f7c9041c6c8a5a84.jpg)  
+ractice, we may pay more attention to the improvements of       nhance the purchase, and achieve a satisfactory (short sessions).Figure 1: The agent-user interactions in MDP: the recommender agent (RA) generates a list of hort sessions).e is huge.candidate items after each user click (green) or purchase (red).
+
+equential recommenders with user historical records. ForHowever, GRU4Rec utilizes the session-parallel mini-batch training to handle the variable lengths of formation Processing Systems (NIPS 2018). Do not distribute.ith buy). using GRU4REC classification problem do notion problem do notchains, our methodsessions; this trick cannot effectively capture sequentiality of sessions, since the network is trained practice, we may pay more attention to the improvements ofhe improvements ofistorical behaviors.using the BP algorithm (not BPTT for RNNs). These models primarily focus on next-click prediction rrent neural networks (RNN) or Markov chains, our methodor recommendation,rical records. Forand model the click-streams via sequential classification, while here we aim at modeling the purchase h buy). using GRU4REC classification problem do notctice, we may pay more attention to the improvements of current interests are influenced by their historical behaviors.sequential recommenders with user historical records. For   atasets.Do not distribute.behavior and enhancing users’ purchase intentions. Besides, IRN is built on RL, which encodes at consider users’ sequential behavior for recommendation,formation Processing Systems (NIPS 2018). Do not distribute. historical behaviors.torical records. Forsequentiality of states into the value function.
+
+uential recommenders with user historical records. ForImagination-augmented Agents All approaches incorporating off-policy experience (e.g., imagmation Processing Systems (NIPS 2018). Do not distribute.ined trajectories) generated by a learned model can be categorized into model-based reinforcement learning (Racanière et al., 2017; Pascanu et al., 2017; Silver et al., 2017; Sutton, 1991). By using an internal model of the world, the agent can generalize to unseen states, remain valid in the real environment, and exploit additional training signals to improve data efficiency. However, the performance of model-based agents usually suffers from model errors resulting from function approximation. I2As (Racanière et al., 2017) were proposed to address this issue. I2As augment model-free agents with imagination and use an interpretation module to handle imperfect predictions. The imagined trajectories of I2As are provided as additional context (i.e., input features) to a policy network, while the proposed IRN uses the trajectories as additional training signals for self-supervised reconstruction.
+
+Self-supervised Reinforcement Learning In many real-world scenarios, reward is extremely sparse and delayed, and the agent updates its policy only if it reaches a pre-defined goal state. To model this phenomenon, self-supervised reinforcement learning have often been used, which accelerates the acquisition of a useful representation with auxiliary task learning (Jaderberg et al., 2016; Pathak et al., 2017; Mirowski et al., 2016; Shelhamer et al., 2016). Specifically, auxiliary tasks provide additional losses for feature learning, and can be trained instantaneously using the self-supervision from the environment. For instance, UNREAL (Jaderberg et al., 2016) maximizes many other pseudo-reward functions simultaneously, e.g., pixel change control, with a common representation shared by all tasks. In contrast, the proposed IRN do not require the external supervision from the environment, i.e., self-supervised reconstruction is performed on internal imagined trajectories.
+
+# 3 PRELIMINARIES
+
+We interpret the sequential recommendation task based on the standard reinforcement learning setting: An recommender agent (RA) interacts with an environment $\mathcal { E }$ (or user sessions) by sequentially choosing a list of recommendation items over a number of discrete time steps, so as to maximize its cumulative reward. As shown in Figure 1, we model this problem as a Markov Decision Process (MDP), which consists of a tuple of five elements $( S , A , P , R , \gamma )$ :
+
+State space $S$ : A state $s _ { t } ~ \in ~ S$ is defined as the previous items that a user clicked/purchased in one session. Specifically, the initial state $s _ { 1 }$ contains the first item $i _ { 0 }$ of one session. The items in $s _ { t } = \{ i _ { 0 } , i _ { 1 } , . . . , i _ { t - 1 } \}$ are sorted in chronological order.
+
+Action space $A$ : An action $a _ { t } \in A$ is to recommend items to a user at time $t$ according to its policy $\pi$ , where $\pi$ is a mapping from $s _ { t }$ to $a _ { t }$ . We assume that the RA only recommends one item to the user each time, since we use the observed click/purchase sequences for off-policy training. During off-policy evaluation, we can recommend a list of $K$ candidates to the user.
+
+Reward $R$ : After the RA takes an action $a _ { t }$ at the state $s _ { t }$ , i.e., recommending an item to a user, the user browses this item and provides her feedback (click or purchase). The agent receives a scalar reward $r ( s _ { t } , a _ { t } )$ according to the user’s feedback. We also define the $k$ -step return starting from state $s _ { t }$ as $\begin{array} { r } { G _ { t , t + k } ( s _ { t } ) = \sum _ { j = t } ^ { t + k } \gamma ^ { j - t } r ( s _ { j } , a _ { j } ) } \end{array}$ , where $\gamma \in [ 0 , 1 ]$ is a discounting factor.
+
+Transition probability $P$ : Transition probability $p ( s _ { t + 1 } | s _ { t } , a _ { t } )$ defines the probability of state transition from $s _ { t }$ to $s _ { t + 1 }$ when the RA takes action $a _ { t }$ . In this case, the state transition is deterministic after taking the ground-true action $a _ { t } = i _ { t }$ , i.e., $p ( s _ { t + 1 } | s _ { t } , i _ { t } ) = 1$ and $s _ { t + 1 } = s _ { t } \cup \{ i _ { t } \}$ .
+
+The goal of the RA is to find an optimal policy $\pi ^ { * }$ , such that $V ^ { \pi ^ { * } } ( s _ { 1 } ) \geq V ^ { \pi } ( s _ { 1 } )$ for all policies $\pi$ and start state $s _ { 1 }$ , where $V ^ { \pi } ( s _ { t } )$ is the expected return for a state $s _ { t }$ when following a policy $\pi$ , i.e., $V ^ { \pi } ( s _ { t } ) = \mathbb { E } _ { s _ { j > t } \sim S , a _ { j > t } \sim \pi } [ G _ { t , \infty } ( s _ { t } ) ]$ (or $\mathrm { \overline { { E } } } _ { s \sim \pi } [ G _ { t , \infty } ( s _ { t } ) ]$ for simplicity).
+
+Asynchronous Advantage Actor-Critic. This paper builds upon the A3C algorithm, an actorcritic approach that constructs a policy network $\pi ( a | s ; \theta )$ and a value function network $V ( s ; \theta _ { v } )$ , with all non-output layers shared (Mnih et al., 2016). The policy and the value function are adjusted towards the bootstrapped $k$ -step return $G _ { t , t + k } ( s _ { t } ) + \gamma ^ { k + 1 } \dot { V } ( s _ { t + k + 1 } ; \theta _ { v } )$ , $\mathcal { L } _ { A 3 C } = \mathcal { L } _ { \pi } + \mathcal { L } _ { V R }$ , where $\mathcal { L } _ { \pi } = - \mathbb { E } _ { s \sim \pi } \left[ G _ { 1 , \infty } ( s _ { 1 } ) \right]$ and $\mathcal { L } _ { V R } = \mathbb { E } _ { s \sim \pi } \left[ A ( s _ { t } , a _ { t } ) \right]$ . The advantage function $A ( s _ { t } , a _ { t } )$ (Baird III, 1993) is computed as the difference of the bootstrapped $k$ -step return and the current state value estimate:
+
+$$
+A ( s _ { t } , a _ { t } ) = G _ { t , t + k } ( s _ { t } ) + \gamma ^ { k + 1 } V ( s _ { t + k + 1 } ; \theta _ { v } ^ { - } ) - V ( s _ { t } ; \theta _ { v } ) ,
+$$
+
+where $\theta _ { v } ^ { - }$ are the parameters of the previous target network. To increase the probability of rewarding actions, A3C applies an update $g ( \bar { \theta ) }$ to the parameters $\theta$ using an unbiased estimation (Sutton et al., 2000):
+
+$$
+g ( \theta ) = \nabla _ { \theta } \log \pi ( a _ { t } | s _ { t } ; \theta ) A ( s _ { t } , a _ { t } ) .
+$$
+
+The value function $V ( s ; \theta _ { v } )$ is updated following the recursive definition of the Bellman Equation, $V ( s _ { t } ; \theta _ { v } ) = \mathbb { E } _ { s \sim \pi } \left[ G _ { t , t + k } ( s _ { t } ) + \gamma ^ { k + 1 } V ( s _ { t + k + 1 } ; \theta _ { v } ) \right]$ . Then $g ( \theta _ { v } )$ is obtained by minimizing a squared error between the target return and the current value estimate:
+
+$$
+g ( \theta _ { v } ) = - A ( s _ { t } , a _ { t } ) \frac { \partial } { \partial \theta _ { v } } V ( s _ { t } ; \theta _ { v } ) .
+$$
+
+In A3C multiple agents interact in parallel, with multiple instances of the environment. The asynchronous execution accelerates and stabilizes learning. In practice, we combine A3C with the session-parallel mini-batches proposed in (Hidasi et al., 2016). Each instance of the agent interacts with multiple sessions simultaneously, gathering $M$ samples from different sessions at a time step. After $k$ steps, the agent updates its policy and value network according to Eq. (2)(3), using $k * M$ samples. This decorrelates updates between samples of one session in the instance level. Besides, to build the A3C agent, we employ an LSTM that jointly approximates both policy $\pi$ and value function $V$ , given the one-hot vectors of previous items clicked/purchased as inputs.
+
+# 4 IRN ARCHITECTURE
+
+In this section we incorporate the imagination reconstruction module into the model-free agents (e.g., A3C) in order to enhance data efficiency, promote more robust learning and ultimately higher performance under the sparse extrinsic reward. Our IRN implements an imagination-augmented policy via three key components (Figure 2). The imagination core $( I C )$ predicts the next time steps conditioned on actions sampled from the imagination policy $\hat { \pi }$ . At a time step $t$ , the trajectory manager (TM) determines how to roll out the $I C$ under the planning strategy, and then produces imagined trajectories $\hat { T _ { 1 } } , \dots , \hat { T _ { n } }$ of an observable world state $s _ { t }$ . Each trajectory $\hat { T _ { j } }$ is a sequence of items $\{ \hat { i } _ { j , t } , \hat { i } _ { j , t + 1 } , \ldots \}$ , that users may purchase (or click) from the current time $t$ . The Imaginationaugmented Executor $( I A E )$ aggregates the internal data resulting from imagination and external rewarding data to update its action policy $\pi$ . Specifically, the $I A E$ optimizes the policy $\pi$ by maximizing the extrinsic reward while minimizing the intrinsic imagination error. In principle, IRN encourages exploration and learns predictive representations via imagination rollouts, which promotes quick adaptation to user interest and robustness to the cold-start scenario.
+
+![](images/f8520ca08c0f83e6c0e4b54ca0deec2292206bd1595905e810a70095d85f4835.jpg)  
+ˆit+⌧ = ˆat+⌧ and sˆt = st , where ⌧ is the length of the imagined rollout, aˆt+⌧ the4agination policy ⇡ˆ. During training, the generated i28 32 31 example, [23] adopted Markov chain toning, the generated item ˆit+⌧ may not be the true puFigure 2: IRN architecture: a) the imagination core $( I C )$ action of theˆit+⌧ may not be the true purchase, but we24 aT 1 28 purchase.chase.any real-world applications, users’ current interests are inel user behavior sequences, and [19, 31] leveragedse, but wepredicts the next time step and then generates imagination policy ⇡ˆ. During training,still use it for self-supervised reconstrill use it for self-supervis32 recurr33 prediconstruction of I2E. This mdistillation [] or fixed targthe imagined trajectories $\hat { \tau }$ errorgenerated item it+⌧ may not be the true purchase, but weon of I2E. This makes the action policy ⇡ more robust to reconstruction of I2E. This makes the action policy ⇡ more robust to25 ⇡, V 30 e.g., sequential r29 Compared with state-of-the-art methods that consider users’ se33        neural networks (RNNs) to embed previously purchased products for current interest.kes the action policy ⇡ more robust toetworkˆ; b) the trajectory manager (TM) employs various planning strategies (e.g., intrinsictrinsicginatio  depth- $\mathbf { \nabla } m$ rs and forces the imagination policy ⇡ˆ to generate moors and forces the imagination popolicy ⇡ˆ to generate more accurat   t here) to control the granularity of $\dot { \mathcal { T } }$ ccurate actions.y ⇡ˆ to generate more accurate actions.26 session-based recom32 In many real-w30 e.g., sequential recommenders with recurrent neural networksSubmitted to 32nd Conference on Neural Information Processing Sysctions.; c) the imagination-augmented executor (IAE) optimizes In practice, the imagination policy ⇡ˆ can be obtained from policy distillation [] or fixed target networklike DQN []. The former distills the action policy ⇡(s ; ✓) into a smaller rollout network ⇡ˆ(s ; ˆ ✓),practice, the imagination policy ⇡ˆ can be obtained from policy distillation [] or fixed target netwo27  28 purchase.33 To m      Submitted to 32nd Conference on Neural Information Processing Systems (NIPS 2018). Do not distribute.⇡ˆ can be obtained from policy distillation [] or fixed target network The latter uses a shared but slowlythe network using the internal imagination data and external rewarding data (e.g., purchases).
+
+ot+1this also helps I2E learn a predictive representation of rewarding states, and in turn should allow the anging target network ⇡ˆ(s ; ✓), where ✓ are previous parameters in ⇡(s ; ✓). By imitating theSubmitted to 32nd Conference on Neural Information Processing Sy ), where ✓ are previous parameters in ⇡(s ; ✓). By imitating theImagination Core In order to simulate imagined trajectories, we rely on environment models that, Sttion policy ⇡, the imagined trajectories will be similar to agent experiences in the real environment;33 To model this phenomctories will be similar to agent experiences in the real environment;given the present state and a candidate action, make predictions about the future states. In general, 2 IRN do not predict the rewards, since it is not useful as reported in []. and in RS, rewards of different actionsis also helps I2E learn a predictive representation of rewarding states, and in turn should allow theive representation of rewarding states, and in turn should allow thewe can employ an environment model that build on action-conditional next-step predictors (Oh et al., ot+2are hard to specifysy learning of the action policy under the sparse reward signals. Submitted to 32nd Confe under the sparse reward signals.       2015), and train it in an unsupervised fashion from agent experiences. However, the predictors usually 4suffer from model errors, resulting in poor agent performance, and require extra computational cost 2(e.g., pre-training). Besides, the predictors may learn a trivial identical function, since the state e hard to specify transition in agent trajectories (or session data) is deterministic, i.e., $s _ { t + 1 } = s _ { t } \cup \{ i _ { t } \}$ and $i _ { t } = a _ { t }$ . In this work, we derive a static environment model from the state transition: $\hat { s } _ { t + \tau + 1 } = \hat { s } _ { t + \tau } \cup \{ \hat { i } _ { t + \tau } \}$ , $\hat { i } _ { t + \tau } = \hat { a } _ { t + \tau }$ and $\hat { s } _ { t } = s _ { t }$ , where $\tau$ is the length of the imagined rollout, $\hat { a } _ { t + \tau }$ the output action of the imagination policy $\hat { \pi }$ . During training, the generated item $\hat { i } _ { t + \tau }$ may not be the true purchase/click, RLAgentbut we still use it for self-supervised reconstruction. This makes the action policy $\pi$ more robust to intrinsic errors and forces the imagination policy $\hat { \pi }$ to generate more accurate actions.
+
+In practice, the imagination policy $\hat { \pi }$ v1can be obtained from policy distillation (Racanière et al., 2017) or a fixed target network like DQN (Mnih et al., 2015). The former distills the action policy $\pi ( s _ { t } ; \theta )$ into a smaller rollout network $\hat { \pi } ( s _ { t } ; \hat { \theta } )$ , using a cross-entropy loss, $\begin{array} { r } { l _ { \pi , \hat { \pi } } ( s _ { t } ) = \sum _ { a } \pi ( a | s _ { t } ) l o g \hat { \pi } ( a | s _ { t } ; \hat { \theta } ) } \end{array}$ . The latter uses a shared but slowly changing network $\hat { \pi } ( s _ { t } ; \theta ^ { - } )$ , where $\theta ^ { - }$ are previous parameters in $\pi ( s _ { t } ; \theta )$ . By imitating the action policy $\pi$ , the imagined trajectories will be similar to agent experiences in the real environment; this also helps $I A E$ learn predictive representations of rewarding states, and in turn should allow the easy learning of the action policy under the sparse reward signals.
+
+Trajectory Manager The $T M$ rolls out the $I C$ over multiple time steps into the future, generating multiple imagined trajectories with the present information. Additionally, various planning strategies are supported for trajectory simulation: breadth- $n$ , depth- $\mathbf { \nabla } m$ and their combination. For breadth- $\mathbf { \nabla } \cdot n$ imagination, the TM generates $n$ trajectories, $\hat { T _ { 1 } } , \dots , \hat { T _ { n } }$ , over one time step from the current state $s _ { t }$ , i.e., $\hat { \mathcal { T } } _ { j } = \{ \hat { i } _ { j , t } \}$ . Empirically, the $I A E$ using breadth- $^ n$ imagination will motivate the agent to focus on short-term events and predict the next step more accurately (e.g., enhancing the next-click prediction performance even when we do not formalize the click event as reward). For depth- $\mathbf { \nabla } m$ imagination, the $T M$ generates only one trajectory $\hat { \mathcal { T } } _ { 1 }$ through $m$ time steps, i.e., $\hat { \mathcal { T } } _ { 1 } = \{ \hat { i } _ { 1 , t } , \dots , \hat { i } _ { 1 , t + m - 1 } \}$ . This enables the agent to learn to plan the long-term future, and thus recommend items that yield high rewards (purchases). Finally, we can also achieve the trade-off between breadth- $\mathbf { \nabla } \cdot n$ and depth- $m$ to balance the long-term rewards and short-term rewards. Specifically, we generate $n$ trajectories, and each has a depth $m$ , i.e., $\{ \hat { T } \} = \{ \{ \hat { i } _ { 1 , t } , . . . , \hat { i } _ { 1 , t + m - 1 } \} , . . . , \{ \hat { i } _ { n , t } , . . . , \hat { i } _ { n , t + m - 1 } \} \}$ .
+
+Imagination-augmented Executor As mentioned before, the $I A E$ uses external rewarding data and internal imagined trajectories to update its action policy $\{ \hat { i } _ { j , t } , \dots , \hat { i } _ { j , t + m - 1 } \}$ T , we define a multi-step reconstruction objective using the mean squared error: . For the $j$ -th trajectory, $\hat { \mathcal { T } } _ { j } =$
+
+$$
+\mathcal { L } _ { j } = \sum _ { \tau = 1 } ^ { m } \gamma ^ { \tau } | | A E ( \phi ( \hat { \mathcal { T } } _ { j , \tau } ) ) - \phi ( \hat { \mathcal { T } } _ { j , \tau } ) | | ^ { 2 } ,
+$$
+
+where $\hat { \mathcal T } _ { j , \tau }$ is the $\tau$ -th imagined item, $\phi ( \cdot )$ is the input encoder shared by $\pi$ (for joint feature learning), $A E$ is the autoencoder that reconstructs the input feature, and the discounting factor $\gamma$ is used to mimic Bellman type operations. In practice, we found that action representation learning (i.e., the output weights of $\pi$ ) is crucial to the final performance due to the large size of candidate items. Therefore, we use the one-hot transformation as $\phi ( \cdot )$ and replace $A E$ with the policy $\pi$ (excluding the final softmax function), and only back-propagate errors in the positions of imagined items. Specifically, for an imagined item, the mean squared error is computed between one and its activation value through $\pi$ ; errors for other items are turned to be zero. In this case, the policy $\pi$ is optimized not only to predict purchases accurately but also to minimize the reconstruction error of imagined items over time. Take a session for example, $\{ i _ { 0 } , i _ { 1 } , . . . , i _ { q - 1 } , i _ { q } \}$ $\dot { \iota } _ { q }$ is the final purchased item), $\pi$ is trained $t + 1$ times using imagination reconstruction and once using A3C updating (for the purchase event); the overall reconstruction loss for this session is defined as $\begin{array} { r } { \dot { \mathcal { L } } _ { I R N } \dot { = } \sum _ { t = 0 } ^ { q } \sum _ { j = 1 } ^ { n } \dot { \mathcal { L } _ { j } } ( s _ { t } ) } \end{array}$ .
+
+There are several advantages associated with the imagination reconstruction. First, imagined trajectories provide auxiliary signals for reward augmentation. This speeds up policy learning when extrinsic reward is delayed and sparse. Second, by using a shared policy network, $I A E$ enables exploration and exploitation, and thus improves feature learning when the number of actions is large. Third, compared with agents that predict the next observations for robust learning (Mirowski et al., 2016), our $I A E$ reconstructs the imagined trajectories generated by the TM over time for predictive learning. When external reward is provided, $I A E$ can be considered as a process of goal-oriented learning or semi-supervised learning. This self-supervised reconstruction approach also achieves excellent click and purchase prediction performance even without any external reward (unsupervised learning in this case, where inputs and output targets used for training $\pi$ are all counterfactual predictions, and the input states are transformed through actions in order to match predictions, i.e., predictive perception in Seth (2014)).
+
+# 5 EXPERIMENTS
+
+# 5.1 EXPERIMENTAL SETUP
+
+We evaluate the proposed model on the dataset of ACM RecSys 2015 Challenge2, which contains click-streams that sometimes end with purchase events. The purchase reward and the click reward (if used) are empirically set as 5 and 1, respectively. Focusing on the most recent events has shown to be effective (Jannach & Ludewig, 2017); therefore we collect the latest one month of data and keep sessions that contain purchases. We follow the preprocessing steps in Hidasi et al. (2016) and use the sessions of the last three day for testing (we also trained IRN and baselines on the full six month training set, with slightly poorer results; the relative improvements remained similar). The training set contains 72274 sessions of 683530 events, and the test set contains 7223 sessions of 63100 events, and the number of items is 9167. We also derive a separate validation set from the training set, with sessions of the last day in the training set. The evaluation is done by incrementally adding the previous observed event to the session and checking the rank of the next event. We adopt Recall and Mean Reciprocal Rank (MRR) for top- $K$ evaluations, and take the averaged scores over all events in the test set. We repeat this procedure 5 times and report the average performance. Without special mention, we set $K$ to 5 for both metrics. Besides, we build an environment using session-parallel mini-batches, where the agent interacts with multiple sessions simultaneously (see section 3).
+
+Baselines We choose various baseline agents for comparison, including: (1) BPR (Rendle et al., 2009), a pairwise ranking approach, widely applied as a benchmark; (2) GRU4Rec (Hidasi et al., 2016), a RNN-based approach for session-based recommendations with a BPR-max loss function (note that original GRU4Rec gives much lower purchase performance, thus we only use the clicked items from the same mini-batch as negative examples); (3) CKNN (Jannach & Ludewig, 2017), a session-based KNN method, which incorporates heuristics to sample similar past sessions as neighbors; (4) A3C-F and A3C-P, the base agents without imagination, using the click and purchase reward (-F) or only the purchase reward (-P); (5) IRN-F and IRN-P, the proposed models that augment A3C with imagiantion; (6) PRN-P, an A3C agent that reconstructs the previous observed trajectories (i.e., click/purchase sequences), using the purchase reward.
+
+Table 1: Recommendation performance for purchase and click events.   
+
+<table><tr><td>Purchase</td><td>Recall@3</td><td>Recall@5</td><td>Recall@10</td><td>MRR@3</td><td>MRR@5</td><td>MRR@10</td></tr><tr><td>BPR CKNN</td><td>0.471 0.519</td><td>0.679 0.685</td><td>0.820 0.805</td><td>0.372 0.420</td><td>0.434 0.470</td><td>0.458 0.490</td></tr><tr><td>GRU4Rec A3C-F</td><td>0.500 0.505</td><td>0.675 0.684</td><td>0.788 0.813</td><td>0.404 0.405</td><td>0.457 0.458</td><td>0.475 0.479</td></tr><tr><td>A3C-P IRN-F</td><td>0.512 0.525</td><td>0.704 0.734</td><td>0.828 0.879</td><td>0.411 0.419</td><td>0.469 0.482</td><td>0.489 0.506</td></tr><tr><td>PRN-P</td><td>0.515</td><td>0.718</td><td>0.867</td><td>0.409</td><td>0.471</td><td>0.492</td></tr><tr><td>IRN-P</td><td>0.537</td><td>0.752</td><td>0.908</td><td>0.427</td><td>0.490</td><td>0.514</td></tr><tr><td>Click</td><td>Recall@3</td><td>Recall@5</td><td>Recall@10</td><td>MRR@3</td><td>MRR@5</td><td>MRR@10</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>BPR</td><td>0.198</td><td>0.249</td><td>0.276</td><td>0.168</td><td>0.182</td><td>0.187</td></tr><tr><td>CKNN</td><td>0.206</td><td>0.292</td><td>0.383</td><td>0.167</td><td>0.190</td><td></td></tr><tr><td>GRU4Rec</td><td></td><td></td><td></td><td></td><td></td><td>0.207</td></tr><tr><td></td><td>0.201</td><td>0.297</td><td>0.413</td><td>0.162</td><td>0.192</td><td>0.209</td></tr><tr><td>A3C-F</td><td>0.207</td><td>0.313</td><td>0.437</td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>0.168</td><td>0.200</td><td>0.218</td></tr><tr><td>A3C-P</td><td>0.197</td><td>0.277</td><td>0.367</td><td>0.160</td><td>0.184</td><td>0.198</td></tr><tr><td>IRN-F</td><td>0.210</td><td>0.310</td><td>0.422</td><td>0.171</td><td>0.198</td><td>0.216</td></tr><tr><td>PRN-P</td><td>0.185</td><td>0.255</td><td>0.328</td><td>0.154</td><td>0.172</td><td>0.184</td></tr><tr><td>IRN-P</td><td>0.212</td><td>0.306</td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td>0.406</td><td>0.173</td><td>0.200</td><td>0.215</td></tr></table>
+
+Architecture We implemented IRN via Tensorflow3, which will be released publicly upon acceptance. We use grid search to tune hyperparameters of IRN and compared baselines on the validation set. Specifically, the input state $s _ { t }$ is passed through a LSTM with 256 units which takes in the one-hot representation of recent clicked/purchased items. The output of the LSTM layer is fed into two separate fully connected layers with linear projections, to predict the value function and the action. A softmax layer is added on top of the action output to generate the probability of 9167 actions. The discounting value $\gamma$ is 0.99. The imagination policy $\hat { \pi }$ is obtained from $\pi$ using the fixed target network, and the weights of $\hat { \pi }$ are updated after every 500 iterations. Without special mentioned, TM employs the combination of breadth-2 and width-2 for internal planning. The imagination reconstruction is performed every one environment step. The A3C updating is performed with immediate purchase reward (when found) or 3-step returns (when click reward is used). Besides, weights of IRN are initialized using Xavier-initializer (Glorot & Bengio, 2010) and trained via Adam optimizer (Kingma & Ba, 2014) with the learning rate and the batch size set to 0.001 and 128, respectively.
+
+# 5.2 RESULTS
+
+We first evaluate the top- $K$ recommendation performance. The experimental results are summarized in Table 1. From the purchase performance comparison, we get:
+
+• A3C-P has already outperformed classical session-based recommenders (BPR, CKNN and GRU4Rec) on Recall metrics and achieved comparable results on MRR metrics. GRU4Rec gives poor purchase performance, as it focuses on next-click prediction. Comparing IRN-P with A3C-P, we can see that the purchase (and click) performance can be significantly improved with imagination reconstruction, demonstrating that IRN-P can guess what you like via internal planning and learn predictive representations. IRN-P consistently outperforms IRN-F, and A3C-P also outperforms A3C-F for purchase prediction. This demonstrates that purchase events can better characterize user interest, and the agents may be biased if clicks are used as reward.
+
+![](images/4994dc825dc07563fe55e1994541f6a5378441befdc39ba6a693f37605410e6d.jpg)  
+Figure 3: Possibility of being stuck in an non-optimal policy with varying reward sparsity for IRN.
+
+![](images/202dd3a3f89630b3e6a3a142cb26343c702ec19124c5fac0752fb6011b2c19bf.jpg)  
+(b) Purchase MRR $\textcircled { a } 5$ on the validation set
+
+(a) Purchase Recall $\textcircled { a } 5$ on the validation set
+
+Table 2: Purchase performance comparison with varying reward density $d$   
+
+<table><tr><td rowspan="2"></td><td colspan="3">Recall@5</td><td colspan="3">MRR@5</td></tr><tr><td>Algorithm</td><td>|d = 0.1 d = 0.05</td><td>d= 0.0</td><td>d=0.1</td><td>d = 0.05</td><td>d= 0.0</td></tr><tr><td>A3C-F</td><td>0.679</td><td>0.676</td><td>0.674</td><td>0.460</td><td>0.459</td><td>0.459</td></tr><tr><td>A3C-P</td><td>0.687</td><td>0.578</td><td>一</td><td>0.464</td><td>0.398</td><td>一</td></tr><tr><td>IRN-F</td><td>0.730</td><td>0.726</td><td>0.720</td><td>0.480</td><td>0.478</td><td>0.473</td></tr><tr><td>IRN-P</td><td>0.735</td><td>0.725</td><td>0.653</td><td>0.482</td><td>0.475</td><td>0.432</td></tr></table>
+
+Comparing PRN-P with A3C-P and IRN-P, we found that reconstructing the previous actual trajectories (i.e., click-streams) also improves the purchase performance (compared to A3CP). This is because that PRN-P can learn better representations for clicked items, and user purchases are sometimes contained in the click-streams. Besides, IRN-P outperforms PRN-P, since PRN-P introduces stronger supervision and may not know what is the final goal, while the imagination reconstruction (without any real trajectories) performs semi-supervised learning, which promotes more robust policy learning.
+
+From the click performance comparison, we get:
+
+• GRU4Rec achieves excellent next-click performance (e.g., top-5 and top-10) compared to BPR and CKNN, as it models the session data via sequential classification. A3C-F performs much better than A3C-P and GRU4Rec. This indicates that RL-based recommenders trained on clicks can generate actions that better preserve the sequential property, possibly due to the accumulated click reward (of longer sessions). Somewhat interesting, IRN-P significantly outperforms A3C-P, and gets comparable results like IRN-F and A3C-F. This demonstrates that the IRN-P agent may learn to plan and reconstruct the previous clicked trajectories even when only the purchase reward is provided.
+
+Varying the degree of purchase reward sparsity We now explore the robustness of four RLbased recommenders to different purchase reward density. We randomly sample a $d$ proportion of purchase events from the training set. The click events remain unchanged. As shown in Table 2, A3C-F and IRN-F are robust to different purchase sparsity, since purchases are sometimes contained in the click sequences. IRN using only the click reward for policy learning can also enhance the purchase prediction performance (see $d = 0$ ). While the performance of A3C-P degrades with sparser purchase reward, the proposed IRN-P achieves comparable performance; the imagination reconstruction promotes predictive learning of rewarding states. To our surprise, we have found that IRN-P performs well even without any external reward from the environment (i.e., predictive perception, see A3C-F and IRN-P with $d = 0$ ). Minimizing the imagination error of predictive trajectories over time enables the agent to learn sequential patterns in an unsupervised fashion. Figure 3 compares the performance of IRN-P on different reward sparsity setting, where one epoch contains nearly 5000 iterations. We can observe that the performance of all models is gradually improved, and IRN-P with a larger $d$ learns faster, indicating better exploration and exploitation. Note that IRN-P with $d = 0$ will adversely decrease the performance due to the local over-training. In extreme cases, a final purchase decision would be unknown, the imagination reconstruction may be applied without external reward, but we can use the click prediction performance for validation and early stopping.
+
+![](images/2ebacfb232dbbb4660f34993bf01a9c03bc1f12f1076eda4d99ff99965d7c7b3.jpg)  
+Figure 4: Purchase performance comparison on Recall $\textcircled { a } 5$ and MRR $@$ 5 metrics. (a, b) Results under the cold-start scenarios. (c, d) Results in online learning.
+
+Table 3: Performance of IRN-P with different planning strategies (breadth- $n$ and depth- $m$ ).   
+
+<table><tr><td colspan="4">Recall@5</td><td colspan="3">MRR@5</td></tr><tr><td>n,m</td><td>First</td><td>Click</td><td>Purchase</td><td>First</td><td>Click</td><td>Purchase</td></tr><tr><td>1,1</td><td>0.397</td><td>0.307</td><td>0.733</td><td>0.299</td><td>0.199</td><td>0.477</td></tr><tr><td>2,1</td><td>0.413</td><td>0.316</td><td>0.736</td><td>0.308</td><td>0.205</td><td>0.479</td></tr><tr><td>1,2</td><td>0.344</td><td>0.294</td><td>0.755</td><td>0.280</td><td>0.190</td><td>0.488</td></tr><tr><td>2,2</td><td>0.372</td><td>0.306</td><td>0.752</td><td>0.290</td><td>0.200</td><td>0.490</td></tr></table>
+
+Effectiveness of the trajectory manager We then analyze the effectiveness of different planners of the TM. Table 3 shows the best results obtained with IRN-P when using alternative measurements. Note that the purchase event in one session is usually the last user interaction, and "First" means that the second event is evaluated separately (the first clicked item is used as the initial state). We can observe that, different planners equip the agent with different prediction capacity. For instance, IRN-P with a larger $n$ performs better on First and Click metrics, indicating that the agent with breadth- $\mathbf { \nabla } \cdot n$ planning focuses more on short-term rewards. On the contrary, a larger $m$ can improve the purchase performance at a cost of lower First and Click results, since depth- $m$ planning enables the agent to imagine the longer future. The combination of breadth- $\mathbf { \nabla } \cdot n$ and depth- $\mathbf { \nabla } m$ can better balance the long-term rewards and short-term rewards. Besides, for IRN-P without any external reward $( d = 0 . 0 )$ ), the depth-2 planner gives better performance than depth-1 and breadth-2 on three measurements (by $2 - 5 \%$ ), possibly due to the more predictive representations learned after unsupervised training. However, for IRN with purchase reward (semi-supervised learning), the purchase performance cannot be improved using longer imagined trajectories. One possible reason is that two steps of imagination reconstruction is sufficient for learning to predict the future events recursively; the first step of IRN learns to capture the difference of adjacent input states, and the second step learns to look ahead the future purchase signal accurately.
+
+Robustness to the cold-start scenario We simulate a cold-start scenario using the test set. Specifically, we use a parameter $c$ to control the number of items in the input state (a set of one-hot vectors of clicked items), i.e., new events will not be added to the input state if the number of items exceeds $c$ , but are still used for evaluations. Figure 4 (a,b) shows the purchase performance w.r.t. the cold-start parameter $c$ . We can see that IRN-P outperforms A3C-P and A3C-F over all ranges of $c$ , verifying the effectiveness of imagination reconstruction. In other words, IRN-P can guess what you like (or learn predictive representations) and obtain a better user (or session) profile. Besides, A3C-F achieves slightly better results than A3C-P, which is different from that in Table 1. A3C-F that trained with the click reward can preserve the sequential property of sessions, and thus provide auxiliary (implicit) information under the cold-start setting (in the warm-start setting, the agent using more clicked items as input may be biased and thus focuses on next-click prediction).
+
+Adaptation to user interest To demonstrate that IRN can improve data efficiency and promote quick adaptation to user interest, we create a more realistic scenario for online learning. Specifically, the training set is sorted in chronological order, and each event is used only once for training. The test set remains unchanged. Figure 4 (c,d) shows the purchase performance that is evaluated on both the training set ("-tr", averaged over a batch of training purchases) and the test set ("-te", averaged over all test purchases); for a given purchase event in the training set, the model first checks its rank and then uses it for an incremental update (measuring the short-term interest). We can see that, IRN-P promotes quick adaptation to user interest (after 2000 iterations) compared to A3C-P and A3C-F on the two datasets, and IRN-P-te shows improved data efficiency and purchase performance compared to A3C-F-te and A3C-P-te after online learning. Different from IRN-P, A3C-F and A3C-P perform poorly on the test set (compared to that of the last training batch); this highlights the importance of most recent events and demonstrates that IRN-P can capture user’s long-term interest ahead of time.
+
+# 6 CONCLUSION
+
+In this paper, we propose the IRN architecture for session-based recommendation, which is inspired by the theories of cognition science. IRN can be regarded as a combination of model-based planning and self-supervised reinforcement learning, which employs a self-supervised reconstruction method for predictive learning, using the imagined trajectories generated by the internal model. We conducted experiments to study the impacts of difference components under different scenarios, verifying the effectiveness of our IRN architecture. We believe this kind of approaches has the potential to make a shift in the way we use recommender systems.
+
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+    {
+        "type": "text",
+        "text": "PURCHASE AS REWARD: SESSION-BASED RECOM-MENDATION BY IMAGINATION RECONSTRUCTION",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Anonymous authors Paper under double-blind review ",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "One of the key challenges of session-based recommender systems is to enhance users’ purchase intentions. In this paper, we formulate the sequential interactions between user sessions and a recommender agent as a Markov Decision Process (MDP). In practice, the purchase reward is delayed and sparse, and may be buried by clicks, making it an impoverished signal for policy learning. Inspired by the prediction error minimization (PEM) and embodied cognition, we propose a simple architecture to augment reward, namely Imagination Reconstruction Network (IRN). Specifically, IRN enables the agent to explore its environment and learn predictive representations via three key components. The imagination core generates predicted trajectories, i.e., imagined items that users may purchase. The trajectory manager controls the granularity of imagined trajectories using the planning strategies, which balances the long-term rewards and short-term rewards. To optimize the action policy, the imagination-augmented executor minimizes the intrinsic imagination error of simulated trajectories by self-supervised reconstruction, while maximizing the extrinsic reward using model-free algorithms. Empirically, IRN promotes quicker adaptation to user interest, and shows improved robustness to the cold-start scenario and ultimately higher purchase performance compared to several baselines. Somewhat surprisingly, IRN using only the purchase reward achieves excellent next-click prediction performance, demonstrating that the agent can \"guess what you like\" via internal planning. ",
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+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "A good recommender system can enhance both satisfaction for users and profit for content providers (Gomez-Uribe & Hunt, 2016). In many real-world scenarios, the recommender systems make recommendations based only on the current browsing session, given the absence of user profiles (because the user is new or not tracked or not logged in, till the final purchase step). A session is a group of sequential interactions between a user and the system within a short period of time. To model this phenomenon, Recurrent Neural Networks (RNNs) were recently employed as session-based recommenders (Hidasi et al., 2016; Jannach & Ludewig, 2017). For instance, GRU4Rec (Hidasi et al., 2016) utilizes the session-parallel mini-batch training to handle the variable lengths of sessions, and predicts the next action given the sequence of items in the current session. However, these approaches primarily focus on next-click prediction and model the session data via sequential classification, and thus cannot distinguish the different effects of user clicks and purchases. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this paper, we consider the session-based recommendation as a Markov Decision Process (MDP), which can take into account both the click reward and the purchase reward (see Figure 1), and leverage Reinforcement Learning (RL) to learn the recommendation strategy. In practice, several challenges need to be addressed. First, the recommender systems involve large numbers of discrete actions (i.e., items), making current RL algorithms difficult to apply (Dulac-Arnold et al., 2015; Sunehag et al., 2015). This requires the agent to explore its environment for action feature learning and develop an ability to generalize over unseen actions. Second, we found it difficult to specify the click reward and the purchase reward; the policy may be biased by long sessions that contain many user clicks, as RL algorithms maximize the accumulated reward. Besides, real-world recommender systems require quick adaptation to user interest and robustness to the cold-start scenario (i.e., enhancing the purchase performance of short sessions). Therefore, we will be particularly interested in a case where only the purchase is used as reward (click sequences are used as inputs of the imagination core for exploration).1 However, the purchase reward is delayed and sparse (one session may contain only one purchase), making it a difficult signal for policy learning. ",
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+    {
+        "type": "text",
+        "text": "To augment reward and encourage exploration, we present the Imagination Reconstruction Network (IRN), which is inspired by the prediction error minimization (PEM) (Hohwy, 2016; Friston, 2010; Lotter et al., 2017) and embodied cognition (Clark, 2013; Burr & Jones, 2016; Seth, 2014; de Bruin & Michael, 2017) from the neuroscience literature. The PEM is an increasingly influential theory that stresses the importance of brain-body-world interactions in cognitive processes, involving perception, action and learning. In particular, IRN can be regarded as a proof-of-concept for the PEM from the recommendation perspective, following the ideas in Burr & Jones (2016) and Seth (2014) — the brain utilizes active sensorimotor predictions (or counterfactual predictions) to represent states of affairs in the world in an action-oriented manner. Specifically, the imagination core of IRN that predicts the future trajectories (i.e., a set of imagined items that user may purchase) conditioned on actions sampled from the imagination policy, can be considered as the generative model of the brain that simulates sensorimotor predictions. To update the action policy, the imagination-augmented executor minimizes the intrinsic imagination error of predicted trajectories by self-supervised reconstruction, while maximizing the extrinsic reward using RL, with shared input state or output action representations for predictive learning. This simulates the active perception (a key aspect of embodied cognition) of the body under the PEM framework, which adapts the agent to possible changes that arise from the ongoing exploratory action. Note that the imagination policy imitates the action policy through distillation or a delayed target network, and thus IRN constructs a loop between brain and body, encouraging the agent to perform actions that can reduce the error in the agent’s ability to predict the future events (Pathak et al., 2017). IRN equips the agent with a planning module, trajectory manager, that controls the granularity of imagined trajectories using the planning strategies (e.g., breadth- $\\mathbf { \\nabla } \\cdot n$ and depth- $\\mathbf { \\nabla } m$ ). Besides, IRN is a combination of model-based planning and self-supervised RL, as the imagined trajectories provide dense training signals for auxiliary task learning (see section 2). ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The key contributions of this paper are summarized as follows: ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "• We formulate the session-based recommendation as a MDP, and leverage deep RL to learn the optimal recommendation policy, and also discuss several challenges when RL is applied. We consider a special case where only the purchase is used as reward, and then propose the IRN architecture to optimize the sparser but more business-critical purchase signals, which draws inspiration from the theories of cognition science. We present a self-supervised reconstruction method for predictive learning, which minimizes the imagination error of simulated trajectories over time. IRN achieves excellent click and purchase performance even without any external reward (predictive perception (Seth, 2014)). We conduct a comprehensive set of experiments to demonstrate the effectiveness of IRN. Compared to several baselines, IRN improves data efficiency, promotes quicker adaptation to user interest, and shows improved robustness to the cold-start scenario and ultimately higher purchase performance. These are highly valuable properties in an industrial context. ",
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+    {
+        "type": "text",
+        "text": "2 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
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+            698,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Session-based Recommenders Classical latent factor models (e.g., matrix factorization) break down in the session-based setting, given the absence of user profiles. A natural solution is the neighborhood approach like item-to-item recommendation (Mirowski et al., 2016). In this setting, an item similarity matrix can be precomputed based on co-occurrences of clicked items in sessions. However, this method only considers the last clicked item of the browsing session for recommendations, ignoring the sequential information of the previous events. Previous works also attempt to apply MDPs in the recommendation systems (Shani et al., 2002; Tavakol & Brefeld, 2014). The main issue is that the state space quickly becomes unmanageable due to the large number of items (IRN employs deep learning to overcome this problem and thus generalizes well to unseen states). Recently, RNNs have been used with success in this area (Hidasi et al., 2016; Hidasi & Karatzoglou, 2017; Jannach & Ludewig, 2017). GRU4Rec (Hidasi et al., 2016) is the first application of RNNs to model the session data, which can provide recommendations after each click for new sessions. ",
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+    {
+        "type": "image",
+        "img_path": "images/7c0479c96ae8d2260faae1dbd823d4c79eda8ec9cf8e5608f7c9041c6c8a5a84.jpg",
+        "image_caption": [
+            "ractice, we may pay more attention to the improvements of       nhance the purchase, and achieve a satisfactory (short sessions).Figure 1: The agent-user interactions in MDP: the recommender agent (RA) generates a list of hort sessions).e is huge.candidate items after each user click (green) or purchase (red). "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "equential recommenders with user historical records. ForHowever, GRU4Rec utilizes the session-parallel mini-batch training to handle the variable lengths of formation Processing Systems (NIPS 2018). Do not distribute.ith buy). using GRU4REC classification problem do notion problem do notchains, our methodsessions; this trick cannot effectively capture sequentiality of sessions, since the network is trained practice, we may pay more attention to the improvements ofhe improvements ofistorical behaviors.using the BP algorithm (not BPTT for RNNs). These models primarily focus on next-click prediction rrent neural networks (RNN) or Markov chains, our methodor recommendation,rical records. Forand model the click-streams via sequential classification, while here we aim at modeling the purchase h buy). using GRU4REC classification problem do notctice, we may pay more attention to the improvements of current interests are influenced by their historical behaviors.sequential recommenders with user historical records. For   atasets.Do not distribute.behavior and enhancing users’ purchase intentions. Besides, IRN is built on RL, which encodes at consider users’ sequential behavior for recommendation,formation Processing Systems (NIPS 2018). Do not distribute. historical behaviors.torical records. Forsequentiality of states into the value function. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "uential recommenders with user historical records. ForImagination-augmented Agents All approaches incorporating off-policy experience (e.g., imagmation Processing Systems (NIPS 2018). Do not distribute.ined trajectories) generated by a learned model can be categorized into model-based reinforcement learning (Racanière et al., 2017; Pascanu et al., 2017; Silver et al., 2017; Sutton, 1991). By using an internal model of the world, the agent can generalize to unseen states, remain valid in the real environment, and exploit additional training signals to improve data efficiency. However, the performance of model-based agents usually suffers from model errors resulting from function approximation. I2As (Racanière et al., 2017) were proposed to address this issue. I2As augment model-free agents with imagination and use an interpretation module to handle imperfect predictions. The imagined trajectories of I2As are provided as additional context (i.e., input features) to a policy network, while the proposed IRN uses the trajectories as additional training signals for self-supervised reconstruction. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Self-supervised Reinforcement Learning In many real-world scenarios, reward is extremely sparse and delayed, and the agent updates its policy only if it reaches a pre-defined goal state. To model this phenomenon, self-supervised reinforcement learning have often been used, which accelerates the acquisition of a useful representation with auxiliary task learning (Jaderberg et al., 2016; Pathak et al., 2017; Mirowski et al., 2016; Shelhamer et al., 2016). Specifically, auxiliary tasks provide additional losses for feature learning, and can be trained instantaneously using the self-supervision from the environment. For instance, UNREAL (Jaderberg et al., 2016) maximizes many other pseudo-reward functions simultaneously, e.g., pixel change control, with a common representation shared by all tasks. In contrast, the proposed IRN do not require the external supervision from the environment, i.e., self-supervised reconstruction is performed on internal imagined trajectories. ",
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+    },
+    {
+        "type": "text",
+        "text": "3 PRELIMINARIES ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We interpret the sequential recommendation task based on the standard reinforcement learning setting: An recommender agent (RA) interacts with an environment $\\mathcal { E }$ (or user sessions) by sequentially choosing a list of recommendation items over a number of discrete time steps, so as to maximize its cumulative reward. As shown in Figure 1, we model this problem as a Markov Decision Process (MDP), which consists of a tuple of five elements $( S , A , P , R , \\gamma )$ : ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "State space $S$ : A state $s _ { t } ~ \\in ~ S$ is defined as the previous items that a user clicked/purchased in one session. Specifically, the initial state $s _ { 1 }$ contains the first item $i _ { 0 }$ of one session. The items in $s _ { t } = \\{ i _ { 0 } , i _ { 1 } , . . . , i _ { t - 1 } \\}$ are sorted in chronological order. ",
+        "bbox": [
+            174,
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Action space $A$ : An action $a _ { t } \\in A$ is to recommend items to a user at time $t$ according to its policy $\\pi$ , where $\\pi$ is a mapping from $s _ { t }$ to $a _ { t }$ . We assume that the RA only recommends one item to the user each time, since we use the observed click/purchase sequences for off-policy training. During off-policy evaluation, we can recommend a list of $K$ candidates to the user. ",
+        "bbox": [
+            174,
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Reward $R$ : After the RA takes an action $a _ { t }$ at the state $s _ { t }$ , i.e., recommending an item to a user, the user browses this item and provides her feedback (click or purchase). The agent receives a scalar reward $r ( s _ { t } , a _ { t } )$ according to the user’s feedback. We also define the $k$ -step return starting from state $s _ { t }$ as $\\begin{array} { r } { G _ { t , t + k } ( s _ { t } ) = \\sum _ { j = t } ^ { t + k } \\gamma ^ { j - t } r ( s _ { j } , a _ { j } ) } \\end{array}$ , where $\\gamma \\in [ 0 , 1 ]$ is a discounting factor. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Transition probability $P$ : Transition probability $p ( s _ { t + 1 } | s _ { t } , a _ { t } )$ defines the probability of state transition from $s _ { t }$ to $s _ { t + 1 }$ when the RA takes action $a _ { t }$ . In this case, the state transition is deterministic after taking the ground-true action $a _ { t } = i _ { t }$ , i.e., $p ( s _ { t + 1 } | s _ { t } , i _ { t } ) = 1$ and $s _ { t + 1 } = s _ { t } \\cup \\{ i _ { t } \\}$ . ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The goal of the RA is to find an optimal policy $\\pi ^ { * }$ , such that $V ^ { \\pi ^ { * } } ( s _ { 1 } ) \\geq V ^ { \\pi } ( s _ { 1 } )$ for all policies $\\pi$ and start state $s _ { 1 }$ , where $V ^ { \\pi } ( s _ { t } )$ is the expected return for a state $s _ { t }$ when following a policy $\\pi$ , i.e., $V ^ { \\pi } ( s _ { t } ) = \\mathbb { E } _ { s _ { j > t } \\sim S , a _ { j > t } \\sim \\pi } [ G _ { t , \\infty } ( s _ { t } ) ]$ (or $\\mathrm { \\overline { { E } } } _ { s \\sim \\pi } [ G _ { t , \\infty } ( s _ { t } ) ]$ for simplicity). ",
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+        "type": "text",
+        "text": "Asynchronous Advantage Actor-Critic. This paper builds upon the A3C algorithm, an actorcritic approach that constructs a policy network $\\pi ( a | s ; \\theta )$ and a value function network $V ( s ; \\theta _ { v } )$ , with all non-output layers shared (Mnih et al., 2016). The policy and the value function are adjusted towards the bootstrapped $k$ -step return $G _ { t , t + k } ( s _ { t } ) + \\gamma ^ { k + 1 } \\dot { V } ( s _ { t + k + 1 } ; \\theta _ { v } )$ , $\\mathcal { L } _ { A 3 C } = \\mathcal { L } _ { \\pi } + \\mathcal { L } _ { V R }$ , where $\\mathcal { L } _ { \\pi } = - \\mathbb { E } _ { s \\sim \\pi } \\left[ G _ { 1 , \\infty } ( s _ { 1 } ) \\right]$ and $\\mathcal { L } _ { V R } = \\mathbb { E } _ { s \\sim \\pi } \\left[ A ( s _ { t } , a _ { t } ) \\right]$ . The advantage function $A ( s _ { t } , a _ { t } )$ (Baird III, 1993) is computed as the difference of the bootstrapped $k$ -step return and the current state value estimate: ",
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+    {
+        "type": "equation",
+        "img_path": "images/fd597887a697669c13003a16d1bf3dc5c6d3070f6229296056c3b4436a778941.jpg",
+        "text": "$$\nA ( s _ { t } , a _ { t } ) = G _ { t , t + k } ( s _ { t } ) + \\gamma ^ { k + 1 } V ( s _ { t + k + 1 } ; \\theta _ { v } ^ { - } ) - V ( s _ { t } ; \\theta _ { v } ) ,\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where $\\theta _ { v } ^ { - }$ are the parameters of the previous target network. To increase the probability of rewarding actions, A3C applies an update $g ( \\bar { \\theta ) }$ to the parameters $\\theta$ using an unbiased estimation (Sutton et al., 2000): ",
+        "bbox": [
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+    {
+        "type": "equation",
+        "img_path": "images/7454562808607f2e43b1588f358bc52e761099c451719d2eccb5d8a8b99bd320.jpg",
+        "text": "$$\ng ( \\theta ) = \\nabla _ { \\theta } \\log \\pi ( a _ { t } | s _ { t } ; \\theta ) A ( s _ { t } , a _ { t } ) .\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "The value function $V ( s ; \\theta _ { v } )$ is updated following the recursive definition of the Bellman Equation, $V ( s _ { t } ; \\theta _ { v } ) = \\mathbb { E } _ { s \\sim \\pi } \\left[ G _ { t , t + k } ( s _ { t } ) + \\gamma ^ { k + 1 } V ( s _ { t + k + 1 } ; \\theta _ { v } ) \\right]$ . Then $g ( \\theta _ { v } )$ is obtained by minimizing a squared error between the target return and the current value estimate: ",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/e30c1e2605ea787a138ad5facec05d2eedc520352f0f019fbba92bf8e4dd7601.jpg",
+        "text": "$$\ng ( \\theta _ { v } ) = - A ( s _ { t } , a _ { t } ) \\frac { \\partial } { \\partial \\theta _ { v } } V ( s _ { t } ; \\theta _ { v } ) .\n$$",
+        "text_format": "latex",
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+        "type": "text",
+        "text": "In A3C multiple agents interact in parallel, with multiple instances of the environment. The asynchronous execution accelerates and stabilizes learning. In practice, we combine A3C with the session-parallel mini-batches proposed in (Hidasi et al., 2016). Each instance of the agent interacts with multiple sessions simultaneously, gathering $M$ samples from different sessions at a time step. After $k$ steps, the agent updates its policy and value network according to Eq. (2)(3), using $k * M$ samples. This decorrelates updates between samples of one session in the instance level. Besides, to build the A3C agent, we employ an LSTM that jointly approximates both policy $\\pi$ and value function $V$ , given the one-hot vectors of previous items clicked/purchased as inputs. ",
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+    {
+        "type": "text",
+        "text": "4 IRN ARCHITECTURE ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In this section we incorporate the imagination reconstruction module into the model-free agents (e.g., A3C) in order to enhance data efficiency, promote more robust learning and ultimately higher performance under the sparse extrinsic reward. Our IRN implements an imagination-augmented policy via three key components (Figure 2). The imagination core $( I C )$ predicts the next time steps conditioned on actions sampled from the imagination policy $\\hat { \\pi }$ . At a time step $t$ , the trajectory manager (TM) determines how to roll out the $I C$ under the planning strategy, and then produces imagined trajectories $\\hat { T _ { 1 } } , \\dots , \\hat { T _ { n } }$ of an observable world state $s _ { t }$ . Each trajectory $\\hat { T _ { j } }$ is a sequence of items $\\{ \\hat { i } _ { j , t } , \\hat { i } _ { j , t + 1 } , \\ldots \\}$ , that users may purchase (or click) from the current time $t$ . The Imaginationaugmented Executor $( I A E )$ aggregates the internal data resulting from imagination and external rewarding data to update its action policy $\\pi$ . Specifically, the $I A E$ optimizes the policy $\\pi$ by maximizing the extrinsic reward while minimizing the intrinsic imagination error. In principle, IRN encourages exploration and learns predictive representations via imagination rollouts, which promotes quick adaptation to user interest and robustness to the cold-start scenario. ",
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+    {
+        "type": "image",
+        "img_path": "images/f8520ca08c0f83e6c0e4b54ca0deec2292206bd1595905e810a70095d85f4835.jpg",
+        "image_caption": [
+            "ˆit+⌧ = ˆat+⌧ and sˆt = st , where ⌧ is the length of the imagined rollout, aˆt+⌧ the4agination policy ⇡ˆ. During training, the generated i28 32 31 example, [23] adopted Markov chain toning, the generated item ˆit+⌧ may not be the true puFigure 2: IRN architecture: a) the imagination core $( I C )$ action of theˆit+⌧ may not be the true purchase, but we24 aT \u00001 28 purchase.chase.any real-world applications, users’ current interests are inel user behavior sequences, and [19, 31] leveragedse, but wepredicts the next time step and then generates imagination policy ⇡ˆ. During training,still use it for self-supervised reconstrill use it for self-supervis32 recurr33 prediconstruction of I2E. This mdistillation [] or fixed targthe imagined trajectories $\\hat { \\tau }$ errorgenerated item it+⌧ may not be the true purchase, but weon of I2E. This makes the action policy ⇡ more robust to reconstruction of I2E. This makes the action policy ⇡ more robust to25 ⇡, V 30 e.g., sequential r29 Compared with state-of-the-art methods that consider users’ se33        neural networks (RNNs) to embed previously purchased products for current interest.kes the action policy ⇡ more robust toetworkˆ; b) the trajectory manager (TM) employs various planning strategies (e.g., intrinsictrinsicginatio  depth- $\\mathbf { \\nabla } m$ rs and forces the imagination policy ⇡ˆ to generate moors and forces the imagination popolicy ⇡ˆ to generate more accurat   t here) to control the granularity of $\\dot { \\mathcal { T } }$ ccurate actions.y ⇡ˆ to generate more accurate actions.26 session-based recom32 In many real-w30 e.g., sequential recommenders with recurrent neural networksSubmitted to 32nd Conference on Neural Information Processing Sysctions.; c) the imagination-augmented executor (IAE) optimizes In practice, the imagination policy ⇡ˆ can be obtained from policy distillation [] or fixed target networklike DQN []. The former distills the action policy ⇡(s ; ✓) into a smaller rollout network ⇡ˆ(s ; ˆ ✓),practice, the imagination policy ⇡ˆ can be obtained from policy distillation [] or fixed target netwo27  28 purchase.33 To m      Submitted to 32nd Conference on Neural Information Processing Systems (NIPS 2018). Do not distribute.⇡ˆ can be obtained from policy distillation [] or fixed target network The latter uses a shared but slowlythe network using the internal imagination data and external rewarding data (e.g., purchases). "
+        ],
+        "image_footnote": [],
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+        "type": "text",
+        "text": "ot+1this also helps I2E learn a predictive representation of rewarding states, and in turn should allow the anging target network ⇡ˆ(s ; ✓\u0000), where ✓\u0000 are previous parameters in ⇡(s ; ✓). By imitating theSubmitted to 32nd Conference on Neural Information Processing Sy ), where ✓\u0000 are previous parameters in ⇡(s ; ✓). By imitating theImagination Core In order to simulate imagined trajectories, we rely on environment models that, Sttion policy ⇡, the imagined trajectories will be similar to agent experiences in the real environment;33 To model this phenomctories will be similar to agent experiences in the real environment;given the present state and a candidate action, make predictions about the future states. In general, 2 IRN do not predict the rewards, since it is not useful as reported in []. and in RS, rewards of different actionsis also helps I2E learn a predictive representation of rewarding states, and in turn should allow theive representation of rewarding states, and in turn should allow thewe can employ an environment model that build on action-conditional next-step predictors (Oh et al., ot+2are hard to specifysy learning of the action policy under the sparse reward signals. Submitted to 32nd Confe under the sparse reward signals.       2015), and train it in an unsupervised fashion from agent experiences. However, the predictors usually 4suffer from model errors, resulting in poor agent performance, and require extra computational cost 2(e.g., pre-training). Besides, the predictors may learn a trivial identical function, since the state e hard to specify transition in agent trajectories (or session data) is deterministic, i.e., $s _ { t + 1 } = s _ { t } \\cup \\{ i _ { t } \\}$ and $i _ { t } = a _ { t }$ . In this work, we derive a static environment model from the state transition: $\\hat { s } _ { t + \\tau + 1 } = \\hat { s } _ { t + \\tau } \\cup \\{ \\hat { i } _ { t + \\tau } \\}$ , $\\hat { i } _ { t + \\tau } = \\hat { a } _ { t + \\tau }$ and $\\hat { s } _ { t } = s _ { t }$ , where $\\tau$ is the length of the imagined rollout, $\\hat { a } _ { t + \\tau }$ the output action of the imagination policy $\\hat { \\pi }$ . During training, the generated item $\\hat { i } _ { t + \\tau }$ may not be the true purchase/click, RLAgentbut we still use it for self-supervised reconstruction. This makes the action policy $\\pi$ more robust to intrinsic errors and forces the imagination policy $\\hat { \\pi }$ to generate more accurate actions. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In practice, the imagination policy $\\hat { \\pi }$ v1can be obtained from policy distillation (Racanière et al., 2017) or a fixed target network like DQN (Mnih et al., 2015). The former distills the action policy $\\pi ( s _ { t } ; \\theta )$ into a smaller rollout network $\\hat { \\pi } ( s _ { t } ; \\hat { \\theta } )$ , using a cross-entropy loss, $\\begin{array} { r } { l _ { \\pi , \\hat { \\pi } } ( s _ { t } ) = \\sum _ { a } \\pi ( a | s _ { t } ) l o g \\hat { \\pi } ( a | s _ { t } ; \\hat { \\theta } ) } \\end{array}$ . The latter uses a shared but slowly changing network $\\hat { \\pi } ( s _ { t } ; \\theta ^ { - } )$ , where $\\theta ^ { - }$ are previous parameters in $\\pi ( s _ { t } ; \\theta )$ . By imitating the action policy $\\pi$ , the imagined trajectories will be similar to agent experiences in the real environment; this also helps $I A E$ learn predictive representations of rewarding states, and in turn should allow the easy learning of the action policy under the sparse reward signals. ",
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+        "type": "text",
+        "text": "Trajectory Manager The $T M$ rolls out the $I C$ over multiple time steps into the future, generating multiple imagined trajectories with the present information. Additionally, various planning strategies are supported for trajectory simulation: breadth- $n$ , depth- $\\mathbf { \\nabla } m$ and their combination. For breadth- $\\mathbf { \\nabla } \\cdot n$ imagination, the TM generates $n$ trajectories, $\\hat { T _ { 1 } } , \\dots , \\hat { T _ { n } }$ , over one time step from the current state $s _ { t }$ , i.e., $\\hat { \\mathcal { T } } _ { j } = \\{ \\hat { i } _ { j , t } \\}$ . Empirically, the $I A E$ using breadth- $^ n$ imagination will motivate the agent to focus on short-term events and predict the next step more accurately (e.g., enhancing the next-click prediction performance even when we do not formalize the click event as reward). For depth- $\\mathbf { \\nabla } m$ imagination, the $T M$ generates only one trajectory $\\hat { \\mathcal { T } } _ { 1 }$ through $m$ time steps, i.e., $\\hat { \\mathcal { T } } _ { 1 } = \\{ \\hat { i } _ { 1 , t } , \\dots , \\hat { i } _ { 1 , t + m - 1 } \\}$ . This enables the agent to learn to plan the long-term future, and thus recommend items that yield high rewards (purchases). Finally, we can also achieve the trade-off between breadth- $\\mathbf { \\nabla } \\cdot n$ and depth- $m$ to balance the long-term rewards and short-term rewards. Specifically, we generate $n$ trajectories, and each has a depth $m$ , i.e., $\\{ \\hat { T } \\} = \\{ \\{ \\hat { i } _ { 1 , t } , . . . , \\hat { i } _ { 1 , t + m - 1 } \\} , . . . , \\{ \\hat { i } _ { n , t } , . . . , \\hat { i } _ { n , t + m - 1 } \\} \\}$ . ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Imagination-augmented Executor As mentioned before, the $I A E$ uses external rewarding data and internal imagined trajectories to update its action policy $\\{ \\hat { i } _ { j , t } , \\dots , \\hat { i } _ { j , t + m - 1 } \\}$ T , we define a multi-step reconstruction objective using the mean squared error: . For the $j$ -th trajectory, $\\hat { \\mathcal { T } } _ { j } =$ ",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/ee270226b976ee0b0e2ded55d71f2fef908ca95ac6c98c59e5c4e1440faaaa20.jpg",
+        "text": "$$\n\\mathcal { L } _ { j } = \\sum _ { \\tau = 1 } ^ { m } \\gamma ^ { \\tau } | | A E ( \\phi ( \\hat { \\mathcal { T } } _ { j , \\tau } ) ) - \\phi ( \\hat { \\mathcal { T } } _ { j , \\tau } ) | | ^ { 2 } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 5
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+    {
+        "type": "text",
+        "text": "where $\\hat { \\mathcal T } _ { j , \\tau }$ is the $\\tau$ -th imagined item, $\\phi ( \\cdot )$ is the input encoder shared by $\\pi$ (for joint feature learning), $A E$ is the autoencoder that reconstructs the input feature, and the discounting factor $\\gamma$ is used to mimic Bellman type operations. In practice, we found that action representation learning (i.e., the output weights of $\\pi$ ) is crucial to the final performance due to the large size of candidate items. Therefore, we use the one-hot transformation as $\\phi ( \\cdot )$ and replace $A E$ with the policy $\\pi$ (excluding the final softmax function), and only back-propagate errors in the positions of imagined items. Specifically, for an imagined item, the mean squared error is computed between one and its activation value through $\\pi$ ; errors for other items are turned to be zero. In this case, the policy $\\pi$ is optimized not only to predict purchases accurately but also to minimize the reconstruction error of imagined items over time. Take a session for example, $\\{ i _ { 0 } , i _ { 1 } , . . . , i _ { q - 1 } , i _ { q } \\}$ $\\dot { \\iota } _ { q }$ is the final purchased item), $\\pi$ is trained $t + 1$ times using imagination reconstruction and once using A3C updating (for the purchase event); the overall reconstruction loss for this session is defined as $\\begin{array} { r } { \\dot { \\mathcal { L } } _ { I R N } \\dot { = } \\sum _ { t = 0 } ^ { q } \\sum _ { j = 1 } ^ { n } \\dot { \\mathcal { L } _ { j } } ( s _ { t } ) } \\end{array}$ . ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "There are several advantages associated with the imagination reconstruction. First, imagined trajectories provide auxiliary signals for reward augmentation. This speeds up policy learning when extrinsic reward is delayed and sparse. Second, by using a shared policy network, $I A E$ enables exploration and exploitation, and thus improves feature learning when the number of actions is large. Third, compared with agents that predict the next observations for robust learning (Mirowski et al., 2016), our $I A E$ reconstructs the imagined trajectories generated by the TM over time for predictive learning. When external reward is provided, $I A E$ can be considered as a process of goal-oriented learning or semi-supervised learning. This self-supervised reconstruction approach also achieves excellent click and purchase prediction performance even without any external reward (unsupervised learning in this case, where inputs and output targets used for training $\\pi$ are all counterfactual predictions, and the input states are transformed through actions in order to match predictions, i.e., predictive perception in Seth (2014)). ",
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+    {
+        "type": "text",
+        "text": "5 EXPERIMENTS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "5.1 EXPERIMENTAL SETUP ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We evaluate the proposed model on the dataset of ACM RecSys 2015 Challenge2, which contains click-streams that sometimes end with purchase events. The purchase reward and the click reward (if used) are empirically set as 5 and 1, respectively. Focusing on the most recent events has shown to be effective (Jannach & Ludewig, 2017); therefore we collect the latest one month of data and keep sessions that contain purchases. We follow the preprocessing steps in Hidasi et al. (2016) and use the sessions of the last three day for testing (we also trained IRN and baselines on the full six month training set, with slightly poorer results; the relative improvements remained similar). The training set contains 72274 sessions of 683530 events, and the test set contains 7223 sessions of 63100 events, and the number of items is 9167. We also derive a separate validation set from the training set, with sessions of the last day in the training set. The evaluation is done by incrementally adding the previous observed event to the session and checking the rank of the next event. We adopt Recall and Mean Reciprocal Rank (MRR) for top- $K$ evaluations, and take the averaged scores over all events in the test set. We repeat this procedure 5 times and report the average performance. Without special mention, we set $K$ to 5 for both metrics. Besides, we build an environment using session-parallel mini-batches, where the agent interacts with multiple sessions simultaneously (see section 3). ",
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+        "text": "Baselines We choose various baseline agents for comparison, including: (1) BPR (Rendle et al., 2009), a pairwise ranking approach, widely applied as a benchmark; (2) GRU4Rec (Hidasi et al., 2016), a RNN-based approach for session-based recommendations with a BPR-max loss function (note that original GRU4Rec gives much lower purchase performance, thus we only use the clicked items from the same mini-batch as negative examples); (3) CKNN (Jannach & Ludewig, 2017), a session-based KNN method, which incorporates heuristics to sample similar past sessions as neighbors; (4) A3C-F and A3C-P, the base agents without imagination, using the click and purchase reward (-F) or only the purchase reward (-P); (5) IRN-F and IRN-P, the proposed models that augment A3C with imagiantion; (6) PRN-P, an A3C agent that reconstructs the previous observed trajectories (i.e., click/purchase sequences), using the purchase reward. ",
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+    {
+        "type": "table",
+        "img_path": "images/75d1401c0f4884477ea3639baa54a2bb0e63a13600b372b39b845648c3ec56da.jpg",
+        "table_caption": [
+            "Table 1: Recommendation performance for purchase and click events. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Purchase</td><td>Recall@3</td><td>Recall@5</td><td>Recall@10</td><td>MRR@3</td><td>MRR@5</td><td>MRR@10</td></tr><tr><td>BPR CKNN</td><td>0.471 0.519</td><td>0.679 0.685</td><td>0.820 0.805</td><td>0.372 0.420</td><td>0.434 0.470</td><td>0.458 0.490</td></tr><tr><td>GRU4Rec A3C-F</td><td>0.500 0.505</td><td>0.675 0.684</td><td>0.788 0.813</td><td>0.404 0.405</td><td>0.457 0.458</td><td>0.475 0.479</td></tr><tr><td>A3C-P IRN-F</td><td>0.512 0.525</td><td>0.704 0.734</td><td>0.828 0.879</td><td>0.411 0.419</td><td>0.469 0.482</td><td>0.489 0.506</td></tr><tr><td>PRN-P</td><td>0.515</td><td>0.718</td><td>0.867</td><td>0.409</td><td>0.471</td><td>0.492</td></tr><tr><td>IRN-P</td><td>0.537</td><td>0.752</td><td>0.908</td><td>0.427</td><td>0.490</td><td>0.514</td></tr><tr><td>Click</td><td>Recall@3</td><td>Recall@5</td><td>Recall@10</td><td>MRR@3</td><td>MRR@5</td><td>MRR@10</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>BPR</td><td>0.198</td><td>0.249</td><td>0.276</td><td>0.168</td><td>0.182</td><td>0.187</td></tr><tr><td>CKNN</td><td>0.206</td><td>0.292</td><td>0.383</td><td>0.167</td><td>0.190</td><td></td></tr><tr><td>GRU4Rec</td><td></td><td></td><td></td><td></td><td></td><td>0.207</td></tr><tr><td></td><td>0.201</td><td>0.297</td><td>0.413</td><td>0.162</td><td>0.192</td><td>0.209</td></tr><tr><td>A3C-F</td><td>0.207</td><td>0.313</td><td>0.437</td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>0.168</td><td>0.200</td><td>0.218</td></tr><tr><td>A3C-P</td><td>0.197</td><td>0.277</td><td>0.367</td><td>0.160</td><td>0.184</td><td>0.198</td></tr><tr><td>IRN-F</td><td>0.210</td><td>0.310</td><td>0.422</td><td>0.171</td><td>0.198</td><td>0.216</td></tr><tr><td>PRN-P</td><td>0.185</td><td>0.255</td><td>0.328</td><td>0.154</td><td>0.172</td><td>0.184</td></tr><tr><td>IRN-P</td><td>0.212</td><td>0.306</td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td>0.406</td><td>0.173</td><td>0.200</td><td>0.215</td></tr></table>",
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+        "type": "text",
+        "text": "Architecture We implemented IRN via Tensorflow3, which will be released publicly upon acceptance. We use grid search to tune hyperparameters of IRN and compared baselines on the validation set. Specifically, the input state $s _ { t }$ is passed through a LSTM with 256 units which takes in the one-hot representation of recent clicked/purchased items. The output of the LSTM layer is fed into two separate fully connected layers with linear projections, to predict the value function and the action. A softmax layer is added on top of the action output to generate the probability of 9167 actions. The discounting value $\\gamma$ is 0.99. The imagination policy $\\hat { \\pi }$ is obtained from $\\pi$ using the fixed target network, and the weights of $\\hat { \\pi }$ are updated after every 500 iterations. Without special mentioned, TM employs the combination of breadth-2 and width-2 for internal planning. The imagination reconstruction is performed every one environment step. The A3C updating is performed with immediate purchase reward (when found) or 3-step returns (when click reward is used). Besides, weights of IRN are initialized using Xavier-initializer (Glorot & Bengio, 2010) and trained via Adam optimizer (Kingma & Ba, 2014) with the learning rate and the batch size set to 0.001 and 128, respectively. ",
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+    {
+        "type": "text",
+        "text": "5.2 RESULTS ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We first evaluate the top- $K$ recommendation performance. The experimental results are summarized in Table 1. From the purchase performance comparison, we get: ",
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+    {
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+        "text": "• A3C-P has already outperformed classical session-based recommenders (BPR, CKNN and GRU4Rec) on Recall metrics and achieved comparable results on MRR metrics. GRU4Rec gives poor purchase performance, as it focuses on next-click prediction. Comparing IRN-P with A3C-P, we can see that the purchase (and click) performance can be significantly improved with imagination reconstruction, demonstrating that IRN-P can guess what you like via internal planning and learn predictive representations. IRN-P consistently outperforms IRN-F, and A3C-P also outperforms A3C-F for purchase prediction. This demonstrates that purchase events can better characterize user interest, and the agents may be biased if clicks are used as reward. ",
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+        "type": "image",
+        "img_path": "images/4994dc825dc07563fe55e1994541f6a5378441befdc39ba6a693f37605410e6d.jpg",
+        "image_caption": [
+            "Figure 3: Possibility of being stuck in an non-optimal policy with varying reward sparsity for IRN. "
+        ],
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+        "img_path": "images/202dd3a3f89630b3e6a3a142cb26343c702ec19124c5fac0752fb6011b2c19bf.jpg",
+        "image_caption": [
+            "(b) Purchase MRR $\\textcircled { a } 5$ on the validation set "
+        ],
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+    {
+        "type": "text",
+        "text": "(a) Purchase Recall $\\textcircled { a } 5$ on the validation set ",
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+        "type": "table",
+        "img_path": "images/4479454d002385287875de6aefa84cdcd0e5c0484a30ea35278750816fdd8645.jpg",
+        "table_caption": [
+            "Table 2: Purchase performance comparison with varying reward density $d$ "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"></td><td colspan=\"3\">Recall@5</td><td colspan=\"3\">MRR@5</td></tr><tr><td>Algorithm</td><td>|d = 0.1 d = 0.05</td><td>d= 0.0</td><td>d=0.1</td><td>d = 0.05</td><td>d= 0.0</td></tr><tr><td>A3C-F</td><td>0.679</td><td>0.676</td><td>0.674</td><td>0.460</td><td>0.459</td><td>0.459</td></tr><tr><td>A3C-P</td><td>0.687</td><td>0.578</td><td>一</td><td>0.464</td><td>0.398</td><td>一</td></tr><tr><td>IRN-F</td><td>0.730</td><td>0.726</td><td>0.720</td><td>0.480</td><td>0.478</td><td>0.473</td></tr><tr><td>IRN-P</td><td>0.735</td><td>0.725</td><td>0.653</td><td>0.482</td><td>0.475</td><td>0.432</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Comparing PRN-P with A3C-P and IRN-P, we found that reconstructing the previous actual trajectories (i.e., click-streams) also improves the purchase performance (compared to A3CP). This is because that PRN-P can learn better representations for clicked items, and user purchases are sometimes contained in the click-streams. Besides, IRN-P outperforms PRN-P, since PRN-P introduces stronger supervision and may not know what is the final goal, while the imagination reconstruction (without any real trajectories) performs semi-supervised learning, which promotes more robust policy learning. ",
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+    {
+        "type": "text",
+        "text": "From the click performance comparison, we get: ",
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+    {
+        "type": "text",
+        "text": "• GRU4Rec achieves excellent next-click performance (e.g., top-5 and top-10) compared to BPR and CKNN, as it models the session data via sequential classification. A3C-F performs much better than A3C-P and GRU4Rec. This indicates that RL-based recommenders trained on clicks can generate actions that better preserve the sequential property, possibly due to the accumulated click reward (of longer sessions). Somewhat interesting, IRN-P significantly outperforms A3C-P, and gets comparable results like IRN-F and A3C-F. This demonstrates that the IRN-P agent may learn to plan and reconstruct the previous clicked trajectories even when only the purchase reward is provided. ",
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+    {
+        "type": "text",
+        "text": "Varying the degree of purchase reward sparsity We now explore the robustness of four RLbased recommenders to different purchase reward density. We randomly sample a $d$ proportion of purchase events from the training set. The click events remain unchanged. As shown in Table 2, A3C-F and IRN-F are robust to different purchase sparsity, since purchases are sometimes contained in the click sequences. IRN using only the click reward for policy learning can also enhance the purchase prediction performance (see $d = 0$ ). While the performance of A3C-P degrades with sparser purchase reward, the proposed IRN-P achieves comparable performance; the imagination reconstruction promotes predictive learning of rewarding states. To our surprise, we have found that IRN-P performs well even without any external reward from the environment (i.e., predictive perception, see A3C-F and IRN-P with $d = 0$ ). Minimizing the imagination error of predictive trajectories over time enables the agent to learn sequential patterns in an unsupervised fashion. Figure 3 compares the performance of IRN-P on different reward sparsity setting, where one epoch contains nearly 5000 iterations. We can observe that the performance of all models is gradually improved, and IRN-P with a larger $d$ learns faster, indicating better exploration and exploitation. Note that IRN-P with $d = 0$ will adversely decrease the performance due to the local over-training. In extreme cases, a final purchase decision would be unknown, the imagination reconstruction may be applied without external reward, but we can use the click prediction performance for validation and early stopping. ",
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+    {
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+        "img_path": "images/2ebacfb232dbbb4660f34993bf01a9c03bc1f12f1076eda4d99ff99965d7c7b3.jpg",
+        "image_caption": [
+            "Figure 4: Purchase performance comparison on Recall $\\textcircled { a } 5$ and MRR $@$ 5 metrics. (a, b) Results under the cold-start scenarios. (c, d) Results in online learning. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "table",
+        "img_path": "images/29da7afa8f5f15620e447056432a87983b2b2e7afedbae877248a362fe79acdf.jpg",
+        "table_caption": [
+            "Table 3: Performance of IRN-P with different planning strategies (breadth- $n$ and depth- $m$ ). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"4\">Recall@5</td><td colspan=\"3\">MRR@5</td></tr><tr><td>n,m</td><td>First</td><td>Click</td><td>Purchase</td><td>First</td><td>Click</td><td>Purchase</td></tr><tr><td>1,1</td><td>0.397</td><td>0.307</td><td>0.733</td><td>0.299</td><td>0.199</td><td>0.477</td></tr><tr><td>2,1</td><td>0.413</td><td>0.316</td><td>0.736</td><td>0.308</td><td>0.205</td><td>0.479</td></tr><tr><td>1,2</td><td>0.344</td><td>0.294</td><td>0.755</td><td>0.280</td><td>0.190</td><td>0.488</td></tr><tr><td>2,2</td><td>0.372</td><td>0.306</td><td>0.752</td><td>0.290</td><td>0.200</td><td>0.490</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "Effectiveness of the trajectory manager We then analyze the effectiveness of different planners of the TM. Table 3 shows the best results obtained with IRN-P when using alternative measurements. Note that the purchase event in one session is usually the last user interaction, and \"First\" means that the second event is evaluated separately (the first clicked item is used as the initial state). We can observe that, different planners equip the agent with different prediction capacity. For instance, IRN-P with a larger $n$ performs better on First and Click metrics, indicating that the agent with breadth- $\\mathbf { \\nabla } \\cdot n$ planning focuses more on short-term rewards. On the contrary, a larger $m$ can improve the purchase performance at a cost of lower First and Click results, since depth- $m$ planning enables the agent to imagine the longer future. The combination of breadth- $\\mathbf { \\nabla } \\cdot n$ and depth- $\\mathbf { \\nabla } m$ can better balance the long-term rewards and short-term rewards. Besides, for IRN-P without any external reward $( d = 0 . 0 )$ ), the depth-2 planner gives better performance than depth-1 and breadth-2 on three measurements (by $2 - 5 \\%$ ), possibly due to the more predictive representations learned after unsupervised training. However, for IRN with purchase reward (semi-supervised learning), the purchase performance cannot be improved using longer imagined trajectories. One possible reason is that two steps of imagination reconstruction is sufficient for learning to predict the future events recursively; the first step of IRN learns to capture the difference of adjacent input states, and the second step learns to look ahead the future purchase signal accurately. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Robustness to the cold-start scenario We simulate a cold-start scenario using the test set. Specifically, we use a parameter $c$ to control the number of items in the input state (a set of one-hot vectors of clicked items), i.e., new events will not be added to the input state if the number of items exceeds $c$ , but are still used for evaluations. Figure 4 (a,b) shows the purchase performance w.r.t. the cold-start parameter $c$ . We can see that IRN-P outperforms A3C-P and A3C-F over all ranges of $c$ , verifying the effectiveness of imagination reconstruction. In other words, IRN-P can guess what you like (or learn predictive representations) and obtain a better user (or session) profile. Besides, A3C-F achieves slightly better results than A3C-P, which is different from that in Table 1. A3C-F that trained with the click reward can preserve the sequential property of sessions, and thus provide auxiliary (implicit) information under the cold-start setting (in the warm-start setting, the agent using more clicked items as input may be biased and thus focuses on next-click prediction). ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Adaptation to user interest To demonstrate that IRN can improve data efficiency and promote quick adaptation to user interest, we create a more realistic scenario for online learning. Specifically, the training set is sorted in chronological order, and each event is used only once for training. The test set remains unchanged. Figure 4 (c,d) shows the purchase performance that is evaluated on both the training set (\"-tr\", averaged over a batch of training purchases) and the test set (\"-te\", averaged over all test purchases); for a given purchase event in the training set, the model first checks its rank and then uses it for an incremental update (measuring the short-term interest). We can see that, IRN-P promotes quick adaptation to user interest (after 2000 iterations) compared to A3C-P and A3C-F on the two datasets, and IRN-P-te shows improved data efficiency and purchase performance compared to A3C-F-te and A3C-P-te after online learning. Different from IRN-P, A3C-F and A3C-P perform poorly on the test set (compared to that of the last training batch); this highlights the importance of most recent events and demonstrates that IRN-P can capture user’s long-term interest ahead of time. ",
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+    {
+        "type": "text",
+        "text": "6 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In this paper, we propose the IRN architecture for session-based recommendation, which is inspired by the theories of cognition science. IRN can be regarded as a combination of model-based planning and self-supervised reinforcement learning, which employs a self-supervised reconstruction method for predictive learning, using the imagined trajectories generated by the internal model. We conducted experiments to study the impacts of difference components under different scenarios, verifying the effectiveness of our IRN architecture. We believe this kind of approaches has the potential to make a shift in the way we use recommender systems. ",
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+    {
+        "type": "text",
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parse/train/SkxpxJBKwS/SkxpxJBKwS.md

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+# EMERGENT TOOL USE FROM MULTI-AGENTAUTOCURRICULA
+
+Bowen Baker∗ OpenAI bowen@openai.com
+
+Ingmar Kanitscheider∗ OpenAI ingmar@openai.com
+
+Todor Markov∗ OpenAI todor@openai.com
+
+Yi Wu∗   
+OpenAI   
+jxwuyi@openai.com
+
+Glenn Powell∗ OpenAI glenn@openai.com
+
+Bob McGrew∗ OpenAI bmcgrew@openai.com
+
+Igor Mordatch∗† Google Brain imordatch@google.com
+
+# ABSTRACT
+
+Through multi-agent competition, the simple objective of hide-and-seek, and standard reinforcement learning algorithms at scale, we find that agents create a selfsupervised autocurriculum inducing multiple distinct rounds of emergent strategy, many of which require sophisticated tool use and coordination. We find clear evidence of six emergent phases in agent strategy in our environment, each of which creates a new pressure for the opposing team to adapt; for instance, agents learn to build multi-object shelters using moveable boxes which in turn leads to agents discovering that they can overcome obstacles using ramps. We further provide evidence that multi-agent competition may scale better with increasing environment complexity and leads to behavior that centers around far more human-relevant skills than other self-supervised reinforcement learning methods such as intrinsic motivation. Finally, we propose transfer and fine-tuning as a way to quantitatively evaluate targeted capabilities, and we compare hide-and-seek agents to both intrinsic motivation and random initialization baselines in a suite of domain-specific intelligence tests.
+
+# 1 INTRODUCTION
+
+Creating intelligent artificial agents that can solve a wide variety of complex human-relevant tasks has been a long-standing challenge in the artificial intelligence community. Of particular relevance to humans will be agents that can sense and interact with objects in a physical world. One approach to creating these agents is to explicitly specify desired tasks and train a reinforcement learning (RL) agent to solve them. On this front, there has been much recent progress in solving physically grounded tasks, e.g. dexterous in-hand manipulation (Rajeswaran et al., 2017; Andrychowicz et al., 2018) or locomotion of complex bodies (Schulman et al., 2015; Heess et al., 2017). However, specifying reward functions or collecting demonstrations in order to supervise these tasks can be time consuming and costly. Furthermore, the learned skills in these single-agent RL settings are inherently bounded by the task description; once the agent has learned to solve the task, there is little room to improve.
+
+![](images/908a03705bb74afd247a1a3272b4c37f56d16e5c497cc2dc17b2c410933b3725.jpg)  
+Figure 1: Emergent Skill Progression From Multi-Agent Autocurricula. Through the reward signal of hide-and-seek (shown on the y-axis), agents go through 6 distinct stages of emergence. (a) Seekers (red) learn to chase hiders, and hiders learn to crudely run away. (b) Hiders (blue) learn basic tool use, using boxes and sometimes existing walls to construct forts. (c) Seekers learn to use ramps to jump into the hiders’ shelter. (d) Hiders quickly learn to move ramps to the edge of the play area, far from where they will build their fort, and lock them in place. (e) Seekers learn that they can jump from locked ramps to unlocked boxes and then surf the box to the hiders’ shelter, which is possible because the environment allows agents to move together with the box regardless of whether they are on the ground or not. (f) Hiders learn to lock all the unused boxes before constructing their fort. We plot the mean over 3 independent training runs with each individual seed shown with a dotted line. Please see openai.com/blog/emergent-tool-use for example videos.
+
+Due to the high likelihood that direct supervision will not scale to unboundedly complex tasks, many have worked on unsupervised exploration and skill acquisition methods such as intrinsic motivation. However, current undirected exploration methods scale poorly with environment complexity and are drastically different from the way organisms evolve on Earth. The vast amount of complexity and diversity on Earth evolved due to co-evolution and competition between organisms, directed by natural selection (Dawkins & Krebs, 1979). When a new successful strategy or mutation emerges, it changes the implicit task distribution neighboring agents need to solve and creates a new pressure for adaptation. These evolutionary arms races create implicit autocurricula (Leibo et al., 2019a) whereby competing agents continually create new tasks for each other. There has been much success in leveraging multi-agent autocurricula to solve multi-player games, both in classic discrete games such as Backgammon (Tesauro, 1995) and Go (Silver et al., 2017), as well as in continuous real-time domains such as Dota (OpenAI, 2018) and Starcraft (Vinyals et al., 2019). Despite the impressive emergent complexity in these environments, the learned behavior is quite abstract and disembodied from the physical world. Our work sees itself in the tradition of previous studies that showcase emergent complexity in simple physically grounded environments (Sims, 1994a; Bansal et al., 2018; Jaderberg et al., 2019; Liu et al., 2019); the success in these settings inspires confidence that inducing autocurricula in physically grounded and open-ended environments could eventually enable agents to acquire an unbounded number of human-relevant skills.
+
+We introduce a new mixed competitive and cooperative physics-based environment in which agents compete in a simple game of hide-and-seek. Through only a visibility-based reward function and competition, agents learn many emergent skills and strategies including collaborative tool use, where agents intentionally change their environment to suit their needs. For example, hiders learn to create shelter from the seekers by barricading doors or constructing multi-object forts, and as a counter strategy seekers learn to use ramps to jump into hiders’ shelter. Moreover, we observe signs of dynamic and growing complexity resulting from multi-agent competition and standard reinforcement learning algorithms; we find that agents go through as many as six distinct adaptations of strategy and counter-strategy, which are depicted in Figure 1. We further present evidence that multi-agent co-adaptation may scale better with environment complexity and qualitatively centers around more human-interpretable behavior than intrinsically motivated agents.
+
+However, as environments increase in scale and multi-agent autocurricula become more open-ended, evaluating progress by qualitative observation will become intractable. We therefore propose a suite of targeted intelligence tests to measure capabilities in our environment that we believe our agents may eventually learn, e.g. object permanence (Baillargeon & Carey, 2012), navigation, and construction. We find that for a number of the tests, agents pretrained in hide-and-seek learn faster or achieve higher final performance than agents trained from scratch or pretrained with intrinsic motivation; however, we find that the performance differences are not drastic, indicating that much of the skill and feature representations learned in hide-and-seek are entangled and hard to fine-tune.
+
+The main contributions of this work are: 1) clear evidence that multi-agent self-play can lead to emergent autocurricula with many distinct and compounding phase shifts in agent strategy, 2) evidence that when induced in a physically grounded environment, multi-agent autocurricula can lead to human-relevant skills such as tool use, 3) a proposal to use transfer as a framework for evaluating agents in open-ended environments as well as a suite of targeted intelligence tests for our domain, and 4) open-sourced environments and code1 for environment construction to encourage further research in physically grounded multi-agent autocurricula.
+
+# 2 RELATED WORK
+
+There is a long history of using self-play in multi-agent settings. Early work explored self-play using genetic algorithms (Paredis, 1995; Pollack et al., 1997; Rosin & Belew, 1995; Stanley & Miikkulainen, 2004). Sims (1994a) and Sims (1994b) studied the emergent complexity in morphology and behavior of creatures that coevolved in a simulated 3D world. Open-ended evolution was further explored in the environments Polyworld (Yaeger, 1994) and Geb (Channon et al., 1998), where agents compete and mate in a 2D world, and in Tierra (Ray, 1992) and Avida (Ofria & Wilke, 2004), where computer programs compete for computational resources. More recent work attempted to formulate necessary preconditions for open-ended evolution (Taylor, 2015; Soros & Stanley, 2014). Co-adaptation between agents and environments can also give rise to emergent complexity (Florensa et al., 2017; Sukhbaatar et al., 2018; Wang et al., 2019). In the context of multi-agent RL, Tesauro (1995), Silver et al. (2016), OpenAI (2018), Jaderberg et al. (2019) and Vinyals et al. (2019) used self-play with deep RL techniques to achieve super-human performance in Backgammon, Go, Dota, Capture-the-Flag and Starcraft, respectively. Bansal et al. (2018) trained agents in a simulated 3D physics environment to compete in various games such as sumo wrestling and soccer goal shooting. In Liu et al. (2019), agents learn to manipulate a soccer ball in a 3D soccer environment and discover emergent behaviors such as ball passing and interception. In addition, communication has also been shown to emerge from multi-agent RL (Sukhbaatar et al., 2016; Foerster et al., 2016; Lowe et al., 2017; Mordatch & Abbeel, 2018).
+
+Intrinsic motivation methods have been widely studied in the literature (Chentanez et al., 2005; Singh et al., 2010). One example is count-based exploration, where agents are incentivized to reach infrequently visited states by maintaining state visitation counts (Strehl & Littman, 2008; Bellemare et al., 2016; Tang et al., 2017) or density estimators (Ostrovski et al., 2017; Burda et al., 2019b). Another paradigm are transition-based methods, in which agents are rewarded for high prediction error in a learned forward or inverse dynamics model (Schmidhuber, 1991; Stadie et al., 2015; Mohamed & Rezende, 2015; Houthooft et al., 2016; Achiam & Sastry, 2017; Pathak et al., 2017; Burda et al., 2019a; Haber et al., 2018). Jaques et al. (2019) consider multi-agent scenarios and adopt causal influence as a motivation for coordination. In our work, we utilize intrinsic motivation methods as an alternative exploration baseline to multi-agent autocurricula. Similar comparisons have also been made in Haber et al. (2018) and Leibo et al. (2019b).
+
+Tool use is a hallmark of human and animal intelligence (Hunt, 1996; Shumaker et al., 2011); however, learning tool use in RL settings can be a hard exploration problem when rewards are unaligned. For example, in Forestier et al. (2017); Xie et al. (2019) a real-world robot learns to solve various tasks requiring tools. In Bapst et al. (2019), an agent solves construction tasks in a 2-D environment using both model-based and model-free methods. Allen et al. (2019) uses a combination of humandesigned priors and model-based policy optimization to solve a collection of physics-based puzzles requiring tool use. However, in each of these works, agents were explicitly incentivized to interact with and use tools, whereas in our environment agents implicitly create this incentive through multi-agent competition.
+
+# 3 HIDE AND SEEK
+
+Agents are tasked with competing in a two-team hide-and-seek game in a physics-based environment. The hiders are tasked with avoiding line of sight from the seekers, and the seekers are tasked with keeping vision of the hiders. There are objects scattered throughout the environment that the agents can grab and also lock in place. There are also randomly generated immovable rooms and walls that the agents must learn to navigate. Before the game of hide-and-seek begins, the hiders are given a preparation phase where the seekers are immobilized, giving the hiders a chance to run away or change their environment.
+
+There are no explicit incentives for agents to interact with objects in the environment; the only supervision given is through the hide-and-seek objective. Agents are given a team based reward; hiders are given a reward of 1 if all hiders are hidden and -1 if any hider is seen by a seeker. Seekers are given the opposite reward, -1 if all hiders are hidden and $+ 1$ otherwise. To confine agent behavior to a reasonable space, agents are penalized with a reward of -10 if they go too far outside of the play area (outside an 18 meter square). An episode lasts 240 timesteps, the first $40 \%$ of which are the preparation phase where all agents are given zero reward.
+
+We simulate the environment in the MUJOCO physics engine (Todorov et al., 2012). The world is populated with 1 to 3 hiders, 1 to 3 seekers, 3 to 9 movable boxes of which at least 3 are elongated, 2 movable ramps, and randomly generated static walls and rooms. We also experiment with a simpler, less randomized environment described in Appendix A.3. Agents observe the position, velocity, and size (in the case of the randomly shaped boxes) of objects and other agents. If entities are not in line-of-sight of the agent or not in a 135 degree cone in front of the agent, then they are masked out in the policy. Agents also have 30 range sensors arrayed evenly around them, similar to a lidar. In addition, each agent observes its own team and other agents’ teams as well as how much time is left in the preparation phase.
+
+Agents are simulated as spherical objects and have 3 action types that can be chosen simultaneously at each time step. They may move by setting a discretized force along their $x$ and $y$ axis and torque around their $z$ -axis. They have a single binary action to grab objects, which binds the agent to the closest object while the action is enabled. Agents may also lock objects in place with a single binary action. Objects may be unlocked only by agents on the team of the agent who originally locked the object. Agents may only grab or lock objects that are in front of them and within a small radius.
+
+# 4 POLICY OPTIMIZATION
+
+Agents are trained using self-play, which acts as a natural curriculum as agents always play opponents of an appropriate level.
+
+Agent policies are composed of two separate networks with different parameters – a policy network which produces an action distribution and a critic network which predicts the discounted future returns. Policies are optimized using Proximal Policy Optimization (PPO) (Schulman et al., 2017) and Generalized Advantage Estimation (GAE) (Schulman et al., 2015), and training is performed using rapid (OpenAI, 2018), a large-scale distributed RL framework. We utilize decentralized execution and centralized training. At execution time, each agent acts given only its own observations and memory state. At optimization time, we use a centralized omniscient value function for each agent, which has access to the full environment state without any information masked due to visibility, similar to Pinto et al. (2017); Lowe et al. (2017); Foerster et al. (2018).
+
+In all reported experiments, agents share the same policy parameters but act and observe independently; however, we found using separate policy parameters per agent also achieved all six stages of emergence but at reduced sample efficiency.
+
+![](images/53be154c76a41399737f60393316e9455df52396e21e45cf0d8530d7e3e7bf8b.jpg)  
+Figure 2: Agent Policy Architecture. All entities are embedded with fully connected layers with shared weights across entity types, e.g. all box entities are encoded with the same function. The policy is ego-centric so there is only one embedding of “self” and $\mathrm { ( \# { a g e n t s - 1 } ) }$ embeddings of other agents. Embeddings are then concatenated and processed with masked residual self-attention and pooled into a fixed sized vector (all of which admits a variable number of entities). $x$ and $v$ stand for state (position and orientation) and velocity.
+
+We utilize entity-centric observations (Dzeroski et al. ˇ , 2001; Diuk et al., 2008) and use attention mechanisms to capture object-level information (Duan et al., 2017; Zambaldi et al., 2018). As shown in Figure 2 we use a self-attention (Vaswani et al., 2017) based policy architecture over entities, which is permutation invariant and generalizes to varying number of entities. More details can be found in Appendix B.
+
+![](images/c22ea8c5c73f24efbf11458563eff0a549cb9d3b050df641b67f34a518782221.jpg)  
+Figure 3: Environment specific statistics used to track stages of emergence in hide-and-seek. We plot the mean across 3 seeds with each individual seed shown in a dotted line, and we overlay the 6 emergent phases of strategy: (1) Running and Chasing, (2) Fort Building, (3) Ramp Use, (4) Ramp Defense, (5) Box Surfing, (6) Surf Defense. We track the maximum movement of any box or ramp during the game as well as during the preparation phase (denoted with “Prep”). We similarly track how many objects of each type were locked at the end of the episode and preparation phase. As agents train, their interaction with the tools in their environment changes. For instance, as the agents learn to build forts they move boxes and lock boxes much more during the preparation phase.
+
+# 5 AUTO-CURRICULA AND EMERGENT BEHAVIOR
+
+As agents train against each other in hide-and-seek, as many as six distinct strategies emerge, each of which creates a previously non-existing pressure for agents to progress to the next stage. Note that there are no direct incentives for agents to interact with objects or to explore, but rather the emergent strategies are solely a result of the autocurriculum induced by multi-agent competition. Figure 1 shows the progression of emergent strategies agents learn in our environment (see Appendix A.1 for trajectory traces of each strategy2).
+
+Initially, hiders and seekers learn to crudely run away and chase. After approximately 25 million episodes of hide-and-seek, the hiders learn to use the tools at their disposal and intentionally modify their environment. They begin to construct secure shelters in which to hide by moving many boxes together or against walls and locking them in place. After another 75 million episodes, the seekers also learn rudimentary tool use; they learn to move and use ramps to jump over obstacles, allowing them to enter the hiders’ shelter. 10 million episodes later, the hiders learn to defend against this strategy; the hiders learn to bring the ramps to the edge of the play area and lock them in place, seemingly removing the only tool the seekers have at their disposal.
+
+We originally believed defending against ramp use would be the last stage of emergence in this environment; however, we were surprised to find that yet two more qualitatively new strategies emerged. After 380 million total episodes of training, the seekers learn to bring a box to the edge of the play area where the hiders have locked the ramps. The seekers then use the ramp to move on top of the box and surf it to the hiders’ shelter. This is possible because the agents’ movement action allows them to apply a force on themselves regardless of whether they are on the ground or not; if they do this while grabbing the box under them, the box will move with while they are on top of it. In response, the hiders learn to lock all of the boxes in place before building their shelter.3
+
+In all stages of strategy agents must learn to coordinate within their team. Similar to Liu et al. (2019), we use team-based rewards such that agents are required to collaborate in order to succeed; however, in our work we require neither population-based training (Jaderberg et al., 2017) or evolved dense rewards (Jaderberg et al., 2019). Notably, hiders learn efficient division of labor; for instance, when constructing shelter they often separately bring their own box to the construction area. Furthermore, as hiders attempt to defend against box surfing by locking boxes in place during the preparation phase, we find that 2 and 3 hider teams are able to lock $2 5 \%$ and $36 \%$ more boxes, respectively, than a single hider team, indicating that larger teams are able to divide labor and accomplish an objective a smaller team could not.
+
+Many stages of emergent strategy can be mapped to behavioral shifts in the way agents interact with the tools in their environment, similar to Leibo et al. (2017); Perolat et al. (2017). We therefore track basic statistics about the agents’ interaction with objects during training, shown in Figure 3. For instance, as the hiders learn to build forts, they move and lock boxes much more during the preparation phase. Similarly, as the seekers learn to move and use ramps, the ramp movement in the main phase of the game increases, and as they learn to “box surf” there is a slight increase in the box movement during the main phase of the game. Finally, as the hiders learn to defend against this strategy by locking all boxes in place, the number of locked boxes in the preparation phase increases.
+
+We found that scale plays a critical role in enabling progression through the emergent autocurricula in hide-and-seek. The default model, which uses a batch size of 64,000 and 1.6 million parameters, requires 132.3 million episodes (31.7 billion frames) over 34 hours of training to reach stage 4 of the skill progression, i.e. ramp defense. In Figure 4 we show the effect of varying the batch size in our agents ability to reach stage 4. We find that larger batch sizes lead to much quicker training time by virtue of reducing the number of required optimization steps, while only marginally affecting sample efficiency down to a batch size of 32,000; however, we found that experiments with batch sizes of 16,000 and 8,000 never converged.
+
+We find the emergent autocurriculum to be fairly robust as long as we randomize the environment during training. If randomization is
+
+![](images/b0221898a7301a15ab5d4f9425cfef74af1db24420f2c0ff4bf6eeb955821d6d.jpg)  
+Figure 4: Effect of Scale on Emergent Autocurricula. Number of episodes (blue) and wall clock time (orange) required to achieve stage 4 (ramp defense) of the emergent skill progression presented in Figure 1. Batch size denotes number of chunks, each of which consists of 10 contiguous transitions (the truncation length for backpropagation through time).
+
+reduced, we find that fewer stages of the skill progression emerges, and at times less sophisticated strategies emerge instead (e.g. hiders can learn to run away and use boxes as moveable shields.); see Appendix A.2 for more details. In addition, we find that design choices such as the minimum number of elongated boxes or giving each agent their own locking mechanism instead of a team based locking mechanism can drastically increase the sample complexity. We also experimented with adding additional objects and objectives to our hide-and-seek environment as well as with several game variants instead of hide-and-seek (see Appendix A.6). We find that these alternative environments also lead to emergent tool use, providing further evidence that multi-agent interaction is a promising path towards self-supervised skill acquisition.
+
+# 6 EVALUATION
+
+In the previous section we presented evidence that hide-and-seek induces a multi-agent autocurriculum such that agents continuously learn new skills and strategies. As is the case with many unsupervised reinforcement learning methods, the objective being optimized does not directly incentivize the learned behavior, making evaluation of those behaviors nontrivial. Tracking reward is an insufficient evaluation metric in multi-agent settings, as it can be ambiguous in indicating whether agents are improving evenly or have stagnated. Metrics like ELO (Elo, 1978) or Trueskill (Herbrich et al., 2007) can more reliably measure whether performance is improving relative to previous policy versions or other policies in a population; however, these metrics still do not give insight into whether improved performance stems from new adaptations or improving previously learned skills. Finally, using environment specific statistics such as object movement (see Figure 3) can also be ambiguous, e.g. the choice to track absolute movement does not illuminate which direction agents moved, and designing sufficient metrics will become difficult and costly as environments scale.
+
+![](images/34dc0597c5574ec3a8597f294f07730382ac32933237ed4d80d402d401eef6f8.jpg)  
+Figure 5: Behavioral Statistics from Count-Based Exploration Variants and Random Network Distillation (RND) Across 3 Seeds. We compare net box movement and maximum agent movement between state representations for count-based exploration: Single agent, 2-D box location (blue); Single agent, box location, rotation and velocity (green); 1-3 agents, full observation space (red). Also shown is RND for 1-3 agents with full observation space (purple). We train all agents to convergence as measured by their behavioral statistics.
+
+In Section 6.1, we first qualitatively compare the behaviors learned in hide-and-seek to those learned from intrinsic motivation, a common paradigm for unsupervised exploration and skill acquisition. In Section 6.2, we then propose a suite of domain-specific intelligence tests to quantitatively measure and compare agent capabilities.
+
+# 6.1 COMPARISON TO INTRINSIC MOTIVATION
+
+Intrinsic motivation has become a popular paradigm for incentivizing unsupervised exploration and skill discovery, and there has been recent success in using intrinsic motivation to make progress in sparsely rewarded settings (Bellemare et al., 2016; Burda et al., 2019b). Because intrinsically motivated agents are incentivized to explore uniformly, it is conceivable that they may not have meaningful interactions with the environment (as with the “noisy-TV” problem (Burda et al., 2019a)). As a proxy for comparing meaningful interaction in the environment, we measure agent and object movement over the course of an episode.
+
+We first compare behaviors learned in hide-and-seek to a count-based exploration baseline (Strehl & Littman, 2008) with an object invariant state representation, which is computed in a similar way as in the policy architecture in Figure 2. Count-based objectives are the simplest form of state density based incentives, where one explicitly keeps track of state visitation counts and rewards agents for reaching infrequently visited states (details can be found in Appendix D). In contrast to the original hide-and-seek environment where the initial locations of agents and objects are randomized, we restrict the initial locations to a quarter of the game area to ensure that the intrinsically motivated agents receive additional rewards for exploring.
+
+We find that count-based exploration leads to the largest agent and box movement if the state representation only contains the 2-D location of boxes: the agent consistently interacts with objects and learns to navigate. Yet, when using progressively higher-dimensional state representations, such as box location, rotation and velocity or 1-3 agents with full observation space, agent movement and, in particular, box movement decrease substantially. This is a severe limitation because it indicates that, when faced with highly complex environments, count-based exploration techniques require identifying by hand the “interesting” dimensions in state space that are relevant for the behaviors one would like the agents to discover. Conversely, multi-agent self-play does not need this degree of supervision. We also train agents with random network distillation (RND) (Burda et al., 2019b), an intrinsic motivation method designed for high dimensional observation spaces, and find it to perform slightly better than count-based exploration in the full state setting.
+
+# 6.2 TRANSFER AND FINE-TUNING AS EVALUATION
+
+We propose to use transfer to a suite of domain-specific tasks in order to asses agent capabilities. To this end, we have created 5 benchmark intelligence tests that include both supervised and reinforcement learning tasks. The tests use the same action space, observation space, and types of objects as in the hide-and-seek environment. We examine whether pretraining agents in our multi-agent environment and then fine-tuning them on the evaluation suite leads to faster convergence or improved overall performance compared to training from scratch or pretraining with count-based intrinsic motivation. We find that on 3 out of 5 tasks, agents pretrained in the hide-and-seek environment learn faster and achieve a higher final reward than both baselines.
+
+![](images/c3ed143983d75e2fa4ab0f13bde7a95b09db3136648f4beaa8e22622a16a2984.jpg)  
+Figure 6: Fine-tuning Results. We plot the mean normalized performance and $90 \%$ confidence interval across 3 seeds smoothed with an exponential moving average, except for Blueprint Construction where we plot over 6 seeds due to higher training variance.
+
+We categorize the 5 intelligence tests into 2 domains: cognition and memory tasks, and manipulation tasks. We briefly describe the tasks here; for the full task descriptions, see Appendix C. For all tasks, we reinitialize the parameters of the final dense layer and layernorm for both the policy and value networks.
+
+# Cognition and memory tasks:
+
+In the Object Counting supervised task, we aim to measure whether the agents have a sense of object permanence; the agent is pinned to a location and watches as 6 boxes each randomly move to the right or left where they eventually become obscured by a wall. It is then asked to predict how many boxes have gone to each side for many timesteps after all boxes have disappeared. The agent’s policy parameters are frozen and we initialize a classification head off of the LSTM hidden state. In the baseline, the policy network has frozen random parameters and only the classification head off of the LSTM hidden state is trained.
+
+In Lock and Return we aim to measure whether the agent can remember its original position while performing a new task. The agent must navigate an environment with 6 random rooms and 1 box, lock the box, and return to its starting position.
+
+In Sequential Lock there are 4 boxes randomly placed in 3 random rooms without doors but with a ramp in each room. The agent needs to lock all the boxes in a particular order — a box is only lockable when it is locked in the correct order — which is unobserved by the agent. The agent must discover the order, remember the position and status of visited boxes, and use ramps to navigate between rooms in order to finish the task efficiently.
+
+Manipulation tasks: With these tasks we aim to measure whether the agents have any latent skill or representation useful for manipulating objects.
+
+In the Construction From Blueprint task, there are 8 cubic boxes in an open room and between 1 and 4 target sites. The agent is tasked with placing a box on each target site.
+
+In the Shelter Construction task there are 3 elongated boxes, 5 cubic boxes, and one static cylinder.   
+The agent is tasked with building a shelter around the cylinder.
+
+Results: In Figure 6 we show the performance on the suite of tasks for the hide-and-seek, countbased, and trained from scratch policies across 3 seeds. The hide-and-seek pretrained policy performs slightly better than both the count-based and the randomly initialized baselines in Lock and Return, Sequential Lock and Construction from Blueprint; however, it performs slightly worse than the count-based baseline on Object Counting, and it achieves the same final reward but learns slightly slower than the randomly initialized baseline on Shelter Construction.
+
+We believe the cause for the mixed transfer results is rooted in agents learning skill representations that are entangled and difficult to fine-tune. We conjecture that tasks where hide-and-seek pretraining outperforms the baseline are due to reuse of learned feature representations, whereas better-than-baseline transfer on the remaining tasks would require reuse of learned skills, which is much more difficult. This evaluation metric highlights the need for developing techniques to reuse skills effectively from a policy trained in one environment to another. In addition, as future environments become more diverse and agents must use skills in more contexts, we may see more generalizable skill representations and more significant signal in this evaluation approach.
+
+In Appendix A.5 we further evaluate policies sampled during each phase of emergent strategy on the suite of targeted intelligence tasks, by which we can gain intuition as to whether the capabilities we measure improve with training, are transient and accentuated during specific phases, or generally uncorrelated to progressing through the autocurriculum. Noteably, we find the agent’s memory improves through training as indicated by performance in the navigation tasks; however, performance in the manipulation tasks is uncorrelated, and performance in object counting changes seems transient with respect to source hide-and-seek performance.
+
+# 7 DISCUSSION AND FUTURE WORK
+
+We have demonstrated that simple game rules, multi-agent competition, and standard reinforcement learning algorithms at scale can induce agents to learn complex strategies and skills. We observed emergence of as many as six distinct rounds of strategy and counter-strategy, suggesting that multiagent self-play with simple game rules in sufficiently complex environments could lead to openended growth in complexity. We then proposed to use transfer as a method to evaluate learning progress in open-ended environments and introduced a suite of targeted intelligence tests with which to compare agents in our domain.
+
+Our results with hide-and-seek should be viewed as a proof of concept showing that multi-agent autocurricula can lead to physically grounded and human-relevant behavior. We acknowledge that the strategy space in this environment is inherently bounded and likely will not surpass the six modes presented as is; however, because it is built in a high-fidelity physics simulator it is physically grounded and very extensible. In order to support further research in multi-agent autocurricula, we are open-sourcing our environment code.
+
+Hide-and-seek agents require an enormous amount of experience to progress through the six stages of emergence, likely because the reward functions are not directly aligned with the resulting behavior. While we have found that standard reinforcement learning algorithms are sufficient, reducing sample complexity in these systems will be an important line of future research. Better policy learning algorithms or policy architectures are orthogonal to our work and could be used to improve sample efficiency and performance on transfer evaluation metrics.
+
+We also found that agents were very skilled at exploiting small inaccuracies in the design of the environment, such as seekers surfing on boxes without touching the ground, hiders running away from the environment while shielding themselves with boxes, or agents exploiting inaccuracies of the physics simulations to their advantage. Investigating methods to generate environments without these unwanted behaviors is another import direction of future research (Amodei et al., 2016; Lehman et al., 2018).
+
+# ACKNOWLEDGMENTS
+
+We thank Pieter Abbeel, Rewon Child, Jeff Clune, Harri Edwards, Jessica Hamrick, Joel Liebo, John Schulman and Peter Welinder for their insightful comments on this manuscript. We also thank Alex Ray for writing parts of our open sourced code.
+
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+
+# Appendix
+
+# Table of Contents
+
+# A Further Emergence Results 17
+
+A.1 Trajectory Traces From Each Stage of Emergent Strategy . . . 17   
+A.2 Dependence of Skill Emergence on Randomness in the Training Distribution of   
+Environments 17   
+A.3 Quadrant Environment . 18   
+A.4 Further Ablations 19   
+A.5 Evaluating Agents at Different Phases of Emergence 19   
+A.6 Alternative Games to Hide-and-Seek with Secondary Objectives 20   
+A.7 Zero-shot generalization . 22
+
+# B Optimization Details 23
+
+B.1 Notation 23   
+B.2 Proximal Policy Optimization (PPO) 23   
+B.3 Generalized advantage estimation 23   
+B.4 Normalization of observations, advantage targets and value function targets 24   
+B.5 Optimization setup . 24   
+B.6 Optimization hyperparameters 24   
+B.7 Policy architecture details 24
+
+# C Intelligence Test Suite Details 25
+
+C.1 Cognition and memory task 25   
+C.2 Manipulation task 25
+
+# D Intrinsic Motivation Methods 26
+
+D.1 Counted-Based Exploration 26   
+D.2 Random Network Distillation 27   
+D.3 Fine-tuning From Intrinsic Motivation Variants . 27
+
+# A FURTHER EMERGENCE RESULTS
+
+A.1 TRAJECTORY TRACES FROM EACH STAGE OF EMERGENT STRATEGY
+
+![](images/4877eab54983afcb8ccae807dd0b93d1ebe5d9e4af418e50a1071b8310abba58.jpg)  
+Figure A.1: Trajectory Traces From Each Stage of Emergent Strategy. Rows correspond to different strategies, columns to characteristic snapshots in chronological order within an episode that showcase the strategy. Running and chasing: Hiders (blue) try to hide behind walls and moveable objects, and seekers (red) chase and search for hiders. Fort building: During the preparation phase (first 3 snapshots), hiders build a fort out of 3 boxes and hide inside. Seekers are not able to overcome this barrier during the remainder of the trial. Ramp use: During the preparation phase, hiders build a fort out of 2 boxes and a wall (1st and 2nd snapshot). After the preparation phase, a seeker grabs a ramp (3rd snapshot), drags it towards the fort (4th snapshot) and uses it to enter the fort (5th snapshot). Ramp defense: Hiders prevent ramp use by dragging ramps away and locking them in place during the preparation phase (1st, 2nd and 3rd snapshot). They then build a fort in safe distance from the ramps (4th snapshot). After the preparation phase, seekers are not able to enter the fort (5th snapshot). Box surfing: A single hider locks both ramps in place and hides inside a fort built from 2 boxes and an interior wall during the preparation phase (1st and 2nd snapshot). The seeker grabs a square box (3rd snapshot) and drags it next to one of the locked ramps to jump on top (4th snapshot). It then “surfs” on the box to the edge of the fort and jumps inside (5th snapshot). Surf defense: During the preparation phase, hiders lock all ramps and boxes in place (1st, 2nd and 3rd snapshot) and construct a fort out of 3 boxes (4th snapshot). After the preparation phase, seekers are not able to enter the fort (5th snapshot).
+
+# A.2 DEPENDENCE OF SKILL EMERGENCE ON RANDOMNESS IN THE TRAINING DISTRIBUTION OF ENVIRONMENTS
+
+Discovering tool use is a difficult exploration problem, as only a very specific set of actions will lead to an increase in reward. During training, we find that randomization over many components of our environment, such as the number of agents in each team, the number of boxes, the shape of boxes (square or elongated), the initial location of agents and objects and the presence and location of interior and exterior walls helps emergence, despite leading to a broader training distribution. As we successively reduce the amount of randomization, we find that fewer stages of skill progression emerges, and with at times less sophisticated strategies (e.g. hiders learn to run away and use boxes as moveable shields), Table A.1.
+
+Table A.1: Number of stages of emergence for different levels of environmental randomization (batch size is held constant).   
+
+<table><tr><td rowspan=1 colspan=1>team size</td><td rowspan=1 colspan=1># boxes</td><td rowspan=1 colspan=1>box shape</td><td rowspan=1 colspan=1>initiallocation</td><td rowspan=1 colspan=1>walls</td><td rowspan=1 colspan=1>emergence</td></tr><tr><td rowspan=1 colspan=1>1-3</td><td rowspan=1 colspan=1>3-9</td><td rowspan=1 colspan=1>random</td><td rowspan=1 colspan=1>random</td><td rowspan=1 colspan=1>random</td><td rowspan=1 colspan=1>6 stages</td></tr><tr><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>3-9</td><td rowspan=1 colspan=1>random</td><td rowspan=1 colspan=1>random</td><td rowspan=1 colspan=1>random</td><td rowspan=1 colspan=1>6 stages</td></tr><tr><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>7</td><td rowspan=1 colspan=1>fixed</td><td rowspan=1 colspan=1>random</td><td rowspan=1 colspan=1>random</td><td rowspan=1 colspan=1>6 stages</td></tr><tr><td rowspan=1 colspan=1>1-3</td><td rowspan=1 colspan=1>3-9</td><td rowspan=1 colspan=1>random</td><td rowspan=1 colspan=1>random</td><td rowspan=1 colspan=1>no walls</td><td rowspan=1 colspan=1>4 stages</td></tr><tr><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>3-9</td><td rowspan=1 colspan=1>random</td><td rowspan=1 colspan=1>random</td><td rowspan=1 colspan=1>no walls</td><td rowspan=1 colspan=1>2 stages*</td></tr><tr><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>7</td><td rowspan=1 colspan=1>fixed</td><td rowspan=1 colspan=1>random</td><td rowspan=1 colspan=1>no walls</td><td rowspan=1 colspan=1>2 stages*</td></tr><tr><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>7</td><td rowspan=1 colspan=1>fixed</td><td rowspan=1 colspan=1>fixed</td><td rowspan=1 colspan=1>no walls</td><td rowspan=1 colspan=1>2 stages</td></tr></table>
+
+∗ Hiders run away and use boxes as movable shields.
+
+![](images/c52f43b4b0880ae0396e77afc492edc1fa9420a663ed5d9649b5276b585e5387.jpg)  
+Figure A.2: Sample Trajectory Traces From Each Stage of Emergent Strategy in the Quadrant Environment. Rows correspond to different strategies, columns to characteristic snapshots in chronological order within an episode that showcase the strategy. Running and chasing: Hiders (blue) try to hide behind walls and moveable objects, seekers (red) chase and search for hiders. Fort building: During the preparation phase (first 3 snapshots), hiders push the two boxes into the two doors of the lower right room and lock them in place. Seekers are not able to overcome this barrier during the remainder of the trial. Ramp use: During the preparation phase, hiders secure the room using the two boxes (1st and 2nd snapshot). After the preparation phase, a seeker grabs the ramp (3rd snapshot), drags it towards the walls of the room (4th snapshot) and both seekers use the ramp to enter the room (5th snapshot). Ramp defense: Hiders prevent ramp use by grabbing the ramp during the preparation phase (2nd snapshot), pulling it inside the room (3rd snapshot), and then secure the doors using the 2 blocks (4th snapshot). After the preparation phase, the seekers are not able to enter the room (5th snapshot). Also, note that while one hider brings the ramp into the room, the other hider drags a box out of corner and then passes it to its team mate (3rd and 4th snapshot), evidence of sophisticated coordination between hiders.
+
+# A.3 QUADRANT ENVIRONMENT
+
+As well as the default random rooms environment described above, we also train and evaluate agents in the much simpler quadrant environment (Figure A.2) for illustration purposes. This environment consists of a room in the lower right corner that is connected by 1-2 doors to the remainder of the environment. Unlike in the main environment, the interior walls are fixed and only the location of the doors vary from episode to episode. Hiders are spawned randomly in the environment, but seekers are only spawned outside the room. Two cubic boxes are spawned inside the room and one ramp is spawned inside or outside the room. Both hiders and seekers receive a negative reward if they leave the environment or if they bring an object outside the environment. Also, in contrast to the main environment, only boxes, but not ramps can be locked in place.
+
+The quadrant environment gives rise to a similar skill progression as in the main environment (Figure A.2): basic running and chasing, then fort building by hiders, ramp use by seekers, and ramp defense by hiders. Hiders create shelter by pushing boxes into the doors of the room in the lower right corner, preventing seekers from entering. Seekers drag ramps to the exterior walls of the room and then use them to jump inside. As ramps are not lockable in this environment, hiders instead defend against ramp use by pulling the ramp inside the room before securing the wall opening with boxes.
+
+![](images/20f9fc38f989450a43fa40b64e0762e95f196517179152745cff0c6d92ed1bcd.jpg)  
+A.4 FURTHER ABLATIONS   
+Figure A.3: Effect of Omniscient Value Function and Pooling Architectures on Emergent Autocurricula. In blue we show the number of episodes required and in orange the wall clock time required to achieve stage 4 (ramp defense) of the emergent skill progression presented in Figure 1 for varying batch and model sizes. Note that in our ablation comparing omniscient and masked value functions, the experiment with a masked value function never reached stage 4 in the allotted time, so here we compare timing to stage 3.
+
+In Figure A.3 we compare the performance between a masked and omniscient value function as well a purely pooling architecture versus self-attention. We find that using an omniscient value function, meaning that the value function has access to the full state of the unobscured environment, is critical to progressing through the emergent autocurricula at the given scale. We found that with the same compute budget, training with a masked value function never progressed past stage 3 (ramp usage). We further found that our self-attention architecture increases sample efficiency as compared to an architecture that only embeds and then pools entities together with a similar number of parameters. However, because self-attention requires more compute despite having the same number of parameters, the wall-clock time to convergence is slightly slower.
+
+![](images/06ac1a67803c6153535d88a7d31196bd070df25af69fd37d7266bbaa00944368.jpg)  
+A.5 EVALUATING AGENTS AT DIFFERENT PHASES OF EMERGENCE   
+Figure A.4: Fine-tuning From Different Phases in the Emergent Autocurriculum. We plot the mean performance on the transfer suite and $90 \%$ confidence interval across 3 seeds and smooth performance and confidence intervals with an exponential moving average. We show the fine-tuning performance for a policy sampled at each of the six phases of emergent strategy (see Figure 1).
+
+In Figure A.4 we evaluate policies sampled during each phase of emergent strategy on the suite of targeted intelligence tasks, by which we can gain intuition as to whether the capabilities we measure improve with training, are transient and accentuated during specific phases, or generally uncorrelated to progressing through the autocurriculum. We find that the hide-and-seek agent improves on the navigation and memory tasks as it progresses; notably on Lock and Return, the performance monotonically increases with emergence phase, and the policy from the phase 6 performs $20 \%$ better than the policy from phase 1. However, performance on Object Counting is transient; during phase 1 the hide-and-seek agent performs extremely well, much better than all baselines and other phases but loses this ability in later stages. Finally, we find that performance on the manipulation tasks is relatively uncorrelated to the phases of emergence, and surprisingly the policy transferred from phase 1, the phase before any tool use emerges, performs comparably well to other phases.
+
+![](images/ad55e2beb58ec433adcee07da862fb566eab8bc9e79f1c252bce978318a6c445.jpg)  
+Figure A.5: Example trajectory in hide-and-seek environment with additional food reward. During the preparation phase, hiders lock the ramps at the boundary of the play area (2nd snapshot) and construct a fort around the food reward (3rd and 4th snapshot). After the preparation phase, hiders can eat food and receive the additional food reward, because they are hidden from seekers inside the fort.
+
+A.6 ALTERNATIVE GAMES TO HIDE-AND-SEEK WITH SECONDARY OBJECTIVES
+
+# A.6.1 HIDE-AND-SEEK WITH FOOD REWARD
+
+In the main hide-and-seek environment, hiders build forts at locations that would give them the best chance of staying hidden from seekers. To test whether hiders could be incentivized by a secondary objective to adapt the location of forts, we add additional food rewards and test whether hiders would bias the location of their forts towards the location of the food. In this environment, hiders can eat food and receive food rewards only under the following conditions: after the preparation phase, when all hiders are hidden from seekers and when the food is sufficiently close and visible to them. Therefore, just chasing after food would not be an effective strategy for hiders, because hiders receive neither hide-and-seek nor food rewards if one or more hiders are seen by a seeker. Instead, hiders are incentivized to build forts around the location of food and then eat the food while being unobserved by seekers (figure A.5).
+
+Food is distributed in the form of 5 food pellets that are spawned close to each other in a rectangular area in the center of the environment whose side length is 1/4 of the room size. Each food pellet can provide a positive food reward of $+ 1$ for each time step. Food rewards are shared between hiders, irrespective of which hider eats a food item. Hiders (as well as seekers) can observe the locations of food pellets as separate entities; if food pellets are obstructed or outside the field of view they are masked out like other type of objects.
+
+As shown in figure A.6, this environment gives rise to four levels of skill progression, similar to the one of the main environment: basic running and chasing, then fort building by hiders, ramp use by seekers, and ramp defense by hiders. Moreover, hiders consume food, and food consumption is highly correlated with their ability to construct stable forts; food consumption decreases during the initial phase as seekers get better at chasing and therefore prevent hiders from eating food. Food consumption then increases again as hiders learn to construct forts and shield themselves from the view of seekers, but plateaus once seekers learn to use ramps. Finally, food consumption rises again as hiders get better at defending against ramp use.
+
+# A.6.2 HIDE-AND-SEEK WITH DYNAMIC FOOD
+
+In the food variant introduce in Sec. A.6.1, the location of food pellets is fixed throughout the episode. Here we consider a dynamic food variant such that a food pellet will be eaten up, i.e., disappear, when a hider is close to it, and then a new food pellet will show up in a different location but still within the center region. More precisely, the game area is simply an empty room without outside walls containing 2 seekers, 3 hiders, 1 dynamic food and 8 elongated boxes. The food will be always located within a square in the center of the environment with side length 1/5 of the game area size. We inherit the same reward and policy structures from the previous game.
+
+In this game, merely building a center fort is not sufficient for obtaining the highest reward since the food might disappear and respawn outside the fort. The agent must ensure that the fort is large enough such that all the possible spawning positions of the food will be inside the fort. Such a behavior does emerge after training for around $4 . 5 \times 1 0 ^ { 1 0 }$ samples.
+
+![](images/6d61b27a496c91a599ca036d162355d8d985ecc3f1dc1f817cc06a7a3a231ce9.jpg)  
+Figure A.6: Reward and environment specific statistics during emergence in hide-and-seek with secondary food rewards for hiders.
+
+We also experimented on variants where the food spawning region has different side length. When the side length is reduced to 1/6 of the game area, the same behavior emerges faster taking $\mathrm { \bar { 1 . 5 } } \times \mathrm { 1 0 ^ { 1 0 } }$ samples. However, when the side length of the dynamic food region is increased to 1/4 of the game area, hiders converge to a policy that ignores the food and only builds a small fort to protect themselves.
+
+# A.6.3 FOOD PROTECTION GAME
+
+In the previous two variants, we introduce extra food reward to the hider in addition to the original hide-and-seek reward for promoting more goal-oriented behavior. Now we consider a different game rule such that the competition between hiders and seekers only depends on the food collecting reward and show that this rule can also lead to tool use and complex behavior.
+
+We consider an empty game area surrounded by walls that contains 50 food pellets randomly distributed in a center square of size 2/3 of the game environment. There are 3 hiders, 2 seekers and 7 elongated boxes in the game. The only goal for seekers is to collect food. Once a food pellet is collected by any of the seeker, a $+ 3$ reward will be given to all the seekers and then the food will disappear permanently from the game. The goal for the hider is to protect the food from seekers and their reward is simply the negative value of seekers. Each episode consists of 200 time steps. The preparation period, in which only hiders can move, extends to the first 100 time steps. The last 60 steps of the game corresponds to a food collecting period, during which the hiders cannot move. Additionally, after the preparation phase we also add a $^ { - 1 }$ “boundary penalty” for hiders when they are too close to the wall to ensure they stay within the food region.
+
+Our initial motivation for this task was to promote hiders to learn to construct complex and large fort structures with a more direct competition pressure. For example, we expected that the agents would learn to build a large fort that would cover as much food as possible. Unfortunately, such behavior did not emerge. However, after around $7 \times 1 0 ^ { 1 0 }$ samples of training, the hiders surprisingly discover an extremely efficient and effective strategy: they learn to physically ‘push’ the immobile seekers to the corner of the environment during the preparation phase and then collaboratively use elongated boxes to trap the seekers in the corner. Figure A.7 illustrates a trajectory corresponding to this strategy. Interestingly, the hiders demonstrate strong collaborations. Since there are 2 seekers and 3 hiders, when the 2 hiders are pushing the seekers to the corner, the 3rd hider will follow the ‘pushing’ hiders distantly, and once the pushing hiders finish the job, this 3rd hider will quickly grab a box to build the trap without blocking the escaping route of those 2 pushing hiders. We emphasize that this behavior was completely surprising to us and further indicates that complex behavior can emerge from multi-agent self-play with a wide range of competition rules.
+
+![](images/c4635d5263304d404349139bee1ff9a43a0b3d5f7d6188de556b16f1a12126d6.jpg)  
+Figure A.7: Example trajectory in the food protection game. During the preparation phase, the hiders first explore the room to find seekers, then physically push the seekers to the corner and eventually collaboratively grab elongated boxes to build a small fort surrounding the seekers to trap them there. To secure the trap, they even learn to build the fort using two elongated boxes to prevent seekers from escaping.
+
+![](images/c6727bb42ce718b6c265a39d92d5f1eb8857d9fa093cae8adc75c20da08e1f6a.jpg)  
+Figure A.8: Zero-shot generalization to a larger number of hiders (left), ramps (center) and boxes (right). The dotted line denotes the boundary of the training distribution (1-3 hiders, 2 ramps, 1-9 boxes). Error bars denote standard error of the mean.
+
+Lastly, we also experimented with different versions of the close-to-wall “boundary penalties”. In all cases, we observe similar fort-building behaviors, namely blocking the seekers to the corner, with tiny variations. When we remove the penalty, the behavior emerges twice faster $( 3 . 5 \times 1 0 ^ { 1 0 }$ samples) and 1 hider will stay in the fort with the seekers instead of getting outside. When we add the penalty throughout the episode, the hiders even learned to stay in the center region while grabbing an elongated box as a tool to push the seekers towards the corner. However, the behavior emerges twice slower in this setting, i.e., $1 . 4 \times 1 0 ^ { 1 1 }$ samples required.
+
+# A.7 ZERO-SHOT GENERALIZATION
+
+We find that the trained policies can zero-shot generalize to environments with slightly larger number of hiders, ramps or boxes in Figure A.8. The hider reward provides a reasonably good measure for generalization performance, since the modifications in question make constructing safe shelter more difficult. First, we looked at increasing the number of hiders from 1-3 hiders, as in the training distribution, to 4-6 hiders; increasing the number of hiders decreases the hider reward because all hiders need to stay hidden from seekers. However, the decline in hider reward is very gradual, indicating that the policy generalizes well to more than 4 hiders. A similar effect occurs when increasing the number of ramps because hiders need to secure more ramps from seekers. If we increase the number of ramps from 2 to 3 or 4 the hider reward drops only gradually. Finally, we find hider performance is remarkably stable, though still slowly declines, when increasing the number of boxes.
+
+# B OPTIMIZATION DETAILS
+
+# B.1 NOTATION
+
+We consider the standard multi-agent reinforcement learning formalism of $N$ agents interacting with each other in an environment. This interaction is defined by a set of states $s$ describing the state of the world and configurations of all agents, a set of observations $\mathcal { O } ^ { 1 } , \ldots \mathcal { O } ^ { N }$ of all agents, a set of actions $\mathcal { A } ^ { 1 } , \ldots , \mathcal { A } ^ { N }$ of all agents, a transition function $\mathcal { T } : \mathcal { S } \times \mathcal { A } ^ { 1 } \ldots \mathcal { A } ^ { N } \to \mathcal { S }$ determining the distribution over next states, and a reward for each agent $i$ which is a function of the state and the agent’s action. Agents choose their actions according to a stochastic policy $\pi _ { \theta _ { i } } : \mathcal { O } ^ { i } \times \mathcal { A } ^ { i }  [ 0 , 1 ]$ , where $\theta _ { i }$ are the parameters of the policy. In our formulation, policies are shared between agents, $\pi _ { \theta _ { i } } = \pi _ { \theta }$ and the set of observations $\mathcal { O }$ contains information for which role (e.g. hider or seeker) the agent will be rewarded. Each agent $i$ aims to maximize its total expected discounted return $\begin{array} { r } { R ^ { i } = \sum _ { t = 0 } ^ { H } \gamma ^ { t } r _ { t } ^ { i } } \end{array}$ , where $H$ is the horizon length and $\gamma$ is a time discounting factor that biases agents towards preferring short term rewards to long term rewards. The action-value function is defined as $Q ^ { \pi _ { i } } \big ( s _ { t } , \bar { a } _ { t } ^ { i } \big ) = \mathbb { E } [ R _ { t } ^ { i } | s _ { t } , a _ { t } ^ { i } ]$ , while the state-value function is defined as $V ^ { \pi _ { i } } ( s _ { t } ) = \mathbb { E } [ R _ { t } | s _ { t } ]$ . The advantage function $\check { A } ^ { \pi _ { i } } ( s _ { t } ^ { - } , a _ { t } ^ { i } ) : = Q ^ { \pi _ { i } } ( s _ { t } , a _ { t } ^ { i } ) - \check { V } ^ { \pi _ { i } } ( s _ { t } )$ describes whether taking action $a _ { t } ^ { \ i }$ is better or worse for agent $i$ when in state $s _ { t }$ than the average action of policy $\pi _ { i }$ .
+
+# B.2 PROXIMAL POLICY OPTIMIZATION (PPO)
+
+Policy gradient methods aim to estimate the gradient of the policy parameters with respect to the discounted sum of rewards, which is often non-differentiable. A typical estimator of the policy gradient is $g : = \mathbb { E } [ \hat { A } _ { t } \nabla _ { \theta } \log \pi _ { \theta } ]$ , where $\hat { A }$ is an estimate of the advantage function. PPO (Schulman et al., 2017), a policy gradient variant, penalizes large changes to the policy to prevent training instabilities. PPO optimizes the objective $L = \mathbb { E } \left[ \operatorname* { m i n } ( l _ { t } ( \theta ) \hat { A } _ { t } , \operatorname { c l i p } ( l _ { t } ( \theta ) , 1 - \epsilon , 1 + \epsilon ) \hat { A } _ { t } \right]$ , where $\begin{array} { r } { l _ { t } ( \theta ) = \frac { \pi _ { \theta } \left( a _ { t } | s _ { t } \right) } { \pi _ { o l d } \left( a _ { t } | s _ { t } \right) } } \end{array}$ denotes the likelihood ratio between new and old policies and $\mathrm { c l i p } ( l _ { t } ( \theta ) , 1 -$ $\epsilon , 1 + \epsilon )$ clips $l _ { t } ( \theta )$ in the interval $[ 1 - \epsilon , 1 + \epsilon ]$ .
+
+# B.3 GENERALIZED ADVANTAGE ESTIMATION
+
+We use Generalized Advantage Estimation (Schulman et al., 2015) with horizon length $H$ to estimate the advantage function. This estimator is given by:
+
+$$
+\hat { A } _ { t } ^ { H } = \sum _ { l = 0 } ^ { H } ( \gamma \lambda ) ^ { l } \delta _ { t + l } , \qquad \delta _ { t + l } : = r _ { t + l } + \gamma V ( s _ { t + l + 1 } ) - V ( s _ { t + l } )
+$$
+
+where $\delta _ { t + l }$ is the TD residual, $\gamma , \lambda \in [ 0 , 1 ]$ are discount factors that control the bias-variance tradeoff of the estimator, $V ( s _ { t } )$ is the value function predicted by the value function network and we set $\hat { A } _ { t } ^ { H } = \delta _ { t } + \gamma \lambda \hat { A } _ { t + 1 } ^ { H - 1 }$ $V ( s _ { t } ) = 0$ if $s _ { t }$ is the last step of an episode. This estimator obeys the reverse recurrence relation .
+
+We calculate advantage targets by concatenating episodes from policy rollouts and truncating them to windows of $\begin{array} { r l r } { T } & { { } = } & { 1 6 0 } \end{array}$ time steps (episodes contain 240 time steps). If a window $\left( s _ { 0 } , \dots , s _ { T - 1 } \right)$ was generated in a single episode we use the advantage targets $( \hat { A } _ { 0 } ^ { H = T } , \hat { A } _ { 1 } ^ { H = T - 1 } , \dots , \hat { A } _ { T - 1 } ^ { H = 1 } )$ arts at time step . $j$ we use the advantage targets $( \hat { A } _ { 0 } ^ { H = j } , \hat { A } _ { 1 } ^ { H = j - 1 } , \dots , \hat { A } _ { j - 1 } ^ { H = 1 } , \hat { A } _ { j } ^ { H = T - j } , \dots , \hat { A } _ { T - 1 } ^ { H = 1 } )$
+
+Similarly we useerated by a singlestarts at time step targets fpisode an, where th $( \hat { G } _ { 0 } ^ { H = T } , \hat { G } _ { 1 } ^ { H = T - 1 } , \dots , \hat { G } _ { T - 1 } ^ { H = 1 } )$ or a window gen- if a new episodeis value function $( \hat { G } _ { 0 } ^ { H = j } , \hat { G } _ { 1 } ^ { H = j - 1 } , \dots , \hat { G } _ { j - 1 } ^ { H = 1 } , \hat { G } _ { j } ^ { H = T - j } , \dots , \hat { G } _ { T - 1 } ^ { H = 1 } )$ $j$ $\hat { G } _ { t } ^ { H } : = \hat { A } _ { t } ^ { H } + V ( s _ { t } )$ $\mathrm { T D } ( \lambda )$ $\&$
+
+B.4 NORMALIZATION OF OBSERVATIONS, ADVANTAGE TARGETS AND VALUE FUNCTION TARGETS
+
+We normalize observations, advantage targets and value function targets. Advantage targets are zscored over each buffer before each optimization step. Observations and value function targets are z-scored using a mean and variance estimator that is obtained from a running estimator with decay parameter $1 - 1 0 ^ { - 5 }$ per optimization substep.
+
+# B.5 OPTIMIZATION SETUP
+
+Training is performed using the distributed rapid framework (OpenAI, 2018). Using current policy and value function parameters, CPU machines roll out the policy in the environment, collect rewards, and compute advantage and value function targets. Rollouts are cut into windows of 160 timesteps and reformatted into 16 chunks of 10 timesteps (the BPTT truncation length). The rollouts are then collected in a training buffer of 320,000 chunks. Each optimization step consists of 60 SGD substeps using Adam with mini-batch size 64,000. One rollout chunk is used for at most 4 optimization steps. This ensures that the training buffer stays sufficiently on-policy.
+
+# B.6 OPTIMIZATION HYPERPARAMETERS
+
+Our optimization hyperparameter settings are as follows:
+
+<table><tr><td rowspan=1 colspan=1>Buffer size</td><td rowspan=1 colspan=1>320,000</td></tr><tr><td rowspan=1 colspan=1>Mini-batch size</td><td rowspan=1 colspan=1>64,000 chunks of 10 timesteps</td></tr><tr><td rowspan=1 colspan=1>Learning rate</td><td rowspan=1 colspan=1>3.10-4</td></tr><tr><td rowspan=1 colspan=1>PPO clipping parameter e</td><td rowspan=1 colspan=1>0.2</td></tr><tr><td rowspan=1 colspan=1>Gradient clipping</td><td rowspan=1 colspan=1>5</td></tr><tr><td rowspan=1 colspan=1>Entropy coefficient</td><td rowspan=1 colspan=1>0.01</td></tr><tr><td rowspan=1 colspan=1>Y</td><td rowspan=1 colspan=1>0.998</td></tr><tr><td rowspan=1 colspan=1>入</td><td rowspan=1 colspan=1>0.95</td></tr><tr><td rowspan=1 colspan=1>Max GAE horizon length T</td><td rowspan=1 colspan=1>160</td></tr><tr><td rowspan=1 colspan=1>BPTT truncation length</td><td rowspan=1 colspan=1>10</td></tr></table>
+
+# B.7 POLICY ARCHITECTURE DETAILS
+
+Lidar observations are first passed through a circular 1D-convolution and concatenated onto the agents representation of self, $x _ { \mathrm { s e l f } }$ . Each object is concatenated with $x _ { \mathrm { s e l f } }$ and then embedded with a dense layer where parameters are shared between objects of the same type, e.g. all boxes share the same embedding weights. All the embedded entities are then passed through a residual selfattention block, similar to Vaswani et al. (2017) but without position embeddings, in the form of $y =$ dense(self attention $( x ) ) + x$ . We then average-pool entity embeddings and concatenate this pooled representation to $x _ { \mathrm { s e l f } }$ . Note that in the policy network the entities not observed by each agent are masked away through self-attention and pooling. Finally, this pooled representation is passed through another dense layer and an LSTM (Hochreiter & Schmidhuber, 1997) before pulling off separate action heads for each of the 3 action types described in Section 3. We also add layer normalization (Ba et al., 2016) to every hidden layer of the policy network except the 1D-convolution layer. We empirically observe that layer normalization leads to faster training and better transfer performance.
+
+<table><tr><td rowspan=1 colspan=1>Size of embedding layer</td><td rowspan=1 colspan=1>128</td></tr><tr><td rowspan=1 colspan=1>Size ofMLPlayer</td><td rowspan=1 colspan=1>256</td></tr><tr><td rowspan=1 colspan=1>Size of LSTM layer</td><td rowspan=1 colspan=1>256</td></tr><tr><td rowspan=1 colspan=1>Residual attention layer</td><td rowspan=1 colspan=1>4attentionheadsofsize32</td></tr><tr><td rowspan=1 colspan=1>Weight decay coefficient</td><td rowspan=1 colspan=1>10-6</td></tr></table>
+
+# C INTELLIGENCE TEST SUITE DETAILS
+
+All evaluation tasks in the intelligence test suite are single-agent tasks. In order to align the observations between the hide-and-seek environment and the evaluation tasks, we add fake hider observations, preparation phase observations and set them all to 0.
+
+# C.1 COGNITION AND MEMORY TASK
+
+All the variations of cognition and memory tasks have a horizon of 120 timesteps, and all boxes are cuboids.
+
+# Object Counting:
+
+An agent is pinned in place and watches as 6 boxes move either to left or right at random. The boxes disappear behind walls such that agent can no longer see them, and the agent is asked to predict how many boxes went left or right far after all the boxes have disappeared. In this test we evaluate the quality of the existing representation by holding the agent’s policy fixed and only train a new classification head from the agent’s LSTM state. The classification head first passes the LSTM state through a layernorm and a single dense layer with 64 units. We then do a 7-class classification predicting whether 0 through 6 boxes have gone to the left.
+
+# Lock and Return:
+
+In this game, the agent needs to navigate towards a hidden box, lock it, and then return to its starting position.
+
+The game area has 6 randomly generated connected rooms with static walls and 1 box. When the box is locked, the agent will be given a reward of $+ 5$ . If the agent unlocks the box during the episode, a -5 penalty will be given. Additionally, if the box remains unlocked at the end of the episode, the agent will be given another -5 penalty. A success is determined when the agent returns to its starting location within 0.1 radius and with the box locked. For promoting fast task accomplishment, we give the agent a $+ 1$ reward for each timestep of success. We also introduce shaped reward with coefficient of 0.5 for easier learning: at each time step, the shaped reward is the decrement in the distance between the agent location towards the target (either the unlocked box or the starting location).
+
+# Sequential Lock:
+
+There are 4 boxes and the agent needs to lock all the boxes in an unobserved order sequentially. A box can be locked only if it is locked in the right order.
+
+The game area is randomly partition into three rooms with 2 walls. The 4 boxes are randomly placed in the game area. Each room has a ramp. The agent has to utilize the ramps to navigate between rooms. When a box is successfully locked (according to the order), a $+ 5$ bonus is given. If a box is unlocked, -5 penalty will be added. When all the boxes get locked, the agent will receives a $+ 1$ per-timestep success bonus. We also use the same shaped distance reward as the lock and return task here.
+
+# C.2 MANIPULATION TASK
+
+All variations of the manipulation task have 8 boxes, but no ramps.
+
+# Construction from Blueprint:
+
+The horizon is at most 240 timesteps, but an episode can end early if the agent successfully finishes the construction. The game area is an empty room. The locations of the construction sites are sampled uniformly at random (we use rejection sampling to ensure that construction sites do not overlap).
+
+For each construction site, agents observe its position and that of its 4 corners. Since there are no construction sites in the hide-and-seek game and the count-based baseline environments, we need to change our policy architecture to integrate the new observations. Each construction site observation is concatenated with $x _ { s e l f }$ and then embedded through a new dense layer shared across all sites. This dense layer is randomly initialized and added to the multi-agent and count-based policies before the start of training. The embedded construction site representations are then concatenated with all other embedded object representations before the residual self-attention block, and the rest of the architecture is the same as the one used in the hide-and-seek game.
+
+The reward at each timestep is equal to a reward scale constant times the mean of the smooth minimum of the distances between each construction site corner and every box corner. Let there be $k$ construction sites and $n$ boxes, and let $d _ { i j }$ be the distance between construction site corner $i$ and box corner $j$ , and let $d _ { i }$ be the smooth minimum of the distances from construction site corner $i$ to all box corners. The reward at each timestep follows the following formula:
+
+$$
+\begin{array} { r c l } { { d _ { i } } } & { { = } } & { { \displaystyle \left( \sum _ { j = 1 } ^ { 4 n } d _ { i j } e ^ { \alpha d _ { i j } } \right) / \sum _ { j = 1 } ^ { 4 n } e ^ { \alpha d _ { i j } } \forall i = 1 , 2 , \ldots , 4 k } } \\ { { r e w } } & { { = } } & { { \displaystyle s _ { d } \left( \sum _ { i = 1 } ^ { 4 k } d _ { i } \right) / 4 k } } \end{array}
+$$
+
+Here, $s _ { d }$ is the reward scale parameter and $\alpha$ is the smoothness hyperparameter ( $\alpha$ must be nonpositive; $\alpha = 0$ gives us the mean, and $\alpha  - \infty$ gives us the regular min function). In addition, when all construction sites have a box placed within a certain distance $d _ { m i n }$ of them, and all construction site corners have a box corner located within $d _ { m i n }$ of them, the episode ends and all agents receive reward equal to $s _ { c } * k$ , where $s _ { c }$ is a separate reward scale parameter. For our experiment, $n = 8$ and $k$ is randomly sampled between 1 and 4 (inclusive) every episode. The hyperparameter values we use for the reward are the following:
+
+$$
+\begin{array} { c } { \alpha = - 1 . 5 } \\ { s _ { d } = 0 . 0 5 } \\ { d _ { m i n } = 0 . 1 } \\ { s _ { c } = 3 } \end{array}
+$$
+
+Shelter construction: The goal of the task is to build a shelter around a cylinder that is randomly placed in the play area. The horizon is 150 timesteps, and the game area is an empty room. The location of the cylinder is uniformly sampled at random a minimum distance away from the edges of the room (this is because if the cylinder is too close to the external walls of the room, the agents are physically unable to complete the whole shelter). The diameter of the cylinder is uniformly randomly sampled between $d _ { m i n }$ and $d _ { m a x }$ . There are 3 movable elongated boxes and 5 movable square boxes. There are 100 rays that originate from evenly spaced locations on the bounding walls of the room and target the cylinder placed within the room. The reward at each timestep is $( - n * s )$ , where $n$ is the number of raycasts that collide with the cylinder that timestep and $s$ is the reward scale hyperparameter.
+
+We use the following hyperparameters:
+
+$$
+\begin{array} { c } { s = 0 . 0 0 \mathrm { { I } } } \\ { d _ { m i n } = 1 . 5 } \\ { d _ { m a x } = 2 } \end{array}
+$$
+
+# D INTRINSIC MOTIVATION METHODS
+
+We inherit the same policy architecture as well as optimization hyperparameters as used in the hideand-seek game.
+
+Note that only the Sequential Lock task in the transfer suite contains ramps, so for the other 4 tasks we remove ramps in the environment for training intrinsic motivation agents.
+
+# D.1 COUNTED-BASED EXPLORATION
+
+For each real value from the continuous state of interest, we discretize it into 30 bins. Then we randomly project each of these discretized integers into a discrete embedding of dimension 16 with integer value ranging from 0 to 9. Here we use discrete embeddings for the purpose of accurate hashing. For each input entity, we concatenate all its obtained discrete embeddings as this entity’s feature embedding. An max-pooling is performed over the feature embeddings of all the entities belonging to each object type (i.e., agent, lidar, box and ramp) to obtain a entity-invariant object representation. Finally, concatenating all the derived object representations results in the final state representation to count.
+
+We run a decentralized version of the count-based exploration where each parallel rollout worker shares the same random projection for computing embeddings but maintains its own counts. Let $N ( S )$ denote the counts for state $S$ in a particular rollout worker. Then the intrinsic reward is calculated by $\frac { 0 . 1 } { \sqrt { N ( S ) } }$ .
+
+# D.2 RANDOM NETWORK DISTILLATION
+
+Random Network Distillation (RND) (Burda et al., 2019b) uses a fixed random network, i.e., a target network, to produce a random projection for each state while learns anther network, i.e., a predictor network, to fit the output from the target network on visited states. The prediction error between two networks is used as the intrinsic motivation.
+
+For the random target network, we use the same architecture as the value network except that we remove the LSTM layer and project the final layer to a 64 dimensional vector instead of a single value. The architecture is the same for predictor network. We use the squared difference between predictor and target network output with an coefficient of 1.0 as the intrinsic reward.
+
+# D.3 FINE-TUNING FROM INTRINSIC MOTIVATION VARIANTS
+
+We compare the performances of different policies pretrained by intrinsic motivation variants on our intelligence test suites in Figure D.1. The pretraining methods of consideration include RND and 3 different count-based exploration variants with different state representations. For policies trained by count-based variants, as discussed in the Section 6.1, we know that more concise state representation for counts leads to better emergent object manipulation skills, i.e., only using object position is better than using position and velocity information while using all the input as state representation performs the worst. In our transfer task suites, we observe that polices with better pretrained skills perform better in 3 of the 5 tasks except the Object Counting task and the Construction from Blueprint task. In Construction from Blueprint, policies with better skills adapt better in the early phase but may have a higher chance of failure later in this challenging task. In Object Counting, the polices with better skills perform worse. Interestingly, this observation is consistent with the transfer result in the main paper (Figure 6), where the policy pretrained by count-based exploration outperforms the multi-agent pretrained policy. We conjecture that the Object Counting task examines some factors of the agents that may not strongly relate to the quality of emergent skills, such as navigation and tool use.
+
+![](images/e8fea408d2275d61753a5c1dc37a293304a74d544fb9ccf8d8485a2f42ce3992.jpg)  
+Figure D.1: Fine-tuning From Intrinsic Motivation Variants. We plot the mean performance on the suite of transfer tasks and $90 \%$ confidence interval across 3 seeds and smooth performance and confidence intervals with an exponential moving average. We vary the state representation used for collecting counts: in blue we show the performance for a single agent where the state is defined on box 2-D positions, in green we show the performance of a single agent where the state is box position but also box rotation and velocity, in red we show the performance of 1-3 agents with the full observation space given to a hide-and-seek policy, and finally in purple we show the performance also with 1-3 agents and a full observation space but with RND which should scale better than count-based exploration.

parse/train/aohkNJxjYJX/aohkNJxjYJX.md

@@ -0,0 +1,323 @@
+# Long Short-Term Transformer for Online Action Detection
+
+Mingze Xu Yuanjun Xiong Hao Chen Xinyu Li Wei Xia Zhuowen Tu Stefano Soatto Amazon/AWS AI {xumingze,yuanjx,hxen,xxnl,wxia,ztu,soattos}@amazon.com
+
+# Abstract
+
+We present Long Short-term TRansformer (LSTR), a temporal modeling algorithm for online action detection, which employs a long- and short-term memory mechanism to model prolonged sequence data. It consists of an LSTR encoder that dynamically leverages coarse-scale historical information from an extended temporal window (e.g., 2048 frames spanning of up to 8 minutes), together with an LSTR decoder that focuses on a short time window (e.g., 32 frames spanning 8 seconds) to model the fine-scale characteristics of the data. Compared to prior work, LSTR provides an effective and efficient method to model long videos with fewer heuristics, which is validated by extensive empirical analysis. LSTR achieves state-of-the-art performance on three standard online action detection benchmarks, THUMOS’14, TVSeries, and HACS Segment. Code has been made available at: https://xumingze0308.github.io/projects/lstr.
+
+# 1 Introduction
+
+Given an incoming stream of video frames, online action detection [14] is concerned with the task of classifying what is happening at each frame without seeing the future. Unlike offline methods that assume the entire video is available, online methods process the data causally, up to the current time. In this paper, we present an online temporal modeling algorithm capable of capturing temporal relations on prolonged sequences up to 8 minutes long, while retaining fine granularity of the event in the representation. This is achieved by modeling activities at different temporal scales, so as to capture a variety of events ranging from bursts to slow trends.
+
+Specifically, we propose a method, named Long Short-term TRansformer (LSTR), to jointly model long- and short-term temporal dependencies. LSTR has two main advantages over prior work. 1) It stores the history directly thus avoiding the pitfalls of recurrent models [18, 50, 28, 10]. Backpropagation through time, BPTT, is not needed as the model can directly attend to any useful frames from memory. 2) It separates long- and short-term memories, which allows modeling short-term context while extracting useful correlations from the long-term history. This allows us to compress the long-term history without losing important fine-scale information.
+
+As shown in Fig. 1, we explicitly divide the entire history into the long- and short-term memories and build our model with an encoder-decoder architecture. Specifically, the LSTR encoder compresses and abstracts the long-term memory into a latent representation of fixed length, and the LSTR decoder uses a short window of transient frames to perform self-attention and cross-attention operations on the extracted token embeddings from the LSTR encoder. In the LSTR encoder, an extended temporal support becomes beneficial in dealing with untrimmed, streaming videos by devising twostage memory compression, which is shown to be computationally efficient in both training and inference. Our overall long short-term Transformer architecture gives rise to an effective and efficient representation for modeling prolonged sequence data.
+
+![](images/2cdfefefe829e4490463771dc0dbe39922829ab172a2bd6b7ac129c1cd3955a3.jpg)  
+Figure 1: Overview of Long Short-term TRansformer (LSTR). Given a live streaming video, LSTR sequentially identifies the actions happening in each incoming frame by using an encoderdecoder architecture, without future context. The dashed brown arrows indicate the data flow of the long- and short-term memories following the first-in-first-out (FIFO) logic. (Best viewed in color.)
+
+We validate LSTR on standard benchmark datasets (THUMOS’14 [30], TVSeries [14], and HACS Segment [76]). These have distinct characteristics such as video length spanning from a few seconds to tens of minutes. Experimental results establish LSTR as the state-of-the-art for online action detection. Ablation studies further showcase LSTR’s abilities in modeling long video sequences.
+
+# 2 Related Work
+
+Online Action Detection. Temporal action localization aims to detect the onset and termination of action instances after observing the entire video [52, 71, 23, 53, 78, 5, 37, 39, 38]. Embodied perception, however, requires causal processing [73], where we can only process the data up to the present. Online action detection focuses on this setting [14]. RED [22] uses a reinforcement loss to encourage recognizing actions as early as possible. TRN [72] models greater temporal context by simultaneously performing online action detection and anticipation. IDN [19] learns discriminative features and accumulates only relevant information for the present. LAP-Net [46] proposes an adaptive sampling strategy to obtain optimal features. PKD [77] transfers knowledge from offline to online models using curriculum learning. As with early action detection [27, 40], Shou et al. [54] focus on online detection of action start (ODAS). StartNet [24] decomposes ODAS into two stages and learns with policy gradient. WOAD [25] uses weakly-supervised learning with video-level labels.
+
+Temporal/Sequence Modeling. Causal time series analysis has traditionally assumed the existence of a latent “state” variable that captures all information in past data, and is updated using only the current datum [49, 28, 10]. While the Separation Principle ensures that such a state exists for linearGaussian time series, in general it is not possible to summarize all past history of complex data in a finite-dimensional sufficient statistic. Therefore, we directly model the history, in accordance with other work on video understanding [69, 45, 68]. Earlier work on action recognition usually relies on heuristic sub-sampling (typically 3 to 7 video frames) for more feasible training [74, 62, 21, 41, 57]. 3D ConvNets [59, 8, 60] are used to perform spatio-temporal feature modeling on more frames, but they fail to capture temporal correlations beyond their receptive field. Recently, Wu et al. [69] propose long-term feature banks to capture objects and scene features, but discarding their temporal order which is clearly informative. Most of work above does not explicitly separate the long- and short-term context modeling, but instead integrates all observed features with simple mechanisms such as pooling or concatenation. We are motivated by work in Cognitive Science [44, 12, 9, 35] that has shed light on the design principles for modeling long-term dependencies with attention mechanism [66, 13, 48, 75].
+
+Transformers for Action Understanding. Transformers have achieved breakthrough success in NLP [47, 15] and are adopted in computer vision for image recognition [17, 58] and object detection [7]. Recent papers exploit Transformers for temporal modeling tasks in videos, such as action recognition [43, 51, 36, 4, 3] and temporal action localization [42, 56], and achieve promising results. However, computational and memory demands result in most work being limited to short video clips, with few exceptions [13, 6] that focuses on designing Transformers to model long-range context. The mechanism for aggregating long- and short-term information is relatively unexplored [32].
+
+# 3 Long Short-Term Transformer
+
+Given a live streaming video, our goal is to identify the actions performed in each video frame using only past and current observations. Future information is not accessible during inference. Formally, a streaming video at time $t$ is represented by a batch of $\tau$ past frames $\mathbf { I } ^ { t } = \{ I _ { t - \tau } , \cdot \cdot \cdot , I _ { t } \}$ , which reads “ $^ Ḋ \cdot Ḍ I Ḍ$ up to time $t$ .” The online action detection system receives $\mathbf { I } ^ { t }$ as input, and classifies the action category $\hat { y } _ { t }$ belonging to one of $( K + 1 )$ classes, $\hat { y } _ { t } \in \{ 0 , 1 , \cdots , K \}$ , ideally using the posterior probability $P ( \hat { y } _ { t } = k | \mathbf { I } ^ { t } )$ , where $k = 0$ denotes the probability that no event is occurring at frame $t$ . We design our method by assuming that there is a pretrained feature extractor [62] that processes each video frame $I _ { t }$ into a feature vector $\mathbf { f } _ { t } \in \mathbb { R } ^ { C }$ of $C$ dimensions1. These vectors form a $( \tau \times C )$ -dimensional temporal sequence that serves as the input of our method.
+
+![](images/35f2a42f1f7b3bb445042e3da20c4f2116f3d01dfe7ca056ac64dfe00b85d781.jpg)  
+Figure 2: Visualization of Long Short-Term Transformer (LSTR), which is formulated in an encoder-decoder manner. Specifically, the LSTR encoder compresses the long-term memory of size $m _ { L }$ to $n _ { 1 }$ encoded latent features, and the LSTR decoder references related context information from the encoded memory with the short-term memory of size $m _ { S }$ for action recognition of the present. The LSTR encoder and decoder are built with Transformer decoder units [61], which take the input tokens (dark green arrows) and output tokens (dark blue arrows) as inputs. During inference, LSTR processes every incoming frame in an online manner, absent future context. (Best viewed in color.)
+
+# 3.1 Overview
+
+Our method is based on the intuition that frames observed recently provide precise information about the ongoing action instance, while frames over an extended period offer contextual references for actions that are potentially happening right now. We propose Long Short-term TRansformer (LSTR) in an explicit encoder-decoder manner, as shown in Fig. 2. In particular, the feature vectors of $m _ { L }$ frames in the distant past are stored in a long-term memory, and a short-term memory stores the features of $m _ { S }$ recent frames. The LSTR encoder compresses and abstracts features in long-term memory to an encoded latent representation of $n _ { 1 }$ vectors. The LSTR decoder queries the encoded long-term memory with the short-term memory for decoding, leading to the action prediction $\hat { y } _ { t }$ . This design follows the line of thought in combining long- and short-term information for action understanding [16, 62, 69], but addresses several key challenges to efficiently achieve this goal, exploiting the flexibility of Transformers [61].
+
+# 3.2 Long- and Short-Term Memories
+
+We store the streaming input of feature vectors into two consecutive memories. The first is the short-term memory which stores only a small number of frames that are recently observed. We implement it with a first-in-first-out (FIFO) queue of $m _ { S }$ slots. At time $T$ , it stores the feature vectors as $\mathbf { M } _ { S } = \{ \mathbf { f } _ { T } , \cdot \cdot \cdot , \mathbf { f } _ { T - m _ { S } + 1 } \}$ . When a frame becomes “older” than $m _ { S }$ time steps, it graduates from $\mathbf { M } _ { S }$ and enters into the long-term memory, which is implemented with another FIFO queue of $m _ { L }$ slots. The long term memory stores $\mathbf { M } _ { L } = \{ \mathbf { f } _ { T - m _ { S } } , \cdot \cdot \cdot , \mathbf { f } _ { t - m _ { S } - m _ { L } + 1 } \}$ . The long-term memory serves as the input memory to the LSTR encoder and the short-term memory serves as the queries for the LSTR decoder. In practice, the long-term memory stores a much longer time span than the short-term memory $( m _ { S } \ll m _ { L } )$ ). A typical choice is $m _ { L } = 2 0 4 8$ , which represents 512 seconds worth of video contents with 4 frames per second (FPS) sampling rate, and $m _ { S } = 3 2$ representing
+
+8 seconds. We add a sinusoidal positional encoding s [61] to each frame feature in the memories relative to current time $T$ (i.e., the frame at $T - \tau$ receives a positional embedding of ${ \bf s } _ { \tau }$ ).
+
+# 3.3 LSTR Encoder
+
+The LSTR encoder aims at encoding the long-term memory of $m _ { L }$ feature vectors into a latent representation that LSTR can use for decoding useful temporal context. This task requires a large capacity in capturing the relations and temporal context across a span of hundreds or even thousands of frames. Prior work on modeling long-term context for action understanding relies on heuristic temporal sub-sampling [69, 62] or recurrent networks [16] to make training feasible, at the cost of losing specific information of each time step. Attention-based architectures, such as Transformer [61], have recently been shown promising for similar tasks that require long-range temporal modeling [51]. A straightforward choice for LSTR encoder would be to use a Transformer encoder based on self-attention. However, its time complexity, $O ( m _ { L } ^ { 2 } C )$ , grows quadratically with the memory sequence length $m _ { L }$ . This limits our ability to model long-term memory with sufficient length to cover long videos. Though recent work [64] has explored self-attention with linear complexity, repeatedly referencing information from the long-term memory with multi-layer Transformers is still computationally heavy. In LSTR, we propose to use the two-stage memory compression mechanism based on Transformer decoder units [61] to achieve more effective memory encoding.
+
+The Transformer decoder unit [61] takes two sets of inputs. The first set includes a fixed number of $n$ learnable output tokens $\ b { \lambda } \in \mathbb { R } ^ { n \times C }$ , where $C$ is the embedding dimension. The second set includes another $m$ input tokens $\pmb { \theta } \in \mathbb { R } ^ { m \times C }$ , where $m$ can be a rather large number. It first applies one layer of multi-head self-attention on $\lambda$ . The outputs $\lambda ^ { \prime }$ are then used as queries in an “QKV cross-attention” operation and the input embeddings $\pmb \theta$ serve as key and value. The two steps can be written as
+
+$$
+\lambda ^ { \prime } = \operatorname { S e l f A t t m } ( \lambda ) = \operatorname { S o f t m a x } ( \frac { \lambda \cdot \lambda ^ { T } } { \sqrt { C } } ) \lambda \ a n d \ \operatorname { C r o s s A t t m } ( \sigma ( \lambda ^ { \prime } ) , \theta ) = \operatorname { S o f t m a x } ( \frac { \sigma ( \lambda ^ { \prime } ) \cdot \theta ^ { T } } { \sqrt { C } } ) \theta ,
+$$
+
+where $\sigma : \mathbb { R } ^ { n \times C }  \mathbb { R } ^ { n \times C }$ denotes the intermediate layers between the two attention operations. One appealing property of this design is that it transforms the $m \times C$ dimensional input tokens into output tokens of $n \times C$ dimensions in $O ( n ^ { 2 } C + n m C )$ time complexity. When $n \ll m$ , the time complexity becomes linear to $m$ , making it an ideal candidate for compressing long-term memory. This property is also utilized in [32] to efficiently process large volume inputs, such as image pixels.
+
+Two-Stage Memory Compression. Stacking multiple Transformer decoder units on the long-term memory, as in [61], can form a memory encoder with linear complexity with respect to the memory size $m _ { L }$ . However, running the encoder at each time step can still be time consuming. We can further reduce the time complexity with a two-stage memory compression design. The first stage has one Transformer decoder unit with $n _ { 0 }$ output tokens. Its input tokens are the entire long-term memory of size $m _ { L }$ . The outputs of the first stage are used as the input tokens to the second stage, which has $\ell _ { e n c }$ stacked Transformer decoder units and $n _ { 1 }$ output tokens. Then, the long-term memory of size $m _ { L } \times C$ is compressed into a latent representation of size $n _ { 1 } \times C$ , which can then be efficiently queried in the LSTR decoder later. This two-stage memory compression design is illustrated in Fig. 2.
+
+Compared to an $( 1 + \ell _ { e n c } )$ -layer Transformer encoder with $O ( m _ { L } ^ { 2 } ( 1 + \ell _ { e n c } ) C )$ time complexity or stacked Transformer decoder units with $n$ output-tokens having $\bar { O } ( ( n ^ { 2 } + n m _ { L } ) ( 1 + \ell _ { e n c } ) C )$ time complexity, the proposed LSTR encoder has complexity of $O ( n _ { 0 } ^ { 2 } C + n _ { 0 } m _ { L } C + ( n _ { 1 } ^ { 2 } + n _ { 1 } n _ { 0 } ) \ell _ { e n c } C )$ . Because both $n _ { 0 }$ and $n _ { 1 }$ are much smaller than $m _ { L }$ , and $\ell _ { e n c }$ is usually larger than 1, using two-stage memory compression could be more efficient. In Sec. 3.6, we will show that, during online inference, it further enables us to reduce the runtime of the Transformer decoder unit of the first stage. In Sec. 4.5, we empirically found this design also leads to better performance for online action detection.
+
+# 3.4 LSTR Decoder
+
+The short-term memory contains informative features for classifying actions on the latest time step. The LSTR decoder uses the short-term memory as queries to retrieve useful information from the encoded long-term memory produced by the LSTR encoder. The LSTR decoder is formed by stacking $\ell _ { d e c }$ layers of Transform decoder units. It takes the outputs of the LSTR encoder as input tokens and the $m _ { S }$ feature vectors in the short-term memory as output tokens. It outputs $m _ { S }$ probability vectors $\{ \mathbf { p } _ { T } , \cdot \cdot \cdot , \mathbf { p } _ { T - m _ { S } + 1 } \} \in [ 0 , 1 ] ^ { K + 1 }$ , each $\mathbf { p } _ { t }$ representing the predicted probability distribution of $K$ action categories and one “background” class at time $t$ . During inference, we only take the probability vector $\mathbf { p } _ { T }$ from the output token corresponding to the current time $T$ for the classification result.
+
+However, having the additional outputs on the older frames allows the model to leverage more supervision signals during training. The details will be described below.
+
+# 3.5 Training LSTR
+
+LSTR can be trained without temporal unrolling and Backpropagation Through Time (BPTT) as in LSTM [28], which is a common property of Transformers [61]. We construct each training sample by randomly sampling an ending time $\dot { T }$ and filling the long- and short-term memories by tracing back in time for $m _ { S } + m _ { L }$ frames. We use the empirical cross entropy loss between the predicted probability distribution $\mathbf { p } _ { T }$ at time $T$ and the ground truth action label $\dot { y } _ { T } \in \{ 0 , 1 , \cdots , K \}$ as
+
+$$
+L ( y _ { T } , { \bf p } _ { T } ; T ) = - \sum _ { k = 0 } ^ { K } \delta ( k - y _ { T } ) \log p _ { T } ^ { k } ,
+$$
+
+where $p _ { T } ^ { k }$ is the $k$ -th element of the probability vector $\mathbf { p } _ { T }$ , predicted on the latest frame at $T$ Additionally, we add a directional attention mask [61] to the short-term memory so that any frame in the short-term memory can only depend on its previous frames. In this way, we can make predictions on all frames in the short-term memory as if they are the latest ones. Thus we can provide supervision on every frame in the short-term memory, and the complete loss function $\mathcal { L }$ is then
+
+$$
+\mathcal { L } _ { T } = \sum _ { t = T - m s + 1 } ^ { T } L ( y _ { t } , \mathbf { p } _ { t } ; T ) ,
+$$
+
+where $\mathbf { p } _ { t }$ denotes the prediction from the output token corresponding to time $t$
+
+# 3.6 Online Inference with LSTR
+
+During online inference, the video frame features are streamed to the model as time passes. Running LSTR’s long-term memory encoder from scratch for each frame results in a time complexity of $O ( n _ { 0 } ^ { 2 } C + n _ { 0 } ^ { - } m _ { L } C )$ and $\dot { O ( ( n _ { 1 } ^ { 2 } + n _ { 1 } n _ { 0 } ) \ell _ { e n c } C ) }$ for the first and second memory compression stages, respectively. However, at each time step, there is only one new video frame to be updated. We show it is possible to achieve even more efficient online inference by storing the intermediate results for the Transformer decoder unit of the first stage. First, the queries of the first Transformer decoder unit are fixed. So their self-attention outputs can be pre-computed and used throughout the inference. Second, the cross-attention operation in the first stage can be written as
+
+$$
+\mathrm { C r o s s A t t n } ( \mathbf { q } _ { i } , \{ \mathbf { f } _ { T - \tau } + \mathbf { s } _ { \tau } \} ) = \sum _ { \tau = m _ { S } } ^ { m _ { S } + m _ { L } - 1 } \frac { \exp ( ( \mathbf { f } _ { T - \tau } + \mathbf { s } _ { \tau } ) \cdot \mathbf { q } _ { i } / \sqrt { C } ) } { \sum _ { \tau = m _ { S } } ^ { m _ { S } + m _ { L } - 1 } \exp ( ( \mathbf { f } _ { T - \tau } + \mathbf { s } _ { \tau } ) \cdot \mathbf { q } _ { i } / \sqrt { C } ) } \cdot ( \mathbf { f } _ { T - \tau } + \mathbf { s } _ { \tau } ) ,
+$$
+
+where the index $\tau = T - t$ is the relative position of a frame $t$ in the long-term memory to the latest time $T$ . This calculation depends on the un-normalized attention weight matrix $\mathbf { A } \in \mathbb { R } ^ { m _ { L } \times n _ { 0 } }$ , with elements $a _ { \tau i } = ( { \bf f } _ { T - \tau } + { \bf s } _ { \tau } ) \cdot { \bf q } _ { i }$ . A can be decomposed into the sum of two matrices $\mathbf { A } ^ { f }$ and ${ \bf A } ^ { s }$ . We have their elements as $a _ { \tau i } ^ { f } = \mathbf { f } _ { T - \tau } \cdot \mathbf { q } _ { i }$ and $a _ { \tau i } ^ { s } = \mathbf s _ { \tau } \cdot \mathbf q _ { i }$ . The queries after the first self-attention operation, $\mathbf { Q } = [ \mathbf { q } _ { 1 } , \dots , \mathbf { q } _ { n _ { 0 } } ]$ , and the position embedding ${ \bf s } _ { \tau }$ are fixed during inference. Thus the matrix ${ \bf A } ^ { s }$ can be pre-computed and used for every incoming frame. We additionally maintain a FIFO queue of vectors $\mathbf { a } _ { t } \doteq \mathbf { Q } ^ { \top } \mathbf { f } _ { t }$ of size $m _ { L }$ . $\mathbf { A } ^ { f }$ at any time step $T$ can be obtained by stacking all vectors currently in this queue. Updating this queue at each time step requires $O ( n _ { 0 } C )$ time complexity for the matrix-vector product. Now we can obtain the matrix A with only $n _ { 0 } \times m _ { L }$ additions by adding ${ \bf A } ^ { s }$ and $\mathbf { A } ^ { f }$ together, instead of $n _ { 0 } \times m _ { L } \times C$ multiplications and additions using Eq. (3). This means the amortized time complexity for computing the attention weights can be reduced to $O ( n _ { 0 } ( m _ { L } + C ) )$ . Although the time complexity of the cross-attention operation is still $O ( n _ { 0 } m _ { L } C )$ due to the inevitable operation of weighted sum, since $C$ is usually larger than 1024 [26], this is still a considerable reduction of runtime. LSTR’s walltime efficiency is discussed in Sec. 4.6.
+
+# 4 Experiments
+
+# 4.1 Datasets
+
+We evaluate our model on three publicly-available datasets: THUMOS’14 [30], TVSeries [14] and HACS Segment [76]. THUMOS’14 includes over 20 hours of sports video annotated with 20 actions. We follow prior work [72, 19] and train on the validation set (200 untrimmed videos) and evaluate on the test set (213 untrimmed videos). TVSeries contains 27 episodes of 6 popular TV series, totaling 16 hours of video. The dataset is annotated with 30 realistic, everyday actions (e.g., open door). HACS Segment is a large-scale dataset of web videos. It contains 35,300 untrimmed videos over 200 human action classes for training and 5,530 untrimmed videos for validation.
+
+# 4.2 Settings
+
+Feature Encoding. We follow the experimental settings of state-of-the-art methods [72, 19]. We extract video frames at 24 FPS and set the video chunk size to 6. Decisions are made at the chunk level, and thus accuracy is evaluated at every 0.25 second. For feature encoding, we adopt the TSN [62] models implemented in an open-source toolbox [11]. Specifically, the features are extracted by one visual model with the ResNet-50 [26] architecture from the central frame of each chunk and one motion model with the BN-Inception [31] architecture from the stacked optical flow fields between 6 consecutive frames [62]. The visual and motion features are concatenated along the channel dimension as the final feature f. We experiment with feature extractors pretrained on two datasets, ActivityNet and Kinetics.
+
+Implementation Details. We implemented our proposed model in PyTorch [1], and performed all experiments on a system with 8 Nvidia V100 graphics cards. For all Transformer units, we set their number of heads as 16 and hidden units as 1024 dimensions. To learn model weights, we used the Adam [34] optimizer with weight decay $5 \times 1 0 ^ { - 5 }$ . The learning rate was linearly increased from zero to $5 \times 1 0 ^ { - 5 }$ in the first $2 / 5$ of training iterations and then reduced to zero following a cosine function. Our models were optimized with batch size of 16, and the training was terminated after 25 epochs.
+
+Evaluation Protocols. We follow prior work and use per-frame mean average precision (mAP) to evaluate the performance of online action detection. We also use per-frame calibrated average precision (cAP) [14] that was proposed for TVSeries to correct the imbalance between positive and negative samples, $\begin{array} { r } { c A P = \sum _ { k } \overset { \cdot } { c } \bar { P r } e c ( k ) * I ( k ) / P } \end{array}$ , where $c P r e c = T P / ( T P + F P / \bar { w } ) ,$ $I ( k )$ is 1 if frame $k$ is a true positive, $P$ is the number of true positives, and $w$ is the negative and positive ratio.
+
+# 4.3 Comparison with the State-of-the-art Methods
+
+Table 1: Online action detection and anticipation results on THUMOS’14 and TVSeries in terms of mAP and cAP, respectively. For online action detection, LSTR outperforms the state-of-the-art methods on THUMOS’14 by $3 . 7 \%$ and $2 . 4 \%$ in mAP and on TVSeries by $2 . 8 \%$ and $2 . 7 \%$ in cAP, using ActivityNet and Kinetics pretrained features, respectively. LSTR also achieves promising results for action anticipation. \*Results are reproduced by us using their papers’ default settings.
+
+(a) Results of online action detection using ActivityNet features   
+
+<table><tr><td colspan="3">THUMOS&#x27;14 TVSeries</td></tr><tr><td></td><td>mAP (%)</td><td>mcAP (%)</td></tr><tr><td>CDC[53]</td><td>44.4</td><td>-</td></tr><tr><td>RED [22]</td><td>45.3</td><td>79.2</td></tr><tr><td>TRN[72]</td><td>47.2</td><td>83.7</td></tr><tr><td>FATS[33]</td><td>51.6</td><td>81.7</td></tr><tr><td>IDN[19]</td><td>50.0</td><td>84.7</td></tr><tr><td>LAP [46]</td><td>53.3</td><td>85.3</td></tr><tr><td>TFN[20]</td><td>55.7</td><td>85.0</td></tr><tr><td>LFB*[69]</td><td>61.6</td><td>84.8</td></tr><tr><td>LSTR (ours)</td><td>65.3</td><td>88.1</td></tr></table>
+
+(b) Results of online action detection using Kinetics features   
+
+<table><tr><td colspan="3">THUMOS&#x27;14 TVSeries</td></tr><tr><td></td><td>mAP (%)</td><td>mcAP (%)</td></tr><tr><td>FATS [33]</td><td>59.0</td><td>84.6</td></tr><tr><td>IDN[19]</td><td>60.3</td><td>86.1</td></tr><tr><td>TRN [72]</td><td>62.1</td><td>86.2</td></tr><tr><td>PKD [77]</td><td>64.5</td><td>86.4</td></tr><tr><td>WOAD [25]</td><td>67.1</td><td>=</td></tr><tr><td>LFB*[69]</td><td>64.8</td><td>85.8</td></tr><tr><td>LSTR (ours)</td><td>69.5</td><td>89.1</td></tr></table>
+
+(c) Results of action anticipation using ActivityNet features   
+
+<table><tr><td colspan="3">THUMOS&#x27;14 TVSeries</td></tr><tr><td></td><td>mAP (%)</td><td>mcAP (%)</td></tr><tr><td>EFC [22]</td><td>34.4</td><td>72.5</td></tr><tr><td>ED[22]</td><td>36.6</td><td>74.5</td></tr><tr><td>RED[22]</td><td>37.5</td><td>75.1</td></tr><tr><td>TRN [72]</td><td>38.9</td><td>75.7</td></tr><tr><td>TTM[65]</td><td>40.9</td><td>77.9</td></tr><tr><td>LAP [46]</td><td>42.6</td><td>78.7</td></tr><tr><td>LSTR (ours)</td><td>50.1</td><td>80.8</td></tr></table>
+
+Table 2: Online action detection results when only portions of videos are considered in cAP $( \% )$ on TVSeries (e.g., $80 \% - 9 0 \%$ means only frames of this range of action instances were evaluated). LSTR outperforms existing methods at every time stage, especially on boundary locations.   
+
+<table><tr><td rowspan="2"></td><td rowspan="2">Features</td><td colspan="10">Portion of Video</td></tr><tr><td>0-10%</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>10-20% 20-30%30-40% 40-50% 50-60% 60-70% 70-80% 80-90% 90-100%</td></tr><tr><td>TRN [72]</td><td rowspan="4">ActivityNet</td><td>78.8</td><td>79.6</td><td>80.4</td><td>81.0</td><td>81.6</td><td>81.9</td><td>82.3</td><td>82.7</td><td>82.9</td><td>83.3</td></tr><tr><td>IDN[19]</td><td>80.6</td><td>81.1</td><td>81.9</td><td>82.3</td><td>82.6</td><td>82.8</td><td>82.6</td><td>82.9</td><td>83.0</td><td>83.9</td></tr><tr><td>TFN [20]</td><td>83.1</td><td>84.4</td><td>85.4</td><td>85.8</td><td>87.1</td><td>88.4</td><td>87.6</td><td>87.0</td><td>86.7</td><td>85.6</td></tr><tr><td>LSTR (ours)</td><td>83.6</td><td>85.0</td><td>86.3</td><td>87.0</td><td>87.8</td><td>88.5</td><td>88.6</td><td>88.9</td><td>89.0</td><td>88.9</td></tr><tr><td>IDN[19]</td><td rowspan="3">Kinetics</td><td>81.7</td><td>81.9</td><td>83.1</td><td>82.9</td><td>83.2</td><td>83.2</td><td>83.2</td><td>83.0</td><td>83.3</td><td>86.6</td></tr><tr><td>PKD[77]</td><td>82.1</td><td>83.5</td><td>86.1</td><td>87.2</td><td>88.3</td><td>88.4</td><td>89.0</td><td>88.7</td><td>88.9</td><td>87.7</td></tr><tr><td>LSTR (ours)</td><td>84.4</td><td>85.6</td><td>87.2</td><td>87.8</td><td>88.8</td><td>89.4</td><td>89.6</td><td>89.9</td><td>90.0</td><td>90.1</td></tr></table>
+
+We compare LSTR against other state-of-the-art methods [72, 19, 25] on THUMOS’14, TVSeries, and HACS Segment. Specifically, on THUMOS’14 and TVSeries, we implement LSTR with the long- and short-term memories of 512 and 8 seconds, respectively. On HACS Segment, we reduce the long-term memory to 256 seconds, considering that its videos are strictly shorter than 4 minutes. For LSTR, we implement the two-stage memory compression using Transformer decoder units. We set the token numbers to $n _ { 0 } = 1 6$ and $n _ { 1 } = 3 2$ and the Transformer layers to $\ell _ { e n c } = 2$ and $\ell _ { d e c } = 2$ .
+
+# 4.3.1 Online Action Detection
+
+THUMOS’14. We compare LSTR with recent work on THUMOS’14, including methods that use 3D ConvNets [53] and RNNs [70, 19, 25], reinforcement learning [22], and curriculum learning [77]. Table 1a and 1b shows that LSTR significantly outperforms the the state-of-the-art methods [69, 25] by $3 . 7 \%$ and $2 . 4 \%$ in terms of mAP using ActivityNet and Kinetics pretrained features, respectively.
+
+TVSeries. Table 1a and 1b show the online action detection results that LSTR outperforms the state-of-the-art methods [20, 77] by $2 . 8 \%$ and $2 . 7 \%$ in terms of cAP using ActivityNet and Kinetics pretrained features, respectively. Following prior work [14], we also investigate LSTR’s performance at different action stages by evaluating each decile (ten-percent interval) of the video frames separately. Table 2 shows that LSTR outperforms existing methods at every stage of action instances.
+
+HACS Segment. LSTR achieves $8 2 . 6 \%$ on HACS Segment in term of mAP using Kinetics pretrained features. Note that HACS Segment is a new large-scale dataset with only a few previous results. LSTR outperforms existing methods RNN [28] $( 7 7 . 6 \% )$ by $5 . 0 \%$ and TRN [72] $( 7 8 . 9 \% )$ by $3 . 7 \%$ .
+
+# 4.3.2 Action Anticipation
+
+We extend the idea of LSTR to action anticipation for up to 2 seconds (i.e., 8 steps in 4 FPS) into the future. Specifically, we concatenate another 8 learnable output tokens (with positional embedding) after the short-term memory in the LSTR decoder to produce the prediction results accordingly. Table 1c shows that LSTR significantly outperforms the state-of-the-art methods [72, 46] by $7 . 5 \%$ mAP on THUMOS and $2 . 1 \%$ cAP on TVSeries, using ActivityNet pretrained features.
+
+# 4.4 Design Choices of Long- and Short-Term Memories
+
+Table 3: Results of LSTR using downsampled long-term memory on THUMOS’14 in mAP $( \% )$ . In particular, we use long-term memory of 512 seconds and short-term memory as 8 seconds.   
+
+<table><tr><td>Temporal Stride</td><td>1</td><td>2</td><td>4</td><td>8</td><td>16</td><td>32</td><td>64</td><td>128</td></tr><tr><td>LSTR</td><td>69.5</td><td>69.5</td><td>69.5</td><td>69.2</td><td>68.7</td><td>67.3</td><td>66.6</td><td>65.9</td></tr></table>
+
+We experiment for design choices of long- and short-term memories. Unless noted otherwise, we use THUMOS’14, which contains various video lengths, and Kinetics pretrained features.
+
+Lengths of long- and short-term memories. We first analyze the effect of different lengths of long-term $m _ { L }$ and short-term $m _ { S }$ memory. In particular, we test $m _ { S } \in \{ 4 , 8 , 1 6 \}$ seconds with $m _ { L }$ starting from 0 second (no long-term memory). Note that we choose the max length (1024 seconds for THUMOS’14 and 256 seconds for HACS Segment) to cover lengths of $9 8 \%$ videos, and do not have proper datasets to test longer $m _ { L }$ . Fig. 3 shows that LSTR is beneficial from larger $m _ { L }$ in most cases. In addition, when $m _ { L }$ is short $\leq 1 6$ in our cases), using larger $m _ { S }$ obtains better results and when $m _ { L }$ is sufficient $\geq 3 2$ in our cases), increasing $m _ { S }$ does not always guarantee better performance.
+
+![](images/6947622b72aa083315ca466cc359b326181d39cbf4e88d85a16518cec5221923.jpg)  
+Figure 3: Effect of using different lengths of long- and short-term memories.
+
+Can we downsample long-term memory? We implement LSTR with $m _ { S }$ as 8 seconds and $m _ { L }$ as 512 seconds, and test the effect of downsampling long-term memory. Table 3 shows the results that downsampling with strides smaller than 4 does not cause performance drop, but more aggressive strides dramatically decrease the detection accuracy. Note that, when extracting frame features in 4 FPS, both LSTR encoder ${ \mathrm { \Delta } n } _ { 0 } = 1 6$ ) and downsampling with stride 128 compress the long-term memory to 16 features, but LSTR achieves much better performance $( 6 9 . 5 \%$ vs. $6 \bar { 5 } . 9 \%$ in mAP). This demonstrates the effectiveness of our “adaptive compression” compared to heuristics downsampling.
+
+Can we compensate reduced memory length with RNN? We note that LSTR’s performance notably decreases when it can only access very limited memory (e.g., $m _ { L } + m _ { S } \leq 1 6$ seconds). Here we test if RNN can compensate LSTR’s reduced memory or even fully replace the LSTR encoder. We implement LSTR using $m _ { S } = 8$ seconds with an extra Gated Recurrent Unit (GRU) [10] (its architecture is visualized in the Supplementary Material) to capture all history outside the long- and short-term memories. The dashed line in Fig. 3 shows the results. Plugging-in RNNs indeed improves the performance when $m _ { L }$ is small, but when $m _ { L }$ is large $\geq 6 4$ seconds), it does not improve the accuracy anymore. Note that RNNs are not used in any other experiments in this paper.
+
+# 4.5 Design Choices of LSTR
+
+Table 4: Results of different designs of the LSTR encoder and decoder. The length of short-term memory is set to 8 seconds. “TR” denotes Transformer. The last row is our proposed LSTR design.   
+
+<table><tr><td rowspan="2">LSTR Encoder</td><td rowspan="2">LSTR Decoder</td><td colspan="8">Length of Long-Term Memory mL (secs)</td></tr><tr><td>8</td><td>16</td><td>32</td><td>64</td><td>128</td><td>256</td><td>512</td><td>1024</td></tr><tr><td>N/A</td><td>TR Encoder</td><td>65.7</td><td>66.8</td><td>67.1</td><td>67.2</td><td>67.3</td><td>66.8</td><td>66.5</td><td>66.2</td></tr><tr><td>N/A</td><td>TR Decoder</td><td>66.5</td><td>67.3</td><td>67.7</td><td>68.1</td><td>68.3</td><td>67.9</td><td>67.0</td><td>66.5</td></tr><tr><td>TR Encoder</td><td>TR Decoder</td><td>65.9</td><td>66.4</td><td>66.7</td><td>67.4</td><td>67.5</td><td>67.2</td><td>67.0</td><td>66.6</td></tr><tr><td>Projection Layer</td><td>TR Decoder</td><td>66.2</td><td>67.1</td><td>67.4</td><td>67.7</td><td>67.5</td><td>67.2</td><td>66.9</td><td>66.8</td></tr><tr><td>TR Decoder</td><td>TR Decoder</td><td>66.1</td><td>67.1</td><td>67.4</td><td>68.0</td><td>68.5</td><td>68.6</td><td>68.7</td><td>68.7</td></tr><tr><td>TRDecoder+ TR Encoder</td><td>TR Decoder</td><td>66.2</td><td>67.3</td><td>67.6</td><td>68.4</td><td>68.6</td><td>68.8</td><td>68.9</td><td>69.0</td></tr><tr><td>TRDecoder +TRDecoder</td><td>N/A</td><td>64.0</td><td>64.7</td><td>65.9</td><td>66.1</td><td>66.5</td><td>66.2</td><td>65.4</td><td>65.2</td></tr><tr><td>TR Decoder + TR Decoder</td><td>TR Decoder</td><td>66.6</td><td>67.8</td><td>68.2</td><td>68.8</td><td>69.2</td><td>69.4</td><td>69.5</td><td>69.5</td></tr></table>
+
+We continue to explore the design trade-offs of LSTR. Unless noted otherwise, we use short-term memory of 8 seconds, long-term memory of 512 seconds, and Kinetics pretrained features.
+
+Number of layers and tokens. First, we assess using different numbers of token embeddings (i.e., $n _ { 0 }$ and $n _ { 1 }$ ) in LSTR encoder. Fig 4 (left) shows that LSTR is quite robust to different choices (the best and worst performance gap is only about $1 . 5 \%$ ), but using $n _ { 0 } = 1 6$ and $n _ { 1 } = 3 2$ gets highest accuracy. Second, we experiment for the effect of using different numbers of Transformer decoder units (i.e., $\ell _ { e n c }$ and $\ell _ { d e c , }$ ). As shown in Fig 4 (right), LSTR does not need a large model to get the best performance, and in practice, using more layers can cause overfitting.
+
+![](images/8676e342cbc8fb148ac0009b33f39bc819e575362c5f30bb5d427b505fa4fc2d.jpg)  
+Figure 4: Left: Results of different number of token embeddings for our two-stage memory compression. Right: Results of different number of Transformer decoder units for $\ell _ { e n c }$ and $\ell _ { d e c }$ .
+
+Can we unify the temporal modeling using only self-attention models? We test if long-term ${ \bf M } _ { L }$ and short-term $\mathbf { M } _ { S }$ memory can be learned as a whole using self-attention models. Specifically, we concatenate ${ \bf { M } } _ { L }$ and $\mathbf { M } _ { S }$ and feed them into a standard Transformer Encoder [61] with a similar model size to LSTR. Table 4 (row 8 vs. row 1) shows that LSTR achieves better performance especially when $m _ { L }$ is large (e.g., $6 9 . 5 \%$ vs. $6 6 . 5 \%$ when $m _ { L } = 5 1 2$ and $6 6 . 6 \%$ vs. ${ \bar { 6 } } 5 . 7 \%$ when $m _ { L } = 8$ ). This shows the advantage of LSTR for temporal modeling on long- and short-term context.
+
+Can we remove the LSTR encoder? We explore this by directly feeding ${ \bf M } _ { L }$ into the LSTR decoder, and using $\mathbf { M } _ { S }$ as tokens to reference useful information. Table 4 shows that LSTR outperforms this baseline (row 8 vs. row 2), especially when $m _ { L }$ is large. We also compare it with self-attention models (row 1) and observe that although neither of them can effectively model prolonged memory, this baseline outperforms the Transformer Encoder. This also demonstrates the effectiveness of our idea of using short-term memory to query related context from long-range context.
+
+Can the LSTR encoder learn effectively using self-attention? To evaluate the “bottleneck” design with cross-attention in LSTR encoder, we try modeling $\mathbf { M } _ { L }$ using standard Transformer Encoder units [61]. Note that this still captures ${ \bf M } _ { L }$ and $\mathbf { M } _ { S }$ with the similar workflow of LSTR, but does not compress and encode ${ \bf M } _ { L }$ using learnable tokens. Table 4 (row 8 vs. row 3) shows that LSTR outperforms this baseline with all $m _ { L }$ settings. In addition, the performance of this baseline decreases when $m _ { L }$ gets larger, which suggests the superior ability of LSTR for modeling long-range patterns.
+
+How to design the memory compression for the LSTR encoder? First, we use a projection layer, consisting of a learnable matrix of size $n _ { 0 } \times m _ { L }$ followed by MLP layers, to compress the long-term memory along the temporal dimension. Table 4 shows that using this simple projection layer (row 4) slightly outperforms the model without long-term memory (row 1), but is worse than attention-based compression methods. Second, we evaluate the one-stage design with $\ell _ { e n c } + 1$ Transformer decoder units. Table 4 (row 8 vs. row 5) shows that two-stage compression is stably better than one-stage, and their performance gap gets larger when using larger $m _ { L }$ $0 . 5 \%$ when $m _ { L } = 8$ and $0 . 8 \%$ when $m _ { L } = 5 1 2$ ). Third, we compare cross-attention and self-attention for two-stage compression by replacing the second Transformer decoder with Transformer encoder. LSTR stably outperforms this baseline (row 6) by about $0 . 5 \%$ in mAP. However, its performance is still better than models with one-stage compression of about $1 . 3 \%$ (row 6 vs. row 3) and $0 . 3 \%$ (row 6 vs. row 5) on average.
+
+Can we remove the LSTR decoder? We remove the LSTR decoder to evaluate its contribution. Specifically, we feed the entire memory to LSTR encoder and attach a multi-layer (MLP) classifier on its output tokens embeddings. Similar to the above experiments, we increase the model size to ensure a fair comparison. Table 4 shows that LSTR outperforms this baseline (row 7) by about $4 \%$ on large $m _ { L }$ (e.g., 512 and 1024) and about $2 . 5 \%$ on relative small $m _ { L }$ (e.g., 8 and 16).
+
+Table 5: Results of LSTR using different memory integration methods in mAP $( \% )$ . Our proposed integration method using cross-attention stably outperforms the heuristic methods.   
+
+<table><tr><td rowspan="2">Memory Integration Methods</td><td colspan="8">Length of Long-Term Memory mL (secs)</td></tr><tr><td>8</td><td>16</td><td>32</td><td>64</td><td>128</td><td>256</td><td>512</td><td>1024</td></tr><tr><td>Average Pooling</td><td>66.1</td><td>67.0</td><td>67.3</td><td>67.5</td><td>68.2</td><td>68.4</td><td>68.6</td><td>68.6</td></tr><tr><td>Concatenation</td><td>65.9</td><td>67.2</td><td>67.5</td><td>67.7</td><td>68.4</td><td>68.5</td><td>68.7</td><td>68.6</td></tr><tr><td>Cross-Attention (ours)</td><td>66.6</td><td>67.8</td><td>68.2</td><td>68.8</td><td>69.2</td><td>69.4</td><td>69.5</td><td>69.5</td></tr></table>
+
+Cross-attention vs. heuristics for integrating long- and short-term memories. We explore integrating the long- and short-term memories by using average pooling and concatenation. Specifically, the encoded long-term features of size $n _ { 1 } \times C$ is converted to a vector of $C$ elements by channel-wise averaging, and the short-term memory of size $m _ { S } \times C$ is encoded by $\ell _ { d e c }$ Transformer encoder units. Then, each slot of the short-term features is either averaged or concatenated with the long-term feature vector for action classification. Note that these models still benefit from LSTR’s effectiveness for long-term modeling. Table 5 shows that using average pooling and concatenation obtain comparable results, but LSTR with cross-attention stably outperforms these baselines.
+
+# 4.6 Runtime
+
+Table 6: Runtime of LSTR with different design choices. The last row is our proposed LSTR design.   
+
+<table><tr><td rowspan="2">LSTR Encoder</td><td rowspan="2">LSTR Decoder</td><td colspan="4">Frames Per Second (FPS)</td></tr><tr><td>OptFlow Computation</td><td>RGB Feature Extraction</td><td>OptFlow Feature Extraction</td><td>LSTR</td></tr><tr><td>N/A</td><td>TR Encoder</td><td rowspan="3">8.1</td><td rowspan="3">70.5</td><td></td><td>43.2</td></tr><tr><td>TR Encoder</td><td>TR Decoder</td><td>14.6</td><td>50.2</td></tr><tr><td>TR Decoder</td><td>TR Decoder TR Decoder</td><td>91.6</td><td>59.5</td></tr></table>
+
+We report LSTR’s runtime in frames per second (FPS) on a system with a single V100 GPU, and use the videos from THUMOS’14 dataset. The results are shown in Table 6.
+
+We start by comparing the runtime between LSTR’s different design choices without considering the pre-processing (e.g., feature extraction). First, LSTR runs at 91.6 FPS using our two-stage memory compression (row 4), whereas using the one-stage design runs at a slower 59.5 FPS (row 3). Our two-stage design is more efficient because it does not need to reference information from the long-term memory multiple times, and can be further accelerated during online inference (see Sec. 3.6). Second, we test the LSTR encoder using self-attention mechanisms (row 2). This design does not compress the long-term memory, thus increasing the computational cost of both the LSTR encoder and decoder, leading to a slower speed of 50.2 FPS. Third, we test the standard Transformer Encoder [61] (row 1), whose runtime speed, 43.2 FPS, is about $2 \times$ slower than LSTR.
+
+We also compare LSTR with state-of-the-art recurrent models. As we are not aware of any prior work that reports their runtime, we test TRN [72] using their official open-source code [2]. The result shows that TRN runs at $1 2 3 . 3 \ \mathrm { F P S }$ , which is faster than LSTR. This is because recurrent models abstract the entire history as a compact representation but LSTR needs to process much more information. On the other hand, LSTR achieves much higher performance, outperforming TRN by about $7 . 5 \%$ in mAP on THUMOS’14 and about $4 . 5 \%$ in cAP on TVSeries.
+
+For end-to-end online inference, we follow the state-of-the-art methods [72, 19, 25] and build LSTR on two-stream features [62]. LSTR together with pre-processing techniques run at 4.6 FPS. Table 6 shows that the speed bottleneck is the motion feature extraction — it accounts for about $90 \%$ of the total runtime including the optical flow computation with DenseFlow [63]. One can improve the efficiency largely by using real-time optical flow extractors (e.g., PWC-Net [55]) or using only visual features extracted by a light-weight backbone (e.g., MobileNet [29] and FBNet [67]).
+
+# 4.7 Error Analysis
+
+Table 7: Action classes with highest and lowest performance on THUMOS’14.   
+
+<table><tr><td>Action Classes HammerThrow PoleVault LongJump Diving BaseballPitch FrisbeeCatch Billirds CricketShot</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>AP (%)</td><td>92.8</td><td>89.7</td><td>86.9</td><td>86.7</td><td>55.4</td><td>49.4</td><td>39.8</td><td>38.6</td></tr></table>
+
+![](images/20b24f9c97d71b7c32f233295d89092d598db050bcdd291259ed08c23dea57c4.jpg)  
+Figure 5: Failure cases on THUMOS’14. Action classes from left to right are “BaseballPitch”, “FrisbeeCatch”, “Billiards”, and “CricketShot”. Red circle indicates where the action is happening.
+
+In Table 7, we list the action classes from THUMOS’14 where LSTR gets the highest (color green) and the lowest (color red) per-frame APs. In Fig. 5, we illustrate four sample frames with incorrect predictions. More visualizations are included in the Supplementary Material. We observe that LSTR sees a decrease in detection accuracy when the action incurs only tiny motion or the subject is very far away from the camera, but excels at recognizing actions with long temporal span and multiple stages, such as “PoleVault” and “Long Jump”. This suggests we may explore extending the temporal modeling capability of LSTR to both spatial and temporal domains.
+
+# 5 Conclusion
+
+We present LSTR which captures both long- and short-term correlations in past observations of a time series by compressing long-term memory into encoded latent features and referencing related temporal context from them with short-term memory. This demonstrates the importance of separately modeling long- and short-term information and then integrating them for online inference tasks. Experiments on multiple datasets and ablation studies validate the effectiveness and efficiency of the LSTR design in dealing with prolonged video sequences. However, we note that LSTR is operating only on the temporal dimension. An end-to-end video understanding system requires simultaneous spatial and temporal modeling for optimal results. Therefore extending the idea of LSTR to spatio-temporal modeling remains an open yet challenging problem.
+
+# 6 Acknowledgments and Disclosure of Funding
+
+We thank the anonymous reviewers for their helpful suggestions. This work was funded by Amazon.
+
+# References
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parse/train/aohkNJxjYJX/aohkNJxjYJX_content_list.json

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+        "type": "text",
+        "text": "Long Short-Term Transformer for Online Action Detection ",
+        "text_level": 1,
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Mingze Xu Yuanjun Xiong Hao Chen Xinyu Li Wei Xia Zhuowen Tu Stefano Soatto Amazon/AWS AI {xumingze,yuanjx,hxen,xxnl,wxia,ztu,soattos}@amazon.com ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Abstract ",
+        "text_level": 1,
+        "bbox": [
+            462,
+            319,
+            535,
+            335
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "We present Long Short-term TRansformer (LSTR), a temporal modeling algorithm for online action detection, which employs a long- and short-term memory mechanism to model prolonged sequence data. It consists of an LSTR encoder that dynamically leverages coarse-scale historical information from an extended temporal window (e.g., 2048 frames spanning of up to 8 minutes), together with an LSTR decoder that focuses on a short time window (e.g., 32 frames spanning 8 seconds) to model the fine-scale characteristics of the data. Compared to prior work, LSTR provides an effective and efficient method to model long videos with fewer heuristics, which is validated by extensive empirical analysis. LSTR achieves state-of-the-art performance on three standard online action detection benchmarks, THUMOS’14, TVSeries, and HACS Segment. Code has been made available at: https://xumingze0308.github.io/projects/lstr. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 Introduction ",
+        "text_level": 1,
+        "bbox": [
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+            540,
+            310,
+            558
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Given an incoming stream of video frames, online action detection [14] is concerned with the task of classifying what is happening at each frame without seeing the future. Unlike offline methods that assume the entire video is available, online methods process the data causally, up to the current time. In this paper, we present an online temporal modeling algorithm capable of capturing temporal relations on prolonged sequences up to 8 minutes long, while retaining fine granularity of the event in the representation. This is achieved by modeling activities at different temporal scales, so as to capture a variety of events ranging from bursts to slow trends. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Specifically, we propose a method, named Long Short-term TRansformer (LSTR), to jointly model long- and short-term temporal dependencies. LSTR has two main advantages over prior work. 1) It stores the history directly thus avoiding the pitfalls of recurrent models [18, 50, 28, 10]. Backpropagation through time, BPTT, is not needed as the model can directly attend to any useful frames from memory. 2) It separates long- and short-term memories, which allows modeling short-term context while extracting useful correlations from the long-term history. This allows us to compress the long-term history without losing important fine-scale information. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "As shown in Fig. 1, we explicitly divide the entire history into the long- and short-term memories and build our model with an encoder-decoder architecture. Specifically, the LSTR encoder compresses and abstracts the long-term memory into a latent representation of fixed length, and the LSTR decoder uses a short window of transient frames to perform self-attention and cross-attention operations on the extracted token embeddings from the LSTR encoder. In the LSTR encoder, an extended temporal support becomes beneficial in dealing with untrimmed, streaming videos by devising twostage memory compression, which is shown to be computationally efficient in both training and inference. Our overall long short-term Transformer architecture gives rise to an effective and efficient representation for modeling prolonged sequence data. ",
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+    {
+        "type": "image",
+        "img_path": "images/2cdfefefe829e4490463771dc0dbe39922829ab172a2bd6b7ac129c1cd3955a3.jpg",
+        "image_caption": [
+            "Figure 1: Overview of Long Short-term TRansformer (LSTR). Given a live streaming video, LSTR sequentially identifies the actions happening in each incoming frame by using an encoderdecoder architecture, without future context. The dashed brown arrows indicate the data flow of the long- and short-term memories following the first-in-first-out (FIFO) logic. (Best viewed in color.) "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We validate LSTR on standard benchmark datasets (THUMOS’14 [30], TVSeries [14], and HACS Segment [76]). These have distinct characteristics such as video length spanning from a few seconds to tens of minutes. Experimental results establish LSTR as the state-of-the-art for online action detection. Ablation studies further showcase LSTR’s abilities in modeling long video sequences. ",
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+        "type": "text",
+        "text": "2 Related Work ",
+        "text_level": 1,
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+    },
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+        "text": "Online Action Detection. Temporal action localization aims to detect the onset and termination of action instances after observing the entire video [52, 71, 23, 53, 78, 5, 37, 39, 38]. Embodied perception, however, requires causal processing [73], where we can only process the data up to the present. Online action detection focuses on this setting [14]. RED [22] uses a reinforcement loss to encourage recognizing actions as early as possible. TRN [72] models greater temporal context by simultaneously performing online action detection and anticipation. IDN [19] learns discriminative features and accumulates only relevant information for the present. LAP-Net [46] proposes an adaptive sampling strategy to obtain optimal features. PKD [77] transfers knowledge from offline to online models using curriculum learning. As with early action detection [27, 40], Shou et al. [54] focus on online detection of action start (ODAS). StartNet [24] decomposes ODAS into two stages and learns with policy gradient. WOAD [25] uses weakly-supervised learning with video-level labels. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Temporal/Sequence Modeling. Causal time series analysis has traditionally assumed the existence of a latent “state” variable that captures all information in past data, and is updated using only the current datum [49, 28, 10]. While the Separation Principle ensures that such a state exists for linearGaussian time series, in general it is not possible to summarize all past history of complex data in a finite-dimensional sufficient statistic. Therefore, we directly model the history, in accordance with other work on video understanding [69, 45, 68]. Earlier work on action recognition usually relies on heuristic sub-sampling (typically 3 to 7 video frames) for more feasible training [74, 62, 21, 41, 57]. 3D ConvNets [59, 8, 60] are used to perform spatio-temporal feature modeling on more frames, but they fail to capture temporal correlations beyond their receptive field. Recently, Wu et al. [69] propose long-term feature banks to capture objects and scene features, but discarding their temporal order which is clearly informative. Most of work above does not explicitly separate the long- and short-term context modeling, but instead integrates all observed features with simple mechanisms such as pooling or concatenation. We are motivated by work in Cognitive Science [44, 12, 9, 35] that has shed light on the design principles for modeling long-term dependencies with attention mechanism [66, 13, 48, 75]. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Transformers for Action Understanding. Transformers have achieved breakthrough success in NLP [47, 15] and are adopted in computer vision for image recognition [17, 58] and object detection [7]. Recent papers exploit Transformers for temporal modeling tasks in videos, such as action recognition [43, 51, 36, 4, 3] and temporal action localization [42, 56], and achieve promising results. However, computational and memory demands result in most work being limited to short video clips, with few exceptions [13, 6] that focuses on designing Transformers to model long-range context. The mechanism for aggregating long- and short-term information is relatively unexplored [32]. ",
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+    {
+        "type": "text",
+        "text": "3 Long Short-Term Transformer ",
+        "text_level": 1,
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+        "text": "Given a live streaming video, our goal is to identify the actions performed in each video frame using only past and current observations. Future information is not accessible during inference. Formally, a streaming video at time $t$ is represented by a batch of $\\tau$ past frames $\\mathbf { I } ^ { t } = \\{ I _ { t - \\tau } , \\cdot \\cdot \\cdot , I _ { t } \\}$ , which reads “ $^ Ḋ \\cdot Ḍ I Ḍ$ up to time $t$ .” The online action detection system receives $\\mathbf { I } ^ { t }$ as input, and classifies the action category $\\hat { y } _ { t }$ belonging to one of $( K + 1 )$ classes, $\\hat { y } _ { t } \\in \\{ 0 , 1 , \\cdots , K \\}$ , ideally using the posterior probability $P ( \\hat { y } _ { t } = k | \\mathbf { I } ^ { t } )$ , where $k = 0$ denotes the probability that no event is occurring at frame $t$ . We design our method by assuming that there is a pretrained feature extractor [62] that processes each video frame $I _ { t }$ into a feature vector $\\mathbf { f } _ { t } \\in \\mathbb { R } ^ { C }$ of $C$ dimensions1. These vectors form a $( \\tau \\times C )$ -dimensional temporal sequence that serves as the input of our method. ",
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+            "Figure 2: Visualization of Long Short-Term Transformer (LSTR), which is formulated in an encoder-decoder manner. Specifically, the LSTR encoder compresses the long-term memory of size $m _ { L }$ to $n _ { 1 }$ encoded latent features, and the LSTR decoder references related context information from the encoded memory with the short-term memory of size $m _ { S }$ for action recognition of the present. The LSTR encoder and decoder are built with Transformer decoder units [61], which take the input tokens (dark green arrows) and output tokens (dark blue arrows) as inputs. During inference, LSTR processes every incoming frame in an online manner, absent future context. (Best viewed in color.) "
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+        "type": "text",
+        "text": "3.1 Overview ",
+        "text_level": 1,
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+        "text": "Our method is based on the intuition that frames observed recently provide precise information about the ongoing action instance, while frames over an extended period offer contextual references for actions that are potentially happening right now. We propose Long Short-term TRansformer (LSTR) in an explicit encoder-decoder manner, as shown in Fig. 2. In particular, the feature vectors of $m _ { L }$ frames in the distant past are stored in a long-term memory, and a short-term memory stores the features of $m _ { S }$ recent frames. The LSTR encoder compresses and abstracts features in long-term memory to an encoded latent representation of $n _ { 1 }$ vectors. The LSTR decoder queries the encoded long-term memory with the short-term memory for decoding, leading to the action prediction $\\hat { y } _ { t }$ . This design follows the line of thought in combining long- and short-term information for action understanding [16, 62, 69], but addresses several key challenges to efficiently achieve this goal, exploiting the flexibility of Transformers [61]. ",
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+        "type": "text",
+        "text": "3.2 Long- and Short-Term Memories ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We store the streaming input of feature vectors into two consecutive memories. The first is the short-term memory which stores only a small number of frames that are recently observed. We implement it with a first-in-first-out (FIFO) queue of $m _ { S }$ slots. At time $T$ , it stores the feature vectors as $\\mathbf { M } _ { S } = \\{ \\mathbf { f } _ { T } , \\cdot \\cdot \\cdot , \\mathbf { f } _ { T - m _ { S } + 1 } \\}$ . When a frame becomes “older” than $m _ { S }$ time steps, it graduates from $\\mathbf { M } _ { S }$ and enters into the long-term memory, which is implemented with another FIFO queue of $m _ { L }$ slots. The long term memory stores $\\mathbf { M } _ { L } = \\{ \\mathbf { f } _ { T - m _ { S } } , \\cdot \\cdot \\cdot , \\mathbf { f } _ { t - m _ { S } - m _ { L } + 1 } \\}$ . The long-term memory serves as the input memory to the LSTR encoder and the short-term memory serves as the queries for the LSTR decoder. In practice, the long-term memory stores a much longer time span than the short-term memory $( m _ { S } \\ll m _ { L } )$ ). A typical choice is $m _ { L } = 2 0 4 8$ , which represents 512 seconds worth of video contents with 4 frames per second (FPS) sampling rate, and $m _ { S } = 3 2$ representing ",
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+        "type": "text",
+        "text": "8 seconds. We add a sinusoidal positional encoding s [61] to each frame feature in the memories relative to current time $T$ (i.e., the frame at $T - \\tau$ receives a positional embedding of ${ \\bf s } _ { \\tau }$ ). ",
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+        "type": "text",
+        "text": "3.3 LSTR Encoder ",
+        "text_level": 1,
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+        "text": "The LSTR encoder aims at encoding the long-term memory of $m _ { L }$ feature vectors into a latent representation that LSTR can use for decoding useful temporal context. This task requires a large capacity in capturing the relations and temporal context across a span of hundreds or even thousands of frames. Prior work on modeling long-term context for action understanding relies on heuristic temporal sub-sampling [69, 62] or recurrent networks [16] to make training feasible, at the cost of losing specific information of each time step. Attention-based architectures, such as Transformer [61], have recently been shown promising for similar tasks that require long-range temporal modeling [51]. A straightforward choice for LSTR encoder would be to use a Transformer encoder based on self-attention. However, its time complexity, $O ( m _ { L } ^ { 2 } C )$ , grows quadratically with the memory sequence length $m _ { L }$ . This limits our ability to model long-term memory with sufficient length to cover long videos. Though recent work [64] has explored self-attention with linear complexity, repeatedly referencing information from the long-term memory with multi-layer Transformers is still computationally heavy. In LSTR, we propose to use the two-stage memory compression mechanism based on Transformer decoder units [61] to achieve more effective memory encoding. ",
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+        "type": "text",
+        "text": "The Transformer decoder unit [61] takes two sets of inputs. The first set includes a fixed number of $n$ learnable output tokens $\\ b { \\lambda } \\in \\mathbb { R } ^ { n \\times C }$ , where $C$ is the embedding dimension. The second set includes another $m$ input tokens $\\pmb { \\theta } \\in \\mathbb { R } ^ { m \\times C }$ , where $m$ can be a rather large number. It first applies one layer of multi-head self-attention on $\\lambda$ . The outputs $\\lambda ^ { \\prime }$ are then used as queries in an “QKV cross-attention” operation and the input embeddings $\\pmb \\theta$ serve as key and value. The two steps can be written as ",
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+        "type": "equation",
+        "img_path": "images/63e089a3693ef14fb8b11673f2efa19703c1901456ebe815300edc3b1e1974e8.jpg",
+        "text": "$$\n\\lambda ^ { \\prime } = \\operatorname { S e l f A t t m } ( \\lambda ) = \\operatorname { S o f t m a x } ( \\frac { \\lambda \\cdot \\lambda ^ { T } } { \\sqrt { C } } ) \\lambda \\ a n d \\ \\operatorname { C r o s s A t t m } ( \\sigma ( \\lambda ^ { \\prime } ) , \\theta ) = \\operatorname { S o f t m a x } ( \\frac { \\sigma ( \\lambda ^ { \\prime } ) \\cdot \\theta ^ { T } } { \\sqrt { C } } ) \\theta ,\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where $\\sigma : \\mathbb { R } ^ { n \\times C }  \\mathbb { R } ^ { n \\times C }$ denotes the intermediate layers between the two attention operations. One appealing property of this design is that it transforms the $m \\times C$ dimensional input tokens into output tokens of $n \\times C$ dimensions in $O ( n ^ { 2 } C + n m C )$ time complexity. When $n \\ll m$ , the time complexity becomes linear to $m$ , making it an ideal candidate for compressing long-term memory. This property is also utilized in [32] to efficiently process large volume inputs, such as image pixels. ",
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+        "text": "Two-Stage Memory Compression. Stacking multiple Transformer decoder units on the long-term memory, as in [61], can form a memory encoder with linear complexity with respect to the memory size $m _ { L }$ . However, running the encoder at each time step can still be time consuming. We can further reduce the time complexity with a two-stage memory compression design. The first stage has one Transformer decoder unit with $n _ { 0 }$ output tokens. Its input tokens are the entire long-term memory of size $m _ { L }$ . The outputs of the first stage are used as the input tokens to the second stage, which has $\\ell _ { e n c }$ stacked Transformer decoder units and $n _ { 1 }$ output tokens. Then, the long-term memory of size $m _ { L } \\times C$ is compressed into a latent representation of size $n _ { 1 } \\times C$ , which can then be efficiently queried in the LSTR decoder later. This two-stage memory compression design is illustrated in Fig. 2. ",
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+        "type": "text",
+        "text": "Compared to an $( 1 + \\ell _ { e n c } )$ -layer Transformer encoder with $O ( m _ { L } ^ { 2 } ( 1 + \\ell _ { e n c } ) C )$ time complexity or stacked Transformer decoder units with $n$ output-tokens having $\\bar { O } ( ( n ^ { 2 } + n m _ { L } ) ( 1 + \\ell _ { e n c } ) C )$ time complexity, the proposed LSTR encoder has complexity of $O ( n _ { 0 } ^ { 2 } C + n _ { 0 } m _ { L } C + ( n _ { 1 } ^ { 2 } + n _ { 1 } n _ { 0 } ) \\ell _ { e n c } C )$ . Because both $n _ { 0 }$ and $n _ { 1 }$ are much smaller than $m _ { L }$ , and $\\ell _ { e n c }$ is usually larger than 1, using two-stage memory compression could be more efficient. In Sec. 3.6, we will show that, during online inference, it further enables us to reduce the runtime of the Transformer decoder unit of the first stage. In Sec. 4.5, we empirically found this design also leads to better performance for online action detection. ",
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+        "type": "text",
+        "text": "3.4 LSTR Decoder ",
+        "text_level": 1,
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+        "text": "The short-term memory contains informative features for classifying actions on the latest time step. The LSTR decoder uses the short-term memory as queries to retrieve useful information from the encoded long-term memory produced by the LSTR encoder. The LSTR decoder is formed by stacking $\\ell _ { d e c }$ layers of Transform decoder units. It takes the outputs of the LSTR encoder as input tokens and the $m _ { S }$ feature vectors in the short-term memory as output tokens. It outputs $m _ { S }$ probability vectors $\\{ \\mathbf { p } _ { T } , \\cdot \\cdot \\cdot , \\mathbf { p } _ { T - m _ { S } + 1 } \\} \\in [ 0 , 1 ] ^ { K + 1 }$ , each $\\mathbf { p } _ { t }$ representing the predicted probability distribution of $K$ action categories and one “background” class at time $t$ . During inference, we only take the probability vector $\\mathbf { p } _ { T }$ from the output token corresponding to the current time $T$ for the classification result. ",
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+        "type": "text",
+        "text": "However, having the additional outputs on the older frames allows the model to leverage more supervision signals during training. The details will be described below. ",
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+        "type": "text",
+        "text": "3.5 Training LSTR ",
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+        "type": "text",
+        "text": "LSTR can be trained without temporal unrolling and Backpropagation Through Time (BPTT) as in LSTM [28], which is a common property of Transformers [61]. We construct each training sample by randomly sampling an ending time $\\dot { T }$ and filling the long- and short-term memories by tracing back in time for $m _ { S } + m _ { L }$ frames. We use the empirical cross entropy loss between the predicted probability distribution $\\mathbf { p } _ { T }$ at time $T$ and the ground truth action label $\\dot { y } _ { T } \\in \\{ 0 , 1 , \\cdots , K \\}$ as ",
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+        "text": "$$\nL ( y _ { T } , { \\bf p } _ { T } ; T ) = - \\sum _ { k = 0 } ^ { K } \\delta ( k - y _ { T } ) \\log p _ { T } ^ { k } ,\n$$",
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+        "type": "text",
+        "text": "where $p _ { T } ^ { k }$ is the $k$ -th element of the probability vector $\\mathbf { p } _ { T }$ , predicted on the latest frame at $T$ Additionally, we add a directional attention mask [61] to the short-term memory so that any frame in the short-term memory can only depend on its previous frames. In this way, we can make predictions on all frames in the short-term memory as if they are the latest ones. Thus we can provide supervision on every frame in the short-term memory, and the complete loss function $\\mathcal { L }$ is then ",
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+        "text": "$$\n\\mathcal { L } _ { T } = \\sum _ { t = T - m s + 1 } ^ { T } L ( y _ { t } , \\mathbf { p } _ { t } ; T ) ,\n$$",
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+        "type": "text",
+        "text": "where $\\mathbf { p } _ { t }$ denotes the prediction from the output token corresponding to time $t$ ",
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+        "type": "text",
+        "text": "3.6 Online Inference with LSTR ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "During online inference, the video frame features are streamed to the model as time passes. Running LSTR’s long-term memory encoder from scratch for each frame results in a time complexity of $O ( n _ { 0 } ^ { 2 } C + n _ { 0 } ^ { - } m _ { L } C )$ and $\\dot { O ( ( n _ { 1 } ^ { 2 } + n _ { 1 } n _ { 0 } ) \\ell _ { e n c } C ) }$ for the first and second memory compression stages, respectively. However, at each time step, there is only one new video frame to be updated. We show it is possible to achieve even more efficient online inference by storing the intermediate results for the Transformer decoder unit of the first stage. First, the queries of the first Transformer decoder unit are fixed. So their self-attention outputs can be pre-computed and used throughout the inference. Second, the cross-attention operation in the first stage can be written as ",
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+        "type": "equation",
+        "img_path": "images/e908a2924901a3333c17b17c8854dd5738964c60e52a0158bf6c6b0f6ea13e5b.jpg",
+        "text": "$$\n\\mathrm { C r o s s A t t n } ( \\mathbf { q } _ { i } , \\{ \\mathbf { f } _ { T - \\tau } + \\mathbf { s } _ { \\tau } \\} ) = \\sum _ { \\tau = m _ { S } } ^ { m _ { S } + m _ { L } - 1 } \\frac { \\exp ( ( \\mathbf { f } _ { T - \\tau } + \\mathbf { s } _ { \\tau } ) \\cdot \\mathbf { q } _ { i } / \\sqrt { C } ) } { \\sum _ { \\tau = m _ { S } } ^ { m _ { S } + m _ { L } - 1 } \\exp ( ( \\mathbf { f } _ { T - \\tau } + \\mathbf { s } _ { \\tau } ) \\cdot \\mathbf { q } _ { i } / \\sqrt { C } ) } \\cdot ( \\mathbf { f } _ { T - \\tau } + \\mathbf { s } _ { \\tau } ) ,\n$$",
+        "text_format": "latex",
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+        "type": "text",
+        "text": "where the index $\\tau = T - t$ is the relative position of a frame $t$ in the long-term memory to the latest time $T$ . This calculation depends on the un-normalized attention weight matrix $\\mathbf { A } \\in \\mathbb { R } ^ { m _ { L } \\times n _ { 0 } }$ , with elements $a _ { \\tau i } = ( { \\bf f } _ { T - \\tau } + { \\bf s } _ { \\tau } ) \\cdot { \\bf q } _ { i }$ . A can be decomposed into the sum of two matrices $\\mathbf { A } ^ { f }$ and ${ \\bf A } ^ { s }$ . We have their elements as $a _ { \\tau i } ^ { f } = \\mathbf { f } _ { T - \\tau } \\cdot \\mathbf { q } _ { i }$ and $a _ { \\tau i } ^ { s } = \\mathbf s _ { \\tau } \\cdot \\mathbf q _ { i }$ . The queries after the first self-attention operation, $\\mathbf { Q } = [ \\mathbf { q } _ { 1 } , \\dots , \\mathbf { q } _ { n _ { 0 } } ]$ , and the position embedding ${ \\bf s } _ { \\tau }$ are fixed during inference. Thus the matrix ${ \\bf A } ^ { s }$ can be pre-computed and used for every incoming frame. We additionally maintain a FIFO queue of vectors $\\mathbf { a } _ { t } \\doteq \\mathbf { Q } ^ { \\top } \\mathbf { f } _ { t }$ of size $m _ { L }$ . $\\mathbf { A } ^ { f }$ at any time step $T$ can be obtained by stacking all vectors currently in this queue. Updating this queue at each time step requires $O ( n _ { 0 } C )$ time complexity for the matrix-vector product. Now we can obtain the matrix A with only $n _ { 0 } \\times m _ { L }$ additions by adding ${ \\bf A } ^ { s }$ and $\\mathbf { A } ^ { f }$ together, instead of $n _ { 0 } \\times m _ { L } \\times C$ multiplications and additions using Eq. (3). This means the amortized time complexity for computing the attention weights can be reduced to $O ( n _ { 0 } ( m _ { L } + C ) )$ . Although the time complexity of the cross-attention operation is still $O ( n _ { 0 } m _ { L } C )$ due to the inevitable operation of weighted sum, since $C$ is usually larger than 1024 [26], this is still a considerable reduction of runtime. LSTR’s walltime efficiency is discussed in Sec. 4.6. ",
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+        "text": "4 Experiments ",
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+        "text": "4.1 Datasets ",
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+        "text": "We evaluate our model on three publicly-available datasets: THUMOS’14 [30], TVSeries [14] and HACS Segment [76]. THUMOS’14 includes over 20 hours of sports video annotated with 20 actions. We follow prior work [72, 19] and train on the validation set (200 untrimmed videos) and evaluate on the test set (213 untrimmed videos). TVSeries contains 27 episodes of 6 popular TV series, totaling 16 hours of video. The dataset is annotated with 30 realistic, everyday actions (e.g., open door). HACS Segment is a large-scale dataset of web videos. It contains 35,300 untrimmed videos over 200 human action classes for training and 5,530 untrimmed videos for validation. ",
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+        "type": "text",
+        "text": "4.2 Settings ",
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+        "text": "Feature Encoding. We follow the experimental settings of state-of-the-art methods [72, 19]. We extract video frames at 24 FPS and set the video chunk size to 6. Decisions are made at the chunk level, and thus accuracy is evaluated at every 0.25 second. For feature encoding, we adopt the TSN [62] models implemented in an open-source toolbox [11]. Specifically, the features are extracted by one visual model with the ResNet-50 [26] architecture from the central frame of each chunk and one motion model with the BN-Inception [31] architecture from the stacked optical flow fields between 6 consecutive frames [62]. The visual and motion features are concatenated along the channel dimension as the final feature f. We experiment with feature extractors pretrained on two datasets, ActivityNet and Kinetics. ",
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+        "type": "text",
+        "text": "Implementation Details. We implemented our proposed model in PyTorch [1], and performed all experiments on a system with 8 Nvidia V100 graphics cards. For all Transformer units, we set their number of heads as 16 and hidden units as 1024 dimensions. To learn model weights, we used the Adam [34] optimizer with weight decay $5 \\times 1 0 ^ { - 5 }$ . The learning rate was linearly increased from zero to $5 \\times 1 0 ^ { - 5 }$ in the first $2 / 5$ of training iterations and then reduced to zero following a cosine function. Our models were optimized with batch size of 16, and the training was terminated after 25 epochs. ",
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+        "type": "text",
+        "text": "Evaluation Protocols. We follow prior work and use per-frame mean average precision (mAP) to evaluate the performance of online action detection. We also use per-frame calibrated average precision (cAP) [14] that was proposed for TVSeries to correct the imbalance between positive and negative samples, $\\begin{array} { r } { c A P = \\sum _ { k } \\overset { \\cdot } { c } \\bar { P r } e c ( k ) * I ( k ) / P } \\end{array}$ , where $c P r e c = T P / ( T P + F P / \\bar { w } ) ,$ $I ( k )$ is 1 if frame $k$ is a true positive, $P$ is the number of true positives, and $w$ is the negative and positive ratio. ",
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+        "type": "text",
+        "text": "4.3 Comparison with the State-of-the-art Methods ",
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+        "type": "text",
+        "text": "Table 1: Online action detection and anticipation results on THUMOS’14 and TVSeries in terms of mAP and cAP, respectively. For online action detection, LSTR outperforms the state-of-the-art methods on THUMOS’14 by $3 . 7 \\%$ and $2 . 4 \\%$ in mAP and on TVSeries by $2 . 8 \\%$ and $2 . 7 \\%$ in cAP, using ActivityNet and Kinetics pretrained features, respectively. LSTR also achieves promising results for action anticipation. \\*Results are reproduced by us using their papers’ default settings. ",
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+        "type": "table",
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+        "table_caption": [
+            "(a) Results of online action detection using ActivityNet features "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"3\">THUMOS&#x27;14 TVSeries</td></tr><tr><td></td><td>mAP (%)</td><td>mcAP (%)</td></tr><tr><td>CDC[53]</td><td>44.4</td><td>-</td></tr><tr><td>RED [22]</td><td>45.3</td><td>79.2</td></tr><tr><td>TRN[72]</td><td>47.2</td><td>83.7</td></tr><tr><td>FATS[33]</td><td>51.6</td><td>81.7</td></tr><tr><td>IDN[19]</td><td>50.0</td><td>84.7</td></tr><tr><td>LAP [46]</td><td>53.3</td><td>85.3</td></tr><tr><td>TFN[20]</td><td>55.7</td><td>85.0</td></tr><tr><td>LFB*[69]</td><td>61.6</td><td>84.8</td></tr><tr><td>LSTR (ours)</td><td>65.3</td><td>88.1</td></tr></table>",
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+    {
+        "type": "table",
+        "img_path": "images/d4322ac6321f4460da96aec15afc884c331fa661d6ddfc7f647ed97e3bca54ca.jpg",
+        "table_caption": [
+            "(b) Results of online action detection using Kinetics features "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"3\">THUMOS&#x27;14 TVSeries</td></tr><tr><td></td><td>mAP (%)</td><td>mcAP (%)</td></tr><tr><td>FATS [33]</td><td>59.0</td><td>84.6</td></tr><tr><td>IDN[19]</td><td>60.3</td><td>86.1</td></tr><tr><td>TRN [72]</td><td>62.1</td><td>86.2</td></tr><tr><td>PKD [77]</td><td>64.5</td><td>86.4</td></tr><tr><td>WOAD [25]</td><td>67.1</td><td>=</td></tr><tr><td>LFB*[69]</td><td>64.8</td><td>85.8</td></tr><tr><td>LSTR (ours)</td><td>69.5</td><td>89.1</td></tr></table>",
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+        "type": "table",
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+        "table_caption": [
+            "(c) Results of action anticipation using ActivityNet features "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"3\">THUMOS&#x27;14 TVSeries</td></tr><tr><td></td><td>mAP (%)</td><td>mcAP (%)</td></tr><tr><td>EFC [22]</td><td>34.4</td><td>72.5</td></tr><tr><td>ED[22]</td><td>36.6</td><td>74.5</td></tr><tr><td>RED[22]</td><td>37.5</td><td>75.1</td></tr><tr><td>TRN [72]</td><td>38.9</td><td>75.7</td></tr><tr><td>TTM[65]</td><td>40.9</td><td>77.9</td></tr><tr><td>LAP [46]</td><td>42.6</td><td>78.7</td></tr><tr><td>LSTR (ours)</td><td>50.1</td><td>80.8</td></tr></table>",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/6c8de60863e7ef2bee95e8234cd78ce360319905f78b7af4ab92e1a03de380f0.jpg",
+        "table_caption": [
+            "Table 2: Online action detection results when only portions of videos are considered in cAP $( \\% )$ on TVSeries (e.g., $80 \\% - 9 0 \\%$ means only frames of this range of action instances were evaluated). LSTR outperforms existing methods at every time stage, especially on boundary locations. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"></td><td rowspan=\"2\">Features</td><td colspan=\"10\">Portion of Video</td></tr><tr><td>0-10%</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>10-20% 20-30%30-40% 40-50% 50-60% 60-70% 70-80% 80-90% 90-100%</td></tr><tr><td>TRN [72]</td><td rowspan=\"4\">ActivityNet</td><td>78.8</td><td>79.6</td><td>80.4</td><td>81.0</td><td>81.6</td><td>81.9</td><td>82.3</td><td>82.7</td><td>82.9</td><td>83.3</td></tr><tr><td>IDN[19]</td><td>80.6</td><td>81.1</td><td>81.9</td><td>82.3</td><td>82.6</td><td>82.8</td><td>82.6</td><td>82.9</td><td>83.0</td><td>83.9</td></tr><tr><td>TFN [20]</td><td>83.1</td><td>84.4</td><td>85.4</td><td>85.8</td><td>87.1</td><td>88.4</td><td>87.6</td><td>87.0</td><td>86.7</td><td>85.6</td></tr><tr><td>LSTR (ours)</td><td>83.6</td><td>85.0</td><td>86.3</td><td>87.0</td><td>87.8</td><td>88.5</td><td>88.6</td><td>88.9</td><td>89.0</td><td>88.9</td></tr><tr><td>IDN[19]</td><td rowspan=\"3\">Kinetics</td><td>81.7</td><td>81.9</td><td>83.1</td><td>82.9</td><td>83.2</td><td>83.2</td><td>83.2</td><td>83.0</td><td>83.3</td><td>86.6</td></tr><tr><td>PKD[77]</td><td>82.1</td><td>83.5</td><td>86.1</td><td>87.2</td><td>88.3</td><td>88.4</td><td>89.0</td><td>88.7</td><td>88.9</td><td>87.7</td></tr><tr><td>LSTR (ours)</td><td>84.4</td><td>85.6</td><td>87.2</td><td>87.8</td><td>88.8</td><td>89.4</td><td>89.6</td><td>89.9</td><td>90.0</td><td>90.1</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "We compare LSTR against other state-of-the-art methods [72, 19, 25] on THUMOS’14, TVSeries, and HACS Segment. Specifically, on THUMOS’14 and TVSeries, we implement LSTR with the long- and short-term memories of 512 and 8 seconds, respectively. On HACS Segment, we reduce the long-term memory to 256 seconds, considering that its videos are strictly shorter than 4 minutes. For LSTR, we implement the two-stage memory compression using Transformer decoder units. We set the token numbers to $n _ { 0 } = 1 6$ and $n _ { 1 } = 3 2$ and the Transformer layers to $\\ell _ { e n c } = 2$ and $\\ell _ { d e c } = 2$ . ",
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+    {
+        "type": "text",
+        "text": "4.3.1 Online Action Detection ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "THUMOS’14. We compare LSTR with recent work on THUMOS’14, including methods that use 3D ConvNets [53] and RNNs [70, 19, 25], reinforcement learning [22], and curriculum learning [77]. Table 1a and 1b shows that LSTR significantly outperforms the the state-of-the-art methods [69, 25] by $3 . 7 \\%$ and $2 . 4 \\%$ in terms of mAP using ActivityNet and Kinetics pretrained features, respectively. ",
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+    {
+        "type": "text",
+        "text": "TVSeries. Table 1a and 1b show the online action detection results that LSTR outperforms the state-of-the-art methods [20, 77] by $2 . 8 \\%$ and $2 . 7 \\%$ in terms of cAP using ActivityNet and Kinetics pretrained features, respectively. Following prior work [14], we also investigate LSTR’s performance at different action stages by evaluating each decile (ten-percent interval) of the video frames separately. Table 2 shows that LSTR outperforms existing methods at every stage of action instances. ",
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+    },
+    {
+        "type": "text",
+        "text": "HACS Segment. LSTR achieves $8 2 . 6 \\%$ on HACS Segment in term of mAP using Kinetics pretrained features. Note that HACS Segment is a new large-scale dataset with only a few previous results. LSTR outperforms existing methods RNN [28] $( 7 7 . 6 \\% )$ by $5 . 0 \\%$ and TRN [72] $( 7 8 . 9 \\% )$ by $3 . 7 \\%$ . ",
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+    },
+    {
+        "type": "text",
+        "text": "4.3.2 Action Anticipation ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We extend the idea of LSTR to action anticipation for up to 2 seconds (i.e., 8 steps in 4 FPS) into the future. Specifically, we concatenate another 8 learnable output tokens (with positional embedding) after the short-term memory in the LSTR decoder to produce the prediction results accordingly. Table 1c shows that LSTR significantly outperforms the state-of-the-art methods [72, 46] by $7 . 5 \\%$ mAP on THUMOS and $2 . 1 \\%$ cAP on TVSeries, using ActivityNet pretrained features. ",
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+    {
+        "type": "text",
+        "text": "4.4 Design Choices of Long- and Short-Term Memories ",
+        "text_level": 1,
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+        "img_path": "images/72b2c5e45a27fcc040f431ecf645f977fbfcb04d528f8e14818c146d900471b7.jpg",
+        "table_caption": [
+            "Table 3: Results of LSTR using downsampled long-term memory on THUMOS’14 in mAP $( \\% )$ . In particular, we use long-term memory of 512 seconds and short-term memory as 8 seconds. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Temporal Stride</td><td>1</td><td>2</td><td>4</td><td>8</td><td>16</td><td>32</td><td>64</td><td>128</td></tr><tr><td>LSTR</td><td>69.5</td><td>69.5</td><td>69.5</td><td>69.2</td><td>68.7</td><td>67.3</td><td>66.6</td><td>65.9</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We experiment for design choices of long- and short-term memories. Unless noted otherwise, we use THUMOS’14, which contains various video lengths, and Kinetics pretrained features. ",
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+    {
+        "type": "text",
+        "text": "Lengths of long- and short-term memories. We first analyze the effect of different lengths of long-term $m _ { L }$ and short-term $m _ { S }$ memory. In particular, we test $m _ { S } \\in \\{ 4 , 8 , 1 6 \\}$ seconds with $m _ { L }$ starting from 0 second (no long-term memory). Note that we choose the max length (1024 seconds for THUMOS’14 and 256 seconds for HACS Segment) to cover lengths of $9 8 \\%$ videos, and do not have proper datasets to test longer $m _ { L }$ . Fig. 3 shows that LSTR is beneficial from larger $m _ { L }$ in most cases. In addition, when $m _ { L }$ is short $\\leq 1 6$ in our cases), using larger $m _ { S }$ obtains better results and when $m _ { L }$ is sufficient $\\geq 3 2$ in our cases), increasing $m _ { S }$ does not always guarantee better performance. ",
+        "bbox": [
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+        "page_idx": 6
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+    {
+        "type": "image",
+        "img_path": "images/6947622b72aa083315ca466cc359b326181d39cbf4e88d85a16518cec5221923.jpg",
+        "image_caption": [
+            "Figure 3: Effect of using different lengths of long- and short-term memories. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Can we downsample long-term memory? We implement LSTR with $m _ { S }$ as 8 seconds and $m _ { L }$ as 512 seconds, and test the effect of downsampling long-term memory. Table 3 shows the results that downsampling with strides smaller than 4 does not cause performance drop, but more aggressive strides dramatically decrease the detection accuracy. Note that, when extracting frame features in 4 FPS, both LSTR encoder ${ \\mathrm { \\Delta } n } _ { 0 } = 1 6$ ) and downsampling with stride 128 compress the long-term memory to 16 features, but LSTR achieves much better performance $( 6 9 . 5 \\%$ vs. $6 \\bar { 5 } . 9 \\%$ in mAP). This demonstrates the effectiveness of our “adaptive compression” compared to heuristics downsampling. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Can we compensate reduced memory length with RNN? We note that LSTR’s performance notably decreases when it can only access very limited memory (e.g., $m _ { L } + m _ { S } \\leq 1 6$ seconds). Here we test if RNN can compensate LSTR’s reduced memory or even fully replace the LSTR encoder. We implement LSTR using $m _ { S } = 8$ seconds with an extra Gated Recurrent Unit (GRU) [10] (its architecture is visualized in the Supplementary Material) to capture all history outside the long- and short-term memories. The dashed line in Fig. 3 shows the results. Plugging-in RNNs indeed improves the performance when $m _ { L }$ is small, but when $m _ { L }$ is large $\\geq 6 4$ seconds), it does not improve the accuracy anymore. Note that RNNs are not used in any other experiments in this paper. ",
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+    {
+        "type": "text",
+        "text": "4.5 Design Choices of LSTR ",
+        "text_level": 1,
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+    {
+        "type": "table",
+        "img_path": "images/f24a9fd244fb3e8feed45fec048804357e33c63d83f487b66b7138a238a6d8fc.jpg",
+        "table_caption": [
+            "Table 4: Results of different designs of the LSTR encoder and decoder. The length of short-term memory is set to 8 seconds. “TR” denotes Transformer. The last row is our proposed LSTR design. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">LSTR Encoder</td><td rowspan=\"2\">LSTR Decoder</td><td colspan=\"8\">Length of Long-Term Memory mL (secs)</td></tr><tr><td>8</td><td>16</td><td>32</td><td>64</td><td>128</td><td>256</td><td>512</td><td>1024</td></tr><tr><td>N/A</td><td>TR Encoder</td><td>65.7</td><td>66.8</td><td>67.1</td><td>67.2</td><td>67.3</td><td>66.8</td><td>66.5</td><td>66.2</td></tr><tr><td>N/A</td><td>TR Decoder</td><td>66.5</td><td>67.3</td><td>67.7</td><td>68.1</td><td>68.3</td><td>67.9</td><td>67.0</td><td>66.5</td></tr><tr><td>TR Encoder</td><td>TR Decoder</td><td>65.9</td><td>66.4</td><td>66.7</td><td>67.4</td><td>67.5</td><td>67.2</td><td>67.0</td><td>66.6</td></tr><tr><td>Projection Layer</td><td>TR Decoder</td><td>66.2</td><td>67.1</td><td>67.4</td><td>67.7</td><td>67.5</td><td>67.2</td><td>66.9</td><td>66.8</td></tr><tr><td>TR Decoder</td><td>TR Decoder</td><td>66.1</td><td>67.1</td><td>67.4</td><td>68.0</td><td>68.5</td><td>68.6</td><td>68.7</td><td>68.7</td></tr><tr><td>TRDecoder+ TR Encoder</td><td>TR Decoder</td><td>66.2</td><td>67.3</td><td>67.6</td><td>68.4</td><td>68.6</td><td>68.8</td><td>68.9</td><td>69.0</td></tr><tr><td>TRDecoder +TRDecoder</td><td>N/A</td><td>64.0</td><td>64.7</td><td>65.9</td><td>66.1</td><td>66.5</td><td>66.2</td><td>65.4</td><td>65.2</td></tr><tr><td>TR Decoder + TR Decoder</td><td>TR Decoder</td><td>66.6</td><td>67.8</td><td>68.2</td><td>68.8</td><td>69.2</td><td>69.4</td><td>69.5</td><td>69.5</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "We continue to explore the design trade-offs of LSTR. Unless noted otherwise, we use short-term memory of 8 seconds, long-term memory of 512 seconds, and Kinetics pretrained features. ",
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+    {
+        "type": "text",
+        "text": "Number of layers and tokens. First, we assess using different numbers of token embeddings (i.e., $n _ { 0 }$ and $n _ { 1 }$ ) in LSTR encoder. Fig 4 (left) shows that LSTR is quite robust to different choices (the best and worst performance gap is only about $1 . 5 \\%$ ), but using $n _ { 0 } = 1 6$ and $n _ { 1 } = 3 2$ gets highest accuracy. Second, we experiment for the effect of using different numbers of Transformer decoder units (i.e., $\\ell _ { e n c }$ and $\\ell _ { d e c , }$ ). As shown in Fig 4 (right), LSTR does not need a large model to get the best performance, and in practice, using more layers can cause overfitting. ",
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+    {
+        "type": "image",
+        "img_path": "images/8676e342cbc8fb148ac0009b33f39bc819e575362c5f30bb5d427b505fa4fc2d.jpg",
+        "image_caption": [
+            "Figure 4: Left: Results of different number of token embeddings for our two-stage memory compression. Right: Results of different number of Transformer decoder units for $\\ell _ { e n c }$ and $\\ell _ { d e c }$ . "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Can we unify the temporal modeling using only self-attention models? We test if long-term ${ \\bf M } _ { L }$ and short-term $\\mathbf { M } _ { S }$ memory can be learned as a whole using self-attention models. Specifically, we concatenate ${ \\bf { M } } _ { L }$ and $\\mathbf { M } _ { S }$ and feed them into a standard Transformer Encoder [61] with a similar model size to LSTR. Table 4 (row 8 vs. row 1) shows that LSTR achieves better performance especially when $m _ { L }$ is large (e.g., $6 9 . 5 \\%$ vs. $6 6 . 5 \\%$ when $m _ { L } = 5 1 2$ and $6 6 . 6 \\%$ vs. ${ \\bar { 6 } } 5 . 7 \\%$ when $m _ { L } = 8$ ). This shows the advantage of LSTR for temporal modeling on long- and short-term context. ",
+        "bbox": [
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+        "page_idx": 7
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+    {
+        "type": "text",
+        "text": "Can we remove the LSTR encoder? We explore this by directly feeding ${ \\bf M } _ { L }$ into the LSTR decoder, and using $\\mathbf { M } _ { S }$ as tokens to reference useful information. Table 4 shows that LSTR outperforms this baseline (row 8 vs. row 2), especially when $m _ { L }$ is large. We also compare it with self-attention models (row 1) and observe that although neither of them can effectively model prolonged memory, this baseline outperforms the Transformer Encoder. This also demonstrates the effectiveness of our idea of using short-term memory to query related context from long-range context. ",
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Can the LSTR encoder learn effectively using self-attention? To evaluate the “bottleneck” design with cross-attention in LSTR encoder, we try modeling $\\mathbf { M } _ { L }$ using standard Transformer Encoder units [61]. Note that this still captures ${ \\bf M } _ { L }$ and $\\mathbf { M } _ { S }$ with the similar workflow of LSTR, but does not compress and encode ${ \\bf M } _ { L }$ using learnable tokens. Table 4 (row 8 vs. row 3) shows that LSTR outperforms this baseline with all $m _ { L }$ settings. In addition, the performance of this baseline decreases when $m _ { L }$ gets larger, which suggests the superior ability of LSTR for modeling long-range patterns. ",
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+    {
+        "type": "text",
+        "text": "How to design the memory compression for the LSTR encoder? First, we use a projection layer, consisting of a learnable matrix of size $n _ { 0 } \\times m _ { L }$ followed by MLP layers, to compress the long-term memory along the temporal dimension. Table 4 shows that using this simple projection layer (row 4) slightly outperforms the model without long-term memory (row 1), but is worse than attention-based compression methods. Second, we evaluate the one-stage design with $\\ell _ { e n c } + 1$ Transformer decoder units. Table 4 (row 8 vs. row 5) shows that two-stage compression is stably better than one-stage, and their performance gap gets larger when using larger $m _ { L }$ $0 . 5 \\%$ when $m _ { L } = 8$ and $0 . 8 \\%$ when $m _ { L } = 5 1 2$ ). Third, we compare cross-attention and self-attention for two-stage compression by replacing the second Transformer decoder with Transformer encoder. LSTR stably outperforms this baseline (row 6) by about $0 . 5 \\%$ in mAP. However, its performance is still better than models with one-stage compression of about $1 . 3 \\%$ (row 6 vs. row 3) and $0 . 3 \\%$ (row 6 vs. row 5) on average. ",
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Can we remove the LSTR decoder? We remove the LSTR decoder to evaluate its contribution. Specifically, we feed the entire memory to LSTR encoder and attach a multi-layer (MLP) classifier on its output tokens embeddings. Similar to the above experiments, we increase the model size to ensure a fair comparison. Table 4 shows that LSTR outperforms this baseline (row 7) by about $4 \\%$ on large $m _ { L }$ (e.g., 512 and 1024) and about $2 . 5 \\%$ on relative small $m _ { L }$ (e.g., 8 and 16). ",
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+    {
+        "type": "table",
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+        "table_caption": [
+            "Table 5: Results of LSTR using different memory integration methods in mAP $( \\% )$ . Our proposed integration method using cross-attention stably outperforms the heuristic methods. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Memory Integration Methods</td><td colspan=\"8\">Length of Long-Term Memory mL (secs)</td></tr><tr><td>8</td><td>16</td><td>32</td><td>64</td><td>128</td><td>256</td><td>512</td><td>1024</td></tr><tr><td>Average Pooling</td><td>66.1</td><td>67.0</td><td>67.3</td><td>67.5</td><td>68.2</td><td>68.4</td><td>68.6</td><td>68.6</td></tr><tr><td>Concatenation</td><td>65.9</td><td>67.2</td><td>67.5</td><td>67.7</td><td>68.4</td><td>68.5</td><td>68.7</td><td>68.6</td></tr><tr><td>Cross-Attention (ours)</td><td>66.6</td><td>67.8</td><td>68.2</td><td>68.8</td><td>69.2</td><td>69.4</td><td>69.5</td><td>69.5</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "Cross-attention vs. heuristics for integrating long- and short-term memories. We explore integrating the long- and short-term memories by using average pooling and concatenation. Specifically, the encoded long-term features of size $n _ { 1 } \\times C$ is converted to a vector of $C$ elements by channel-wise averaging, and the short-term memory of size $m _ { S } \\times C$ is encoded by $\\ell _ { d e c }$ Transformer encoder units. Then, each slot of the short-term features is either averaged or concatenated with the long-term feature vector for action classification. Note that these models still benefit from LSTR’s effectiveness for long-term modeling. Table 5 shows that using average pooling and concatenation obtain comparable results, but LSTR with cross-attention stably outperforms these baselines. ",
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+    {
+        "type": "text",
+        "text": "4.6 Runtime ",
+        "text_level": 1,
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+    },
+    {
+        "type": "table",
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+        "table_caption": [
+            "Table 6: Runtime of LSTR with different design choices. The last row is our proposed LSTR design. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">LSTR Encoder</td><td rowspan=\"2\">LSTR Decoder</td><td colspan=\"4\">Frames Per Second (FPS)</td></tr><tr><td>OptFlow Computation</td><td>RGB Feature Extraction</td><td>OptFlow Feature Extraction</td><td>LSTR</td></tr><tr><td>N/A</td><td>TR Encoder</td><td rowspan=\"3\">8.1</td><td rowspan=\"3\">70.5</td><td></td><td>43.2</td></tr><tr><td>TR Encoder</td><td>TR Decoder</td><td>14.6</td><td>50.2</td></tr><tr><td>TR Decoder</td><td>TR Decoder TR Decoder</td><td>91.6</td><td>59.5</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "We report LSTR’s runtime in frames per second (FPS) on a system with a single V100 GPU, and use the videos from THUMOS’14 dataset. The results are shown in Table 6. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We start by comparing the runtime between LSTR’s different design choices without considering the pre-processing (e.g., feature extraction). First, LSTR runs at 91.6 FPS using our two-stage memory compression (row 4), whereas using the one-stage design runs at a slower 59.5 FPS (row 3). Our two-stage design is more efficient because it does not need to reference information from the long-term memory multiple times, and can be further accelerated during online inference (see Sec. 3.6). Second, we test the LSTR encoder using self-attention mechanisms (row 2). This design does not compress the long-term memory, thus increasing the computational cost of both the LSTR encoder and decoder, leading to a slower speed of 50.2 FPS. Third, we test the standard Transformer Encoder [61] (row 1), whose runtime speed, 43.2 FPS, is about $2 \\times$ slower than LSTR. ",
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+    },
+    {
+        "type": "text",
+        "text": "We also compare LSTR with state-of-the-art recurrent models. As we are not aware of any prior work that reports their runtime, we test TRN [72] using their official open-source code [2]. The result shows that TRN runs at $1 2 3 . 3 \\ \\mathrm { F P S }$ , which is faster than LSTR. This is because recurrent models abstract the entire history as a compact representation but LSTR needs to process much more information. On the other hand, LSTR achieves much higher performance, outperforming TRN by about $7 . 5 \\%$ in mAP on THUMOS’14 and about $4 . 5 \\%$ in cAP on TVSeries. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "For end-to-end online inference, we follow the state-of-the-art methods [72, 19, 25] and build LSTR on two-stream features [62]. LSTR together with pre-processing techniques run at 4.6 FPS. Table 6 shows that the speed bottleneck is the motion feature extraction — it accounts for about $90 \\%$ of the total runtime including the optical flow computation with DenseFlow [63]. One can improve the efficiency largely by using real-time optical flow extractors (e.g., PWC-Net [55]) or using only visual features extracted by a light-weight backbone (e.g., MobileNet [29] and FBNet [67]). ",
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+    {
+        "type": "text",
+        "text": "4.7 Error Analysis ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/a9e35f43782c0dadecb67cb67b5142cc768436a294a7d7b1839cf6fcde1454c5.jpg",
+        "table_caption": [
+            "Table 7: Action classes with highest and lowest performance on THUMOS’14. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Action Classes HammerThrow PoleVault LongJump Diving BaseballPitch FrisbeeCatch Billirds CricketShot</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>AP (%)</td><td>92.8</td><td>89.7</td><td>86.9</td><td>86.7</td><td>55.4</td><td>49.4</td><td>39.8</td><td>38.6</td></tr></table>",
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+        "page_idx": 9
+    },
+    {
+        "type": "image",
+        "img_path": "images/20b24f9c97d71b7c32f233295d89092d598db050bcdd291259ed08c23dea57c4.jpg",
+        "image_caption": [
+            "Figure 5: Failure cases on THUMOS’14. Action classes from left to right are “BaseballPitch”, “FrisbeeCatch”, “Billiards”, and “CricketShot”. Red circle indicates where the action is happening. "
+        ],
+        "image_footnote": [],
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+    },
+    {
+        "type": "text",
+        "text": "In Table 7, we list the action classes from THUMOS’14 where LSTR gets the highest (color green) and the lowest (color red) per-frame APs. In Fig. 5, we illustrate four sample frames with incorrect predictions. More visualizations are included in the Supplementary Material. We observe that LSTR sees a decrease in detection accuracy when the action incurs only tiny motion or the subject is very far away from the camera, but excels at recognizing actions with long temporal span and multiple stages, such as “PoleVault” and “Long Jump”. This suggests we may explore extending the temporal modeling capability of LSTR to both spatial and temporal domains. ",
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "5 Conclusion ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "We present LSTR which captures both long- and short-term correlations in past observations of a time series by compressing long-term memory into encoded latent features and referencing related temporal context from them with short-term memory. This demonstrates the importance of separately modeling long- and short-term information and then integrating them for online inference tasks. Experiments on multiple datasets and ablation studies validate the effectiveness and efficiency of the LSTR design in dealing with prolonged video sequences. However, we note that LSTR is operating only on the temporal dimension. An end-to-end video understanding system requires simultaneous spatial and temporal modeling for optimal results. Therefore extending the idea of LSTR to spatio-temporal modeling remains an open yet challenging problem. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "6 Acknowledgments and Disclosure of Funding ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We thank the anonymous reviewers for their helpful suggestions. This work was funded by Amazon. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
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