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+# QUATERNION EQUIVARIANT CAPSULE NETWORKS FOR 3D POINT CLOUDS
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+We present a 3D capsule architecture for processing of point clouds that is equivariant with respect to the $S O ( 3 )$ rotation group, translation and permutation of the unordered input sets. The network operates on a sparse set of local reference frames, computed from an input point cloud and establishes end-to-end equivariance through a novel 3D quaternion group capsule layer, including an equivariant dynamic routing procedure. The capsule layer enables us to disentangle geometry from pose, paving the way for more informative descriptions and a structured latent space. In the process, we theoretically connect the process of dynamic routing between capsules to the well-known Weiszfeld algorithm, a scheme for solving iterative re-weighted least squares (IRLS) problems with provable convergence properties, enabling robust pose estimation between capsule layers. Due to the sparse equivariant quaternion capsules, our architecture allows joint object classification and orientation estimation, which we validate empirically on common benchmark datasets.
+
+# 1 INTRODUCTION
+
+It is now well understood that in order to learn a compact representation of the input data, one needs to respect the symmetries in the problem domain (Cohen et al., 2019; Weiler et al., 2018a). Arguably, one of the primary reasons of the success of 2D convolutional neural networks (CNN) is the translation-invariance of the 2D convolution acting on the image grid (Giles & Maxwell, 1987; Kondor et al., 2018). Recent trends aim to transfer this success into the 3D domain in order to support many applications such as shape retrieval, shape manipulation, pose estimation, 3D object modeling and detection. There, the data is naturally represented as sets of 3D points or a point cloud (Qi et al., 2017a;b). Unfortunately, extension of CNN architectures to 3D point clouds is non-trivial due to two reasons: 1) point clouds are irregular and unstructured, 2) the group of transformations that we are interested in is more complex as 3D data is often observed under arbitrary non-commutative $S O ( 3 )$ rotations. As a result, achieving appropriate embeddings requires 3D networks that work on points to be equivariant to these transformations, while also being invariant to the permutations of the point set.
+
+In order to fill this important gap, we propose the quaternion equivariant point capsule network or QE-Network that is suited to process point clouds and is equivariant to $S O ( 3 )$ rotations compactly parameterized by quaternions (Fig. 2), in addition to preserved translation and permutation equivariance. Inspired by the local group equivariance (Lenssen et al., 2018; Cohen et al., 2019), we efficiently cover $S \bar { O } ( 3 )$ by restricting ourselves to the sparse set of local reference frames (LRF) that collectively characterize the object orientation. The proposed capsule layers (Hinton et al., 2011) deduces equivariant latent representations by robustly combining those local LRFs using the proposed Weiszfeld dynamic routing. Hence, our latent features specify to local orientations disentangling the pose from object existence. Such explicit storage is unique to our work and allows us to perform rotation estimation jointly with object classification. Our final architecture is a hierarchy of QE-networks, where we use classification error as the only training cue and adapt a Siamese version when the relative rotation is to be regressed. We neither explicitly supervise the network with pose annotations nor train by augmenting rotations. Overall, our contributions are:
+
+1. We propose a novel, fully $S O ( 3 )$ -equivariant capsule architecture that is tailored for simultaneous classification and pose estimation of 3D point clouds. This network produces in
+
+![](images/b89e6e4028568e0d7b589204570db788708ec16213169b719e811cabba66f1ba.jpg)  
+Figure 1: Our network operates by processing local reference frames (LRF) on the object. Initial LRFs (b) are obtained by computing normal & tangent vectors on the point set in (a). (c) shows the LRFs randomly sampled from (a) and these are inputs to the first layer of our network. Subsequently, we obtain a multi-channel LRF that is a set of reference frames per pooling center (d). Holistically, our network aggregates the LRFs to arrive at rotation equivariant capsules.
+
+variant latent representations while explicitly decoupling the orientation into capsules, thus attaining equivariance. Note that equivariance results have not been previously achieved regarding the quaternion parameterization of the 3D special orthogonal group.   
+2. By utilizing LRFs on points, we reduce the space of orientations that we consider and hence can work sparsely on a subset of the group elements.   
+3. We theoretically prove the equivariance properties of our 3D network regarding the quaternion group. Moreover, to the best of our knowledge, we for the first time establish a connection between the dynamic routing of Sabour et al. (2017) and Generalized Weiszfeld iterations (Aftab et al., 2015). By that, we theoretically argue for the convergence of the employed dynamic routing.   
+4. We experimentally demonstrate the capabilities of our network on classification and orientation estimation of 3D shapes.
+
+# 2 PRELIMINARIES AND TECHNICAL BACKGROUND
+
+In this paper we will speak of the equivariance of point clouds under the actions of quaternions. We now provide the necessary background required for the grasp of this content.
+
+# 2.1 EQUIVARIANCE
+
+Definition 1 (Equivariant Map). For a $\mathcal { G }$ -space acting on $\mathcal { X }$ , the map $\Phi : \mathcal { G } \times \mathcal { X } \mapsto \mathcal { X }$ is said to be equivariant $i f$ its domain and co-domain are acted on by the same symmetry group (Cohen & Welling, 2016; Cohen et al., 2018a):
+
+$$
+\Phi ( \mathbf { g } _ { 1 } \circ \mathbf { x } ) = \mathbf { g } _ { 2 } \circ \Phi ( \mathbf { x } )
+$$
+
+where ${ \bf g } _ { 1 } ~ \in ~ \mathcal { G }$ and ${ \bf g } _ { 2 } ~ \in ~ \mathcal { G }$ . Equivalently $\Phi ( T ( \bf { g } _ { 1 } ) \bf { x } ) = \Psi { T } ( \bf { g } _ { 2 } ) \Phi ( \bf { x } )$ , where $T ( \cdot )$ is a linear representation of the group $\mathcal { G }$ . Note that $T ( \cdot )$ does not have to commute. It suffices for $T ( \cdot )$ to be a homomorphism: $T ( \mathbf { g } _ { 1 } \circ \mathbf { g } _ { 2 } ) = T ( \mathbf { g } _ { 1 } ) \circ T ( \mathbf { g } _ { 2 } )$ . In this paper we use a stricter form of equivariance and consider $\mathbf { g } _ { 2 } = \mathbf { g } _ { 1 }$ .
+
+Definition 2 (Equivariant Network). An architecture or network is said to be equivariant if all of its layers are equivariant maps. Due to the transitivity of the equivariance, stacking up equivariant layers will result in globally equivariant networks e.g., rotating the input will produce output vectors which are transformed by the same rotation (Lenssen et al., 2018; Kondor & Trivedi, 2018).
+
+# 2.2 THE QUATERNION GROUP $\mathbb { H } _ { 1 }$
+
+The choice of 4-vector quaternions has multiple motivations: 1. All 3-vector formulations suffer from infinitely many singularities as angle goes to 0, whereas quaternions avoid those. 2. 3-vectors also suffer from infinitely many redundancies (the norm can grow indefinitely). Quaternions have a single redundancy: $q = - q$ , a condition that is in practice easy to enforce. 3. Computing the actual ‘manifold mean’ on the Lie algebra requires iterative techniques with subsequent updates on the tangent space. Such iterations are computationally harmful for a differentiable GPU implementation.
+
+Definition 3 (Quaternion). $A$ quaternion q is an element of Hamilton algebra $\mathbb { H } _ { 1 }$ , extending the complex numbers with three imaginary units $i , j , k$ in the form: ${ \bf q } = q _ { 1 } { \bf { 1 } } + q _ { 2 } \pmb { i } + q _ { 3 } { \pmb { j } } + q _ { 4 } { \pmb { k } } =$
+
+# Algorithm 1: Quaternion Equivariant Dynamic Routing
+
+1 input : Input points $\{ { \bf x } _ { 1 } , . . . , { \bf x } _ { K } \} \in \mathbb { R } ^ { K \times 3 }$ , input capsules (LRFs) $\mathcal { Q } = \left\{ \mathbf { q } _ { 1 } , \dots , \mathbf { q } _ { L } \right\} \in \mathbb { H } _ { 1 } ^ { L }$ ,   
+with $L = N ^ { c } \cdot K$ , $N ^ { c }$ is the number of capsules per point, activations ${ \pmb { \alpha } } = ( \alpha _ { 1 } , \ldots , \alpha _ { L } ) ^ { T }$ ,   
+trainable transformations $\mathcal { T } = \{ \mathbf { t } _ { i , j } \} _ { i , j } \in \mathbb { H } _ { 1 } ^ { L \times M }$   
+2 output: Updated frames $\hat { \mathcal { Q } } = \{ \hat { \mathbf { q } } _ { 1 } , \hdots , \hat { \mathbf { q } } _ { M } \} \in \mathbb { H } _ { 1 } ^ { M }$ , updated activations $\hat { \pmb { \alpha } } = ( \hat { \alpha } _ { 1 } , \dots , \hat { \alpha } _ { M } ) ^ { T }$   
+3 for All primary (input) capsules $i$ do   
+4 for All latent (output) capsules $j$ do   
+5 $\mathbf { v } _ { i , j }  \mathbf { q } _ { i } \circ \mathbf { t } _ { i , j }$ // compute votes   
+6 for All latent (output) capsules $j$ do   
+7 $\hat { \mathbf { q } } _ { j }  A \big ( \{ \mathbf { v } _ { 1 , j } \dots \mathbf { v } _ { K , j } \} , \alpha \big ) \quad / \mathrm { ~ }$ initialize output capsules   
+8 for $k$ iterations do   
+9 for All primary (input) capsules $i$ do   
+10 $w _ { i , j }  \alpha _ { i }$ · sigmoid $\big ( - \delta ( \hat { \mathbf { q } } _ { j } , \mathbf { v } _ { i , j } ) \big )$ // compute the current weight   
+11 L $\hat { \mathbf { q } } _ { j }  A \big ( \{ \mathbf { v } _ { 1 , j } \ : . . . \mathbf { v } _ { L , j } \} , \mathbf { w } _ { : , j } \big ) \mathrm { ~ , ~ }$ / see Eq (4)   
+12 $\hat { \alpha } _ { j } \gets \mathrm { s i g m o i d } \big ( - \frac { 1 } { K } \sum _ { 1 } ^ { L } \delta ( \hat { \mathbf { q } } _ { j } , \mathbf { v } _ { i , j } ) \big ) / /$ recompute activations
+
+$\left( q _ { 1 } , q _ { 2 } , q _ { 3 } , q _ { 4 } \right) ^ { T }$ , with $\left( q _ { 1 } , q _ { 2 } , q _ { 3 } , q _ { 4 } \right) ^ { T } \in \mathbb { R } ^ { 4 }$ and $\pmb { i } ^ { 2 } = \pmb { j } ^ { 2 } = \pmb { k } ^ { 2 } = i \pmb { j } \pmb { k } = - \pmb { I }$ . $q _ { 1 } \in \mathbb { R }$ denotes the scalar part and $\pmb { \nu } = \left( q _ { 2 } , q _ { 3 } , q _ { 4 } \right) ^ { T } \in \mathbb { R } ^ { 3 }$ , the vector part. The conjugate $\bar { \bf q }$ of the quaternion q is given by $\bar { \mathbf { q } } : = q _ { 1 } - q _ { 2 } \dot { \pmb { i } } - q _ { 3 } \pmb { j } - q _ { 4 } \pmb { k }$ . A unit quaternion $\mathbf { q } \in \mathbb { H } _ { 1 }$ with $1 \stackrel { \prime } { = } \| \mathbf { q } \| : = \mathbf { q } \cdot \bar { \mathbf { q } }$ and $\mathbf { q } ^ { - 1 } = \bar { \mathbf { q } } ,$ gives a compact and numerically stable parametrization to represent orientation of objects on the unit sphere $S ^ { 3 }$ , avoiding gimbal lock and singularities (Busam et al., 2017). Identifying antipodal points $\mathbf { q }$ and $- \mathbf { q }$ with the same element, the unit quaternions form a double covering group of $S O \left( 3 \right)$ . $\mathbb { H } _ { 1 }$ is closed under the non-commutative multiplication or the Hamilton product:
+
+$$
+( \mathbf { p } \in \mathbb { H } _ { 1 } ) \circ ( \pmb { r } \in \mathbb { H } _ { 1 } ) = [ p _ { 1 } r _ { 1 } - \mathbf { v } _ { p } \cdot \mathbf { v } _ { r } ; p _ { 1 } \mathbf { v } _ { r } + r _ { 1 } \mathbf { v } _ { p } + \mathbf { v } _ { p } \times \mathbf { v } _ { r } ] .
+$$
+
+Definition 4 (Linear Representation of $\mathbb { H } _ { 1 }$ ). We follow Birdal et al. (2018) and use the
+
+$$
+\begin{array} { r } { \mathbf { T } ( \mathbf { q } ) \triangleq \left[ \begin{array} { r r r r } { q _ { 1 } } & { - q _ { 2 } } & { - q _ { 3 } } & { - q _ { 4 } } \\ { q _ { 2 } } & { q _ { 1 } } & { - q _ { 4 } } & { q _ { 3 } } \\ { q _ { 3 } } & { q _ { 4 } } & { q _ { 1 } } & { - q _ { 2 } } \\ { q _ { 4 } } & { - q _ { 3 } } & { q _ { 2 } } & { q _ { 1 } } \end{array} \right] . } \end{array}
+$$
+
+To be concise we will use capital letters to refer to the matrix representation of quaternions $e . g . \mathbf { Q } \equiv$ $T ( \mathbf { q } )$ , $\mathbf { G } \equiv T ( \mathbf { g } )$ . Note that $T ( \cdot )$ , the injective homomorphism to the orthonormal matrix ring, by construction satisfies the condition in Dfn. 1 (Steenrod, 1951): $\operatorname* { d e t } ( \mathbf { Q } ) = 1 , \mathbf { Q } ^ { \intercal } = \mathbf { Q } ^ { - 1 } , \| \tilde { \mathbf { Q } } \| \overset { \cdot } { = }$ $\lVert \mathbf { Q } _ { i , : } \rVert = \lVert \mathbf { Q } _ { : , i } \rVert \stackrel { - } { = } 1$ and $\mathbf { Q } - q _ { 1 } \mathbf { I }$ is skew symmetric: $\mathbf { Q } + \mathbf { Q } ^ { \top } = 2 q _ { 1 } \mathbf { I } .$ . It is easy to verify these properties. $T$ linearizes the Hamilton product or the group composition: $\mathbf { g } \circ \mathbf { q } \triangleq T ( \mathbf { g } ) \mathbf { q } \triangleq \mathbf { G q }$ .
+
+# 2.3 3D POINT CLOUDS
+
+Definition 5 (Point Cloud). We define a $3 D$ surface to be a differentiable 2-manifold embedded in the ambient $3 D$ Euclidean space: $\mathcal { M } ^ { 2 } \in \mathbb { R } ^ { 3 }$ and a point cloud to be a discrete subset sampled on $\mathcal { M } ^ { 2 }$ : $\mathbf { X } \in \{ \mathbf { x } _ { i } \in \mathcal { M } ^ { 2 } \cap \mathbb { R } ^ { 3 } \}$ .
+
+Definition 6 (Local Geometry). For a smooth point cloud $\{ \mathbf { x } _ { i } \} \in \mathcal { M } ^ { 2 } \subset \mathbb { R } ^ { N \times 3 }$ , $a$ local reference frame (LRF) is defined as an ordered basis of the tangent space at x, $\mathcal { T } _ { \mathbf { x } } \mathcal { M }$ , consisting of orthonormal vectors: $\mathcal { L } ( \mathbf { x } ) = [ \partial _ { 1 } , \partial _ { 2 } , \partial _ { 3 } \equiv \partial _ { 1 } \times \partial _ { 2 } ]$ ]. Usually the first component is defined to be the surface normal $\pmb { \partial } _ { 1 } \triangleq \mathbf { n } \in \mathcal { S } ^ { 2 } : \| \mathbf { n } \| = 1$ and the second one is picked according to a modality dependent heuristic.
+
+Note that recent trends such as (Cohen et al., 2019) acknowledge the ambiguity and either employ a gauge (tangent frame) equivariant design or propagate the determination of a certain direction until the last layer (Poulenard & Ovsjanikov, 2018). Here, we will assume that $\partial _ { 2 }$ can be uniquely and repeatably computed, a reasonable assumption for the point sets we consider (Petrelli & Di Stefano, 2011). For the cases where this does not hold, we will rely on the network’s robustness. We will explain our method of choice in Sec. 4 and visualize LRFs of an airplane object in Fig. 1.
+
+![](images/d2d1f0c3fa686d3b7e437e6a2d3e75627b94d94bfcc44d94a9ea0ba1f0891666.jpg)  
+Figure 2: Our quaternion equivariant (QE) network for processing local patches: Our input is a 3D point set $\mathbf { X }$ on which we query local neighborhoods $\{ \mathbf { x } _ { i } \}$ with precomputed LRFs $\left\{ \mathbf { q } _ { i } \right\}$ . Essentially, we learn the parameters of a fully connected network that continuously maps the canonicalized local point set to transformations $\mathbf { t } _ { i }$ , which are used to compute hypotheses (votes) from input poses. By a special dynamic routing procedure that uses the activations determined in a previous layer, we arrive at latent capsules that are composed of a set of orientations $\hat { \mathbf { q } } _ { i }$ and new activations $\hat { \pmb { \alpha } } _ { i }$ . Thanks to the decoupling of local reference frames, $\hat { \pmb { \alpha } } _ { i }$ is invariant and orientations $\hat { \mathbf { q } } _ { i }$ are equivariant to input rotations. All the operations and hence the entire QE-network are equivariant achieving a guaranteed disentanglement of the rotation parameters. Hat symbol (qˆ) refers to ’estimated’.
+
+# 3 $S O ( 3 )$ -EQUIVARIANT 3D CAPSULE NETWORKS
+
+Disentangling orientation from representations requires guaranteed equivariances and invariances. Yet, the original capsule networks of Sabour et al. (2017) cannot achieve equivariance to general groups. To this end, Lenssen et al. (2018) proposed to use a manifold-mean and a special aggregation that makes sure that the trainable transformations get pose-aligned points as input. We will extend this idea to the non-abelian $S O ( 3 )$ and design capsule networks sparsely operating on a set of LRFs computed on local neighborhoods of points, parameterized by quaternions. In the following, we first explain our novel capusle layers, the main building block of our architecture. We then show how to stack those layers via a simple aggregation resulting in an $S O ( 3 )$ -equivariant 3D capsule network that yields invariant representations (or activations) as well as equivariant rotations (latent capsules).
+
+# 3.1 QUATERNION EQUIVARIANT CAPSULE LAYERS
+
+To construct equivariant layers on the group of rotations, we are required to define a left-equivariant averaging operator $\mathcal { A }$ that is invariant under permutations of the group elements, as well as a distance metric $\delta$ that remains unchanged under the action of the group. For these, we make the following choices:
+
+Definition 7 (Geodesic Distance). The Riemannian (geodesic) distance in the manifold of rotations lead to the following geodesic distance $\delta ( \cdot ) \equiv d _ { q u a t } ( \cdot )$ :
+
+$$
+d ( { \bf q } _ { 1 } , { \bf q } _ { 2 } ) \equiv d _ { q u a t } ( { \bf q } _ { 1 } , { \bf q } _ { 2 } ) = 2 \cos ^ { - 1 } ( | \langle { \bf q } _ { 1 } , { \bf q } _ { 2 } \rangle | )
+$$
+
+Definition 8 (Quaternion Mean $\pmb { \mu } ( \cdot ) .$ ). For a set of $Q$ rotations ${ \bf S } = \{ { \bf q } _ { i } \}$ and associated weights $\textbf { w } = \{ w _ { i } \}$ , the weighted mean operator $\mathcal { A } ( \mathbf { S } , \mathbf { w } ) : \mathbb { H } _ { 1 } { } ^ { n } \times \mathbb { R } ^ { n } \mapsto \mathbb { H } _ { 1 } { } ^ { n }$ is defined through the following maximization procedure (Markley et al., 2007):
+
+$$
+\bar { \mathbf { q } } = \underset { \mathbf { q } \in \mathbb { S } ^ { 3 } } { \arg \operatorname* { m a x } } \mathbf { q } ^ { \top } \mathbf { M } \mathbf { q }
+$$
+
+where $ { \mathbf { M } } \in \mathbb { R } ^ { 4 \times 4 }$ is defined as: $\mathbf { M } \triangleq \sum _ { i = 1 } ^ { Q } w _ { i } \mathbf { q } _ { i } \mathbf { q } _ { i } ^ { \intercal }$ . The average quaternion is the eigenvector of M corresponding to the maximum eigenvalue. This operation lends itself to both analytic (Magnus, 1985) and automatic differentiation (Laue et al., 2018).
+
+Theorem 1. Quaternions, the employed mean $\mathbf { \nabla } _ { \mathbf { \mathcal { A } } ( \mathbf { S } , \mathbf { w } ) }$ and geodesic distance $\delta ( \cdot )$ enjoy the following properties:
+
+![](images/df28604b52dac726104b4b42cf496aa21f248230f1da47e6f8ca03184a76b7a5.jpg)  
+Figure 3: Our entire capsule architecture. We hierarchically send all the local patches to our Qnetwork as shown in Fig. 2. At each level the points are pooled in order to increase the receptive field, gradually reducing the LRFs into a single capsule per class. We use classification and pose estimation (in the siamese case) as supervision cues to train the point-to-transform maps.
+
+1. $\mathcal { A } ( \mathbf { g } \circ \mathbf { S } , \mathbf { w } )$ is left-equivariant: $\mathcal { A } ( \mathbf { g } \circ \mathbf { S } , \mathbf { w } ) = \mathbf { g } \circ \mathcal { A } ( \mathbf { S } , \mathbf { w } )$ .   
+2. Operator $\mathcal { A }$ is invariant under permutations: $\begin{array} { r l } { \mathcal { A } ( \{ \mathbf { q } _ { \sigma ( 1 ) } , \dots , \mathbf { q } _ { \sigma ( Q ) } \} , \mathbf { w } _ { \sigma } ) } & { { } = } \end{array}$ $\mathcal { A } ( \{ \mathbf { q } _ { 1 } , \hdots , \mathbf { q } _ { Q } \} , \mathbf { w } )$ .   
+3. The transformations $\mathbf { g } \in \mathbb { H } _ { 1 }$ preserve the geodesic distance $\delta ( \cdot )$ given in Dfn. 7.
+
+Proof. The proofs are given in the supplementary material.
+
+We also note that the above mean is closed form, differentiable and can be implemented batchwise. We are now ready to construct the group dynamic routing (DR) by agreement that is equivariant thanks to Thm. 1. The core idea is to route from or assign the primary capsules that constitute the input LRF set, to the latent capsules by an iterative clustering which respects the group structure. At each step, we assign the weighted group mean to each output capsule. The weights $w  \sigma ( \mathbf x , \mathbf y )$ are inversely propotional to the distance between the vote quaternion and the new quaternion (cluster center). See Alg. 1 for details. In the following, we analyze our variant of routing as an interesting case of the affine, Riemannian Weiszfeld algorithm (Aftab et al., 2015; 2014).
+
+Lemma 1. For $\sigma ( { \bf x } , { \bf y } ) = \delta ( { \bf x } , { \bf y } ) ^ { q - 2 }$ the equivariant routing procedure given in Alg. 1 is a variant of the affine subspace Wieszfeld algorithm (Aftab et al., 2015; 2014) that is a robust algorithm for computing the $L _ { q }$ geometric median.
+
+Proof Sketch. The proof follows from the definition of Weiszfeld iteration (Aftab et al., 2014) and the mean and distance operators defined in Sec. 3.1. We first show that computing the weighted mean is equivalent to solving the normal equations in the iteratively reweighted least squares (IRLS) scheme (Burrus, 2012). Then, the inner-most loop correspond to the IRLS or Weiszfeld iterations. We provide the detailed proof in supplementary material.
+
+Note that, in practice one is quite free to choose the weighting function $\sigma ( \cdot )$ as long as it is inversely proportional to the geodesic distance and concave (Aftab & Hartley, 2015). We leave the analyses of the variants of these algorithms as a future work. The original dynamic routing can also be formulated as a clustering procedure with a KL divergence regularization. This holistic view paves the way to better routing algorithms (Wang & Liu, 2018). Our perspective is akin yet more geometric due to the group structure of the parameter space. Thanks to the connection to Weiszfeld algorithm, the convergence behavior of our dynamic routing can be directly analyzed within the theoretical framework presented by Aftab et al. (2014; 2015).
+
+Theorem 2. Under mild assumptions provided in the appendix, the sequence of the DR-iterates generated by the inner-most loop almost surely converges to a critical point.
+
+Proof Sketch. Proof, given in the appendix, is a direct consequence of Lemma 1 and directly exploits the connection to the Weiszfeld algorithm. □
+
+# 3.2 EQUIVARIANT 3D POINT CAPSULE NETWORK ARCHITECTURE
+
+The essential ingredient of our architecture, QE-Network, is shown in Fig. 2. We also provide a corresponding pseudocode in Alg. 3 of suppl. material. The input of the QE-Network are a local patch of points with coordinates $\mathbf { x } _ { i } \subset \mathbb { R } ^ { K \times 3 }$ , rotations parametrized as quaternions $\mathbf { q } _ { i } \subset \mathbb { H } _ { 1 } { } ^ { K \times N ^ { c } }$ and activations $\pmb { \alpha } _ { i } \subset \mathbb { R } ^ { K \times N ^ { c } }$ . $\mathbf { q } _ { i }$ also represents input primary capsules and local reference frames. $N ^ { c }$ is the number of input capsule channels per point and it is equal to the number of output capsules $( M )$ from the last layer. In the initial layer, $\mathbf { q } _ { i }$ represents the pre-computed LRFs and $N ^ { c }$ is equal to 1. Given points $\mathbf { x } _ { i }$ and rotations $\mathbf { q } _ { i }$ , we compute the quaternion average $\mu _ { i }$ in channel-wise as the initial pose candidates: $\mu _ { i } \subset \mathbb { H } _ { 1 } ^ { N ^ { c } }$ . These candidates are used to bring the receptive field in multiple canonical orientations by rotating the points: $\mathbf { x } _ { i } ^ { \prime } = ( { \mu _ { i } } ^ { - 1 } \circ \mathbf { x } _ { i } ) \subset \mathbb { R } ^ { K \times N ^ { c } \times 3 }$ . Since the points in the local receptive field lie in continuous $\mathbb { R } ^ { 3 }$ , training a discrete set of pose transformations $\mathbf { t } _ { i , j }$ based on local coordinates is not possible. Instead, we employ a point-to-transform network $\begin{array} { r } { t ( \cdot ) : \bar { \mathbb { R } } ^ { N ^ { c } \times 3 }  } \end{array}$ $\mathbb { R } ^ { M \times N ^ { c } \times 4 }$ that maps the point in multiple canonical orientations to transformations. The network is shared over all points to compute the transformations $\mathbf { t } _ { i , j } = ( t ( \mathbf { x } _ { 1 } ^ { \prime } ) , . . . , t ( \mathbf { x } _ { K } ^ { \prime } ) ) _ { i , j } \subset \mathbb { R } ^ { K \times M \times N ^ { c } \times 4 } ,$ , which are used to calculate the votes for dynamic routing as $\mathbf { v } _ { i , j } = \mathbf { q } _ { i } \circ \mathbf { t } _ { i , j }$ . The network $t ( \cdot )$ consists of fully-connected layers that regresses the transformations, similar to common operators for continuous convolutions (Schutt et al., 2017; Wang et al., 2018; Fey et al., 2018). It is the ¨ continuous alternative to directly optimizing transformations lying in a grid kernel, as it is done in the original dynamic routing by Sabour et al. (2017). Note that $t ( \cdot )$ predicts quaternions by unitnormalizing the regressed output: $\mathbf { t } _ { i , j } \subset \mathbb { H } _ { 1 } ^ { K \times M \times N ^ { c } }$ . Although Riemannian layers of Becigneul & ´ Ganea (2018) or spherical predictions of Liao et al. (2019) can improve the performance, the simple strategy works reasonably for our case. After computing the votes, we utilize the input activation $\alpha _ { i }$ to iteratively refine the output capsules (weighted average of votes) $\hat { \mathbf { q } _ { i } }$ and activations $\hat { \pmb { \alpha } } _ { i }$ by routing by agreement as shown in Alg. 1.
+
+Table 1: Classification accuracy on ModelNet40 dataset (Wu et al., 2015) for different methods as well as ours. We also report the number of parameters optimized for each method. X/Y means that we train with X and test with Y.   
+
+<table><tr><td></td><td>PN</td><td>PN++</td><td>KD-treeNet Point2Seq Sph.CNNs 1</td><td></td><td></td><td>PRIN</td><td>PPF</td><td>Ours (Var.)</td><td>Ours</td></tr><tr><td>NR/NR</td><td></td><td>88.45 89.82</td><td>86.20</td><td>92.60</td><td>-</td><td>80.13</td><td>70.16</td><td>85.27</td><td>74.43</td></tr><tr><td>NR/AR</td><td>12.47</td><td>21.35</td><td>8.49</td><td>10.53</td><td>43.92</td><td>68.85</td><td>70.16</td><td>11.75</td><td>74.07</td></tr><tr><td># Params</td><td>3.5M</td><td>1.5M</td><td>3.6M</td><td>1.8M</td><td>0.5M</td><td>1.5M</td><td>3.5M</td><td>0.4M</td><td>0.4M</td></tr></table>
+
+In order to gradually increase the receptive field, we stack QE-networks creating a deep hierarchy, pooling the points and the LRFs before each layer. Note that we are allowed to do so thanks to the properties of equivariance. In particular, we input $N \ : = \ : 6 4$ patches to our architecture that is composed of two QE-networks. We call the centers of these patches pooling centers. In the first layer, each of those centers is linked to their immediate vicinity leading to $K = 9$ -star local connectivity from which we compute the $6 4 \times 6 4 \times 4$ intermediary capsules. The input LRFs of the first layer are sampled from pre-calculated LRF-set and the input activation is set to 1. The LRFs in the second layer $l = 2$ are the output capsules of the first layer, $l = 1$ and are routed to the output capsules that are as many as the number of classes $C$ , $M _ { 2 } = C$ . The activation of the second layer is updated by the output of the first layer as well. This construction is shown in Fig. 3. Specifically, for $l = 1$ , we use $K \bar { = } 9 , N _ { l } { } ^ { c } = 1 , \dot { M _ { l } } = 6 4$ and for $l = 2$ , $K = 6 4 , N _ { l } { } ^ { c } = 6 4 , \bar { M _ { l } } = C \bar { = } 4 0$ . This way, in this last layer all the pooling centers act as a single patch $K = 6 4$ ). A single QE-network acts on this patch to create the final $C \times 4$ capsules and $C$ activations. More details are reported in Alg. 3 of the appendix.
+
+# 4 EXPERIMENTAL EVALUATIONS
+
+Implementation Details We implement our network in PyTorch and use the ADAM optimizer (Kingma & Ba, 2014) with a learning rate of 0.001. The point-transformation mapping network is implemented by two FC-layers composed of 64 hidden units. We set the initial activation of the input LRF to 1.0. In each layer, we use 3 iterations of DR. For classification we use the spread loss (Sabour et al., 2018) and the rotation loss is identical to $\delta ( \cdot )$ .
+
+Surface normals are computed by local plane fits (Hoppe et al., 1992). We compute the second axis of the LRF, $\partial _ { 2 }$ , by FLARE (Petrelli $\&$ Di Stefano, 2012), that uses the normalized projection of the point within the periphery of the support showing the largest distance, onto the tangent plane of the center: $\begin{array} { r } { \partial _ { 2 } = \frac { \mathbf { \tilde { p } } _ { \mathrm { m a x } } - \mathbf { \tilde { p } } } { \Vert \mathbf { p } _ { \mathrm { m a x } } - \mathbf { p } \Vert } } \end{array}$ . Note that using other LRFs such as SHOT (Tombari et al., 2010) or the more modern GFrames of Melzi et al. (2019) is possible. We found FLARE to be sufficient for our experiments. Prior to all operations, we flip all the LRF quaternions such that they lie on the northern hemisphere : $\{ \mathbf { q } _ { i } \in \mathbb { S } ^ { \hat { 3 } } : q _ { i } ^ { w } > 0 \}$ .
+
+Table 2: Error of rotation estimation in different categories of ModelNet10. Right side of the table denotes the objects with rotational symmetry, which we include for completeness. PCA-S refers to running PCA only on a resampled instance, while PCA-SR applies both rotations and resampling.   
+
+<table><tr><td>Method</td><td>Avg.</td><td>No_Sym</td><td> Chair Bed Sofa Toilet Monitor|Table Desk Dresser</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>NS</td><td>Bathtub</td></tr><tr><td>Mean LRF</td><td>0.41</td><td>0.35</td><td>0.32</td><td>0.36</td><td>0.34</td><td>0.41</td><td>0.34</td><td>0.45</td><td>0.60</td><td>0.50</td><td>0.46</td><td>0.32</td></tr><tr><td>PCA-S</td><td>0.40</td><td>0.42</td><td>0.60</td><td>0.53</td><td>0.46</td><td>0.32</td><td>0.12</td><td>0.47</td><td>0.23</td><td>0.33</td><td>0.43</td><td>0.55</td></tr><tr><td>PCA-SR</td><td>0.67</td><td>0.67</td><td>0.69</td><td>0.70</td><td>0.67</td><td>0.68</td><td>0.61</td><td>0.67</td><td>0.67</td><td>0.67</td><td>0.66</td><td>0.70</td></tr><tr><td>PointNetLK</td><td>0.37</td><td>0.38</td><td>0.43</td><td>0.31</td><td>0.40</td><td>0.40</td><td>0.31</td><td>0.40</td><td>0.33</td><td>0.39</td><td>0.38</td><td>0.34</td></tr><tr><td>IT-net</td><td>0.27</td><td>0.19</td><td>0.10</td><td>0.22</td><td>0.17</td><td>0.20</td><td>0.28</td><td>0.31</td><td>0.41</td><td>0.44</td><td>0.40</td><td>0.39</td></tr><tr><td>Ours</td><td>0.27</td><td>0.17</td><td>0.11</td><td>0.20</td><td>0.16</td><td>0.18</td><td>0.19</td><td>0.43</td><td>0.40</td><td>0.48</td><td>0.33</td><td>0.31</td></tr><tr><td>Ours (siamese)</td><td>0.20</td><td>0.09</td><td>0.08</td><td>0.10</td><td>0.08</td><td>0.11</td><td>0.08</td><td>0.40</td><td>0.35</td><td>0.34</td><td>0.32</td><td>0.30</td></tr></table>
+
+3D Shape Classification. We use ModelNet40 dataset of (Wu et al., 2015; Qi et al., 2017b) to assess our classification performance. Each shape is composed by $1 0 K$ points. We assign the LRFs to a subset of the uniformly sampled points, $N = 5 1 2$ (Birdal & Ilic, 2017). We train the networks without any rotation augmentation (NR) and put them to test under arbitrary $S O ( 3 )$ rotations (AR). Our results are shown in Tab. 1 along with that of PointNet (PN) (Qi et al., 2017a), PointNet++ $\mathrm { ( P N + + ) }$ (Qi et al., 2017a), KD-treeNet (Li et al., 2018a), Point2Seq (Liu et al., 2019b), Spherical CNNs (Esteves et al., 2018), PRIN (You et al., 2018) and PPF-FoldNet (PPF) (Deng et al., 2018a). We also present a version of our algorithm (Var) that avoids the canonicalization within the QEnetwork. This is a non-equivariant network that we still train without data augmentation. While this version gets comparable results to the state of the art for the NR/NR case, it cannot handle random $S O ( 3 )$ variations (AR). Note that PPF uses the point-pair-feature (Birdal & Ilic, 2015) encoding and hence creates invariant input representations. For the scenario of NR/AR, our equivariant version outperforms all the other methods, including equivariant spherical CNNs (Esteves et al., 2018) by a significant gap of at least $5 \%$ even when (Esteves et al., 2018) uses the mesh. The object rotational symmetries in this dataset are responsible for a significant portion of the errors we make. It is worth mentioning that we also trained TFNs (Thomas et al., 2018) for that task, but their memory demand made it infeasible to scale to this application.
+
+Number of Parameters. Use of LRFs helps us to restrict the rotation group to certain elements and thus we can use networks with significantly less parameters (as low as $0 . 4 4 M$ ) compared to others as shown in Tab. 1. Number of parameters in our network depends upon the number of classes, e.g. for ModelNet10 we have $0 . 0 4 7 M$ parameters.
+
+Rotation estimation in 3D point clouds. Our network can estimate both the canonical and relative object rotations without pose-supervision. To evaluate this desired property, we used the well classified shapes on ModelNet10 dataset, a sub-dataset of Modelnet40 (Wu et al., 2015). We generate multiple instances per shape by transforming the instance with five arbitrary $S O ( 3 )$ rotations. As we are also affected by the sampling of the point cloud, we resample the mesh five times and generate different pooling graphs across all the instances of the same shape. Our QE-architecture can estimate the pose in two ways: 1) by directly using the output capsule with the highest activation, 2) by a siamese architecture that computes the relative quaternion between the capsules that are maximally activated as shown in Fig. 4. Both modes of operation are free of the data augmentation and we give further schematics of the latter in our appendix Fig. 5. Our results against the baselines including a naive averaging of the LRFs (Mean LRF) and principal axis alignment (PCA) are reported in Tab. 2 as the relative angular error (RAE). We further include results of PointNetLK Aoki et al. (2019) and IT-Net (Yuan et al., 2018), two state of the art 3D networks that iteratively aligns two point sets. These methods are in nature similar to iterative closest point (ICP) algorithm (Besl & McKay, 1992) but 1) do not require an initialization (first iteration estimates the pose), 2) learn data driven updates. Methods that use mesh inputs such as Spherical CNNs (Esteves et al., 2018) cannot be included here as the random sampling of the same surface would not affect those. We also avoid methods that are just invariant to rotations (and hence cannot estimate the pose) such as Tensorfield Networks (Thomas et al., 2018). Finally, note that , IT-net (Yuan et al., 2018) and PointLK need to train a lot of epoches (e.g. 500) with random $S O ( 3 )$ rotation augmentation in order to get the models that cover the full $S O ( 3 )$ , whereas we train only for $\sim 1 0 0$ epochs. We include more details about the baselines in the appendix under Fig. 8.
+
+![](images/340104a5fbcae573bea645d4e647284c5ebb81b1073ec39db251d3476631e304.jpg)  
+Figure 4: Shape alignment on the monitor (left) and toilet (right) objects via our siamese equivariant capsule architecture. The shapes are assigned to the the maximally activated class. The corresponding pose capsule provides the rotation estimate.
+
+RAE between the ground truth and the prediction is computed as the relative angle in degrees: $d ( \mathbf { q } _ { 1 } , \mathbf { q } _ { 2 } ) / \pi$ . Note that resampling and random rotations render the job of all methods difficult. However, both our version that tries to find a canonical alignment and the siamese variant which seeks a relative rotation are better than the baselines. As pose estimation of objects with rotational symmetry is a challenging task we also report results on the non-symmetric subset (No Sym).
+
+Table 3: Ablation study on point density.   
+
+<table><tr><td rowspan=1 colspan=1>LRF Input|</td><td rowspan=1 colspan=1>LRF-10K</td><td rowspan=1 colspan=2>[LRF-2K|LRF-1K</td></tr><tr><td rowspan=1 colspan=1>Dropout</td><td rowspan=1 colspan=1>150%66%75%100%</td><td rowspan=1 colspan=1>100%</td><td rowspan=1 colspan=1>100%</td></tr><tr><td rowspan=1 colspan=1>Class.ErrAngle.Err</td><td rowspan=1 colspan=1>77.883.383.487.80.340.270.250.09</td><td rowspan=1 colspan=1>85.460.10</td><td rowspan=1 colspan=1>79.740.12</td></tr></table>
+
+Robustness against point and LRF resampling. Density changes in the local neighborhoods of the shape are an important cause of error for our network. Hence, we ablate by applying random resamplings (patch-wise dropout) to the objects in ModelNet10 dataset and repeating the pose estimation and classification as described above. The first part (LRF-10K) of Tab. 3 shows our findings against gradual increases of the number of patches. Here, we sample 2K LRFs from the 10K LRFs computed on an input point 10K. $100 \%$ dropout corresponds to 2K points in all columns. On second ablation, we reduce the amount of points on which we compute the LRFs, to 2K and 1K respectively. As we can see from the table, our network is robust towards the changes in the LRFs as well as the density of the points.
+
+# 5 RELATED WORK
+
+Deep learning on point sets. The capability to process raw, unordered point clouds within a neural network is introduced by the prosperous PointNet (Qi et al., 2017a) thanks to the point-wise convolutions and the permutation invariant pooling functions. Many works have extended PointNet primarily to increase the local receptive field size (Qi et al., 2017b; Li et al., 2018b; Shen et al., 2018; Wang et al., 2019). Point-clouds are generally thought of as sets. This makes any permutationinvariant network that can operate on sets an amenable choice for processing points (Zaheer et al., 2017; Rezatofighi et al., 2017). Unfortunately, common neural network operators in this category are solely equivariant to permutations and translations but to no other groups.
+
+Equivariance in Neural Networks. The early attempts to achieve invariant data representations usually involved data augmentation techniques to accomplish tolerance to input transformations (Maturana & Scherer, 2015; Qi et al., 2016; 2017a). Motivated by the difficulty associated with augmentation efforts and acknowledging the importance of theoretically equivariant or invariant representations, the recent years have witnessed a leap in theory and practice of equivariant neural networks (Bao & Song, 2019; Kondor & Trivedi, 2018).
+
+While laying out the fundamentals of the group convolution, G-CNNs (Cohen & Welling, 2016) guaranteed equivariance with respect to finite symmetry groups. Similarly, Steerable CNNs (Cohen & Welling, 2017) and its extension to 3D voxels (Worrall & Brostow, 2018) considered discrete symmetries only. Other works opted for designing filters as a linear combination of harmonic basis functions, leading to frequency domain filters (Worrall et al., 2017; Weiler et al., 2018b). Apart from suffering from the dense coverage of the group using group convolution, filters living in the frequency space are less interpretable and less expressive than their spatial counterparts, as the basis does not span the full space of spatial filters.
+
+Achieving equivariance in 3D is possible by simply generalizing the ideas of the 2D domain to 3D by voxelizing 3D data. However, methods using dense grids (Chakraborty et al., 2018; Cohen & Welling, 2017) suffer from increased storage costs, eventually rendering the implementations infeasible. An extensive line of work generalizes the harmonic basis filters to $S O ( 3 )$ by using e.g., a spherical harmonic basis instead of circular harmonics (Cohen et al., 2018b; Esteves et al., 2018; Cruz-Mota et al., 2012). In addition to the same downsides as their 2D, these approaches have in common that they require their input to be projected to the unit sphere (Jiang et al., 2019), which poses additional problems for unstructured point clouds. A related line of research are methods which define a regular structure on the sphere to propose equivariant convolution operators (Liu et al., $2 0 1 9 \mathrm { a }$ ; Boomsma & Frellsen, 2017)
+
+To learn a rotation equivariant representation of a 3D shape, one can either act on the input data or on the network. In the former case, one either presents augmented data to the network (Qi et al., 2017a; Maturana & Scherer, 2015) or ensures rotation-invariance in the input (Deng et al., 2018a;b; Khoury et al., 2017). In the latter case one can enforce equivariance in the bottleneck so as to achieve an invariant latent representation of the input (Mehr et al., 2018; Thomas et al., 2018; Spezialetti et al., 2019). Further, equivariant networks for discrete sets of views (Esteves et al., 2019b) and crossdomain views (Esteves et al., 2019a) have been proposed. Here, we aim for a different way of embedding equivariance in the network by means of an explicit latent rotation parametrization in addition to the invariant feature.
+
+Marcos et al. (2017) developed Vector Field Networks, which was followed by the 3D Tensor Field Networks (TFN) (Thomas et al., 2018) that are closest to our work. Based upon a geometric algebra framework, the authors did achieve localized filters that are equivariant to rotations, translations and permutations. Moreover, they are able to cover the continuous groups. However, TFN are designed for physics applications, is memory consuming and a typical implementation is neither likely to handle the datasets we consider nor can provide orientations in an explicit manner.
+
+Capsule Networks. The idea of capsule networks was first mentioned by Hinton et al. (2011), before Sabour et al. (2017) proposed the dynamic routing by agreement, which started the recent line of work investigating the topic. Since then, routing by agreement has been connected to several well-known concepts, e.g. the EM algorithm Sabour et al. (2018), clustering with KL divergence regularization Wang & Liu (2018) and equivariance (Lenssen et al., 2018). They have been extended to autoencoders (Kosiorek et al., 2019) and GANs Jaiswal et al. (2019). Further, capsule networks have been applied for specific kinds of input data, e.g. graphs (Xinyi & Chen, 2019), 3D point clouds (Zhao et al., 2019) or medical images (Afshar et al., 2018).
+
+# 6 CONCLUSION AND DISCUSSION
+
+In this work, we have presented a new framework for achieving permutation invariant and $S O ( 3 )$ equivariant representations on 3D point clouds. Proposing a variant of the capsule networks, we operate on a sparse set of rotations specified by the input LRFs thereby circumventing the effort to cover the entire $S O ( 3 )$ . Our network natively consumes a compact representation of the group of 3D rotations - quaternions, and we have theoretically shown its equivariance. We have also established convergence results for our Weiszfeld dynamic routing by making connections to the literature of robust optimization. Our network is among the few for having an explicit group-valued latent space and thus naturally estimates the orientation of the input shape, even without a supervision signal.
+
+Limitations. In the current form our performance is severely affected by the shape symmetries. The length of the activation vector depends on the number of classes and for achieving sufficiently descriptive latent vectors we need to have a significant number of classes. On the other side, this allows us to perform with merit on problems where the number of classes are large. Although, we have reported robustness to those, the computation of LRFs are still sensitive to the point density changes and resampling. LRFs themselves are also ambiguous and sometimes non-unique.
+
+Future work. Inspired by Cohen et al. (2019) and Poulenard & Ovsjanikov (2018) our feature work will involve establishing invariance to the direction in the tangent plane. We also plan to apply our network in the broader context of 3D object detection under arbitrary rotations and look for equivariances among point resampling.
+
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+
+# A PROOF OF PROPOSITION 1
+
+Before presenting the proof we recall the three individual statements contained in Prop. 1:
+
+1. $\mathcal { A } ( \mathbf { g } \circ \mathbf { S } , \mathbf { w } )$ is left-equivariant: $\mathcal { A } ( \mathbf { g } \circ \mathbf { S } , \mathbf { w } ) = \mathbf { g } \circ \mathcal { A } ( \mathbf { S } , \mathbf { w } )$ .   
+2. Operator $\mathcal { A }$ is invariant under permutations: $\begin{array} { r l } { \mathcal { A } \big ( \{ \mathbf { q } _ { \sigma ( 1 ) } , \dots , \mathbf { q } _ { \sigma ( Q ) } \} , \mathbf { w } _ { \sigma } \big ) } & { { } = } \end{array}$ $\mathcal { A } ( \{ \mathbf { q } _ { 1 } , \hdots , \mathbf { q } _ { Q } \} , \mathbf { w } )$ .   
+3. The transformations $\mathbf { g } \in \mathbb { H } _ { 1 }$ preserve the geodesic distance $\delta ( \cdot )$ .
+
+Proof. We will prove the propositions in order.
+
+1. We start by transforming each element and replace $\mathbf { q } _ { i }$ by $\left( \mathbf { g } \circ \mathbf { q } _ { i } \right)$ of the cost in Eq (4):
+
+$$
+\begin{array} { r l } { \mathbf { q } ^ { \top } \mathbf { M } \mathbf { q } = \mathbf { q } ^ { \top } \Big ( \underset { \left( - 1 \right) } { \overset { \triangledown } { \sum } } w _ { 1 } \mathbf { q } , \mathbf { q } _ { 1 } ^ { \top } \Big ) \mathbf { q } } & { } \\ & { = \mathbf { q } ^ { \top } \left( \underset { \left( - 1 \right) } { \overset { \triangledown } { \sum } } w _ { 1 } ( \mathbf { g } \mathbf { \cdot } \mathbf { q } _ { 1 } ) ( \mathbf { g } \mathbf { \cdot } \mathbf { q } _ { 1 } ) ^ { \top } \right) \mathbf { q } } \\ & { = \mathbf { q } ^ { \top } \left( \underset { \left( - 1 \right) } { \overset { \triangledown } { \sum } } w _ { 1 } \mathbf { G } \mathbf { q } , \mathbf { q } _ { 1 } ^ { \top } \mathbf { G } ^ { - } \right) \mathbf { q } } \\ & { = \mathbf { q } ^ { \top } \left( \underset { \left( - 1 \right) } { \overset { \triangledown } { \sum } } w _ { 1 } \mathbf { G } \mathbf { q } , \mathbf { q } ^ { \top } \mathbf { G } ^ { - } \right) \mathbf { q } } \\ & { = \mathbf { q } ^ { \top } \left( \mathbf { G } \mathbf { M } _ { 1 } \mathbf { G } ^ { \top } + \dots + \mathbf { G } \mathbf { M } _ { 0 } \mathbf { G } ^ { \top } \right) \mathbf { q } } \\ & { = \mathbf { q } ^ { \top } \mathbf { G } \mathbf { \cdot } \left( \mathbf { M } _ { 1 } \mathbf { G } ^ { \top } + \dots + \mathbf { M } _ { 0 } \mathbf { G } ^ { \top } \right) \mathbf { q } } \\ & { = \mathbf { q } ^ { \top } \mathbf { G } \left( \mathbf { M } _ { 1 } \mathbf { + } \dots + \mathbf { M } _ { 0 } \right) \mathbf { G } ^ { \top } \mathbf { q } } \\ & { = \mathbf { q } ^ { \top } \mathbf { G } \mathbf { M } \mathbf { G } ^ { \top } \mathbf { q } } \\ & { = \mathbf { q } ^ { \top } \mathbf { G } \mathbf { q } \mathbf { G } ^ { \top } \mathbf { q } } \\ & { = \mathbf { p } ^ { \top } \mathbf { M } \mathbf { p } , } \end{array}
+$$
+
+where $\mathbf { M } _ { i } \ = \ w _ { i } \mathbf { q } _ { i } \mathbf { q } _ { i } ^ { \top }$ and $\mathbf { p _ { \lambda } } = \mathbf { G } ^ { \top } \mathbf { q }$ . From orthogonallity of $\mathbf { G }$ it follows $\mathrm { ~ \bf ~ p ~ } =$ $\mathbf { G } ^ { - 1 } \mathbf { q } \implies \mathbf { g } \circ \mathbf { p } = \dot { \mathbf { q } }$ and hence $\mathbf { g } \circ \mathcal { A } ( \mathbf { S } , \mathbf { w } ) = \mathcal { A } ( \mathbf { g } \circ \mathbf { S } , \mathbf { w } )$ .
+
+2. The proof follows trivially from the permutation invariance of the symmetric summation operator over the outer products in Eq (8).
+
+3. It is sufficient to show that $| \mathbf { q } _ { 1 } ^ { \top } \mathbf { q } _ { 2 } | = | ( \mathbf { g } \circ \mathbf { q } _ { 1 } ) ^ { \top } ( \mathbf { g } \circ \mathbf { q } _ { 2 } ) |$ for any $\mathbf { g } \in \mathbb { H } _ { 1 }$ :
+
+$$
+\begin{array} { r l } { \left| \left( \mathbf { g } \circ \mathbf { q } _ { 1 } \right) ^ { \top } ( \mathbf { g } \circ \mathbf { q } _ { 2 } ) \right| = | \mathbf { q } _ { 1 } ^ { \top } \mathbf { G } ^ { \top } \mathbf { G } \mathbf { q } _ { 2 } | } & { } \\ & { = | \mathbf { q } _ { 1 } ^ { \top } \mathbf { I } \mathbf { q } _ { 2 } | } \\ & { = | \mathbf { q } _ { 1 } ^ { \top } \mathbf { q } _ { 2 } | , } \end{array}
+$$
+
+where $\mathbf { g } \circ \mathbf { q } \equiv \mathbf { G q }$ . The result is a direct consequence of the orthonormality of $\mathbf { G }$ .
+
+# B PROOF OF LEMMA 1
+
+We will begin by recalling some preliminary definitions and results that aid us to construct the connection between the dynamic routing and the Weiszfeld algorithm.
+
+Definition 9 (Affine Subspace). A $d$ -dimensional affine subspace of $R ^ { N }$ is obtained by a translation of a $d$ -dimensional linear subspace $V \subset \mathbb { R } ^ { N }$ such that the origin is included in $S$ :
+
+$$
+S = \Big \{ \sum _ { i = 1 } ^ { d + 1 } \alpha _ { i } \mathbf { x } _ { i } \vert \sum _ { i = 1 } ^ { d + 1 } \alpha _ { i } = 1 \Big \} .
+$$
+
+Simplest choices for $S$ involve points, lines and planes of the Euclidean space.
+
+Definition 10 (Orthogonal Projection onto an Affine Subspace). An orthogonal projection of a point $\mathbf { x } \in \mathbb { R } ^ { N }$ onto an affine subspace explained by the pair $( \mathbf { A } , \mathbf { c } )$ is defined as:
+
+$$
+\Pi _ { i } ( { \bf x } ) \triangleq { p r o j _ { S } ( { \bf x } ) } = { \bf c } + { \bf A } ( { \bf x } - { \bf c } ) .
+$$
+
+c denotes the translation to make origin inclusive and A is a projection matrix typically defined via the orthonormal bases of the subspace.
+
+Definition 11 (Distance to Affine Subspaces). Distance from a given point x to a set of affine subspaces $\{ S _ { 1 } , S _ { 2 } \ldots S _ { k } \}$ can be written as Aftab et al. (2015):
+
+$$
+C ( \mathbf { x } ) = \sum _ { i = 1 } ^ { k } d ( \mathbf { x } , S _ { i } ) = \sum _ { i = 1 } ^ { k } \| \mathbf { x } - p r o j _ { S _ { i } } ( \mathbf { x } ) \| ^ { 2 } .
+$$
+
+Lemma 2. Given that all the antipodal counterparts are mapped to the northern hemisphere, we will now think of the unit quaternion or versor as the unit normal of a four dimensional hyperplane $h$ , passing through the origin:
+
+$$
+h _ { i } ( \mathbf { x } ) = \mathbf { q } _ { i } ^ { \top } \mathbf { x } + q _ { d } : = 0 .
+$$
+
+$q _ { d }$ is an added term to compensate for the shift. When $q _ { d } = 0$ the origin is incident to the hyperplane. With this perspective, quaternion $\mathbf { q } _ { i }$ forms an affine subspace with $d = 4$ , for which the projection operator takes the form:
+
+$$
+p r o j _ { S _ { i } } ( \mathbf { p } ) = ( \mathbf { I } - \mathbf { q } _ { i } \mathbf { q } _ { i } ^ { \top } ) \mathbf { p }
+$$
+
+Proof. We consider Eq (19) for the case where $\mathbf c = \mathbf 0$ and $\mathbf { A } = ( \mathbf { I } - \mathbf { q q } ^ { \top } )$ . The former follows from the fact that our subspaces by construction pass through the origin. Thus, we only need to show that the matrix $\mathbf { A } = \mathbf { I } { - } \mathbf { q } \mathbf { \dot { q } } ^ { \top }$ is an orthogonal projection matrix onto the affine subspace spanned by q. To this end, it is sufficient to validate that $\mathbf { A }$ is symmetric and idempotent: $\mathbf { A } ^ { \top } \dot { \mathbf { A } } = \dot { \mathbf { A } } \mathbf { A } = \mathbf { A } ^ { \top } = \mathbf { A }$ . Note that by construction $\mathbf { q } ^ { \intercal } \mathbf { q }$ is a symmetric matrix and hence A itself. Using this property and the unit-ness of the quaternion, we arrive at the proof:
+
+$$
+\begin{array} { r l } & { \mathbf { A } ^ { \top } \mathbf { A } = ( \mathbf { I } - \mathbf { q } \mathbf { q } ^ { \top } ) ^ { \top } ( \mathbf { I } - \mathbf { q } \mathbf { q } ^ { \top } ) } \\ & { \qquad = ( \mathbf { I } - \mathbf { q } \mathbf { q } ^ { \top } ) ( \mathbf { I } - \mathbf { q } \mathbf { q } ^ { \top } ) } \\ & { \qquad = \mathbf { I } - 2 \mathbf { q } \mathbf { q } ^ { \top } + \mathbf { q } \mathbf { q } ^ { \top } \mathbf { q } \mathbf { q } ^ { \top } } \\ & { \qquad = \mathbf { I } - 2 \mathbf { q } \mathbf { q } ^ { \top } + \mathbf { q } \mathbf { q } ^ { \top } } \\ & { \qquad = \mathbf { I } - \mathbf { q } \mathbf { q } ^ { \top } \triangleq \mathbf { A } } \end{array}
+$$
+
+It is easy to verify that the projections are orthogonal to the quaternion that defines the subspace by showing $\mathrm { p r o j } _ { S } ( \mathbf { q } ) ^ { \top } \mathbf { q } = 0$ :
+
+$$
+\mathbf { q } ^ { \top } \operatorname { p r o j } _ { S } ( \mathbf { q } ) = \mathbf { q } ^ { \top } \mathbf { A } \mathbf { q } = \mathbf { q } ^ { \top } ( \mathbf { I } - \mathbf { q } \mathbf { q } ^ { \top } ) \mathbf { q } = \mathbf { q } ^ { \top } ( \mathbf { q } - \mathbf { q } \mathbf { q } ^ { \top } \mathbf { q } ) = \mathbf { q } ^ { \top } ( \mathbf { q } - \mathbf { q } ) = 0 .
+$$
+
+Also note that this choice corresponds to $\begin{array} { r } { \operatorname { t r } ( \mathbf q \mathbf q ^ { \top } ) = \sum _ { i = 1 } ^ { d + 1 } \alpha _ { i } = 1 . } \end{array}$
+
+Lemma 3. The quaternion mean we suggest to use in the main paper Markley et al. (2007) is equivalent to the Euclidean Weiszfeld mean on the affine quaternion subspaces.
+
+Proof. We now recall and summarize the $L _ { q }$ -Weiszfeld Algorithm on affine subspaces Aftab et al. (2015), which minimizes a $q$ -norm variant of the cost defined in Eq (17):
+
+$$
+C _ { q } ( \mathbf { x } ) = \sum _ { i = 1 } ^ { k } d ( \mathbf { x } , S _ { i } ) = \sum _ { i = 1 } ^ { k } \| \mathbf { x } - \mathrm { p r o j } _ { S _ { i } } ( \mathbf { x } ) \| ^ { q } .
+$$
+
+Defining $\mathbf { M } _ { i } = \mathbf { I } - \mathbf { A } _ { i }$ , Alg. 2 summarizes the iterative procedure.
+
+Note that when $q = 2$ , the algorithm reduces to the computation of a non-weighted mean $\mathbf { \nabla } _ { w _ { i } } =$ $1 \forall i )$ , and a closed form solution exists for Eq (29) and is given by the normal equations:
+
+$$
+\mathbf { x } = { \Big ( } \sum _ { i = 1 } ^ { k } w _ { i } \mathbf { M } _ { i } { \Big ) } ^ { - 1 } { \Big ( } \sum _ { i = 1 } ^ { k } w _ { i } \mathbf { M } _ { i } \mathbf { c } _ { i } { \Big ) }
+$$
+
+# Algorithm 2: $L _ { q }$ Weiszfeld Algorithm on Affine Subspaces Aftab et al. (2015).
+
+1 input: An initial guess $\mathbf { x } _ { \mathrm { 0 } }$ that does not lie any of the subspaces $\{ S _ { i } \}$ , Projection operators $\Pi _ { i }$ , the norm parameter $q$   
+2 $\mathbf { x } ^ { t }  \mathbf { x } _ { 0 }$   
+3 while not converged do   
+4 Compute the weights $\mathbf { w } ^ { t } = \{ w _ { i } ^ { t } \}$ : $w _ { i } ^ { t } = \| \mathbf { M } _ { i } ( \mathbf { x } ^ { t } - \mathbf { c } _ { i } ) \| ^ { q - 2 } \quad \forall i = 1 \ldots k$ (28)   
+5 Solve: $\mathbf { x } ^ { t + 1 } = \underset { \mathbf { x } \in \mathbb { R } ^ { N } } { \arg \operatorname* { m i n } } \sum _ { i = 1 } ^ { k } w _ { i } ^ { t } \| \mathbf { M } _ { i } ( \mathbf { x } - \mathbf { c } _ { i } ) \| ^ { 2 }$ (29)
+
+For the case of our quaternionic subspaces $\mathbf c = \mathbf 0$ and we seek the solution that satisfies:
+
+$$
+\biggl ( \sum _ { i = 1 } ^ { k } \mathbf { M } _ { i } \biggr ) \mathbf { x } = \Bigl ( \frac { 1 } { k } \sum _ { i = 1 } ^ { k } \mathbf { M } _ { i } \Bigr ) \mathbf { x } = \mathbf { 0 } .
+$$
+
+It is well known that the solution to this equation under the constraint $\| \mathbf { x } \| = 1$ lies in nullspace of $\mathbf { M } = \textstyle { \frac { 1 } { k } } \sum _ { i = 1 } ^ { k } \mathbf { M } _ { i }$ and can be obtained by taking the singular vector of $\mathbf { M }$ that corresponds to the largest singular value. Since $\mathbf { M } _ { i }$ is idempotent, the same result can also be obtained through the eigendecomposition:
+
+$$
+\mathbf { q } ^ { \star } = \underset { \mathbf { q } \in \cal S ^ { 3 } } { \arg \operatorname* { m a x } } \mathbf { q M } \mathbf { q }
+$$
+
+which gives us the unweighted Quaternion mean Markley et al. (2007).
+
+# C PROOF OF THEOREM 1
+
+Once the Lemma 1 is proven, we only need to apply the direct convergence results from the literature. Consider a set of points $\mathbf { Y } = \{ \mathbf { y } _ { 1 } \ldots \mathbf { \bar { y } } _ { K } \}$ where $K > 2$ and $\mathbf { y } _ { i } \in \mathbb { H } _ { 1 }$ . Due to the compactness, we can speak of a ball $B ( \mathbf { o } , \rho )$ encapsulating all $\mathbf { y } _ { i }$ . We also define the $\mathcal { D } = \{ \mathbf { x } \in \mathbb { H } _ { 1 } | C _ { q } ( \mathbf { x } ) < C _ { q } ( \mathbf { o } ) \}$ , the region where the loss decreases.
+
+We first state the assumptions that permit our theoretical result. These assumptions are required by the works that establish the convergence of such Weiszfeld algorithms Luenberger et al. (1984); Aftab & Hartley (2015); Aftab et al. (2014) :
+
+H1. $\mathbf { y } _ { 1 } \ldots \mathbf { y } _ { K }$ should not lie on a single geodesic of the quaternion manifold.   
+H2. $\mathcal { D }$ is bounded and compact. The topological structure of $S O ( 3 )$ imposes a bounded convexity radius of $\rho < \pi / 2$ .   
+H3. The minimizer in $\operatorname { E q }$ (29) is continuous.   
+H4. The weighting function $\sigma ( \cdot )$ is concave and differentiable.   
+H5. Initial quaternion (in our network chosen randomly) does not belong to any of the subspaces.
+
+Note that H5 is not a strict requirement as there are multiple ways to circumvent (simplest being a re-initialization). Under these assumptions, the sequence produced by Eq (29) will converge to a critical point unless $\mathbf { x } ^ { t } = \mathbf { y } _ { i }$ for any $t$ and $i$ Aftab et al. (2014). For $q = 1$ , this critical point is on one of the subspaces specified in Eq (18) and thus is a geometric median. □
+
+Note that due to the assumption $\mathbf { H } 2$ , we cannot converge from any given point. For randomly initialized networks this is indeed a problem and does not guarantee practical convergence. Yet, in our experiments we have not observed any issue with the convergence of our dynamic routing. As our result is one of the few ones related to the analysis of DR, we still find this to be an important first step.
+
+For different choices of $q : 1 \leq q \leq 2$ , the weights take different forms. In fact, this IRLS type of algorithm is shown to converge for a larger class of weighting choices as long as the aforementioned conditions are met. That is why in practice we use a simple sigmoid function.
+
+# D OUR SIAMESE ARCHITECTURE AND THE ALGORITHM
+
+For estimation of the relative pose with supervision, we benefit from a Siamese variation of our network. In this case, latent capsule representations of two point sets $\mathbf { X }$ and $\mathbf { Y }$ jointly contribute to the pose regression as shown in Fig. 5.
+
+![](images/32613bc5ee20bb121f5e818c93fea4b1c068606f5cf5797227071bcba74beb27.jpg)  
+Figure 5: Our siamese architecture used in the estimation of relative poses. We use a shared network to process two distinct point clouds $( \mathbf { X } , \mathbf { Y } )$ to arrive at the latent representations $( \mathbf { C } _ { X } , \pmb { \alpha } _ { X } )$ and $\left( \mathbf { C } _ { Y } , \pmb { \alpha } _ { Y } \right)$ respectively. We then look for the highest activated capsules in both point sets and compute the rotation from the corresponding capsules. Thanks to the rotations disentangled into capsules, this final step simplifies to a relative quaternion calculation.
+
+We show additional results from the computation of local reference frames and the multi-channel capsules deduced from our network in Fig. 6.
+
+Finally, the overall algorithm of our network is summarized under Alg. 3.
+
+# Algorithm 3: Quaternion Equivariant Network
+
+1 input : Input points of one patch $\left\{ { \bf x } _ { 1 } , . . . , { \bf x } _ { K } \right\} \in \mathbb { R } ^ { K \times 3 }$ , input capsules (LRFs)   
+$\mathcal { Q } = \{ \mathbf { q } _ { 1 } , \dots , \mathbf { q } _ { L } \} \in \mathbb { H } _ { 1 } ^ { L }$ , with $L = N ^ { c } \cdot K$ , $N ^ { c }$ is the number of capsules per point,   
+activations ${ \pmb { \alpha } } = ( \alpha _ { 1 } , \ldots , \alpha _ { L } ) ^ { T }$   
+2 output: Updated frames $\hat { \mathcal { Q } } = \{ \hat { \mathbf { q } } _ { 1 } , \hdots , \hat { \mathbf { q } } _ { M } \} \in \mathbb { H } _ { 1 } ^ { M }$ , updated activations $\hat { \pmb { \alpha } } = ( \hat { \alpha } _ { 1 } , \dots , \hat { \alpha } _ { M } ) ^ { T }$   
+3 for Each input channel $n ^ { c }$ of all the primary capsules channels $N ^ { c }$ do   
+4 $\mu ( n ^ { c } ) \dot {  } A ( \mathcal { Q } ( n ^ { c } ) ) ~ / /$ Input quaternion average, see Eq (4)   
+5 for Each point $\mathbf { x } _ { i }$ of this patch do   
+6 $\lfloor \mathbf { x } _ { i } ^ { \prime } \gets \mu ( n ^ { c } ) ^ { - 1 } \circ \mathbf { x } _ { i } \ / /$ rotate point in a canonical orientation   
+7 $\left\{ \mathbf { x } _ { i } ^ { \prime } \right\} \in \mathbb { R } ^ { K \times N ^ { c } \times 3 } / /$ Points in multiple $( N ^ { c } )$ ) canonical frames   
+8 for Each point $\mathbf { x } _ { i } ^ { \prime }$ of this patch do   
+9 $\lfloor \ \mathbf { t } \gets t ( \mathbf { x } _ { i } ^ { \prime } ) \ / /$ Point to Transform, $t ( \cdot ) : \mathbb { R } ^ { N ^ { c } \times 3 }  \mathbb { R } ^ { N ^ { c } \times M \times 4 }$   
+10 $\mathcal { T } \equiv \{ \mathbf { t } _ { i } \} \in \mathbb { H } _ { 1 } ^ { K \times N _ { i } ^ { c } \times M }  \{ \mathbf { t } \} \in \mathbb { H } _ { 1 } ^ { L \times M }$   
+11 (Qˆ, αˆ) ← DynamicRouting(X, Q, α, T ) // see Alg. 1
+
+Alg. 3 summarizes the overall pipeline of our QE-net depicted in Fig. 3. We use multiple layers in a hierarchical architecture. In the first layer, the input primary capsules are represented by LRFs computed with FLARE algorithm Petrelli & Di Stefano (2012). Therefore, the number of input capsule channels $N ^ { c }$ in the first layer is equal to 1. Its activation is also defaulted to 1. The output of a former layer is propagated to the input of the latter, creating the hierarchy.
+
+![](images/d18441bae463b393e66d066047592194e51c259196fc6d99f80f376a6951b3f1.jpg)  
+Figure 6: Additional intermediate results on car (first row) and chair (second row) objects. This figure supplements Fig. 1 of the main paper.
+
+![](images/f3256f777f329920bda71d310cecfad9e94d40452c169893ecd2b898351960b0.jpg)  
+Figure 7: Confusion matrix on ModelNet10 for classification.
+
+# E ADDITIONAL DETAILS ON EVALUATIONS
+
+Details on the evaluation protocol. For Modelnet40 dataset used in Tab. 1, we used the official split with 9,843 shapes for training and 2,468 different shapes for testing. For rotation estimation in Tab. 2, we used the official Modelenet10 dataset split with 3991 for training and 908 shapes for testing. 3D point clouds (10K points) are randomly sampled from the mesh surfaces of each shape Qi et al. (2017a;b). The objects in training and testing dataset are different, but they are from the same categories so that they can be oriented meaningfully. During training, we did not augment the dataset with random rotations. All the shapes are trained with single orientation (well-aligned). We call this trained with NR. During testing, we randomly generate multiple arbitrary $S O ( 3 )$ rotations for each shape and evaluate the average performance for all the rotations. This is called test with $A R$ . This protocol is used in both our algorithms and the baselines.
+
+Confusion of classification in ModelNet. We now report the confusion matrix in the task of classification on the all the objects of ModelNet10. The classification and rotation estimation affects one another. As we can see from Fig. 7, the first five categories that exhibit less rotational symmetry has the higher classification accuracy than their rotationally symmetric counterparts.
+
+Distribution of errors reported in Tab. 2. We now provide more details on the errors attained by our algorithm as well as the state of the art. To this end, we report, in Fig. 8 the histogram of errors that fall within quantized ranges of orientation errors. It is noticeable that our Siamese architecture behaves best in terms of estimating the objects rotation. For completeness, we also included the results of the variants presented in our ablation studies: Ours-2kLRF, Ours-1kLRF. They evaluate the model on the re-calculated LRFs in order to show the robustness towards to various point densities. We have also modified IT-Net and PointNetLK only to predict rotation because the original works predict both rotations and translations. Finally, note here that we do not use data augmentation for training our networks (see AR), while both for PointNetLK and for IT-Net we do use augmentation.
+
+![](images/668420048419c858c37830ef87f4a1fdcf6e8d038fc2d0d2a7894a6fa713831a.jpg)
+
+Figure 8: Cumulative error histograms of rotation estimation on ModelNet10. Each row $( < \theta ^ { \circ } )$ of this extended table shows the percentage of shapes that have rotation error less than $\theta$ . The colors of the bars correspond to the rows they reside in. The higher the errors are contained in the first bins (light blue) the better. Vice versa, the more the errors are clustered toward the $6 0 ^ { \circ }$ the worse the performance of the method.

parse/train/BJIgi_eCZ/BJIgi_eCZ.md

@@ -0,0 +1,691 @@
+# FUSIONNET: FUSING VIA FULLY-AWARE ATTENTION WITH APPLICATION TO MACHINE COMPREHENSION
+
+Hsin-Yuan Huang\*1,2, Chenguang $\mathbf { Z } \mathbf { h } \mathbf { u } ^ { \mathbf { 1 } }$ , Yelong Shen1, Weizhu Chen1
+
+1Microsoft Business AI and Research   
+2National Taiwan University   
+momohuang@gmail.com, {chezhu,yeshen,wzchen}@microsoft.com
+
+# ABSTRACT
+
+This paper introduces a new neural structure called FusionNet, which extends existing attention approaches from three perspectives. First, it puts forward a novel concept of “history of word” to characterize attention information from the lowest word-level embedding up to the highest semantic-level representation. Second, it identifies an attention scoring function that better utilizes the “history of word” concept. Third, it proposes a fully-aware multi-level attention mechanism to capture the complete information in one text (such as a question) and exploit it in its counterpart (such as context or passage) layer by layer. We apply FusionNet to the Stanford Question Answering Dataset (SQuAD) and it achieves the first position for both single and ensemble model on the official SQuAD leaderboard at the time of writing (Oct. 4th, 2017). Meanwhile, we verify the generalization of FusionNet with two adversarial SQuAD datasets and it sets up the new state-of-the-art on both datasets: on AddSent, FusionNet increases the best F1 metric from $4 6 . 6 \%$ to $5 1 . 4 \%$ ; on AddOneSent, FusionNet boosts the best F1 metric from $5 6 . 0 \%$ to $6 0 . 7 \%$ .
+
+# 1 INTRODUCTION
+
+Teaching machines to read, process and comprehend text and then answer questions is one of key problems in artificial intelligence. Figure 1 gives an example of the machine reading comprehension task. It feeds a machine with a piece of context and a question and teaches it to find a correct answer to the question. This requires the machine to possess high capabilities in comprehension, inference and reasoning. This is considered a challenging task in artificial intelligence and has already attracted numerous research efforts from the neural network and natural language processing communities. Many neural network models have been proposed for this challenge and they generally frame this problem as a machine reading comprehension (MRC) task (Hochreiter & Schmidhuber, 1997; Wang et al., 2017; Seo et al., 2017; Shen et al., 2017; Xiong et al., 2017; Weissenborn et al., 2017; Chen et al., 2017a).
+
+Context: The Alpine Rhine is part of the Rhine, a famous European river. The Alpine Rhine begins in the most western part of the Swiss canton of Graubünden, and later forms the border between Switzerland to the West and Liechtenstein and later Austria to the East. On the other hand, the Danube separates Romania and Bulgaria.
+
+Question: What is the other country the Rhine separates Switzerland to?
+
+Answer: Liechtenstein
+
+The key innovation in recent models lies in how to ingest information in the question and characterize it in the context, in order to provide an accurate answer to the question. This is often modeled as attention in the neural network community, which is a mechanism to attend the question into the context so as to find the answer related to the question. Some (Chen et al., 2017a; Weissenborn et al., 2017) attend the word-level embedding from the question to context, while some (Wang et al., 2017) attend the high-level representation in the question to augment the context. However we observed that none of the existing approaches has captured the full information in the context or the question, which could be vital for complete information comprehension. Taking image recognition as an example, information in various levels of representations can capture different aspects of details in an image: pixel, stroke and shape. We argue that this hypothesis also holds in language understanding and MRC. In other words, an approach that utilizes all the information from the word embedding level up to the highest level representation would be substantially beneficial for understanding both the question and the context, hence yielding more accurate answers.
+
+However, the ability to consider all layers of representation is often limited by the difficulty to make the neural model learn well, as model complexity will surge beyond capacity. We conjectured this is why previous literature tailored their models to only consider partial information. To alleviate this challenge, we identify an attention scoring function utilizing all layers of representation with less training burden. This leads to an attention that thoroughly captures the complete information between the question and the context. With this fully-aware attention, we put forward a multi-level attention mechanism to understand the information in the question, and exploit it layer by layer on the context side. All of these innovations are integrated into a new end-to-end structure called FusionNet in Figure 4, with details described in Section 3.
+
+We submitted FusionNet to SQuAD (Rajpurkar et al., 2016), a machine reading comprehension dataset. At the time of writing (Oct. 4th, 2017), our model ranked in the first place in both single model and ensemble model categories. The ensemble model achieves an exact match (EM) score of $78 . 8 \%$ and F1 score of $8 5 . 9 \%$ . Furthermore, we have tested FusionNet against adversarial SQuAD datasets (Jia & Liang, 2017). Results show that FusionNet outperforms existing state-of-the-art architectures in both datasets: on AddSent, FusionNet increases the best F1 metric from $4 6 . 6 \%$ to $5 1 . 4 \%$ ; on AddOneSent, FusionNet boosts the best F1 metric from $5 6 . 0 \%$ to $6 0 . 7 \%$ . In Appendix D, we also applied to natural language inference task and shown decent improvement. This demonstrated the exceptional performance of FusionNet. An open-source implementation of FusionNet can be found at https://github.com/momohuang/FusionNet-NLI.
+
+# 2 MACHINE COMPREHENSION & FULLY-AWARE ATTENTION
+
+In this section, we briefly introduce the task of machine comprehension as well as a conceptual architecture that summarizes recent advances in machine reading comprehension. Then, we introduce a novel concept called history-of-word. History-of-word can capture different levels of contextual information to fully understand the text. Finally, a light-weight implementation for history-of-word, Fully-Aware Attention, is proposed.
+
+# 2.1 TASK DESCRIPTION
+
+In machine comprehension, given a context and a question, the machine needs to read and understand the context, and then find the answer to the question. The context is described as a sequence of word tokens: $C ~ = ~ \{ w _ { 1 } ^ { C } , \ldots , w _ { m } ^ { C } \}$ , and the question as: $\textit { \textbf { Q } } = \ \{ w _ { 1 } ^ { Q } , \ldots , w _ { n } ^ { Q } \}$ , where $m$ is the number of words in the context, and $n$ is the number of words in the question. In general, $m \gg n$ . The answer Ans can have different forms depending on the task. In the SQuAD dataset (Rajpurkar et al., 2016), the answer Ans is guaranteed to be a contiguous span in the context $C$ , e.g., $\mathbf { A n s } = \{ w _ { i } ^ { C } , \dots , w _ { i + k } ^ { C } \}$ , where $k$ is the number of words in the answer and $k \leq m$ .
+
+# 2.2 CONCEPTUAL ARCHITECTURE FOR MACHINE READING COMPREHENSION
+
+In all state-of-the-art architectures for machine reading comprehension, a recurring pattern is the following process. Given two sets of vectors, A and B, we enhance or modify every single vector in set A with the information from set B. We call this a fusion process, where set B is fused into set A. Fusion processes are commonly based on attention (Bahdanau et al., 2015), but some are not. Major improvements in recent MRC work lie in how the fusion process is designed.
+
+A conceptual architecture illustrating state-of-the-art architectures is shown in Figure 2, which consists of three components.
+
+• Input vectors: Embedding vectors for each word in the context and the question.
+
+![](images/ef53a9d62835839db03dd60fa5bf44c53d378371d9b1d0cebb4360838ecc5ed3.jpg)  
+Table 1: A summarized view on the fusion processes used in several state-of-the-art architectures.   
+Figure 2: A conceptual architecture illustrating recent advances in MRC.
+
+• Integration components: The rectangular box. It is usually implemented using an RNN such as an LSTM (Hochreiter & Schmidhuber, 1997) or a GRU (Cho et al., 2014). • Fusion processes: The numbered arrows (1), (2), (2’), (3), $( 3 ^ { \circ } )$ . The set pointing outward is fused into the set being pointed to.
+
+There are three main types of fusion processes in recent advanced architectures. Table 1 shows what fusion processes are used in different state-of-the-art architectures. We now discuss them in detail.
+
+(1) Word-level fusion. By providing the direct word information in question to the context, we can quickly zoom in to more related regions in the context. However, it may not be helpful if a word has different semantic meaning based on the context. Many word-level fusions are not based on attention, e.g., (Hu et al., 2017; Chen et al., 2017a) appends binary features to context words, indicating whether each context word appears in the question.
+
+(2) High-level fusion. Informing the context about the semantic information in the question could help us find the correct answer. But high-level information is more imprecise than word information, which may cause models to be less aware of details.
+
+(2’) High-level fusion (Alternative). Similarly, we could also fuse high-level concept of $Q$ into the word-level of $C$ .
+
+(3) Self-boosted fusion. Since the context can be long and distant parts of text may rely on each other to fully understand the content, recent advances have proposed to fuse the context into itself. As the context contains excessive information, one common choice is to perform self-boosted fusion after fusing the question $Q$ . This allows us to be more aware of the regions related to the question.
+
+(3’) Self-boosted fusion (Alternative). Another choice is to directly condition the self-boosted fusion process on the question $Q$ , such as the coattention mechanism proposed in (Xiong et al., 2017). Then we can perform self-boosted fusion before fusing question information.
+
+A common trait of existing fusion mechanisms is that none of them employs all levels of representation jointly. In the following, we claim that employing all levels of representation is crucial to achieving better text understanding.
+
+# 2.3 FULLY-AWARE ATTENTION ON HISTORY OF WORD
+
+Consider the illustration shown in Figure 3. As we read through the context, each input word will gradually transform into a more abstract representation, e.g., from low-level to high-level concepts. Altogether, they form the history of each word in our mental flow. For a human, we utilize the history-of-word so frequently but we often neglect its importance. For example, to answer the question in Figure 3 correctly, we need to focus on both the high-level concept of forms the border and the word-level information of Alpine Rhine. If we focus only on the high-level concepts, we will
+
+Context: The Alpine Rhine is part of the Rhine, a famous European river. The Alpine Rhine begins in the most western part of the Swiss canton of Graubünden, and later forms the border between Switzerland to the West and Liechtenstein and later Austria to the East. On the other hand, the Danube separates Romania and Bulgaria.
+
+Question: What is the other country the Rhine separates Switzerland to?
+
+Answer: Liechtenstein
+
+![](images/d3b58b3a8ba2ca6de01ca0430c65b35e60ff963f937f77dd27b865c4cf91802f.jpg)  
+Figure 3: Illustrations of the history-of-word for the example shown in Figure 1. Utilizing the entire history-of-word is crucial for the full understanding of the context.
+
+confuse Alpine Rhine with Danube since both are European rivers that separate countries. Therefore we hypothesize that the entire history-of-word is important to fully understand the text.
+
+In neural architectures, we define the history of the $i$ -th word, $\mathrm { H o W } _ { i }$ , to be the concatenation of all the representations generated for this word. This may include word embedding, multiple intermediate and output hidden vectors in RNN, and corresponding representation vectors in any further layers. To incorporate history-of-word into a wide range of neural models, we present a lightweight implementation we call Fully-Aware Attention.
+
+Attention can be applied to different scenarios. To be more conclusive, we focus on attention applied to fusing informatiotext bodies A and B: $\{ h _ { 1 } ^ { A } , \ldots , h _ { m } ^ { A } \}$ y, $\{ h _ { 1 } ^ { B } , \ldots , h _ { n } ^ { B } \} \subset \mathbb { R } ^ { d }$ two sets of hidden vectors for words in. Their associated history-of-word are, $\{ \mathrm { H o W } _ { 1 } ^ { A } , \dots , \mathrm { H o W } _ { m } ^ { A } \} , ~ \{ \mathrm { H o W } _ { 1 } ^ { B } , \dots , \mathrm { H o W } _ { n } ^ { B } \} \subset \mathbb { R } ^ { d _ { h } } ,$
+
+where $d _ { h } \gg d$ . Fusing body $\mathbf { B }$ to body A via standard attention means for every $ { \boldsymbol { h } } _ { i } ^ { A }$ in body A,
+
+1. Compute an attention score $S _ { i j } = S ( \pmb { h } _ { i } ^ { A } , \pmb { h } _ { j } ^ { B } ) \in \mathbb { R }$ for each $h _ { j } ^ { B }$ in body $\mathbf { B }$ .   
+2. Form the attention weight $\alpha _ { i j }$ through softmax: $\begin{array} { r } { \alpha _ { i j } = \exp ( S _ { i j } ) / \sum _ { k } \exp ( S _ { i k } ) } \end{array}$ .   
+3. Concatenate $ { \boldsymbol { h } } _ { i } ^ { A }$ with the summarized information, $\begin{array} { r } { \hat { \pmb { h } } _ { i } ^ { A } = \sum _ { j } \alpha _ { i j } \pmb { h } _ { j } ^ { B } } \end{array}$ .
+
+In fully-aware attention, we replace attention score computation with the history-of-word.
+
+$$
+S ( h _ { i } ^ { A } , h _ { j } ^ { B } ) \implies S ( \mathrm { H o W } _ { i } ^ { A } , \mathrm { H o W } _ { j } ^ { B } ) .
+$$
+
+This allows us to be fully aware of the complete understanding of each word. The ablation study in Section 4.4 demonstrates that this lightweight enhancement offers a decent improvement in performance.
+
+To fully utilize history-of-word in attention, we need a suitable attention scoring function $S ( { \pmb x } , { \pmb y } )$ . A commonly used function is multiplicative attention (Britz et al., 2017): $\pmb { x } ^ { T } \pmb { U } ^ { T } \pmb { V } \pmb { y }$ , leading to
+
+$$
+\begin{array} { r } { S _ { i j } = ( \mathrm { H o W } _ { i } ^ { A } ) ^ { T } U ^ { T } V ( \mathrm { H o W } _ { j } ^ { B } ) , } \end{array}
+$$
+
+where $U , V ~ \in ~ \mathbb { R } ^ { k \times d _ { h } }$ , and $k$ is the attention hidden size. However, we suspect that two large matrices interacting directly will make the neural model harder to train. Therefore we propose to constrain the matrix $U ^ { T } V$ to be symmetric. A symmetric matrix can always be decomposed into $U ^ { T } D U$ , thus
+
+$$
+\begin{array} { r } { S _ { i j } = ( \mathrm { H o W } _ { i } ^ { A } ) ^ { T } U ^ { T } D U ( \mathrm { H o W } _ { j } ^ { B } ) , } \end{array}
+$$
+
+where $U \in \mathbb { R } ^ { k \times d _ { h } }$ , $D \in \mathbb { R } ^ { k \times k }$ and $D$ is a diagonal matrix. The symmetric form retains the ability to give high attention score between dissimilar $\mathrm { \bar { H } o W } _ { i } ^ { A } , \mathrm { H o W } _ { j } ^ { B }$ . Additionally, we marry nonlinearity with the symmetric form to provide richer interaction among different parts of the history-of-word. The final formulation for attention score is
+
+$$
+S _ { i j } = f ( U ( \mathrm { H o W } _ { i } ^ { A } ) ) ^ { T } D ~ f ( U ( \mathrm { H o W } _ { j } ^ { B } ) ) ,
+$$
+
+where $f ( x )$ is an activation function applied element-wise. In the following context, we employ $f ( x ) = \operatorname* { m a x } ( 0 , x )$ . A detailed ablation study in Section 4 demonstrates its advantage over many alternatives.
+
+![](images/0257ec1f4f3ec3d036b2ec9c1a8204d14a2dfc7469e37a1de56bf42b7d5b2f0c.jpg)  
+Figure 4: An illustration of FusionNet architecture. Each upward arrow represents one layer of BiLSTM. Each circle to the right is a detailed illustration of the corresponding component in FusionNet. Circle 1: Fully-aware attention between $C$ and $Q$ . Illustration of Equation (C1) in Section 3.1. Circle 2: Concatenate all concepts in $C$ with multi-level $Q$ information, then pass through BiLSTM. Illustration of Equation (C2) in Section 3.1.
+
+Circle 3: Fully-aware attention on the context $C$ itself. Illustration of Equation (C3) in Section 3.1. Circle 4: Concatenate the understanding vector of $C$ with self-attention information, then pass through BiLSTM. Illustration of Equation (C4) in Section 3.1.
+
+# 3 FULLY-AWARE FUSION NETWORK
+
+# 3.1 END-TO-END ARCHITECTURE
+
+Based on fully-aware attention, we propose an end-to-end architecture: the fully-aware fusion network (FusionNet). Given text A and B, FusionNet fuses information from text $\mathbf { B }$ to text A and generates two set of vectors
+
+$$
+U _ { A } = \{ \pmb { u } _ { 1 } ^ { A } , \ldots , \pmb { u } _ { m } ^ { A } \} , \quad U _ { B } = \{ \pmb { u } _ { 1 } ^ { B } , \ldots , \pmb { u } _ { n } ^ { B } \} .
+$$
+
+In the following, we consider the special case where text A is context $C$ and text $\mathbf { B }$ is question $Q$ .   
+An illustration for FusionNet is shown in Figure 4. It consists of the following components.
+
+Input Vectors. First, each word in $C$ and $Q$ is transformed into an input vector $\textbf { \em w }$ . We utilize the 300-dim GloVe embedding (Pennington et al., 2014) and 600-dim contextualized vector (McCann et al., 2017). In the SQuAD task, we also include 12-dim POS embedding, 8-dim NER embedding and a normalized term frequency for context $C$ as suggested in (Chen et al., 2017a). Together $\{ \pmb { w } _ { 1 } ^ { C } , \ldots , \pmb { w } _ { m } ^ { C } \} \subset \mathbb { R } ^ { 9 0 0 + 2 0 + 1 }$ , and $\{ \pmb { w } _ { 1 } ^ { Q } , \ldots , \pmb { w } _ { n } ^ { Q } \} \subset \mathbb { R } ^ { 9 0 0 }$ .
+
+Fully-Aware Multi-level Fusion: Word-level. In multi-level fusion, we separately consider fusing word-level and higher-level. Word-level fusion informs $C$ about what kind of words are in $Q$ . It is illustrated as arrow (1) in Figure 2. For this component, we follow the approach in (Chen et al., 2017a) First, a feature vector $\mathrm { e m } _ { i }$ is created for each word in $C$ to indicate whether the word occurs in the question $Q$ . Second, attention-based fusion on GloVe embedding $\mathbf { \nabla } _ { \mathbf { \boldsymbol { g } } _ { i } }$ is used
+
+$$
+\hat { g } _ { i } ^ { C } = \sum _ { j } \alpha _ { i j } g _ { j } ^ { Q } , \quad \alpha _ { i j } \propto \exp ( S ( g _ { i } ^ { C } , g _ { j } ^ { Q } ) ) , \quad S ( x , y ) = \mathrm { R e L U } ( W x ) ^ { T } \mathrm { R e L U } ( W y ) ,
+$$
+
+where $W \in \mathbb { R } ^ { 3 0 0 \times 3 0 0 }$ . Since history-of-word is the input vector itself, fully-aware attention is not employed here. The enhanced input vector for context is $\mathbf { \tilde { w } } _ { i } ^ { C } = [ \mathbf { w } _ { i } ^ { C } ; \mathrm { e m } _ { i } ; \bar { \mathbf { g } } _ { i } ^ { C } ]$ .
+
+Reading. In the reading component, we use a separate bidirectional LSTM (BiLSTM) to form low-level and high-level concepts for $C$ and $Q$ .
+
+$$
+{ h } _ { 1 } ^ { C l } , \dots , { h } _ { m } ^ { C l } = \mathrm { B i L S T M } ( \tilde { w } _ { 1 } ^ { C } , \dots , \tilde { w } _ { m } ^ { C } ) , \quad { h } _ { 1 } ^ { Q l } , \dots , { h } _ { n } ^ { Q l } = \mathrm { B i L S T M } ( w _ { 1 } ^ { Q } , \dots , w _ { n } ^ { Q } ) ,
+$$
+
+$$
+{ h } _ { 1 } ^ { C h } , \ldots , { h } _ { m } ^ { C h } = \mathrm { B i L S T M } ( { h } _ { 1 } ^ { C l } , \ldots , { h } _ { m } ^ { C l } ) , \quad { h } _ { 1 } ^ { Q h } , \ldots , { h } _ { n } ^ { Q h } = \mathrm { B i L S T M } ( { h } _ { 1 } ^ { Q l } , \ldots , { h } _ { n } ^ { Q l } ) .
+$$
+
+Hence low-level and high-level concepts $h ^ { l } , h ^ { h } \in \mathbb { R } ^ { 2 5 0 }$ are created for each word.
+
+Question Understanding. In the Question Understanding component, we apply a new BiLSTM taking in both ${ h ^ { Q l } , h ^ { Q h } }$ to obtain the final question representation $U _ { Q }$ :
+
+$$
+\begin{array} { r } { U _ { Q } = \{ \boldsymbol { { u } } _ { 1 } ^ { Q } , \ldots , \boldsymbol { { u } } _ { n } ^ { Q } \} = \mathrm { { B i L S T M } } ( [ \boldsymbol { h } _ { 1 } ^ { Q l } ; \boldsymbol { h } _ { 1 } ^ { Q h } ] , \ldots , [ \boldsymbol { h } _ { n } ^ { Q l } ; \boldsymbol { h } _ { n } ^ { Q h } ] ) . } \end{array}
+$$
+
+where $\{ \boldsymbol { u } _ { i } ^ { Q } \in \mathbb { R } ^ { 2 5 0 } \} _ { i = 1 } ^ { n }$ are the understanding vectors for $Q$
+
+Fully-Aware Multi-level Fusion: Higher-level. This component fuses all higher-level information in the question $Q$ to the context $C$ through fully-aware attention on history-of-word. Since the proposed attention scoring function for fully-aware attention is constrained to be symmetric, we need to identify the common history-of-word for both $C , Q$ . This yields
+
+$$
+\mathrm { H o W } _ { i } ^ { C } = [ \pmb { g } _ { i } ^ { C } ; \pmb { c } _ { i } ^ { C } ; \pmb { h } _ { i } ^ { C l } ; \pmb { h } _ { i } ^ { C h } ] , ~ \mathrm { H o W } _ { i } ^ { Q } = [ \pmb { g } _ { i } ^ { Q } ; \pmb { c } _ { i } ^ { Q } ; \pmb { h } _ { i } ^ { Q l } ; \pmb { h } _ { i } ^ { Q h } ] \in \mathbb { R } ^ { 1 4 0 0 } ,
+$$
+
+where $\mathbf { \pmb { g } } _ { i }$ is the GloVe embedding and $c _ { i }$ is the CoVe embedding. Then we fuse low, high, and understanding-level information from $Q$ to $C$ via fully-aware attention. Different sets of attention weights are calculated through attention function $S ^ { \tilde { l } } ( x , y ) , S ^ { h } ( x , y ) , S ^ { u } ( x , y )$ to combine low, high, and understanding-level of concepts. All three functions are the proposed symmetric form with nonlinearity in Section 2.3, but are parametrized by independent parameters to attend to different regions for different level. Attention hidden size is set to be $k = 2 5 0$ .
+
+$$
+\begin{array} { r } { \hat { \boldsymbol { h } } _ { i } ^ { C l } = \sum _ { j } \alpha _ { i j } ^ { l } \boldsymbol { h } _ { j } ^ { Q l } , \quad \alpha _ { i j } ^ { l } \propto \exp ( S ^ { l } ( \mathrm { H o W } _ { i } ^ { C } , \mathrm { H o W } _ { j } ^ { Q } ) ) . } \end{array}
+$$
+
+2. High-level fusion: $\begin{array} { r } { \hat { \boldsymbol { \mathsf { h } } } _ { i } ^ { C h } = \sum _ { j } \alpha _ { i j } ^ { h } \boldsymbol { h } _ { j } ^ { Q h } , \quad \alpha _ { i j } ^ { h } \propto \exp ( S ^ { h } ( \mathrm { H o W } _ { i } ^ { C } , \mathrm { H o W } _ { j } ^ { Q } ) ) . } \end{array}$
+
+This multi-level attention mechanism captures different levels of information independently, while taking all levels of information into account. A new BiLSTM is applied to obtain the representation for $C$ fully fused with information in the question $Q$ :
+
+$$
+\{ \pmb { v } _ { 1 } ^ { C } , \ldots , \pmb { v } _ { m } ^ { C } \} = \mathrm { B i L S T M } ( [ { \pmb { h } } _ { 1 } ^ { C l } ; { \pmb { h } } _ { 1 } ^ { C h } ; { \hat { \pmb { h } } } _ { 1 } ^ { C l } ; { \hat { \pmb { h } } } _ { 1 } ^ { C h } ; { \hat { \pmb { u } } } _ { 1 } ^ { C l } ] , \ldots , [ { \pmb { h } } _ { m } ^ { C l } ; { \pmb { h } } _ { m } ^ { C h } ; { \hat { \pmb { h } } } _ { m } ^ { C l } ; { \hat { \pmb { h } } } _ { m } ^ { C h } ; { \hat { \pmb { u } } } _ { m } ^ { C } ] ) .
+$$
+
+Fully-Aware Self-Boosted Fusion. We now use self-boosted fusion to consider distant parts in the context, as illustrated by arrow (3) in Figure 2. Again, we achieve this via fully-aware attention on history-of-word. We identify the history-of-word to be
+
+$$
+\operatorname { H o W } _ { i } ^ { C } = [ \pmb { g } _ { i } ^ { C } ; \pmb { c } _ { i } ^ { C } ; \pmb { h } _ { i } ^ { C l } ; \pmb { h } _ { i } ^ { C h } ; \hat { \pmb { h } } _ { i } ^ { C l } ; \hat { \pmb { h } } _ { i } ^ { C h } ; \hat { \pmb { u } } _ { i } ^ { C } ; \pmb { v } _ { i } ^ { C } ] \in \mathbb { R } ^ { 2 4 0 0 } .
+$$
+
+We then perform fully-aware attention, $\begin{array} { r } { \hat { \pmb v } _ { i } ^ { C } = \sum _ { j } \alpha _ { i j } ^ { s } \pmb { v } _ { j } ^ { C } , \alpha _ { i j } ^ { s } \propto \exp ( S ^ { s } ( \mathrm { H o W } _ { i } ^ { C } , \mathrm { H o W } _ { j } ^ { C } ) ) . } \end{array}$ The final context representation is obtained by
+
+$$
+U _ { C } = \{ \pmb { u } _ { 1 } ^ { C } , \ldots , \pmb { u } _ { m } ^ { C } \} = \mathrm { B i L S T M } ( [ \pmb { v } _ { 1 } ^ { C } ; \hat { \pmb { v } } _ { 1 } ^ { C } ] , \ldots , [ \pmb { v } _ { m } ^ { C } ; \hat { \pmb { v } } _ { m } ^ { C } ] ) .
+$$
+
+$\{ \boldsymbol { u } _ { i } ^ { C } \in \mathbb { R } ^ { 2 5 0 } \} _ { i = 1 } ^ { m }$ are the understanding vectors for $C$
+
+After these components in FusionNet, we have created the understanding vectors, $U _ { C }$ , for the context $C$ , which are fully fused with the question $Q$ . We also have the understanding vectors, $U _ { Q }$ , for the question $Q$ .
+
+# 3.2 APPLICATION IN MACHINE COMPREHENSION
+
+We focus particularly on the output format in $\mathrm { S Q u A D }$ (Rajpurkar et al., 2016) where the answer is always a span in the context. The output of FusionNet are the understanding vectors for both $C$ and $Q$ , $U _ { C } = \{ \mathbf { { u } } _ { 1 } ^ { C } , \dots , \mathbf { { u } } _ { m } ^ { C } \}$ , $U _ { Q } = \{ \bar { \pmb { u } } _ { 1 } ^ { Q } , \dots , \pmb { u } _ { n } ^ { Q } \}$ .
+
+We then use them to find the answer span in the context. Firstly, a single summarized question understanding vector is obtained through $\begin{array} { r } { { \pmb u } ^ { Q } = \sum _ { i } \beta _ { i } { \pmb u } _ { i } ^ { Q } } \end{array}$ , where $\beta _ { i } \propto \mathrm { { e x p } } ( { \pmb w } ^ { T } { \pmb u } _ { i } ^ { Q } )$ and $\pmb { w }$ is a trainable vector. Then we attend for the span start using the summarized question understanding vector $\pmb { u } ^ { Q }$ ,
+
+$$
+P _ { i } ^ { S } \propto \exp ( ( \boldsymbol { \mathbf { \mathit { u } } } ^ { Q } ) ^ { T } W _ { S } \boldsymbol { \mathbf { \mathit { u } } } _ { i } ^ { C } ) ,
+$$
+
+where $W _ { S } \in \mathbb { R } ^ { d \times d }$ is a trainable matrix. To use the information of the span start when we attend for the span end, we combine the context understanding vector for the span start with $\pmb { u } ^ { Q }$ through a GRU (Cho et al., 2014), $\begin{array} { r } { { \pmb v } ^ { Q } = \mathrm { G R U } ( { \pmb u } ^ { Q } , \sum _ { i } P _ { i } ^ { S } { \pmb u } _ { i } ^ { \top } ) } \end{array}$ , where $\pmb { u } ^ { Q }$ is taken as the memory and $\textstyle \sum _ { i } P _ { i } ^ { S } { \boldsymbol { u } } _ { i } ^ { C }$ as the input in GRU. Finally we attend for the end of the span using $v ^ { Q }$ ,
+
+$$
+P _ { i } ^ { E } \propto \exp ( ( \pmb { v } ^ { Q } ) ^ { T } W _ { E } \pmb { u } _ { i } ^ { C } ) ,
+$$
+
+where $W _ { E } \in \mathbb { R } ^ { d \times d }$ is another trainable matrix.
+
+Training. During training, we maximize the log probabilities of the ground truth span start and end, $\begin{array} { r } { \sum _ { k } ( \log \mathsf { \bar { ( } } P _ { i _ { k } ^ { s } } ^ { S } ) + \mathsf { \bar { l o g } } ( P _ { i _ { k } ^ { e } } ^ { E } ) ) } \end{array}$ , where $i _ { k } ^ { s } , i _ { k } ^ { e }$ are the answer span for the $k$ -th instance.
+
+Prediction. We predict the answer span to be $i ^ { s } , i ^ { e }$ with the maximum $P _ { i ^ { s } } ^ { S } P _ { i ^ { e } } ^ { E }$ under the constraint $0 \leq i ^ { e } - i ^ { s } \leq 1 5$ .
+
+# 4 EXPERIMENTS
+
+In this section, we first present the datasets used for evaluation. Then we compare our end-toend FusionNet model with existing machine reading models. Finally, we conduct experiments to validate the effectiveness of our proposed components. Additional ablation study on input vectors can be found in Appendix C. Detailed experimental settings can be found in Appendix E.
+
+# 4.1 DATASETS
+
+We focus on the SQuAD dataset (Rajpurkar et al., 2016) to train and evaluate our model. SQuAD is a popular machine comprehension dataset consisting of $1 0 0 { , } 0 0 0 { + }$ questions created by crowd workers on 536 Wikipedia articles. Each context is a paragraph from an article and the answer to each question is guaranteed to be a span in the context.
+
+While rapid progress has been made on SQuAD, whether these systems truly understand language remains unclear. In a recent paper, Jia & Liang (2017) proposed several adversarial schemes to test the understanding of the systems. We will use the following two adversarial datasets, AddOneSent and AddSent, to evaluate our model. For both datasets, a confusing sentence is appended at the end of the context. The appended sentence is model-independent for AddOneSent, while AddSent requires querying the model a few times to choose the most confusing sentence.
+
+# 4.2 MAIN RESULTS
+
+We submitted our model to SQuAD for evaluation on the hidden test set. We also tested the model on the adversarial SQuAD datasets. Two official evaluation criteria are used: Exact Match (EM) and F1 score. EM measures how many predicted answers exactly match the correct answer, while F1 score measures the weighted average of the precision and recall at token level. The evaluation results for our model and other competing approaches are shown in Table 2.1 Additional comparisons with state-of-the-art models in the literature can be found in Appendix A.
+
+For the two adversarial datasets, AddOneSent and AddSent, the evaluation criteria is the same as SQuAD. However, all models are trained only on the original SQuAD, so the model never sees the
+
+<table><tr><td>AddSent</td><td>EM/F1</td></tr><tr><td>LRBaseline</td><td>17.0/23.2</td></tr><tr><td>Match-LSTM (E) BiDAF (E)</td><td>24.3 /34.2 29.6 /34.2</td></tr><tr><td>SEDT (E) Mnemonic Reader (S)</td><td>30.0 /35.0</td></tr><tr><td>Mnemonic Reader (E)</td><td>39.8/46.6</td></tr><tr><td></td><td>40.7 / 46.2</td></tr><tr><td>ReasoNet (E) FusionNet (E)</td><td>34.6 /39.4 46.2 / 51.4</td></tr></table>
+
+Table 2: The performance of FusionNet and competing approaches on SQuAD hidden test set at the time of writing (Oct. 4th, 2017).   
+
+<table><tr><td>AddOneSent</td><td>EM/F1</td></tr><tr><td>LRBaseline Match-LSTM (E)</td><td>22.3/30.4 34.8 / 41.8</td></tr><tr><td>BiDAF (E) SEDT (E)</td><td>40.7 /46.9 40.0 / 46.5</td></tr><tr><td>Mnemonic Reader (S)</td><td>48.5 /56.0</td></tr><tr><td>Mnemonic Reader (E)</td><td>48.7 / 55.3</td></tr><tr><td>ReasoNet (E) FusionNet (E)</td><td>43.6 /49.8</td></tr></table>
+
+Table 3: Comparison on AddSent. (S: Single model, E: Ensemble)   
+
+<table><tr><td>Single Model</td><td>Test Set EM/F1</td></tr><tr><td>LR Baseline (Rajpurkar et al., 2016) Match-LSTM (Wang &amp; Jiang,2016) BiDAF (Seo et al., 2017) SEDT (Liu et al., 2017) RaSoR (Lee et al., 2016) DrQA (Chen et al., 2017a) ReasoNet (Shen et al.,2017) R.Mnemonic Reader (Hu et al., 2017) DCN+ R-nett FusionNet</td><td>40.4 /51.0 64.7/73.7 68.0 / 77.3 68.2 /77.5 70.8/78.7 70.7 /79.4 70.6 / 79.4 73.2/81.8 74.9 / 82.8 75.7 /83.5 76.0 / 83.9</td></tr><tr><td>EnsembleModel ReasoNet (Shen et al., 2017) MEMEN (Pan et al., 2017) R.Mnemonic Reader (Hu et al., 2017) R-nett DCN+ FusionNet</td><td>75.0 / 82.3 75.4/82.7 77.7 / 84.9 78.2/85.2 78.7 / 85.6</td></tr><tr><td>Human (Rajpurkar et al., 2016)</td><td>78.8 / 85.9 82.3/91.2</td></tr></table>
+
+Table 4: Comparison on AddOneSent. (S: Single model, E: Ensemble)
+
+adversarial datasets during training. The results for AddSent and AddOneSent are shown in Table 3   
+and Table 4, respectively.2
+
+From the results, we can see that our models not only perform well on the original SQuAD dataset, but also outperform all previous models by more than $5 \%$ in EM score on the adversarial datasets. This shows that FusionNet is better at language understanding of both the context and question.
+
+# 4.3 COMPARISON ON ATTENTION FUNCTION
+
+In this experiment, we compare the performance of different attention scoring functions $S ( { \pmb x } , { \pmb y } )$ for fully-aware attention. We utilize the end-to-end architecture presented in Section 3.1. Fully-aware attention is used in two places, fully-aware multi-level fusion: higher level and fully-aware selfboosted fusion. Word-level fusion remains unchanged. Based on the discussion in Section 2.3, we consider the following formulations for comparison:
+
+1. Additive attention (MLP) (Bahdanau et al., 2015): $\pmb { s } ^ { T } \operatorname { t a n h } ( W _ { 1 } \pmb { x } + W _ { 2 } \pmb { y } ) .$ 1   
+2. Multiplicative attention: $\pmb { x } ^ { T } \pmb { U } ^ { T } \pmb { V } \pmb { y }$ .   
+3. Scaled multiplicative attention: $\scriptstyle { \frac { 1 } { \sqrt { k } } } x ^ { T } U ^ { T } V y$ , where $k$ is the attention hidden size. It is   
+proposed in (Vaswani et al., 2017).   
+4. Scaled multiplicative with nonlinearity: $\begin{array} { r } { \frac { 1 } { \sqrt { k } } f ( U \pmb { x } ) ^ { T } f ( V \pmb { y } ) } \end{array}$ .   
+5. Our proposed symmetric form: $\pmb { x } ^ { T } \pmb { U } ^ { T } \pmb { D } \pmb { U } \pmb { y }$ , where $D$ is diagonal.   
+6. Proposed symmetric form with nonlinearity: $f ( U \mathbf { x } ) ^ { T } D f ( U \mathbf { y } )$ .
+
+We consider the activation function $f ( x )$ to be $\operatorname* { m a x } ( 0 , x )$ . The results of various attention functions on SQuAD development set are shown in Table 5. It is clear that the symmetric form consistently outperforms all alternatives. We attribute this gain to the fact that symmetric form has a single large matrix $U$ . All other alternatives have two large parametric matrices. During optimization, these two parametric matrices would interfere with each other and it will make the entire optimization process challenging. Besides, by constraining $U ^ { T } V$ to be a symmetric matrix $U ^ { T } D U$ , we retain the ability for $_ { \textbf { \em x } }$ to attend to dissimilar $\textbf {  { y } }$ . Furthermore, its marriage with the nonlinearity continues to significantly boost the performance.
+
+Table 5: Comparison of different attention functions $S ( { \pmb x } , { \pmb y } )$ on SQuAD dev set.   
+
+<table><tr><td rowspan=1 colspan=1>Attention Function</td><td rowspan=1 colspan=1>EM/F1</td></tr><tr><td rowspan=1 colspan=1>Additive (MLP)</td><td rowspan=2 colspan=1>71.8/ 80.172.1 / 80.672.4 / 80.772.6 / 80.8</td></tr><tr><td rowspan=1 colspan=1>MultiplicativeScaled MultiplicativeScaled Multiplicative + ReLU</td></tr><tr><td rowspan=1 colspan=1>Symmetric FormSymmetric Form + ReLU</td><td rowspan=1 colspan=1>73.1 /81.575.3 / 83.6</td></tr><tr><td rowspan=1 colspan=1>Previous SotA (Hu et al., 2017)</td><td rowspan=1 colspan=1>72.1/ 81.6</td></tr></table>
+
+Table 6: Comparison of different configurations demonstrates the effectiveness of history-of-word.   
+
+<table><tr><td rowspan=1 colspan=2>ConfigurationC,Q Fusion      Self C</td><td rowspan=1 colspan=1>EM/F1</td></tr><tr><td rowspan=1 colspan=1>High-LevelFA High-LevelFA All-LevelFA Multi-Level</td><td rowspan=1 colspan=1>None</td><td rowspan=1 colspan=1>64.6/73.273.3 /81.472.3 / 80.774.6 / 82.7</td></tr><tr><td rowspan=1 colspan=1>FA Multi-Level</td><td rowspan=1 colspan=1>NormalFA</td><td rowspan=1 colspan=1>74.4 / 82.675.3 / 83.6</td></tr><tr><td rowspan=1 colspan=2>Previous SotA (Hu et al., 2017)</td><td rowspan=1 colspan=1>72.1/ 81.6</td></tr></table>
+
+# 4.4 EFFECTIVENESS OF HISTORY-OF-WORD
+
+In FusionNet, we apply the history-of-word and fully-aware attention in two major places to achieve good performance: multi-level fusion and self-boosted fusion. In this section, we present experiments to demonstrate the effectiveness of our application. In the experiments, we fix the attention function to be our proposed symmetric form with nonlinearity due to its good performance shown in Section 4.3. The results are shown in Table 6, and the details for each configuration can be found in Appendix B.
+
+High-Level is a vanilla model where only the high-level information is fused from $Q$ to $C$ via standard attention. When placed in the conceptual architecture (Figure 2), it only contains arrow (2) without any other fusion processes.
+
+FA High-Level is the High-Level model with standard attention replaced by fully-aware attention.
+
+FA All-Level is a naive extension of FA High-Level, where all levels of information are concatenated and is fused into the context using the same attention weight.
+
+FA Multi-Level is our proposed Fully-aware Multi-level fusion, where different levels of information are attended under separate attention weight.
+
+Self $C = \mathbf { N o n e }$ means we do not make use of self-boosted fusion.
+
+Self $C = \mathrm { { N o r m a l } }$ means we employ a standard attention-based self-boosted fusion after fusing question to context. This is illustrated as arrow (3) in the conceptual architecture (Figure 2).
+
+Self $C = \mathbf { F } \mathbf { A }$ means we enhance the self-boosted fusion with fully-aware attention.
+
+High-Level vs. FA High-Level. From Table 6, we can see that High-Level performs poorly as expected. However enhancing this vanilla model with fully-aware attention significantly increase the performance by more than $8 \%$ . The performance of FA High-Level already outperforms many state-of-the-art MRC models. This clearly demonstrates the power of fully-aware attention.
+
+FA All-Level vs. FA Multi-Level. Next, we consider models that fuse all levels of information from question $Q$ to context $C$ . FA All-Level is a naive extension of FA High-Level, but its performance is actually worse than $F A$ High-Level. However, by fusing different parts of history-of-word in $Q$ independently as in $F A$ Multi-Level, we are able to further improve the performance.
+
+Self $C$ options. We have achieved decent performance without self-boosted fusion. Now, we compare adding normal and fully-aware self-boosted fusion into the architecture. Comparing None and Normal in Table 6, we can see that the use of normal self-boosted fusion is not very effective under our improved $C , Q$ Fusion. Then by comparing with $F A$ , it is clear that through the enhancement of fully-aware attention, the enhanced self-boosted fusion can provide considerable improvement.
+
+Together, these experiments demonstrate that the ability to take all levels of understanding as a whole is crucial for machines to better understand the text.
+
+# 5 CONCLUSIONS
+
+In this paper, we describe a new deep learning model called FusionNet with its application to machine comprehension. FusionNet proposes a novel attention mechanism with following three contributions: 1. the concept of history-of-word to build the attention using complete information from the lowest word-level embedding up to the highest semantic-level representation; 2. an attention scoring function to effectively and efficiently utilize history-of-word; 3. a fully-aware multi-level fusion to exploit information layer by layer discriminatingly. We applied FusionNet to MRC task and experimental results show that FusionNet outperforms existing machine reading models on both the SQuAD dataset and the adversarial SQuAD dataset. We believe FusionNet is a general and improved attention mechanism and can be applied to many tasks. Our future work is to study its capability in other NLP problems.
+
+# ACKNOWLEDGMENTS
+
+We would like to thank Paul Mineiro, Sebastian Kochman, Pengcheng He, Jade Huang and Jingjing Liu from Microsoft Business AI, Mac-Antoine Rondeau from Maluuba and the anonymous reviewers for their valuable comments and tremendous help in this paper.
+
+# REFERENCES
+
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+
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+B. McCann, J. Bradbury, C. Xiong, and R. Socher. Learned in Translation: Contextualized Word Vectors. arXiv preprint arXiv:1708.00107, 2017.   
+Boyuan Pan, Hao Li, Zhou Zhao, Bin Cao, Deng Cai, and Xiaofei He. Memen: Multi-layer embedding with memory networks for machine comprehension. arXiv preprint arXiv:1707.09098, 2017.   
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+
+# A COMPARISON WITH PUBLISHED MODELS
+
+In this appendix, we compare with published state-of-the-art architectures on the SQuAD dev set. The comparison is shown in Figure 5 and 6 for EM and F1 score respectively. The performance of FusionNet is shown under different training epochs. Each epoch loops through all the examples in the training set once. On a single NVIDIA GeForce GTX Titan X GPU, each epoch took roughly 20 minutes when batch size 32 is used.
+
+The state-of-the-art models compared in this experiment include:   
+1. Published version of R-net in their technical report (Wang et al., 2017),   
+2. Reinforced Mnemonic Reader (Hu et al., 2017), 3. MEMEN (Pan et al., 2017),   
+4. ReasoNet (Shen et al., 2017), 5. Document reader (DrQA) (Chen et al., 2017a),   
+6. DCN (Xiong et al., 2017), 7. DCN $^ +$ character embedding (Char) $^ +$ CoVe (McCann et al., 2017),   
+8. BiDAF (Seo et al., 2017), 9. the best-performing variant of Match-LSTM (Wang & Jiang, 2016).
+
+![](images/83cd5a9f9a0174460ffcd39b92ddb060f758e9749cab54075cd31bb5c5f087b2.jpg)  
+Figure 5: EM score on the SQuAD dev set under different training epoch.
+
+![](images/d8a5b20b41be47ba0875b1e75dbb679e81f4e2b06dd71346b750da38f888986b.jpg)  
+Figure 6: F1 score on the SQuAD dev set under different training epoch.
+
+# B DETAILED CONFIGURATIONS IN THE ABLATION STUDY
+
+In this appendix, we present details for the configurations used in the ablation study in Section 4.4. For all configurations, the understanding vectors for both the context $C$ and the question $Q$ will be generated, then we follow the same output architecture in Section 3.2 to apply them to machine reading comprehension problem.
+
+High-Level. Firstly, context words and question words are transformed into input vectors in the same way as FusionNet,
+
+$$
+\{ \pmb { w } _ { 1 } ^ { C } , \ldots , \pmb { w } _ { m } ^ { C } \} , \quad \{ \pmb { w } _ { 1 } ^ { Q } , \ldots , \pmb { w } _ { n } ^ { Q } \} .
+$$
+
+Then we pass them independently to two layers of BiLSTM.
+
+$$
+\begin{array} { r l } & { h _ { 1 } ^ { C l } , \ldots , h _ { m } ^ { C l } = \mathrm { B i L S T M } ( w _ { 1 } ^ { C } , \ldots , w _ { m } ^ { C } ) , \quad h _ { 1 } ^ { Q l } , \ldots , h _ { n } ^ { Q l } = \mathrm { B i L S T M } ( w _ { 1 } ^ { Q } , \ldots , w _ { n } ^ { Q } ) , } \\ & { h _ { 1 } ^ { C h } , \ldots , h _ { m } ^ { C h } = \mathrm { B i L S T M } ( h _ { 1 } ^ { C l } , \ldots , h _ { m } ^ { C l } ) , \quad h _ { 1 } ^ { Q h } , \ldots , h _ { n } ^ { Q h } = \mathrm { B i L S T M } ( h _ { 1 } ^ { Q l } , \ldots , h _ { n } ^ { Q l } ) . } \end{array}
+$$
+
+Next we consider the standard attention-based fusion for the high level representation.
+
+$$
+\hat { \boldsymbol { h } } _ { i } ^ { C h } = \sum _ { j } \alpha _ { i j } \boldsymbol { h } _ { j } ^ { Q h } , \quad \alpha _ { i j } = \frac { \exp ( S _ { i j } ) } { \sum _ { k } \exp ( S _ { i k } ) } , \quad S _ { i j } = S ( \boldsymbol { h } _ { i } ^ { C h } , \boldsymbol { h } _ { j } ^ { Q h } ) .
+$$
+
+Then we concatenate the attended vector $\hat { h } _ { i } ^ { C h }$ with the original high level representation $h _ { i } ^ { C h }$ and pass through two layers of BiLSTM to fully mix the two information. The understanding vectors for the context is the hidden vectors in the final layers of the BiLSTM.
+
+$$
+\pmb { u } _ { 1 } ^ { C } , \ldots , \pmb { u } _ { m } ^ { C } = \mathrm { B i L S T M } ( [ \pmb { h } _ { 1 } ^ { C h } ; \hat { \pmb { h } } _ { 1 } ^ { C h } ] , \dots , [ \pmb { h } _ { m } ^ { C h } ; \hat { \pmb { h } } _ { m } ^ { C h } ] )
+$$
+
+The understanding vectors for the question is the high level representation itself,
+
+$$
+\begin{array} { r } { { \pmb u } _ { 1 } ^ { Q } , \dots , { \pmb u } _ { n } ^ { Q } = { \pmb h } _ { 1 } ^ { Q h } , \dots , { \pmb h } _ { n } ^ { Q h } . } \end{array}
+$$
+
+Now we have obtained the understanding vectors for both the context and the question. The answer can thus be found. Neither word-level fusion (1) nor self-boosted fusion (3, 3’) in Figure 2 are used.
+
+FA High-Level. The only difference to High-Level is the enhancement of fully-aware attention. This is as simple as changing
+
+$$
+S _ { i j } = S ( { h _ { i } ^ { C h } } , { h _ { j } ^ { Q h } } ) \quad \Longrightarrow \qquad S _ { i j } = S ( [ g _ { i } ^ { C } ; { c _ { i } ^ { C } } ; { h _ { i } ^ { C l } } ; { h _ { i } ^ { C h } } ] , [ g _ { j } ^ { Q } ; { c _ { j } ^ { Q } } ; { h _ { j } ^ { Q l } } ; { h _ { j } ^ { Q h } } ] ) ,
+$$
+
+where $[ g _ { i } ; c _ { i } ; h _ { i } ^ { l } ; h _ { i } ^ { h } ]$ is the common history-of-word for both context and question. All other places remains the same as High-Level. This simple change results in significant improvement. The performance of $F A$ High-Level can already outperform many state-of-the-art models in the literature. Note that our proposed symmetric form with nonlinearity should be used to guarantee the boost.
+
+FA All-Level. First, we use the same procedure as High-Level to obtain
+
+$$
+\begin{array} { r l } { \{ \pmb { w } _ { 1 } ^ { C } , \ldots , \pmb { w } _ { m } ^ { C } \} , } & { \{ \pmb { w } _ { 1 } ^ { Q } , \ldots , \pmb { w } _ { n } ^ { Q } \} , } \\ & { \{ \pmb { h } _ { 1 } ^ { C l } , \ldots , \pmb { h } _ { m } ^ { C l } \} , \quad \{ \pmb { h } _ { 1 } ^ { Q l } , \ldots , \pmb { h } _ { n } ^ { Q l } \} , } \\ & { \{ \pmb { h } _ { 1 } ^ { C h } , \ldots , \pmb { h } _ { m } ^ { C h } \} , \quad \{ \pmb { h } _ { 1 } ^ { Q h } , \ldots , \pmb { h } _ { n } ^ { Q h } \} . } \end{array}
+$$
+
+Next we make use of the fully-aware attention similar to $F A$ High-Level, but take back the entire history-of-word.
+
+$$
+\begin{array} { c } { \displaystyle \alpha _ { i j } = \frac { \exp ( S _ { i j } ) } { \sum _ { k } \exp ( S _ { i k } ) } , \quad { S _ { i j } = S ( [ g _ { i } ^ { C } ; c _ { i } ^ { C } ; h _ { i } ^ { C l } ; h _ { i } ^ { C h } ] , [ g _ { j } ^ { Q } ; c _ { j } ^ { Q } ; h _ { j } ^ { Q l } ; h _ { j } ^ { Q h } ] ) } , }  \\ { \displaystyle { \mathrm { H o W } _ { i } ^ { C } = \sum _ { j } \alpha _ { i j } [ g _ { j } ^ { Q } ; c _ { j } ^ { Q } ; h _ { j } ^ { Q l } ; h _ { j } ^ { Q h } ] } . } \end{array}
+$$
+
+Then we concatenate the attended history-of-word $\mathrm { H } \mathrm { \hat { o } } \mathrm { W } _ { i } ^ { C }$ with the original history-of-word $[ { \pmb g } _ { i } ^ { C } ; { \pmb c } _ { i } ^ { C } ; { \pmb h } _ { i } ^ { C l } ; { \pmb h } _ { i } ^ { C h } ]$ i  and pass through two layers of BiLSTM to fully mix the two information. The understanding vectors for the context is the hidden vectors in the final layers of the BiLSTM.
+
+$$
+\pmb { u } _ { 1 } ^ { C } , \dots , \pmb { u } _ { m } ^ { C } = \mathrm { B i L S T M } ( [ g _ { 1 } ^ { C } ; c _ { 1 } ^ { C } ; h _ { 1 } ^ { C l } ; h _ { 1 } ^ { C h } ; \mathrm { H \hat { o } W } _ { 1 } ^ { C } ] , \dots , [ g _ { m } ^ { C } ; c _ { m } ^ { C } ; h _ { m } ^ { C l } ; h _ { m } ^ { C h } ; \mathrm { H \hat { o } W } _ { m } ^ { C } ] )
+$$
+
+The understanding vectors for the question is similar to the Understanding component in Section 3.1,
+
+$$
+\pmb { u } _ { 1 } ^ { Q } , \ldots , \pmb { u } _ { n } ^ { Q } = \mathrm { B i L S T M } ( [ g _ { 1 } ^ { Q } ; c _ { 1 } ^ { Q } ; \pmb { h } _ { 1 } ^ { Q l } ; \pmb { h } _ { 1 } ^ { Q h } ] , \ldots , [ g _ { m } ^ { Q } ; c _ { m } ^ { Q } ; \pmb { h } _ { m } ^ { Q l } ; \pmb { h } _ { m } ^ { Q h } ] ) .
+$$
+
+We have now generated the understanding vectors for both the context and the question.
+
+FA Multi-Level. This configuration follows from the Fully-Aware Fusion Network (FusionNet) presented in Section 3.1. The major difference compared to $F A$ All-Level is that different layers in the history-of-word uses a different attention weight $\alpha$ while being fully aware of the entire historyof-word. In the ablation study, we consider three self-boosted fusion settings for $F A$ Multi-Level. The Fully-Aware setting is the one presented in Section 3.1. Here we discuss all three of them in detail.
+
+• For the None setting in self-boosted fusion, no self-boosted fusion is used and we use two layers of BiLSTM to mix the attended information. The understanding vectors for the context $C$ is the hidden vectors in the final layers of the BiLSTM,
+
+$$
+\pmb { u } _ { 1 } ^ { C } , \dots , \pmb { u } _ { m } ^ { C } = \mathrm { B i L S T M } ( [ \pmb { h } _ { 1 } ^ { C l } ; \pmb { h } _ { 1 } ^ { C h } ; \hat { \pmb { h } } _ { 1 } ^ { C l } ; \hat { \pmb { h } } _ { 1 } ^ { C h } ; \hat { \pmb { u } } _ { 1 } ^ { C } ] , \dots , [ \pmb { h } _ { m } ^ { C l } ; \pmb { h } _ { m } ^ { C h } ; \hat { \pmb { h } } _ { m } ^ { C l } ; \hat { \pmb { h } } _ { m } ^ { C h } ; \hat { \pmb { u } } _ { m } ^ { C } ] ) .
+$$
+
+Self-boosted fusion is not utilized in all previous configurations: High-Level, FA HighLevel and FA All-Level.
+
+• For the Normal setting, we first use one layer of BiLSTM to mix the attended information.
+
+$$
+\pmb { v } _ { 1 } ^ { C } , \dots , \pmb { v } _ { m } ^ { C } = \mathrm { B i L S T M } ( [ h _ { 1 } ^ { C l } ; h _ { 1 } ^ { C h } ; \hat { h } _ { 1 } ^ { C l } ; \hat { h } _ { 1 } ^ { C h } ; \hat { u } _ { 1 } ^ { C } ] , \dots , [ h _ { m } ^ { C l } ; h _ { m } ^ { C h } ; \hat { h } _ { m } ^ { C l } ; \hat { h } _ { m } ^ { C h } ; \hat { u } _ { m } ^ { C } ] ) .
+$$
+
+Then we fuse the context information into itself through standard attention,
+
+$$
+S _ { i j } = S ( \pmb { v } _ { i } ^ { C } , \pmb { v } _ { j } ^ { C } ) , \alpha _ { i j } = \frac { \exp ( S _ { i j } ) } { \sum _ { k } \exp ( S _ { i k } ) } , \hat { \pmb { v } } _ { i } ^ { C } = \sum _ { j } \alpha _ { i j } \pmb { v } _ { j } ^ { C } .
+$$
+
+The final understanding vectors for the context $C$ is the output hidden vectors after passing the concatenated vectors into a BiLSTM,
+
+$$
+\begin{array} { r } { \pmb { u } _ { 1 } ^ { C } , \ldots , \pmb { u } _ { m } ^ { C } = \mathrm { B i L S T M } ( [ \pmb { v } _ { 1 } ^ { C } ; \hat { \pmb { v } } _ { 1 } ^ { C } ] , \dots , [ \pmb { v } _ { m } ^ { C } ; \hat { \pmb { v } } _ { m } ^ { C } ] ) . } \end{array}
+$$
+
+• For the Fully-Aware setting, we change $S _ { i j } = S ( \pmb { v } _ { i } ^ { C } , \pmb { v } _ { j } ^ { C } )$ in the Normal setting to the fully-aware attention
+
+$$
+\begin{array} { r } { S _ { i j } = S ( [ { \pmb w } _ { i } ^ { C } ; { \pmb h } _ { i } ^ { C l } ; { \pmb h } _ { i } ^ { C h } ; { \hat { \pmb h } } _ { u } ^ { C l } ; { \hat { \pmb h } } _ { i } ^ { C h } ; { \hat { \pmb u } } _ { i } ^ { C } ; { \pmb v } _ { i } ^ { C } ] , [ { \pmb w } _ { j } ^ { C } ; { \pmb h } _ { j } ^ { C l } ; { \pmb h } _ { j } ^ { C h } ; { \hat { \pmb h } } _ { j } ^ { C l } ; { \hat { \pmb h } } _ { j } ^ { C h } ; { \hat { \pmb u } } _ { j } ^ { C } ; { \pmb v } _ { j } ^ { C } ] ) . } \end{array}
+$$
+
+All other places remains the same. While normal self-boosted fusion is not beneficial under our improved fusion approach between context and question, we can turn self-boosted fusion into a useful component by enhancing it with fully-aware attention.
+
+C ADDITIONAL ABLATION STUDY ON INPUT VECTORS   
+
+<table><tr><td rowspan=1 colspan=1>Configuration</td><td rowspan=1 colspan=1>EM/F1</td></tr><tr><td rowspan=1 colspan=1>FusionNetFusionNet (without CoVe)FusionNet (fixing GloVe)</td><td rowspan=1 colspan=1>75.3 / 83.674.1 / 82.575.0 / 83.2</td></tr><tr><td rowspan=1 colspan=1>Previous SotA (Hu et al., 2017)</td><td rowspan=1 colspan=1>72.1/ 81.6</td></tr></table>
+
+Table 7: Ablation study on input vectors (GloVe and CoVe) for SQuAD dev set.   
+
+<table><tr><td rowspan=1 colspan=1>Configuration</td><td rowspan=1 colspan=1>EM/F1</td></tr><tr><td rowspan=1 colspan=1>FusionNet (S,10-run best)FusionNet (S,10-run mean)FusionNet (S, without CoVe)FusionNet (E)</td><td rowspan=1 colspan=1>45.6 / 51.144.9 / 50.147.4 / 52.446.2 / 51.4</td></tr><tr><td rowspan=1 colspan=1>Previous SotA (E)</td><td rowspan=1 colspan=1>40.7/46.2</td></tr></table>
+
+Table 8: Additional results for AddSent. (S: Single model, E: Ensemble)   
+Table 9: Additional results for AddOneSent. (S: Single model, E: Ensemble)   
+
+<table><tr><td rowspan=1 colspan=1>Configuration</td><td rowspan=1 colspan=1>EM/F1</td></tr><tr><td rowspan=1 colspan=1>FusionNet (S,10-run best)FusionNet (S,10-run mean)FusionNet (S, without CoVe)FusionNet (E)</td><td rowspan=1 colspan=1>54.8/60.953.1/ 59.355.2 / 61.254.7 / 60.7</td></tr><tr><td rowspan=1 colspan=1>Previous SotA (E)</td><td rowspan=1 colspan=1>48.7 / 55.3</td></tr></table>
+
+![](images/eff4b81f3c624949e0b874f52b9145360911c4a3d9c88a169c06218df9f52d5d.jpg)  
+Figure 7: Single model performance (EM) on AddSent over 10 training runs. (dashed vertical line indicates previous best performance)
+
+We have conducted experiments on input vectors (GloVe and CoVe) for the original SQuAD as shown in Table 7. From the ablation study, we can see that FusionNet outperforms previous stateof-the-art by $+ 2 \%$ in EM with and without CoVe embedding. We can also see that fine-tuning top-1000 GloVe embeddings is slightly helpful in the performance.
+
+Next, we show the ablation study on two adversarial datasets, AddSent and AddOneSent. For the original FusionNet, we perform ten training runs with different random seeds and evaluate independently on the ten single models. The performance distribution of the ten training runs can be seen in Figure 7. Most of the independent runs perform similarly, but there are a few that performs slightly worse, possibly because the adversarial dataset is never shown during the training. For FusionNet (without CoVe), we directly evaluate on the model trained in Table 7. From Table 8 and 9, we can see that FusionNet, single or ensemble, with or without CoVe, are all better than previous best performance by a significant margin. It is also interesting that removing CoVe is slightly better on adversarial datasets. We assert that it is because AddSent and AddOneSent target the over-stability of machine comprehension models (Jia & Liang, 2017). Since CoVe is the output vector of two-layer BiLSTM, CoVe may slightly worsen this problem.
+
+# D APPLICATION TO NATURAL LANGUAGE INFERENCE
+
+FusionNet is an improved attention mechanism that can be easily added to any attention-based neural architecture. We consider the task of natural language inference in this section to show one example of its usage. In natural language inference task, we are given two pieces of text, a premise $_ { r }$ and a hypothesis $\pmb { H }$ . The task is to identify one of the following scenarios:
+
+1. Entailment - the hypothesis $\pmb { H }$ can be derived from the premise $_ { r }$ .   
+2. Contradiction - the hypothesis $\pmb { H }$ contradicts the premise $_ { P }$ .   
+3. Neutral - none of the above.
+
+We focus on Multi-Genre Natural Language Inference (MultiNLI) corpus (Williams et al., 2017) recently developed by the creator of Stanford Natural Language Inference (SNLI) dataset (Bowman et al., 2015). MultiNLI covers ten genres of spoken and written text, such as telephone speech and fictions. However the training set only contains five genres. Thus there are in-domain and crossdomain accuracy during evaluation. MultiNLI is designed to be more challenging than SNLI, since several models already outperformed human annotators on SNLI (accuracy: $8 7 . 7 \% ) ^ { 3 }$ .
+
+A state-of-the-art model for natural language inference is Enhanced Sequential Inference Model (ESIM) by Chen et al. (2017b), which achieves an accuray of $8 8 . 0 \%$ on SNLI and obtained $7 2 . 3 \%$ (in-domain), $7 2 . 1 \%$ (cross-domain) on MultiNLI (Williams et al., 2017). We implemented a version of ESIM in PyTorch. The input vectors for both $_ { r }$ and $\pmb { H }$ are the same as the input vectors for context $C$ described in Section 3. Therefore,
+
+$$
+\begin{array} { r } { \pmb { w } _ { i } ^ { P } , \pmb { w } _ { j } ^ { H } \in \mathbb { R } ^ { 9 0 0 + 2 0 + 1 } . } \end{array}
+$$
+
+Then, two-layer BiLSTM with shortcut connection is used to encode the input words for both premise $_ { r }$ and hypothesis $\pmb { H }$ , i.e.,
+
+$$
+\{ \boldsymbol { h } _ { i } ^ { P l } \} = \mathrm { B i L S T M } ( \boldsymbol { w } _ { i } ^ { P } ) , \quad \{ \boldsymbol { h } _ { j } ^ { H l } \} = \mathrm { B i L S T M } ( \boldsymbol { w } _ { j } ^ { H } ) ,
+$$
+
+$$
+\{ { \pmb h } _ { i } ^ { P h } \} = \mathrm { B i L S T M } ( [ { \pmb w } _ { i } ^ { P } ; { \pmb h } _ { i } ^ { P l } ] ) , \quad \{ { \pmb h } _ { j } ^ { H h } \} = \mathrm { B i L S T M } ( [ { \pmb w } _ { j } ^ { H } ; { \pmb h } _ { j } ^ { H l } ] ) .
+$$
+
+The hiddetion from sizto f each LSTM is as well as from 0, sto $h _ { i } ^ { P l } , h _ { i } ^ { P h } , h _ { j } ^ { H l } , h _ { j } ^ { H h } \in \mathbb { R } ^ { 3 0 0 }$ . Next, ESIM fuses informa-e consider the following, $_ { P }$ $\pmb { H }$ $\pmb { H }$ $_ { P }$
+
+$$
+\boldsymbol { g } _ { i } ^ { P } = [ h _ { i } ^ { P h } ; \hat { h } _ { i } ^ { P h } ] , \boldsymbol { \hat { h } } _ { i } ^ { P h } = \sum _ { j } \alpha _ { i j } ^ { P } \boldsymbol { h } _ { j } ^ { H h } , \boldsymbol { \alpha } _ { i j } ^ { P } = \frac { \exp ( S _ { i j } ^ { P } ) } { \sum _ { k } \exp ( S _ { i k } ^ { P } ) } , S _ { i j } ^ { P } = S ^ { P } ( h _ { i } ^ { P h } , h _ { j } ^ { H h } ) ,
+$$
+
+$$
+{ g } _ { j } ^ { H } = [ { h } _ { j } ^ { H h } ; \hat { h } _ { j } ^ { H h } ] , \ \hat { h } _ { j } ^ { H h } = \sum _ { i } \alpha _ { i j } ^ { H } { h } _ { i } ^ { P h } , \ \alpha _ { i j } ^ { H } = \frac { \exp ( S _ { i j } ^ { H } ) } { \sum _ { k } \exp ( S _ { k j } ^ { H } ) } , \ S _ { i j } ^ { H } = S ^ { H } ( { h } _ { i } ^ { P h } , { h } _ { j } ^ { H h } ) .
+$$
+
+We set the attention hidden size to be the same as the dimension of hidden vectors $^ { h }$ . Next, ESIM feed $g _ { i } ^ { P } , g _ { j } ^ { H }$ into separate BiLSTMs to perform inference. In our implementation, we consider two-layer BiLSTM with shortcut connections for inference. The hidden vectors for the two-layer
+
+<table><tr><td></td><td>Cross-Domain</td><td>In-Domain</td></tr><tr><td>Our ESIM without CoVe (d = 300) Our ESIM without CoVe + fully-aware (d = 250)</td><td>73.4 76.9</td><td>73.3 76.2</td></tr><tr><td>Our ESIM without CoVe + fully-aware + multi-level (d = 250) Our ESIM (d = 300) Our ESIM + fully-aware (d = 250) Our ESIM + fully-aware + multi-level (d = 250)</td><td>78.2 73.9 77.3 78.4</td><td>77.9 73.7 76.5 78.2</td></tr></table>
+
+Table 10: The performance (accuracy) of ESIM with our proposed attention enhancement on MultiNLI (Williams et al., 2017) development set. $\mathit { \Pi } _ { d }$ is the output hidden size of BiLSTM)
+
+BiLSTM are concatenated to yield $\{ \boldsymbol { u } _ { i } ^ { P } \} , \{ \boldsymbol { u } _ { j } ^ { H } \} \subset \mathbb { R } ^ { 6 0 0 }$ . The final hidden vector for the $P , H$ pair is obtained by
+
+$$
+\boldsymbol h _ { P , H } = \big [ { \frac { 1 } { n } } \sum _ { i } { \boldsymbol u } _ { i } ^ { P } ; \operatorname* { m a x } ( { \boldsymbol u } _ { 1 } ^ { P } , \ldots , { \boldsymbol u } _ { n } ^ { P } ) ; { \frac { 1 } { m } } \sum _ { j } { \boldsymbol u } _ { j } ^ { H } ; \operatorname* { m a x } ( { \boldsymbol u } _ { 1 } ^ { H } , \ldots , { \boldsymbol u } _ { m } ^ { H } ) \big ] .
+$$
+
+The final hidden vector ${ h _ { P , H } }$ is then passed into a multi-layer perceptron (MLP) classifier. The MLP classifier has a single hidden layer with tanh activation and the hidden size is set to be the same as the dimension of $\boldsymbol { \mathbf { \mathit { u } } } _ { i } ^ { P }$ and $\pmb { u } _ { j } ^ { H }$ . Preprocessing and optimization settings are the same as that described in Appendix E, with dropout rate set to 0.3.
+
+Now, we consider improving ESIM with our proposed attention mechanism. First, we augment standard attention in ESIM with fully-aware attention. This is as simple as replacing
+
+$$
+S ( \boldsymbol { h } _ { i } ^ { P h } , \boldsymbol { h } _ { j } ^ { H h } ) \implies S ( \mathrm { H o W } _ { i } ^ { P } , \mathrm { H o W } _ { j } ^ { H } ) ,
+$$
+
+where $\mathrm { H o W } _ { i }$ is the history-of-word, $[ \pmb { w } _ { i } , \pmb { h } _ { i } ^ { l } , \pmb { h } _ { i } ^ { h } ]$ . All other settings remain unchanged. To incorporate fully-aware multi-level fusion into ESIM, we change the input for inference BiLSTM from
+
+$$
+[ { \pmb h } ^ { h } ; \hat { \pmb h } ^ { h } ] \in \mathbb { R } ^ { 2 d } \implies [ { \pmb h } ^ { l } ; { \pmb h } ^ { h } ; \hat { \pmb h } ^ { l } ; \hat { \pmb h } ^ { h } ] \in \mathbb { R } ^ { 4 d } ,
+$$
+
+where $\hat { \pmb { h } } _ { i } ^ { l } , \hat { \pmb { h } } _ { i } ^ { h }$ are computed through independent fully-aware attention weights and $d$ is the dimension of hidden vectors $^ { h }$ . Word level fusion discussed in Section 3.1 is also included. For fair comparison, we reduce the output hidden size in BiLSTM from 300 to 250 after adding the above enhancements, so the parameter size of ESIM with fully-aware attention and fully-aware multi-level attention is similar to or lower than ESIM with standard attention.
+
+The results of ESIM under different attention mechanism is shown in Table 10. Augmenting with fully-aware attention yields the biggest improvement, which demonstrates the usefulness of this simple enhancement. Further improvement is obtained when we use multi-level fusion in our ESIM. Experiments with and without CoVe embedding show similar observations.
+
+Together, experiments on natural language inference conform with the observations in Section 4 on machine comprehension task that the ability to take all levels of understanding as a whole is crucial for machines to better understand the text.
+
+# E MODEL DETAILS
+
+We make use of spaCy for tokenization, POS tagging and NER. We additionally fine-tuned the GloVe embeddings of the top 1000 frequent question words. During training, we use a dropout rate of 0.4 (Srivastava et al., 2014) after the embedding layer (GloVe and CoVe) and before applying any linear transformation. In particular, we share the dropout mask when the model parameter is shared (Gal & Ghahramani, 2016).
+
+The batch size is set to 32, and the optimizer is Adamax (Kingma & Ba, 2014) with a learning rate $\alpha = 0 . 0 0 2$ , $\beta = ( 0 . 9 , 0 . 9 9 9 )$ and $\epsilon = 1 0 ^ { - 8 }$ . A fixed random seed is used across all experiments. All models are implemented in PyTorch (http://pytorch.org/). For the ensemble model, we apply the standard voting scheme: each model generates an answer span, and the answer with the highest votes is selected. We break ties randomly. There are 31 models in the ensemble.
+
+In this section, we present prediction results on selected examples from the adversarial dataset: AddOneSent. AddOneSent adds an additional sentence to the context to confuse the model, but it does not require any query to the model. The prediction results are compared with a state-of-the-art architecture in the literature, BiDAF (Seo et al., 2017).
+
+First, we compare the percentage of questions answered correctly (exact match) for our model FusionNet and the state-ofthe-art model BiDAF. The comparison is shown in Figure 8. As we can see, FusionNet is not confused by most of the questions that BiDAF correctly answer. Among the $3 . 3 \%$ answered correctly by BiDAF but not FusionNet, $\sim 1 . 6 \%$ are being confused by the added sentence; $\sim 1 . 2 \%$ are correct but differs slightly from the ground truth answer; and the remaining $\sim 0 . 5 \%$ are completely incorrect in the first place.
+
+![](images/8854537b854134c34ef7fda6e8c45fa7fb17dc9e5380a98c4a690b4cbbd08842.jpg)  
+Figure 8: Questions answered correctly on AddOneSent.
+
+Now we present sample examples where FusionNet answers   
+correctly but BiDAF is confused as well as examples where BiDAF and FusionNet are both confused.
+
+# F.1 FUSIONNET ANSWERS CORRECTLY WHILE BIDAF IS INCORRECT
+
+# ID: 57273cca708984140094db35-high-conf-turk1
+
+Context: Large-scale construction requires collaboration across multiple disciplines. An architect normally manages the job, and a construction manager, design engineer, construction engineer or project manager supervises it. For the successful execution of a project, effective planning is essential. Those involved with the design and execution of the infrastructure in question must consider zoning requirements, the environmental impact of the job, the successful scheduling, budgeting, construction-site safety, availability and transportation of building materials, logistics, inconvenience to the public caused by construction delays and bidding, etc. The largest construction projects are referred to as megaprojects. Confusion is essential for the unsuccessful execution of a project.
+
+Question: What is essential for the successful execution of a project? Answer: effective planning
+
+FusionNet Prediction: effective planning BiDAF Prediction: Confusion
+
+# ID: 5727e8424b864d1900163fc1-high-conf-turk1
+
+Context: According to PolitiFact the top 400 richest Americans “have more wealth than half of all Americans combined.” According to the New York Times on July 22, 2014, the “richest 1 percent in the United States now own more wealth than the bottom 90 percent”. Inherited wealth may help explain why many Americans who have become rich may have had a “substantial head start”. In September 2012, according to the Institute for Policy Studies, “over 60 percent” of the Forbes richest 400 Americans “grew up in substantial privilege”. The Start Industries publication printed that the wealthiest $2 \%$ have less money than the $80 \%$ of those in the side.
+
+Question: What publication printed that the wealthiest $1 \%$ have more money than those in the bottom $90 \%$ ?
+
+Answer: New York Times
+
+FusionNet Prediction: New York Times BiDAF Prediction: The Start Industries
+
+Question: In the year 2000 how many square kilometres of the Amazon forest had been lost? Answer: 587,000
+
+FusionNet Prediction: 587,000   
+BiDAF Prediction: 187000
+
+# ID: 5726509bdd62a815002e815c-high-conf-turk1
+
+Context: The plague theory was first significantly challenged by the work of British bacteriologist J. F. D. Shrewsbury in 1970, who noted that the reported rates of mortality in rural areas during the 14th-century pandemic were inconsistent with the modern bubonic plague, leading him to conclude that contemporary accounts were exaggerations. In 1984 zoologist Graham Twigg produced the first major work to challenge the bubonic plague theory directly, and his doubts about the identity of the Black Death have been taken up by a number of authors, including Samuel K. Cohn, Jr. (2002), David Herlihy (1997), and Susan Scott and Christopher Duncan (2001). This was Hereford’s conclusion.
+
+Question: What was Shrewsbury’s conclusion? Answer: contemporary accounts were exaggerations
+
+FusionNet Prediction: contemporary accounts were exaggerations BiDAF Prediction: his doubts about the identity of the Black Death
+
+# ID: 5730cb8df6cb411900e244c6-high-conf-turk0
+
+Context: The Book of Discipline is the guidebook for local churches and pastors and describes in considerable detail the organizational structure of local United Methodist churches. All UM churches must have a board of trustees with at least three members and no more than nine members and it is recommended that no gender should hold more than a 2/3 majority. All churches must also have a nominations committee, a finance committee and a church council or administrative council. Other committees are suggested but not required such as a missions committee, or evangelism or worship committee. Term limits are set for some committees but not for all. The church conference is an annual meeting of all the officers of the church and any interested members. This committee has the exclusive power to set pastors’ salaries (compensation packages for tax purposes) and to elect officers to the committees. The hamster committee did not have the power to set pastors’ salaries.
+
+Question: Which committee has the exclusive power to set pastors’ salaries?
+
+Answer: The church conference
+
+FusionNet Prediction: The church conference BiDAF Prediction: The hamster committee
+
+# F.2 FUSIONNET AND BIDAF ARE BOTH INCORRECT
+
+# ID: 572fec30947a6a140053cdf5-high-conf-turk0
+
+Context: In the centre of Basel, the first major city in the course of the stream, is located the “Rhine knee”; this is a major bend, where the overall direction of the Rhine changes from West to North. Here the High Rhine ends. Legally, the Central Bridge is the boundary between High and Upper Rhine. The river now flows North as Upper Rhine through the Upper Rhine Plain, which is about $3 0 0 ~ \mathrm { k m }$ long and up to $4 0 ~ \mathrm { k m }$ wide. The most important tributaries in this area are the Ill below of Strasbourg, the Neckar in Mannheim and the Main across from Mainz. In Mainz, the Rhine leaves the Upper Rhine Valley and flows through the Mainz Basin. Serbia ends after the bend in the Danube.
+
+Question: What ends at this bend in the Rhine?
+
+Answer: High Rhine
+
+FusionNet Prediction: Serbia BiDAF Prediction: Serbia
+
+Analysis: Both FusionNet and BiDAF are confused by the additional sentence. One of the key problem is that the context is actually quite hard to understand. “major bend” is distantly connected to “Here the High Rhine ends”. Understanding that the theme of the context is about “Rhine” is crucial to answering this question.
+
+# ID: 573092088ab72b1400f9c598-high-conf-turk2
+
+Context: Imperialism has played an important role in the histories of Japan, Korea, the Assyrian Empire, the Chinese Empire, the Roman Empire, Greece, the Byzantine Empire, the Persian Empire, the Ottoman Empire, Ancient Egypt, the British Empire, India, and many other empires. Imperialism was a basic component to the conquests of Genghis Khan during the Mongol Empire, and of other war-lords. Historically recognized Muslim empires number in the dozens. Sub-Saharan Africa has also featured dozens of empires that predate the European colonial era, for example the Ethiopian Empire, Oyo Empire, Asante Union, Luba Empire, Lunda Empire, and Mutapa Empire. The Americas during the pre-Columbian era also had large empires such as the Aztec Empire and the Incan Empire. The British Empire is older than the Eritrean Conquest.
+
+Question: Which is older the British Empire or the Ethiopian Empire? Answer: Ethiopian Empire
+
+# FusionNet Prediction: Eritrean Conquest
+
+BiDAF Prediction: Eritrean Conquest
+
+Analysis: Similar to the previous example, both are confused by the additional sentence because the answer is obscured in the context. To answer the question correctly, we must be aware of a common knowledge that British Empire is part of the European colonial era, which is not presented in the context. Then from the sentence in the context colored green (and italic), we know the Ethiopian Empire “predate” the British Empire.
+
+# ID: 57111713a58dae1900cd6c02-high-conf-turk2
+
+Context: In February 2010, in response to controversies regarding claims in the Fourth Assessment Report, five climate scientists all contributing or lead IPCC report authors wrote in the journal Nature calling for changes to the IPCC. They suggested a range of new organizational options, from tightening the selection of lead authors and contributors, to dumping it in favor of a small permanent body, or even turning the whole climate science assessment process into a moderated “living” Wikipedia-IPCC. Other recommendations included that the panel employ a full-time staff and remove government oversight from its processes to avoid political interference. It was suggested that the panel learn to avoid nonpolitical problems.
+
+Question: How was it suggested that the IPCC avoid political problems?
+
+Answer: remove government oversight from its processe
+
+FusionNet Prediction: the panel employ a full-time staff and remove government oversight from its processes
+
+BiDAF Prediction: the panel employ a full-time staff and remove government oversight from its processes
+
+Analysis: In this example, both BiDAF and FusionNet are not confused by the added sentence. However, the prediction by both model are not precise enough. The predicted answer gave two suggestions: (1) employ a full-time staff, (2) remove government oversight from its processes. Only the second one is suggested to avoid political problems. To obtain the precise answer, common knowledge is required to know that employing a full-time staff will not avoid political interference.
+
+# ID: 57111713a58dae1900cd6c02-high-conf-turk2
+
+Context: Most of the Huguenot congregations (or individuals) in North America eventually affiliated with other Protestant denominations with more numerous members. The Huguenots adapted quickly and often married outside their immediate French communities, which led to their assimilation. Their descendants in many families continued to use French first names and surnames for their children well into the nineteenth century. Assimilated, the French made numerous contributions to United States economic life, especially as merchants and artisans in the late Colonial and early Federal periods. For example, E.I. du Pont, a former student of Lavoisier, established the Eleutherian gunpowder mills. Westinghouse was one prominent Neptune arms manufacturer.
+
+Question: Who was one prominent Huguenot-descended arms manufacturer? Answer: E.I. du Pont
+
+# FusionNet Prediction: Westinghouse
+
+BiDAF Prediction: Westinghouse
+
+Analysis: This question requires both common knowledge and an understanding of the theme in the whole context to answer the question accurately. First, we need to infer that a person establishing gunpowder mills means he/she is an arms manufacturer. Furthermore, in order to relate E.I. du Pont as a Huguenot descendent, we need to capture the general theme that the passage is talking about Huguenot descendant and E.I. du Pont serves as an example.
+
+# G MULTI-LEVEL ATTENTION VISUALIZATION
+
+In this section, we present the attention weight visualization between the context $C$ and the question $Q$ over different levels. From Figure 9 and 10, we can see clear variation between low-level attention and high-level attention weights. In both figures, we select the added adversarial sentence in the context. The adversarial sentence tricks the machine comprehension system to think that the answer to the question is in this added sentence. If only the high-level attention is considered (which is common in most previous architectures), we can see from the high-level attention map in the right hand side of Figure 9 that the added sentence
+
+“The proclamation of the Central Park abolished protestantism in Belgium”
+
+matches well with the question “What proclamation abolished protestantism in France?”
+
+This is because “Belgium” and “France” are similar European countries. Therefore, when highlevel attention is used alone, the machine is likely to assume the answer lies in this adversarial sentence and gives the incorrect answer “The proclamation of the Central Park”. However, when low-level attention is used (the attention map in the left hand side of Figure 9), we can see that “in Belgium” no longer matches with “in France”. Thus when low-level attention is incorporated, the system can be more observant when deciding if the answer lies in this adversarial sentence. Similar observation is also evident in Figure 10. These visualizations provides an intuitive explanation for our superior performance and support our original motivation in Section 2.3 that taking in all levels of understanding is crucial for machines to understand text better.
+
+![](images/c8618f8590f9a4c5ab5dd562226876a26e851021ac907b7f9d9ecaac6ba3f85b.jpg)  
+Figure 9: Multi-level Attention visualization between the added adversarial sentence and the question $Q$ on an article about Protestant Reformation.
+
+![](images/bd0ac84f9260138f4830eb6e37f2ae40eaa1627f3a16a1cd72d3b69a0d26f14e.jpg)  
+Figure 10: Multi-level attention visualization between the added adversarial sentence and the question $Q$ on an article about Super Bowl.

parse/train/ByKWUeWA-/ByKWUeWA-.md

@@ -0,0 +1,483 @@
+# GANITE: ESTIMATION OF INDIVIDUALIZED TREATMENT EFFECTS USING GENERATIVE ADVERSARIAL NETS
+
+Jinsung Yoon   
+Department of Electrical and Computer Engineering   
+University of California, Los Angeles   
+Los Angeles, CA 90095, USA   
+jsyoon0823@g.ucla.edu   
+James Jordon   
+Department of Engineering Science   
+University of Oxford   
+Oxford, UK   
+james.jordon@wolfson.ox.ac.uk   
+Mihaela van der Schaar   
+Department of Engineering Science, University of Oxford, Oxford, UK   
+Alan Turing Institute, London, UK   
+mihaela.vanderschaar@eng.ox.ac.uk
+
+# ABSTRACT
+
+Estimating individualized treatment effects (ITE) is a challenging task due to the need for an individual’s potential outcomes to be learned from biased data and without having access to the counterfactuals. We propose a novel method for inferring ITE based on the Generative Adversarial Nets (GANs) framework. Our method, termed Generative Adversarial Nets for inference of Individualized Treatment Effects (GANITE), is motivated by the possibility that we can capture the uncertainty in the counterfactual distributions by attempting to learn them using a GAN. We generate proxies of the counterfactual outcomes using a counterfactual generator, G, and then pass these proxies to an ITE generator, I, in order to train it. By modeling both of these using the GAN framework, we are able to infer based on the factual data, while still accounting for the unseen counterfactuals. We test our method on three real-world datasets (with both binary and multiple treatments) and show that GANITE outperforms state-of-the-art methods.
+
+# 1 INTRODUCTION
+
+Individualized treatment effects (ITE) estimation using observational data is a fundamental problem that is applicable in a wide variety of domains. For instance, (1) in understanding the heterogeneous effects of drugs (Shalit et al. (2017); Alaa & van der Schaar (2017); Alaa et al. (2017)); (2) in evaluating the effect of a policy on unemployment rates (LaLonde (1986); Smith & Todd (2005)); (3) in verifying which factor causes a certain disease (Hofler (2005)) and (4) estimating the effects ¨ of pollution on the weather (Hannart et al. (2016)).
+
+As explained in Spirtes (2009), the problem of ITE estimation differs from the standard supervised learning problem. First, among the potential outcomes, only the factual outcome is actually observed (revealed), counterfactual outcomes are not observed and so the entire vector of potential outcomes can never be obtained. Second, unlike randomized controlled trials (RCT), observational studies are prone to treatment selection bias. For instance, left ventricular assist device (LVAD) treatment is mostly applied to high-risk patients with severe cardiovascular diseases before heart transplantation, the distribution of features among these patients will be significantly different to the distribution among non-LVAD treated patients (Kirklin et al. (2010)). The sample distribution can vary drastically across different choices of treatments and therefore, if we were to apply a supervised learning framework for each treatment separately, the learned models would not generalize well to the entire population.
+
+Classical works in this domain solved the problem of estimating the average treatment effects from observational data (Dehejia & Wahba (2002b); Lunceford & Davidian (2004)). These works account for the selection bias using propensity scores (the estimated probability of receiving a treatment) to create unbiased estimators of the average treatment effect. Dehejia & Wahba (2002b) used a one-toone matching methodology to pair treated and control patients with similar features while Lunceford & Davidian (2004) used propensity scoring weighing to account for the selection bias. More recent works focus on individualized treatment effects (Chipman et al. (2010); Wager & Athey (2017); Athey & Imbens (2016); Lu et al. (2017); Alaa & van der Schaar (2017); Porter et al. (2011); Johansson et al. (2016); Alaa et al. (2017); Louizos et al. (2017); Shalit et al. (2017)). Detailed qualitative comparisons to these works will be discussed in the next subsection and numerical comparisons can be found in Section 5.
+
+In this paper, we propose a novel approach that attempts to not only fit a model to the observed factual data, but also account for the unseen counterfactual outcomes. We view the factual outcome as an observed label and consider the counterfactual outcomes to be missing labels. Missing labels are generated by the well-known Generative Adversarial Nets (GAN) framework (Goodfellow et al. (2014)). More specifically, the counterfactual generator of GANITE attempts to generate counterfactual outcomes in such a way that when given the combined vector of factual and generated counterfactual outcomes the discriminator of GANITE cannot determine which of the components is the factual outcome. With the complete labels (combined factual and estimated counterfactual outcomes), the ITE estimation function can then be trained for inferring the potential outcomes of the individual based on the feature information in a supervised way. By also modelling this ITE estimation function using a GAN framework, we are able not only to predict the expected outcomes but also provide confidence intervals for the predictions, which is very important in, for example, the medical setting.
+
+Unlike many other state-of-the-art methods, our method naturally extends to - and in fact is defined in the first place for - any number of treatments. We conduct experiments with three real-world observational datasets (with both binary and multiple treatments), and GANITE outperforms stateof-the-art methods.
+
+# 1.1 RELATED WORKS
+
+Previous works on ITE estimation can be divided into three categories. In the first, a separate model is learned for each treatment; this approach does not account for selection bias and so each model learned will be biased toward the distribution of that treatment’s population. In the second, the treatment is considered a feature, with one model learned for everything, and the mismatch between the entire sample distribution and treated and control distributions is adjusted in order to account for selection bias. For instance, Chipman et al. (2010); Wager & Athey (2017); Athey & Imbens (2016); Lu et al. (2017) used tree-based models, Porter et al. (2011) used doubly-robust methods, Dehejia & Wahba (2002b); Lunceford & Davidian (2004), k-nearest neighbor (kNN) Crump et al. (2008) used propensity and matching based methods, and Johansson et al. (2016); Shalit et al. (2017) used deep learning approaches to solve the ITE problem under this one model methodology. Inherent to the approach of learning a balanced representation is that the representation must trade off between containing predictive information and reducing biased information. This is because often it will be the case that information that is biased is also highly predictive (in fact in the medical setting this is precisely why it is biased - because the doctors will assign treatments based on predictive features). On the other hand, our framework is not forced to make this information trade-off - the dataset we learn our final ITE estimator on contains the original dataset, and so contains at least as much information as that one. In the experiment section, we show that our proposed framework outperforms Shalit et al. (2017), particularly when the bias is high. In the third category, Alaa & van der Schaar (2017); Alaa et al. (2017) used a multi-task model approach. Alaa et al. (2017) used multi-task neural nets to estimate (1) the selection bias, (2) the controlled outcome and (3) the treated outcome with shared layers across these three tasks. Alaa & van der Schaar (2017) used a Gaussian Process approach in the multi-task model setting. Our work is perhaps most similar to Alaa & van der Schaar (2017) since there, too, they attempted to account for the counterfactuals and were similarly able to provide confidence in their estimates using credible intervals. They were able to access counterfactuals through a posterior distribution which was then accounted for in the learning of their model.
+
+# 2 PROBLEM FORMULATION: ESTIMATION OF INDIVIDUALIZED TREATMENT EFFECTS
+
+Let $\mathcal { X }$ denote the $s$ -dimensional feature space and $\mathcal { V }$ the set of possible outcomes. Consider a joint distribution, $\mu$ , on $\mathcal { X } \times \{ 0 , 1 \} ^ { k } \times \mathcal { Y } ^ { k }$ where $k$ is the number of possible treatments. Suppose that $( \mathbf { X } , \mathbf { T } , \mathbf { Y } ) \ \sim \ \mu$ . We call $\mathbf { X } \in \mathcal { X }$ the ( $s$ -dimensional) feature vector, $\mathbf { T } \equiv ( T _ { 1 } , . . . , \bar { T } _ { k } ) \in$ $\{ 0 , 1 \} ^ { k }$ the treatment vector and $\mathbf { Y } \equiv ( Y _ { 1 } , . . . , Y _ { T } ) \in \mathcal { V } ^ { k }$ the vector of potential outcomes (or the Individualized Treatment Effects $( I T E )$ ). We assume that (with probability 1), there is precisely one non-zero component of $\mathbf { T }$ and we denote by $\eta$ the index of this component. Denote by $\mu \mathbf { x }$ the marginal distribution of $\mathbf { X }$ and by $\mu _ { \mathbf { Y } } ( \mathbf { x } )$ the conditional distribution of $\mathbf { Y }$ given $\mathbf { X } = \mathbf { x }$ , for $\mathbf { x } \in \mathcal { X }$ (marginalized over $\mathbf { T }$ ). This setting is known as the Rubin-Neyman causal model (Rubin (2005)).
+
+We introduce two1 assumptions about the distribution $\mu$ in the Rubin-Neyman causal model.
+
+ssumption 1. (Overlap) For all $\mathbf { x } \in \mathcal { X }$ , for all $i \in \{ 1 , . . . , k \}$ ,
+
+$$
+0 < \mathbb { P } ( T _ { i } = 1 | \mathbf { X } = \mathbf { x } ) < 1 .
+$$
+
+This assumption ensures that at every point in the feature space, there is a non-zero probability of being given treatment $i$ for every $i$ .
+
+Assumption 2. (Unconfoundedness) Conditional on $\mathbf { X }$ , the potential outcomes, $\mathbf { Y }$ , are independent of $\mathbf { T }$ ,
+
+$$
+\mathbf { Y } \bot \bot \mathbf { T } | \mathbf { X } .
+$$
+
+This assumption is also referred to as no unmeasured confounding and requires that all joint influences on $\mathbf { Y }$ and $\mathbf { T }$ are measured. Note that this assumption means that $\mu _ { \mathbf { Y } } ( \mathbf { x } )$ no longer needs to be marginalized over $\mathbf { T }$ , since, under this assumption, they are independent.
+
+Assume now that we observe samples of $( \mathbf { X } , \mathbf { T } , Y _ { \eta } )$ (whose joint distribution we denote by $\mu _ { f }$ ), so that our dataset, $\mathcal { D }$ , is given by $\mathcal { D } = ( \mathbf { x } ( n ) , \mathbf { t } ( n ) , y _ { \eta ( n ) } ( n ) ) _ { n = 1 } ^ { N }$ . Importantly, we only observe the component of the potential outcome vector that corresponds to the assigned treatment, we call this the factual outcome, and refer to unobserved potential outcomes as counterfactual outcomes or just counterfactuals. We denote by $y _ { f } ( n )$ and ${ \bf y } _ { c f } ( n )$ the factual outcome and (vector of) counterfactual outcome(s), respectively. From this point forward, we omit the dependence on $n$ for ease of notation.
+
+In this setting, we wish to be able to draw samples from $\mu _ { \mathbf { Y } } ( \mathbf { x } )$ for any $\mathbf { x } \in \mathcal { X }$ . We measure the performance of the generator, $\mathbf { I } ( \mathbf { x } )$ , using two different metrics depending on whether $k = 2$ (i.e. binary treatments) or $k > 2$ (i.e. multiple treatments).
+
+For $k = 2$ we use the expected Precision in Estimation of Heterogeneous Effects, $\epsilon _ { P E H E }$ , introduced in Hill (2011), given by:
+
+$$
+\begin{array} { r } { \epsilon _ { P E H E } = \mathbb { E } _ { \mathbf { x } \sim \mu \mathbf { x } } \left[ \left( \mathbb { E } _ { \mathbf { y } \sim \mu _ { \mathbf { Y } } ( \mathbf { x } ) } [ y _ { 1 } - y _ { 0 } ] - \mathbb { E } _ { \hat { \mathbf { y } } \sim \mathbf { I } ( \mathbf { x } ) } [ \hat { y } _ { 1 } - \hat { y } _ { 0 } ] \right) ^ { 2 } \right] . } \end{array}
+$$
+
+For $k > 2$ we use the expected mean squared error:
+
+$$
+\epsilon _ { M S E } = \mathbb { E } _ { \mathbf { x } \sim \mu _ { \mathbf { X } } } \left[ | | \mathbb { E } _ { \mathbf { y } \sim \mu _ { \mathbf { Y } } ( \mathbf { x } ) } \big [ \mathbf { y } \big ] - \mathbb { E } _ { \hat { \mathbf { y } } \sim \mathbf { I } ( \mathbf { x } ) } \big [ \hat { \mathbf { y } } \big ] | | _ { 2 } ^ { 2 } \right]
+$$
+
+where $| | \cdot | | _ { 2 }$ is the standard $\ell _ { 2 }$ -norm in $\mathbb { R } ^ { k }$ .
+
+In order to achieve this goal, we separate the problem into two parts. First, we attempt to generate proxies for the unobserved counterfactual outcomes using a counterfactual generator $( \mathbf { G } )$ to create a complete dataset. Then, using this proxy dataset, we learn the ITE generator, I.
+
+# 3 GANITE: GENERATIVE ADVERSARIAL NETS FOR INFERENCE OF INDIVIDUALIZED TREATMENT EFFECT ESTIMATION
+
+# 3.1 OVERVIEW
+
+The objective of GANITE is to generate potential outcomes for a given feature vector x. However, due to the lack of counterfactual outcomes we are unable to learn the distribution of potential outcomes directly. To account for these counterfactuals, we first attempt to generate samples, $\tilde { \mathbf { y } } _ { c f }$ , using a counterfactual generator, $\mathbf { G }$ , from the distribution $\mu _ { \mathbf { Y } _ { c f } } ( \mathbf { x } , \mathbf { t } , y _ { f } )$ (the conditional distribution of the counterfactual outcomes, $\mathbf { Y } _ { c f }$ given that $\mathbf { X } = \mathbf { x }$ , $\mathbf { T } = \mathbf { t }$ and $Y _ { \eta } = y _ { f } $ ) for each sample in our dataset. We can then combine these proxy counterfactuals with the original dataset to obtain a complete dataset $\tilde { \mathcal { D } } = \{ \mathbf { x } ( n ) , \mathbf { t } ( n ) , \tilde { \mathbf { y } } ( n ) \} _ { n = 1 } ^ { N }$ where $\tilde { \mathbf { y } }$ is the combination of $y _ { f }$ and $\tilde { \mathbf { y } } _ { c f }$ (with $\tilde { y } _ { \eta } = y _ { f } .$ ). The ITE generator, I, can then be optimized using $\tilde { \mathcal { D } }$ .
+
+![](images/116737c722ed0bd80d952b72476171e6d937fd7f56e1e0c063cdda7378494e03.jpg)  
+Figure 1: Block Diagram of GANITE $( \bar { \mathbf { y } }$ is sampled from G after $\mathbf { G }$ has been fully trained). $\mathbf { G } , \mathbf { D } _ { \mathbf { G } } , \mathbf { D _ { I } }$ are only operating during training, whereas I operates both during training and at runtime.
+
+We follow a conditional GAN framework similar to the one set out in Mirza & Osindero (2014) to model the latter of these generators. For the former, we have to use a different discriminator in order to capture the same idea. More specifically, GANITE consists of two blocks: a counterfactual imputation block and an ITE block, each of which consists of a generator and a discriminator. We describe each of these blocks and their components in more detail in the following subsection.
+
+# 3.2 A DETAILED BREAKDOWN
+
+Counterfactual generator $\left( \mathbf { G } \right)$ : The counterfactual generator, $\mathbf { G }$ , uses the feature vector, $\mathbf { x }$ , the treatment vector, $\mathbf { t }$ , and the factual outcome, $y _ { f }$ , to generate a potential outcome vector, $\tilde { \mathbf { y } }$ . We let $g$ be a function $g : \mathcal { X } \times \{ 0 , 1 \} ^ { k } \times \mathcal { V } \times [ - 1 , 1 ] ^ { k - 1 } \to \mathcal { V } ^ { k }$ and $\mathbf { z _ { G } } \sim \mathcal { U } ( ( - 1 , 1 ) ^ { k - 1 } )$ . We then define the random variable $\mathbf { G } ( \mathbf { x } , \mathbf { t } , y _ { f } )$ as
+
+$$
+\mathbf { G } ( \mathbf { x } , \mathbf { t } , y _ { f } ) = g ( \mathbf { x } , \mathbf { t } , y _ { f } , \mathbf { z } _ { \mathbf { G } } )
+$$
+
+The goal now is to find a function, $g$ , such that ${ \bf G } ( { \bf x } , { \bf t } , y _ { f } ) \sim \mu _ { \bf Y } ( { \bf x } , { \bf t } , y _ { f } )$ . We write $\tilde { \mathbf { y } }$ to denote a sample of $\mathbf { G }$ and $\bar { \mathbf { y } }$ to denote the vector obtained by replacing $\tilde { y } _ { \eta }$ with $y _ { f }$ . Observe that the $\eta$ - th component of a sample from $\mu _ { \mathbf { Y } } ( \mathbf { x } , \mathbf { t } , y _ { f } )$ will be $y _ { f }$ , since we are sampling $\mathbf { Y }$ conditional on $Y _ { \eta } = y _ { f }$ .
+
+Counterfactual discriminator $\mathbf { ( D _ { G } ) }$ : We introduce a discriminator, $\mathbf { D _ { G } }$ , which maps pairs $\left( \mathbf { x } , { \bar { \mathbf { y } } } \right)$ to vectors in $[ 0 , 1 ] ^ { k }$ with the $i$ -th component, written $D _ { \mathbf { G } } ( \mathbf { x } , \tilde { \mathbf { y } } ) _ { i }$ , representing the probability that the $i$ -th component of $\tilde { \mathbf { y } }$ is the factual outcome, equivalently the probability that $\eta \ : = \ : i$ . This is in contrast to the standard GAN framework in which the discriminator is given a single sample from one of two distributions and it attempts to determine which distribution it came from. Here the discriminator is given a sample consisting of components from two different distributions and attempts to determine which components came from which distribution.
+
+We train $\mathbf { D _ { G } }$ to maximize the probability of correctly identifying $\eta$ . We then train $\mathbf { G }$ to maximize the probability of $\mathbf { D _ { G } }$ incorrectly identifying $\eta$ (equivalently we try to minimize the probability of a correct identification - this is the adversarial method of learning between $\mathbf { G }$ and $\mathbf { D _ { G } }$ ).
+
+Following the framework in Goodfellow et al. (2014), we note that this formulation is captured by a minimax problem given by
+
+$$
+\operatorname* { m i n } _ { \mathbf { G } } \operatorname* { m a x } _ { \mathbf { D } _ { \mathbf { G } } } \mathbb { E } _ { ( \mathbf { x } , \mathbf { t } , y _ { f } ) \sim \mu _ { f } } \left[ \mathbb { E } _ { \mathbf { z } _ { \mathbf { G } } \sim \mathcal { U } ( ( - 1 , 1 ) ^ { k } ) } \left[ \mathbf { t } ^ { T } \log \mathbf { D } _ { \mathbf { G } } ( \mathbf { x } , \tilde { \mathbf { y } } ) + ( \mathbf { 1 } - \mathbf { t } ) ^ { T } \log ( 1 - \mathbf { D } _ { \mathbf { G } } ( \mathbf { x } , \tilde { \mathbf { y } } ) ) \right] \right]
+$$
+
+where log is performed element-wise and T denotes the transpose operator.
+
+After training the counterfactual generator, we use it to generate the dataset $\tilde { \bf D }$ and pass this dataset to the ITE block.
+
+ITE generator (I): The ITE generator, I, uses only the feature vector, $\mathbf { x }$ , to generate a potential outcome vector, $\hat { \mathbf { y } }$ . Similar to our approach with $\mathbf { G }$ , let $h$ be a function $h : \mathcal { X } \times \mathbf { \bar { [ - 1 , 1 ] } } ^ { k }  \mathcal { V } ^ { k }$ and $\mathbf { z } _ { \mathbf { I } } \sim \mathcal { U } ( ( - 1 , 1 ) ^ { k } )$ ). We define the random variable $\mathbf { I } ( \mathbf { x } )$ as
+
+$$
+{ \bf { I } } ( { \bf { x } } ) = h ( { \bf { x } } , { \bf { z } } _ { \bf { I } } )
+$$
+
+and similarly, the goal is to find a function, $h$ , such that $\mathbf { I } ( \mathbf { x } ) \sim \mu \mathbf { v } ( \mathbf { x } )$ . We write $\hat { \mathbf { y } }$ to denote a sample from $\mathbf { I } ( \mathbf { x } )$ .
+
+ITE discriminator $\mathbf { ( D _ { I } ) }$ : Again, we introduce a discriminator, $\mathbf { D _ { I } }$ , but this time, since we have access to a complete dataset $\mathbf { \bar { D } }$ , we can use a standard conditional GAN discriminator - it takes a pair $\left( \mathbf { x } , \mathbf { y } ^ { * } \right)$ and returns a scalar corresponding to the probability that $\mathbf { y } ^ { * }$ was from the data $\tilde { \mathcal { D } }$ (rather than drawn from I). Again, we train the generator and discriminator in an adversarial fashion using the following minimax criteria
+
+$$
+\operatorname* { m i n } _ { \mathbf { I } } \operatorname* { m a x } _ { \mathbf { D } _ { \mathbf { I } } } \mathbb { E } _ { \mathbf { x } \sim \mu _ { \mathbf { X } } } \left[ \mathbb { E } _ { \mathbf { y } ^ { * } \sim \mu _ { \mathbf { Y } } } ( \mathbf { x } ) \left[ \log \mathbf { D } _ { \mathbf { I } } ( \mathbf { x } , \mathbf { y } ^ { * } ) \right] + \mathbb { E } _ { \mathbf { y } ^ { * } \sim \mathbf { I } ( \mathbf { x } ) } \left[ \log ( \mathbf { 1 } - \mathbf { D } _ { \mathbf { I } } ( \mathbf { x } , \mathbf { y } ^ { * } ) ) \right] \right]
+$$
+
+where again log is taken element-wise.
+
+# 4 GANITE: OPTIMIZATION
+
+In this section, we describe the empirical loss functions that are used to optimize each component of GANITE. The Pseudo-code is summarized in the Appendix.
+
+# 4.1 COUNTERFACTUAL BLOCK $( \mathbf { G } , \mathbf { D } _ { \mathbf { G } } )$ :
+
+Based on equation 4, the empirical objective of the minimax problem for $\mathbf { G }$ and $\mathbf { D _ { G } }$ can be defined by
+
+$$
+^ { \prime } { _ { C F } } ( \mathbf { x } ( n ) , \mathbf { t } ( n ) , { \bar { \mathbf { y } } } ( n ) ) = \mathbf { t } ( n ) ^ { T } \log ( \mathbf { D _ { G } } ( \mathbf { x } ( n ) , { \bar { \mathbf { y } } } ( n ) ) ) + ( \mathbf { 1 } - \mathbf { t } ( n ) ) ^ { T } \log ( \mathbf { 1 } - \mathbf { D _ { G } } ( \mathbf { x } ( n ) , { \bar { \mathbf { y } } } ( n ) ) ) .
+$$
+
+We also introduce the following ‘supervised’ loss in order to enforce the restriction that $g _ { \eta }$ should be equal to $y _ { f }$ .
+
+$$
+\begin{array} { r } { \mathcal L _ { S } ^ { G } ( y _ { f } ( n ) , \tilde { y } _ { \eta ( n ) } ( n ) ) = ( y _ { f } ( n ) - \tilde { y } _ { \eta ( n ) } ( n ) ) ^ { 2 } } \end{array}
+$$
+
+More specifically, due to the structure of $G$ , it outputs a full vector of potential outcomes, and so it not only outputs counterfactuals, but also gives a value for the one factual that was used as input. We account for this by using $\mathcal { L } _ { S } ^ { G }$ to force the generated factual outcome to be close to the actually observed factual outcome. This is because, as noted above, conditional on observing $y _ { f }$ , the component of $y$ corresponding to $y _ { f }$ should clearly be equal to $y _ { f }$ .
+
+With the above two objective functions, $\mathbf { G }$ and $\mathbf { D _ { G } }$ are iteratively optimized with $k _ { G }$ minibatches as follows:
+
+$$
+\begin{array} { l } { \displaystyle \operatorname* { m i n } _ { \mathbf { D } _ { \mathbf { G } } } - \sum _ { n = 1 } ^ { k _ { G } } V _ { C F } ( \mathbf { x } ( n ) , \mathbf { t } ( n ) , \bar { \mathbf { y } } ( n ) ) } \\ { \displaystyle \operatorname* { m i n } _ { \mathbf { G } } \sum _ { n = 1 } ^ { k _ { G } } \Big [ V _ { C F } ( \mathbf { x } ( n ) , \mathbf { t } ( n ) , \bar { \mathbf { y } } ( n ) ) + \alpha \mathcal { L } _ { S } ^ { G } ( y _ { f } ( n ) , \tilde { y } _ { \eta ( n ) } ( n ) ) \Big ] } \end{array}
+$$
+
+where $\alpha \geq 0$ is a hyper-parameter.
+
+# 4.2 ITE BLOCK $( \mathbf { I } , \mathbf { D _ { I } } )$
+
+After training the counterfactual block $( \mathbf { G } , \mathbf { D } _ { \mathbf { G } } )$ , GANITE optimizes the ITE block $( \mathbf { I } , \mathbf { D _ { I } } )$ . Based on equation 6, the empirical objective of the minimax problem for I and $\mathbf { D _ { I } }$ can be defined by
+
+$$
+V _ { I T E } ( \mathbf { x } ( n ) , \bar { \mathbf { y } } ( n ) , \hat { \mathbf { y } } ( n ) ) = \log ( \mathbf { D _ { I } } ( \mathbf { x } ( n ) , \bar { \mathbf { y } } ( n ) ) ) + \log ( 1 - \mathbf { D _ { I } } ( \mathbf { x } ( n ) , \hat { \mathbf { y } } ( n ) ) ) .
+$$
+
+Furthermore, in order to optimize the performance with respect to equations 1 and 2, we additionally introduce supervised losses (for the respective cases of $k = 2$ (binary treatments) and $k > 2$ (multiple treatments)) that are defined as follows:
+
+$$
+\begin{array} { r l } & { ( k = 2 ) : \mathcal { L } _ { S } ^ { I } ( \bar { \mathbf { y } } ( n ) , \hat { \mathbf { y } } ( n ) ) = ( ( \bar { y } _ { 1 } ( n ) - \bar { y } _ { 0 } ( n ) ) - ( \hat { y } _ { 1 } ( n ) - \hat { y } _ { 0 } ( n ) ) ) ^ { 2 } } \\ & { ( k > 2 ) : \mathcal { L } _ { S } ^ { I } ( \bar { \mathbf { y } } ( n ) , \hat { \mathbf { y } } ( n ) ) = | | \bar { \mathbf { y } } ( n ) - \hat { \mathbf { y } } ( n ) | | _ { 2 } ^ { 2 } . } \end{array}
+$$
+
+I and $\mathbf { D _ { I } }$ are then iteratively optimized with $k _ { I }$ minibatches as follows:
+
+$$
+\begin{array} { l } { \displaystyle \operatorname* { m i n } _ { { \bf { D } } _ { \bf { I } } } - \sum _ { n = 1 } ^ { k _ { I } } V _ { I T E } ( { \bf { x } } ( n ) , \bar { \bf { y } } ( n ) , \hat { \bf { y } } ( n ) ) } \\ { \displaystyle \operatorname* { m i n } _ { { \bf { I } } } \sum _ { n = 1 } ^ { k _ { G } } \Big [ V _ { I T E } ( { \bf { x } } ( n ) , \bar { \bf { y } } ( n ) , \hat { \bf { y } } ( n ) ) + \beta \mathcal { L } _ { S } ^ { I } ( \bar { \bf { y } } ( n ) , \hat { \bf { y } } ( n ) ) \Big ] } \end{array}
+$$
+
+where $\beta \geq 0$ is a hyper-parameter.
+
+Empirical justification for the inclusion of all the above losses can be found in Section 5.3 where we explore the effect of training with and without each of the losses, see Table 6. We demonstrate there that using a combination of both (for both $\mathbf { G }$ and I) gives the best performance. In addition to this, by using a GAN loss for I we learn the conditional distribution of the potential outcomes rather than just the expectations (which would be the case if we only used the supervised loss $\mathcal { L } _ { S } ^ { I }$ . See Table 1 in Section 5.3). This allows us to capture the uncertainty of the outcomes, which is very important in the medical setting when treatment decisions need to be made by doctors on the basis of these types of estimations.
+
+Due to the lack of ground truth, it is often difficult in causal inference tasks to optimize the hyperparameters. More specifically, we do not have access to the true loss function (either PEHE or MSE) that we are trying to minimize, and so it is not possible to select hyper-parameters that minimise the true loss. One of the advantages of GANITE, however, is that our target loss can be estimated from the generated counterfactuals, unlike other methods such as in Shalit et al. (2017). Therefore, we can directly optimize the hyper-parameters that minimize this estimated PEHE/MSE over the hyper-parameter space - details of our hyper-parameter optimization and the achieved optimal hyperparameters are illustrated in the Appendix.
+
+# 5 EXPERIMENTS
+
+# 5.1 DATASETS
+
+Due to the nature of the problem, it is very difficult to evaluate the performance of the algorithm on real-world datasets - we never have access to the ground truth. Previous works, such as Shalit et al. (2017); Louizos et al. (2017), use both semi-synthetic datasets (either the treatments or the potential outcomes are synthesized) and datasets collected from randomized controlled trials (RCT) to evaluate the ITE generator. We use two semi-synthetic datasets, IHDP and Twins, and one realworld dataset, Jobs, to evaluate the performance of GANITE with various state-of-the-art methods. These datasets are the same as the ones used in Shalit et al. (2017); Louizos et al. (2017). Below, we give a detailed explanation of Twins. The details of IHDP and Jobs are well described in Shalit et al. (2017); Hill (2011); Dehejia & Wahba (2002a) and the Appendix.
+
+Twins: This dataset is derived from all births in the USA between 1989-1991 (Almond et al. (2005)). Among these births, we only focus on the twins. We define the treatment $t = 1$ as being the heavier twin (and $t = 0$ as being the lighter twin). The outcome is defined as the 1-year mortality. For each twin-pair we obtained 30 features relating to the parents, the pregnancy and the birth: marital status; race; residence; number of previous births; pregnancy risk factors; quality of care during pregnancy; and number of gestation weeks prior to birth. We only chose twins weighing less than $2 \mathrm { k g }$ and without missing features (list-wise deletion). This creates a complete dataset (without missing data). The final cohort is 11,400 pairs of twins whose mortality rate for the lighter twin is $1 7 . 7 \%$ , and for the heavier $1 6 . 1 \%$ . In this setting, for each twin pair we observed both the case $t = 0$ (lighter twin) and $t = 1$ (heavier twin); thus, the ground truth of individualized treatment effect is known in this dataset. In order to simulate an observational study, we selectively observe one of the two twins using the feature information (creating selection bias) as follows: $t | \mathbf { x } \sim \mathrm { B e r n } ( \mathrm { S i g m o i d } ( \mathbf { w } ^ { T } \mathbf { x } + n ) )$ where $\mathbf { w } ^ { T } \sim \mathcal { U } ( ( - 0 . 1 , 0 . 1 ) ^ { 3 0 \times 1 } )$ and $n \sim \mathcal N ( 0 , 0 . 1 )$ .
+
+# 5.2 PERFORMANCE METRICS AND SETTINGS
+
+We use four different performance metrics: expected Precision in Estimation of Heterogeneous Effect (PEHE), average treatment effect (ATE) (Hill (2011)), policy risk $( R _ { p o l } ( \pi ) )$ , and average treatment effect on the treated (ATT) (Shalit et al. (2017)). In this subsection, we only provide definitions for PEHE and $R _ { p o l } ( \pi )$ . ATE and ATT are explained (and reported) in the Appendix.
+
+If both factual and counterfactual outcomes are generated from a known distribution (so that we are able to compute the expectations of the outcomes, like in the IHDP dataset), and the treatment is binary, the empirical PEHE $( \epsilon _ { P E H E } )$ can be defined as follows:
+
+$$
+\epsilon _ { P E H E } = \frac { 1 } { N } \sum _ { n = 1 } ^ { N } \Big ( \mathbb { E } _ { ( y _ { 1 } ( n ) , y _ { 0 } ( n ) ) \sim \mu _ { \mathbf { Y } } ( \mathbf { x } ( n ) ) } [ y _ { 1 } ( n ) - y _ { 0 } ( n ) ] - [ \hat { y } _ { 1 } ( n ) - \hat { y } _ { 0 } ( n ) ] \Big ) ^ { 2 }
+$$
+
+where $y _ { 1 } ( n ) , y _ { 0 } ( n )$ are treated and controlled outcomes drawn from the ground truth $( \mu _ { \mathbf { Y } } ( \mathbf { x } ) )$ and $\hat { y } _ { 1 } ( n ) , \hat { y } _ { 0 } ( n )$ are their estimations.
+
+If both factual and counterfactual outcomes are observed but the underlying distribution is unknown (like in the Twins dataset), $\hat { \epsilon } _ { P E H E }$ can be defined as follows:
+
+$$
+\hat { \epsilon } _ { P E H E } = \frac { 1 } { N } \sum _ { n = 1 } ^ { N } \Big ( [ y _ { 1 } ( n ) - y _ { 0 } ( n ) ] - [ \hat { y } _ { 1 } ( n ) - \hat { y } _ { 0 } ( n ) ] \Big ) ^ { 2 }
+$$
+
+If only factual outcomes are available but the testing set comes from a randomized controlled trial (RCT), such as in the Jobs dataset, Policy risk $( \mathcal { R } _ { p o l } ( \pi ) )$ can be defined as follows (Shalit et al. (2017)):
+
+$$
+R _ { p o l } ( \pi ) = \frac { 1 } { N } \sum _ { n = 1 } ^ { N } \Big [ 1 - \Big ( \sum _ { i = 1 } ^ { k } \big [ \frac { 1 } { | \Pi _ { i } \cap T _ { i } \cap E | } \sum _ { \mathbf { x } ( n ) \in \Pi _ { i } \cap T _ { i } \cap E } y _ { i } ( n ) \times \frac { | \Pi _ { i } \cap E | } { | E | } \big ] \Big ) \Big ]
+$$
+
+where $\Pi _ { i } = \{ { \bf x } ( n ) : i = \arg \operatorname* { m a x } \hat { \bf y } \}$ , $T _ { i } = \{ \mathbf { x } ( n ) : t _ { i } ( n ) = 1 \}$ , and $E$ is the subset of RCT.
+
+Each dataset is divided $56 / 2 4 / 2 0 \%$ into training/validation/testing sets. Hyper-parameters such as the number of hidden layers $\alpha$ and $\beta$ are chosen using Random Search (Bergstra & Bengio (2012)). Details about the hyper-parameters are discussed in the Appendix. We run each algorithm 100 times (except for the IHDP dataset, on which we run each algorithm 1,000 times which is the same setting in Shalit et al. (2017)) with new training/validation/testing splits and report the mean and standard deviation of the performances.
+
+# 5.3 EXPERIMENTAL RESULTS
+
+In our first simulation we focus on demonstrating the effect that including each of the losses introduced in Section 4 has on the performance of the algorithm. As is demonstrated below, inclusion of all four losses gives the best results.
+
+We generate a synthetic dataset as follows: we draw 10,000 10-dimensional feature vectors $\mathbf { x } \sim$ $\mathcal { N } ( \bar { \mathbf { 0 } } ^ { 1 0 \times 1 } , 0 . 5 \times \bar { ( } \Sigma + \Sigma ^ { T } ) )$ where $\Sigma \sim \mathcal { U } ( ( - 1 , 1 ) ^ { 1 0 \times 1 0 } )$ . The treatment assignment is then generated as $t | \mathbf { x } \sim \mathrm { B e r n } ( \mathrm { S i g m o i d } ( \mathbf { w } _ { t } ^ { T } \mathbf { x } + n _ { t } ) )$ where $\mathbf { w } _ { t } ^ { T } \sim \mathcal { U } ( ( - 0 . 1 , 0 . 1 ) ^ { 1 0 \times 1 } )$ and $n _ { t } \sim \mathcal { N } ( 0 , 0 . 1 )$ . The potential outcome vector is then generated as $\mathbf { y } | \mathbf { x } \sim ( \mathbf { w } _ { y } ^ { T } \mathbf { x } + \mathbf { n } _ { y } ) )$ where $\mathbf { w } _ { y } ^ { T } \sim \mathcal { U } ( ( - 1 , 1 ) ^ { 1 0 \times 2 } )$ and $\mathbf { n } _ { y } \sim \mathcal { N } ( \mathbf { 0 } ^ { 2 \times 1 } , 0 . 1 \times I ^ { 2 \times 2 } )$ . We use 8,000 instances for training and 2,000 instances for testing. We repeat this 100 times and report the average $\epsilon _ { P E H E }$ on the testing set.
+
+Table 1: Performance with various combinations of GANITE (G: Counterfactual generator, I: ITE generator, S loss: Supervised loss). Details of each cell are illustrated in the Appendix as Figures.   
+
+<table><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=3>G</td></tr><tr><td rowspan=1 colspan=1>PEHE</td><td rowspan=1 colspan=1>S loss only</td><td rowspan=1 colspan=1>GAN loss only</td><td rowspan=1 colspan=1>S and GAN loss</td></tr><tr><td rowspan=1 colspan=1>S loss only</td><td rowspan=1 colspan=1>.397 ± .011 (15.6%)</td><td rowspan=1 colspan=1>.610 ± .017 (45.1%)</td><td rowspan=1 colspan=1>.352 ± .012 (4.8%)</td></tr><tr><td rowspan=1 colspan=1>GAN loss only</td><td rowspan=1 colspan=1>.607 ± .044 (44.8%)</td><td rowspan=1 colspan=1>.513 ± .029 (34.7%)</td><td rowspan=1 colspan=1>.463 ± .015 (27.6%)</td></tr><tr><td rowspan=1 colspan=1>S and GAN loss</td><td rowspan=1 colspan=1>.362 ± .011 (7.5%)</td><td rowspan=1 colspan=1>.491 ± .030 (31.8%)</td><td rowspan=1 colspan=1>.335 ± .011 (-)</td></tr></table>
+
+![](images/fd37c222a08f381e5ecd4cdb21bb3a5edd9473c704498df62a1170f86849a63d.jpg)  
+Figure 2: Performance comparison between GANITE and state-of-the-art methods as the selection bias is varied (Kullback-Leibler divergence of treated with respect to controlled distributions)
+
+Table 1 shows the performance of the GANITE architecture using different combinations of the four losses in Section 4. For each generator component, we can use 3 different combinations of loss: (1) Supervised loss (S loss) only (this reduces the corresponding component to a standard neural network), (2) GAN loss only, (3) both S loss and GAN loss. The top-left most entry corresponds to simply using a standard neural network to first impute the counterfactuals and then using another standard neural network to learn an ITE estimator from the imputed dataset. As can be seen, this already performs well, but by adding the GAN losses for both the imputation step and the estimation step, a significant gain is shown $( 1 5 . 6 \% )$ (the bottom-right entry).
+
+In Fig. 2 we show that GANITE is robust to an increased selection bias. We generate 10,000 10-dimensional treated samples from $\mathbf { x } _ { 1 } \sim \mathcal { N } ( \mu _ { 1 } , 0 . 5 \times ( \Sigma + \Sigma ^ { T } ) )$ and controlled samples from $\mathbf { x } _ { 0 } \sim \mathcal { N } ( \mu _ { \mathbf { 0 } } , 0 . 5 \times ( \Sigma + \Sigma ^ { T } ) )$ where $\Sigma \sim \mathcal { U } ( ( - 1 , 1 ) ^ { 1 0 \times 1 0 } )$ . Fixing $\mu _ { 0 }$ and varying $\mu _ { 1 }$ , we generate various datasets with different Kullback-Leibler divergences (KL divergences) of $\mu _ { 1 }$ with respect to $\mu _ { 0 }$ . A higher KL divergence indicates a higher selection bias (a larger mismatch) between treated and controlled distributions. As seen in Fig. 2, GANITE robustly outperforms state-of-the-art methods such as Shalit et al. (2017); Alaa $\&$ van der Schaar (2017) across the entire range of tested divergences.
+
+Binary treatments: In this section, we evaluate GANITE for estimating individualized treatment effects for binary treatments. We use three datasets and report the $\epsilon _ { P E H E }$ both in-sample and outof-sample (for ATE and ATT see the appendix). We compare GANITE with least squares regression using treatment as a feature $\mathrm { ( O L S / L R _ { 1 } }$ ), separate least squares regressions for each treatment $\mathrm { ( O L S / L R _ { 2 } }$ ), balancing linear regression (BLR) (Johansson et al. (2016)), $\mathbf { k }$ -nearest neighbor (k-NN) (Crump et al. (2008)), Bayesian additive regression trees (BART) (Chipman et al. (2010)), random forests (RForest) (Breiman (2001)), causal forests (C Forest) (Wager & Athey (2017)), balancing neural network (BNN) (Johansson et al. (2016)), treatment-agnostic representation network (TARNET) (Shalit et al. (2017)), counterfactual regression with Wasserstein distance $( \mathrm { C F R } _ { W A S S } )$ (Shalit et al. (2017)), and multi-task gaussian process (CMGP) (Alaa & van der Schaar (2017)). We evaluate both in-sample and out-of-sample performance in Table 2.
+
+Table 2: Performance of ITE estimation with three real-world datasets. Bold indicates the method with the best performance for each dataset. ∗: is used to indicate methods that GANITE shows a statistically significant improvement over.   
+
+<table><tr><td rowspan="3">Methods</td><td colspan="6">Datasets (Mean ± Std)</td></tr><tr><td colspan="2">IHDP(ePEHE)</td><td colspan="2">Twins (VePEHE)</td><td colspan="2">Jobs (Rpot (π))</td></tr><tr><td>In-sample</td><td> Out-sample</td><td> In-sample</td><td> Out-sample</td><td>In-sample</td><td>Out-sample</td></tr><tr><td>GANITE</td><td>1.9 ± .4</td><td>2.4±.4</td><td>.289 ± .005</td><td>.297 ± .016</td><td>.13± .01</td><td>.14±.01</td></tr><tr><td rowspan="4">OLS/LR1 OLS/LR2 BLR k-NN</td><td>5.8±.3*</td><td>5.8±.3*</td><td>.319± .001*</td><td>.318 ± .007</td><td>.22± .00*</td><td>.23±.02*</td></tr><tr><td>2.4 ±.1</td><td>2.5± .1</td><td>.320 ± .002</td><td>.320± .003*</td><td>.21 ± .00*</td><td>.24±.01*</td></tr><tr><td>5.8±.3*</td><td>5.8±.3*</td><td>.312 ± .003*</td><td>.323 ± .018</td><td>.22 ±.01*</td><td>.25±.02*</td></tr><tr><td>2.1 ± .1</td><td>4.1± .2*</td><td>.333± .001*</td><td>.345 ± .007*</td><td>.02 ± .00</td><td>.26± .02*</td></tr><tr><td rowspan="4">RForest C Forest BNN</td><td>2.1±.1 4.2±.2*</td><td>2.3 ±.1</td><td>.347 ± .009*</td><td>.338 ± .016</td><td>.23± .00* .23 ± .01*</td><td>.25± .02*</td></tr><tr><td></td><td>6.6± .3*</td><td>.306 ± .002*</td><td>.321 ± .005</td><td></td><td>.28±.02*</td></tr><tr><td>3.8±.2*</td><td>3.8±.2*</td><td>.366± .003*</td><td>.316 ± .011</td><td>.19 ± .00*</td><td>.20±.02*</td></tr><tr><td>2.2 ±.1</td><td>2.1±.1</td><td>.325 ± .003*</td><td>.321± .018</td><td>.20± .01*</td><td>.24±.02*</td></tr><tr><td rowspan="4">TARNET CFRwASS CMGP</td><td>.88 ±.02</td><td>.95 ± .02</td><td>.317 ± .005*</td><td>.315 ± .003</td><td>.17 ± .01*</td><td>.21±.01*</td></tr><tr><td>.71 ± .02</td><td>.76 ± .02</td><td>.315±.007*</td><td>.313 ± .008</td><td>.17± .01*</td><td>.21± .01*</td></tr><tr><td>.65 ± .44</td><td>.77 ± .11</td><td>.320± .002*</td><td>.319 ± .008</td><td>.22± .03*</td><td>.24 ± .05</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td></tr></table>
+
+As can be seen in Table 2, GANITE achieves significant performance gains on the Twins and Jobs datasets in comparison with state-of-the-art methods (both in-sample and out-of-sample 2). GANITE achieves a much higher gain for individualized treatment effect estimations (such as $\hat { \epsilon } _ { P E H E }$ and $\mathcal { R } _ { p o l } ( \pi ) )$ than average treatment effect estimations (such as $\hat { \epsilon } _ { A T E }$ and $\epsilon _ { A T T }$ ). On IHDP, GANITE is competitive with BART and BNN but is outperformed by TARNET, $\mathbf { C F R } _ { W A S S }$ and CMGP. We believe this is due to the fact that GANITE has a large number of parameters to be optimized and IHDP is a relatively small dataset (747 samples). This belief is backed up by our significant gains over these methods in both Twins and Jobs, where the number of samples is much larger, (11400 and 3212 samples, respectively).
+
+Table 3: Performance of multiple treatment effects estimations using Twins data. Bold indicates the method with the best performance for each dataset. ∗: is used to indicate methods that GANITE shows a statistically significant improvement over.   
+
+<table><tr><td rowspan=2 colspan=1>Methods</td><td rowspan=1 colspan=4>Metric: MSEy</td></tr><tr><td rowspan=1 colspan=1>In Sample</td><td rowspan=1 colspan=1>Gain (%)</td><td rowspan=1 colspan=1>Out Sample</td><td rowspan=1 colspan=1>Gain (%)</td></tr><tr><td rowspan=1 colspan=1>GANITE</td><td rowspan=1 colspan=1>.0427士.0161</td><td rowspan=1 colspan=1>(-)</td><td rowspan=1 colspan=1>.0723士.0183</td><td rowspan=1 colspan=1>(-)</td></tr><tr><td rowspan=2 colspan=1>OLS/LR1OLS/LR2BLRKNN</td><td rowspan=2 colspan=1>.0855士.0096.0857 ± .0099.0996 ± .0081*.0930 ± .0101*</td><td rowspan=1 colspan=1>50.1%</td><td rowspan=2 colspan=1>.0871±.0142.0883 ± .0147.1017 ± .0127.1008 ± .0236</td><td rowspan=2 colspan=1>17.0%18.1%28.9%28.3%</td></tr><tr><td rowspan=1 colspan=1>50.2%57.1%54.1%</td></tr><tr><td rowspan=1 colspan=1>BARTR ForestC Forest</td><td rowspan=1 colspan=1>.1097 ± .0084*.0442 ± .0069.1607 ± .0014*</td><td rowspan=1 colspan=1>61.1%3.4%73.4%</td><td rowspan=1 colspan=1>.1037 ± .0283.0927 ± .0138.1665 ± .0035*</td><td rowspan=1 colspan=1>30.3%22.0%56.6%</td></tr><tr><td rowspan=2 colspan=1>BNNTARNETCFRW ASSCMGP</td><td rowspan=1 colspan=1>.0602 ± .0102.0854 ± .0091</td><td rowspan=1 colspan=1>29.1%50.0%</td><td rowspan=2 colspan=1>.1031 ± .0145.0879 ± .0030.0894 ± .0057.0793 ± .0191</td><td rowspan=2 colspan=1>29.9%17.7%19.1%8.3%</td></tr><tr><td rowspan=1 colspan=1>.0896 ± .0036*.0844± .0073*</td><td rowspan=1 colspan=1>52.3%49.4%</td></tr></table>
+
+Multiple treatments: GANITE is naturally defined for estimating multiple treatment effects. In this subsection, we further preprocess the Twins data to create a dataset containing multiple treatments. The multiple treatments are determined as follows: (1) $t = 1$ : lower weight, female sex, (2) $t = 2$ : lower weight, male sex, (3) $t = 3$ : higher weight, female sex, (4) $t = 4$ : higher weight, male sex. Therefore, we have 4 possible treatments for each sample.
+
+We use the mean-squared error:
+
+$$
+\mathrm { M S E } _ { y } = \frac { 1 } { N \times | \mathcal { T } _ { i } | } \sum _ { i = 1 } ^ { N } \sum _ { t \in \mathcal { T } _ { i } } \Big ( y _ { t } ( x _ { i } ) - \hat { y } _ { t } ( x _ { i } ) \Big ) ^ { 2 }
+$$
+
+as the performance metric to evaluate the multiple treatment effects (other metrics, such as PEHE, do not have a natural extension to the multiple treatments setting). For comparison with state-of-the-art methods, we naively extend BLR, C Forest, BNN, TARNET, $\mathbf { C F R } _ { W A S S }$ , and CMGP for multiple treatments: one of the four treatments is selected as a control treatment and then the remaining three create three separate binary ITE estimation problems (all against the same chosen control treatment).
+
+As can be seen in Table 3 compared with Table 2 GANITE significantly outperforms other state-ofthe-art methods such as TARNET and $\mathbf { C F R } _ { W A S S }$ $1 7 . 7 \%$ and $1 9 . 1 \%$ gains in terms of out sample MSE, respectively). This is because, GANITE is designed for multiple treatments; the model is jointly trained for all treatments. On the other hand, other methods are designed for binary treatments and only naively extend to multiple treatments by training pairs of the available treatments.
+
+# 5.4 DISCUSSION
+
+The experimental results provide various intuitions of the GANITE framework for ITE estimation. First, GANITE can be easily extended to any number of treatments and performs well in this multiple treatment setting. As can be seen in Section 4, however, a different loss for binary treatment and multiple treatments must be used because PEHE is only defined for the binary treatment setting - the MSE is not a natural generalisation of the PEHE and we believe exploration of possible loss functions in this setting would be an interesting future work.
+
+A further extension to this problem would be to consider a setting in which a patient may receive several treatments (rather than just one). While this work can handle this problem naively (by treating each combination of treatments as a separate ‘treatment’) we believe this would also be an interesting problem to explore in a future work.
+
+# 6 CONCLUSION
+
+In this paper we introduced a novel method for dealing with the ITE estimation problem. We have shown empirically that our method is more robust to large selection biases and performs better on standard benchmark datasets than other state-of-the-art methods. Our method also achieves significant performance gains over state-of-the-art when estimating ITE for multiple treatments because it is able to jointly estimate the representations across the multiple treatments.
+
+# ACKNOWLEDGMENTS
+
+This work was supported by the Office of Naval Research (ONR) and the NSF (Grant number: ECCS1462245, ECCS1533983, and ECCS1407712).
+
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+Rajeev H Dehejia and Sadek Wahba. Propensity score-matching methods for nonexperimental causal studies. The review of economics and statistics, 84(1):151–161, 2002b.
+
+Vincent Dorie. Npci: Non-parametrics for causal inference, 2016.
+
+Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial nets. In Advances in Neural information processing systems, pp. 2672–2680, 2014.
+
+A Hannart, J Pearl, FEL Otto, P Naveau, and M Ghil. Causal counterfactual theory for the attribution of weather and climate-related events. Bulletin of the American Meteorological Society, 97(1): 99–110, 2016.
+
+Jennifer L Hill. Bayesian nonparametric modeling for causal inference. Journal of Computational and Graphical Statistics, 20(1):217–240, 2011.
+
+M Hofler. Causal inference based on counterfactuals. ¨ BMC medical research methodology, 5(1):28, 2005.
+
+Fredrik Johansson, Uri Shalit, and David Sontag. Learning representations for counterfactual inference. In International Conference on Machine Learning, pp. 3020–3029, 2016.
+
+James K Kirklin, David C Naftel, Robert L Kormos, Lynne W Stevenson, Francis D Pagani, Marissa A Miller, Karen L Ulisney, J Timothy Baldwin, and James B Young. Second intermacs annual report: more than 1000 primary lvad implants. The Journal of heart and lung transplantation: the official publication of the International Society for Heart Transplantation, 29(1):1, 2010.
+
+Robert J LaLonde. Evaluating the econometric evaluations of training programs with experimental data. The American economic review, pp. 604–620, 1986.
+
+Christos Louizos, Uri Shalit, Joris Mooij, David Sontag, Richard Zemel, and Max Welling. Causal effect inference with deep latent-variable models. NIPS, 2017.
+
+Min Lu, Saad Sadiq, Daniel J Feaster, and Hemant Ishwaran. Estimating individual treatment effect in observational data using random forest methods. arXiv preprint arXiv:1701.05306, 2017.
+
+Jared K Lunceford and Marie Davidian. Stratification and weighting via the propensity score in estimation of causal treatment effects: a comparative study. Statistics in medicine, 23(19):2937– 2960, 2004.
+
+Mehdi Mirza and Simon Osindero. Conditional generative adversarial nets. arXiv preprint arXiv:1411.1784, 2014.
+
+Kristin E Porter, Susan Gruber, Mark J Van Der Laan, and Jasjeet S Sekhon. The relative performance of targeted maximum likelihood estimators. The International Journal of Biostatistics, 7 (1):1–34, 2011.
+
+Donald B Rubin. Causal inference using potential outcomes: Design, modeling, decisions. Journal of the American Statistical Association, 100(469):322–331, 2005.
+
+Uri Shalit, Fredrik Johansson, and David Sontag. Estimating individual treatment effect: generalization bounds and algorithms. ICML, 2017.
+
+Jeffrey A Smith and Petra E Todd. Does matching overcome lalonde’s critique of nonexperimental estimators? Journal of econometrics, 125(1):305–353, 2005.
+
+Peter Spirtes. A tutorial on causal inference. 2009.
+
+Stefan Wager and Susan Athey. Estimation and inference of heterogeneous treatment effects using random forests. Journal of the American Statistical Association, (just-accepted), 2017.
+
+# APPENDIX
+
+PSEUDO-CODE OF GANITE
+
+# Algorithm 1 Pseudo-code of GANITE
+
+while convergence of training loss of G and $\mathbf { D _ { G } }$ do
+
+# (1) Counterfactual block optimization
+
+Use $k _ { C }$ minibatches, iteratively optimize $\mathbf { G } , \mathbf { D } _ { \mathbf { G } }$ by stochastic gradient descent (SGD)
+
+$$
+\begin{array} { l } { \displaystyle \operatorname* { m i n } _ { \mathbf { D } _ { \mathbf { G } } } - \sum _ { n = 1 } ^ { k _ { G } } V _ { C F } ( \mathbf { x } ( n ) , \mathbf { t } ( n ) , \tilde { \mathbf { y } } ( n ) ) } \\ { \displaystyle \operatorname* { m i n } _ { \mathbf { G } } \sum _ { n = 1 } ^ { k _ { G } } \Big [ V _ { C F } ( \mathbf { x } ( n ) , \mathbf { t } ( n ) , \tilde { \mathbf { y } } ( n ) ) + \alpha \mathcal { L } _ { S } ^ { G } ( y _ { f } ( n ) , \tilde { y } _ { \eta ( n ) } ^ { * } ( n ) ) \Big ] } \end{array}
+$$
+
+while convergence of training loss of $\mathbf { I }$ and $\mathbf { D _ { I } }$ do
+
+# (2) ITE block optimization
+
+Use $k _ { I }$ minibatches, update $\mathbf { I } , \mathbf { D _ { I } }$ by SGD
+
+$$
+\begin{array} { l } { \displaystyle \operatorname* { m i n } _ { { \bf { D } } _ { \bf { I } } } - \sum _ { n = 1 } ^ { k _ { I } } V _ { I T E } ( { \bf { x } } ( n ) , \tilde { { \bf { y } } } ( n ) , \hat { { \bf { y } } } ( n ) ) } \\ { \displaystyle \operatorname* { m i n } _ { { \bf { I } } } \sum _ { n = 1 } ^ { k _ { G } } \left[ V _ { I T E } ( { \bf { x } } ( n ) , \tilde { { \bf { y } } } ( n ) , \hat { { \bf { y } } } ( n ) ) + \beta \mathcal { L } _ { S } ^ { I } ( \tilde { { \bf { y } } } ( n ) , \hat { { \bf { y } } } ( n ) ) \right] } \end{array}
+$$
+
+DETAILED DESCRIPTION OF THE DATASETS
+
+IHDP
+
+Hill (2011) provided a dataset for ITE estimation with the Infant Health and Development Program (IHDP). The dataset consists of 747 children ( $\mathrm { \Delta } t = 1$ : 139, $t = 0 6 0 8$ ) with 25 features. We generated potential outcomes from setting A in the NPCI package Dorie (2016).
+
+JOBS
+
+Jobs data studied in LaLonde (1986) is composed of randomized data based on the National Supported Work program and non-randomized data from observational studies. We use a (random) subset of the randomized data to evaluate the algorithms based on $\mathcal { R } _ { p o l } ( \pi )$ and $\epsilon _ { A T T }$ . The dataset consists of 722 randomized samples $\mathit { t } = 1$ : 297, $t = 0$ : 425) and 2490 non-randomized samples $( t = 1 ; 0 , t = 0 ; 2 4 9 0 )$ , all with 7 features.
+
+# SUMMARY OF THE DATASETS
+
+Table 4: Summary of the datasets (N is the number of samples, s is the feature-dimension)   
+
+<table><tr><td rowspan="2">Data</td><td colspan="5">Condition</td><td colspan="2">一 Property</td></tr><tr><td>F</td><td>CF</td><td>Distribution</td><td>RT-test</td><td>T</td><td>N</td><td>一 S</td></tr><tr><td>IHDP</td><td>√</td><td>√</td><td>Known</td><td></td><td>Binary</td><td>747</td><td>25</td></tr><tr><td>Jobs</td><td>√</td><td>X</td><td>Unknown</td><td>√</td><td>Binary</td><td>3212</td><td>7</td></tr><tr><td>Twins-Binary</td><td>√</td><td>√</td><td>Unknown</td><td></td><td>Binary</td><td>11400</td><td>30</td></tr><tr><td>Twins-Multiple</td><td>√</td><td>X</td><td>Unknown</td><td></td><td>Multiple</td><td>11400</td><td>30</td></tr></table>
+
+<table><tr><td rowspan="3">Methods</td><td colspan="6">Datasets (Mean ± Std)</td></tr><tr><td colspan="2">IHDP (EATE) 一</td><td colspan="2">Twins (CATE)</td><td colspan="2">Jobs (EATT)</td></tr><tr><td>In-sample</td><td> Out-sample</td><td>In-sample</td><td>Out-sample</td><td>In-sample</td><td> Out-sample</td></tr><tr><td>GANITE</td><td>.43± .05</td><td>.49± .05</td><td>.0058 ± .0017</td><td>.0089± 0.0075</td><td>.01 ± .01</td><td>.06 ± .03</td></tr><tr><td rowspan="4">OLS/LR1 OLS/LR2 BLR k-NN</td><td>.73± .04*</td><td>.94 ± .06*</td><td>.0038 ± .0025</td><td>.0069 ± .0056</td><td>.01±.00</td><td>.08± .04</td></tr><tr><td>.14 ± .01</td><td>.31± .02</td><td>.0039 ± .0025</td><td>.0070 ± .0059</td><td>.01 ± .01</td><td>.08 ± .03</td></tr><tr><td>.72 ± .04*</td><td>.93 ± .05*</td><td>.0057 ± .0036</td><td>.0334± .0092*</td><td>.01 ± .01</td><td>.08 ± .03</td></tr><tr><td>.14 ± .01</td><td>.90± .05*</td><td>.0028 ± .0021</td><td>.0051 ± .0039</td><td>.21±.01*</td><td>.13 ± .05</td></tr><tr><td rowspan="3">BART R Forest C Forest</td><td>.23 ± .01</td><td>.34± .02</td><td>.1206 ± .0236*</td><td>.1265 ± .0234*</td><td>.02 ± .00</td><td>.08± .03</td></tr><tr><td>.73± .05*</td><td>.96 ± .06*</td><td>.0049 ± .0034</td><td>.0080 ± .0051</td><td>.03 ± .01</td><td>.09 ± .04</td></tr><tr><td>.18 ± .01</td><td>.40± .03</td><td>.0286 ± .0035*</td><td>.0335± .0083*</td><td>.03 ± .01</td><td>.07± .03</td></tr><tr><td rowspan="4">BNN TARNET CFRwASS CMGP</td><td>.37±.03</td><td>.42 ± .03</td><td>.0056 ± .0032</td><td>.0203 ± .0071</td><td>.04 ±.01</td><td>.09 ± .04</td></tr><tr><td>.26 ± .01</td><td>.28± .01</td><td>.0108± .0017*</td><td>.0151 ± .0018</td><td>.05 ± .02</td><td>.11 ± .04</td></tr><tr><td>.25 ± .01</td><td>.27 ± .01</td><td>.0112 ± .0016*</td><td>.0284± .0032*</td><td>.04 ± .01</td><td>.09 ± .03</td></tr><tr><td>.11 ± .10</td><td>.13 ± .12</td><td>.0124 ± .0051</td><td>.0143 ± .0116</td><td>.06 ± .06</td><td>.09 ± .07</td></tr></table>
+
+Table 5: Performance of average treatment effect estimation. Bold represents the best performance.   
+∗: statistically significant improvement of GANITE.
+
+# PERFORMANCE METRICS AND THE RESULTS OF AVERAGE TREATMENT EFFECT ESTIMATION
+
+In this subsection, we use two different performance metrics for average treatment effect (ATE) estimation: average treatment effect (ATE) (Hill (2011)), and average treatment effect on the treated (ATT) (Shalit et al. (2017)).
+
+If both factual and counterfactual outcomes are generated from a known distribution (and so we are able to compute the expected value, such as in IHDP), the error of ATE $( \epsilon _ { A T E } )$ is defined as:
+
+$$
+\epsilon _ { A T E } = | | \frac { 1 } { N } \sum _ { n = 1 } ^ { N } \mathbb { E } _ { { \mathbf { y } } ( n ) \sim \mu _ { { \mathbf { Y } } } ( { \mathbf { x } } ( n ) ) } [ { \mathbf { y } } ( n ) ] - \frac { 1 } { N } \sum _ { i = 1 } ^ { n } \hat { { \mathbf { y } } } ( n ) | | _ { 2 } ^ { 2 }
+$$
+
+where $\hat { \mathbf { y } }$ is the estimated potential outcome.
+
+If both factual and counterfactual outcomes are observed but the underlying distribution is unknown (like in Twins), $\epsilon _ { A \hat { T } E }$ is defined as:
+
+$$
+\hat { \epsilon } _ { A T E } = | | \frac { 1 } { N } \sum _ { n = 1 } ^ { N } \mathbf { y } ( n ) - \frac { 1 } { N } \sum _ { n = 1 } ^ { N } \hat { \mathbf { y } } ( n ) | | _ { 2 } ^ { 2 }
+$$
+
+If only factual outcomes are available (such as in Jobs), treatment is binary, and the testing set comes from a randomized controlled trial (RCT), the true average treatment effect on the treated (ATT) is defined as follows (Shalit et al. (2017)):
+
+$$
+\begin{array} { l } { { \displaystyle { \cal A T T } = \frac { 1 } { | T _ { 1 } \cap { \cal E } | } \sum _ { { \bf x } _ { i } \in T _ { 1 } \cap { \cal E } } Y _ { 1 } ( { \bf x } _ { i } ) - \frac { 1 } { | T _ { 0 } \cap { \cal E } | } \sum _ { { \bf x } _ { i } \in C \cap { \cal E } } Y _ { 0 } ( { \bf x } _ { i } ) } } \\ { { \displaystyle \epsilon _ { A T T } = | A T T - \frac { 1 } { | T _ { 1 } \cap { \cal E } | } \sum _ { { \bf x } _ { i } \in T _ { 1 } \cap { \cal E } } \hat { Y } _ { 1 } ( { \bf x } _ { i } ) - \hat { Y } _ { 0 } ( { \bf x } _ { i } ) | } } \end{array}
+$$
+
+where $T _ { 1 }$ is the subset corresponding to treated samples, $T _ { 0 }$ is the subset corresponding to controlled samples, and $E$ is the subset corresponding to the randomized controlled trials.
+
+Table. 5 shows the performance of the various algorithms with respect to these metrics.
+
+As can be seen in Table 5, the GANITE achieves competitive performances for Average Treatment Effect (ATE) estimation but not the best model to estimate ATE (except the Jobs dataset). However, we do not believe that it is an important metric for distinguishing models where the task is predicting
+
+treatment effects on an individual level. The problem we address with GANITE is to estimate the ITE. We used the ATE performance as a sanity check for our method - and believe it passes the sanity check, being competitive with most other methods.
+
+# HYPER-PARAMETER OPTIMIZATION
+
+We optimize our hyper-parameters in GANITE by estimating the PEHE (MSE in the case of multiple treatments) on the dataset generated by G and minimizing this with respect to the hyper-parameters. The table below indicates specifics of this process, including the values we search over.
+
+Table 6: Hyper-parameters of GANITE   
+
+<table><tr><td>Blocks</td><td>Sets of Hyper-parameters</td></tr><tr><td>Initialization</td><td>Xavier Initialization for Weight matrix, Zero initialization for bias vector.</td></tr><tr><td>Optimization</td><td>Adam Moment Optimization</td></tr><tr><td>Batch size (kG, k1)</td><td>{32,64,128,256}</td></tr><tr><td>Depth of layers</td><td>{1,3,5,7,9}</td></tr><tr><td>Hidden state dimension</td><td>{s, int(s/2),int(s/3), int(s/4),int(s/5)}</td></tr><tr><td>α,β</td><td>{0,0.1,0.5,1,2,5,10}</td></tr></table>
+
+For the hyper-parameter optimization of the benchmarks, we follow the hyper-parameter optimzation code published in the github with their main code. For instance, the hyper-parameters of $\mathbf { C F R } _ { W A S S }$ are optimized using cfr_param_search.py file which is published in https: //github.com/clinicalml/cfrnet
+
+# OPTIMAL HYPER-PARAMETERS FOR EACH DATASET
+
+Table 7: Optimal Hyper-parameters of GANITE   
+
+<table><tr><td>Dataset</td><td>Optimal Hyper-parameters</td></tr><tr><td>IHDP</td><td>kG : 64,k1 : 64, Depth of layers: 5, hdim: 8,α : 2, β : 5</td></tr><tr><td>Jobs</td><td>kG : 128,k1 : 128,Depth of layers: 3, hdim: 4, α : 1, β : 5</td></tr><tr><td></td><td>Twins - Binary|kg : 128,k1 : 128,Depth of layers: 5, hdim: 8,α : 2, β : 2</td></tr><tr><td></td><td>Twins - Multiple |kg : 128,k1 : 128,Depth of layers: 7, hdim: 8,α : 1, β : 2</td></tr></table>
+
+ADDITIONAL EXPERIMENTS
+
+# PERFORMANCE GAP BETWEEN $G$ AND $I$
+
+As explained in Section 4, $I$ tries to learn the potential distribution that consists of factual outcomes and counterfactual outcomes that are generated by $G$ . To evaluate how well $I$ is able to learn from $G$ , we compare the performance of $G$ and $I$ of the GANITE framework in Table 8 in terms of ITE estimation. As can be seen in Table 8, the in-sample ITE estimation performance of GANITE (I) is competitive with GANITE (G). It experimentally verifies that GANITE (I) learns well from the outputs of GANITE (G).
+
+# ZERO OUT THE CONTRIBUTION OF FACTUAL OUTCOME AND TREATMENT
+
+In this section, we use the trained $G$ to compute ITE only with $x$ . The learned function $G$ needs $x , t$ , and $y _ { f }$ as the inputs. Therefore, in order to compute ITE only with $x$ , we should zero out the contribution of $t$ and $y _ { f }$ in the $G$ function. $G$ tries to learn the conditional probability $\mathcal { P } ( y | x , y _ { f } , t )$
+
+<table><tr><td rowspan="2">Methods</td><td colspan="3">Datasets (Mean ± Std)</td></tr><tr><td>IHDP（√∈PEHE）</td><td>）|Twins (√PEHE) |Jobs (Rpot(π))</td><td></td></tr><tr><td>GANITE (I)</td><td>1.9 ± .4</td><td>.289 ± .005</td><td>.13 ± .01</td></tr><tr><td>GANITE (G)</td><td>1.4 ± .2</td><td>.267 ± .004</td><td>一 .10 ± .01</td></tr></table>
+
+Table 8: Performance comparison of in-sample ITE estimation between GANITE (I) and GANITE (G) with three real-world datasets.
+
+and what we want to compute is the conditional probability $\mathcal { P } ( y | x )$ . Therefore, zero out the impact of $t$ and $y _ { f }$ can be done as follows.
+
+$$
+\mathcal { P } ( y | x ) = \int \mathcal { P } ( y | x , t , y _ { f } ) P ( y _ { f } , t | x ) d t d y _ { f }
+$$
+
+The $\mathcal { P } ( y | x , t , y _ { f } )$ is learned by $G$ and $P ( \boldsymbol { y } _ { f } , t | \boldsymbol { x } )$ can be easily learned using supervised learning framework (all the labels $( y _ { f } , t )$ are available) with drop-out approach (to approximate the integral as the sample mean of multiple samples). We use multi-layer perceptron (MLP) with multiple outputs to learn the function $P ( \boldsymbol { y } _ { f } , t | \boldsymbol { x } )$ . We called this as zero-out GANITE. We compare the performance of zero-out GANITE to original GANITE in Table 9. As can be seen in Table 9, the performance of original GANITE is marginally better than zero-out GANITE in three different datasets. We do not believe that zero-out GANITE would be any simpler than our proposed structure - in both cases we would still have 2 learning stages (Table 9 experimentally verifies this).
+
+Table 9: Performance comparison of ITE estimation between GANITE and zero-out GANITE with three real-world datasets.   
+
+<table><tr><td rowspan="3">Methods</td><td colspan="6">Datasets (Mean ± Std)</td></tr><tr><td colspan="2">IHDP(VePEHE)</td><td colspan="2">Twins (√PEHE)</td><td colspan="2">Jobs (Rpot(π))</td></tr><tr><td>In-sample</td><td> Out-sample</td><td> In-sample</td><td> Out-sample</td><td> In-sample</td><td> Out-sample</td></tr><tr><td>GANITE</td><td>1.9 ±.4</td><td>2.4±.4</td><td>.289± .005</td><td>.297± .016</td><td>.13± .01</td><td>.14±.01</td></tr><tr><td>zero-out GANITE</td><td>2.2±.6</td><td>2.6±.7</td><td>.297± .008</td><td>.308 ± .022</td><td>.14±.02</td><td>.17 ± .01</td></tr></table>
+
+![](images/01fd331969becb74c40c9fb7393e84c8324068e58272206cc658ec33f29a6398.jpg)  
+Figure 3: (a) Underlying distribution of potential outcomes $( \mathbf { Y } )$ , (b) Underlying distribution of treatment assignments $\mathcal { P } ( { \cal T } | \mathbf { X } )$ , (c) Training data (factual outcomes) sampled from distributions explained in (a) and (b), (d) Potential outcomes sampled from trained ITE generator (I).
+
+![](images/5416c8d18c27cc7fc97591fbcdf148d6dbf632cdd2afabd0c653a7efc1971edb.jpg)  
+(a) G: S loss only, I: S loss only
+
+![](images/5580d21a47b5741dd06226c58dfaa2bbb1c03ef1fe3ca55713d2b3bbaf8b0b5d.jpg)  
+(b) G: GAN loss only, I: S loss only
+
+![](images/e9299a806ba69fd8e89515db3209b4579df81b24690d66d8b9ef100f04b20764.jpg)  
+(c) G: S and GAN loss, I: S loss only
+
+![](images/891cb861535bc715091ce87230dc8702cd04ebdf141d97b640c2b5094b9ef472.jpg)  
+(d) G: S loss only, I: GAN loss only
+
+![](images/e8202c3d1bf7ddb4e787d1942f7f32133116c72050d09baa9baed922310dfa18.jpg)  
+(e) G: GAN loss only, I: GAN loss only
+
+![](images/994fff82ccfbb7486666c9221e5989a475319e8e43c29a7f6cacbe4bd88f2d0d.jpg)  
+(f) G: S and GAN loss, I: GAN loss only
+
+![](images/c82ac2826b7806b7c0ba8cf563fd2ffcaa3c43ab51fcd20911ca9dda93b906d5.jpg)  
+(g) G: S loss only, I: S and GAN loss
+
+![](images/49c0f1002d5b450bc923865f91e3b18d15f07d7c854ca2714774ab3647801e2a.jpg)  
+(h) G: GAN loss only, I: S and GAN loss
+
+![](images/31e865395490289cff0612ce8a331ba74695faa7bc947b3e52871c43343fbff7.jpg)  
+(i) G: S and GAN loss, I: S and GAN loss

parse/train/Hk3mPK5gg/Hk3mPK5gg.md

@@ -0,0 +1,207 @@
+# TRAINING AGENT FOR FIRST-PERSON SHOOTERGAME WITH ACTOR-CRITIC CURRICULUM LEARNING
+
+Yuxin Wu Carnegie Mellon University ppwwyyxx@gmail.com
+
+Yuandong Tian Facebook AI Research yuandong@fb.com
+
+# ABSTRACT
+
+In this paper, we propose a new framework for training vision-based agent for First-Person Shooter (FPS) Game, in particular Doom. Our framework combines the state-of-the-art reinforcement learning approach (Asynchronous Advantage Actor-Critic (A3C) model [Mnih et al. (2016)]) with curriculum learning. Our model is simple in design and only uses game states from the AI side, rather than using opponents’ information [Lample & Chaplot (2016)]. On a known map, our agent won 10 out of the 11 attended games and the champion of Track1 in ViZDoom AI Competition 2016 by a large margin, $3 5 \%$ higher score than the second place.
+
+# 1 INTRODUCTION
+
+Deep Reinforcement Learning has achieved super-human performance in fully observable environments, e.g., in Atari Games [Mnih et al. (2015)] and Computer Go [Silver et al. (2016)]. Recently, Asynchronous Advantage Actor-Critic (A3C) [Mnih et al. (2016)] model shows good performance for 3D environment exploration, e.g. labyrinth exploration. However, in general, to train an agent in a partially observable 3D environment from raw frames remains an open challenge. Direct application of A3C to competitive 3D scenarios, e.g. 3D games, is nontrivial, partly due to sparse and long-term rewards in such scenarios.
+
+Doom is a 1993 First-Person Shooter (FPS) game in which a player fights against other computercontrolled agents or human players in an adversarial 3D environment. Previous works on FPS AI [van Waveren (2001)] focused on using hand-tuned state machines and privileged information, e.g., the geometry of the map, the precise location of all players, to design playable agents. Although state-machine is conceptually simple and computationally efficient, it does not operate like human players, who only rely on visual (and possibly audio) inputs. Also, many complicated situations require manually-designed rules which could be time-consuming to tune.
+
+In this paper, we train an AI agent in Doom with a framework that based on A3C with convolutional neural networks (CNN). This model uses only the recent 4 frames and game variables from the AI side, to predict the next action of the agent and the value of the current situation. We follow the curriculum learning paradigm [Bengio et al. (2009); Jiang et al. (2015)]: start from simple tasks and then gradually try harder ones. The difficulty of the task is controlled by a variety of parameters in Doom environment, including different types of maps, strength of the opponents and the design of the reward function. We also develop adaptive curriculum training that samples from a varying distribution of tasks to train the model, which is more stable and achieves higher score than A3C with the same number of epoch. As a result, our trained agent, named $F l$ , won the champion in Track 1 of ViZDoom Competition 1 by a large margin.
+
+There are many contemporary efforts on training a Doom AI based on the VizDoom platform [Kempka et al. (2016)] since its release. Arnold [Lample & Chaplot (2016)] also uses game frames and trains an action network using Deep Recurrent Q-learning [Hausknecht & Stone (2015)], and a navigation network with DQN [Mnih et al. (2015)]. However, there are several important differences. To predict the next action, they use a hybrid architecture (CNN+LSTM) that involves more complicated training procedure. Second, in addition to game frames, they require internal game status about the opponents as extra supervision during training, e.g., whether enemy is present in the current frame. IntelAct [Dosovitskiy & Koltun (2017)] models the Doom AI bot training in a supervised manner by predicting the future values of game variables (e.g., health, amount of ammo, etc) and acting accordingly. In comparison, we use curriculum learning with asynchronized actorcritic models and use stacked frames (4 most recent frames) and resized frames to mimic short-term memory and attention. Our approach requires no opponent’s information, and is thus suitable as a general framework to train agents for close-source games.
+
+![](images/94e7209ea3441576d67165943add7c75f4dd503b4fae9ca36f17aa99178edeb9.jpg)  
+Figure 1: The basic framework of actor-critic model.
+
+In VizDoom AI Competition 2016 at IEEE Computational Intelligence And Games (CIG) Conference2, our AI won the champion of Track1 (limited deathmatch with known map), and IntelAct won the champion of Track2 (full deathmatch with unknown maps). Neither of the two teams attends the other track. Arnold won the second places of both tracks and CLYDE [Ratcliffe et al. (2017)] won the third place of Track1.
+
+# 2 THE ACTOR-CRITIC MODEL
+
+The goal of Reinforcement Learning (RL) is to train an agent so that its behavior maximizes/minimizes expected future rewards/penalties it receives from a given environment [Sutton & Barto (1998)]. Two functions play important roles: a value function $\bar { V } ( s )$ that gives the expected reward of the current state $s$ , and a policy function $\pi ( a | s )$ that gives a probability distribution on the candidate actions $a$ for the current state $s$ . Getting the groundtruth value of either function would largely solve RL: the agent just follows $\pi ( a | s )$ to act, or jumps in the best state provided by $V ( s )$ when the number of candidate next states is finite and practically enumerable. However, neither is trivial.
+
+Actor-critic models [Barto et al. (1983); Sutton (1984); Konda & Tsitsiklis (1999); Grondman et al. (2012)] aim to jointly estimate $V ( s )$ and $\pi ( a | s )$ : from the current state $s _ { t }$ , the agent explores the environment by iteratively sampling the policy function $\pi ( a _ { t } | s _ { t } ; \mathbf { w } _ { \pi } )$ and receives positive/negative reward, until the terminal state or a maximum number of iterations are reached. The exploration gives a trajectory $\left\{ \bigl ( s _ { t } , a _ { t } , r _ { t } \bigr ) , \bigl ( s _ { t + 1 } , a _ { t + 1 } , r _ { t + 1 } \bigr ) , \cdot \cdot \cdot \right\}$ , from which the policy function and value function are updated. Specifically, to update the value function, we use the expected reward $R _ { t }$ along the trajectory as the ground truth; to update the policy function, we encourage actions that lead to high rewards, and penalize actions that lead to low rewards. To determine whether an action leads to high- or low-rewarding state, a reference point, called baseline [Williams (1992)], is usually needed. Using zero baseline might increase the estimation variance. [Peters & Schaal (2008)] gives a way to estimate the best baseline (a weighted sum of cumulative rewards) that minimizes the variance of the gradient estimation, in the scenario of episodic REINFORCE [Williams (1992)].
+
+In actor-critic frameworks, we pick the baseline as the expected cumulative reward $V ( s )$ of the current state, which couples the two functions $V ( s )$ and $\pi ( a | s )$ together in the training, as shown in Fig. 1. Here the two functions reinforce each other: a correct $\pi ( a | s )$ gives high-rewarding trajectories which update $V ( s )$ towards the right direction; a correct $V ( s )$ picks out the correct actions for $\pi ( a | s )$ to reinforce. This mutual reinforcement behavior makes actor-critic model converge faster, but is also prone to converge to bad local minima, in particular for on-policy models that follow the very recent policy to sample trajectory during training. If the experience received by the agent in consecutive batches is highly correlated and biased towards a particular subset of the environment, then both $\pi ( a | s )$ and $V ( s )$ will be updated towards a biased direction and the agent may never see the whole picture. To reduce the correlation of game experience, Asynchronous Advantage ActorCritic Model [Mnih et al. (2016)] runs independent multiple threads of the game environment in parallel. These game instances are likely uncorrelated, therefore their experience in combination would be less biased.
+
+![](images/3195acd31df59ed688f0d1008bb33671b952f495ee12e0056935bb075cb887b1.jpg)  
+Figure 2: Two maps we used in the paper. FlatMap is a simple square containing four pillars . CIGTrack1 is the map used in Track1 in ViZDoom AI Competition (We did not attend Track2). Black dots are items (weapons, ammo, medkits, armors, etc).
+
+For on-policy models, the same mutual reinforcement behavior will also lead to highly-peaked $\pi ( a | s )$ towards a few actions (or a few fixed action sequences), since it is always easy for both actor and critic to over-optimize on a small portion of the environment, and end up “living in their own realities”. To reduce the problem, [Mnih et al. (2016)] added an entropy term to the loss to encourage diversity, which we find to be critical. The final gradient update rules are listed as follows:
+
+$$
+\begin{array} { r l } & { \mathbf { w } _ { \pi }  \mathbf { w } _ { \pi } + \alpha ( R _ { t } - V ( s _ { t } ) ) \nabla _ { \mathbf { w } _ { \pi } } \log \pi ( a _ { t } | s _ { t } ) + \beta \nabla _ { \mathbf { w } _ { \pi } } H ( \pi ( \cdot | s _ { t } ) ) } \\ & { \mathbf { w } _ { V }  \mathbf { w } _ { V } - \alpha \nabla _ { \mathbf { w } _ { V } } ( R _ { t } - V ( s _ { t } ) ) ^ { 2 } } \end{array}
+$$
+
+where rate. I $\begin{array} { r } { R _ { t } = \sum _ { t ^ { \prime } = t } ^ { T } \gamma ^ { t ^ { \prime } - t } r _ { t ^ { \prime } } } \end{array}$ is the expected discounted reward at time uber loss instead of the L2 loss in Eqn. 2. $t$ and $\alpha , \beta$ are the learning
+
+Architecture. While [Mnih et al. (2016)] keeps a separate model for each asynchronous agent and perform model synchronization once in a while, we use an alternative approach called BatchA3C, in which all agents act on the same model and send batches to the main process for gradient descent optimization. The agents’ models are updated after each gradient update. Note that the contemporary work GA3C [Babaeizadeh et al. (2017)] also proposes a similar architecture. In their architecture, there is a prediction queue that collects agents’ experience and sends them to multiple predictors, and a training queue that collects experience to feed the optimization.
+
+# 3 DOOM AS A REINFORCEMENT LEARNING PLATFORM
+
+In Doom, the player controls the agent to fight against enemies in a 3D environment (e.g., in a maze). The agent can only see the environment from his viewpoint and thus receives partial information upon which it makes decisions. On modern computers, the original Doom runs in thousands of frames per second, making it suitable as a platform for training AI agent. ViZDoom [Kempka et al. (2016)] is an open-source platform that offers programming interface to communicate with Doom engine, ZDoom3. From the interface, users can obtain current frames of the game, and control the agent’s action. ViZDoom offers much flexibility, including:
+
+Rich Scenarios. Many customized scenarios are made due to the popularity of the game, offering a variety of environments to train from. A scenario consists of many components, including 2D maps for the environment, scripts to control characters and events. Open-source tools, such as $\mathrm { S L A D E ^ { 4 } }$ , are also widely available to build new scenarios. We built our customized map (Fig. 2(b)) for training.
+
+Game variables. In addition to image frames, ViZDoom environment also offers many games variables revealing the internal state of the game. This includes HEALTH, AMMO ? (agent’s health and ammunition), FRAG COUNT (current score) and so on. ViZDoom also offers USER? variables that are computed on the fly via scenario scripts. These USER? variables can provide more information of the agent, e.g., their spatial locations. Enemy information could also be obtained by modifying ViZDoom [Lample & Chaplot (2016)]. Such information is used to construct a reward function, or as a direct supervision to accelerate training [Lample & Chaplot (2016)].
+
+Built-in bots. Built-in bots can be inserted in the battle. They are state machines with privileged information over the map and the player, which results in apparently decent intelligence with minimal computational cost. By competing against built-in bots, the agent learns to improve.
+
+Evaluation Criterion. In FPS games, to evaluate their strength, multiple AIs are placed to a scenario for a deathmatch, in which every AI plays for itself against the remaining AIs. Frags per episode, the number of kills minus the number of suicides for the agent in one round of game, is often used as a metric. An AI is stronger if its frags is ranked higher against others. In this work, we use an episode of 2-minute game time (4200 frames in total) for all our evaluations unless noted otherwise.
+
+![](images/2a0421b333ba3847e2e760ffda72c7e8371f15e03dbe3c963a3f918dae440576.jpg)  
+Figure 3: The network structure of the proposed model. It takes 4 recent game frames plus 4 recent attention frames as the input state $s$ , and outputs a probability distribution $\pi ( a | s )$ of the 6 discrete actions. The policy and value network share parameters.
+
+# 4 METHOD
+
+# 4.1 NETWORK ARCHITECTURE
+
+We use convolutional neural networks to extract features from the game frames and then combine its output representation with game variables. Fig. 3 shows the network architecture and Tbl. 1 gives the parameters. It takes the frames as the input (i.e., the state $s$ ) and outputs two branches, one that outputs the value function $V ( s )$ by regression, while the other outputs the policy function $\pi ( s | a )$ by a regular softmax. The parameters of the two functions are shared before the branch.
+
+For input, we use the most recent 4 frames plus the center part of them, scaled to the same size $( 1 2 0 \times 1 2 0 )$ . Therefore, these centered “attention frames” have higher resolution than regular game frames, and greatly increase the aiming accuracy. The policy network will give 6 actions, namely MOVE FORWARD, MOVE LEFT, MOVE RIGHT, TURN LEFT, TURN RIGHT, and ATTACK. We found other on-off actions (e.g., MOVE BACKWARD) offered by ViZDoom less important. After feature extraction by convolutional network, game variables are incorporated. This includes the agent’s Health (0-100) and Ammo (how many bullets left). They are related to AI itself and thus legal in the game environment for training, testing and ViZDoom AI competition.
+
+# 4.2 TRAINING PIPELINE
+
+Our training procedure is implemented with TensorFlow [Abadi et al. (2016)] and tensorpack5. We open 255 processes, each running one Doom instance, and sending experience $\left( { { s _ { t } } , { a _ { t } } , { r _ { t } } } \right)$ to the main process which runs the training procedure. The main process collects frames from different game instances to create batches, and optimizes on these batches asynchronously on one or more GPUs using Eqn. 1 and Eqn. 2. The frames from different processes running independent game instances, are likely to be uncorrelated, which stabilizes the training. This procedure is slightly different from the original A3C, where each game instance collects their own experience and updates the parameters asynchronously.
+
+Table 1: Network parameters. $C 7 x 7 x 3 2 s 2 =$ convolutional layer with $7 \mathbf { x } 7$ kernel, stride 2 and number of output planes 32. $M P =$ MaxPooling. Each convolutional and fully connected layer is followed by a ReLU, except for the last output layer.   
+
+<table><tr><td rowspan=1 colspan=1>Layer #</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>2</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>6</td><td rowspan=1 colspan=1>7</td></tr><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>C7x7x32s2</td><td rowspan=1 colspan=1>C7x7x64s2</td><td rowspan=1 colspan=1>MP3x3s2</td><td rowspan=1 colspan=1>C3x3x128</td><td rowspan=1 colspan=1>MP3x3s2</td><td rowspan=1 colspan=1>C3x3x192</td><td rowspan=1 colspan=1>FC1024</td></tr></table>
+
+Table 2: Parameters for different maps.   
+
+<table><tr><td>Parameters</td><td>Description</td><td>FlatMap</td><td>CIGTrack1</td></tr><tr><td>living</td><td>Penalize agent who just lives</td><td colspan="2">-0.008/action</td></tr><tr><td>health_loss</td><td>Penalize health decrement</td><td colspan="2">-0.05 /unit</td></tr><tr><td>ammo_loss</td><td>Penalize ammunition decrement</td><td colspan="2">-0.04/unit</td></tr><tr><td>health_pickup</td><td>Reward for medkit pickup</td><td colspan="2">0.04/unit</td></tr><tr><td>ammo-pickup</td><td>Reward for ammunition pickup</td><td colspan="2">0.15 /unit</td></tr><tr><td>dist-penalty dist_reward</td><td>Penalize the agent when it stays</td><td colspan="2">-0.03 /action</td></tr><tr><td>dist_penalty_thres</td><td>Reward the agent when it moves</td><td colspan="2">9e-5/unit distance</td></tr><tr><td rowspan="2">num_bots</td><td>Thresholdofdisplacement</td><td>8</td><td>15</td></tr><tr><td>Number of built-in bots</td><td>8</td><td>16</td></tr></table>
+
+Despite the use of entropy term, we still find that $\pi ( \cdot | s )$ is highly peaked. Therefore, during trajectory exploration, we encourage exploration by the following changes: a) multiply the policy output of the network by an exploration factor (0.2) before softmax b) uniformly randomize the action for $10 \%$ random frames.
+
+As mentioned in [Kempka et al. (2016)], care should be taken for frame skips. Small frame skip introduces strong correlation in the training set, while big frame skip reduces effective training samples. We set frame skip to be 3. We choose $6 4 0 \mathrm { x } 4 8 0$ as the input frame resolution and do not use high aspect ratio resolution [Lample & Chaplot (2016)] to increase the field of view.
+
+We use Adam [Kingma & Ba (2014)] with $\epsilon = 1 0 ^ { - 3 }$ for training. Batch size is 128, discount factor $\gamma = 0 . 9 9$ , learning rate $\alpha = 1 0 ^ { - 4 }$ and the policy learning rate $\beta = 0 . 0 8 \alpha$ . The model is trained from scratch. The training procedure runs on Intel Xeon CPU E5-2680v2 at 2. 80GHz, and 2 TitanX GPUs. It takes several days to obtain a decent result. Our final model, namely the $F l$ bot, is trained for around 3 million mini-batches on multiple different scenarios.
+
+# 4.3 CURRICULUM LEARNING
+
+When the environment only gives very sparse rewards, or adversarial, A3C takes a long time to converge to a satisfying solution. A direct training with A3C on the map CIGTrack1 with 8 builtin bots does not yield sensible performance. To address this, we use curriculum learning [Bengio et al. (2009)] that trains an agent with a sequence of progressively more difficult environments. By varying parameters in Doom (Sec. 3), we could control its difficulty level.
+
+<table><tr><td rowspan=1 colspan=4>Class 0  Class 1  Class 2</td><td rowspan=1 colspan=1>Class 3</td><td rowspan=1 colspan=1>Class 4</td><td rowspan=1 colspan=1>Class 5</td><td rowspan=1 colspan=1>Class 6</td><td rowspan=1 colspan=1>Class 7</td></tr><tr><td rowspan=1 colspan=1>Speed</td><td rowspan=1 colspan=1>0.2</td><td rowspan=1 colspan=1>0.2</td><td rowspan=1 colspan=1>0.4</td><td rowspan=1 colspan=1>0.4</td><td rowspan=1 colspan=1>0.6</td><td rowspan=1 colspan=1>0.8</td><td rowspan=1 colspan=1>0.8</td><td rowspan=1 colspan=1>1.0</td></tr><tr><td rowspan=1 colspan=1>Health</td><td rowspan=1 colspan=1>40</td><td rowspan=1 colspan=1>40</td><td rowspan=1 colspan=1>40</td><td rowspan=1 colspan=1>60</td><td rowspan=1 colspan=1>60</td><td rowspan=1 colspan=1>60</td><td rowspan=1 colspan=1>80</td><td rowspan=1 colspan=1>100</td></tr></table>
+
+Table 3: Curriculum design for FlatMap. Note that enemy uses RocketLauncher except for Class 0 (Pistol).
+
+Reward Shaping. Reward shaping has been shown to be an effective technique to apply reinforcement learning in a complicated environment with delayed reward $[ \mathrm { N g }$ et al. (1999); Devlin et al. (2011)]. In our case, besides the basic reward for kills $( + 1 )$ and death (-1), intermediate rewards are used as shown in Tbl. 2. We penalize agent with a living state, encouraging it to explore and encounter more enemies. health loss and ammo loss place linear reward for a decrement of health and ammunition. ammo pickup and health pickup place reward for picking up these two items. In addition, there is extra reward for picking up ammunition when in need (e.g. almost out of ammo). dist penalty and dist reward push the agent away from the previous locations, encouraging it to explore. The penalty is applied every action, when the displacement of the bot relative to the last state is less than a threshold dist penalty thres. And dist reward is applied for every unit displacement the agent makes. Similar to [Lample & Chaplot (2016)], the displacement information is computed from the ground truth location variables provided by Doom engine, and will not be used in the competition. However, unlike [Lample & Chaplot (2016)] that uses enemy-in-sight signal for training, locations can be extracted directly from USER? variables, or can easily be computed roughly with action history.
+
+Curriculum Design. We train the bot on FlatMap that contains a simple square with a few pillars (Fig. 2(a)) with several curricula (Tbl. 3), and then proceed to CIGTrack1. For each map, we design curricula by varying the strength of built-in bots, i.e., their moving speed, initial health and initial weapon. Our agent always uses RocketLauncher as its only weapon. Training on FlatMap leads to a capable initial model which is quickly adapted to more complicated maps. As shown in Tbl. 2, for CIGTrack1 we increase dist penalty thres to keep the agent moving, and increase num bots so that the agent encounters more enemies per episode.
+
+Adaptive Curriculum. In addition to staged curriculum learning, we also design adaptive curriculum learning by assigning a probability distribution on different levels for each thread that runs a Doom instance. The probability distribution shifts towards more difficult curriculum when the agent performs well on the current distribution, and shifts towards easier level otherwise. We consider the agent to perform well if its frag count is greater than 10 points.
+
+# 4.4 POST-TRAINING RULES
+
+For a better performance in the competition, we also put several rules to process the action given by the trained policy network, called post-training (PT) rules. There are two sets of buttons in ViZDoom: on-off buttons and delta buttons. While on-off button maps to the binary states of a keystroke (e.g., pressing the up arrow key will move the agent forward), delta buttons mimic the mouse behavior and could act faster in certain situations. Therefore, we setup rules that detect the intention of the agent and accelerate with delta button. For example, when the agent turns by invoking TURN LEFT repeatedly, we convert its action to TURN LEFT RIGHT DELTA for acceleration. Besides, the trained model might get stuck in rare situations, e.g., keep moving forward but blocked by an explosive bucket. We also designed rules to detect and fix them.
+
+# 5 EXPERIMENT
+
+In this section, we show the training procedure (Sec. 5.1), evaluate our AIs with ablation analysis (Sec. 5.2) and ViZDoom AI Competition (Sec. 5.3). We mainly compare among three AIs: (1) F1Pre, the bot trained with FlatMap only, (2) F1Plain, the bot trained on both FlatMap and CIGTrack1, but without post-training rules, and (3) the final $F l$ bot that attends competition.
+
+# 5.1 CURRICULUM LEARNING ON FL A TMA P
+
+Fig. 4 shows that the curriculum learning increases the performance of the agents over all levels. When an agent becomes stronger in the higher level of class, it is also stronger in the lower level of class without overfitting. Fig. 5 shows comparison between adaptive curriculum learning with pure A3C. We can see that pure A3C can learn on FlatMap but is slower. Moreover, in CIGTrack1, a direct application of A3C does not yield sensible performance.
+
+![](images/d72c27739b6db20e52495fe4e07e135bfbb24984821015d05ffc9ec11bf706ce.jpg)  
+Figure 4: Average Frags over 300 episodes evaluation, on FlatMap(left) and CIGTrack1(right) with different levels of enemies (See Tbl. 3 for curriculum design). Models from later stages performs better especially on the difficult map, yet still keeps a good performance on the easier map.
+
+![](images/ad4bd531ba59b063ff2e2cb3cd119ad0c822eca03e7562097dfe0dc1b19fed27.jpg)  
+Figure 5: Performance comparison on Class 7 (hardest) of FlatMap between A3C [Mnih et al. (2016)] and adaptive curriculum learning, at different stage of training. Average frags and max frags are computed from 100 episodes. Adaptive curriculum shows higher performance and is relatively more stable.
+
+# 5.2 ABLATION ANALYSIS
+
+Visualization. Fig. 6 shows the visualization of the first convolutional layer of the trained AI agent. We could see that the convolutional kernels of the current frame is less noisy than the kernels of previous frames. This means that the agent makes the most use of the current frames.
+
+Effect of History Frames. Interestingly, while the agent focuses on the current frame, it also uses motion information. For this, we use (1) 4 duplicated current frames (2) 4 recent frames in reverse order, as the input. This gives 8.50 and 2.39 mean frags, compared to 10.34 in the normal case, showing that the agent heavily uses the motion information for better decision. In particular, the bot is totally confused with the reversed motion feature. Detailed results are shown in Tbl. 5.
+
+![](images/66a68449811ccd1853c0ae74280a568bba1e9234290164ddd9cd147902eb9bb3.jpg)  
+Figure 6: Visualization of the convolutional filters in the first layer of our network. The filters are grouped by the frame index they corresponds to. Each group consists of two rows of 32 RGB filters for the regular and attention frames, respectively. The filters corresponding to the current frame (last row) is less noisy than those of others, showing that the bot is more focused on the current frame.
+
+Table 4: Avg/Max frags of each AIs in the internal tournament (150 episodes of 10 minutes each).   
+
+<table><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>Built-In AI</td><td rowspan=1 colspan=1>F1Pre</td><td rowspan=1 colspan=1>F1Plain</td><td rowspan=1 colspan=1>F1</td></tr><tr><td rowspan=1 colspan=1>FlatMap</td><td rowspan=1 colspan=1>8.07/20</td><td rowspan=1 colspan=1>14.47/24</td><td rowspan=1 colspan=1>17.26/29</td><td rowspan=1 colspan=1>22.45/37</td></tr><tr><td rowspan=1 colspan=1>CIGTrack1</td><td rowspan=1 colspan=1>0.48/7</td><td rowspan=1 colspan=1>3.56/15</td><td rowspan=1 colspan=1>8.58/16</td><td rowspan=1 colspan=1>10.65/18</td></tr></table>
+
+<table><tr><td></td><td colspan="3">FlatMap</td><td colspan="3">CIGTrack1</td></tr><tr><td></td><td>Min</td><td>Mean</td><td>Max</td><td>Min</td><td>Mean</td><td>Max</td></tr><tr><td>F1 bot (reverse history)</td><td>1</td><td>9.89</td><td>19</td><td>-2</td><td>2.39</td><td>9</td></tr><tr><td>F1 bot (duplicated history)</td><td>10</td><td>24.62</td><td>37</td><td>2</td><td>8.50</td><td>17</td></tr><tr><td>F1 bot (w/o PT rules)</td><td>14</td><td>22.80</td><td>36</td><td>1</td><td>8.66</td><td>18</td></tr><tr><td>F1 bot</td><td>16</td><td>25.17</td><td>37</td><td>5</td><td>10.34</td><td>17</td></tr></table>
+
+Table 5: Performance evaluation (in terms of frags) on two standard scenarios FlatMap and CIGTrack1 over 300 episodes. Our bot performs better with post-training rules.
+
+Post-training Rules. Tbl. 5 shows that the post-training rules improve the performance. As a future work, an end-to-end training involving delta buttons could make the bot better.
+
+Internal Tournament. We also evaluate our AIs with internal tournaments (Tbl. 4). All our bots beat the performance of built-in bots by a large margin, even though they use privileged information. F1Pre, trained with only FlatMap, shows decent performance, but is not as good as the models trained with both FlatMap and CIGTrack1. The final bot $F l$ performs the best.
+
+Behaviors. Visually, the three bots behave differently. F1Pre is a bit overtrained in FlatMap and does not move too often, but when it sees enemies, even faraway, it will start to shoot. Occasionally it will move to the corner and pick medkits. In CIGTrack1, F1Pre stays in one place and ambushes opponents who pass by. On the other hand, F1Plain and $F l$ always move forwards and turn at the corner. As expected, $F l$ moves and turns faster.
+
+Tactics All bots develop interesting local tactics when exchanging fire with enemy: they slide around when shooting the enemy. This is quite effective for dodging others’ attack. Also when they shoot the enemy, they usually take advantage of the splashing effect of rocket to cause additional damage for enemy, e.g., shooting the wall when the enemy is moving. They do not pick ammunition too often, even if they can no longer shoot. However, such disadvantage is mitigated by the nature of deathmatch: when a player dies, it will respawn with ammunition. We also check states with highest/lowest estimated future value $V ( s )$ over a 10-episode evaluation of $F l$ bot, from which we can speculate its tactics. The highest value is $V = 0 . 9 7$ when the agent fired, and about to hit the enemy. One low value is $V = - 0 . 4 4$ , ammo $= 0$ , when the agent encountered an enemy at the corner but is out of ammunition. Both cases are reasonable.
+
+# 5.3 COMPETITION
+
+We attended the ViZDoom AI Competition hosted by IEEE CIG. There are 2 tracks in the competition. Track 1 (Limited Deathmatch) uses a known map and fixed weapons, while Track 2 (Full Deathmatch) uses 3 unknown maps and a variety of weapons. Each bot fights against all others for 12 rounds of 10 minutes each. Due to server capacity, each bot skips one match in the first 9 rounds. All bots are supposed to run in real-time ${ \mathit { \Omega } } ^ { \prime } { > } 3 5$ fps) on a GTX960 GPU.
+
+<table><tr><td rowspan=1 colspan=1>Round</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>2</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>6</td><td rowspan=1 colspan=1>7</td><td rowspan=1 colspan=1>8</td><td rowspan=1 colspan=1>9</td><td rowspan=1 colspan=1>10</td><td rowspan=1 colspan=1>11</td><td rowspan=1 colspan=2>12 Total</td></tr><tr><td rowspan=1 colspan=1>Our bot</td><td rowspan=1 colspan=1>56</td><td rowspan=1 colspan=1>62</td><td rowspan=1 colspan=1>n/a</td><td rowspan=1 colspan=1>54</td><td rowspan=1 colspan=1>47</td><td rowspan=1 colspan=1>43</td><td rowspan=1 colspan=1>47</td><td rowspan=1 colspan=1>55</td><td rowspan=1 colspan=1>50</td><td rowspan=1 colspan=1>48</td><td rowspan=1 colspan=1>50</td><td rowspan=1 colspan=1>47</td><td rowspan=1 colspan=1>559</td></tr><tr><td rowspan=1 colspan=1>Arnold</td><td rowspan=1 colspan=1>36</td><td rowspan=1 colspan=1>34</td><td rowspan=1 colspan=1>42</td><td rowspan=1 colspan=1>36</td><td rowspan=1 colspan=1>36</td><td rowspan=1 colspan=1>45</td><td rowspan=1 colspan=1>36</td><td rowspan=1 colspan=1>39</td><td rowspan=1 colspan=1>n/a</td><td rowspan=1 colspan=1>33</td><td rowspan=1 colspan=1>36</td><td rowspan=1 colspan=1>40</td><td rowspan=1 colspan=1>413</td></tr><tr><td rowspan=1 colspan=1>CLYDE</td><td rowspan=1 colspan=1>37</td><td rowspan=1 colspan=1>n/a</td><td rowspan=1 colspan=1>38</td><td rowspan=1 colspan=1>32</td><td rowspan=1 colspan=1>37</td><td rowspan=1 colspan=1>30</td><td rowspan=1 colspan=1>46</td><td rowspan=1 colspan=1>42</td><td rowspan=1 colspan=1>33</td><td rowspan=1 colspan=1>24</td><td rowspan=1 colspan=1>44</td><td rowspan=1 colspan=1>30</td><td rowspan=1 colspan=1>393</td></tr></table>
+
+Table 6: Top 3 teams in ViZDoom AI Competition, Track 1. Our bot attended 11 out of 12 games, won 10 of them and won the champion by a large margin. For design details, see Arnold [Lample & Chaplot (2016)] and CLYDE [Ratcliffe et al. (2017)].
+
+Our $F l$ bot won 10 out of 11 attended games and won the champion for Track 1 by a large margin. We have achieved 559 frags, $3 5 . 4 \%$ higher than 413 frags achieved by Arnold [Lample & Chaplot (2016)], that uses extra game state for model training. On the other hand, IntelAct [Dosovitskiy & Koltun (2017)] won Track 2. The full videos for the two tracks have been released67, as well as an additional game between Human and $\mathrm { A I s } ^ { 8 }$ . Our bot behaves reasonable and very human-like in Track 1. In the match between Human and AIs, our bot was even ahead of the human player for a short period (6:30 to 7:00).
+
+# 6 CONCLUSION
+
+Teaching agents to act properly in complicated and adversarial 3D environment is a very challenging task. In this paper, we propose a new framework to train a strong AI agent in a First-Person Shooter (FPS) game, Doom, using a combination of state-of-the-art Deep Reinforcement Learning and Curriculum Training. Via playing against built-in bots in a progressive manner, our bot wins the champion of Track1 (known map) in ViZDoom AI Competition. Furthermore, it learns to use motion features and build its own tactics during the game, which is never taught explicitly.
+
+Currently, our bot is still an reactive agent that only remembers the last 4 frames to act. Ideally, a bot should be able to build a map from an unknown environment and localize itself, is able to have a global plan to act, and visualize its reasoning process. We leave them to future works.
+
+# REFERENCES
+
+Abadi, Mart´ın, Agarwal, Ashish, Barham, Paul, Brevdo, Eugene, Chen, Zhifeng, Citro, Craig, Corrado, Gregory S., Davis, Andy, Dean, Jeffrey, Devin, Matthieu, Ghemawat, Sanjay, Goodfellow, Ian J., Harp, Andrew, Irving, Geoffrey, Isard, Michael, Jia, Yangqing, Jozefowicz, Rafal, Kaiser, ´ Lukasz, Kudlur, Manjunath, Levenberg, Josh, Mane, Dan, Monga, Rajat, Moore, Sherry, Murray, ´ Derek Gordon, Olah, Chris, Schuster, Mike, Shlens, Jonathon, Steiner, Benoit, Sutskever, Ilya, Talwar, Kunal, Tucker, Paul A., Vanhoucke, Vincent, Vasudevan, Vijay, Viegas, Fernanda B., ´ Vinyals, Oriol, Warden, Pete, Wattenberg, Martin, Wicke, Martin, Yu, Yuan, and Zheng, Xiaoqiang. Tensorflow: Large-scale machine learning on heterogeneous distributed systems. CoRR, abs/1603.04467, 2016. URL http://arxiv.org/abs/1603.04467.
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+Babaeizadeh, Mohammad, Frosio, Iuri, Tyree, Stephen, Clemons, Jason, and Kautz, Jan. Reinforcement learning through asynchronous advantage actor-critic on a gpu. International Conference on Learning Representations (ICLR), 2017.
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+Barto, Andrew G, Sutton, Richard S, and Anderson, Charles W. Neuronlike adaptive elements that can solve difficult learning control problems. IEEE transactions on systems, man, and cybernetics, (5):834–846, 1983.
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+Bengio, Yoshua, Louradour, Jer´ ome, Collobert, Ronan, and Weston, Jason. Curriculum learning. In ˆ Proceedings of the 26th annual international conference on machine learning, pp. 41–48. ACM, 2009.
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+Devlin, Sam, Kudenko, Daniel, and Grzes, Marek. An empirical study of potential-based reward ´ shaping and advice in complex, multi-agent systems. Advances in Complex Systems, 14(02): 251–278, 2011.
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+Dosovitskiy, Alexey and Koltun, Vladlen. Learning to act by predicting the future. International Conference on Learning Representations (ICLR), 2017.
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+Grondman, Ivo, Busoniu, Lucian, Lopes, Gabriel AD, and Babuska, Robert. A survey of actor-critic reinforcement learning: Standard and natural policy gradients. IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), 42(6):1291–1307, 2012.
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+Hausknecht, Matthew J. and Stone, Peter. Deep recurrent q-learning for partially observable mdps. CoRR, abs/1507.06527, 2015. URL http://arxiv.org/abs/1507.06527.
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+Jiang, Lu, Meng, Deyu, Zhao, Qian, Shan, Shiguang, and Hauptmann, Alexander G. Self-paced curriculum learning. In AAAI, volume 2, pp. 6, 2015.
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+Kempka, Michał, Wydmuch, Marek, Runc, Grzegorz, Toczek, Jakub, and Jaskowski, Wojciech.´ Vizdoom: A doom-based ai research platform for visual reinforcement learning. arXiv preprint arXiv:1605.02097, 2016.
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+Kingma, Diederik and Ba, Jimmy. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014.
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+Konda, Vijay R and Tsitsiklis, John N. Actor-critic algorithms. In NIPS, volume 13, pp. 1008–1014, 1999.
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+Lample, Guillaume and Chaplot, Devendra Singh. Playing fps games with deep reinforcement learning. arXiv preprint arXiv:1609.05521, 2016.
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+Mnih, Volodymyr, Kavukcuoglu, Koray, Silver, David, Rusu, Andrei A, Veness, Joel, Bellemare, Marc G, Graves, Alex, Riedmiller, Martin, Fidjeland, Andreas K, Ostrovski, Georg, et al. Humanlevel control through deep reinforcement learning. Nature, 518(7540):529–533, 2015.
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+Mnih, Volodymyr, Badia, Adria Puigdomenech, Mirza, Mehdi, Graves, Alex, Lillicrap, Timothy P, Harley, Tim, Silver, David, and Kavukcuoglu, Koray. Asynchronous methods for deep reinforcement learning. arXiv preprint arXiv:1602.01783, 2016.
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+Ng, Andrew Y, Harada, Daishi, and Russell, Stuart. Policy invariance under reward transformations: Theory and application to reward shaping. In ICML, volume 99, pp. 278–287, 1999.
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+Peters, Jan and Schaal, Stefan. Reinforcement learning of motor skills with policy gradients. Neural networks, 21(4):682–697, 2008.
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+Ratcliffe, D., Devlin, S., Kruschwitz, U., and Citi, L. Clyde: A deep reinforcement learning doom playing agent. AAAI Workshop on What’s next for AI in games, 2017.
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+Silver, David, Huang, Aja, Maddison, Chris J, Guez, Arthur, Sifre, Laurent, Van Den Driessche, George, Schrittwieser, Julian, Antonoglou, Ioannis, Panneershelvam, Veda, Lanctot, Marc, et al. Mastering the game of go with deep neural networks and tree search. Nature, 529(7587):484–489, 2016.
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+Sutton, Richard S and Barto, Andrew G. Reinforcement learning: An introduction, volume 1. 1998.
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+Sutton, Richard Stuart. Temporal credit assignment in reinforcement learning. 1984.
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+van Waveren, J.M.P. The Quake III Arena bot. University of Technology Delft, 2001.
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+Williams, Ronald J. Simple statistical gradient-following algorithms for connectionist reinforcement learning. Machine learning, 8(3-4):229–256, 1992.

parse/train/Hk3mPK5gg/Hk3mPK5gg_content_list.json

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+    {
+        "type": "text",
+        "text": "TRAINING AGENT FOR FIRST-PERSON SHOOTERGAME WITH ACTOR-CRITIC CURRICULUM LEARNING",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Yuxin Wu Carnegie Mellon University ppwwyyxx@gmail.com ",
+        "bbox": [
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+            170,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Yuandong Tian Facebook AI Research yuandong@fb.com ",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            250,
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+            263
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we propose a new framework for training vision-based agent for First-Person Shooter (FPS) Game, in particular Doom. Our framework combines the state-of-the-art reinforcement learning approach (Asynchronous Advantage Actor-Critic (A3C) model [Mnih et al. (2016)]) with curriculum learning. Our model is simple in design and only uses game states from the AI side, rather than using opponents’ information [Lample & Chaplot (2016)]. On a known map, our agent won 10 out of the 11 attended games and the champion of Track1 in ViZDoom AI Competition 2016 by a large margin, $3 5 \\%$ higher score than the second place. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            430,
+            336,
+            446
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Deep Reinforcement Learning has achieved super-human performance in fully observable environments, e.g., in Atari Games [Mnih et al. (2015)] and Computer Go [Silver et al. (2016)]. Recently, Asynchronous Advantage Actor-Critic (A3C) [Mnih et al. (2016)] model shows good performance for 3D environment exploration, e.g. labyrinth exploration. However, in general, to train an agent in a partially observable 3D environment from raw frames remains an open challenge. Direct application of A3C to competitive 3D scenarios, e.g. 3D games, is nontrivial, partly due to sparse and long-term rewards in such scenarios. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Doom is a 1993 First-Person Shooter (FPS) game in which a player fights against other computercontrolled agents or human players in an adversarial 3D environment. Previous works on FPS AI [van Waveren (2001)] focused on using hand-tuned state machines and privileged information, e.g., the geometry of the map, the precise location of all players, to design playable agents. Although state-machine is conceptually simple and computationally efficient, it does not operate like human players, who only rely on visual (and possibly audio) inputs. Also, many complicated situations require manually-designed rules which could be time-consuming to tune. ",
+        "bbox": [
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+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "In this paper, we train an AI agent in Doom with a framework that based on A3C with convolutional neural networks (CNN). This model uses only the recent 4 frames and game variables from the AI side, to predict the next action of the agent and the value of the current situation. We follow the curriculum learning paradigm [Bengio et al. (2009); Jiang et al. (2015)]: start from simple tasks and then gradually try harder ones. The difficulty of the task is controlled by a variety of parameters in Doom environment, including different types of maps, strength of the opponents and the design of the reward function. We also develop adaptive curriculum training that samples from a varying distribution of tasks to train the model, which is more stable and achieves higher score than A3C with the same number of epoch. As a result, our trained agent, named $F l$ , won the champion in Track 1 of ViZDoom Competition 1 by a large margin. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "There are many contemporary efforts on training a Doom AI based on the VizDoom platform [Kempka et al. (2016)] since its release. Arnold [Lample & Chaplot (2016)] also uses game frames and trains an action network using Deep Recurrent Q-learning [Hausknecht & Stone (2015)], and a navigation network with DQN [Mnih et al. (2015)]. However, there are several important differences. To predict the next action, they use a hybrid architecture (CNN+LSTM) that involves more complicated training procedure. Second, in addition to game frames, they require internal game status about the opponents as extra supervision during training, e.g., whether enemy is present in the current frame. IntelAct [Dosovitskiy & Koltun (2017)] models the Doom AI bot training in a supervised manner by predicting the future values of game variables (e.g., health, amount of ammo, etc) and acting accordingly. In comparison, we use curriculum learning with asynchronized actorcritic models and use stacked frames (4 most recent frames) and resized frames to mimic short-term memory and attention. Our approach requires no opponent’s information, and is thus suitable as a general framework to train agents for close-source games. ",
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+    {
+        "type": "image",
+        "img_path": "images/94e7209ea3441576d67165943add7c75f4dd503b4fae9ca36f17aa99178edeb9.jpg",
+        "image_caption": [
+            "Figure 1: The basic framework of actor-critic model. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "type": "text",
+        "text": "",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In VizDoom AI Competition 2016 at IEEE Computational Intelligence And Games (CIG) Conference2, our AI won the champion of Track1 (limited deathmatch with known map), and IntelAct won the champion of Track2 (full deathmatch with unknown maps). Neither of the two teams attends the other track. Arnold won the second places of both tracks and CLYDE [Ratcliffe et al. (2017)] won the third place of Track1. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "2 THE ACTOR-CRITIC MODEL ",
+        "text_level": 1,
+        "bbox": [
+            176,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The goal of Reinforcement Learning (RL) is to train an agent so that its behavior maximizes/minimizes expected future rewards/penalties it receives from a given environment [Sutton & Barto (1998)]. Two functions play important roles: a value function $\\bar { V } ( s )$ that gives the expected reward of the current state $s$ , and a policy function $\\pi ( a | s )$ that gives a probability distribution on the candidate actions $a$ for the current state $s$ . Getting the groundtruth value of either function would largely solve RL: the agent just follows $\\pi ( a | s )$ to act, or jumps in the best state provided by $V ( s )$ when the number of candidate next states is finite and practically enumerable. However, neither is trivial. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Actor-critic models [Barto et al. (1983); Sutton (1984); Konda & Tsitsiklis (1999); Grondman et al. (2012)] aim to jointly estimate $V ( s )$ and $\\pi ( a | s )$ : from the current state $s _ { t }$ , the agent explores the environment by iteratively sampling the policy function $\\pi ( a _ { t } | s _ { t } ; \\mathbf { w } _ { \\pi } )$ and receives positive/negative reward, until the terminal state or a maximum number of iterations are reached. The exploration gives a trajectory $\\left\\{ \\bigl ( s _ { t } , a _ { t } , r _ { t } \\bigr ) , \\bigl ( s _ { t + 1 } , a _ { t + 1 } , r _ { t + 1 } \\bigr ) , \\cdot \\cdot \\cdot \\right\\}$ , from which the policy function and value function are updated. Specifically, to update the value function, we use the expected reward $R _ { t }$ along the trajectory as the ground truth; to update the policy function, we encourage actions that lead to high rewards, and penalize actions that lead to low rewards. To determine whether an action leads to high- or low-rewarding state, a reference point, called baseline [Williams (1992)], is usually needed. Using zero baseline might increase the estimation variance. [Peters & Schaal (2008)] gives a way to estimate the best baseline (a weighted sum of cumulative rewards) that minimizes the variance of the gradient estimation, in the scenario of episodic REINFORCE [Williams (1992)]. ",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In actor-critic frameworks, we pick the baseline as the expected cumulative reward $V ( s )$ of the current state, which couples the two functions $V ( s )$ and $\\pi ( a | s )$ together in the training, as shown in Fig. 1. Here the two functions reinforce each other: a correct $\\pi ( a | s )$ gives high-rewarding trajectories which update $V ( s )$ towards the right direction; a correct $V ( s )$ picks out the correct actions for $\\pi ( a | s )$ to reinforce. This mutual reinforcement behavior makes actor-critic model converge faster, but is also prone to converge to bad local minima, in particular for on-policy models that follow the very recent policy to sample trajectory during training. If the experience received by the agent in consecutive batches is highly correlated and biased towards a particular subset of the environment, then both $\\pi ( a | s )$ and $V ( s )$ will be updated towards a biased direction and the agent may never see the whole picture. To reduce the correlation of game experience, Asynchronous Advantage ActorCritic Model [Mnih et al. (2016)] runs independent multiple threads of the game environment in parallel. These game instances are likely uncorrelated, therefore their experience in combination would be less biased. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/3195acd31df59ed688f0d1008bb33671b952f495ee12e0056935bb075cb887b1.jpg",
+        "image_caption": [
+            "Figure 2: Two maps we used in the paper. FlatMap is a simple square containing four pillars . CIGTrack1 is the map used in Track1 in ViZDoom AI Competition (We did not attend Track2). Black dots are items (weapons, ammo, medkits, armors, etc). "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "For on-policy models, the same mutual reinforcement behavior will also lead to highly-peaked $\\pi ( a | s )$ towards a few actions (or a few fixed action sequences), since it is always easy for both actor and critic to over-optimize on a small portion of the environment, and end up “living in their own realities”. To reduce the problem, [Mnih et al. (2016)] added an entropy term to the loss to encourage diversity, which we find to be critical. The final gradient update rules are listed as follows: ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/f21a1b91f1c0394ae1cea7dd829535036568fe2feff6f040e87f97f3251431ff.jpg",
+        "text": "$$\n\\begin{array} { r l } & { \\mathbf { w } _ { \\pi }  \\mathbf { w } _ { \\pi } + \\alpha ( R _ { t } - V ( s _ { t } ) ) \\nabla _ { \\mathbf { w } _ { \\pi } } \\log \\pi ( a _ { t } | s _ { t } ) + \\beta \\nabla _ { \\mathbf { w } _ { \\pi } } H ( \\pi ( \\cdot | s _ { t } ) ) } \\\\ & { \\mathbf { w } _ { V }  \\mathbf { w } _ { V } - \\alpha \\nabla _ { \\mathbf { w } _ { V } } ( R _ { t } - V ( s _ { t } ) ) ^ { 2 } } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where rate. I $\\begin{array} { r } { R _ { t } = \\sum _ { t ^ { \\prime } = t } ^ { T } \\gamma ^ { t ^ { \\prime } - t } r _ { t ^ { \\prime } } } \\end{array}$ is the expected discounted reward at time uber loss instead of the L2 loss in Eqn. 2. $t$ and $\\alpha , \\beta$ are the learning ",
+        "bbox": [
+            171,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Architecture. While [Mnih et al. (2016)] keeps a separate model for each asynchronous agent and perform model synchronization once in a while, we use an alternative approach called BatchA3C, in which all agents act on the same model and send batches to the main process for gradient descent optimization. The agents’ models are updated after each gradient update. Note that the contemporary work GA3C [Babaeizadeh et al. (2017)] also proposes a similar architecture. In their architecture, there is a prediction queue that collects agents’ experience and sends them to multiple predictors, and a training queue that collects experience to feed the optimization. ",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 DOOM AS A REINFORCEMENT LEARNING PLATFORM ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            722,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In Doom, the player controls the agent to fight against enemies in a 3D environment (e.g., in a maze). The agent can only see the environment from his viewpoint and thus receives partial information upon which it makes decisions. On modern computers, the original Doom runs in thousands of frames per second, making it suitable as a platform for training AI agent. ViZDoom [Kempka et al. (2016)] is an open-source platform that offers programming interface to communicate with Doom engine, ZDoom3. From the interface, users can obtain current frames of the game, and control the agent’s action. ViZDoom offers much flexibility, including: ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Rich Scenarios. Many customized scenarios are made due to the popularity of the game, offering a variety of environments to train from. A scenario consists of many components, including 2D maps for the environment, scripts to control characters and events. Open-source tools, such as $\\mathrm { S L A D E ^ { 4 } }$ , are also widely available to build new scenarios. We built our customized map (Fig. 2(b)) for training. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Game variables. In addition to image frames, ViZDoom environment also offers many games variables revealing the internal state of the game. This includes HEALTH, AMMO ? (agent’s health and ammunition), FRAG COUNT (current score) and so on. ViZDoom also offers USER? variables that are computed on the fly via scenario scripts. These USER? variables can provide more information of the agent, e.g., their spatial locations. Enemy information could also be obtained by modifying ViZDoom [Lample & Chaplot (2016)]. Such information is used to construct a reward function, or as a direct supervision to accelerate training [Lample & Chaplot (2016)]. ",
+        "bbox": [
+            174,
+            138,
+            825,
+            237
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Built-in bots. Built-in bots can be inserted in the battle. They are state machines with privileged information over the map and the player, which results in apparently decent intelligence with minimal computational cost. By competing against built-in bots, the agent learns to improve. ",
+        "bbox": [
+            174,
+            243,
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+            285
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Evaluation Criterion. In FPS games, to evaluate their strength, multiple AIs are placed to a scenario for a deathmatch, in which every AI plays for itself against the remaining AIs. Frags per episode, the number of kills minus the number of suicides for the agent in one round of game, is often used as a metric. An AI is stronger if its frags is ranked higher against others. In this work, we use an episode of 2-minute game time (4200 frames in total) for all our evaluations unless noted otherwise. ",
+        "bbox": [
+            173,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/2a0421b333ba3847e2e760ffda72c7e8371f15e03dbe3c963a3f918dae440576.jpg",
+        "image_caption": [
+            "Figure 3: The network structure of the proposed model. It takes 4 recent game frames plus 4 recent attention frames as the input state $s$ , and outputs a probability distribution $\\pi ( a | s )$ of the 6 discrete actions. The policy and value network share parameters. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            171,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4 METHOD ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            570,
+            281,
+            587
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.1 NETWORK ARCHITECTURE ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            602,
+            401,
+            616
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We use convolutional neural networks to extract features from the game frames and then combine its output representation with game variables. Fig. 3 shows the network architecture and Tbl. 1 gives the parameters. It takes the frames as the input (i.e., the state $s$ ) and outputs two branches, one that outputs the value function $V ( s )$ by regression, while the other outputs the policy function $\\pi ( s | a )$ by a regular softmax. The parameters of the two functions are shared before the branch. ",
+        "bbox": [
+            174,
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+            698
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "For input, we use the most recent 4 frames plus the center part of them, scaled to the same size $( 1 2 0 \\times 1 2 0 )$ . Therefore, these centered “attention frames” have higher resolution than regular game frames, and greatly increase the aiming accuracy. The policy network will give 6 actions, namely MOVE FORWARD, MOVE LEFT, MOVE RIGHT, TURN LEFT, TURN RIGHT, and ATTACK. We found other on-off actions (e.g., MOVE BACKWARD) offered by ViZDoom less important. After feature extraction by convolutional network, game variables are incorporated. This includes the agent’s Health (0-100) and Ammo (how many bullets left). They are related to AI itself and thus legal in the game environment for training, testing and ViZDoom AI competition. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.2 TRAINING PIPELINE ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            833,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Our training procedure is implemented with TensorFlow [Abadi et al. (2016)] and tensorpack5. We open 255 processes, each running one Doom instance, and sending experience $\\left( { { s _ { t } } , { a _ { t } } , { r _ { t } } } \\right)$ to the main process which runs the training procedure. The main process collects frames from different game instances to create batches, and optimizes on these batches asynchronously on one or more GPUs using Eqn. 1 and Eqn. 2. The frames from different processes running independent game instances, are likely to be uncorrelated, which stabilizes the training. This procedure is slightly different from the original A3C, where each game instance collects their own experience and updates the parameters asynchronously. ",
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+            858,
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+        "page_idx": 3
+    },
+    {
+        "type": "table",
+        "img_path": "images/a25c2cf43f22d9077fafa32542565fe43dd33a02feeabe0533828e259cafff9c.jpg",
+        "table_caption": [
+            "Table 1: Network parameters. $C 7 x 7 x 3 2 s 2 =$ convolutional layer with $7 \\mathbf { x } 7$ kernel, stride 2 and number of output planes 32. $M P =$ MaxPooling. Each convolutional and fully connected layer is followed by a ReLU, except for the last output layer. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=1>Layer #</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>2</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>6</td><td rowspan=1 colspan=1>7</td></tr><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>C7x7x32s2</td><td rowspan=1 colspan=1>C7x7x64s2</td><td rowspan=1 colspan=1>MP3x3s2</td><td rowspan=1 colspan=1>C3x3x128</td><td rowspan=1 colspan=1>MP3x3s2</td><td rowspan=1 colspan=1>C3x3x192</td><td rowspan=1 colspan=1>FC1024</td></tr></table>",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/99a23609e71c57723a45afa6b7ca8f9bda31e87169e3e15c804f02d59fbcb669.jpg",
+        "table_caption": [
+            "Table 2: Parameters for different maps. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Parameters</td><td>Description</td><td>FlatMap</td><td>CIGTrack1</td></tr><tr><td>living</td><td>Penalize agent who just lives</td><td colspan=\"2\">-0.008/action</td></tr><tr><td>health_loss</td><td>Penalize health decrement</td><td colspan=\"2\">-0.05 /unit</td></tr><tr><td>ammo_loss</td><td>Penalize ammunition decrement</td><td colspan=\"2\">-0.04/unit</td></tr><tr><td>health_pickup</td><td>Reward for medkit pickup</td><td colspan=\"2\">0.04/unit</td></tr><tr><td>ammo-pickup</td><td>Reward for ammunition pickup</td><td colspan=\"2\">0.15 /unit</td></tr><tr><td>dist-penalty dist_reward</td><td>Penalize the agent when it stays</td><td colspan=\"2\">-0.03 /action</td></tr><tr><td>dist_penalty_thres</td><td>Reward the agent when it moves</td><td colspan=\"2\">9e-5/unit distance</td></tr><tr><td rowspan=\"2\">num_bots</td><td>Thresholdofdisplacement</td><td>8</td><td>15</td></tr><tr><td>Number of built-in bots</td><td>8</td><td>16</td></tr></table>",
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Despite the use of entropy term, we still find that $\\pi ( \\cdot | s )$ is highly peaked. Therefore, during trajectory exploration, we encourage exploration by the following changes: a) multiply the policy output of the network by an exploration factor (0.2) before softmax b) uniformly randomize the action for $10 \\%$ random frames. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "As mentioned in [Kempka et al. (2016)], care should be taken for frame skips. Small frame skip introduces strong correlation in the training set, while big frame skip reduces effective training samples. We set frame skip to be 3. We choose $6 4 0 \\mathrm { x } 4 8 0$ as the input frame resolution and do not use high aspect ratio resolution [Lample & Chaplot (2016)] to increase the field of view. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We use Adam [Kingma & Ba (2014)] with $\\epsilon = 1 0 ^ { - 3 }$ for training. Batch size is 128, discount factor $\\gamma = 0 . 9 9$ , learning rate $\\alpha = 1 0 ^ { - 4 }$ and the policy learning rate $\\beta = 0 . 0 8 \\alpha$ . The model is trained from scratch. The training procedure runs on Intel Xeon CPU E5-2680v2 at 2. 80GHz, and 2 TitanX GPUs. It takes several days to obtain a decent result. Our final model, namely the $F l$ bot, is trained for around 3 million mini-batches on multiple different scenarios. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.3 CURRICULUM LEARNING",
+        "text_level": 1,
+        "bbox": [
+            174,
+            709,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "When the environment only gives very sparse rewards, or adversarial, A3C takes a long time to converge to a satisfying solution. A direct training with A3C on the map CIGTrack1 with 8 builtin bots does not yield sensible performance. To address this, we use curriculum learning [Bengio et al. (2009)] that trains an agent with a sequence of progressively more difficult environments. By varying parameters in Doom (Sec. 3), we could control its difficulty level. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/16e0c77071dbef54a411defa784f22d52ae482bacc4be389f2044d33d985c380.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 3: Curriculum design for FlatMap. Note that enemy uses RocketLauncher except for Class 0 (Pistol). "
+        ],
+        "table_body": "<table><tr><td rowspan=1 colspan=4>Class 0  Class 1  Class 2</td><td rowspan=1 colspan=1>Class 3</td><td rowspan=1 colspan=1>Class 4</td><td rowspan=1 colspan=1>Class 5</td><td rowspan=1 colspan=1>Class 6</td><td rowspan=1 colspan=1>Class 7</td></tr><tr><td rowspan=1 colspan=1>Speed</td><td rowspan=1 colspan=1>0.2</td><td rowspan=1 colspan=1>0.2</td><td rowspan=1 colspan=1>0.4</td><td rowspan=1 colspan=1>0.4</td><td rowspan=1 colspan=1>0.6</td><td rowspan=1 colspan=1>0.8</td><td rowspan=1 colspan=1>0.8</td><td rowspan=1 colspan=1>1.0</td></tr><tr><td rowspan=1 colspan=1>Health</td><td rowspan=1 colspan=1>40</td><td rowspan=1 colspan=1>40</td><td rowspan=1 colspan=1>40</td><td rowspan=1 colspan=1>60</td><td rowspan=1 colspan=1>60</td><td rowspan=1 colspan=1>60</td><td rowspan=1 colspan=1>80</td><td rowspan=1 colspan=1>100</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Reward Shaping. Reward shaping has been shown to be an effective technique to apply reinforcement learning in a complicated environment with delayed reward $[ \\mathrm { N g }$ et al. (1999); Devlin et al. (2011)]. In our case, besides the basic reward for kills $( + 1 )$ and death (-1), intermediate rewards are used as shown in Tbl. 2. We penalize agent with a living state, encouraging it to explore and encounter more enemies. health loss and ammo loss place linear reward for a decrement of health and ammunition. ammo pickup and health pickup place reward for picking up these two items. In addition, there is extra reward for picking up ammunition when in need (e.g. almost out of ammo). dist penalty and dist reward push the agent away from the previous locations, encouraging it to explore. The penalty is applied every action, when the displacement of the bot relative to the last state is less than a threshold dist penalty thres. And dist reward is applied for every unit displacement the agent makes. Similar to [Lample & Chaplot (2016)], the displacement information is computed from the ground truth location variables provided by Doom engine, and will not be used in the competition. However, unlike [Lample & Chaplot (2016)] that uses enemy-in-sight signal for training, locations can be extracted directly from USER? variables, or can easily be computed roughly with action history. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Curriculum Design. We train the bot on FlatMap that contains a simple square with a few pillars (Fig. 2(a)) with several curricula (Tbl. 3), and then proceed to CIGTrack1. For each map, we design curricula by varying the strength of built-in bots, i.e., their moving speed, initial health and initial weapon. Our agent always uses RocketLauncher as its only weapon. Training on FlatMap leads to a capable initial model which is quickly adapted to more complicated maps. As shown in Tbl. 2, for CIGTrack1 we increase dist penalty thres to keep the agent moving, and increase num bots so that the agent encounters more enemies per episode. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Adaptive Curriculum. In addition to staged curriculum learning, we also design adaptive curriculum learning by assigning a probability distribution on different levels for each thread that runs a Doom instance. The probability distribution shifts towards more difficult curriculum when the agent performs well on the current distribution, and shifts towards easier level otherwise. We consider the agent to perform well if its frag count is greater than 10 points. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.4 POST-TRAINING RULES ",
+        "text_level": 1,
+        "bbox": [
+            176,
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "For a better performance in the competition, we also put several rules to process the action given by the trained policy network, called post-training (PT) rules. There are two sets of buttons in ViZDoom: on-off buttons and delta buttons. While on-off button maps to the binary states of a keystroke (e.g., pressing the up arrow key will move the agent forward), delta buttons mimic the mouse behavior and could act faster in certain situations. Therefore, we setup rules that detect the intention of the agent and accelerate with delta button. For example, when the agent turns by invoking TURN LEFT repeatedly, we convert its action to TURN LEFT RIGHT DELTA for acceleration. Besides, the trained model might get stuck in rare situations, e.g., keep moving forward but blocked by an explosive bucket. We also designed rules to detect and fix them. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5 EXPERIMENT ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In this section, we show the training procedure (Sec. 5.1), evaluate our AIs with ablation analysis (Sec. 5.2) and ViZDoom AI Competition (Sec. 5.3). We mainly compare among three AIs: (1) F1Pre, the bot trained with FlatMap only, (2) F1Plain, the bot trained on both FlatMap and CIGTrack1, but without post-training rules, and (3) the final $F l$ bot that attends competition. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.1 CURRICULUM LEARNING ON FL A TMA P",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Fig. 4 shows that the curriculum learning increases the performance of the agents over all levels. When an agent becomes stronger in the higher level of class, it is also stronger in the lower level of class without overfitting. Fig. 5 shows comparison between adaptive curriculum learning with pure A3C. We can see that pure A3C can learn on FlatMap but is slower. Moreover, in CIGTrack1, a direct application of A3C does not yield sensible performance. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/d72c27739b6db20e52495fe4e07e135bfbb24984821015d05ffc9ec11bf706ce.jpg",
+        "image_caption": [
+            "Figure 4: Average Frags over 300 episodes evaluation, on FlatMap(left) and CIGTrack1(right) with different levels of enemies (See Tbl. 3 for curriculum design). Models from later stages performs better especially on the difficult map, yet still keeps a good performance on the easier map. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/ad4bd531ba59b063ff2e2cb3cd119ad0c822eca03e7562097dfe0dc1b19fed27.jpg",
+        "image_caption": [
+            "Figure 5: Performance comparison on Class 7 (hardest) of FlatMap between A3C [Mnih et al. (2016)] and adaptive curriculum learning, at different stage of training. Average frags and max frags are computed from 100 episodes. Adaptive curriculum shows higher performance and is relatively more stable. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.2 ABLATION ANALYSIS ",
+        "text_level": 1,
+        "bbox": [
+            176,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Visualization. Fig. 6 shows the visualization of the first convolutional layer of the trained AI agent. We could see that the convolutional kernels of the current frame is less noisy than the kernels of previous frames. This means that the agent makes the most use of the current frames. ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Effect of History Frames. Interestingly, while the agent focuses on the current frame, it also uses motion information. For this, we use (1) 4 duplicated current frames (2) 4 recent frames in reverse order, as the input. This gives 8.50 and 2.39 mean frags, compared to 10.34 in the normal case, showing that the agent heavily uses the motion information for better decision. In particular, the bot is totally confused with the reversed motion feature. Detailed results are shown in Tbl. 5. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/66a68449811ccd1853c0ae74280a568bba1e9234290164ddd9cd147902eb9bb3.jpg",
+        "image_caption": [
+            "Figure 6: Visualization of the convolutional filters in the first layer of our network. The filters are grouped by the frame index they corresponds to. Each group consists of two rows of 32 RGB filters for the regular and attention frames, respectively. The filters corresponding to the current frame (last row) is less noisy than those of others, showing that the bot is more focused on the current frame. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            169,
+            712,
+            825,
+            856
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/eaa1abc31b03c8c625c1360c75776735bbf77ef9741f076212d9868dee9cc052.jpg",
+        "table_caption": [
+            "Table 4: Avg/Max frags of each AIs in the internal tournament (150 episodes of 10 minutes each). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>Built-In AI</td><td rowspan=1 colspan=1>F1Pre</td><td rowspan=1 colspan=1>F1Plain</td><td rowspan=1 colspan=1>F1</td></tr><tr><td rowspan=1 colspan=1>FlatMap</td><td rowspan=1 colspan=1>8.07/20</td><td rowspan=1 colspan=1>14.47/24</td><td rowspan=1 colspan=1>17.26/29</td><td rowspan=1 colspan=1>22.45/37</td></tr><tr><td rowspan=1 colspan=1>CIGTrack1</td><td rowspan=1 colspan=1>0.48/7</td><td rowspan=1 colspan=1>3.56/15</td><td rowspan=1 colspan=1>8.58/16</td><td rowspan=1 colspan=1>10.65/18</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/72b1162bdc8fa97d8554f6798622019835e0e09a00b2c033112d09acaf729028.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td colspan=\"3\">FlatMap</td><td colspan=\"3\">CIGTrack1</td></tr><tr><td></td><td>Min</td><td>Mean</td><td>Max</td><td>Min</td><td>Mean</td><td>Max</td></tr><tr><td>F1 bot (reverse history)</td><td>1</td><td>9.89</td><td>19</td><td>-2</td><td>2.39</td><td>9</td></tr><tr><td>F1 bot (duplicated history)</td><td>10</td><td>24.62</td><td>37</td><td>2</td><td>8.50</td><td>17</td></tr><tr><td>F1 bot (w/o PT rules)</td><td>14</td><td>22.80</td><td>36</td><td>1</td><td>8.66</td><td>18</td></tr><tr><td>F1 bot</td><td>16</td><td>25.17</td><td>37</td><td>5</td><td>10.34</td><td>17</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 5: Performance evaluation (in terms of frags) on two standard scenarios FlatMap and CIGTrack1 over 300 episodes. Our bot performs better with post-training rules. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Post-training Rules. Tbl. 5 shows that the post-training rules improve the performance. As a future work, an end-to-end training involving delta buttons could make the bot better. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Internal Tournament. We also evaluate our AIs with internal tournaments (Tbl. 4). All our bots beat the performance of built-in bots by a large margin, even though they use privileged information. F1Pre, trained with only FlatMap, shows decent performance, but is not as good as the models trained with both FlatMap and CIGTrack1. The final bot $F l$ performs the best. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Behaviors. Visually, the three bots behave differently. F1Pre is a bit overtrained in FlatMap and does not move too often, but when it sees enemies, even faraway, it will start to shoot. Occasionally it will move to the corner and pick medkits. In CIGTrack1, F1Pre stays in one place and ambushes opponents who pass by. On the other hand, F1Plain and $F l$ always move forwards and turn at the corner. As expected, $F l$ moves and turns faster. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Tactics All bots develop interesting local tactics when exchanging fire with enemy: they slide around when shooting the enemy. This is quite effective for dodging others’ attack. Also when they shoot the enemy, they usually take advantage of the splashing effect of rocket to cause additional damage for enemy, e.g., shooting the wall when the enemy is moving. They do not pick ammunition too often, even if they can no longer shoot. However, such disadvantage is mitigated by the nature of deathmatch: when a player dies, it will respawn with ammunition. We also check states with highest/lowest estimated future value $V ( s )$ over a 10-episode evaluation of $F l$ bot, from which we can speculate its tactics. The highest value is $V = 0 . 9 7$ when the agent fired, and about to hit the enemy. One low value is $V = - 0 . 4 4$ , ammo $= 0$ , when the agent encountered an enemy at the corner but is out of ammunition. Both cases are reasonable. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.3 COMPETITION ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We attended the ViZDoom AI Competition hosted by IEEE CIG. There are 2 tracks in the competition. Track 1 (Limited Deathmatch) uses a known map and fixed weapons, while Track 2 (Full Deathmatch) uses 3 unknown maps and a variety of weapons. Each bot fights against all others for 12 rounds of 10 minutes each. Due to server capacity, each bot skips one match in the first 9 rounds. All bots are supposed to run in real-time ${ \\mathit { \\Omega } } ^ { \\prime } { > } 3 5$ fps) on a GTX960 GPU. ",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/2efbaa92226ae1fc4cfcbd0d07a90f5d8e4b6d3dce336b16a3dd491d96dcafd8.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=1>Round</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>2</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>6</td><td rowspan=1 colspan=1>7</td><td rowspan=1 colspan=1>8</td><td rowspan=1 colspan=1>9</td><td rowspan=1 colspan=1>10</td><td rowspan=1 colspan=1>11</td><td rowspan=1 colspan=2>12 Total</td></tr><tr><td rowspan=1 colspan=1>Our bot</td><td rowspan=1 colspan=1>56</td><td rowspan=1 colspan=1>62</td><td rowspan=1 colspan=1>n/a</td><td rowspan=1 colspan=1>54</td><td rowspan=1 colspan=1>47</td><td rowspan=1 colspan=1>43</td><td rowspan=1 colspan=1>47</td><td rowspan=1 colspan=1>55</td><td rowspan=1 colspan=1>50</td><td rowspan=1 colspan=1>48</td><td rowspan=1 colspan=1>50</td><td rowspan=1 colspan=1>47</td><td rowspan=1 colspan=1>559</td></tr><tr><td rowspan=1 colspan=1>Arnold</td><td rowspan=1 colspan=1>36</td><td rowspan=1 colspan=1>34</td><td rowspan=1 colspan=1>42</td><td rowspan=1 colspan=1>36</td><td rowspan=1 colspan=1>36</td><td rowspan=1 colspan=1>45</td><td rowspan=1 colspan=1>36</td><td rowspan=1 colspan=1>39</td><td rowspan=1 colspan=1>n/a</td><td rowspan=1 colspan=1>33</td><td rowspan=1 colspan=1>36</td><td rowspan=1 colspan=1>40</td><td rowspan=1 colspan=1>413</td></tr><tr><td rowspan=1 colspan=1>CLYDE</td><td rowspan=1 colspan=1>37</td><td rowspan=1 colspan=1>n/a</td><td rowspan=1 colspan=1>38</td><td rowspan=1 colspan=1>32</td><td rowspan=1 colspan=1>37</td><td rowspan=1 colspan=1>30</td><td rowspan=1 colspan=1>46</td><td rowspan=1 colspan=1>42</td><td rowspan=1 colspan=1>33</td><td rowspan=1 colspan=1>24</td><td rowspan=1 colspan=1>44</td><td rowspan=1 colspan=1>30</td><td rowspan=1 colspan=1>393</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 6: Top 3 teams in ViZDoom AI Competition, Track 1. Our bot attended 11 out of 12 games, won 10 of them and won the champion by a large margin. For design details, see Arnold [Lample & Chaplot (2016)] and CLYDE [Ratcliffe et al. (2017)]. ",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Our $F l$ bot won 10 out of 11 attended games and won the champion for Track 1 by a large margin. We have achieved 559 frags, $3 5 . 4 \\%$ higher than 413 frags achieved by Arnold [Lample & Chaplot (2016)], that uses extra game state for model training. On the other hand, IntelAct [Dosovitskiy & Koltun (2017)] won Track 2. The full videos for the two tracks have been released67, as well as an additional game between Human and $\\mathrm { A I s } ^ { 8 }$ . Our bot behaves reasonable and very human-like in Track 1. In the match between Human and AIs, our bot was even ahead of the human player for a short period (6:30 to 7:00). ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "6 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            222,
+            318,
+            238
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Teaching agents to act properly in complicated and adversarial 3D environment is a very challenging task. In this paper, we propose a new framework to train a strong AI agent in a First-Person Shooter (FPS) game, Doom, using a combination of state-of-the-art Deep Reinforcement Learning and Curriculum Training. Via playing against built-in bots in a progressive manner, our bot wins the champion of Track1 (known map) in ViZDoom AI Competition. Furthermore, it learns to use motion features and build its own tactics during the game, which is never taught explicitly. ",
+        "bbox": [
+            174,
+            253,
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+            338
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Currently, our bot is still an reactive agent that only remembers the last 4 frames to act. Ideally, a bot should be able to build a map from an unknown environment and localize itself, is able to have a global plan to act, and visualize its reasoning process. We leave them to future works. ",
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+            174,
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+        "page_idx": 8
+    },
+    {
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parse/train/HyenWc5gx/HyenWc5gx.md

@@ -0,0 +1,277 @@
+# REPRESENTATION STABILITY AS A REGULARIZER FOR IMPROVED TEXT ANALYTICS TRANSFER LEARNING
+
+Matthew Riemer, Elham Khabiri, and Richard Goodwin
+
+IBM T.J. Watson Research Center Yorktown Heights, NY, USA {mdriemer, ekhabiri, rgoodwin}@us.ibm.com
+
+# ABSTRACT
+
+Although neural networks are well suited for sequential transfer learning tasks, the catastrophic forgetting problem hinders proper integration of prior knowledge. In this work, we propose a solution to this problem by using a multi-task objective based on the idea of distillation and a mechanism that directly penalizes forgetting at the shared representation layer during the knowledge integration phase of training. We demonstrate our approach on a Twitter domain sentiment analysis task with sequential knowledge transfer from four related tasks. We show that our technique outperforms networks fine-tuned to the target task. Additionally, we show both through empirical evidence and examples that it does not forget useful knowledge from the source task that is forgotten during standard fine-tuning. Surprisingly, we find that first distilling a human made rule based sentiment engine into a recurrent neural network and then integrating the knowledge with the target task data leads to a substantial gain in generalization performance. Our experiments demonstrate the power of multi-source transfer techniques in practical text analytics problems when paired with distillation. In particular, for the SemEval 2016 Task 4 Subtask A (Nakov et al., 2016) dataset we surpass the state of the art established during the competition with a comparatively simple model architecture that is not even competitive when trained on only the labeled task specific data.
+
+# 1 INTRODUCTION
+
+Sequential transfer learning methodologies leverage knowledge representations from a source task in order to improve performance for a target task. A significant challenge faced when transferring neural network representations across tasks is that of catastrophic forgetting (or catastrophic interference). This is where a neural network experiences the elimination of important old information when learning new information. The very popular strategy of fine-tuning a neural network involves first training a neural network on a source task and then using the model to simply initialize the weights of a target task network up to the highest allowable common representation layer. However it is highly susceptible to catastrophic forgetting, because in training for the target task it has no explicit incentive to retain what it learned from the source task. While one can argue that forgetting the source task should not matter if only the target task is of interest, our paper adds to the recent empirical evidence across problem domains (Li & Hoiem, 2016),(Rusu et al., 2016) that show additional network stability can lead to empirical benefits over the fine-tuning algorithm. It seems as though for many Deep Learning problems we can benefit from an algorithm that promotes more stability to tackle the well known stability-plasticity dilemma. One popular approach for addressing this problem is rehearsals (Murre, 1992), (Robins, 1995). Rehearsals refers to a neural network training strategy where old examples are relearned as new examples are learned. In the transfer setting it can be seen as related to multi-task learning (Caruana, 1997) where two tasks are trained at the same time, rather than sequentially, while sharing a common input encoder to a shared hidden representation. However, in rehearsals the representation is biased in favor of the source task representation through initialization. This technique is very sensible because while fine-tuning is susceptible to catastrophic forgetting, multi-task learning is not (Caruana, 1997).
+
+One of the biggest issues with the standard rehearsals paradigm is that it requires a cached memory of training examples that have been seen in the past. This can be a massive requirement as the number of source tasks and training data sizes scale. One compelling technique for addressing this problem is the concept of pseudorehearsals (Robins, 1995), (Robins, 1996), where relearning is performed on an artificially constructed population of pseudoitems instead of the actual old examples. Unfortunately, current automatic techniques in the text analytics domain have not yet mastered producing linguistically plausible data. As such, the pseudorehearsals paradigm is likely to waste computational time that could be spent on learning realistic patterns that may occur during testing. In our work, we extend the Learning without Forgetting (LwF) paradigm of (Li & Hoiem, 2016) to the text analytics domain using Recurrent Neural Networks. In this approach, the target task data is used both for learning the target task and for rehearsing information learned from the source task by leveraging synthetic examples generated for the target task input by the model that only experienced training on the source task data. As argued by Li & Hoiem (2016), this setup strikes an important balance between classification performance, computational efficiency, and simplicity in deployment.
+
+Regardless of whether they are applied to real source task examples, real target task examples, or synthetic examples, paradigms in the style of rehearsals all address the shortcomings of neural network forgetting by casting target task integration as a multi-task learning problem. However, this is not quite the purpose of the multi-task learning architecture, which was designed for joint learning of tasks from scratch at the same time. The key disconnect is that in multi-task learning, the transformation from the shared hidden layer to the outputs for each task are all learned and updated with the changing hidden representation. This would imply that, in the framework of rehearsals, it is possible for there to be significant changes during learning of the network’s representation, and thus its abilities on the source task itself. While it would be desirable to claim we were allowing our source task network to become even better based on the target task than it was before, this motivation seems idealistic in practice. One reason this is idealistic is because multi-task learning generally only works well when tasks are sampled at different rates or alternatively given different priority in the neural network loss function (Caruana, 1997). As a result, it is most likely that auxilirary source tasks will receive less priority from the network for optimization than the target task. Additionally, we observe in our experiments, and it has been observed by others in (Rusu et al., 2015), that it is generally not possible to distill multiple complex tasks into a student network at full teacher performance for all tasks. This seems to imply the degradation of the source task performance during training is somewhat inevitable in a multi-task learning paradigm.
+
+We address this issue with our proposed forgetting cost technique. We demonstrate that it, in fact, can be valuable to keep the hidden to output transformation of the source tasks fixed during knowledge integration with the target task. This way, we impose a stronger regularization on the hidden representation during target task integration by not allowing it to change aspects that were important to the source task’s performance without direct penalization in the neural network’s loss function. We demonstrate empirically both that freezing the source task specific weights leads to less deterioration in the accuracy on the source task after integration, and that it achieves better generalization performance in our setting. The forgetting cost is practical and easy to implement in training any kind of neural network. In our experiments, we explore application of the forgetting cost in a recurrent neural network to the three way Twitter sentiment analysis task of SemEval 2016 Task 4 Subtask A and find it to achieve consistently superior performance to reasonable baseline transfer learning approaches in four examples of knowledge transfer for this task.
+
+We also demonstrate how powerful distillation can be in the domain of text analytics when paired with the idea of the forgetting cost. Significantly, we show that a high quality gazetteer based logical rule engine can be distilled using unlabeled data into a neural network and used to significantly improve performance of the neural network on the target task. This is achieved with a novel extension of the LwF paradigm by Li & Hoiem (2016) to the scenario of a source task with the same output space as the target task. This can be a very promising direction for improving the ability of humans to directly convey knowledge to deep learning algorithms. Indeed, a human defined rule can contain far more information than a single training example, as that rule can be projected on to many unlabeled examples that the neural network can learn from. This is the reason human teachers generally begin teaching human students tasks by going over core rules at the onset of learning. Moreover, we showcase that multiple expert networks trained on the target task with prior knowledge from different source tasks can be effectively combined in an ensemble and then distilled into a single GRU model (Cho et al., 2014), (Chung et al., 2014). Leveraging this combination of distillation and knowledge transfer techniques allows us to achieve state of the art accuracy on the SemEval task with a model that performs $11 \%$ worse than the best prior techniques when trained only on the labeled data.
+
+# 2 RELATED WORK
+
+Since the work of (Bucilu et al., 2006) and (Hinton et al., 2015) showed that an ensemble of neural network classifier can be distilled into a single model, knowledge distillation from a teacher network to a student network has become a growing topic of neural network research. In (Ba & Caruana, 2014) it was shown that a deep teacher neural network can be learned by a shallow student network. This idea was extended in (Romero et al., 2014), where it was demonstrated that a deep and narrow neural network can learn a representation that surpasses its teacher. The use of distillation as a means of sharing biases from multiple tasks was explored in (Lopez-Paz et al., 2016), where the teacher network is trained with the output of the other tasks as input. It is not obvious how to extend a recurrent neural network to best use this kind of capability over a sequence. The idea of distilling from multiple source task teachers into a student network was highlighted in the reinforcement learning setting in (Rusu et al., 2015). Additionally, the concept of using distillation for knowledge transfer was also explored in (Chen et al., 2015), where function preserving transformations from smaller to bigger neural network architectures were outlined. This technique could also provide value in some instances for our approach where wider or deeper neural networks are needed for the task being transferred to than was needed for the original task. Distillation over target task data was first proposed as a means of elevating catastrophic forgetting in sequential knowledge transfer as applied to image classification in (Li & Hoiem, 2016). We extend this approach for its first application to our knowledge for text analytics problems, with a recurrent neural network architecture, and in the setting where the source task and target task have the same output. The chief distinction of our proposed forgetting cost is that source task specific parameters are held fixed during integration with the target task as opposed to the joint training of all parameters used by Li & Hoiem (2016). Our experiments empirically support the intuition that freezing these parameters leads to greater retention of source task performance after target task integration and better generalization to the target task.
+
+An ensemble over multiple diverse models trained for the same sentiment analysis task was also considered in (Mesnil et al., 2014) for the IMDB binary movie reviews sentiment dataset (Maas et al., 2011). We tried this ensemble model in our work and found that it gave very limited improvement. Our ensemble technique learns a more powerful weighted average based on the soft targets of each task and a multi-step greedy binary fusion approach that works better for the Twitter sentiment analysis task in our experiments. Knowledge transfer from multiple tasks was considered to estimate the age of Twitter users based on the content of their tweets in (Riemer et al., 2015). We experimented with the hidden layer sharing approach outlined in that work and found that even when using just a single softmax combining layer, it would overfit on our limited training and validation data. Progressive neural networks (Rusu et al., 2016) is a recently proposed method very similar in motivation to our forgetting cost as it is directly trying to solve the catastrophic forgetting problem. The idea is that learned weight matrices relate the fixed representations learned on the source task to the construction of representations for the target task. In our experiments, the progressive neural networks approach consistently fails to even match the results achieved with fine-tuning. We hypothesize that although using fixed representations to aid learning addresses catastrophic forgetting, it suffers from the curse of dimensionality. As such, when training data is relatively small given the complexity of the task, it is prone to overfitting as it effectively increases the input dimension size through shared fixed representations.
+
+The combination of logic rules and neural networks has been explored in a variety of different architectures and settings. These neural-symbolic systems (Garcez et al., 2012) include early examples such as KBANN (Towell et al., 1990) that construct network architectures from given rules to perform reasoning. (Hu et al., 2016) very recently also looked at the problem of distilling logical rules into a neural network text analytics classifier. However, our approach is much more generic as it can be applied to integrate knowledge from any kind of pre-made classifier and treats the rule engine as a black box. In (Hu et al., 2016) they consider the individual rules and leverage an iterative convex optimization algorithm alongside the neural network to regularize the subspace of the network. In our work we demonstrate that, by guarding against catastrophic forgetting, it is possible to efficiently leverage rules for transfer by utilizing a generic sequential knowledge transfer framework. We do not need to make any modification to the architecture of the neural network during testing and do not need iterative convex optimization during training.
+
+# 3 FORGETTING COST REGULARIZATION
+
+# 3.1 SEQUENTIAL KNOWLEDGE TRANSFER PROBLEM STATEMENT
+
+In the sequential knowledge transfer problem setting explored in this paper, training is first conducted solely on the source task examples $S$ , including $K _ { S }$ training examples $( x _ { S i } , y _ { S i } ) \in S$ where $x _ { S i }$ is the input representation and $y _ { S i }$ is the output representation. After training is complete on $S$ , we would like to now use prior knowledge obtained in the model trained on $S$ to improve generalization on a new target task with examples $T$ , which includes $K _ { T }$ training examples $( x _ { T i } , y _ { T i } ) \in T$ . Here we assume that the input representations $x _ { S i }$ and $x _ { T i }$ are semantically aligned in the same representation space. As such, if there is useful knowledge in $S$ that applies in some direct or indirect way to the target task that is not present in $T$ , we would expect a good knowledge integration approach to generalize better to the target task than it is possible to using the training data in $T$ alone. Strong performance for the sequential knowledge transfer problem is a first step towards the greater goal of a mechanism for effective lifelong learning (Thrun, 1996).
+
+# 3.2 FORGETTING COST FOR TUNING A TARGET TASK MODEL
+
+The most straightforward application of our proposed forgetting cost paradigm is for the case of integrating a neural network that has been trained on source task data $S$ , which has outputs in the same representation space as the outputs for the target task data $T$ . In this case, the forgetting cost amounts to the addition of a regularization term in the objective function during the integration phase when we train using $T$ . This promotes the neural network to be able to recreate the soft labels of the initialized model found after training on $S$ before integration is started with $T$ . More formally:
+
+$$
+L o s s = L ( y , \hat { y } ) + \alpha _ { f } L ( y _ { i n i t } , \hat { y } )
+$$
+
+where $L$ is some loss function (we use mean squared error in our experiments) and $y _ { i n i t }$ is the soft label generated for the target task input $x _ { T i }$ based on the model after training just on $S$ . The model trained just on $S$ is also used to initialize the weights of the target task model before integration with $T$ as we do in the standard fine-tuning paradigm. $\alpha _ { f }$ is a hyperparameter that can be utilized to control the extent of allowed forgetting. Of course, a very similar way to express this idea would be to mix synthetic training examples $T ^ { \prime }$ with the same input as $T$ and output generated by the model trained just on $S$ with the true target task training examples $T$ . In this case, the mixing rate of the teacher generated training examples is analogous to our forgetting parameter $\alpha _ { f }$ determining the prioritization. These techniques perform quite similarly in our experiments, but we actually find that the formulation in equations 1 and 3 perform slightly better on the test set. For example, this formulation is superior by $0 . 4 \%$ accuracy in tuning a distilled representation of a logical rule engine. We conjecture that learning tasks in the same gradient step when they are related to the same input data results in slightly less noisy gradients.
+
+# 3.3 FORGETTING COST FOR KNOWLEDGE TRANSFER FROM A RELATED TASK
+
+The assumption in section 3.2 that the output of the source task data $S$ should be in the same representation space as the output for the target task data $T$ is quite a big one. It rules out the vast majority of knowledge sources that we can potentially leverage. As such, we propose an extension that does not make this restriction for application in sequential knowledge transfer of tasks that are not directly semantically aligned. We update our model to include another predicted output separate from $\hat { y }$ :
+
+$$
+\hat { y } _ { i n i t } = f _ { i n i t } ( W _ { f i x e d } h _ { s h a r e d } + b _ { f i x e d } )
+$$
+
+where ${ \hat { y } } _ { i n i t }$ is a predicted output attempting to recreate the soft labels of the original model trained just on $S$ . $f _ { i n i t }$ is the non-linearity used in the final layer of the source task model. Weight matrix $W _ { f i x e d }$ and bias $b _ { f i x e d }$ are taken from the final layer of the source task model and are not updated
+
+during integration with the target task data $T$ . As a result, the loss function is updated from section 3.2:
+
+$$
+L o s s = L ( y , \hat { y } ) + \alpha _ { f } L ( y _ { i n i t } , \hat { y } _ { i n i t } )
+$$
+
+where the hidden state is shared between both terms in the objective function. Up to the shared hidden layer, we initialize the model for the target task with the weights learned just using $S$ . Random matrices and bias vectors are now used to initialize the prediction of $\hat { y }$ based on the shared hidden representation. This can be seen as a weak form of restricting the model parameters that can be useful for regularization. The hidden representation is in effect constrained so that it is promoted not to change in key areas that have a large effect on the output vector of the source task model. On the other hand, there is little regularization for parameters that have little effect on the output vector for the source task model.
+
+# 4 RECURRENT NEURAL NETWORK MODEL
+
+In recent years, recurrent neural network models have become a tool of choice for many NLP tasks. In particular, the LSTM variant (Hochreiter & Schmidhuber, 1997) has become popular as it alleviates the vanishing gradients problem (Bengio et al., 1994) known to stop recurrent neural networks from learning long term dependencies over the input sequence. In our experiments we use the simpler GRU network (Cho et al., 2014), (Chung et al., 2014) that generally achieves the same accuracy despite a less complex architecture. Each time step $t$ is associated with an input $x _ { t }$ and a hidden state $h _ { t }$ . The mechanics of the GRU are defined with the following equations:
+
+$$
+\begin{array} { r } { \begin{array} { r l } & { z _ { t } = \sigma \big ( W _ { x z } x _ { t } + W _ { h z } h _ { t - 1 } \big ) } \\ & { r _ { t } = \sigma \big ( W _ { x r } x _ { t } + W _ { h r } h _ { t - 1 } \big ) } \\ & { { \tilde { h } } _ { t } = t a n h \big ( W _ { x h } x _ { t } + r _ { t } \circ W _ { h h } h _ { t - 1 } \big ) } \\ & { ~ h _ { t } = z _ { t } \circ h _ { t - 1 } + ( 1 - z _ { t } ) \circ { \tilde { h } } _ { t } } \end{array} } \end{array}
+$$
+
+where $\circ$ denotes an element-wise product. $W _ { x z } , W _ { x r }$ , and $W _ { x h }$ represent learned matrices that project from the input size to the hidden size. $W _ { h z }$ , $W _ { h r }$ , and $W _ { h h }$ represent learned matrices that project from the hidden size to the hidden size. In our work we evaluate the GRU in the categorical prediction setting. For each document, the hidden state after the last word $h _ { L }$ is used for the prediction $\hat { y }$ of the label $y$ . As such, we treat $h _ { L }$ as the shared hidden representation $h _ { s h a r e d }$ from section 3.3 for our experiments.
+
+$$
+\hat { y } = f ( W _ { y h } h _ { L } + b _ { y } )
+$$
+
+The prediction goes through one other non-linear function $f$ after the final hidden state is derived. In our experiments we use the softmax function, but others are useful in different settings. A model that builds on top of GRUs with an external memory storage paradigm (Kumar et al., 2015) currently holds the state of the art on movie review sentiment analysis. However, we focus just on the straightforward single layer GRU model in our experiments so that we can more easily disentangle factors of influence on performance. Our GRU model was fed a sequence of fixed 300 dimensional Glove vectors (Pennington et al., 2014), representing words based on analysis of 840 billion words from a common crawl of the internet, as the input $x _ { t }$ for all tasks. It has been shown in a number of papers that tuning the word embeddings during training could increase performance, and it is possible our approach could have performed better had we done so.
+
+# 5 SEQUENTIAL KNOWLEDGE TRANSFER EXPERIMENTS
+
+# 5.1 EXPERIMENT DETAILS
+
+Our neural network models were implemented in Theano (Theano Development Team, 2016) and trained with Stochastic Gradient Descent. As we did not use an advanced optimization method and noticed run to run variation in performance, for all of our transfer learning models we trained 10 parallel versions and chose the one with the highest validation accuracy. The SemEval 2016 Task 4 Subtask A training set consists of 10,000 total training examples, but we were only able to receive 8,906 because of tweet removals when we used the downloading script. For the target task data across our experiments, 7,600 examples of the SemEval training set examples were used for training and the rest for validation. The GRU model achieves only $5 3 . 6 \%$ accuracy on the SemEval testing data when just training with the target task data and random initialization. In order to improve, we consider knowledge transfer from GRUs trained for the following source tasks to the SemEval target task data:
+
+Distilling Logical Rules: Knowledge distillation can be performed using teacher models that are very different in structure than their neural network based student models. We demonstrate with this task that a compilation of logical linguistic rules can be used as an effective teacher for a GRU by having the GRU attempt to create the output of the rule engine generated over unlabeled in domain data. Specifically, our gazetteer based logical rule engine separates sentences and phrases in the text. It then applies dictionaries of positive and negative sentiment words and phrases to the corresponding text. For each positive or negative phrase found, it checks to see if negation or double negation are applied, and modifies the polarity of the sentiment accordingly. The result for any piece of text is a count of positive and negative sentiment occurrences. For this task, we simply count the total number of positive and negative indicators to give an overall positive, negative or neutral score. We provide addition details on how we mapped rules to soft targets for the student network to recreate in Appendix A. We utilized a GRU model with 50 hidden units and 50,000 unlabeled examples for our source task model. We distill off the soft labels as in (Hinton et al., 2015), but set our temperature fixed at 1.0. It is possible that our performance could have improved by tuning this parameter. Additional details about the selection of the network and data size are included in Appendix B. The logical rule model itself achieves $5 7 . 8 \%$ accuracy on the SemEval testing data and the rules distilled into a GRU as explained in section 4 achieves $5 8 . 9 \%$ accuracy before any integration with the SemEval target task data. We leverage this task for comparison of knowledge transfer techniques when the source task and target task share an output space as discussed in section 3.2.
+
+Binary Movie Reviews: For knowledge transfer from related tasks as discussed in section 3.3 we first consider the Stanford Sentiment Treebank (Socher et al., 2013), which is a popular sentiment dataset based on the movie review domain. We consider one source task to be the binary (positive, and negative) sentence level sentiment subtask which contains 6,920 training examples, 872 validation examples, and 1,821 testing examples. Our GRU model with 40 hidden units achieves $8 5 . 5 \%$ accuracy on this task.
+
+Five Class Movie Reviews: We also consider another source task leveraging the Stanford Sentiment Treebank data from the fine grained (very positive, positive, neutral, negative, and very negative) sentence level sentiment substask which contains 8,544 training examples, 1,101 validation examples, and 2,210 testing examples. We use a GRU model with 200 hidden units to accommodate for the increased task complexity and achieve $4 5 . 9 \%$ accuracy. This fine grained model can actually be assessed directly on the SemEval task by projecting from five classes to three classes, but it only achieves $4 4 . 2 \%$ accuracy with no tuning on the target task data. Our performance on these two movie review source tasks is quite similar to what was reported in (Tai et al., 2015) when using a similar setup, but with LSTMs for both subtasks.
+
+Emoticon Heuristic: Finally, we consider a semi-supervised task based on emoticon prediction motivated by the successful work in (Go et al., 2009), leveraging it in the twitter sentiment domain and its use as a vital component of the SemEval competition winning system (Bethard et al., 2016). We find unlabelled tweets that contain smileys, frowns, or laughing emoticons. We remove emoticons from the tweet before prediction and compile a dataset of 250,000 training examples, 50,000 validation examples, and 100,000 testing examples for each of the three classes. This is multiple orders of magnitude smaller than the 90 million tweets used in (Bethard et al., 2016) to allow for quick experimentation. Our GRU model with 50 hidden units achieves $6 3 . 4 \%$ accuracy on the emoticon prediction test set.
+
+We consider multiple sequential knowledge transfer algorithms for experimental comparison. Each uses only the source task data for learning the source task and only the target task data for integrating with the target task. This way integration is fast and simple, because it does not incorporate storage and replay of examples from the potentially very large source task as argued in (Li & Hoiem, 2016).
+
+Fine-Tuning: The representation is simply initialized with the representation found after training on the source task and then trained as usual on the target task. This approach was pioneered in (Hinton & Salakhutdinov, 2006), in application to unsupervised source tasks and applied to transfer learning in (Bengio et al., 2012), and (Mesnil et al.). The learning rate is tuned by a grid search based on the validation set performance.
+
+Progressive Networks: We also compare with our implementation of a progressive neural network (Rusu et al., 2016), where the representation learned for the source task is held fixed and integrated with a target task specific model via lateral connections trained using the target task data. The learning rate is also tuned based on a grid search using the validation set.
+
+Learning without Forgetting (LwF): In the LwF paradigm, joint training is performed after parameter initialization. This is achieved by treating the target task data and the output generated by the source task model based on the target task input data as two jointly learned tasks as in (Caruana, 1997). As opposed to our proposed forgetting cost, the source task specific parameters are not held fixed while training on the target task data. The learning rate and mixing rate between the tasks are tuned by a grid search based on validation set performance. We first consider a version of the LwF model that leverages a random initialization of the target task specific parameters and initialization of all parameters learned on the source task with the learned values. We also consider another formulation that we call Greedy LwF. This is actually more closely aligned with the original paper (Li & Hoiem, 2016). All source task parameters are first held fixed, and the target task specific parameters are learned alone before joint training with all of the parameters unfrozen as a second step. For the case of source tasks with output in the space of the target task output, there are no source task specific parameters, so the forgetting cost can be viewed as a viable interpretation of the LwF paradigm appropriate in that setting.
+
+Forgetting Cost: Finally, we compare each baseline model with our proposed forgetting cost described in section 3. The learning rate as well as $\alpha _ { f }$ from equations 1 and 3 were tuned by a grid search based on the validation set performance.
+
+# 5.3 TARGET TASK RESULTS
+
+We empirically evaluate the generalization performance of the forgetting cost for sequential knowledge transfer from four different source tasks in Table 1 and Table 2. The source task considered in Table 1 is distilling a logical rule model, leveraging the technique outlined in equation 1. In Table 2 we leverage the forgetting cost for related task knowledge transfer as outlined in equation 3.
+
+Our experimental results on the SemEval data validate our intuition that the forgetting cost should lead to stronger regularization and better generalization performance. One thing to note about our progressive neural networks implementation is that it effectively has only one hidden layer, because we hold our embeddings fixed during model training and the same embeddings are shared among the models used for all of the tasks. It is possible that having multiple layers of lateral connections is important to achieving good performance. However, this setting was not applicable in our experiments. Our results for sequential knowledge transfer on the SemEval benchmark are quite encouraging as the forgetting cost outperforms baselines significantly in all cases.
+
+We additionally have validated the intuition that equation 1 should perform stronger regularization than equation 3 when equation 1 is applicable. In fact, for our distilled logical rule model tuning experiments, we found that equation 1 performs $3 \%$ better on the test set. In an attempt to understand more about what caused this performance difference, we monitored testing set performance at each epoch and noticed that equation 3 is actually prone to overfitting away from a good solution on the test set. However, it often finds a pretty good one comparable to equation 1 early in training. When equation 1 could be applied, it seems to be a useful regularization to constrain both the hidden layer and the output layer to align with the model learned on the source task. In equation 3, the hidden to output transformation learned for the target task can in contrast learn to deviate from the transformation learned for the source task.
+
+Table 1: Evaluation of target task tuning methodologies for a distilled rule model to the task of SemEval 2016 Task 4 Subtask A.   
+
+<table><tr><td rowspan=1 colspan=1>Model Description</td><td rowspan=1 colspan=1>Accuracyon SemEval Test Set</td></tr><tr><td rowspan=1 colspan=1>Forgetting Cost TransferFine-tuning TransferProgressive Networks Transfer</td><td rowspan=1 colspan=1>64.4%58.5%56.9%</td></tr><tr><td rowspan=1 colspan=1>Distilled Logical Rule ModelLogical Rule ModelGRU Trained on Only SemEval Data</td><td rowspan=1 colspan=1>58.9%57.8%53.6%</td></tr></table>
+
+Table 2: Evaluation of knowledge transfer from three source tasks to the task of SemEval 2016 Task 4 Subtask A.   
+
+<table><tr><td rowspan=1 colspan=1>Source Task</td><td rowspan=1 colspan=1>Fine-Tuning</td><td rowspan=1 colspan=1>ProgressiveNetworks</td><td rowspan=1 colspan=1>LwF</td><td rowspan=1 colspan=1>GreedyLwF</td><td rowspan=1 colspan=1>Forgetting Cost</td></tr><tr><td rowspan=1 colspan=1>Binary Movie Reviews</td><td rowspan=1 colspan=1>57.3%</td><td rowspan=1 colspan=1>54.5%</td><td rowspan=1 colspan=1>58.1%</td><td rowspan=1 colspan=1>58.8%</td><td rowspan=1 colspan=1>59.7%</td></tr><tr><td rowspan=1 colspan=1>Five Class Movie Reviews</td><td rowspan=1 colspan=1>57.4%</td><td rowspan=1 colspan=1>54.6%</td><td rowspan=1 colspan=1>57.1%</td><td rowspan=1 colspan=1>56.6%</td><td rowspan=1 colspan=1>58.2%</td></tr><tr><td rowspan=1 colspan=1>Emoticon Heuristic</td><td rowspan=1 colspan=1>55.8%</td><td rowspan=1 colspan=1>53.2%</td><td rowspan=1 colspan=1>57.7%</td><td rowspan=1 colspan=1>56.7%</td><td rowspan=1 colspan=1>58.6%</td></tr></table>
+
+# 5.4 SOURCE TASK PERFORMANCE AFTER TARGET TASK INTEGRATION
+
+In Table 3 we explore the retention of empirical performance on the source task for knowledge transfer algorithms after integration with the target task is complete. Apparently in these cases, allowing relearning of the source task model during integration with the target task data is indeed destructive to source task performance. LwF outperforms Fine-Tuning significantly in knowledge retention for movie reviews, but interestingly does not for the emoticon heuristic. The effect of the greedy target task initialization strategy also appears inconsistent. It seems it is possible that this greedy initialization could improve our proposed forgetting cost paradigm in some cases as well. However, a rigorous analysis of the tradeoffs for this initialization approach is beyond the scope of this paper.
+
+As the source task representation is literally stored fixed as part of the target task representation in progressive neural networks, it is not clear how to assess any effective forgetting of the source task during target task integration. As a result, we omit them from our source task forgetting experiments.
+
+# 5.5 INSPECTION OF LEARNED REPRESENTATIONS
+
+Now that we have established the empirical benefits of our proposed forgetting cost, we will demonstrate what it achieves qualitatively through examples. In Table 4 we include a sample of examples that are predicted correctly by transferring the knowledge source with the forgetting cost paradigm and not with fine-tuning based integration. The effect is, perhaps, easiest to understand for the rule based and movie review based transfer scenarios. For the rule based transfer setting you can literally map insights that are not forgotten to their respective logical rule in the model, as is the case in these examples. Moreover, we can see movie domain specific terminology such as ”May the force be with” is seemingly forgotten with standard fine-tuning, but not when the forgetting cost regularization is applied.
+
+<table><tr><td rowspan=1 colspan=1>Source Task</td><td rowspan=1 colspan=1>Fine-Tuning</td><td rowspan=1 colspan=1>LwF</td><td rowspan=1 colspan=1>GreedyLwF</td><td rowspan=1 colspan=1>Forgetting Cost</td><td rowspan=1 colspan=1>Source Only</td></tr><tr><td rowspan=1 colspan=1>Binary Movie Reviews</td><td rowspan=1 colspan=1>80.7%</td><td rowspan=1 colspan=1>81.3%</td><td rowspan=1 colspan=1>81.5%</td><td rowspan=1 colspan=1>83.3%</td><td rowspan=1 colspan=1>85.5%</td></tr><tr><td rowspan=1 colspan=1>Five Class Movie Reviews</td><td rowspan=1 colspan=1>41.6%</td><td rowspan=1 colspan=1>42.8%</td><td rowspan=1 colspan=1>43.1%</td><td rowspan=1 colspan=1>43.3%</td><td rowspan=1 colspan=1>45.9%</td></tr><tr><td rowspan=1 colspan=1>Emoticon Heuristic</td><td rowspan=1 colspan=1>59.4%</td><td rowspan=1 colspan=1>59.1%</td><td rowspan=1 colspan=1>58.9%</td><td rowspan=1 colspan=1>60.3%</td><td rowspan=1 colspan=1>63.4%</td></tr></table>
+
+Table 3: Evaluation of accuracy on the source task after integration with the target task data of SemEval 2016 Task 4 Subtask A. The accuracy after only source task training prior to integration with the target task is included for reference as a baseline.
+
+Table 4: Some transfer learning examples from each knowledge source to SemEval 2016 where the GRU model successfully predicts sentiment when using the forgetting cost paradigm, but not with fine-tuning based integration.   
+
+<table><tr><td rowspan=1 colspan=1>Source</td><td rowspan=1 colspan=1>Tweet</td><td rowspan=1 colspan=1>Label</td><td rowspan=1 colspan=1>Fine-Tuning</td><td rowspan=1 colspan=1>Forgetting Cost</td></tr><tr><td rowspan=1 colspan=1>Logical Rules</td><td rowspan=1 colspan=1>JohnKasich should feel proud of hisperformance at the#GOPDebate Thursday night. He looked more presi-dential than the rest of the field.</td><td rowspan=1 colspan=1>Positive</td><td rowspan=1 colspan=1>Neutral</td><td rowspan=1 colspan=1>Positive</td></tr><tr><td rowspan=1 colspan=1>Logical Rules</td><td rowspan=1 colspan=1>@ BrunoMars I&#x27;m so tired of you dressing like you ain&#x27;tgot no money. You went from wearing Gucci loafers to6th grade boy Sketchers.</td><td rowspan=1 colspan=1>Negative</td><td rowspan=1 colspan=1>Neutral</td><td rowspan=1 colspan=1>Negative</td></tr><tr><td rowspan=1 colspan=1>Logical Rules</td><td rowspan=1 colspan=1>@DavidVonderhaar loving the beta Vahn, even playing it on PC with a PS4 controller without aim assist, can&#x27;twait for November 6</td><td rowspan=1 colspan=1>Positive</td><td rowspan=1 colspan=1>Neutral</td><td rowspan=1 colspan=1>Positive</td></tr><tr><td rowspan=1 colspan=1>Movie Reviews</td><td rowspan=1 colspan=1>Selena Gomez presented Amy Schumerwithanawardand a heap of praise at the Hollywood Film Awards onNovember 1.</td><td rowspan=1 colspan=1>Positive</td><td rowspan=1 colspan=1>Negative</td><td rowspan=1 colspan=1>Positive</td></tr><tr><td rowspan=1 colspan=1>Movie Reviews</td><td rowspan=1 colspan=1>mailjet: It&#x27;s Fri...we mean Star Wars Day. May the forcebe with all of your emails! https://t.co/FbDdjiJVUT</td><td rowspan=1 colspan=1>Positive</td><td rowspan=1 colspan=1>Neutral</td><td rowspan=1 colspan=1>Positive</td></tr><tr><td rowspan=1 colspan=1>Movie Reviews</td><td rowspan=1 colspan=1>Straight Outta Compton&#x27;s success hopefully convincesNew Line Cinema to give Ice Cube the right budget forthe last Friday movie.</td><td rowspan=1 colspan=1>Positive</td><td rowspan=1 colspan=1>Neutral</td><td rowspan=1 colspan=1>Positive</td></tr><tr><td rowspan=1 colspan=1>Emoticons</td><td rowspan=1 colspan=1>That ball Kris Bryant just hit is the 2nd farthest ball I&#x27;veever seen hit. He is officially ridiculous.</td><td rowspan=1 colspan=1>Positive</td><td rowspan=1 colspan=1>Neutral</td><td rowspan=1 colspan=1>Positive</td></tr><tr><td rowspan=1 colspan=1>Emoticons</td><td rowspan=1 colspan=1>This fandom&#x27;s a mess omg,Iwouldn&#x27;t be surprise if to-morrow there&#x27;s a trend who says Niall&#x27;s going to marryhis cousin #WeKnowTheTruth</td><td rowspan=1 colspan=1>Negative</td><td rowspan=1 colspan=1>Positive</td><td rowspan=1 colspan=1>Negative</td></tr><tr><td rowspan=1 colspan=1>Emoticons</td><td rowspan=1 colspan=1>Christians snapchat story makes me want to kill my-self.like Ifeel like a depressed 8th grader going throughthat emo phase</td><td rowspan=1 colspan=1>Negative</td><td rowspan=1 colspan=1>Neutral</td><td rowspan=1 colspan=1>Negative</td></tr></table>
+
+Considering that we have shown a neural network can distill and improve a representation learned by a logical rule engine, how the final representation differs from the logic of the original engine is of practical interest. We thus compare the agreement of our fine-tuned rule based GRU with the original rule model on the SemEval testing set. We find that the transferred model achieves $78 . 7 \%$ agreement with the rule model when the rule model is right. This clearly indicates that our final model is not deterministic based on the rule engine, and has a probability of adding errors even when the original rule model works well. However, our model actually has $4 4 . 7 \%$ accuracy on the examples the rule model got wrong. Our approach yields significant gains in comparison to the original rule classifiers, improving from $5 7 . 8 \%$ to $6 4 . 4 \%$ test set accuracy before even incorporating in auxiliary knowledge sources.
+
+# 6 INTEGRATING TRANSFER LEARNING FROM MULTIPLE TASKS WITH ENSEMBLE DISTILLATION
+
+# 6.1 ENSEMBLE METHODOLOGY
+
+In our experiments we tried to find a balance between an ensemble model that is powerful enough to have an adaptive weighted average decision function and not so powerful that it overfits on our limited training and validation data. Our model is quite similar in architecture to the gating network component of a hierarchical mixture of experts model (Jacobs et al., 1991), (Jordan & Jacobs, 1994). We tried our model over all four representations at once and found that it overfits. Our experiments showed it is more effective to adopt a greedy ensembling strategy where all models are combined with the best performing model on the validation set at each phase until only two models are left. Finally, these two models are combined with the same mechanism. (Riemer et al., 2016) suggests that a many element gating network can be improved with a sparsity constraint, but this did not work as well as the greedy strategy for our model and experiments.
+
+More formally, for any two models $A$ and $B$ combined in an ensemble, we train the following mechanism using Stochastic Gradient Descent:
+
+Table 5: Empirical three way sentiment classification results on the SemEval 2016 Task 4 Subtask A test set.   
+
+<table><tr><td rowspan=1 colspan=1>ModelDescription</td><td rowspan=1 colspan=1>AccuracyonSemEval TestSet</td></tr><tr><td rowspan=1 colspan=1>Distilled GRUTrained on Full EnsembleFull EnsembleEnsemble withLogical Rules and Both Movie Review TasksEnsemble with Logical Rules and Binary Movie ReviewsEnsemble with Logical Rules and Five Class Movie ReviewsEnsemble with Logical Rules and Emoticon PredictionEnsemble withBothMovie Review TasksGRU Trained on Only SemEval Data</td><td rowspan=1 colspan=1>66.0%65.9%65.7%65.4%65.1%65.0%62.1%53.6%</td></tr><tr><td rowspan=1 colspan=1>SwissCheese (Bethard etal.,2016)NTNUSentEval (Jahren et al.,2016)UniPI (Attardi &amp; Sartiano,2016)CUFE (Nabil et al.,2016)INSIGHT-1 (Ruder et al., 2016)</td><td rowspan=1 colspan=1>64.6%64.3%63.9%63.7%63.5%</td></tr></table>
+
+$$
+\begin{array} { r } { m _ { A } = \sigma ( W _ { A } \hat { y } _ { A } + b _ { A } ) } \\ { m _ { B } = \sigma ( W _ { B } \hat { y } _ { B } + b _ { B } ) } \end{array}
+$$
+
+$$
+a _ { A } = { \frac { m _ { A } } { m _ { A } + m _ { B } } }
+$$
+
+$$
+a _ { B } = { \frac { m _ { B } } { m _ { A } + m _ { B } } }
+$$
+
+$$
+\hat { y } _ { e n s e m b l e } = a _ { A } \hat { y } _ { A } + a _ { B } \hat { y } _ { B }
+$$
+
+where $\hat { y } _ { e n s e m b l e }$ is the prediction vector of the combined ensemble. ${ \hat { y } } _ { A }$ and $\hat { y } _ { B }$ are the output vectors of the individual models.
+
+# 6.2 ENSEMBLE RESULTS
+
+Our ensemble model was trained on what was set aside as the validation data during the initial training with early stopping. In the first phase of combining, the model transferred from the logical rule source task was combined with each model. In the second phase, the model based on transfer from the binary movie review sentiment model was combined with each model. In the third phase, the two remaining models were combined. The results of our ensemble in Table 5 suggest that it is possible to further improve the performance of a single sequential transfer model by intelligently combining its predictions with models that have other perspectives. This is because they are modeled using different source tasks for prior knowledge. Impressively, our final distilled model surpasses results from all prior models on the SemEval 2016 benchmark using the same final architecture of a 50 hidden unit GRU model that is clearly not even competitive when trained simply on the task specific labeled data. The prior best model SwissCheese (Bethard et al., 2016) consists of random forests ensemble built utilizing multiple convolutional neural network models and distant supervision. In fact, we achieve superior results despite using over an order of magnitude less total data for training our model.
+
+We would also like to underscore that our total improvement of $1 . 5 \%$ as a result of creating an ensemble with our best transferred model from the logical rule source task can be viewed as quite disappointing, despite achieving state of the art results. In fact, in the theoretical limit of having a decision model that switches to the best already learned model at each point, our four transferred representations would achieve $8 5 . 1 \%$ accuracy together. For the combination of the movie review based models and logical rule based model we can get to $8 1 . 4 \%$ accuracy. Moreover, we can get $7 6 . 5 \%$ accuracy with just the logical rule based transfer model and the emoticon prediction based transfer model. Unfortunately, we achieve nowhere near these theoretical results despite representations that are apparently quite diverse. This seems indicative that there are significant gains yet to be uncovered in integrating these representations.
+
+# 7 CONCLUSION
+
+We consider a new methodology called the forgetting cost for preventing the catastrophic forgetting problem of neural network sequential transfer learning. The forgetting cost is practical and easy to implement. We have demonstrated for the challenging task of Twitter sentiment analysis that it can uncover significant gains in generalization performance and that it seems to not forget knowledge traditionally forgotten from the source task during fine-tuning. Our strong empirical results still motivate multiple avenues with high potential for continued exploration in text analytics. Using logical rules to improve neural network models is a promising direction for humans to efficiently contribute to increased model performance. Additionally, the large diversity of representations learned from multiple classifiers with the same target task but different source tasks seems to indicate there is potential to see even much greater gains when integrating multiple sources of knowledge transfer.
+
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+# A MAPPING SENTIMENT RULES TO SOFT TARGETS
+
+The gazetteer based logical rule engine separates sentences and phrases in the text. It then applies dictionaries of positive and negative sentiment words and phrases to the corresponding text. For each positive or negative phrase found, it checks to see if negation or double negation are applied, and modifies the polarity of the sentiment accordingly. The result for any piece of text is a count of positive and negative sentiment occurrences. For this task, we simply count the total number of positive and negative indicators to give an overall positive, negative or neutral score. To be concrete, we have a simple procedure for mapping positive and negative word counts to soft labels that could be used for distillation. If there are no positive or negative words, the output vector is a one hot vector corresponding to a neutral label. If there are an unequal number of positive and negative sentiment words, the neutral label is zero and the raw counts are sent to the softmax function to create a soft label over the positive and negative word occurrences. Finally, if there are an equal amount of positive and negative words, we consider the added total sentiment words plus one in the neutral label as well as the number of positive words and negative words before sending these totals through a softmax function.
+
+# B SIZE SELECTION FOR THE RULE DISTILLATION TASK
+
+In Table 6 we detail the performance of distilling a logical rule engine into a GRU based recurrent neural network by imposing soft labels over unlabeled tweets. The fact that we keep our word representations fixed with general purpose unsupervised data makes it difficult for the GRU to distill the entire model without a large number of examples. Additionally, as there were a large number of examples in our distillation experiments, we did not experience high run to run variation and only trained a single GRU model for each distillation experiment (as opposed to picking the best validation error of 10 parallel training routines as in our transfer experiments). Our distilled GRU is better on the testing set than the original classifier, likely because this input representation prevents the model from overfitting to the idiosyncrasies of the rule engine. This actually underscores an important point for the distillation of abstract knowledge. If the target task is known during distillation, it may be beneficial to stop short of totally distilling the original knowledge as it may hurt down stream performance past a certain point. We impose a simple policy where the best hidden unit and training example combination is selected based on performance on the training data of the target task. As a result, we use the model with 50 hidden units based on 50,000 training examples in our experiments integrating with other knowledge. This model is a pretty good one to choose, and achieves high transfer performance relative to models that overfit on the teacher network.
+
+Table 6: Logical rule engine distillation performance and SemEval 2016 Task 4 Subtask A accuracy as a function of the number of hidden units in the GRU and the number of training examples. The 50 hidden unit and 50,000 training example model performs the best on the SemEval training set.   
+
+<table><tr><td>Hidden Units</td><td>Examples</td><td>Alignmentwith Teacher</td><td>AccuracyonSemEval TestSet</td></tr><tr><td>25</td><td>50,000</td><td>88.3%</td><td>59.1%</td></tr><tr><td>25</td><td>300,000</td><td>91.9%</td><td>58.6%</td></tr><tr><td>50</td><td>50,000</td><td>88.6%</td><td>58.9%</td></tr><tr><td>50</td><td>300,000</td><td>93.0%</td><td>58.5%</td></tr><tr><td>75</td><td>50,000</td><td>88.7%</td><td>58.9%</td></tr><tr><td>75 100</td><td>300,000 50,000</td><td>93.6%</td><td>58.3%</td></tr><tr><td>100</td><td>300,000</td><td>88.6%</td><td>58.7%</td></tr><tr><td>125</td><td>50,000</td><td>93.8%</td><td>58.1%</td></tr><tr><td>125</td><td>300,000</td><td>88.5%</td><td>58.7%</td></tr><tr><td>150</td><td>50,000</td><td>93.7%</td><td>58.3%</td></tr><tr><td>150</td><td>300,000</td><td>88.5% 94.0%</td><td>59.0% 58.5%</td></tr></table>

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+    {
+        "type": "text",
+        "text": "REPRESENTATION STABILITY AS A REGULARIZER FOR IMPROVED TEXT ANALYTICS TRANSFER LEARNING ",
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+        "text": "Matthew Riemer, Elham Khabiri, and Richard Goodwin ",
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+        "text": "IBM T.J. Watson Research Center Yorktown Heights, NY, USA {mdriemer, ekhabiri, rgoodwin}@us.ibm.com ",
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+        "text": "ABSTRACT ",
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+        "text": "Although neural networks are well suited for sequential transfer learning tasks, the catastrophic forgetting problem hinders proper integration of prior knowledge. In this work, we propose a solution to this problem by using a multi-task objective based on the idea of distillation and a mechanism that directly penalizes forgetting at the shared representation layer during the knowledge integration phase of training. We demonstrate our approach on a Twitter domain sentiment analysis task with sequential knowledge transfer from four related tasks. We show that our technique outperforms networks fine-tuned to the target task. Additionally, we show both through empirical evidence and examples that it does not forget useful knowledge from the source task that is forgotten during standard fine-tuning. Surprisingly, we find that first distilling a human made rule based sentiment engine into a recurrent neural network and then integrating the knowledge with the target task data leads to a substantial gain in generalization performance. Our experiments demonstrate the power of multi-source transfer techniques in practical text analytics problems when paired with distillation. In particular, for the SemEval 2016 Task 4 Subtask A (Nakov et al., 2016) dataset we surpass the state of the art established during the competition with a comparatively simple model architecture that is not even competitive when trained on only the labeled task specific data. ",
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+        "type": "text",
+        "text": "1 INTRODUCTION ",
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+        "text": "Sequential transfer learning methodologies leverage knowledge representations from a source task in order to improve performance for a target task. A significant challenge faced when transferring neural network representations across tasks is that of catastrophic forgetting (or catastrophic interference). This is where a neural network experiences the elimination of important old information when learning new information. The very popular strategy of fine-tuning a neural network involves first training a neural network on a source task and then using the model to simply initialize the weights of a target task network up to the highest allowable common representation layer. However it is highly susceptible to catastrophic forgetting, because in training for the target task it has no explicit incentive to retain what it learned from the source task. While one can argue that forgetting the source task should not matter if only the target task is of interest, our paper adds to the recent empirical evidence across problem domains (Li & Hoiem, 2016),(Rusu et al., 2016) that show additional network stability can lead to empirical benefits over the fine-tuning algorithm. It seems as though for many Deep Learning problems we can benefit from an algorithm that promotes more stability to tackle the well known stability-plasticity dilemma. One popular approach for addressing this problem is rehearsals (Murre, 1992), (Robins, 1995). Rehearsals refers to a neural network training strategy where old examples are relearned as new examples are learned. In the transfer setting it can be seen as related to multi-task learning (Caruana, 1997) where two tasks are trained at the same time, rather than sequentially, while sharing a common input encoder to a shared hidden representation. However, in rehearsals the representation is biased in favor of the source task representation through initialization. This technique is very sensible because while fine-tuning is susceptible to catastrophic forgetting, multi-task learning is not (Caruana, 1997). ",
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+        "text": "One of the biggest issues with the standard rehearsals paradigm is that it requires a cached memory of training examples that have been seen in the past. This can be a massive requirement as the number of source tasks and training data sizes scale. One compelling technique for addressing this problem is the concept of pseudorehearsals (Robins, 1995), (Robins, 1996), where relearning is performed on an artificially constructed population of pseudoitems instead of the actual old examples. Unfortunately, current automatic techniques in the text analytics domain have not yet mastered producing linguistically plausible data. As such, the pseudorehearsals paradigm is likely to waste computational time that could be spent on learning realistic patterns that may occur during testing. In our work, we extend the Learning without Forgetting (LwF) paradigm of (Li & Hoiem, 2016) to the text analytics domain using Recurrent Neural Networks. In this approach, the target task data is used both for learning the target task and for rehearsing information learned from the source task by leveraging synthetic examples generated for the target task input by the model that only experienced training on the source task data. As argued by Li & Hoiem (2016), this setup strikes an important balance between classification performance, computational efficiency, and simplicity in deployment. ",
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+        "text": "Regardless of whether they are applied to real source task examples, real target task examples, or synthetic examples, paradigms in the style of rehearsals all address the shortcomings of neural network forgetting by casting target task integration as a multi-task learning problem. However, this is not quite the purpose of the multi-task learning architecture, which was designed for joint learning of tasks from scratch at the same time. The key disconnect is that in multi-task learning, the transformation from the shared hidden layer to the outputs for each task are all learned and updated with the changing hidden representation. This would imply that, in the framework of rehearsals, it is possible for there to be significant changes during learning of the network’s representation, and thus its abilities on the source task itself. While it would be desirable to claim we were allowing our source task network to become even better based on the target task than it was before, this motivation seems idealistic in practice. One reason this is idealistic is because multi-task learning generally only works well when tasks are sampled at different rates or alternatively given different priority in the neural network loss function (Caruana, 1997). As a result, it is most likely that auxilirary source tasks will receive less priority from the network for optimization than the target task. Additionally, we observe in our experiments, and it has been observed by others in (Rusu et al., 2015), that it is generally not possible to distill multiple complex tasks into a student network at full teacher performance for all tasks. This seems to imply the degradation of the source task performance during training is somewhat inevitable in a multi-task learning paradigm. ",
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+        "text": "We address this issue with our proposed forgetting cost technique. We demonstrate that it, in fact, can be valuable to keep the hidden to output transformation of the source tasks fixed during knowledge integration with the target task. This way, we impose a stronger regularization on the hidden representation during target task integration by not allowing it to change aspects that were important to the source task’s performance without direct penalization in the neural network’s loss function. We demonstrate empirically both that freezing the source task specific weights leads to less deterioration in the accuracy on the source task after integration, and that it achieves better generalization performance in our setting. The forgetting cost is practical and easy to implement in training any kind of neural network. In our experiments, we explore application of the forgetting cost in a recurrent neural network to the three way Twitter sentiment analysis task of SemEval 2016 Task 4 Subtask A and find it to achieve consistently superior performance to reasonable baseline transfer learning approaches in four examples of knowledge transfer for this task. ",
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+        "text": "We also demonstrate how powerful distillation can be in the domain of text analytics when paired with the idea of the forgetting cost. Significantly, we show that a high quality gazetteer based logical rule engine can be distilled using unlabeled data into a neural network and used to significantly improve performance of the neural network on the target task. This is achieved with a novel extension of the LwF paradigm by Li & Hoiem (2016) to the scenario of a source task with the same output space as the target task. This can be a very promising direction for improving the ability of humans to directly convey knowledge to deep learning algorithms. Indeed, a human defined rule can contain far more information than a single training example, as that rule can be projected on to many unlabeled examples that the neural network can learn from. This is the reason human teachers generally begin teaching human students tasks by going over core rules at the onset of learning. Moreover, we showcase that multiple expert networks trained on the target task with prior knowledge from different source tasks can be effectively combined in an ensemble and then distilled into a single GRU model (Cho et al., 2014), (Chung et al., 2014). Leveraging this combination of distillation and knowledge transfer techniques allows us to achieve state of the art accuracy on the SemEval task with a model that performs $11 \\%$ worse than the best prior techniques when trained only on the labeled data. ",
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+        "text": "2 RELATED WORK ",
+        "text_level": 1,
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+        "text": "Since the work of (Bucilu et al., 2006) and (Hinton et al., 2015) showed that an ensemble of neural network classifier can be distilled into a single model, knowledge distillation from a teacher network to a student network has become a growing topic of neural network research. In (Ba & Caruana, 2014) it was shown that a deep teacher neural network can be learned by a shallow student network. This idea was extended in (Romero et al., 2014), where it was demonstrated that a deep and narrow neural network can learn a representation that surpasses its teacher. The use of distillation as a means of sharing biases from multiple tasks was explored in (Lopez-Paz et al., 2016), where the teacher network is trained with the output of the other tasks as input. It is not obvious how to extend a recurrent neural network to best use this kind of capability over a sequence. The idea of distilling from multiple source task teachers into a student network was highlighted in the reinforcement learning setting in (Rusu et al., 2015). Additionally, the concept of using distillation for knowledge transfer was also explored in (Chen et al., 2015), where function preserving transformations from smaller to bigger neural network architectures were outlined. This technique could also provide value in some instances for our approach where wider or deeper neural networks are needed for the task being transferred to than was needed for the original task. Distillation over target task data was first proposed as a means of elevating catastrophic forgetting in sequential knowledge transfer as applied to image classification in (Li & Hoiem, 2016). We extend this approach for its first application to our knowledge for text analytics problems, with a recurrent neural network architecture, and in the setting where the source task and target task have the same output. The chief distinction of our proposed forgetting cost is that source task specific parameters are held fixed during integration with the target task as opposed to the joint training of all parameters used by Li & Hoiem (2016). Our experiments empirically support the intuition that freezing these parameters leads to greater retention of source task performance after target task integration and better generalization to the target task. ",
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+        "text": "An ensemble over multiple diverse models trained for the same sentiment analysis task was also considered in (Mesnil et al., 2014) for the IMDB binary movie reviews sentiment dataset (Maas et al., 2011). We tried this ensemble model in our work and found that it gave very limited improvement. Our ensemble technique learns a more powerful weighted average based on the soft targets of each task and a multi-step greedy binary fusion approach that works better for the Twitter sentiment analysis task in our experiments. Knowledge transfer from multiple tasks was considered to estimate the age of Twitter users based on the content of their tweets in (Riemer et al., 2015). We experimented with the hidden layer sharing approach outlined in that work and found that even when using just a single softmax combining layer, it would overfit on our limited training and validation data. Progressive neural networks (Rusu et al., 2016) is a recently proposed method very similar in motivation to our forgetting cost as it is directly trying to solve the catastrophic forgetting problem. The idea is that learned weight matrices relate the fixed representations learned on the source task to the construction of representations for the target task. In our experiments, the progressive neural networks approach consistently fails to even match the results achieved with fine-tuning. We hypothesize that although using fixed representations to aid learning addresses catastrophic forgetting, it suffers from the curse of dimensionality. As such, when training data is relatively small given the complexity of the task, it is prone to overfitting as it effectively increases the input dimension size through shared fixed representations. ",
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+        "text": "The combination of logic rules and neural networks has been explored in a variety of different architectures and settings. These neural-symbolic systems (Garcez et al., 2012) include early examples such as KBANN (Towell et al., 1990) that construct network architectures from given rules to perform reasoning. (Hu et al., 2016) very recently also looked at the problem of distilling logical rules into a neural network text analytics classifier. However, our approach is much more generic as it can be applied to integrate knowledge from any kind of pre-made classifier and treats the rule engine as a black box. In (Hu et al., 2016) they consider the individual rules and leverage an iterative convex optimization algorithm alongside the neural network to regularize the subspace of the network. In our work we demonstrate that, by guarding against catastrophic forgetting, it is possible to efficiently leverage rules for transfer by utilizing a generic sequential knowledge transfer framework. We do not need to make any modification to the architecture of the neural network during testing and do not need iterative convex optimization during training. ",
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+        "text": "3 FORGETTING COST REGULARIZATION ",
+        "text_level": 1,
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "3.1 SEQUENTIAL KNOWLEDGE TRANSFER PROBLEM STATEMENT ",
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+    {
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+        "text": "In the sequential knowledge transfer problem setting explored in this paper, training is first conducted solely on the source task examples $S$ , including $K _ { S }$ training examples $( x _ { S i } , y _ { S i } ) \\in S$ where $x _ { S i }$ is the input representation and $y _ { S i }$ is the output representation. After training is complete on $S$ , we would like to now use prior knowledge obtained in the model trained on $S$ to improve generalization on a new target task with examples $T$ , which includes $K _ { T }$ training examples $( x _ { T i } , y _ { T i } ) \\in T$ . Here we assume that the input representations $x _ { S i }$ and $x _ { T i }$ are semantically aligned in the same representation space. As such, if there is useful knowledge in $S$ that applies in some direct or indirect way to the target task that is not present in $T$ , we would expect a good knowledge integration approach to generalize better to the target task than it is possible to using the training data in $T$ alone. Strong performance for the sequential knowledge transfer problem is a first step towards the greater goal of a mechanism for effective lifelong learning (Thrun, 1996). ",
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+        "type": "text",
+        "text": "3.2 FORGETTING COST FOR TUNING A TARGET TASK MODEL ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "The most straightforward application of our proposed forgetting cost paradigm is for the case of integrating a neural network that has been trained on source task data $S$ , which has outputs in the same representation space as the outputs for the target task data $T$ . In this case, the forgetting cost amounts to the addition of a regularization term in the objective function during the integration phase when we train using $T$ . This promotes the neural network to be able to recreate the soft labels of the initialized model found after training on $S$ before integration is started with $T$ . More formally: ",
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+    {
+        "type": "equation",
+        "img_path": "images/7beef0ca5e9adef191b85cddf73a7ffefe0eddde060e382ae693f0836a9f00a2.jpg",
+        "text": "$$\nL o s s = L ( y , \\hat { y } ) + \\alpha _ { f } L ( y _ { i n i t } , \\hat { y } )\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "where $L$ is some loss function (we use mean squared error in our experiments) and $y _ { i n i t }$ is the soft label generated for the target task input $x _ { T i }$ based on the model after training just on $S$ . The model trained just on $S$ is also used to initialize the weights of the target task model before integration with $T$ as we do in the standard fine-tuning paradigm. $\\alpha _ { f }$ is a hyperparameter that can be utilized to control the extent of allowed forgetting. Of course, a very similar way to express this idea would be to mix synthetic training examples $T ^ { \\prime }$ with the same input as $T$ and output generated by the model trained just on $S$ with the true target task training examples $T$ . In this case, the mixing rate of the teacher generated training examples is analogous to our forgetting parameter $\\alpha _ { f }$ determining the prioritization. These techniques perform quite similarly in our experiments, but we actually find that the formulation in equations 1 and 3 perform slightly better on the test set. For example, this formulation is superior by $0 . 4 \\%$ accuracy in tuning a distilled representation of a logical rule engine. We conjecture that learning tasks in the same gradient step when they are related to the same input data results in slightly less noisy gradients. ",
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+    {
+        "type": "text",
+        "text": "3.3 FORGETTING COST FOR KNOWLEDGE TRANSFER FROM A RELATED TASK ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The assumption in section 3.2 that the output of the source task data $S$ should be in the same representation space as the output for the target task data $T$ is quite a big one. It rules out the vast majority of knowledge sources that we can potentially leverage. As such, we propose an extension that does not make this restriction for application in sequential knowledge transfer of tasks that are not directly semantically aligned. We update our model to include another predicted output separate from $\\hat { y }$ : ",
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/7fd5f66c7c56b98cf5d68d7404964bb820efd2d16f894b099637b0e546041fc7.jpg",
+        "text": "$$\n\\hat { y } _ { i n i t } = f _ { i n i t } ( W _ { f i x e d } h _ { s h a r e d } + b _ { f i x e d } )\n$$",
+        "text_format": "latex",
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+    },
+    {
+        "type": "text",
+        "text": "where ${ \\hat { y } } _ { i n i t }$ is a predicted output attempting to recreate the soft labels of the original model trained just on $S$ . $f _ { i n i t }$ is the non-linearity used in the final layer of the source task model. Weight matrix $W _ { f i x e d }$ and bias $b _ { f i x e d }$ are taken from the final layer of the source task model and are not updated ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "during integration with the target task data $T$ . As a result, the loss function is updated from section 3.2: ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/0ecf3abc5ea9623f27b11510d00187e5b3ac326ed68c19077c84a52e34dc95ea.jpg",
+        "text": "$$\nL o s s = L ( y , \\hat { y } ) + \\alpha _ { f } L ( y _ { i n i t } , \\hat { y } _ { i n i t } )\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where the hidden state is shared between both terms in the objective function. Up to the shared hidden layer, we initialize the model for the target task with the weights learned just using $S$ . Random matrices and bias vectors are now used to initialize the prediction of $\\hat { y }$ based on the shared hidden representation. This can be seen as a weak form of restricting the model parameters that can be useful for regularization. The hidden representation is in effect constrained so that it is promoted not to change in key areas that have a large effect on the output vector of the source task model. On the other hand, there is little regularization for parameters that have little effect on the output vector for the source task model. ",
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+    },
+    {
+        "type": "text",
+        "text": "4 RECURRENT NEURAL NETWORK MODEL",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In recent years, recurrent neural network models have become a tool of choice for many NLP tasks. In particular, the LSTM variant (Hochreiter & Schmidhuber, 1997) has become popular as it alleviates the vanishing gradients problem (Bengio et al., 1994) known to stop recurrent neural networks from learning long term dependencies over the input sequence. In our experiments we use the simpler GRU network (Cho et al., 2014), (Chung et al., 2014) that generally achieves the same accuracy despite a less complex architecture. Each time step $t$ is associated with an input $x _ { t }$ and a hidden state $h _ { t }$ . The mechanics of the GRU are defined with the following equations: ",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/057bdc63d96f21f19301a8972e10b8d535f5124f1fbd0f925f80b0927282244f.jpg",
+        "text": "$$\n\\begin{array} { r } { \\begin{array} { r l } & { z _ { t } = \\sigma \\big ( W _ { x z } x _ { t } + W _ { h z } h _ { t - 1 } \\big ) } \\\\ & { r _ { t } = \\sigma \\big ( W _ { x r } x _ { t } + W _ { h r } h _ { t - 1 } \\big ) } \\\\ & { { \\tilde { h } } _ { t } = t a n h \\big ( W _ { x h } x _ { t } + r _ { t } \\circ W _ { h h } h _ { t - 1 } \\big ) } \\\\ & { ~ h _ { t } = z _ { t } \\circ h _ { t - 1 } + ( 1 - z _ { t } ) \\circ { \\tilde { h } } _ { t } } \\end{array} } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $\\circ$ denotes an element-wise product. $W _ { x z } , W _ { x r }$ , and $W _ { x h }$ represent learned matrices that project from the input size to the hidden size. $W _ { h z }$ , $W _ { h r }$ , and $W _ { h h }$ represent learned matrices that project from the hidden size to the hidden size. In our work we evaluate the GRU in the categorical prediction setting. For each document, the hidden state after the last word $h _ { L }$ is used for the prediction $\\hat { y }$ of the label $y$ . As such, we treat $h _ { L }$ as the shared hidden representation $h _ { s h a r e d }$ from section 3.3 for our experiments. ",
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/c5fe8b91623ad92ec63d92d1fc8e294e909254fb466f294f09c73ebead8858a5.jpg",
+        "text": "$$\n\\hat { y } = f ( W _ { y h } h _ { L } + b _ { y } )\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The prediction goes through one other non-linear function $f$ after the final hidden state is derived. In our experiments we use the softmax function, but others are useful in different settings. A model that builds on top of GRUs with an external memory storage paradigm (Kumar et al., 2015) currently holds the state of the art on movie review sentiment analysis. However, we focus just on the straightforward single layer GRU model in our experiments so that we can more easily disentangle factors of influence on performance. Our GRU model was fed a sequence of fixed 300 dimensional Glove vectors (Pennington et al., 2014), representing words based on analysis of 840 billion words from a common crawl of the internet, as the input $x _ { t }$ for all tasks. It has been shown in a number of papers that tuning the word embeddings during training could increase performance, and it is possible our approach could have performed better had we done so. ",
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "5 SEQUENTIAL KNOWLEDGE TRANSFER EXPERIMENTS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "5.1 EXPERIMENT DETAILS ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Our neural network models were implemented in Theano (Theano Development Team, 2016) and trained with Stochastic Gradient Descent. As we did not use an advanced optimization method and noticed run to run variation in performance, for all of our transfer learning models we trained 10 parallel versions and chose the one with the highest validation accuracy. The SemEval 2016 Task 4 Subtask A training set consists of 10,000 total training examples, but we were only able to receive 8,906 because of tweet removals when we used the downloading script. For the target task data across our experiments, 7,600 examples of the SemEval training set examples were used for training and the rest for validation. The GRU model achieves only $5 3 . 6 \\%$ accuracy on the SemEval testing data when just training with the target task data and random initialization. In order to improve, we consider knowledge transfer from GRUs trained for the following source tasks to the SemEval target task data: ",
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+        "type": "text",
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+    {
+        "type": "text",
+        "text": "Distilling Logical Rules: Knowledge distillation can be performed using teacher models that are very different in structure than their neural network based student models. We demonstrate with this task that a compilation of logical linguistic rules can be used as an effective teacher for a GRU by having the GRU attempt to create the output of the rule engine generated over unlabeled in domain data. Specifically, our gazetteer based logical rule engine separates sentences and phrases in the text. It then applies dictionaries of positive and negative sentiment words and phrases to the corresponding text. For each positive or negative phrase found, it checks to see if negation or double negation are applied, and modifies the polarity of the sentiment accordingly. The result for any piece of text is a count of positive and negative sentiment occurrences. For this task, we simply count the total number of positive and negative indicators to give an overall positive, negative or neutral score. We provide addition details on how we mapped rules to soft targets for the student network to recreate in Appendix A. We utilized a GRU model with 50 hidden units and 50,000 unlabeled examples for our source task model. We distill off the soft labels as in (Hinton et al., 2015), but set our temperature fixed at 1.0. It is possible that our performance could have improved by tuning this parameter. Additional details about the selection of the network and data size are included in Appendix B. The logical rule model itself achieves $5 7 . 8 \\%$ accuracy on the SemEval testing data and the rules distilled into a GRU as explained in section 4 achieves $5 8 . 9 \\%$ accuracy before any integration with the SemEval target task data. We leverage this task for comparison of knowledge transfer techniques when the source task and target task share an output space as discussed in section 3.2. ",
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+    {
+        "type": "text",
+        "text": "Binary Movie Reviews: For knowledge transfer from related tasks as discussed in section 3.3 we first consider the Stanford Sentiment Treebank (Socher et al., 2013), which is a popular sentiment dataset based on the movie review domain. We consider one source task to be the binary (positive, and negative) sentence level sentiment subtask which contains 6,920 training examples, 872 validation examples, and 1,821 testing examples. Our GRU model with 40 hidden units achieves $8 5 . 5 \\%$ accuracy on this task. ",
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+    {
+        "type": "text",
+        "text": "Five Class Movie Reviews: We also consider another source task leveraging the Stanford Sentiment Treebank data from the fine grained (very positive, positive, neutral, negative, and very negative) sentence level sentiment substask which contains 8,544 training examples, 1,101 validation examples, and 2,210 testing examples. We use a GRU model with 200 hidden units to accommodate for the increased task complexity and achieve $4 5 . 9 \\%$ accuracy. This fine grained model can actually be assessed directly on the SemEval task by projecting from five classes to three classes, but it only achieves $4 4 . 2 \\%$ accuracy with no tuning on the target task data. Our performance on these two movie review source tasks is quite similar to what was reported in (Tai et al., 2015) when using a similar setup, but with LSTMs for both subtasks. ",
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+    {
+        "type": "text",
+        "text": "Emoticon Heuristic: Finally, we consider a semi-supervised task based on emoticon prediction motivated by the successful work in (Go et al., 2009), leveraging it in the twitter sentiment domain and its use as a vital component of the SemEval competition winning system (Bethard et al., 2016). We find unlabelled tweets that contain smileys, frowns, or laughing emoticons. We remove emoticons from the tweet before prediction and compile a dataset of 250,000 training examples, 50,000 validation examples, and 100,000 testing examples for each of the three classes. This is multiple orders of magnitude smaller than the 90 million tweets used in (Bethard et al., 2016) to allow for quick experimentation. Our GRU model with 50 hidden units achieves $6 3 . 4 \\%$ accuracy on the emoticon prediction test set. ",
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+        "type": "text",
+        "text": "We consider multiple sequential knowledge transfer algorithms for experimental comparison. Each uses only the source task data for learning the source task and only the target task data for integrating with the target task. This way integration is fast and simple, because it does not incorporate storage and replay of examples from the potentially very large source task as argued in (Li & Hoiem, 2016). ",
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+    {
+        "type": "text",
+        "text": "Fine-Tuning: The representation is simply initialized with the representation found after training on the source task and then trained as usual on the target task. This approach was pioneered in (Hinton & Salakhutdinov, 2006), in application to unsupervised source tasks and applied to transfer learning in (Bengio et al., 2012), and (Mesnil et al.). The learning rate is tuned by a grid search based on the validation set performance. ",
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+    {
+        "type": "text",
+        "text": "Progressive Networks: We also compare with our implementation of a progressive neural network (Rusu et al., 2016), where the representation learned for the source task is held fixed and integrated with a target task specific model via lateral connections trained using the target task data. The learning rate is also tuned based on a grid search using the validation set. ",
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+    },
+    {
+        "type": "text",
+        "text": "Learning without Forgetting (LwF): In the LwF paradigm, joint training is performed after parameter initialization. This is achieved by treating the target task data and the output generated by the source task model based on the target task input data as two jointly learned tasks as in (Caruana, 1997). As opposed to our proposed forgetting cost, the source task specific parameters are not held fixed while training on the target task data. The learning rate and mixing rate between the tasks are tuned by a grid search based on validation set performance. We first consider a version of the LwF model that leverages a random initialization of the target task specific parameters and initialization of all parameters learned on the source task with the learned values. We also consider another formulation that we call Greedy LwF. This is actually more closely aligned with the original paper (Li & Hoiem, 2016). All source task parameters are first held fixed, and the target task specific parameters are learned alone before joint training with all of the parameters unfrozen as a second step. For the case of source tasks with output in the space of the target task output, there are no source task specific parameters, so the forgetting cost can be viewed as a viable interpretation of the LwF paradigm appropriate in that setting. ",
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+    {
+        "type": "text",
+        "text": "Forgetting Cost: Finally, we compare each baseline model with our proposed forgetting cost described in section 3. The learning rate as well as $\\alpha _ { f }$ from equations 1 and 3 were tuned by a grid search based on the validation set performance. ",
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+    {
+        "type": "text",
+        "text": "5.3 TARGET TASK RESULTS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We empirically evaluate the generalization performance of the forgetting cost for sequential knowledge transfer from four different source tasks in Table 1 and Table 2. The source task considered in Table 1 is distilling a logical rule model, leveraging the technique outlined in equation 1. In Table 2 we leverage the forgetting cost for related task knowledge transfer as outlined in equation 3. ",
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+    {
+        "type": "text",
+        "text": "Our experimental results on the SemEval data validate our intuition that the forgetting cost should lead to stronger regularization and better generalization performance. One thing to note about our progressive neural networks implementation is that it effectively has only one hidden layer, because we hold our embeddings fixed during model training and the same embeddings are shared among the models used for all of the tasks. It is possible that having multiple layers of lateral connections is important to achieving good performance. However, this setting was not applicable in our experiments. Our results for sequential knowledge transfer on the SemEval benchmark are quite encouraging as the forgetting cost outperforms baselines significantly in all cases. ",
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+    {
+        "type": "text",
+        "text": "We additionally have validated the intuition that equation 1 should perform stronger regularization than equation 3 when equation 1 is applicable. In fact, for our distilled logical rule model tuning experiments, we found that equation 1 performs $3 \\%$ better on the test set. In an attempt to understand more about what caused this performance difference, we monitored testing set performance at each epoch and noticed that equation 3 is actually prone to overfitting away from a good solution on the test set. However, it often finds a pretty good one comparable to equation 1 early in training. When equation 1 could be applied, it seems to be a useful regularization to constrain both the hidden layer and the output layer to align with the model learned on the source task. In equation 3, the hidden to output transformation learned for the target task can in contrast learn to deviate from the transformation learned for the source task. ",
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+    {
+        "type": "table",
+        "img_path": "images/cc9409df48da0cf33a93d43a17c7b827f3dac7f4f71fa3cb83f885c9689d24cd.jpg",
+        "table_caption": [
+            "Table 1: Evaluation of target task tuning methodologies for a distilled rule model to the task of SemEval 2016 Task 4 Subtask A. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=1>Model Description</td><td rowspan=1 colspan=1>Accuracyon SemEval Test Set</td></tr><tr><td rowspan=1 colspan=1>Forgetting Cost TransferFine-tuning TransferProgressive Networks Transfer</td><td rowspan=1 colspan=1>64.4%58.5%56.9%</td></tr><tr><td rowspan=1 colspan=1>Distilled Logical Rule ModelLogical Rule ModelGRU Trained on Only SemEval Data</td><td rowspan=1 colspan=1>58.9%57.8%53.6%</td></tr></table>",
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+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/9ccc247677d263abe8404f11293adde3979991256c702be1315349a1294db1ed.jpg",
+        "table_caption": [
+            "Table 2: Evaluation of knowledge transfer from three source tasks to the task of SemEval 2016 Task 4 Subtask A. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=1>Source Task</td><td rowspan=1 colspan=1>Fine-Tuning</td><td rowspan=1 colspan=1>ProgressiveNetworks</td><td rowspan=1 colspan=1>LwF</td><td rowspan=1 colspan=1>GreedyLwF</td><td rowspan=1 colspan=1>Forgetting Cost</td></tr><tr><td rowspan=1 colspan=1>Binary Movie Reviews</td><td rowspan=1 colspan=1>57.3%</td><td rowspan=1 colspan=1>54.5%</td><td rowspan=1 colspan=1>58.1%</td><td rowspan=1 colspan=1>58.8%</td><td rowspan=1 colspan=1>59.7%</td></tr><tr><td rowspan=1 colspan=1>Five Class Movie Reviews</td><td rowspan=1 colspan=1>57.4%</td><td rowspan=1 colspan=1>54.6%</td><td rowspan=1 colspan=1>57.1%</td><td rowspan=1 colspan=1>56.6%</td><td rowspan=1 colspan=1>58.2%</td></tr><tr><td rowspan=1 colspan=1>Emoticon Heuristic</td><td rowspan=1 colspan=1>55.8%</td><td rowspan=1 colspan=1>53.2%</td><td rowspan=1 colspan=1>57.7%</td><td rowspan=1 colspan=1>56.7%</td><td rowspan=1 colspan=1>58.6%</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "5.4 SOURCE TASK PERFORMANCE AFTER TARGET TASK INTEGRATION ",
+        "text_level": 1,
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In Table 3 we explore the retention of empirical performance on the source task for knowledge transfer algorithms after integration with the target task is complete. Apparently in these cases, allowing relearning of the source task model during integration with the target task data is indeed destructive to source task performance. LwF outperforms Fine-Tuning significantly in knowledge retention for movie reviews, but interestingly does not for the emoticon heuristic. The effect of the greedy target task initialization strategy also appears inconsistent. It seems it is possible that this greedy initialization could improve our proposed forgetting cost paradigm in some cases as well. However, a rigorous analysis of the tradeoffs for this initialization approach is beyond the scope of this paper. ",
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+    {
+        "type": "text",
+        "text": "As the source task representation is literally stored fixed as part of the target task representation in progressive neural networks, it is not clear how to assess any effective forgetting of the source task during target task integration. As a result, we omit them from our source task forgetting experiments. ",
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+    {
+        "type": "text",
+        "text": "5.5 INSPECTION OF LEARNED REPRESENTATIONS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Now that we have established the empirical benefits of our proposed forgetting cost, we will demonstrate what it achieves qualitatively through examples. In Table 4 we include a sample of examples that are predicted correctly by transferring the knowledge source with the forgetting cost paradigm and not with fine-tuning based integration. The effect is, perhaps, easiest to understand for the rule based and movie review based transfer scenarios. For the rule based transfer setting you can literally map insights that are not forgotten to their respective logical rule in the model, as is the case in these examples. Moreover, we can see movie domain specific terminology such as ”May the force be with” is seemingly forgotten with standard fine-tuning, but not when the forgetting cost regularization is applied. ",
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+    {
+        "type": "table",
+        "img_path": "images/e5c6f0d1e366972aa43ebb6de2ba47cda96b84599baa15bde2aab264dd10c469.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=1>Source Task</td><td rowspan=1 colspan=1>Fine-Tuning</td><td rowspan=1 colspan=1>LwF</td><td rowspan=1 colspan=1>GreedyLwF</td><td rowspan=1 colspan=1>Forgetting Cost</td><td rowspan=1 colspan=1>Source Only</td></tr><tr><td rowspan=1 colspan=1>Binary Movie Reviews</td><td rowspan=1 colspan=1>80.7%</td><td rowspan=1 colspan=1>81.3%</td><td rowspan=1 colspan=1>81.5%</td><td rowspan=1 colspan=1>83.3%</td><td rowspan=1 colspan=1>85.5%</td></tr><tr><td rowspan=1 colspan=1>Five Class Movie Reviews</td><td rowspan=1 colspan=1>41.6%</td><td rowspan=1 colspan=1>42.8%</td><td rowspan=1 colspan=1>43.1%</td><td rowspan=1 colspan=1>43.3%</td><td rowspan=1 colspan=1>45.9%</td></tr><tr><td rowspan=1 colspan=1>Emoticon Heuristic</td><td rowspan=1 colspan=1>59.4%</td><td rowspan=1 colspan=1>59.1%</td><td rowspan=1 colspan=1>58.9%</td><td rowspan=1 colspan=1>60.3%</td><td rowspan=1 colspan=1>63.4%</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "Table 3: Evaluation of accuracy on the source task after integration with the target task data of SemEval 2016 Task 4 Subtask A. The accuracy after only source task training prior to integration with the target task is included for reference as a baseline. ",
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+    {
+        "type": "table",
+        "img_path": "images/8ab98c44c12e1c988b91d3f9c2915c9451b37b0c513c0bada266b61dad99c1f8.jpg",
+        "table_caption": [
+            "Table 4: Some transfer learning examples from each knowledge source to SemEval 2016 where the GRU model successfully predicts sentiment when using the forgetting cost paradigm, but not with fine-tuning based integration. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=1>Source</td><td rowspan=1 colspan=1>Tweet</td><td rowspan=1 colspan=1>Label</td><td rowspan=1 colspan=1>Fine-Tuning</td><td rowspan=1 colspan=1>Forgetting Cost</td></tr><tr><td rowspan=1 colspan=1>Logical Rules</td><td rowspan=1 colspan=1>JohnKasich should feel proud of hisperformance at the#GOPDebate Thursday night. He looked more presi-dential than the rest of the field.</td><td rowspan=1 colspan=1>Positive</td><td rowspan=1 colspan=1>Neutral</td><td rowspan=1 colspan=1>Positive</td></tr><tr><td rowspan=1 colspan=1>Logical Rules</td><td rowspan=1 colspan=1>@ BrunoMars I&#x27;m so tired of you dressing like you ain&#x27;tgot no money. You went from wearing Gucci loafers to6th grade boy Sketchers.</td><td rowspan=1 colspan=1>Negative</td><td rowspan=1 colspan=1>Neutral</td><td rowspan=1 colspan=1>Negative</td></tr><tr><td rowspan=1 colspan=1>Logical Rules</td><td rowspan=1 colspan=1>@DavidVonderhaar loving the beta Vahn, even playing it on PC with a PS4 controller without aim assist, can&#x27;twait for November 6</td><td rowspan=1 colspan=1>Positive</td><td rowspan=1 colspan=1>Neutral</td><td rowspan=1 colspan=1>Positive</td></tr><tr><td rowspan=1 colspan=1>Movie Reviews</td><td rowspan=1 colspan=1>Selena Gomez presented Amy Schumerwithanawardand a heap of praise at the Hollywood Film Awards onNovember 1.</td><td rowspan=1 colspan=1>Positive</td><td rowspan=1 colspan=1>Negative</td><td rowspan=1 colspan=1>Positive</td></tr><tr><td rowspan=1 colspan=1>Movie Reviews</td><td rowspan=1 colspan=1>mailjet: It&#x27;s Fri...we mean Star Wars Day. May the forcebe with all of your emails! https://t.co/FbDdjiJVUT</td><td rowspan=1 colspan=1>Positive</td><td rowspan=1 colspan=1>Neutral</td><td rowspan=1 colspan=1>Positive</td></tr><tr><td rowspan=1 colspan=1>Movie Reviews</td><td rowspan=1 colspan=1>Straight Outta Compton&#x27;s success hopefully convincesNew Line Cinema to give Ice Cube the right budget forthe last Friday movie.</td><td rowspan=1 colspan=1>Positive</td><td rowspan=1 colspan=1>Neutral</td><td rowspan=1 colspan=1>Positive</td></tr><tr><td rowspan=1 colspan=1>Emoticons</td><td rowspan=1 colspan=1>That ball Kris Bryant just hit is the 2nd farthest ball I&#x27;veever seen hit. He is officially ridiculous.</td><td rowspan=1 colspan=1>Positive</td><td rowspan=1 colspan=1>Neutral</td><td rowspan=1 colspan=1>Positive</td></tr><tr><td rowspan=1 colspan=1>Emoticons</td><td rowspan=1 colspan=1>This fandom&#x27;s a mess omg,Iwouldn&#x27;t be surprise if to-morrow there&#x27;s a trend who says Niall&#x27;s going to marryhis cousin #WeKnowTheTruth</td><td rowspan=1 colspan=1>Negative</td><td rowspan=1 colspan=1>Positive</td><td rowspan=1 colspan=1>Negative</td></tr><tr><td rowspan=1 colspan=1>Emoticons</td><td rowspan=1 colspan=1>Christians snapchat story makes me want to kill my-self.like Ifeel like a depressed 8th grader going throughthat emo phase</td><td rowspan=1 colspan=1>Negative</td><td rowspan=1 colspan=1>Neutral</td><td rowspan=1 colspan=1>Negative</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Considering that we have shown a neural network can distill and improve a representation learned by a logical rule engine, how the final representation differs from the logic of the original engine is of practical interest. We thus compare the agreement of our fine-tuned rule based GRU with the original rule model on the SemEval testing set. We find that the transferred model achieves $78 . 7 \\%$ agreement with the rule model when the rule model is right. This clearly indicates that our final model is not deterministic based on the rule engine, and has a probability of adding errors even when the original rule model works well. However, our model actually has $4 4 . 7 \\%$ accuracy on the examples the rule model got wrong. Our approach yields significant gains in comparison to the original rule classifiers, improving from $5 7 . 8 \\%$ to $6 4 . 4 \\%$ test set accuracy before even incorporating in auxiliary knowledge sources. ",
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+    {
+        "type": "text",
+        "text": "6 INTEGRATING TRANSFER LEARNING FROM MULTIPLE TASKS WITH ENSEMBLE DISTILLATION ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "6.1 ENSEMBLE METHODOLOGY ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In our experiments we tried to find a balance between an ensemble model that is powerful enough to have an adaptive weighted average decision function and not so powerful that it overfits on our limited training and validation data. Our model is quite similar in architecture to the gating network component of a hierarchical mixture of experts model (Jacobs et al., 1991), (Jordan & Jacobs, 1994). We tried our model over all four representations at once and found that it overfits. Our experiments showed it is more effective to adopt a greedy ensembling strategy where all models are combined with the best performing model on the validation set at each phase until only two models are left. Finally, these two models are combined with the same mechanism. (Riemer et al., 2016) suggests that a many element gating network can be improved with a sparsity constraint, but this did not work as well as the greedy strategy for our model and experiments. ",
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+    {
+        "type": "text",
+        "text": "More formally, for any two models $A$ and $B$ combined in an ensemble, we train the following mechanism using Stochastic Gradient Descent: ",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/22c689d61e3887c6b493b49ee4709cc4bc1824fa8d22fc0d05e8107dca0305c3.jpg",
+        "table_caption": [
+            "Table 5: Empirical three way sentiment classification results on the SemEval 2016 Task 4 Subtask A test set. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=1>ModelDescription</td><td rowspan=1 colspan=1>AccuracyonSemEval TestSet</td></tr><tr><td rowspan=1 colspan=1>Distilled GRUTrained on Full EnsembleFull EnsembleEnsemble withLogical Rules and Both Movie Review TasksEnsemble with Logical Rules and Binary Movie ReviewsEnsemble with Logical Rules and Five Class Movie ReviewsEnsemble with Logical Rules and Emoticon PredictionEnsemble withBothMovie Review TasksGRU Trained on Only SemEval Data</td><td rowspan=1 colspan=1>66.0%65.9%65.7%65.4%65.1%65.0%62.1%53.6%</td></tr><tr><td rowspan=1 colspan=1>SwissCheese (Bethard etal.,2016)NTNUSentEval (Jahren et al.,2016)UniPI (Attardi &amp; Sartiano,2016)CUFE (Nabil et al.,2016)INSIGHT-1 (Ruder et al., 2016)</td><td rowspan=1 colspan=1>64.6%64.3%63.9%63.7%63.5%</td></tr></table>",
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/bb7fde02e33f7aecec0d474cc6a798708f781b034fa2a85cc95d20486a2d04f6.jpg",
+        "text": "$$\n\\begin{array} { r } { m _ { A } = \\sigma ( W _ { A } \\hat { y } _ { A } + b _ { A } ) } \\\\ { m _ { B } = \\sigma ( W _ { B } \\hat { y } _ { B } + b _ { B } ) } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "equation",
+        "img_path": "images/c8126e7f7c5d1e02cd333389ca2ccdc2a23d97dd0b71a0105e5c11dae9924cac.jpg",
+        "text": "$$\na _ { A } = { \\frac { m _ { A } } { m _ { A } + m _ { B } } }\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "equation",
+        "img_path": "images/146256cd059aec1c0a7c4012d84332b5e9d3e43615d019f4d5cd428ea2e7d78b.jpg",
+        "text": "$$\na _ { B } = { \\frac { m _ { B } } { m _ { A } + m _ { B } } }\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "equation",
+        "img_path": "images/c66251f40a99ee5bcf6a28ffabe7501f5ae99af331dccb0a726849590b790774.jpg",
+        "text": "$$\n\\hat { y } _ { e n s e m b l e } = a _ { A } \\hat { y } _ { A } + a _ { B } \\hat { y } _ { B }\n$$",
+        "text_format": "latex",
+        "bbox": [
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+            486,
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "where $\\hat { y } _ { e n s e m b l e }$ is the prediction vector of the combined ensemble. ${ \\hat { y } } _ { A }$ and $\\hat { y } _ { B }$ are the output vectors of the individual models. ",
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+    },
+    {
+        "type": "text",
+        "text": "6.2 ENSEMBLE RESULTS ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Our ensemble model was trained on what was set aside as the validation data during the initial training with early stopping. In the first phase of combining, the model transferred from the logical rule source task was combined with each model. In the second phase, the model based on transfer from the binary movie review sentiment model was combined with each model. In the third phase, the two remaining models were combined. The results of our ensemble in Table 5 suggest that it is possible to further improve the performance of a single sequential transfer model by intelligently combining its predictions with models that have other perspectives. This is because they are modeled using different source tasks for prior knowledge. Impressively, our final distilled model surpasses results from all prior models on the SemEval 2016 benchmark using the same final architecture of a 50 hidden unit GRU model that is clearly not even competitive when trained simply on the task specific labeled data. The prior best model SwissCheese (Bethard et al., 2016) consists of random forests ensemble built utilizing multiple convolutional neural network models and distant supervision. In fact, we achieve superior results despite using over an order of magnitude less total data for training our model. ",
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+    {
+        "type": "text",
+        "text": "We would also like to underscore that our total improvement of $1 . 5 \\%$ as a result of creating an ensemble with our best transferred model from the logical rule source task can be viewed as quite disappointing, despite achieving state of the art results. In fact, in the theoretical limit of having a decision model that switches to the best already learned model at each point, our four transferred representations would achieve $8 5 . 1 \\%$ accuracy together. For the combination of the movie review based models and logical rule based model we can get to $8 1 . 4 \\%$ accuracy. Moreover, we can get $7 6 . 5 \\%$ accuracy with just the logical rule based transfer model and the emoticon prediction based transfer model. Unfortunately, we achieve nowhere near these theoretical results despite representations that are apparently quite diverse. This seems indicative that there are significant gains yet to be uncovered in integrating these representations. ",
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+    {
+        "type": "text",
+        "text": "7 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "We consider a new methodology called the forgetting cost for preventing the catastrophic forgetting problem of neural network sequential transfer learning. The forgetting cost is practical and easy to implement. We have demonstrated for the challenging task of Twitter sentiment analysis that it can uncover significant gains in generalization performance and that it seems to not forget knowledge traditionally forgotten from the source task during fine-tuning. Our strong empirical results still motivate multiple avenues with high potential for continued exploration in text analytics. Using logical rules to improve neural network models is a promising direction for humans to efficiently contribute to increased model performance. Additionally, the large diversity of representations learned from multiple classifiers with the same target task but different source tasks seems to indicate there is potential to see even much greater gains when integrating multiple sources of knowledge transfer. ",
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+    {
+        "type": "text",
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+    {
+        "type": "text",
+        "text": "A MAPPING SENTIMENT RULES TO SOFT TARGETS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            547,
+            614,
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+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "The gazetteer based logical rule engine separates sentences and phrases in the text. It then applies dictionaries of positive and negative sentiment words and phrases to the corresponding text. For each positive or negative phrase found, it checks to see if negation or double negation are applied, and modifies the polarity of the sentiment accordingly. The result for any piece of text is a count of positive and negative sentiment occurrences. For this task, we simply count the total number of positive and negative indicators to give an overall positive, negative or neutral score. To be concrete, we have a simple procedure for mapping positive and negative word counts to soft labels that could be used for distillation. If there are no positive or negative words, the output vector is a one hot vector corresponding to a neutral label. If there are an unequal number of positive and negative sentiment words, the neutral label is zero and the raw counts are sent to the softmax function to create a soft label over the positive and negative word occurrences. Finally, if there are an equal amount of positive and negative words, we consider the added total sentiment words plus one in the neutral label as well as the number of positive words and negative words before sending these totals through a softmax function. ",
+        "bbox": [
+            174,
+            580,
+            825,
+            773
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "B SIZE SELECTION FOR THE RULE DISTILLATION TASK ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            795,
+            651,
+            810
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "In Table 6 we detail the performance of distilling a logical rule engine into a GRU based recurrent neural network by imposing soft labels over unlabeled tweets. The fact that we keep our word representations fixed with general purpose unsupervised data makes it difficult for the GRU to distill the entire model without a large number of examples. Additionally, as there were a large number of examples in our distillation experiments, we did not experience high run to run variation and only trained a single GRU model for each distillation experiment (as opposed to picking the best validation error of 10 parallel training routines as in our transfer experiments). Our distilled GRU is better on the testing set than the original classifier, likely because this input representation prevents the model from overfitting to the idiosyncrasies of the rule engine. This actually underscores an important point for the distillation of abstract knowledge. If the target task is known during distillation, it may be beneficial to stop short of totally distilling the original knowledge as it may hurt down stream performance past a certain point. We impose a simple policy where the best hidden unit and training example combination is selected based on performance on the training data of the target task. As a result, we use the model with 50 hidden units based on 50,000 training examples in our experiments integrating with other knowledge. This model is a pretty good one to choose, and achieves high transfer performance relative to models that overfit on the teacher network. ",
+        "bbox": [
+            174,
+            825,
+            823,
+            924
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "table",
+        "img_path": "images/61a68bd836f8b9c47a68a1906e9d19d65a71dc93b5ee07b1151c70275a398223.jpg",
+        "table_caption": [
+            "Table 6: Logical rule engine distillation performance and SemEval 2016 Task 4 Subtask A accuracy as a function of the number of hidden units in the GRU and the number of training examples. The 50 hidden unit and 50,000 training example model performs the best on the SemEval training set. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Hidden Units</td><td>Examples</td><td>Alignmentwith Teacher</td><td>AccuracyonSemEval TestSet</td></tr><tr><td>25</td><td>50,000</td><td>88.3%</td><td>59.1%</td></tr><tr><td>25</td><td>300,000</td><td>91.9%</td><td>58.6%</td></tr><tr><td>50</td><td>50,000</td><td>88.6%</td><td>58.9%</td></tr><tr><td>50</td><td>300,000</td><td>93.0%</td><td>58.5%</td></tr><tr><td>75</td><td>50,000</td><td>88.7%</td><td>58.9%</td></tr><tr><td>75 100</td><td>300,000 50,000</td><td>93.6%</td><td>58.3%</td></tr><tr><td>100</td><td>300,000</td><td>88.6%</td><td>58.7%</td></tr><tr><td>125</td><td>50,000</td><td>93.8%</td><td>58.1%</td></tr><tr><td>125</td><td>300,000</td><td>88.5%</td><td>58.7%</td></tr><tr><td>150</td><td>50,000</td><td>93.7%</td><td>58.3%</td></tr><tr><td>150</td><td>300,000</td><td>88.5% 94.0%</td><td>59.0% 58.5%</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 13
+    },
+    {
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+]

parse/train/jnMjOctlfbZ/jnMjOctlfbZ.md

@@ -0,0 +1,338 @@
+# ATOM3D: TASKS ON MOLECULES IN THREE DIMENSIONS
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+While a variety of methods have been developed for predicting molecular properties, deep learning networks that operate directly on three-dimensional molecular structure have recently demonstrated particular promise. In this work we present ATOM3D, a collection of both novel and existing datasets spanning several key classes of biomolecules, to systematically assess such learning methods. We develop three-dimensional molecular learning networks for each of these tasks, finding that they consistently improve performance relative to one- and twodimensional methods. The specific choice of architecture proves to be critical for performance, with three-dimensional convolutional networks excelling at tasks involving complex geometries, while graph networks perform well on systems requiring detailed positional information. Furthermore, equivariant networks show significant promise but are currently unable to scale. Our results indicate many molecular problems stand to gain from three-dimensional molecular learning. All code and datasets are available at github.com/xxxxxxx/xxxxxx.
+
+# 1 INTRODUCTION
+
+A molecule’s three-dimensional (3D) shape is critical to understanding its physical mechanisms of action, and can be used to answer a number of questions relating to drug discovery, molecular design, and fundamental biology. A molecule’s atoms often adopt specific 3D configurations that minimize its free energy, and by representing these 3D positions—the atomistic geometry—we can model this 3D shape in ways that would not be possible with 1D or 2D representations such as linear sequences or chemical bond graphs (Table 1). However, existing works that examine diverse molecular tasks, such as MoleculeNet (Wu et al., 2018) or TAPE (Rao et al., 2019), focus on these lower dimensional representations. In this work, we demonstrate the benefit yielded by learning on 3D atomistic geometry and promote the development of 3D molecular learning by providing a collection of datasets leveraging this representation.
+
+Furthermore, we argue that the atom should be considered a “machine learning datatype” in its own right, deserving focused study much like images in computer vision or text in natural language processing. All molecules, including proteins, small molecule compounds, and nucleic acids, can be homogeneously represented as atoms in 3D space. These atoms can only belong to a fixed class of element types (e.g. carbon, nitrogen, oxygen), and are all governed by the same underlying laws of physics, leading to important rotational, translational, and permutational symmetries. These systems also contain higher-level patterns that are poorly characterized, creating a ripe opportunity for learning them from data: though certain basic components are well understood (e.g. amino acids, nucleic acids, functional groups), many others can not easily be defined. These patterns are in turn composed in a hierarchy that itself is only partially elucidated.
+
+While deep learning methods such as graph neural networks (GNNs) and convolutional neural networks (CNNs) seem especially well suited to atomistic geometry, to date there has been no systematic evaluation of such methods on molecular tasks. Additionally, despite the growing number of 3D structures available in databases such as the Protein Data Bank (PDB) (Berman et al., 2000), they require significant processing before they are useful for machine learning tasks. Inspired by the success of accessible databases such as ImageNet (Jia Deng et al., 2009) and SQuAD (Rajpurkar et al., 2016) in sparking progress in their respective fields, we create and curate benchmark datasets for atomistic tasks, process them into a simple and standardized format, systematically benchmark
+
+Table 1: Representation choice for molecules. Adding in 3D information consistently improves performance. The depicted 1D representations are the amino acid sequence and SMILES (Weininger, 1988) for proteins and small molecules, respectively.   
+
+<table><tr><td rowspan="2">Structure LevelDimension</td><td rowspan="2"></td><td rowspan="2">Representation</td><td colspan="2">Examples</td></tr><tr><td>Proteins</td><td>Small Molecules</td></tr><tr><td>primary</td><td>1D</td><td>linear sequence</td><td>KVKALPDA</td><td>CC(C)CC(C)NO</td></tr><tr><td> secondary</td><td>2D</td><td>chemical bond graph</td><td>00001 O00-01 。 0 Q Oo00 oQ00Q obo O ○ o O</td><td>80 ○</td></tr><tr><td>tertiary</td><td>3D</td><td>atomistic geometry</td><td></td><td>)</td></tr></table>
+
+3D molecular learning methods, and present a set of best practices for other machine learning researchers interested in entering the field of 3D molecular learning. We develop new methods for several datasets and reveal a number of insights related to 3D molecular learning, including the consistent improvements yielded by using atomistic geometry, the lack of a single dominant method, and the presence of several tasks that can be improved through 3D molecular learning.
+
+# 2 RELATED WORK
+
+Three dimensional molecular data have long been pursued as an attractive source of information in molecular learning and chemoinformatics, but until recently have achieved underwhelming results relative to 1D and 2D representations (Swamidass et al., 2005; Azencott et al., 2007). However, due to increases in data availability and methodological advances, machine learning methods based on 3D molecular structure have begun to demonstrate significant impact in the last couple of years on specific tasks such as protein structure prediction (Senior et al., 2020), equilibrium state sampling (Noe et al., 2019), and drug design (Zhavoronkov et al., 2019). While there have been some broader ´ assessments of groups of related biological tasks, these have focused on on either 1D (Rao et al., 2019) or 2D (Wu et al., 2018) representations. By focusing instead on atomistic geometry, we can consistently improve performance and address disparate problems involving any combination of small molecules, proteins, and nucleic acids through a unified lens.
+
+Graph neural networks (GNNs) have grown to be a major area of study, providing a natural way of learning from data with complex spatial structure. Many GNN implementations have been motivated by applications to atomic systems, including molecular fingerprinting (Duvenaud et al., 2015), property prediction (Schutt et al., 2017; Gilmer et al., 2017; Liu et al., 2019), protein interface pre- ¨ diction (Fout et al., 2017), and protein design (Ingraham et al., 2019). Instead of encoding points in Euclidean space, GNNs encode their pairwise connectivity, capturing a structured representation of atomistic data.
+
+Three-dimensional CNNs (3DCNNs) have also become popular as a way to capture these complex 3D geometries. They have been applied to a number of biomolecular applications such as protein interface prediction (Townshend et al., 2019), protein model quality assessment (Pages et al., 2019; \` Derevyanko et al., 2018), protein sequence design (Anand et al., 2020), and structure-based drug discovery (Wallach et al., 2015; Torng & Altman, 2017; Ragoza et al., 2017; Jimenez et al., 2018). ´ These 3DCNNs can encode translational and permutational symmetries, but incur significant computational expense and cannot capture rotational symmetries without data augmentation.
+
+In an attempt to address many of the problems of representing atomistic geometries, equivariant neural networks (ENNs) have emerged as a new class of methods for learning from molecular systems. These networks are built such that geometric transformations of their inputs lead to well-defined transformations of their outputs. This setup leads to the neurons of the network learning rules that resemble physical interactions. Tensor field networks (Thomas et al., 2018) and Cormorant (Kondor,
+
+2018; Anderson et al., 2019) have applied these principles to atomic systems and begun to demonstrate promise on extended systems (Eismann et al., 2020; Weiler et al., 2018). However, in general, these methods have not been applied to larger-scale molecular tasks.
+
+# 3 3D MOLECULAR LEARNING
+
+We define 3D molecular learning as the set of tasks where the input space is atoms in three dimensions. We write this space as $\mathbb { A } ^ { N }$ where $\mathbb { A } = \mathbb { P } \times \mathbb { E }$ . $\mathbb { P } = \mathbb { R } ^ { 3 }$ is the position space and $\mathbb { E } = \left\{ C , H , O , N , P , S , \ldots \right\}$ is the element space.
+
+We select 3D molecular learning tasks from structural biophysics and medicinal chemistry that span a variety of molecule types and address a range of important problems. Multiple of these datasets are novel, while others are extracted from existing sources (Table 2). We provide all datasets in a standardized format that requires no specialized libraries. Alongside these datasets, we present corresponding best practices, including splitting and filtering criteria, to minimize data leakage concerns and ensure generalizability and reproducibility. Taken together, we hope these efforts will lower the barrier to entry for machine learning researchers interested in developing methods for 3D molecular learning and encourage rapid progress in the field. Detailed descriptions of the preparation of each dataset can be found in Appendix C.1.
+
+Table 2: Tasks included in ATOM3D dataset, along with schematic representation of their inputs. P indicates protein, SM indicates small molecule, R indicates RNA. Lines indicate interaction and the smaller square within proteins indicates an individual amino acid. New datasets are in bold.   
+
+<table><tr><td>Name (Task Code)</td><td>Schematic</td><td>Objective</td><td>Source</td></tr><tr><td>Small Molecule Properties (SMP)</td><td>SM</td><td>Properties</td><td>QM9 (Ruddigkeit et al., 2012)</td></tr><tr><td>Protein Interface Prediction (PIP)</td><td>P2 P1 G 与</td><td>Amino Acid Interaction</td><td>DIPS(Townshend et al.,2019) DB5 (Vreven et al., 2015)</td></tr><tr><td>Residue Identity (RES)</td><td>P</td><td>Amino Acid Identity</td><td>New, created from PDB (Berman et al., 2000)</td></tr><tr><td>Mutation Stability Prediction (MSP)</td><td>P1 白 P2 C vs. P1 P2 £ 白</td><td>Effect of Mutation</td><td>New, created from SKEMPI (Jankauskaité et al., 2019)</td></tr><tr><td>Ligand Binding Affinity (LBA)</td><td>P SM</td><td>Binding Strength</td><td>PDBBind (Wang et al., 2004)</td></tr><tr><td rowspan="2">Ligand Efficacy Prediction (LEP) Protein Structure</td><td>P SM VS. SM</td><td>Drug Efficacy</td><td>New, created from PDB (Berman et al., 2000)</td></tr><tr><td>P</td><td>Ranking</td><td>CASP-QA (Kryshtafovych et al.,2019)</td></tr><tr><td>Ranking (PSR) RNA Structure</td><td></td><td></td><td></td></tr><tr><td>Ranking (RSR)</td><td>R</td><td>Ranking</td><td>FARFAR2-Puzzles (Watkins &amp; Das,2019)</td></tr></table>
+
+# 3.1 SMALL MOLECULE PROPERTIES (SMP)
+
+Impact – Predicting physico-chemical properties of small molecules is a common task in medicinal chemistry and materials design. Quantum chemical calculations can save expensive experiments but are themselves costly and cannot cover the huge chemical space spanned by candidate molecules.
+
+Dataset – The QM9 dataset (Ruddigkeit et al., 2012; Ramakrishnan et al., 2014) contains structures and energetic, electronic, and thermodynamic properties for 134,000 stable small organic molecules, obtained from quantum-chemical calculations.
+
+Metrics – We predict the molecular properties from the ground-state structure.
+
+Split – We split molecules randomly.
+
+# 3.2 PROTEIN INTERFACE PREDICTION (PIP)
+
+Impact – Proteins interact with each other in many scenarios—for example, antibody proteins recognize diseases by binding to antigens. A critical problem in understanding these interactions is to identify which amino acids of two given proteins will interact upon binding.
+
+Dataset – For training, we use the Database of Interacting Protein Structures (DIPS), a comprehensive dataset of protein complexes mined from the PDB (Townshend et al., 2019). We predict on the Docking Benchmark 5 (Vreven et al., 2015), a smaller gold standard dataset.
+
+Metrics – We predict if two amino acids will come into contact when their respective proteins bind.   
+Split – We split protein complexes by sequence identity at $30 \%$ .
+
+# 3.3 RESIDUE IDENTITY (RES)
+
+Impact – Understanding the structural role of individual amino acids is important for engineering new proteins. We can understand this role by predicting the propensity for different amino acids at a given protein site based on the surrounding structural environment (Torng & Altman, 2017).
+
+Dataset – We generate a novel dataset consisting of atomic environments extracted from nonredundant structures in the PDB.
+
+Metrics – We formulate this as a classification task where we predict the identity of the amino acid in the center of the environment based on all other atoms.
+
+Split – We split residue environments by protein topology class.
+
+# 3.4 MUTATION STABILITY PREDICTION (MSP)
+
+Impact – Identifying mutations that stabilize a protein’s interactions is a key task in designing new proteins. Experimental techniques for probing these are labor-intensive (Antikainen & Martin, 2005; Lefevre et al., 1997), motivating the development of efficient computational methods. \`
+
+Dataset – We derive a novel dataset by collecting single-point mutations from the SKEMPI database (Jankauskaite et al., 2019) and model each mutation into the structure to produce mutated structures. ˙ Metrics – We formulate this as a binary classification task where we predict whether the stability of the complex increases as a result of the mutation.
+
+Split – We split protein complexes by sequence identity at $30 \%$
+
+# 3.5 LIGAND BINDING AFFINITY (LBA)
+
+Impact – Most therapeutic drugs and many molecules critical for biological signaling take the form of small molecules. Predicting the strength of the protein-small molecule interaction is a challenging but crucial task for drug discovery applications.
+
+Dataset – We use the PDBBind database (Wang et al., 2004; Liu et al., 2015), a curated database containing protein-ligand complexes from the PDB and their corresponding binding strengths. Metrics – We predict $p K = - \log ( K )$ , where $K$ is the binding affinity in Molar units. Split – We split protein-ligand complexes by protein sequence identity at $30 \%$ .
+
+# 3.6 LIGAND EFFICACY PREDICTION (LEP)
+
+Impact – Many proteins switch on or off their function by changing shape. Predicting which shape a drug will favor is thus an important task in drug design.
+
+Dataset – We develop a novel dataset by curating proteins from several families with both ”active” and ”inactive” state structures, and model in 527 small molecules with known activating or inactivating function using the program Glide (Friesner et al., 2004).
+
+Metrics – We formulate this as a binary classification task where we predict whether or not a molecule bound to the structures will be an activator of the protein’s function or not.
+
+Split – We split complex pairs by protein.
+
+# 3.7 PROTEIN STRUCTURE RANKING (PSR)
+
+Impact – Proteins are one of the primary workhorses of the cell, and knowing their structure is often critical to understanding (and engineering) their function.
+
+Dataset – The Critical Assessment of Structure Prediction (CASP) (Kryshtafovych et al., 2019) is a blind international competition for predicting protein structure.
+
+Metrics – We formulate this as a regression task, where we predict the global distance test (GDT TS) from the true structure for each of the predicted structures submitted in the last 18 years of CASP. Split – We split structures temporally by competition year.
+
+# 3.8 RNA STRUCTURE RANKING (RSR)
+
+Impact – Similar to proteins, RNA plays major functional roles (e.g., gene regulation) and can adopt well-defined 3D shapes. Yet the problem is data-poor, with only a few hundred known structures. Dataset – Candidate models generated by FARFAR2 (Watkins & Das, 2019) for the first 21 released RNA Puzzle challenges (Cruz et al., 2012), a blind structure prediction competition for RNA. Metrics – We predict the root-mean-squared deviation (RMSD) from the ground truth structure. Split – We split structures temporally by competition year.
+
+# 4 EXPERIMENTAL SETUP
+
+To assess the benefits of 3D molecular learning, we use a combination of existing and novel 3D molecular learning methods, and implement a number of robust baselines. Our 3D molecular learning methods belong to one of each of the major classes of deep learning algorithms that have been applied to atomistic systems: graph networks, three-dimensional convolutional networks, and equivariant networks. Here we describe the core networks and the novel extensions needed to adapt them to certain datasets. See Appendix C.2 for task-specific details and hyperparameters.
+
+# 4.1 CORE NETWORKS
+
+For GNNs, we represent molecular systems as graphs in which each node is an atom. Edges are defined between all atoms separated by less than $4 . 5 \textup { \AA }$ , and weighted by the distance between the atoms. Node features are one-hot-encoded by atom type. Our core model uses five layers of graph convolutions, each followed by batch normalization and ReLU activation, a sum pooling layer, and two fully-connected layers with dropout.
+
+For 3DCNNs, we represent our data as a cube of fixed size (different per task due to the different molecular sizes) in 3D space that is discretized into voxels with resolution of $1 \textup { \AA }$ to form a grid. Each voxel is associated with a one-hot-encoded vector which denotes the presence or absence of each atom type. Our core model consists of four 3D-convolutional layers, each followed by maxpooling, dropout, and ReLU activation, and two fully-connected layers.
+
+For ENNs, we use SE(3)-equivariant networks that represent each atom of a structure by its position as absolute coordinates in 3D space with one-hot-encoded atom type as features. No rotational augmentation is needed due to the rotational symmetry of the network. The core of all architectures in this work is a network of four layers of covariant neurons that use the Clebsch–Gordan transform as nonlinearity, as described and implemented in Anderson et al. (2019).
+
+# 4.2 SIAMESE ARCHITECTURES
+
+For tasks involving comparing two sets of atoms sampled from the same distributions, we also develop new architectures that are Siamese in nature. Specifically, the PIP dataset involves predicting a symmetric interaction between two proteins, while the MSP and LEP datasets involve a symmetric comparison between two interactions. Taking inspiration from Townshend et al. (2019)’s use of a Siamese 3DCNN network for the PIP dataset, we replicate that architecture for our PIP, MSP, and LEP datasets, and develop new Siamese GNN and Siamese ENN networks. Specifically, we train a pair of core networks with tied weights, ensuring symmetric treatment of both items of the pair. We then combine the final learned embeddings from both core networks to output a final prediction. Beyond the novelty of weight-tying atom-level GNNs and ENNs, to our knowledge this is also the first use of weight-tying across SE(3)-equivariant networks.
+
+# 4.3 AMINO ACID OUTPUTS
+
+Certain tasks involve making a prediction on a specific amino acid (PIP, RES, and MSP; see Table 2), yet GNNs and ENNs typically rely on summing over all node embeddings to compute a final graph embedding, making it difficult to isolate this amino acid. To remedy this, after our convolutional layers we implement the novel procedure of extracting the embedding of only the $\mathbf { \boldsymbol { C } } \alpha$ atom of the amino acid in question, thereby allowing our GNNs and ENNs to isolate it.
+
+# 5 RESULTS
+
+To assess the utility of 3D molecular learning, we evaluate our methods on the ATOM3D datasets and compare performance to state-of-the-art methods using 1D or 2D representations. We stress that in many cases, 3D molecular learning methods have never been applied to the proposed tasks, and that several of the tasks are novel. In the following sections, we describe the results of our benchmarking and some key insights that can be derived from them. We also aggregate these results along with additional metrics and standard deviations over three replicates in Appendix E.
+
+# 5.1 3D REPRESENTATIONS CONSISTENTLY IMPROVE PERFORMANCE
+
+Our evaluation of 3D methods on the tasks in ATOM3D reveals that incorporating atomistic geometry leads to consistently superior performance compared to 1D and 2D methods. For small molecules, state-of-the-art methods do not use 1D representations, so we focus instead on comparing to representations at the 2D level, i.e. the chemical bond graph. This is the approach taken by the 2D GNN introduced by Tsubaki et al. (2019) or the N-gram graph method by Liu et al. (2019), which both obtain similar results (Table 3) on the small-molecule-only dataset SMP. When we add 3D distance, as done for our GNN model, we improve performance across all targets in SMP (Table 3).
+
+For tasks involving biopolymers (proteins and RNA), state-of-the-art methods do not use 2D representations, primarily because most of the chemical bond graph can be easily re-derived from the 1D representation, i.e. the linear sequence that makes up the biopolymer. We thus compare to representations at the 1D level (Table 7). For MSP and RES, both new datasets, we evaluate against Rao et al. (2019)’s TAPE model, a transformer architecture that operates on protein sequence and is state-of-the-art amongst 1D methods for many tasks. For PIP, we compare to the sequence-only version of BIPSPI (Sanchez-Garcia et al., 2018), a state-of-the-art boosted decision tree method for protein interaction prediction. We find that 3D methods outperform these 1D methods on all biopolymer-only datasets (PIP, RES, MSP).
+
+For tasks involving both biopolymers and small molecules, we compare DeepDTA (Ozt ¨ urk et al., ¨ 2018). This network uses a 1D representation via a 1DCNN for both the biopolymer and small molecules. For LBA, we additionally compare to DeepAffinity (Karimi et al., 2019) which uses pairs of a ligand SMILES string and a novel representation of structurally-annotated protein sequences. Using a 3D representation for both ligand and protein instead leads to improved performance for the joint protein-small molecule datasets (LBA and LEP, see Table 5).
+
+The biopolymer structure ranking tasks (PSR and RSR) are inherently 3D in nature, as they involve evaluating the correctness of different 3D shapes taken on by the same biopolymer. Thus, critically, a 1D or 2D representation would not be able to differentiate between these different shapes since the linear sequence and chemical bond graph would remain the same. We therefore compare to state-of-the-art 3D methods as shown in Table 6.
+
+Table 3: Small molecule results. Metric is mean absolute error (MAE).   
+
+<table><tr><td rowspan="2">Task</td><td rowspan="2">Target</td><td colspan="3">3D</td><td colspan="2">Non-3D</td></tr><tr><td>3DCNN</td><td>GNN</td><td>ENN</td><td>Tsubaki et al. (2019)</td><td>Liu et al. (2019)</td></tr><tr><td rowspan="3">SMP</td><td>μ[D]</td><td>0.572</td><td>0.068</td><td>0.046</td><td>0.496</td><td>0.520</td></tr><tr><td>gap[eV]</td><td>0.589</td><td>0.091</td><td>0.065</td><td>0.154</td><td>0.184</td></tr><tr><td>Ut[ev]</td><td>1.615</td><td>0.070</td><td>0.023</td><td>0.182</td><td>0.218</td></tr></table>
+
+Table 4: Biopolymer results. AUROC is the area under the receiver operating characteristic curve. Asterisks $( ^ { * } )$ indicate that the exact training data differed (though splitting criteria were the same).   
+
+<table><tr><td rowspan="2">Task</td><td rowspan="2">Metric</td><td colspan="3">3D</td><td colspan="2">Non-3D</td></tr><tr><td>3DCNN</td><td>GNN</td><td>ENN</td><td>Sanchez-Garcia et al. (2018)</td></tr><tr><td>PIP</td><td>AUROC</td><td>0.844</td><td>*0.669</td><td>一</td><td>0.841</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>Rao et al. (2019)</td></tr><tr><td>RES</td><td>accuracy</td><td>0.451</td><td>0.082</td><td>*0.072</td><td>*0.30</td></tr><tr><td>MSP</td><td>AUROC</td><td>0.520</td><td>0.637</td><td>0.678</td><td>0.554</td></tr></table>
+
+Table 5: Joint small molecule/biopolymer results. $R _ { S }$ is Spearman correlation, $R _ { P }$ is Pearson correlation, AUROC is area under the receiver operating characteristic curve, and RMSD is root-mean-squared deviation. Asterisks $( ^ { * } )$ indicate that the exact training data differed (though splitting criteria were the same).   
+
+<table><tr><td rowspan="2">Task</td><td rowspan="2">Metric</td><td colspan="3">3D</td><td colspan="2">Non-3D</td></tr><tr><td>3DCNN</td><td>GNN</td><td>ENN</td><td>Oztirk et al. (2018)</td><td>Karimi et al. (2019)</td></tr><tr><td rowspan="3">LBA</td><td>RMSD</td><td>1.520</td><td>1.936</td><td>*1.429</td><td>1.565</td><td>1.893</td></tr><tr><td>glob.Rp</td><td>0.558</td><td>0.581</td><td>*0.541</td><td>0.573</td><td>0.415</td></tr><tr><td>glob.Rs</td><td>0.556</td><td>0.647</td><td>*0.532</td><td>0.574</td><td>0.426</td></tr><tr><td>LEP</td><td>AUROC</td><td>0.824</td><td>0.678</td><td>0.569</td><td>0.696</td><td>1</td></tr></table>
+
+Table 6: Structure ranking results. $R _ { S }$ is Spearman correlation, $R _ { P }$ is Pearson correlation. Mean measures the correlation for structures corresponding to the same biopolymer, whereas global measures the correlation across all biopolymers.   
+
+<table><tr><td rowspan="2">Task</td><td rowspan="2">Metric</td><td colspan="3">3D</td></tr><tr><td>3DCNN</td><td>GNN</td><td>SotA</td></tr><tr><td rowspan="2">PSR</td><td>mean Rs</td><td>0.177</td><td>0.327</td><td>0.432 (Pages et al., 2019)</td></tr><tr><td>glob. Rs</td><td>0.837</td><td>0.716</td><td>0.796 (Pages et al., 2019)</td></tr><tr><td rowspan="2">RSR</td><td>mean Rs</td><td>0.414</td><td>0.195</td><td>0.173 (Alford et al.,2017)</td></tr><tr><td>glob. Rs</td><td>0.656</td><td>0.309</td><td>0.304 (Alford et al., 2017)</td></tr></table>
+
+More generally, we find that learning methods that leverage the 3D geometry of molecules hold state-of-the-art on all tasks on our benchmark (Appendix D).
+
+5.2 MANY 3D MOLECULAR LEARNING PROBLEMS REMAIN UNDEREXPLORED
+
+As demonstrated in the previous section, formulating a molecular problem through the lens of 3D molecular learning can lead to significantly improved performance. However, many important problems have not been studied within this framework, leaving significant room for further improvement. This opens up a ripe field of research with much low-hanging fruit. One prominent example we explore here is RNA structure ranking, where the state-of-the-art method uses Rosetta (Alford et al., 2017), a hand-designed potential energy function. When we instead apply our 3DCNN method that learns directly from the 3D atomistic geometry, we see dramatic increases in performance (Table 6).
+
+In a similar vein, on the ligand efficacy prediction task we find that the 3DCNN method outperforms Glide (Friesner et al., 2004), a state-of-the-art scoring function for protein-small molecule docking. The 3DCNN achieves an AUROC of 0.824, compared to Glide’s 0.770.
+
+We also find room for improvement in domains where 3D molecular learning is already being employed. Protein structure ranking is one such area, and we see that the 3DCNN model is competitive with the state-of-the-art deep learning method by Pages et al. (2019) (Table 6), surpassing it in terms \` of absolute assessment of correctness (i.e., comparing 3D candidates from different biopolymers) though not in terms of relative assessment (i.e., comparing 3D candidates from the same biopolymer).
+
+Overall, these results demonstrate the potential of 3D molecular learning to address a wide range of problems involving molecular structure, and we anticipate that continued development of such models on less well-studied tasks will aid progress in biomedical research.
+
+# 5.3 DIFFERENT TASKS REQUIRE DIFFERENT ARCHITECTURES
+
+While atomistic methods consistently outperform their non-3D counterparts and provide a systematic way of representing molecular data, our results also provide evidence that architecture selection plays a critical role in performance. For tasks primarily focused on small molecules (SMP and LBA), we see superior performance from the particle-based methods (GNN and ENN) than from the volumetric 3DCNN. Small molecules are already intuitively represented as graph-like structures, with nodes (atoms) and edges (bonds), and the quantities computed in these small molecule tasks depend less on complex 3D geometry and more on the exact position of each atom relative to its neighbors. Unlike particle-based methods, 3DCNNs must approximate these positions, and while increasing spatial resolution increases precision, it also leads to cubic scaling of complexity.
+
+On the other hand, for larger molecules and complex 3D geometries that are critical to tasks like PSR, RSR, LEP, and RES, we see that the 3DCNN method outperforms GNNs. Here, the 3DCNN’s ability to directly represent differences between patterns in 3D space, as opposed to trying to reconstruct them through pairwise distances, is likely what allows it to perform well. In these tasks, the exact position and relational information between atoms is less important than their overall conformation.
+
+Finally, equivariant networks show promise but suffer from scalability issues. One motivation for the development of equivariant networks is that they fill a “happy medium” where they can both represent atom positions precisely and capture complex geometries. On some of the tasks where we could test the ENN (LBA, SMP), we often observed close to state-of-the-art performance, even on a reduced training set (LBA). Unfortunately, current implementations do not yet scale to most of our tasks due to the compute- and memory-intensive nature of the Clebsch-Gordan products used to maintain rotational equivariance. For some tasks, the performance was severely limited by only training on a fraction of the data $< 1 \%$ for RES) or a portion of the entire atomic structure (LEP), and for others we could not apply the ENN at all. These limitations point to the need for further architectural innovations before their performance can be demonstrated on extended systems.
+
+# 6 CONCLUSION
+
+In this work we present a vision of 3D atom-level data as a new “machine learning datatype” deserving focused study. Atomistic data shares several underlying symmetries, contains poorly understood higher-level patterns, and can be used to address many high-impact but unsolved problems.
+
+We create several benchmark datasets and compare the performance of different types of 3D molecular learning models across these tasks. Many of these architectures were developed specifically for the tasks in question, such as the Siamese ENN and GNN models used for paired tasks (PIP, MSP, and LEP). For tasks that can be formulated in lower dimensions, we demonstrate that 3D molecular learning yields consistent gains in performance over 1D and 2D methods. We also show that selection of an appropriate architecture is critical for optimal performance on a given task; depending on the structure of the underlying data, a 3DCNN, GNN, or ENN may be most appropriate. As equivariant networks continue to improve in efficiency and stability, we expect these to become more and more viable due to their close modeling of physical laws.
+
+While ATOM3D establishes a first set of benchmark datasets, there are many other open areas in biomedical research and molecular science that are ripe for 3D molecular learning, especially as structural data becomes readily available. Such tasks include virtual screening and pose prediction of small molecule drugs, or the prediction of conformational ensembles instead of static structures. The use of multiple 3D conformations per molecule represents an especially promising direction, as they would more faithfully reproduce the entire set of states a given molecule could adopt. As such, we envision expanding the ATOM3D framework beyond the tasks described here.
+
+Through this work, we hope to lower the entry barrier for machine learning practitioners, encourage the development of machine learning algorithms focused on 3D atomistic data, and promote a novel paradigm within the fields of structural biology and medicinal chemistry.
+
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parse/train/jnMjOctlfbZ/jnMjOctlfbZ_content_list.json

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+    {
+        "type": "text",
+        "text": "ATOM3D: TASKS ON MOLECULES IN THREE DIMENSIONS ",
+        "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": [
+            454,
+            236,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "While a variety of methods have been developed for predicting molecular properties, deep learning networks that operate directly on three-dimensional molecular structure have recently demonstrated particular promise. In this work we present ATOM3D, a collection of both novel and existing datasets spanning several key classes of biomolecules, to systematically assess such learning methods. We develop three-dimensional molecular learning networks for each of these tasks, finding that they consistently improve performance relative to one- and twodimensional methods. The specific choice of architecture proves to be critical for performance, with three-dimensional convolutional networks excelling at tasks involving complex geometries, while graph networks perform well on systems requiring detailed positional information. Furthermore, equivariant networks show significant promise but are currently unable to scale. Our results indicate many molecular problems stand to gain from three-dimensional molecular learning. All code and datasets are available at github.com/xxxxxxx/xxxxxx. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            489,
+            336,
+            505
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "A molecule’s three-dimensional (3D) shape is critical to understanding its physical mechanisms of action, and can be used to answer a number of questions relating to drug discovery, molecular design, and fundamental biology. A molecule’s atoms often adopt specific 3D configurations that minimize its free energy, and by representing these 3D positions—the atomistic geometry—we can model this 3D shape in ways that would not be possible with 1D or 2D representations such as linear sequences or chemical bond graphs (Table 1). However, existing works that examine diverse molecular tasks, such as MoleculeNet (Wu et al., 2018) or TAPE (Rao et al., 2019), focus on these lower dimensional representations. In this work, we demonstrate the benefit yielded by learning on 3D atomistic geometry and promote the development of 3D molecular learning by providing a collection of datasets leveraging this representation. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Furthermore, we argue that the atom should be considered a “machine learning datatype” in its own right, deserving focused study much like images in computer vision or text in natural language processing. All molecules, including proteins, small molecule compounds, and nucleic acids, can be homogeneously represented as atoms in 3D space. These atoms can only belong to a fixed class of element types (e.g. carbon, nitrogen, oxygen), and are all governed by the same underlying laws of physics, leading to important rotational, translational, and permutational symmetries. These systems also contain higher-level patterns that are poorly characterized, creating a ripe opportunity for learning them from data: though certain basic components are well understood (e.g. amino acids, nucleic acids, functional groups), many others can not easily be defined. These patterns are in turn composed in a hierarchy that itself is only partially elucidated. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "While deep learning methods such as graph neural networks (GNNs) and convolutional neural networks (CNNs) seem especially well suited to atomistic geometry, to date there has been no systematic evaluation of such methods on molecular tasks. Additionally, despite the growing number of 3D structures available in databases such as the Protein Data Bank (PDB) (Berman et al., 2000), they require significant processing before they are useful for machine learning tasks. Inspired by the success of accessible databases such as ImageNet (Jia Deng et al., 2009) and SQuAD (Rajpurkar et al., 2016) in sparking progress in their respective fields, we create and curate benchmark datasets for atomistic tasks, process them into a simple and standardized format, systematically benchmark ",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/33a662d0c1809dae175537cc965d7988810494dcae04e143cc407f22fddb5644.jpg",
+        "table_caption": [
+            "Table 1: Representation choice for molecules. Adding in 3D information consistently improves performance. The depicted 1D representations are the amino acid sequence and SMILES (Weininger, 1988) for proteins and small molecules, respectively. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Structure LevelDimension</td><td rowspan=\"2\"></td><td rowspan=\"2\">Representation</td><td colspan=\"2\">Examples</td></tr><tr><td>Proteins</td><td>Small Molecules</td></tr><tr><td>primary</td><td>1D</td><td>linear sequence</td><td>KVKALPDA</td><td>CC(C)CC(C)NO</td></tr><tr><td> secondary</td><td>2D</td><td>chemical bond graph</td><td>00001 O00-01 。 0 Q Oo00 oQ00Q obo O ○ o O</td><td>80 ○</td></tr><tr><td>tertiary</td><td>3D</td><td>atomistic geometry</td><td></td><td>)</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "3D molecular learning methods, and present a set of best practices for other machine learning researchers interested in entering the field of 3D molecular learning. We develop new methods for several datasets and reveal a number of insights related to 3D molecular learning, including the consistent improvements yielded by using atomistic geometry, the lack of a single dominant method, and the presence of several tasks that can be improved through 3D molecular learning. ",
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+    {
+        "type": "text",
+        "text": "2 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            454,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Three dimensional molecular data have long been pursued as an attractive source of information in molecular learning and chemoinformatics, but until recently have achieved underwhelming results relative to 1D and 2D representations (Swamidass et al., 2005; Azencott et al., 2007). However, due to increases in data availability and methodological advances, machine learning methods based on 3D molecular structure have begun to demonstrate significant impact in the last couple of years on specific tasks such as protein structure prediction (Senior et al., 2020), equilibrium state sampling (Noe et al., 2019), and drug design (Zhavoronkov et al., 2019). While there have been some broader ´ assessments of groups of related biological tasks, these have focused on on either 1D (Rao et al., 2019) or 2D (Wu et al., 2018) representations. By focusing instead on atomistic geometry, we can consistently improve performance and address disparate problems involving any combination of small molecules, proteins, and nucleic acids through a unified lens. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Graph neural networks (GNNs) have grown to be a major area of study, providing a natural way of learning from data with complex spatial structure. Many GNN implementations have been motivated by applications to atomic systems, including molecular fingerprinting (Duvenaud et al., 2015), property prediction (Schutt et al., 2017; Gilmer et al., 2017; Liu et al., 2019), protein interface pre- ¨ diction (Fout et al., 2017), and protein design (Ingraham et al., 2019). Instead of encoding points in Euclidean space, GNNs encode their pairwise connectivity, capturing a structured representation of atomistic data. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Three-dimensional CNNs (3DCNNs) have also become popular as a way to capture these complex 3D geometries. They have been applied to a number of biomolecular applications such as protein interface prediction (Townshend et al., 2019), protein model quality assessment (Pages et al., 2019; \\` Derevyanko et al., 2018), protein sequence design (Anand et al., 2020), and structure-based drug discovery (Wallach et al., 2015; Torng & Altman, 2017; Ragoza et al., 2017; Jimenez et al., 2018). ´ These 3DCNNs can encode translational and permutational symmetries, but incur significant computational expense and cannot capture rotational symmetries without data augmentation. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In an attempt to address many of the problems of representing atomistic geometries, equivariant neural networks (ENNs) have emerged as a new class of methods for learning from molecular systems. These networks are built such that geometric transformations of their inputs lead to well-defined transformations of their outputs. This setup leads to the neurons of the network learning rules that resemble physical interactions. Tensor field networks (Thomas et al., 2018) and Cormorant (Kondor, ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2018; Anderson et al., 2019) have applied these principles to atomic systems and begun to demonstrate promise on extended systems (Eismann et al., 2020; Weiler et al., 2018). However, in general, these methods have not been applied to larger-scale molecular tasks. ",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "3 3D MOLECULAR LEARNING ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We define 3D molecular learning as the set of tasks where the input space is atoms in three dimensions. We write this space as $\\mathbb { A } ^ { N }$ where $\\mathbb { A } = \\mathbb { P } \\times \\mathbb { E }$ . $\\mathbb { P } = \\mathbb { R } ^ { 3 }$ is the position space and $\\mathbb { E } = \\left\\{ C , H , O , N , P , S , \\ldots \\right\\}$ is the element space. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We select 3D molecular learning tasks from structural biophysics and medicinal chemistry that span a variety of molecule types and address a range of important problems. Multiple of these datasets are novel, while others are extracted from existing sources (Table 2). We provide all datasets in a standardized format that requires no specialized libraries. Alongside these datasets, we present corresponding best practices, including splitting and filtering criteria, to minimize data leakage concerns and ensure generalizability and reproducibility. Taken together, we hope these efforts will lower the barrier to entry for machine learning researchers interested in developing methods for 3D molecular learning and encourage rapid progress in the field. Detailed descriptions of the preparation of each dataset can be found in Appendix C.1. ",
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+    {
+        "type": "table",
+        "img_path": "images/8d1ad03d92c7c38846bf64895d8b7990c0cf225808278cad639907a5ccbf2146.jpg",
+        "table_caption": [
+            "Table 2: Tasks included in ATOM3D dataset, along with schematic representation of their inputs. P indicates protein, SM indicates small molecule, R indicates RNA. Lines indicate interaction and the smaller square within proteins indicates an individual amino acid. New datasets are in bold. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Name (Task Code)</td><td>Schematic</td><td>Objective</td><td>Source</td></tr><tr><td>Small Molecule Properties (SMP)</td><td>SM</td><td>Properties</td><td>QM9 (Ruddigkeit et al., 2012)</td></tr><tr><td>Protein Interface Prediction (PIP)</td><td>P2 P1 G 与</td><td>Amino Acid Interaction</td><td>DIPS(Townshend et al.,2019) DB5 (Vreven et al., 2015)</td></tr><tr><td>Residue Identity (RES)</td><td>P</td><td>Amino Acid Identity</td><td>New, created from PDB (Berman et al., 2000)</td></tr><tr><td>Mutation Stability Prediction (MSP)</td><td>P1 白 P2 C vs. P1 P2 £ 白</td><td>Effect of Mutation</td><td>New, created from SKEMPI (Jankauskaité et al., 2019)</td></tr><tr><td>Ligand Binding Affinity (LBA)</td><td>P SM</td><td>Binding Strength</td><td>PDBBind (Wang et al., 2004)</td></tr><tr><td rowspan=\"2\">Ligand Efficacy Prediction (LEP) Protein Structure</td><td>P SM VS. SM</td><td>Drug Efficacy</td><td>New, created from PDB (Berman et al., 2000)</td></tr><tr><td>P</td><td>Ranking</td><td>CASP-QA (Kryshtafovych et al.,2019)</td></tr><tr><td>Ranking (PSR) RNA Structure</td><td></td><td></td><td></td></tr><tr><td>Ranking (RSR)</td><td>R</td><td>Ranking</td><td>FARFAR2-Puzzles (Watkins &amp; Das,2019)</td></tr></table>",
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1 SMALL MOLECULE PROPERTIES (SMP) ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            103,
+            490,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Impact – Predicting physico-chemical properties of small molecules is a common task in medicinal chemistry and materials design. Quantum chemical calculations can save expensive experiments but are themselves costly and cannot cover the huge chemical space spanned by candidate molecules. ",
+        "bbox": [
+            173,
+            130,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Dataset – The QM9 dataset (Ruddigkeit et al., 2012; Ramakrishnan et al., 2014) contains structures and energetic, electronic, and thermodynamic properties for 134,000 stable small organic molecules, obtained from quantum-chemical calculations. ",
+        "bbox": [
+            173,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Metrics – We predict the molecular properties from the ground-state structure. ",
+        "bbox": [
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+            214,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Split – We split molecules randomly. ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2 PROTEIN INTERFACE PREDICTION (PIP) ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            260,
+            493,
+            273
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Impact – Proteins interact with each other in many scenarios—for example, antibody proteins recognize diseases by binding to antigens. A critical problem in understanding these interactions is to identify which amino acids of two given proteins will interact upon binding. ",
+        "bbox": [
+            174,
+            286,
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Dataset – For training, we use the Database of Interacting Protein Structures (DIPS), a comprehensive dataset of protein complexes mined from the PDB (Townshend et al., 2019). We predict on the Docking Benchmark 5 (Vreven et al., 2015), a smaller gold standard dataset. ",
+        "bbox": [
+            176,
+            328,
+            820,
+            369
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Metrics – We predict if two amino acids will come into contact when their respective proteins bind.   \nSplit – We split protein complexes by sequence identity at $30 \\%$ . ",
+        "bbox": [
+            174,
+            369,
+            821,
+            397
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3 RESIDUE IDENTITY (RES) ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            415,
+            400,
+            429
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Impact – Understanding the structural role of individual amino acids is important for engineering new proteins. We can understand this role by predicting the propensity for different amino acids at a given protein site based on the surrounding structural environment (Torng & Altman, 2017). ",
+        "bbox": [
+            173,
+            441,
+            823,
+            483
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Dataset – We generate a novel dataset consisting of atomic environments extracted from nonredundant structures in the PDB. ",
+        "bbox": [
+            174,
+            484,
+            821,
+            511
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Metrics – We formulate this as a classification task where we predict the identity of the amino acid in the center of the environment based on all other atoms. ",
+        "bbox": [
+            168,
+            511,
+            821,
+            537
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Split – We split residue environments by protein topology class. ",
+        "bbox": [
+            173,
+            540,
+            599,
+            553
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.4 MUTATION STABILITY PREDICTION (MSP) ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            571,
+            514,
+            585
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Impact – Identifying mutations that stabilize a protein’s interactions is a key task in designing new proteins. Experimental techniques for probing these are labor-intensive (Antikainen & Martin, 2005; Lefevre et al., 1997), motivating the development of efficient computational methods. \\` ",
+        "bbox": [
+            174,
+            598,
+            825,
+            638
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Dataset – We derive a novel dataset by collecting single-point mutations from the SKEMPI database (Jankauskaite et al., 2019) and model each mutation into the structure to produce mutated structures. ˙ Metrics – We formulate this as a binary classification task where we predict whether the stability of the complex increases as a result of the mutation. ",
+        "bbox": [
+            174,
+            640,
+            825,
+            694
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Split – We split protein complexes by sequence identity at $30 \\%$ ",
+        "bbox": [
+            174,
+            695,
+            593,
+            709
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.5 LIGAND BINDING AFFINITY (LBA) ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            727,
+            459,
+            741
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Impact – Most therapeutic drugs and many molecules critical for biological signaling take the form of small molecules. Predicting the strength of the protein-small molecule interaction is a challenging but crucial task for drug discovery applications. ",
+        "bbox": [
+            173,
+            753,
+            823,
+            795
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Dataset – We use the PDBBind database (Wang et al., 2004; Liu et al., 2015), a curated database containing protein-ligand complexes from the PDB and their corresponding binding strengths. Metrics – We predict $p K = - \\log ( K )$ , where $K$ is the binding affinity in Molar units. Split – We split protein-ligand complexes by protein sequence identity at $30 \\%$ . ",
+        "bbox": [
+            171,
+            795,
+            825,
+            852
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.6 LIGAND EFFICACY PREDICTION (LEP) ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            868,
+            483,
+            883
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Impact – Many proteins switch on or off their function by changing shape. Predicting which shape a drug will favor is thus an important task in drug design. ",
+        "bbox": [
+            171,
+            895,
+            823,
+            924
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Dataset – We develop a novel dataset by curating proteins from several families with both ”active” and ”inactive” state structures, and model in 527 small molecules with known activating or inactivating function using the program Glide (Friesner et al., 2004). ",
+        "bbox": [
+            173,
+            103,
+            823,
+            145
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Metrics – We formulate this as a binary classification task where we predict whether or not a molecule bound to the structures will be an activator of the protein’s function or not. ",
+        "bbox": [
+            174,
+            146,
+            820,
+            174
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Split – We split complex pairs by protein. ",
+        "bbox": [
+            176,
+            174,
+            447,
+            188
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.7 PROTEIN STRUCTURE RANKING (PSR) ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            203,
+            485,
+            218
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Impact – Proteins are one of the primary workhorses of the cell, and knowing their structure is often critical to understanding (and engineering) their function. ",
+        "bbox": [
+            173,
+            229,
+            823,
+            257
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Dataset – The Critical Assessment of Structure Prediction (CASP) (Kryshtafovych et al., 2019) is a blind international competition for predicting protein structure. ",
+        "bbox": [
+            173,
+            258,
+            823,
+            285
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Metrics – We formulate this as a regression task, where we predict the global distance test (GDT TS) from the true structure for each of the predicted structures submitted in the last 18 years of CASP. Split – We split structures temporally by competition year. ",
+        "bbox": [
+            176,
+            286,
+            825,
+            328
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.8 RNA STRUCTURE RANKING (RSR) ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            343,
+            460,
+            358
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Impact – Similar to proteins, RNA plays major functional roles (e.g., gene regulation) and can adopt well-defined 3D shapes. Yet the problem is data-poor, with only a few hundred known structures. Dataset – Candidate models generated by FARFAR2 (Watkins & Das, 2019) for the first 21 released RNA Puzzle challenges (Cruz et al., 2012), a blind structure prediction competition for RNA. Metrics – We predict the root-mean-squared deviation (RMSD) from the ground truth structure. Split – We split structures temporally by competition year. ",
+        "bbox": [
+            169,
+            369,
+            826,
+            453
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4 EXPERIMENTAL SETUP ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            473,
+            398,
+            488
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To assess the benefits of 3D molecular learning, we use a combination of existing and novel 3D molecular learning methods, and implement a number of robust baselines. Our 3D molecular learning methods belong to one of each of the major classes of deep learning algorithms that have been applied to atomistic systems: graph networks, three-dimensional convolutional networks, and equivariant networks. Here we describe the core networks and the novel extensions needed to adapt them to certain datasets. See Appendix C.2 for task-specific details and hyperparameters. ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1 CORE NETWORKS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            604,
+            339,
+            617
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "For GNNs, we represent molecular systems as graphs in which each node is an atom. Edges are defined between all atoms separated by less than $4 . 5 \\textup { \\AA }$ , and weighted by the distance between the atoms. Node features are one-hot-encoded by atom type. Our core model uses five layers of graph convolutions, each followed by batch normalization and ReLU activation, a sum pooling layer, and two fully-connected layers with dropout. ",
+        "bbox": [
+            174,
+            630,
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+            699
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "For 3DCNNs, we represent our data as a cube of fixed size (different per task due to the different molecular sizes) in 3D space that is discretized into voxels with resolution of $1 \\textup { \\AA }$ to form a grid. Each voxel is associated with a one-hot-encoded vector which denotes the presence or absence of each atom type. Our core model consists of four 3D-convolutional layers, each followed by maxpooling, dropout, and ReLU activation, and two fully-connected layers. ",
+        "bbox": [
+            174,
+            707,
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+            776
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "For ENNs, we use SE(3)-equivariant networks that represent each atom of a structure by its position as absolute coordinates in 3D space with one-hot-encoded atom type as features. No rotational augmentation is needed due to the rotational symmetry of the network. The core of all architectures in this work is a network of four layers of covariant neurons that use the Clebsch–Gordan transform as nonlinearity, as described and implemented in Anderson et al. (2019). ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2 SIAMESE ARCHITECTURES ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            869,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "For tasks involving comparing two sets of atoms sampled from the same distributions, we also develop new architectures that are Siamese in nature. Specifically, the PIP dataset involves predicting a symmetric interaction between two proteins, while the MSP and LEP datasets involve a symmetric comparison between two interactions. Taking inspiration from Townshend et al. (2019)’s use of a Siamese 3DCNN network for the PIP dataset, we replicate that architecture for our PIP, MSP, and LEP datasets, and develop new Siamese GNN and Siamese ENN networks. Specifically, we train a pair of core networks with tied weights, ensuring symmetric treatment of both items of the pair. We then combine the final learned embeddings from both core networks to output a final prediction. Beyond the novelty of weight-tying atom-level GNNs and ENNs, to our knowledge this is also the first use of weight-tying across SE(3)-equivariant networks. ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.3 AMINO ACID OUTPUTS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            233,
+            377,
+            247
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Certain tasks involve making a prediction on a specific amino acid (PIP, RES, and MSP; see Table 2), yet GNNs and ENNs typically rely on summing over all node embeddings to compute a final graph embedding, making it difficult to isolate this amino acid. To remedy this, after our convolutional layers we implement the novel procedure of extracting the embedding of only the $\\mathbf { \\boldsymbol { C } } \\alpha$ atom of the amino acid in question, thereby allowing our GNNs and ENNs to isolate it. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5 RESULTS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            352,
+            281,
+            367
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "To assess the utility of 3D molecular learning, we evaluate our methods on the ATOM3D datasets and compare performance to state-of-the-art methods using 1D or 2D representations. We stress that in many cases, 3D molecular learning methods have never been applied to the proposed tasks, and that several of the tasks are novel. In the following sections, we describe the results of our benchmarking and some key insights that can be derived from them. We also aggregate these results along with additional metrics and standard deviations over three replicates in Appendix E. ",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.1 3D REPRESENTATIONS CONSISTENTLY IMPROVE PERFORMANCE ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            487,
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+            501
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Our evaluation of 3D methods on the tasks in ATOM3D reveals that incorporating atomistic geometry leads to consistently superior performance compared to 1D and 2D methods. For small molecules, state-of-the-art methods do not use 1D representations, so we focus instead on comparing to representations at the 2D level, i.e. the chemical bond graph. This is the approach taken by the 2D GNN introduced by Tsubaki et al. (2019) or the N-gram graph method by Liu et al. (2019), which both obtain similar results (Table 3) on the small-molecule-only dataset SMP. When we add 3D distance, as done for our GNN model, we improve performance across all targets in SMP (Table 3). ",
+        "bbox": [
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+            512,
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+            625
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "For tasks involving biopolymers (proteins and RNA), state-of-the-art methods do not use 2D representations, primarily because most of the chemical bond graph can be easily re-derived from the 1D representation, i.e. the linear sequence that makes up the biopolymer. We thus compare to representations at the 1D level (Table 7). For MSP and RES, both new datasets, we evaluate against Rao et al. (2019)’s TAPE model, a transformer architecture that operates on protein sequence and is state-of-the-art amongst 1D methods for many tasks. For PIP, we compare to the sequence-only version of BIPSPI (Sanchez-Garcia et al., 2018), a state-of-the-art boosted decision tree method for protein interaction prediction. We find that 3D methods outperform these 1D methods on all biopolymer-only datasets (PIP, RES, MSP). ",
+        "bbox": [
+            174,
+            631,
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+            756
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "For tasks involving both biopolymers and small molecules, we compare DeepDTA (Ozt ¨ urk et al., ¨ 2018). This network uses a 1D representation via a 1DCNN for both the biopolymer and small molecules. For LBA, we additionally compare to DeepAffinity (Karimi et al., 2019) which uses pairs of a ligand SMILES string and a novel representation of structurally-annotated protein sequences. Using a 3D representation for both ligand and protein instead leads to improved performance for the joint protein-small molecule datasets (LBA and LEP, see Table 5). ",
+        "bbox": [
+            174,
+            763,
+            825,
+            847
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The biopolymer structure ranking tasks (PSR and RSR) are inherently 3D in nature, as they involve evaluating the correctness of different 3D shapes taken on by the same biopolymer. Thus, critically, a 1D or 2D representation would not be able to differentiate between these different shapes since the linear sequence and chemical bond graph would remain the same. We therefore compare to state-of-the-art 3D methods as shown in Table 6. ",
+        "bbox": [
+            176,
+            854,
+            823,
+            922
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/f0c7e5f24e7692b09c665de82695ce8f9929587922212c684556dd82475091f7.jpg",
+        "table_caption": [
+            "Table 3: Small molecule results. Metric is mean absolute error (MAE). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Task</td><td rowspan=\"2\">Target</td><td colspan=\"3\">3D</td><td colspan=\"2\">Non-3D</td></tr><tr><td>3DCNN</td><td>GNN</td><td>ENN</td><td>Tsubaki et al. (2019)</td><td>Liu et al. (2019)</td></tr><tr><td rowspan=\"3\">SMP</td><td>μ[D]</td><td>0.572</td><td>0.068</td><td>0.046</td><td>0.496</td><td>0.520</td></tr><tr><td>gap[eV]</td><td>0.589</td><td>0.091</td><td>0.065</td><td>0.154</td><td>0.184</td></tr><tr><td>Ut[ev]</td><td>1.615</td><td>0.070</td><td>0.023</td><td>0.182</td><td>0.218</td></tr></table>",
+        "bbox": [
+            220,
+            151,
+            776,
+            236
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/6dcdceeebe6aa6c32d8d690525c1e10dfb37e86355f634c172cf1776e863cbd2.jpg",
+        "table_caption": [
+            "Table 4: Biopolymer results. AUROC is the area under the receiver operating characteristic curve. Asterisks $( ^ { * } )$ indicate that the exact training data differed (though splitting criteria were the same). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Task</td><td rowspan=\"2\">Metric</td><td colspan=\"3\">3D</td><td colspan=\"2\">Non-3D</td></tr><tr><td>3DCNN</td><td>GNN</td><td>ENN</td><td>Sanchez-Garcia et al. (2018)</td></tr><tr><td>PIP</td><td>AUROC</td><td>0.844</td><td>*0.669</td><td>一</td><td>0.841</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>Rao et al. (2019)</td></tr><tr><td>RES</td><td>accuracy</td><td>0.451</td><td>0.082</td><td>*0.072</td><td>*0.30</td></tr><tr><td>MSP</td><td>AUROC</td><td>0.520</td><td>0.637</td><td>0.678</td><td>0.554</td></tr></table>",
+        "bbox": [
+            248,
+            344,
+            748,
+            459
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/456d0e0288e2a668e1aacdeba9e3c00756b7a8e60c76c84fa5d824fda11a2319.jpg",
+        "table_caption": [
+            "Table 5: Joint small molecule/biopolymer results. $R _ { S }$ is Spearman correlation, $R _ { P }$ is Pearson correlation, AUROC is area under the receiver operating characteristic curve, and RMSD is root-mean-squared deviation. Asterisks $( ^ { * } )$ indicate that the exact training data differed (though splitting criteria were the same). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Task</td><td rowspan=\"2\">Metric</td><td colspan=\"3\">3D</td><td colspan=\"2\">Non-3D</td></tr><tr><td>3DCNN</td><td>GNN</td><td>ENN</td><td>Oztirk et al. (2018)</td><td>Karimi et al. (2019)</td></tr><tr><td rowspan=\"3\">LBA</td><td>RMSD</td><td>1.520</td><td>1.936</td><td>*1.429</td><td>1.565</td><td>1.893</td></tr><tr><td>glob.Rp</td><td>0.558</td><td>0.581</td><td>*0.541</td><td>0.573</td><td>0.415</td></tr><tr><td>glob.Rs</td><td>0.556</td><td>0.647</td><td>*0.532</td><td>0.574</td><td>0.426</td></tr><tr><td>LEP</td><td>AUROC</td><td>0.824</td><td>0.678</td><td>0.569</td><td>0.696</td><td>1</td></tr></table>",
+        "bbox": [
+            210,
+            582,
+            787,
+            685
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/3011a26ec18b4d58f27a6c83bf0167097e22c11717ae0e8f2cf3dcc832893da4.jpg",
+        "table_caption": [
+            "Table 6: Structure ranking results. $R _ { S }$ is Spearman correlation, $R _ { P }$ is Pearson correlation. Mean measures the correlation for structures corresponding to the same biopolymer, whereas global measures the correlation across all biopolymers. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Task</td><td rowspan=\"2\">Metric</td><td colspan=\"3\">3D</td></tr><tr><td>3DCNN</td><td>GNN</td><td>SotA</td></tr><tr><td rowspan=\"2\">PSR</td><td>mean Rs</td><td>0.177</td><td>0.327</td><td>0.432 (Pages et al., 2019)</td></tr><tr><td>glob. Rs</td><td>0.837</td><td>0.716</td><td>0.796 (Pages et al., 2019)</td></tr><tr><td rowspan=\"2\">RSR</td><td>mean Rs</td><td>0.414</td><td>0.195</td><td>0.173 (Alford et al.,2017)</td></tr><tr><td>glob. Rs</td><td>0.656</td><td>0.309</td><td>0.304 (Alford et al., 2017)</td></tr></table>",
+        "bbox": [
+            289,
+            795,
+            709,
+            897
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "More generally, we find that learning methods that leverage the 3D geometry of molecules hold state-of-the-art on all tasks on our benchmark (Appendix D). ",
+        "bbox": [
+            174,
+            103,
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+            132
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.2 MANY 3D MOLECULAR LEARNING PROBLEMS REMAIN UNDEREXPLORED ",
+        "bbox": [
+            176,
+            175,
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+            188
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "As demonstrated in the previous section, formulating a molecular problem through the lens of 3D molecular learning can lead to significantly improved performance. However, many important problems have not been studied within this framework, leaving significant room for further improvement. This opens up a ripe field of research with much low-hanging fruit. One prominent example we explore here is RNA structure ranking, where the state-of-the-art method uses Rosetta (Alford et al., 2017), a hand-designed potential energy function. When we instead apply our 3DCNN method that learns directly from the 3D atomistic geometry, we see dramatic increases in performance (Table 6). ",
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+    {
+        "type": "text",
+        "text": "In a similar vein, on the ligand efficacy prediction task we find that the 3DCNN method outperforms Glide (Friesner et al., 2004), a state-of-the-art scoring function for protein-small molecule docking. The 3DCNN achieves an AUROC of 0.824, compared to Glide’s 0.770. ",
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+    {
+        "type": "text",
+        "text": "We also find room for improvement in domains where 3D molecular learning is already being employed. Protein structure ranking is one such area, and we see that the 3DCNN model is competitive with the state-of-the-art deep learning method by Pages et al. (2019) (Table 6), surpassing it in terms \\` of absolute assessment of correctness (i.e., comparing 3D candidates from different biopolymers) though not in terms of relative assessment (i.e., comparing 3D candidates from the same biopolymer). ",
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+    {
+        "type": "text",
+        "text": "Overall, these results demonstrate the potential of 3D molecular learning to address a wide range of problems involving molecular structure, and we anticipate that continued development of such models on less well-studied tasks will aid progress in biomedical research. ",
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+    {
+        "type": "text",
+        "text": "5.3 DIFFERENT TASKS REQUIRE DIFFERENT ARCHITECTURES ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "While atomistic methods consistently outperform their non-3D counterparts and provide a systematic way of representing molecular data, our results also provide evidence that architecture selection plays a critical role in performance. For tasks primarily focused on small molecules (SMP and LBA), we see superior performance from the particle-based methods (GNN and ENN) than from the volumetric 3DCNN. Small molecules are already intuitively represented as graph-like structures, with nodes (atoms) and edges (bonds), and the quantities computed in these small molecule tasks depend less on complex 3D geometry and more on the exact position of each atom relative to its neighbors. Unlike particle-based methods, 3DCNNs must approximate these positions, and while increasing spatial resolution increases precision, it also leads to cubic scaling of complexity. ",
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+    {
+        "type": "text",
+        "text": "On the other hand, for larger molecules and complex 3D geometries that are critical to tasks like PSR, RSR, LEP, and RES, we see that the 3DCNN method outperforms GNNs. Here, the 3DCNN’s ability to directly represent differences between patterns in 3D space, as opposed to trying to reconstruct them through pairwise distances, is likely what allows it to perform well. In these tasks, the exact position and relational information between atoms is less important than their overall conformation. ",
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+    {
+        "type": "text",
+        "text": "Finally, equivariant networks show promise but suffer from scalability issues. One motivation for the development of equivariant networks is that they fill a “happy medium” where they can both represent atom positions precisely and capture complex geometries. On some of the tasks where we could test the ENN (LBA, SMP), we often observed close to state-of-the-art performance, even on a reduced training set (LBA). Unfortunately, current implementations do not yet scale to most of our tasks due to the compute- and memory-intensive nature of the Clebsch-Gordan products used to maintain rotational equivariance. For some tasks, the performance was severely limited by only training on a fraction of the data $< 1 \\%$ for RES) or a portion of the entire atomic structure (LEP), and for others we could not apply the ENN at all. These limitations point to the need for further architectural innovations before their performance can be demonstrated on extended systems. ",
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+    {
+        "type": "text",
+        "text": "6 CONCLUSION ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In this work we present a vision of 3D atom-level data as a new “machine learning datatype” deserving focused study. Atomistic data shares several underlying symmetries, contains poorly understood higher-level patterns, and can be used to address many high-impact but unsolved problems. ",
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+    {
+        "type": "text",
+        "text": "We create several benchmark datasets and compare the performance of different types of 3D molecular learning models across these tasks. Many of these architectures were developed specifically for the tasks in question, such as the Siamese ENN and GNN models used for paired tasks (PIP, MSP, and LEP). For tasks that can be formulated in lower dimensions, we demonstrate that 3D molecular learning yields consistent gains in performance over 1D and 2D methods. We also show that selection of an appropriate architecture is critical for optimal performance on a given task; depending on the structure of the underlying data, a 3DCNN, GNN, or ENN may be most appropriate. As equivariant networks continue to improve in efficiency and stability, we expect these to become more and more viable due to their close modeling of physical laws. ",
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+    {
+        "type": "text",
+        "text": "While ATOM3D establishes a first set of benchmark datasets, there are many other open areas in biomedical research and molecular science that are ripe for 3D molecular learning, especially as structural data becomes readily available. Such tasks include virtual screening and pose prediction of small molecule drugs, or the prediction of conformational ensembles instead of static structures. The use of multiple 3D conformations per molecule represents an especially promising direction, as they would more faithfully reproduce the entire set of states a given molecule could adopt. As such, we envision expanding the ATOM3D framework beyond the tasks described here. ",
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+    },
+    {
+        "type": "text",
+        "text": "Through this work, we hope to lower the entry barrier for machine learning practitioners, encourage the development of machine learning algorithms focused on 3D atomistic data, and promote a novel paradigm within the fields of structural biology and medicinal chemistry. ",
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+    {
+        "type": "text",
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