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+# ViSER: Video-Specific Surface Embeddings for Articulated 3D Shape Reconstruction
+
+Gengshan Yang1 Deqing Sun2 Varun Jampani2 Daniel Vlasic2 Forrester Cole2 Ce Liu4∗ Deva Ramanan1,3
+
+1Carnegie Mellon University
+
+2Google Research 3Argo AI 4Microsoft Azure AI
+
+ViSER-webpage
+
+# Abstract
+
+We introduce ViSER, a method for recovering articulated 3D shapes and dense 3D trajectories from monocular videos. Previous work on high-quality reconstruction of dynamic 3D shapes typically relies on multiple synchronized cameras, strong category-specific priors, or 2D keypoint supervision. We show that none of these are required if one can reliably estimate long-range correspondences in a video, making use of only 2D object masks and two-frame optical flow as inputs. ViSER infers correspondences by matching 2D pixels to a canonical, deformable 3D mesh via video-specific surface embeddings that capture the view-independent appearance features of each surface point. These embeddings behave as a continuous set of keypoint descriptors defined over the mesh surface, which can be used to establish dense long-range correspondences across pixels. The surface embeddings are implemented as coordinate-based MLPs that are fit to each video via self-supervised losses. Experimental results show that ViSER compares favorably against prior work on challenging videos of humans with loose clothing and unusual poses as well as animal videos from DAVIS and YTVOS.
+
+# 1 Introduction
+
+Reconstructing the world from a sequence of monocular frames is a long-standing task in computer vision. While there has been tremendous progress in reconstructing rigid scenes (via SfM and SLAM [7, 39, 43], or recent techniques based on neural rendering [28]), reconstructing dynamic scenes with articulated objects remains elusive. For example, given a monocular video, it is still challenging to reconstruct an everyday scene of a moving person with loose clothing. In this work, we tackle the problem of estimating the deforming mesh of articulated objects given a segmented monocular video of that object. Our method avoids the use of any mesh templates or category-specific priors and generalizes to unknown deformable articulated objects in the wild.
+
+Nonrigid shape recovery is highly under-constrained due to fundamental ambiguities between shape, appearance, and time-varying deformation. Current approaches for addressing these challenges fall into two camps: better data “likelihoods” or better “priors”. The first camp extracts richer sensor data, via multi-camera studio setups [15] or depth sensors [30], but requires substantial efforts to work in the wild. The second camp makes use of category-level priors over object shapes [18, 20] and is particularly effective for human reconstruction. However, building such models requires considerable offline efforts in the form of registered 3D scans [26] or manual keypoint annotations [12], both of which are difficult to scale to arbitrary object categories.
+
+![](images/c5024c4b9aaa8a762cdc7d035eea0072af4cfb73583565fe4600659f978d57ee.jpg)  
+Figure 1: Given a long video (or multiple short videos), ViSER jointly learns articulated 3D shapes (represented as a mesh with vertices $\bar { \bf V }$ and faces $\mathbf { F }$ ) and joint pixel-surface embeddings (including a surface embedding $\mathbf { F _ { S } }$ and a pixel embedding $\mathbf { F _ { I } }$ ) that establishes dense long-range pixel correspondences over time. As a result, ViSER produces accurate shapes, long term trajectories and meaningful part segmentation.
+
+In this work, we use a practical but less explored variant of the data-likelihood camp: we use multiple frames of a video rather than multiple cameras or depth sensors. This considerably complicates analysis for dynamic, non-rigid scenes. Nonrigid structure-from-motion (NRSfM) [4, 38] attempts to constrain the problem by relying on motion correspondences such as 2D point tracks. While 2D correspondences over short time scales (i.e., optical flow) are relatively robust to extract, correspondences over long time scales are notoriously difficult to estimate because of appearance variations arising from viewpoint changes, occlusion and fast motion. In practice, this limits the applicability of NRSfM methods to controlled lab sequences.
+
+We propose ViSER (Video-Specific Surface Embeddings for Reconstruction), which establishes long-range correspondence and reconstructs articulated 3D shapes from a monocular video. Fig. 1 shows a sample outdoor video and the corresponding ViSER results. The key insight behind ViSER is to force long-range video pixel correspondences to be consistent with an underlying canonical 3D mesh through the use of video-specific embeddings that capture the pixel appearance of each surface point. These embeddings behave as a continuous set of keypoint descriptors defined over the surface mesh, learned with coordinate-based MLPs that are fit to each video via self-supervised losses. ViSER simultaneously optimizes the image CNN, surface MLP, and 3D shape so as to fit the observed video frames. It reconstructs state-of-the-art articulated 3D shape and 3D trajectories without using category-specific priors, making it easily scalable to diverse videos including humans with challenging clothing and poses as well as animals. Lastly, we demonstrate that ViSER recovers meaningful part segmentation and blend skinning weights from videos, which typically require considerable manual effort from 3D artists.
+
+# 2 Related Work
+
+Low-level correspondence. Optical flow is a well-studied representation for short-term correspondence between adjacent frames of a video. After decades of research, recent CNN models [40, 42, 48] for optical flow have achieved an impressive level of accuracy as evidenced by the Sintel and KITTI benchmarks [5, 9]. However, it is challenging to concatenate optical flow for reliable long-range correspondence due to occlusions and strong appearance changes [33, 37, 41]. ViSER does not concatenate optical flow but use it as a constraint to establishes long-range correspondence.
+
+The layered approach [6, 14, 45] segments a video into different moving objects with coherent motion, thereby establishing long-range correspondence for every frames through the shared layers. Early layered methods assume parameter motion for each layer and can only handle limited scenes. Unwrap Mosiacs [32] uses a dense 2D-to-2D mapping from a texture map to every input frame, and editing operations on the texture map naturally transfers to each individual frame. However, the 2D representation cannot flexibly model complex 3D phenomena, such as occlusions.
+
+![](images/85a0b0d499cfbf36b2e52416eddbbd27a71c5a591aa10f920a05d7b53bc2d6ab.jpg)  
+Figure 2: We learn a joint pixel-surface embedding space for dense correspondence between pixels in video frames $I _ { t }$ and points on a canonical 3D surface $( \bar { \mathbf { V } } , \mathbf { \check { F } } )$ . Such embedding space is optimized through “top-down” differentiable rendering $\mathcal { R } ( \cdot )$ and “bottom-up” correspondence matching $\hat { \bf S } [ x , y ]$ (Sec 3.2). We introduce a 3D matching loss to optimize the embeddings, where the matched surface locations are encouraged to be close to the rendered surface locations. The embedding further enables articulated shape optimization through a 2D-3D-2D cycle reprojection: pixel $[ x , y ] $ matched surface ${ \hat { \mathbf { S } } } [ x , y ] \to$ re-projected pixel $\pi ( \hat { \mathbf { S } } [ x , y ] )$ (Sec. 3.3).
+
+Dense pose and surface mappings. DensePose [12] directly maps pixels to the 3D surface of a human body model. It requires large amounts of training data with annotated image-to-surface correspondence and is hard to generalize to other categories. Articulation-aware Canonical Surface Mapping (A-CSM) [20] uses geometric cycle consistency for learning to map pixels to corresponding points on a template shape without using keypoint annotations. However, it requires a pre-defined template shape for each category. Continuous Surface Embeddings (CSE) [29] establishes dense correspondences between image pixels and 3D object geometry by predicting an embedding vector of the corresponding vertex in the object mesh for each pixel in a 2D image. While applicable to multiple categories, CSE requires annotations and only applies to categories in the training set. ViSER requires neither a template shape nor annotations to work on categories in the wild.
+
+Nonrigid shape reconstruction. One way to accurately reconstruct articulated shapes is to rely on rich sensor data, e.g., multi-view [15] or depth sensors [30], which requires substantial efforts to setup and reconstruct objects in the wild. For monocular videos/images, one popular approach is to adopt strong 3D shape and pose priors [18, 26, 35, 36, 53, 54] but it works well only on limited categories, whose 3D data are easy to collect. To deal with more nonrigid object categories, a recent trend is to learn a category-level 3D shape model from a collection of images or videos with 2D annotations, such as keypoints and object silhouettes [10, 16, 20, 22, 23, 44, 46, 50]. Although they are able to reconstruct more object categories, such as birds and quadruped animals, the reconstruction usually lacks details, and the level of deformation recovered tends to be low.
+
+Category-agnostic methods, such as nonrigid structure from motion (NRSfM) methods [4, 11, 19, 38] reconstruct nonrigid 3D shapes from a set of 2D point trajectories. However, due to the difficulty in obtaining accurate long-range correspondences [37, 41] they do not work well for videos in the wild. A recent work, LASR [49], uses two-frame optical flow to reconstruct articulate shapes from a monocular video with differentiable rendering. Despite the promising results, LASR does not reason about long-range correspondences and can only reliably reconstruct what is visible in a short video. ViSER establishes reliable long-range correspondence that are robust to moderate shape variations and appearance changes. Thus, ViSER can obtain much higher-quality reconstruction by using either a long video or several videos of a category.
+
+# 3 Approach
+
+Fig. 2 provides an overview of our approach, which follows a typical framework of differentiable rendering [16, 25]. Borrowing the notation from LASR [49], we formalize our task as follows. Given a set of video observations including RGB pixel color, segmentation masks, and optical flow estimates $\{ I _ { t } , S _ { t } , u _ { t } \} _ { t = \{ 0 , \ldots , T \} }$ , our goal is to recover a set of shape and motion parameters $\{ \mathbf { S } , \mathbf { D } _ { t } \}$ that produce reconstructions $\{ \hat { I } _ { t } , \hat { S } _ { t } , \hat { u } _ { t } \} _ { t = \{ 0 , \dots , T \} }$ that match the video observations. We refer to supplementary material for a complete list of notations defined in the paper.
+
+# 3.1 Preliminaries
+
+We represent an object’s shape as a triangular mesh $\mathbf { S } = \{ \bar { \mathbf { V } } , \mathbf { F } \}$ with canonical vertices $\bar { \mathbf { V } } \in \mathbb { R } ^ { 3 \times N }$ and a fixed topology (edge connectivity) $\mathbf { \bar { F } } \in \mathbb { R } ^ { 3 \times M }$ . To render an object, we displace mesh vertices with motion parameters $\mathbf { D } _ { t }$ , apply a perspective projection with camera intrinsics $\mathbf { K } _ { t }$ , and rasterize.
+
+We model vertex motion with root body transformations $\mathbf { G } _ { 0 }$ and object articulations $\{ \mathbf { G _ { 1 } } , \cdots , \mathbf { G _ { B } } \}$ using linear blend skinning (LBS) [20, 21]. LBS constrains vertex motion by linearly blending $B$ rigid “bone” transformations with a skinning weight matrix $\mathbf { W } \in \mathbb { R } ^ { B \times N }$ , transforming the canonical shape into frame $t$ as
+
+$$
+\mathbf { V } _ { i , t } = \mathbf { G _ { 0 , t } } \left( \sum _ { b } \mathbf { W } _ { b , i } \mathbf { G } _ { b , t } \right) \bar { \mathbf { V } } _ { i }
+$$
+
+where $i$ is the vertex index, $b$ is the bone index. Similar to LASR, the root body and bone transformations are represented as the outputs of a pose CNN given an input image, $( \mathbf { G _ { 0 } } , \cdot \cdot \cdot , \mathbf { G _ { B } } ) = \psi _ { p } ( I _ { t } )$ .
+
+We define a set of surface properties for rendering, including vertex 3D coordinates, textures and features, and rasterize them in a differentiable manner [25]. We denote the differentiable rendering function that renders the property $\mathbf { C }$ defined on a canonical surface to an image as $\mathcal { R } ( \mathbf { C } ; \mathbf { V } , \mathbf { W } , \mathbf { G } )$ , which executes the blending skinning function in Eq. (1) and softly blends the surface property based on their depth and barycentric coordinates [25]. For simplicity, we omit the shape, skinning, and motion parameters parameters and write the differentiable rendering function as $\mathcal { R } ( \mathbf { C } )$ . To render optical flow, we rasterize and project vertex coordinates in two consecutive frames and compute their 2D displacements [49]. Such renderings are compared against video observations to compute gradients for updating model parameters.
+
+# 3.2 Video-specific Surface Embedding
+
+Pixel-surface embeddings. We learn pixel and surface embeddings that map corresponding pixels in different frames to the same point on a canonical 3D surface. Intuitively, consider a particular region on the canonical surface mesh that is the “nose” of an articulated human. The surface embedding captures a descriptor for the nose, which can then be matched to pixel-level descriptors at each frame.
+
+Given an input image $I _ { t }$ , the pixel-wise descriptor embedding is computed by a U-Net [34] encoder:
+
+$$
+\mathbf { F _ { I } } [ x , y , t ] = \psi _ { e } ( I _ { t } ) [ x , y ] \in \mathbb { R } ^ { 1 6 } ,
+$$
+
+where $[ x , y , t ]$ are pixel locations at frame $t$ . The surface embedding is computed by a positionencoded MLP:
+
+$$
+\mathbf { F _ { S } } ( X , Y , Z ) = \phi _ { e } ( X , Y , Z ) \in \mathbb { R } ^ { 1 6 } ,
+$$
+
+where $\phi _ { e } ( \cdot )$ is an MLP defined over 3D points $( X , Y , Z )$ in the canonical space, augmented with Fourier positional encoding [28]. The two embeddings are optimized on test videos such that pixels representing the same surface location in different frames are mapped to the same canonical surface point [20].
+
+Correspondence via soft-argmax regression. Given the pixel and surface embeddings, we construct a per-frame cost volume $D ( \mathbf { F _ { I } } , \mathbf { F _ { S } } )$ of size $H \times W \times N _ { s }$ over pixels and surface points (we randomly sample $N _ { s } = 2 0 0$ surface points at each step) by considering their cosine feature distances,
+
+$$
+D ( \mathbf { F } _ { \mathbf { I } } , \mathbf { F } _ { \mathbf { S } } ) [ x , y , i ] = 1 - \cos \big ( \mathbf { F } _ { \mathbf { I } } [ x , y ] , \mathbf { F } _ { \mathbf { S } } ( X _ { i } , Y _ { i } , Z _ { i } ) \big ) .
+$$
+
+Normalizing the cost volume over the surface point dimension yields a softmax “heatmap” over surface points that potentially match to pixel $( x , y )$ , as shown in Fig. 3 (Left):
+
+$$
+\sigma _ { \left( x , y \right) } [ i ] = \frac { e ^ { - D [ x , y , i ] / \tau } } { \sum _ { j } e ^ { - D [ x , y , j ] / \tau } } ,
+$$
+
+where $\tau$ is a temperature scaling parameter that is jointly optimized with the feature embeddings. To output a single surface point for pixel $( x , y )$ , we can compute a “soft” argmax [17, 48] by taking the expectation of the softmax distribution over the 3D locations of the points samples,
+
+$$
+\hat { \mathbf { S } } [ x , y ] = \sum _ { i } \sigma _ { ( x , y ) } [ i ] ( X _ { i } , Y _ { i } , Z _ { i } ) ,
+$$
+
+where $( X _ { i } , Y _ { i } , Z _ { i } )$ is the i-th sampled surface point and $\sigma _ { ( } x , y ) [ i ]$ is the matching probability of pixel $( x , y )$ over the sampled points $i \in \{ 1 , 2 , \ldots , N _ { s } \}$ .
+
+![](images/2ebf45b5b43939195594f2e62ce87906cefbbdcdadb94eac45fe28f932ffe5f0.jpg)  
+Figure 3: Pixel-surface embeddings establish a continuous mapping between pixels and points on a canonical surface. Left: Given a query pixel at $( \mathbf { x } , \mathbf { y } )$ , we match it to a set of canonical surface points, where the matching distribution is used to regress a continuous mapping to the canonical surface. Right: Given a query surface point (X,Y,Z), a matching distribution over pixels can be computed. Warm color indicates high matching probability.
+
+We can also normalize the $H \times W \times N _ { s }$ cost volume over spatial positions to capture a distribution of pixel locations that match to each surface point $( X _ { i } , Y _ { i } , Z _ { i } )$ :
+
+$$
+\sigma _ { ( X _ { i } , Y _ { i } , Z _ { i } ) } [ x , y ] = \frac { e ^ { - D [ x , y , i ] / \tau } } { \sum _ { [ x , y ] } e ^ { - D [ x , y , j ] / \tau } } .
+$$
+
+and compute a similar soft argmax mapping of surface points to pixels, as shown in Fig. 3 (Right).
+
+Relation to keypoints. The output of classic keypoint detectors are often represented as $K$ -channel heatmaps over the pixel grid, where $K$ is the number of keypoints. To define dense keypoints, one may increase the number of channels, which is computationally heavy. Similar to CSE [29], we represent dense keypoints as low-dimensional pixel-surface embeddings, which establishes a mapping between pixels and a canonical 3D surface, but far more efficiently. DensePose [12] and CSM [20] use an alternative pixel-to-surface mapping that regresses a surface coordinate at every pixel. In contrast, our pixel-surface embedding captures multimodal uncertainties over keypoints; for example, $\sigma _ { ( x , y ) } [ i ]$ can capture the fact that a particular pixel matches well to both the left and right ankle, as visualized in Fig. 3, while a regressor may “regress” to the mean of the two surface coordinates.
+
+# 3.3 Learning Embeddings and Articulated Shapes
+
+Next we will introduce the loss functions that enable learning both embeddings and articulated shapes from monocular videos without a pre-defined shape template or annotated correspondence. To learn non-degenerate embeddings and overcome the local optima issue in differertiable renderers, we carefully construct a 3D matching loss and a 2D cycle loss.
+
+3D match loss. Arguably, the simplest loss to learn embeddings is to minimize the difference between the rendered surface features and the observed pixel features:
+
+$$
+L _ { \mathrm { f e a t u r e - c o n s i s t e n c y } } = \sum _ { x , y } { \Big ( } 1 - \cos ( \mathcal { R } ( \mathbf { F } _ { \mathbf { S } } ) [ x , y ] , \mathbf { F } _ { \mathbf { I } } [ x , y ] ) { \Big ) } ,
+$$
+
+where $\cos ( \cdot )$ denotes the inner product between two normalized vectors, and $\mathcal { R } ( \mathbf { F _ { S } } )$ is the differentiably rendered surface descriptors. However, the feature consistency loss admits a trivial solution, where all pixel and surface features are the same constant (yielding zero error). To address this, we introduce a 3D matching loss that ensures pixel embeddings only match to surface embeddings rendered at the pixel location:
+
+$$
+L _ { \mathrm { m a t c h i n g } } = \sum _ { x , y } \left. \mathcal { R } ( \bar { \mathbf { V } } ) [ x , y ] - \hat { \mathbf { S } } [ x , y ] \right. _ { 2 }
+$$
+
+where $\mathcal { R } ( \bar { \bf V } )$ is the rendered 3D surface location and $\hat { \mathbf { S } } [ x , y ]$ is the estimated pixel-to-surface mapping from Eq. (6), computed through sampling and computing the softmax distributions $\sigma [ i ]$ over surface points [17]. To minimize the loss, the embeddings of surface points that do not project to $( x , y )$ will be pulled away from the pixel embedding of $( x , y )$ in a contrastive way [13].
+
+2D cycle loss. The match loss aims to learn pixel-surface embeddings that are consistent over video frames and discriminative over difference surface locations. However for articulation optimization, the match loss suffers from bad local optima issue similar to other losses based on differentiable rendering [25]. For instance, when the rendering of a body part is outside the ground-truth object silhouette, a gradient update of articulation parameters would likely not incur a lower loss.
+
+To guide articulated 3D shape learning using the learned pixel-surface embeddings, we further define a cycle-based re-projection loss, inspired by prior approaches in 3D model fitting with keypoints [3] and canonical surface mappings [20]. Given an input image, we establish a 2D-3D mapping by extracting a pixel embedding and matching it to surface embedding. Then, we compute the expected surface coordinate $\hat { \mathbf { S } } [ x , y ]$ at every pixel using Eq. (6), and ensure the differentiably rendered canonical surface coordinate lands back on the original pixel coordinate $( x , y )$ ,
+
+$$
+L _ { \mathrm { r e p r o j } } = \sum _ { x , y } \left\| \mathcal { R } ( \hat { \mathbf { S } } [ x , y ] ) - ( x , y ) \right\| _ { 2 } .
+$$
+
+Reconstruction loss. Finally, we make use of reconstruction losses to ensure that generated images, masks, and flows match their estimated counterparts:
+
+$$
+L _ { \mathrm { r e c o n } } = \beta _ { 1 } \lvert | \hat { S } _ { t } ^ { i } - S _ { t } \rvert | _ { 2 } ^ { 2 } + \beta _ { 2 } \lvert | \hat { I } _ { t } ^ { i } - I _ { t } \rvert | _ { 2 } ^ { 2 } + \beta _ { 3 } \sigma _ { t } \lvert | \hat { u } _ { t } ^ { i } - u _ { t } \rvert | _ { 2 } + \beta _ { 4 } \mathrm { p d i s t } ( \hat { I } _ { t } , I _ { t } )
+$$
+
+where $\{ \beta _ { 1 } , \cdot \cdot \cdot , \beta _ { 4 } \}$ are weights empirically chosen, $\sigma _ { t }$ is the normalized confidence map for flow measurement, and pdist $( \cdot , \cdot )$ is the perceptual distance [51] measured by an ImageNet-pretrained AlexNet. The reconstruction losses ensure the match between rendered and observed optical flow, texture and silhouette images.
+
+Regularization. To avoid degenerate shapes, we use mesh Laplacian regularization [16, 49] to enforce the recovered shape to be smooth, and as-rigid-as-possible (ARAP) regularization to enforce the deformation to be locally rigid [44]. Different from prior work that only preserves the length of edges after articulation, we encourage both the area and length of faces to be the same after articulation. The area preserving term is defined as
+
+$$
+L _ { \mathrm { A R A P - a r e a } } = \sum _ { i = 1 } ^ { | E | } \sum _ { j \in N _ { i } } \mid \left| \mathbf { E _ { i } ^ { t } } \times \mathbf { E _ { j } ^ { t } } \right| - \left| \mathbf { E _ { i } ^ { t + 1 } } \times \mathbf { E _ { j } ^ { t + 1 } } \right| \mid ,
+$$
+
+where $| E |$ is the number of edges and $N _ { i }$ the indices of neighbouring edges.
+
+# 3.4 Representing Surface Properties with MLPs
+
+By extending surface embedding MLPs with additional dimensions, we can model other surface properties including textures and even surface-based geometric deformations. Compared to explicitly defined textures, such continuous implicit representations have the capacity to encode arbitrary amount of details and are empirically easier to optimize.
+
+Surface appearance. The appearance of the object is represented by a coordinate-MLP queried at points on the canonical mesh surface. To handle view-dependent appearance (such as shadow and lighting), we further concatenate the Fourier features of the $( X , Y , Z )$ coordinates with a frame appearance code, as the input to the texture MLP,
+
+$$
+\mathbf { C _ { i , t } } = \phi _ { t e x } ( \mathcal { F } ( \bar { \mathbf { V } } _ { i } ) , \omega _ { t } ) \in \mathbb { R } ^ { 3 } ,
+$$
+
+where $\bar { \bf V } _ { i }$ is the i-th canonical mesh vertex, which is passed through a Fourier encoder $\mathcal F ( \cdot )$ as used in NeRF [28], and concatenated with $\omega _ { t }$ , a 64-dimensional frame appearance code associated each image frame $t$ , predicted from a ResNet-18, as $\omega _ { t } = \psi _ { t e x } ( I _ { t } )$ .
+
+Instance shape deformation fields. To deal with videos of multiple instances of the same category, as experiments in Sec. 4.3, we model shape variations across instances by a continuous surface deformation field defined on the canonical surface. Similar to the surface texture, we represent the surface deformation field by a shape MLP,
+
+$$
+\mathbf { V _ { i , k } } = \bar { \mathbf { V _ { i } } } + \phi _ { s h a p e } ( \mathcal { F } ( \bar { \mathbf { V } } _ { i } ) , \alpha _ { k } ) \in \mathbb { R } ^ { 3 } ,
+$$
+
+where $\mathbf { V _ { k } }$ is the rest shape of instance $k$ and $\alpha _ { k }$ is a video-specific 64-dimensional shape code that is randomly initialized and optimized together with the shape MLP.
+
+# 4 Experiments
+
+We evaluate ViSER in three different scenarios where objects are highly articulating, making it challenging to reconstruct and estimate long-range correspondences. First, we consider long human videos with loose clothing and unusual poses. Next, we evaluate on videos of articulated animals for which accurate shape templates are missing. Finally, we analyze a multi-video variant of ViSER that learns a single model from multiple videos of the same category. All scenarios require jointly establishing long-range correspondences and reconstructing articulated 3D shapes at the same time.
+
+Table 1: 2D Keypoint transfer accuracy on athletic videos. Methods with ∗ use keypoint annotations to train. Best results are in bold.   
+
+<table><tr><td>Method</td><td>break-1</td><td>break-2</td><td>dance</td><td>parkour</td><td>ballet-1</td><td>ballet-2</td><td>ballet-3</td><td>Ave.</td></tr><tr><td>*DensePose CSE [29]</td><td>56.0</td><td>13.2</td><td>77.2</td><td>85.9</td><td>45.6</td><td>49.0</td><td>64.5</td><td>55.9</td></tr><tr><td>*VIBE+SMPLify [18]</td><td>37.1</td><td>8.2</td><td>70.4</td><td>83.8</td><td>55.4</td><td>53.0</td><td>78.8</td><td>55.2</td></tr><tr><td>LASR [49]</td><td>29.1</td><td>18.1</td><td>56.6</td><td>49.8</td><td>44.5</td><td>47.4</td><td>48.6</td><td>42.0</td></tr><tr><td>ViSER (Ours)</td><td>70.5</td><td>22.5</td><td>80.7</td><td>62.9</td><td>52.7</td><td>56.1</td><td>59.9</td><td>57.9</td></tr></table>
+
+Table 2: 2D Keypoint transfer accuracy on multiple elephant videos. Best results are in bold.   
+
+<table><tr><td>Method</td><td>inner</td><td>across</td></tr><tr><td>CSE [29]</td><td>55.7</td><td>52.2</td></tr><tr><td>Flow-VCN[48]</td><td>51.1</td><td>41.2</td></tr><tr><td>LASR [49]</td><td>57.8</td><td>-</td></tr><tr><td>ViSER (Ours)</td><td>80.4</td><td>68.9</td></tr></table>
+
+Table 3: 2D Keypoint transfer accuracy on BADJA dataset. Best results are in bold.   
+
+<table><tr><td>Method</td><td>camel</td><td>dog</td><td>cows</td><td>horse</td><td>bear</td><td>Ave.</td></tr><tr><td>CSE [29]</td><td>48.8</td><td>38.6</td><td>63.8</td><td>60.2</td><td>76.6</td><td>57.6</td></tr><tr><td>Flow-VCN [48]</td><td>47.9</td><td>25.7</td><td>60.7</td><td>14.4</td><td>63.8</td><td>42.5</td></tr><tr><td>N-NRSfM[38]</td><td>67.8</td><td>17.9</td><td>70.0</td><td>8.7</td><td>60.2</td><td>44.9</td></tr><tr><td>LASR [49]</td><td>81.9</td><td>65.8</td><td>83.7</td><td>49.3</td><td>85.1</td><td>73.2</td></tr><tr><td>ViSER (Ours)</td><td>80.1</td><td>73.8</td><td>82.9</td><td>76.3</td><td>87.3</td><td>80.1</td></tr></table>
+
+Optimization details We use the AdamW [27] optimizer with a batch of 4 consecutive image pairs. We reconstruct a long video sequence in an incremental manner similar to classic SfM. First, we use an initial set of around 20 consecutive frames to initialize the shape and pixel surface embeddings. The initial set is selected such that the viewpoint coverage is large enough. Then we gradually add in new frames. When a new frame is added, we first apply the 2D cycle loss $L _ { r e p r o j }$ to optimize its articulations, and then jointly optimize all frames with all losses. Empirically, simultaneously optimizing all the video frames produces unstable results of root body poses (or equivalently camera poses).
+
+# 4.1 Athletic Video Reconstruction
+
+Dataset. To evaluate ViSER on long-videos, we construct an athletic video dataset that is challenging due to loose clothing and unusual body poses. It consists of four videos from DAVIS [31] and three ballet videos. All videos are segmented and manually annotated with keypoints following the MSCOCO format [24]. We only use keypoint annotations for evaluation purposes.
+
+Metrics. Due to the lack of ground-truth 3D data for challenging athletic human videos, we use 2D keypoint transfer as a proxy metric [2, 52]. Given any two frames from a video, the goal is to transfer an annotated 2D keypoint from one frame to another. The accuracy is measured by percentage of correctly transferred keypoints over all T(T-1) pairs of frames in a T-frame video. A transferred keypoint is marked as correct when its distance to the ground-truth annotation is lower than $d _ { t h } = 0 . 2 \sqrt { | \boldsymbol { S } | }$ , where $| S |$ is the area of the ground-truth silhouette [2]. In general, a more accurate reconstruction leads to a higher transfer accuracy.
+
+Baselines. To compare with template-based approaches for video human reconstruction, we use VIBE with SMPLify temporal smoothing [18]. To compare with template-free methods, we use LASR [49], which also reconstructs articulated shapes using the same input setting as ours. To transfer keypoints from a reference frame to a target frame, we back-project the annotated keypoint in the reference frame to the canonical surface, and then project the intersected 3D point to the target frame. We also compare against Densepose CSE [29], which produces dense pixel-to-surface correspondences for a given category, but does not produce 3D reconstructions. To transfer keypoints for Densepose CSE, we compute pixelwise surface mappings for both frames and find the best matching w.r.t.geodesic distance on the surface. We further qualitatively compare against a state-ofthe-art human reconstruction method, PiFUHD [36] in Fig. 4, which only produces reconstruction, but not correspondence.
+
+![](images/fbe091753c2f0495ced8cb953c6fbf2f59e8ee2d1da65f5d598e70f3690e086d.jpg)  
+Figure 4: Qualitative comparisons for athletic video articulated shape reconstruction. Compared to methods that uses shape and pose priors (VIBE $^ +$ SMPLify and PiFUHD), our method achieves comparable performance for common appearance and poses, and does much better on unusual poses such as break-dancers.
+
+![](images/166855c4415d8702b655a7dc42e4809baf2c3b46ebfba6bba2cf6a0b7a6990f9.jpg)  
+Figure 5: Qualitative comparisons for elephant shape reconstruction from multiple videos. Notice that ViSER is able to take advantage of multiple videos to improve the category-level shape reconstruction but also reconstruct instance-specific details (as shown in red circles).
+
+![](images/16aec4a0675c4cd1f54df8a58f8265aa7b4db992bddc92c4e4686871ea10a196.jpg)  
+Figure 6: Part segmentation results. Colors are determined by hard-assigning vertices to the closest rigid bones.
+
+![](images/8d21ac3a175e69d94bbae955b587e18f58587f3cb36c3a814a1ad4d8dd719e12.jpg)  
+Figure 7: Comparison between single video ViSER and multi-video ViSER in terms of reconstructing YTVOS elephants. We find using multiple videos helps reconstructing the body parts that may be occluded in a single video. While single-video ViSER reconstructs a flattened shape and misses the hidden rear leg of the elephant, multiple video ViSER reconstructs a more plausible shape and recovers both the two rear limbs.
+
+Results. Fig. 4 shows visual reconstruction results on sample videos and for different techniques. ViSER estimates reconstructions that are more faithful to the input than the baselines, especially when the humans have unusual poses like in the first two rows. The accurate long-range correspondence enables ViSER to reconstruct finer details than LASR that does not explicitly try to estimate longrange correspondences. We summarize quantitative comparisons in Tab. 1. There is a moderate performance gap between ViSER and template-based methods when the input fits the latter, such as parkour with tight clothing and usual pose. Note that the supervised Densepose CSE and OpenPose methods fail on breakdance videos due to the novel pose, and also do not work well on ballet dancers due to loose clothing. As a result, template-based approaches that rely on accurate pose recognition, such as VIBE [18] fails. In contrast. our method does not suffer from such poor out-of-distribution generalization. By establishing long-range correspondences, ViSER achieves higher keypoint transfer accuracy and better 3D reconstruction than LASR.
+
+# 4.2 Reconstructing Animals from a Video
+
+We use BADJA [2] to evaluate ViSER on animal videos including camel, cow, dog, bear and horse. Similar to the athletic human video dataset, we compare against template-free methods such as LASR and neural-dense-NRSfM (N-NRSfM) [38]. Similar to LASR and our setup, N-NRSfM learns a video-specific model for object shape, deformation and camera parameters from multi-frame optical flow estimations [8]. We further report performance comparison with dense correspondence methods such as CSE and an optical flow method, VCN. We use the CSE model trained on corresponding animal categories (except that we use the horse model for camel), and the “robust” model of VCN [1], which is the input to our method. As shown in Tab. 3, ViSER achieves better or similar accuracy on all five animal videos compared to LASR and N-NRSfM. While the input optical flow is not robust at estimating long-range correspondences, our method integrates local optical flow to a dense long-range correspondences via a canonical shape, and achieves much better keypoint transfer accuracy. Note that CSE performs well for categories it has been trained on, such as cow, horse and bear, but performs poorly on novel animal categories, such as camel and a novel breed of dog.
+
+# 4.3 Multi-video Shape and Correspondence
+
+We curate a set of seven videos of different elephants from YTVOS [47] for multi-video shape and correspondence recovery. The annotations will be released for further research. We treat multiple videos as a single long video with strong appearance changes and shape variations. In the multi-video setup, We evaluate keypoint transfer accuracy on both the same instance (with video frames) and over different instances (across video frames), as denoted by “inner” and “across”. Quantitative results in Tab. 2 shows that ViSER is more accurate than the baseline methods in both cross-video keypoint transfer and inner-video keypoint transfer by a large margin, without using any keypoint annotations or pre-defined shape templates. Fig. 5 show visual result comparisons. While LASR recovers the visible surfaces in a video, it cannot infer the invisible parts. In contrast, our method is able to take advantage of multiple videos from the same category and produce a much better shape reconstruction. Note that LASR cannot handle multiple videos as it requires optical flow computed between every adjacent frame pairs. ViSER, on the other hand, also uses correspondences via estimated 3D shape, thereby allowing the use of multiple videos even when the optical flow is missing across videos.
+
+Table 4: Ablation study on keypoint transfer. Best results are in bold.   
+
+<table><tr><td>Method</td><td>break-1</td><td>elephants-inner</td><td>elephants-cross</td></tr><tr><td>Full</td><td>70.5</td><td>80.4</td><td>68.9</td></tr><tr><td>w/o matching loss Lmatching, Eq. (9)</td><td>36.2</td><td>51.3</td><td>42.6</td></tr><tr><td>w/o reprojection loss Lreproj, Eq. (10)</td><td>38.3</td><td>80.1</td><td>62.5</td></tr><tr><td>CSM regression [20]</td><td>47.1</td><td>77.4</td><td>63.3</td></tr></table>
+
+Benefit of Using Multiple Videos. To examine the benefits of using multiple videos, we further compare multi-video ViSER with single-video ViSER, as shown in Fig. 7. We find using multiple videos helps reconstructing the body parts that may be occluded in a single video.
+
+# 4.4 Part Discovery and Ablations
+
+Part discovery. ViSER can discover detailed 3D part segmentation without any manual annotation, as shown in Fig. 6. After training either on a collection of videos or a long video, ViSER can segment the 3D shape into meaningful parts, such as the trunk of the elephants and the feet of the dancer.
+
+Ablation study. We perform an ablation study on break-1 and elephants, as shown in Tab. 4. Without the contrastive matching loss, the pixel-surface embedding converges to a trivial solution with a significant decrease of accuracy. Removing the re-projection loss leads to much lower keypoint transfer (KPT) accuracy on the breakdance-1 sequence and cross-video KPT accuracy on the elephant videos. Likely the surface reprojection loss plays an important role in learning correct articulation that follows the bottom-up dense keypoint predictions. This may effectively avoid the local minimum issue for the differentiable rendering optimization. Finally, replacing the pixel-surface embedding with direct CSM regression [20] does not reason about distribution of possible matches and results in worse performance.
+
+Limitations. We find ViSER to be sensitive to the random initialization of network parameters. We run optimization with different random seeds for initializing the network parameters and find some perform considerably worse than the others, due to the convergence to bad local optima. Although in practice, one could spot the convergence to a bad local optimum by visualizing the articulated shapes and re-run the optimization with a different random seed, an automatic method for selecting the best model parameters over different trials is desired. We leave how to make the optimization of ViSER robust for future research.
+
+ViSER also relies on optical flow to kick-start with a reasonable initial shape and pose for learning pixel-surface embeddings. Although recent optical flow models generalize well in many scenarios, they may fail when a video is of low resolution or contains significant motion blur. In such challenging cases, using category shape and pose priors to initialize ViSER would be a promising direction.
+
+# 5 Conclusions
+
+We have introduced ViSER, a method to reconstruct articulate shapes, dense trajectories, and object parts from monocular videos. ViSER establishes long-range correspondence by matching 2D pixels to a canonical 3D mesh via learned video-specific surface embeddings. Experimental results show that ViSER, without a template shape or keypoint annotations, compares favorably against prior work on challenging human and animal videos. ViSER shows that it could be fruitful to reconstruct articulate shapes for categories in the wild, and we hope to see more work in this direction.
+
+Broader impact. ViSER has many potential applications, e.g., in robotics, AR/VR, and film industry, but may be used for malicious purposes, e.g., producing fake videos or extracting bio-metric information without prior consent. ViSER is only suitable to offline applications as it takes about several hours to process a 80-frame video on one NVIDIA P100 GPU.
+
+# Acknowledgments
+
+This work was supported by Google Cloud Platform (GCP) awards received from Google and the CMU Argo AI Center for Autonomous Vehicle Research. We thank William T. Freeman and many others from CMU and Google for valuable feedback.
+
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+# COUNTERING LANGUAGE DRIFT VIA GROUNDING
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+While reinforcement learning (RL) shows a lot of promise for natural language processing—e.g. when fine-tuning natural language systems for optimizing a certain objective—there has been little investigation into potential language drift: when an external reward is used to train a system, the agents’ communication protocol may easily and radically diverge from natural language. By re-casting translation as a communication game, we show that language drift indeed happens when pre-trained agents are fine-tuned with policy gradient methods. We contend that simply adding a “naturalness” constraint to the reward, e.g. by using language model log likelihood, does not fully address the issue, and argue that (perceptual) grounding is required. That is, while language model constraints impose syntactic conformity, they do not lead to semantic correspondence. Our experiments show that grounded models give the best communication performance, while retaining English syntax along with the ability to convey the intended semantics.
+
+# 1 INTRODUCTION
+
+In the summer of 2017, the internet was briefly abuzz with the mistaken viral message that a leading AI research lab had to “unplug its AI” because it “had gone rogue”. What had in fact happened was that two chatbots, under certain conditions, had, rather unsurprisingly, started diverging from their English training data and had instead reverted to their own ungrammatical communication protocol for solving a negotiation task (Lewis et al., 2017). Instead of saying something like “hats have no value for me” the system would starting saying things like “hat have zero to me to me to me to me”. As was soon made clear by the parties involved, this sort of language drift is to be expected if we are optimizing for an external reward, for example one based on whether or not two agents successfully accomplish a negotiation.
+
+While language drift is to be expected under external reward, it is natural to ask what we can do to avoid it. Consider policy gradient methods, for example, and suppose we sample an output sequence from an English language decoder for a given task: sampling a non-grammatical sequence might still be rewarded if we manage to solve the task (e.g., due to some correct words; or because an interlocutor understood us anyway, or guessed correctly), which would quickly move the decoder away (drifting) from English. If we were able to keep drift in check, we could maximize reward while retaining the “Englishness” of the decoder, with obvious benefits for interpretability and interaction with humans. That is, while search space size prohibits the direct usage of policy gradient methods for training natural language decoders from scratch, we could prevent pre-trained models from drifting while we optimize for the desired reward using policy gradients.
+
+Thus, the ability to stop policy gradient methods from diverging from natural language enables interesting long-term possibilities for exploration: imagine e.g. fine-tuning a pre-trained language model trained on large amounts of data, call it a “language module”, for a given generation task with limited data. When training chit-chat dialogue agents, for example, we often want to optimize for some very high-level reward, such as engagingness or consistency, with hardly enough data to learn simple English grammar. Or consider what might happen when we train agents using self-play to actively use natural language to change the other agent’s (mental) state, rather than having a model passively observe language usage in some corpus or dataset, as usually happens.
+
+In this work, we study the question of language drift. Drawing inspiration from Lee et al. (2018), we re-cast translation as a communication game. Two machine translation (MT) agents—i.e., encoderdecoder models with attention—are tasked with successfully translating source language sequences to the target language using a third pivot language as an intermediary. The communication channel (the output of the first agent’s decoder, which is fed to the second agent’s encoder as input) is updated via policy gradient methods to optimize for translating into the target language, effectively fine-tuning two separate pre-trained MT models via a pivot language.
+
+![](images/53614ee295bce2f819a6bb953e51c3e581ad69c269e32405f55577253146ce19.jpg)  
+Figure 1: Diagram of our communication game.
+
+While the subject of communication need not be language (e.g., for Lee et al. (2018), agents learn to translate by communicating about images), three-way translation via pivot is an excellent way for studying the current problem: we can check exactly to what extent the communicated sequence corresponds to both the intended meaning, as well as to the gold standard sequence. We can think of this setup as an agent aiming to communicate its state to another agent via some protocol—yet in this case, the mental states and intermediary communication protocol are completely interpretable.
+
+In what follows, we show that language drift happens, and quite dramatically so, when fine-tuning using policy gradients. We then show that the most intuitive way of solving this problem—adding an “Englishness” constraint, such as the log-probability assigned by a language model, to the reward function—does not in fact lead to the desired consequences. Indeed, there is nothing preventing such models from learning to translate “Two giraffes standing next to a white truck in the savanna” from French to German via “Democracy is a political system” as the English intermediary.
+
+Hence, we contend that what is missing is grounding: while language model constraints impose syntactic conformity, they do not lead to semantic correspondence. Humans don’t invent unique idiolects for every individual interlocutor, exactly because they are grounded: we share strong priors, social and behavioral norms, and a common sensorimotor experience of our physical environment. Thus, “not going rogue” means not only sticking to the prescribed language, but more importantly preserving meaning, which means staying grounded.
+
+Our experiments show that fine-tuning the communication channel with visual grounding leads to the highest communication performance $( \mathrm { F r  E n  D e } )$ ) as well as the best retention of original syntax and intended semantics. Our token frequency analysis corroborates our hypothesis, and shows that grounding is key for preserving the token frequency distribution of the pivot language (English).
+
+# 2 PRIOR WORK
+
+Our work is inspired by recent work in protocols or languages that emerge from multi-agent interaction (Lazaridou et al., 2017; Lee et al., 2018; Andreas et al., 2017; Evtimova et al., 2018; Kottur et al., 2017; Havrylov & Titov, 2017; Mordatch & Abbeel, 2017). Work on the emergence of language in multi-agent settings goes back a long way (Steels, 1997; Nowak & Krakauer, 1999; Kirby, 2001; Briscoe, 2002; Skyrms, 2010). In our case, we are specifically interested in tabula inscripta agents that are already pre-trained to generate natural language, and we are primarily concerned with keeping their language natural during further training.
+
+Reinforcement Learning (RL) has been applied to fine-tuning models for various natural language generation tasks, including summarization (Ranzato et al., 2015; Paulus et al., 2017), information retrieval (Nogueira & Cho, 2017), MT (Gu et al., 2017; Bahdanau et al., 2016) and dialogue (Li et al., 2017). Our work can be viewed as fine-tuning MT systems using an intermediary pivot language. In MT, there is a long line of work of pivot-based approaches, most notably Muraki (1986) and more recently with neural approaches (Wang et al., 2017; Cheng et al., 2017; Chen et al., 2018). There has also been work on using visual pivots directly (Hitschler et al., 2016; Nakayama & Nishida, 2017; Lee et al., 2018). Grounded language learning in general has been shown to give significant practical improvements in various natural language understanding tasks (Gella et al., 2017; Elliott & Kad´ ar, 2017; Chrupała et al., 2015; Kiela et al., 2017; K ´ ad´ ar et al., 2018). Meanwhile, Bowman ´ et al. (2016) found a powerful decoder to ignore the latent representation in VAEs for language.
+
+# 3 TASK AND MODELS
+
+We recast translation as a communication game involving two MT agents: $\mathrm { F r } {  } \mathrm { E n }$ and $\mathrm { E n } {  } \mathrm { D e }$ (see Figure 1). Our dataset consists of $N$ triples of aligned sentences $\{ \mathrm { F r } _ { i } , \mathrm { E n } _ { i } , \mathrm { D e } _ { i } \} _ { i = 1 } ^ { N }$ , where $\operatorname { E n } _ { i }$ is only used for evaluation. We first feed the French sentence $\mathrm { F r } _ { i }$ to Agent A, which generates an English message $\overline { { \mathrm { E n } _ { i } } }$ as output. Agent B is then trained to maximize the log likelihood of the ground truth German sentence given the English message, i.e. $\log p ( \mathrm { D e } _ { i } | \overline { { \mathrm { E n } _ { i } } } )$ . Agent A is trained using REINFORCE (Williams, 1992) with reward $R = \log p _ { B } ( { \bf D e } _ { i } | \overline { { \bf E n _ { i } } } )$ .1 This encourages Agent A to develop helpful communication policies for Agent B, and allows Agent B to adapt to Agent A’s new policies. In other words: communication via the pivot language (English) is a success if we are able to translate the intended source sequence (French) into the desired target sequence (German).
+
+Both agents are pre-trained individually before communication, meaning that we start off with English as an intermediate language in the early stages of the game. This work examines what happens to the intermediate language as we fine-tune the system jointly: will the agents keep communicating in English, or diverge? And if so, what can we do to prevent that from happening?
+
+# 3.1 AUXILIARY TASKS
+
+To help reduce the search space of intermediate languages, we use two auxiliary tasks: language modelling (LM) and image-caption retrieval (henceforth called the grounding model).
+
+Language Model Given a language model pre-trained on a standard English corpus, the log likelihood of the English message informs its general “Englishness”. We incorporate this into the reward for Agent A, so that it learns to send messages that are plausible English.2 Reward for Agent A is:
+
+$$
+R _ { \mathrm { L M } } = \log p _ { B } ( \mathrm { D e } _ { i } | \overline { { \mathrm { E n } _ { i } } } ) + \beta _ { L M } \log p _ { L M } ( \overline { { \mathrm { E n } _ { i } } } ) .
+$$
+
+Grounding Model Let us assume we have access to a set of images $\{ \mathrm { I m } \mathbf { g } _ { i } \}$ associated with each triple $\{ \mathrm { F r } _ { i } , \mathrm { E n } _ { i } , \mathrm { D e } _ { i } \}$ . Given a pre-trained image-caption retrieval model, such as ${ \mathrm { V S E } } { + } { + }$ (Faghri et al., 2018), the log likelihood of the image given the English message (and vice versa) informs how much the English message is grounded in the original semantic content (Kiela et al., 2017). We incorporate the ranking loss into Agent A’s reward.
+
+$$
+R _ { { \bf G } } = \log p _ { B } ( { \bf D e } _ { i } | \overline { { { \bf E } { \bf n } _ { i } } } ) + \beta _ { G } \log p _ { G } ( { \bf I m g } _ { i } | \overline { { { \bf E } { \bf n } _ { i } } } ) .
+$$
+
+Note that $\beta _ { L M } , \beta _ { G }$ are hyperparameters.
+
+# 3.2 TRAINING OBJECTIVE
+
+For brevity the $t$ -th token in the $i$ -th English sentence $\mathrm { E n } _ { i ; t }$ is abbreviated to $\mathrm { E n } _ { t }$ , and $\operatorname { E n } _ { i }$ to En.
+
+Policy Gradient Training At decoding timestep $t$ , Agent A takes an action (outputs token $\overline { { \mathrm { E n } _ { t } } }$ ) given an environment (previous hidden states and previous token $\overline { { \mathrm { E n } _ { t - 1 } } } )$ . It receives reward $R$ at the end of the sequence, from which we subtract a state-dependent baseline $\overline { { R _ { t } } }$ to reduce variance. Therefore, we maximize $( R - \overline { { R _ { t } } } ) \log p ( \overline { { \mathrm { E n } _ { t } } } | \overline { { \mathrm { E n } _ { < t } } } , \mathrm { F r } )$ . In addition, we employ entropy regularization on Agent A’s decoder to encourage exploration. Hence, Agent A’s overall objective function is given as:
+
+$$
+\mathbb { L } _ { A } = \alpha _ { \mathrm { p g } } ( R - \overline { { R } } _ { t } ) \log p ( \overline { { \mathrm { E n } _ { t } } } | \overline { { \mathrm { E n } _ { < t } } } , \mathrm { F r } ) + \alpha _ { \mathrm { e n t } } H ( p ( \overline { { \mathrm { E n } _ { t } } } | \overline { { \mathrm { E n } _ { < t } } } , \mathrm { F r } ) ) - \alpha _ { \mathrm { b } } \mathbf { M } \mathrm { S E } ( R , \overline { { R } } _ { t } ) ,
+$$
+
+where $H$ and MSE denote entropy and mean squared error losses.
+
+Cross Entropy Training Agent $\mathbf { B }$ is trained using standard cross entropy loss, i.e.
+
+$$
+\mathbb { L } _ { B } = \log p ( \mathrm { { D e } } _ { t } | { \mathrm { D e } } _ { < t } , \overline { { \mathrm { E n } } } ) .
+$$
+
+We jointly train both agents by maximizing $\mathbb { L } = \mathbb { L } _ { A } + \mathbb { L } _ { B }$
+
+# 4 EXPERIMENTAL SETTINGS
+
+In this section we provide the details of our experimental setup: a $\mathrm { F r }  \mathrm { X }  \mathrm { D e }$ translation task where the intermediate language X is initialized as English, and subsequently fine-tuned with policy gradient. On a trilingual corpus consisting of three languages (Fr, En and De), we can measure communication success with $\mathrm { F r } {  }$ De BLEU (Papineni et al., 2002), while $\mathrm { F r } {  } \mathrm { E n }$ BLEU informs how closely the intermediate language resembles English, at any given point during fine-tuning.
+
+Datasets Agents are initially pre-trained on IWSLT $\mathrm { F r } {  } \mathrm { E n }$ and $\mathrm { E n } {  } \mathrm { D e }$ . Fine-tuning is performed on Multi30k Task 1(Elliott et al., 2016). That is, importantly, there is no overlap in the pre-training data and the fine-tuning data. Multi30k Task 1 consists of $3 0 \mathrm { k }$ images and one caption per image in English, French, German and Czech (of which we only use the first three). For the English language model, we compare four different datasets: WikiText103, MS COCO and Flickr30k. The image-caption retrieval model is trained on Flickr30k: the same set of $3 0 \mathrm { k }$ images as Multi30k but containing 5 English captions per image. Following Faghri et al. (2018), we randomly crop training images at every epoch. We use 2048-dimensional final-layer features from a pretrained and fixed ResNet-152 (He et al., 2016).
+
+Preprocessing The same tokenization and vocabulary are used across different tasks and datasets. We lowercase and tokenize our corpora with Moses (Koehn et al., 2007) and use subword tokenization with Byte Pair Encoding (BPE) (Sennrich et al., 2016) with $1 0 \mathrm { k }$ merge operations. This allows us to use the same vocabulary across different models seamlessly (translation, language model, image-caption ranker model).
+
+Controlling the English message length When fine-tuning the agents, we observe that the length of English messages becomes excessively long. As Agent A has no explicit incentive to output the $\langle { \mathrm { E O S } } \rangle$ symbol, it tends to keep transmitting the same token repeatedly. Excessively long messages obscure evaluation of the communication protocol. For instance, BLEU score quickly deteriorates as the message length becomes longer, as it is a precision metric. When the message length is fixed, a drop in BLEU score will by necessity mean that the intermediate language has drifted away more. For this reason, we constrain the length of English messages to be no longer than the length of their French source sentence, or shorter if the model outputs the $\langle { \mathrm { E O S } } \rangle$ symbol early. Recall that Agent B is supervised to predict the $\langle \mathrm { E O S } \rangle$ symbol, so does not suffer from this issue.
+
+Model Architecture and Pretraining Our MT agents are standard sequence-to-sequence models with attention (Bahdanau et al., 2015) with unidirectional, 1-layer GRU with 256 hidden units and 256-dimensional embeddings. During initial pre-training on IWSLT, we early-stop based on BLEU score on the development set (tst2013). The best checkpoints give 34.05 BLEU and 21.94 BLEU on IWSLT $\mathrm { F r } {  } \mathrm { E n }$ and $\mathrm { E n } {  } \mathrm { D e }$ development sets with greedy decoding. For our value function, we use a 2-layer MLP with a ReLU nonlinearity.
+
+The language model is a 1-layer recurrent language model with 512 LSTM hidden units. The imagecaption retrieval model is a recently proposed ${ \mathrm { V S E } } { + } { + }$ model (Faghri et al., 2018), with unidirectional 1-layer GRU with 512 hidden units and a single fully connected layer from 2048-dimensional ResNet features to 512-dimensional GRU hidden states. We report the performance of the pretrained models used in our experiments in Tables 1, 2 and 3.
+
+Table 1: Translation performance of our pre-trained agents (BLEU)   
+
+<table><tr><td></td><td>IWSLT</td><td>Multi30k</td></tr><tr><td>Fr-→En</td><td>34.05</td><td>26.80</td></tr><tr><td>En→De</td><td>21.94</td><td>18.56</td></tr></table>
+
+Table 2: Development NLL of pretrained language models   
+
+<table><tr><td>WikiText103</td><td>3.51</td></tr><tr><td>MS COCO</td><td>2.66</td></tr><tr><td>Flickr30k</td><td>2.85</td></tr></table>
+
+Table 3: Retrieval results for our ${ \mathrm { V S E } } { + } { + }$ model on Flickr30k test set.   
+
+<table><tr><td></td><td>R@1</td><td>R@5</td><td>R@10</td></tr><tr><td>Caption</td><td>50.1</td><td>76.3</td><td>84.6</td></tr><tr><td>Image</td><td>35.7</td><td>65.3</td><td>75.9</td></tr></table>
+
+Training Details When fine-tuning our agents, we perform learning rate annealing and early stopping based on $\mathrm { F r {  } D e }$ BLEU (communication performance) on the Multi30k development set. We use Adam (Kingma & Ba, 2014) with initial learning rate of 0.001 and dropout (Srivastava et al., 2014) rate of 0.1. We grid search over learning rate schedule and reward coefficients $( \alpha _ { \mathrm { p g } } , \alpha _ { \mathrm { e n t r } } , \alpha _ { \mathbf { b } } , \beta _ { L M } , \beta _ { G } )$ .
+
+For our joint systems with policy gradient fine-tuning, we run every model three times with different random seeds and report averaged results (see Table 4).
+
+Baseline and Upper Bound Our main quantitative experiment has three baselines:
+
+• Pretrained checkpoints (on IWSLT).   
+• Ensembling $:$ Given Fr, we let Agent A generate $K$ English hypotheses with beam search, $\{ \overline { { \mathrm { E n } _ { j } } } \} _ { j = 1 } ^ { K }$ . Then, we let Agent B generate the German translation $\overline { { \mathrm { D e } } }$ using an ensemble of $K$ source sentences (Firat et al., 2016; Zoph & Knight, 2016).   
+• $\mathrm { F r } {  }$ En fixed $:$ We fix Agent A and only fine-tune Agent B using $\mathbb { L } _ { B }$ .
+
+Meanwhile, we also train an NMT model of the same architecture and size directly on the $\mathrm { F r } {  } \mathrm { D e }$ task in Multi30k Task 1. This serves as an upper bound on the $\mathrm { F r  D e }$ performance achievable with available data.
+
+# 5 QUANTITATIVE RESULTS
+
+Table 4: Results in BLEU score on Multi30k Task 1. For our models using policy gradient fine-tuning, we report results averaged over three runs and provide standard deviations in brackets. PG: trained with vanilla policy gradient fine-tuning. $_ \mathrm { P G + L M }$ : trained with the “Englishness” constraint in reward. For MS COCO and Flickr30k, the LM was trained directly on image captions. $\mathrm { P G } { + } \mathrm { L M } { + } \mathrm { G }$ : trained with grounding loss as well as the LM loss. $\mathrm { F r } {  } \mathrm { E n }$ : degree of intermediate language drift from English; lower indicates more drift. $\mathrm { F r }  \mathrm { E n }  \mathrm { D e }$ : metric for communication accuracy; higher is better. All: LM was trained on all three datasets combined. Improvements of $\mathrm { P G } { + } \mathrm { L M } { + } \mathrm { G }$ over $_ { \mathrm { P G + L M } }$ were found to be significant in all cases, using the approximate randomization test for significance testing (Riezler & Maxwell III, 2005).   
+
+<table><tr><td></td><td>LM</td><td>Ranker</td><td>Fr-→En</td><td>Fr→En→De</td></tr><tr><td>Pretrained</td><td></td><td></td><td>27.18</td><td>16.30</td></tr><tr><td>Ensembling</td><td></td><td></td><td></td><td>16.95</td></tr><tr><td>Fr-→En fixed</td><td></td><td></td><td>27.18</td><td>22.37</td></tr><tr><td>PG</td><td>No LM</td><td></td><td>12.38 (0.67)</td><td>24.51 (1.48)</td></tr><tr><td rowspan="4">PG+LM</td><td>WikiText103</td><td></td><td>21.63 (1.25)</td><td>26.88 (0.12)</td></tr><tr><td>MS COCO</td><td></td><td>25.05 (1.40)</td><td>27.66 (0.34)</td></tr><tr><td>Flickr30k</td><td></td><td>24.85 (1.14)</td><td>27.60 (0.27)</td></tr><tr><td>All</td><td></td><td>23.60 (1.05)</td><td>27.67 (0.39)</td></tr><tr><td rowspan="5">PG+LM+G</td><td>No LM</td><td>1</td><td>14.20 (1.58)</td><td>26.23 (1.08)</td></tr><tr><td>WikiText103</td><td></td><td>23.65 (1.91)</td><td>27.87 (0.15)</td></tr><tr><td>MS COCO</td><td>v</td><td>26.24 (0.28)</td><td>27.86 (0.24)</td></tr><tr><td>Flickr30k</td><td>←</td><td>25.99 (1.62)</td><td>27.82 (0.41)</td></tr><tr><td>All</td><td>专</td><td>24.75 (0.40)</td><td>28.08 (0.73)</td></tr><tr><td>Fr→De</td><td></td><td></td><td></td><td>30.73</td></tr></table>
+
+In Table 4, the top three rows are our baselines. The pretrained model performs relatively poorly on $\mathrm { F r {  } D e }$ , conceivably because it was pretrained on a different corpus, and Agent B was was given Agent A’s output as source. Ensembling multiple English hypotheses for Agent B (row 2) gives negligible increase in $\mathrm { F r {  } D e }$ performance. When only Agent B is fine-tuned, we observe 6 BLEU score increase in $\mathrm { F r } {  } \mathrm { D e }$ .
+
+When the joint system is fine-tuned on German log likelihood with policy gradients (PG), we observe a large, 8 BLEU increase increase in $\mathrm { F r {  } D e }$ at the cost of a substanstial, 15 BLEU score drop in $\mathrm { F r } {  } \mathrm { E n }$ . This clearly shows that optimizing on some external reward causes a drastic language drift.
+
+![](images/2e6473a16038c59a8aaa522125782b8b39bf55d63c60d9db4ff14d556179de4a.jpg)  
+Figure 2: Learning curves for PG, $_ \mathrm { P G + L M }$ and $\mathrm { P G + L M + G }$ . En LM NLL curves show the NLL of English messages, computed by a language model trained on WikiText103. Lower En BLEU indicates more language drift, and higher En LM NLL indicates more language drift.
+
+When the agent is trained with the “Englishness” constraint $( \mathrm { P G + L M } )$ , we notice a significant improvement in $\mathrm { F r } {  } \mathrm { E n }$ BLEU. When the LM is trained on WikiText103, a widely used language modelling dataset, we observe improvement of 9 BLEU scores. When the training corpus is closer to the target domain, such as MS COCO or Flickr30k, we see more than 10 BLEU score increase. $\mathrm { F r {  } D e }$ translation also improves by 2–3 BLEU scores.
+
+However, we see the biggest improvements in performance when agents are trained using visual grounding feedback. This is particularly pronounced with the LM trained on WikiText103: introducing visual grounding leads to more than 2 BLEU score improvement in $\mathrm { F r } {  } \mathrm { E n }$ , and 1 BLEU score improvement in $\mathrm { F r } {  } \mathrm { D e }$ . We hypothesize that the “Englishness” constraint forces agents to communicate with correct syntax and fluency, while the image-caption retrieval model restricts the search space of languages to ones that are grounded by visual semantics. To see if grounding is really necessary, we train a stronger LM on all three datasets combined, but find this still leads to more language drift than using visual grounding: the $\mathrm { P G } { + } \mathrm { L M } { + } \mathrm { G }$ model with the LM trained on MS COCO outperforms this by 3 BLEU scores on $\mathrm { F r } {  } \mathrm { E n }$ .
+
+In Figure 2, we observe that vanilla PG fine-tuning quickly leads to highly “un-English” communication, as can be seen from a distinct increase in LM NLL. It is also worth noting that while $\mathrm { P G } { + } \mathrm { L M }$ achieves better LM NLL than $\mathrm { P G } { + } \mathrm { L M } { + } \mathrm { G }$ , it gives much lower $\mathrm { F r } {  } \mathrm { E n }$ BLEU score than the grounded model $\mathbf { \left( P G + L M + G \right) }$ ). This is another indication that simply encouraging naturalness is not enough; grounding is key.
+
+A close investigation into the token statistics of each communication strategy reveals that PG finetuning causes the word frequency distribution to be flatter. The PG model has negative frequency difference values for the most frequent tokens, indicating that PG downweighs frequent words severely. On the other hand, $\mathrm { P G + L M }$ gives highly positive frequency differences, meaning that language modelling alone disproportionately emphasizes frequent tokens. Visual grounding keeps the token frequency distribution close to the original pretrained regimes. Analyzing the top- $\mathbf { \nabla } \cdot \mathbf { k }$ most frequent
+
+![](images/bf2a3c8025d92e906f110c433c6960b32090a0846ae259233c5305646f5999a4.jpg)  
+Figure 3: Token frequency analysis on three different models (PG, $_ \mathrm { P G + L M }$ , $\mathrm { P G + L M + G }$ ) as well as the pretrained model before any fine-tuning (Pretrained). We show the word frequency curves (sorted in decreasing order) for each model, after subtracting the reference English frequency statistics (also sorted). Positive y values indicate higher frequency values than the English reference, and negative y values indicate lower frequency values than English. Note that y-axis is the frequency difference in thousands, and $\mathbf { X }$ -axis shows the vocabulary index (sorted with frequency) in log scale.
+
+words shows that $\mathrm { P G } { + } \mathrm { L M }$ disproportionately favors quotation marks, which are very common tokens in many language modelling datasets but occur rarely in Multi30k (see also Appendix A).   
+Table 5: Additional token frequency analysis. unique: the number of unique English tokens used in the whole development set. /sent: the number of unique English tokens used per sentence. /all: (the number of unique English tokens / the number of all English tokens.)   
+
+<table><tr><td></td><td colspan="3">IWSLT</td><td colspan="3">Multi30k</td></tr><tr><td></td><td>unique</td><td>/sent</td><td>/all</td><td>unique</td><td>/sent</td><td>/all</td></tr><tr><td>Reference</td><td>5,303</td><td>19.7</td><td>0.86</td><td>3,046</td><td>11.9</td><td>0.91</td></tr><tr><td>Pretrained</td><td>4,657</td><td>17.9</td><td>0.85</td><td>2,867</td><td>12.0</td><td>0.87</td></tr><tr><td>PG</td><td>4,933</td><td>13.6</td><td>0.56</td><td>3,197</td><td>9.2</td><td>0.65</td></tr><tr><td>PG+LM</td><td>3,819</td><td>14.6</td><td>0.61</td><td>2,438</td><td>10.9</td><td>0.78</td></tr><tr><td>PG+LM+G</td><td>4,327</td><td>15.7</td><td>0.74</td><td>2,550</td><td>10.7</td><td>0.84</td></tr></table>
+
+Table 5 reinforces the finding that vanilla PG fine-tuning leads to flatter token frequency distributions, as the number of unique tokens used by PG is greater than that of the pretrained model. Meanwhile, $\mathrm { P G + L M }$ uses fewer tokens overall, signifying that it uses a relatively small set of tokens frequently.
+
+Also note that PG, despite using a more diverse set of tokens, uses the smallest number of unique symbols per sentence (/sent) and overall (/all). This implies that PG communication is often repetitive. Introducing extra tasks seems to mitigate this, and the grounded model $\mathrm { ( P G + L M + G }$ ) learns a frequency distribution that most closely resembles the original distribution.
+
+To gain further insight into the agents’ communication protocols, we compare the degree of drift by part-of-speech. Table 6 shows that PG tends to ignore function words, such as periods and infinitives. Models trained with LM and grounding losses retain function words with much higher accuracy. PG fares relatively better with content words (nouns and verbs), but adding LM and grounding losses still outperform PG. Grounding leads to overall improvements in recall, particularly with content words.
+
+Conceivably, when optimizing Agent A’s policy on the communication task alone, it is more crucial to relay content information to Agent B, and this might cause agents to ignore syntactic conformity in the original intermediate language. We argue that LM and grounding reduces the space of intermediate languages to a much reasonable language space, facilitating learning.
+
+# 6 QUALITATIVE RESULTS
+
+In the first example of Table 7, it is clear that PG’s English message has significantly diverged from English: it is highly repetitive (“table table table table table”) and is missing some key content words such as “man” and “jacket”. However, Agent B still generates the German word for ‘man’. The grounded model’s message $\mathbf { \Gamma } ( \mathbf { P G + L M + G }$ ) is distinctly the most fluent and semantically correct.
+
+In the second example, observe that the PG Agent B misinterprets “talking talking a coach a coach” into “spricht mit einem spieler” (talking to a player). The $\mathrm { P G } { + } \mathrm { L M } { + } \mathrm { G }$ model again generates a flawless English sentence. Also note that it communicates both colors (red and white) successfully from French to German, while the other two models fail to do so.
+
+Table 6: Exact-match word recall by POS-tag on IWSLT development set: when the English reference contains a word of a certain POS tag, how often does the agent correctly produces that word. TO: infinitive to, (.): period, DT: determiner, Noun: (NN, NNS, NNP, NNPS), Verb: (VB, VBD, VBG, VBN, VBP, VBZ), Adj: adjective (JJ, JJR, JJS), Adv: adverb (RB, RBR, RBS)   
+
+<table><tr><td></td><td colspan="3">Function words</td><td colspan="4">Content words</td></tr><tr><td></td><td>TO</td><td>：</td><td>DT</td><td>Noun</td><td>Verb</td><td>Adj</td><td>Adv</td></tr><tr><td>PG</td><td>0.22</td><td>0.36</td><td>0.57</td><td>0.38</td><td>0.17</td><td>0.32</td><td>0.26</td></tr><tr><td>PG+LM</td><td>0.55</td><td>0.84</td><td>0.72</td><td>0.39</td><td>0.18</td><td>0.21</td><td>0.25</td></tr><tr><td>PG+LM+G</td><td>0.62</td><td>0.88</td><td>0.74</td><td>0.43</td><td>0.26</td><td>0.33</td><td>0.29</td></tr></table>
+
+![](images/b8bd9351b4fea398c0d397a493640b4af135973616c5c8b1d5f10437ca4bcc25.jpg)
+
+![](images/4726323f7f35665892b7da69121761a1df8453ebbbde432c6c2e91c381fc4bf2.jpg)
+
+Table 7: Two random examples from Multi30k development set with different models (PG, $\mathrm { P G + L M } .$ , $\mathrm { P G + L M + G }$ . The top three rows list the ground truth sentences, the middle three rows are the English messages sent by the $\mathrm { F r } {  } \mathrm { E n }$ agent, and the bottom three rows show the German output from the $\mathrm { E n } {  } \mathrm { D e }$ agent. We also show the corresponding images, which were only used to train the image-caption retrieval modal.   
+
+<table><tr><td>Ref</td><td>Fr De En</td><td>un vieil homme vétu d&#x27;une veste noire regarde sur la table ein alter mann in einer schwarzen jacke blickt auf den tisch an old man wearing a black jacket is looking on the table</td></tr><tr><td>En</td><td>PG +LM +G</td><td>a old teaching black watching on the table table table table table table a old man in a jacket looking on the table .”” an old man in a black jacket looking on the table .</td></tr><tr><td>De</td><td>PG +LM +G</td><td>ein älterer mann in einem schwarzen hemd schaut auf den tisch. einalter mann in einer jacke beobachtet einen tisch . ein älterer mann in einer schwarzen jacke schaut auf den tisch .</td></tr><tr><td>Ref</td><td>Fr De En</td><td>un joueur de football américain en blanc et rouge parle â un entraineur . einrot-weiB gekleideter footballspieler spricht mit einem trainer . a football player in red and white is talking to a coach .</td></tr><tr><td>En</td><td>PG +LM +G PG</td><td>a player football american football american and red talking talking a coach a player of white and red talking to a coach .””” a football player in white and red talking to a coach . ein footballspieler spricht mit einem spieler in einem roten trikot .</td></tr><tr><td>De</td><td>+LM +G</td><td>ein weiB gekleideter fuBballspieler spricht zu einem trainer. ein fuBballspieler in einem rot-weiBen trikot spricht mit einem trainer .</td></tr></table>
+
+![](images/e5a1c81ab55fbbd4fc089d67ea7e21f83e1026db91dcd7e04eda1ef185ccb23d.jpg)
+
+Table 8: Evidence of token flipping in the PG model.   
+
+<table><tr><td>Fr src En ref En hyp De ref De hyp Fr src</td><td>un enfant assis sur un rocher. a child sitting on a rock formation. a punk sitting sitting on on a broken ein kind sitzt auf einem felsen. ein kind sitzt auf einem felsen .</td></tr></table>
+
+We observe some instances of token flipping with the PG model. For example, one particular PG model uses “punk” to describe “child” (see Table 8). As no occurrence of “punk” in any training data is associated with “child”, the agents must have acquired this new meaning assignment during fine-tuning. Among 35 examples in Multi30k development set where the English reference contains “child”, the model uses “punk” 15 times, indicating this is no random phenomenon. We show similar examples from the $\mathrm { P G } { + } \mathrm { L M }$ model in Appendix B. We did not observe such examples with the $\mathrm { P G } { + } \mathrm { L M } { + } \mathrm { G }$ model.
+
+# 7 CONCLUSION
+
+In this paper, we show that language drift happens when fine-tuning natural language agents with some external (non-linguistic) reward using policy gradients, and propose a few approaches to avoid this. Most importantly, we find that simply encouraging “naturalness”, e.g. via adding a language model log likelihood to the reward, does not lead to the desired consequences. Instead, we contend that grounding is what we need to avoid language drift. Our empirical results show that grounding leads to best communication performance (highest $\mathrm { F r {  } D e }$ BLEU), while also showing least signs of language drift (highest $\mathrm { F r } {  } \mathrm { E n }$ BLEU). Analyzing token frequencies in exchanged messages reveals that pure PG finetuning tends to learn flatter token distributions, and encouraging naturalness disproportionately emphasizes frequent tokens, while the grounded model best retains the original token frequencies.
+
+# ACKNOWLEDGMENTS
+
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+
+# A FREQUENCY ANALYSIS
+
+![](images/9e511079724de538a32385cc7d00d066fef883bd26a28323d6a23aff275760a7.jpg)  
+Figure 4: Token frequency analysis similar to Figure 3, but with the $\mathbf { X }$ -axis fixed to the token indices sorted with respect to English reference, in decreasing order.
+
+In Figure 4, where the $\mathbf { X }$ -axis is fixed to the token indices sorted with respect to the English reference, we observe that the $_ { \mathrm { P G + L M } }$ model does indeed favor one word particularly strongly. From investigating top- $\mathbf { \nabla } \cdot \mathbf { k }$ most frequent tokens in each model, we find that quotation mark is the most common token for $\mathrm { P G } { + } \mathrm { L M }$ in both datasets we experimented with. It is plausible that quotation marks occur with high frequency in language modelling datasets, causing them to be disproportionately overweighed during fine-tuning.
+
+Table 9: Top 20 most frequent tokens in English reference (Reference) or the output from $\mathrm { F r } {  } \mathrm { E n }$ models.   
+
+<table><tr><td colspan="2">IWSLT</td></tr><tr><td>Reference Pretrained PG PG+LM PG+LM+G</td><td>,. the and to of a that i in is it you we &amp;apos;s this &amp;quot; , the .to of and a i that in it we you &amp;apos;s is this &amp;quot; was a the and ,. in i &amp;quot; this of to is we you ? that not for &amp;quot; the ,of .and in a to this is i es you for we that with the ，. of a and to in is i this es we for that you at what</td></tr><tr><td colspan="2">Multi30k</td></tr></table>
+
+![](images/cdc9523d1fd0a40d08c8cb48cf753b771e9f9b219b763ce2e343543a98889b45.jpg)  
+Figure 5: Token frequency curves (before subtracting the reference frequencies). Both $\mathbf { X }$ (vocabulary index) and y (frequency) axes are in log scale.
+
+In Figure 5, we show the token frequency curves before subtracting the reference frequencies. Similarly to Figure 4, we observe that the PG model discourages frequent (mostly functional) words, while the $\mathrm { P G + L M }$ model excessively prefers frequent words.
+
+# B EVIDENCE OF TOKEN FLIPPING IN THE PG+LM MODEL
+
+![](images/8610b3cd658e44b02f9aebeb193fb86d3b8c66dec8b2faf3ffd2fc745d7d06e8.jpg)
+
+Table 10: Evidence of token flipping in the $\mathrm { P G + L M }$ model.   
+
+<table><tr><td>Fr src En ref En hyp De ref</td><td>un caniche noir joue avec un autre chien sur un terrain sec. a black poodle plays with another dog in a dry field . a canblack on a day,a day,a day,a day,</td></tr></table>
+
+Similar to Table 8, we find evidence of token flipping for the $\mathrm { P G + L M }$ model, where the agents use “can $@ ( a ) ^ { , }$ ( $@ \textcircled{ a }$ is a subword BPE token marker) to mean “poodle”. This shows that language drift still happens even when a language model is used.

md/train/gZ9hCDWe6ke/gZ9hCDWe6ke.md

@@ -0,0 +1,308 @@
+# DEFORMABLE DETR: DEFORMABLE TRANSFORMERS FOR END-TO-END OBJECT DETECTION
+
+Xizhou $\mathbf { Z } \mathbf { h } \mathbf { u } ^ { 1 * }$ , Weijie $\mathbf { S } \mathbf { u } ^ { 2 * \ddagger }$ , Lewei ${ { \bf L } } { \bf u } ^ { 1 }$ , Bin $\mathbf { L i } ^ { 2 }$ , Xiaogang Wang $^ { 1 , 3 }$ , Jifeng Dai1†
+
+1SenseTime Research   
+2University of Science and Technology of China   
+3The Chinese University of Hong Kong   
+{zhuwalter,luotto,daijifeng}@sensetime.com   
+jackroos@mail.ustc.edu.cn, binli@ustc.edu.cn   
+xgwang@ee.cuhk.edu.hk
+
+# ABSTRACT
+
+DETR has been recently proposed to eliminate the need for many hand-designed components in object detection while demonstrating good performance. However, it suffers from slow convergence and limited feature spatial resolution, due to the limitation of Transformer attention modules in processing image feature maps. To mitigate these issues, we proposed Deformable DETR, whose attention modules only attend to a small set of key sampling points around a reference. Deformable DETR can achieve better performance than DETR (especially on small objects) with $1 0 \times$ less training epochs. Extensive experiments on the COCO benchmark demonstrate the effectiveness of our approach. Code is released at https:// github.com/fundamentalvision/Deformable-DETR.
+
+# 1 INTRODUCTION
+
+Modern object detectors employ many hand-crafted components (Liu et al., 2020), e.g., anchor generation, rule-based training target assignment, non-maximum suppression (NMS) post-processing. They are not fully end-to-end. Recently, Carion et al. (2020) proposed DETR to eliminate the need for such hand-crafted components, and built the first fully end-to-end object detector, achieving very competitive performance. DETR utilizes a simple architecture, by combining convolutional neural networks (CNNs) and Transformer (Vaswani et al., 2017) encoder-decoders. They exploit the versatile and powerful relation modeling capability of Transformers to replace the hand-crafted rules, under properly designed training signals.
+
+Despite its interesting design and good performance, DETR has its own issues: (1) It requires much longer training epochs to converge than the existing object detectors. For example, on the COCO (Lin et al., 2014) benchmark, DETR needs 500 epochs to converge, which is around 10 to 20 times slower than Faster R-CNN (Ren et al., 2015). (2) DETR delivers relatively low performance at detecting small objects. Modern object detectors usually exploit multi-scale features, where small objects are detected from high-resolution feature maps. Meanwhile, high-resolution feature maps lead to unacceptable complexities for DETR. The above-mentioned issues can be mainly attributed to the deficit of Transformer components in processing image feature maps. At initialization, the attention modules cast nearly uniform attention weights to all the pixels in the feature maps. Long training epoches is necessary for the attention weights to be learned to focus on sparse meaningful locations. On the other hand, the attention weights computation in Transformer encoder is of quadratic computation w.r.t. pixel numbers. Thus, it is of very high computational and memory complexities to process high-resolution feature maps.
+
+In the image domain, deformable convolution (Dai et al., 2017) is of a powerful and efficient mechanism to attend to sparse spatial locations. It naturally avoids the above-mentioned issues. While it lacks the element relation modeling mechanism, which is the key for the success of DETR.
+
+![](images/ac1a46c037234d475045a6be7626e2adbd10dfddcdc0be35c4f5fb8277a23e7a.jpg)  
+Figure 1: Illustration of the proposed Deformable DETR object detector.
+
+In this paper, we propose Deformable DETR, which mitigates the slow convergence and high complexity issues of DETR. It combines the best of the sparse spatial sampling of deformable convolution, and the relation modeling capability of Transformers. We propose the deformable attention module, which attends to a small set of sampling locations as a pre-filter for prominent key elements out of all the feature map pixels. The module can be naturally extended to aggregating multi-scale features, without the help of FPN (Lin et al., 2017a). In Deformable DETR , we utilize (multi-scale) deformable attention modules to replace the Transformer attention modules processing feature maps, as shown in Fig. 1.
+
+Deformable DETR opens up possibilities for us to exploit variants of end-to-end object detectors, thanks to its fast convergence, and computational and memory efficiency. We explore a simple and effective iterative bounding box refinement mechanism to improve the detection performance. We also try a two-stage Deformable DETR, where the region proposals are also generated by a vaiant of Deformable DETR, which are further fed into the decoder for iterative bounding box refinement.
+
+Extensive experiments on the COCO (Lin et al., 2014) benchmark demonstrate the effectiveness of our approach. Compared with DETR, Deformable DETR can achieve better performance (especially on small objects) with $1 0 \times$ less training epochs. The proposed variant of two-stage Deformable DETR can further improve the performance. Code is released at https://github. com/fundamentalvision/Deformable-DETR.
+
+# 2 RELATED WORK
+
+Efficient Attention Mechanism. Transformers (Vaswani et al., 2017) involve both self-attention and cross-attention mechanisms. One of the most well-known concern of Transformers is the high time and memory complexity at vast key element numbers, which hinders model scalability in many cases. Recently, many efforts have been made to address this problem (Tay et al., 2020b), which can be roughly divided into three categories in practice.
+
+The first category is to use pre-defined sparse attention patterns on keys. The most straightforward paradigm is restricting the attention pattern to be fixed local windows. Most works (Liu et al., 2018a; Parmar et al., 2018; Child et al., 2019; Huang et al., 2019; Ho et al., 2019; Wang et al., 2020a; Hu et al., 2019; Ramachandran et al., 2019; Qiu et al., 2019; Beltagy et al., 2020; Ainslie et al., 2020; Zaheer et al., 2020) follow this paradigm. Although restricting the attention pattern to a local neighborhood can decrease the complexity, it loses global information. To compensate, Child et al. (2019); Huang et al. (2019); Ho et al. (2019); Wang et al. (2020a) attend key elements at fixed intervals to significantly increase the receptive field on keys. Beltagy et al. (2020); Ainslie et al. (2020); Zaheer et al. (2020) allow a small number of special tokens having access to all key elements. Zaheer et al. (2020); Qiu et al. (2019) also add some pre-fixed sparse attention patterns to attend distant key elements directly.
+
+The second category is to learn data-dependent sparse attention. Kitaev et al. (2020) proposes a locality sensitive hashing (LSH) based attention, which hashes both the query and key elements to different bins. A similar idea is proposed by Roy et al. (2020), where k-means finds out the most related keys. Tay et al. (2020a) learns block permutation for block-wise sparse attention.
+
+The third category is to explore the low-rank property in self-attention. Wang et al. (2020b) reduces the number of key elements through a linear projection on the size dimension instead of the channel dimension. Katharopoulos et al. (2020); Choromanski et al. (2020) rewrite the calculation of selfattention through kernelization approximation.
+
+In the image domain, the designs of efficient attention mechanism (e.g., Parmar et al. (2018); Child et al. (2019); Huang et al. (2019); Ho et al. (2019); Wang et al. (2020a); Hu et al. (2019); Ramachandran et al. (2019)) are still limited to the first category. Despite the theoretically reduced complexity, Ramachandran et al. (2019); Hu et al. (2019) admit such approaches are much slower in implementation than traditional convolution with the same FLOPs (at least $3 \times$ slower), due to the intrinsic limitation in memory access patterns.
+
+On the other hand, as discussed in Zhu et al. (2019a), there are variants of convolution, such as deformable convolution (Dai et al., 2017; Zhu et al., 2019b) and dynamic convolution (Wu et al., 2019), that also can be viewed as self-attention mechanisms. Especially, deformable convolution operates much more effectively and efficiently on image recognition than Transformer self-attention. Meanwhile, it lacks the element relation modeling mechanism.
+
+Our proposed deformable attention module is inspired by deformable convolution, and belongs to the second category. It only focuses on a small fixed set of sampling points predicted from the feature of query elements. Different from Ramachandran et al. (2019); Hu et al. (2019), deformable attention is just slightly slower than the traditional convolution under the same FLOPs.
+
+Multi-scale Feature Representation for Object Detection. One of the main difficulties in object detection is to effectively represent objects at vastly different scales. Modern object detectors usually exploit multi-scale features to accommodate this. As one of the pioneering works, FPN (Lin et al., 2017a) proposes a top-down path to combine multi-scale features. PANet (Liu et al., 2018b) further adds an bottom-up path on the top of FPN. Kong et al. (2018) combines features from all scales by a global attention operation. Zhao et al. (2019) proposes a U-shape module to fuse multi-scale features. Recently, NAS-FPN (Ghiasi et al., 2019) and Auto-FPN (Xu et al., 2019) are proposed to automatically design cross-scale connections via neural architecture search. Tan et al. (2020) proposes the BiFPN, which is a repeated simplified version of PANet. Our proposed multi-scale deformable attention module can naturally aggregate multi-scale feature maps via attention mechanism, without the help of these feature pyramid networks.
+
+# 3 REVISITING TRANSFORMERS AND DETR
+
+Multi-Head Attention in Transformers. Transformers (Vaswani et al., 2017) are of a network architecture based on attention mechanisms for machine translation. Given a query element (e.g., a target word in the output sentence) and a set of key elements (e.g., source words in the input sentence), the multi-head attention module adaptively aggregates the key contents according to the attention weights that measure the compatibility of query-key pairs. To allow the model focusing on contents from different representation subspaces and different positions, the outputs of different attention heads are linearly aggregated with learnable weights. Let $q \in \Omega _ { q }$ indexes a query element with representation feature $z _ { q } \in \mathbb { R } ^ { C }$ , and $k \in \Omega _ { k }$ indexes a key element with representation feature $\pmb { x } _ { k } \in \mathbb { R } ^ { C }$ , where $C$ is the feature dimension, $\Omega _ { q }$ and $\Omega _ { k }$ specify the set of query and key elements, respectively. Then the multi-head attention feature is calculated by
+
+$$
+\mathrm { M u l t i H e a d A t t n } ( z _ { q } , \pmb { x } ) = \sum _ { m = 1 } ^ { M } W _ { m } \big [ \sum _ { k \in \Omega _ { k } } A _ { m q k } \cdot W _ { m } ^ { \prime } \pmb { x } _ { k } \big ] ,
+$$
+
+where $m$ indexes the attention head, $W _ { m } ^ { \prime } \in \mathbb { R } ^ { C _ { v } \times C }$ and $W _ { m } \in \mathbb { R } ^ { C \times C _ { v } }$ are of learnable weights $( C _ { v } = C / M$ by default). The attention weights $\begin{array} { r } { A _ { m q k } \ \propto \ \exp \{ \frac { z _ { q } ^ { T } U _ { m } ^ { T } \ : V _ { m } \ : x _ { k } } { \sqrt { C _ { v } } } \} } \end{array}$ { zTq UTm Vmxk √ } are normalized as $\sum _ { k \in \Omega _ { k } } A _ { m q k } = 1$ , in which $U _ { m } , V _ { m } \in \mathbb { R } ^ { C _ { v } \times C }$ are also learnable weights. To disambiguate kdifferent spatial positions, the representation features $z _ { q }$ and $\scriptstyle { \mathbf { { \mathit { x } } } } _ { k }$ are usually of the concatenation/summation of element contents and positional embeddings.
+
+There are two known issues with Transformers. One is Transformers need long training schedules before convergence. Suppose the number of query and key elements are of $N _ { q }$ and $N _ { k }$ , respectively. Typically, with proper parameter initialization, $U _ { m } z _ { q }$ and $V _ { m } \mathbf { x } _ { k }$ follow distribution with mean of 0 and variance of 1, which makes attention weights $\begin{array} { r } { A _ { m q k } \approx \frac { 1 } { N _ { k } } } \end{array}$ , when $N _ { k }$ is large. It will lead to ambiguous gradients for input features. Thus, long training schedules are required so that the attention weights can focus on specific keys. In the image domain, where the key elements are usually of image pixels, $N _ { k }$ can be very large and the convergence is tedious.
+
+On the other hand, the computational and memory complexity for multi-head attention can be very high with numerous query and key elements. The computational complexity of Eq. 1 is of $O ( \bar { N } _ { q } \bar { C ^ { 2 } } + N _ { k } C ^ { 2 } + N _ { q } \bar { N _ { k } C } )$ . In the image domain, where the query and key elements are both of pixels, $N _ { q } = N _ { k } \gg C$ , the complexity is dominated by the third term, as $O ( N _ { q } N _ { k } C )$ . Thus, the multi-head attention module suffers from a quadratic complexity growth with the feature map size.
+
+DETR. DETR (Carion et al., 2020) is built upon the Transformer encoder-decoder architecture, combined with a set-based Hungarian loss that forces unique predictions for each ground-truth bounding box via bipartite matching. We briefly review the network architecture as follows.
+
+Given the input feature maps $\pmb { x } \in \mathbb { R } ^ { C \times H \times W }$ extracted by a CNN backbone (e.g., ResNet (He et al., 2016)), DETR exploits a standard Transformer encoder-decoder architecture to transform the input feature maps to be features of a set of object queries. A 3-layer feed-forward neural network (FFN) and a linear projection are added on top of the object query features (produced by the decoder) as the detection head. The FFN acts as the regression branch to predict the bounding box coordinates $\pmb { b } \in [ 0 , 1 ] ^ { 4 }$ , where $\boldsymbol { b } = \{ b _ { x } , b _ { y } , b _ { w } , b _ { h } \}$ encodes the normalized box center coordinates, box height and width (relative to the image size). The linear projection acts as the classification branch to produce the classification results.
+
+For the Transformer encoder in DETR, both query and key elements are of pixels in the feature maps. The inputs are of ResNet feature maps (with encoded positional embeddings). Let $H$ and $W$ denote the feature map height and width, respectively. The computational complexity of self-attention is of $O ( H ^ { 2 } W ^ { 2 } C )$ , which grows quadratically with the spatial size.
+
+For the Transformer decoder in DETR, the input includes both feature maps from the encoder, and $N$ object queries represented by learnable positional embeddings (e.g., $N = 1 0 0$ ). There are two types of attention modules in the decoder, namely, cross-attention and self-attention modules. In the cross-attention modules, object queries extract features from the feature maps. The query elements are of the object queries, and key elements are of the output feature maps from the encoder. In it, $N _ { q } = N$ , $N _ { k } = H \times W$ and the complexity of the cross-attention is of $O ( H W C ^ { 2 } + N H W C )$ . The complexity grows linearly with the spatial size of feature maps. In the self-attention modules, object queries interact with each other, so as to capture their relations. The query and key elements are both of the object queries. In it, $N _ { q } = N _ { k } = N$ , and the complexity of the self-attention module is of $O ( 2 N C ^ { 2 } + N ^ { 2 } C )$ . The complexity is acceptable with moderate number of object queries.
+
+DETR is an attractive design for object detection, which removes the need for many hand-designed components. However, it also has its own issues. These issues can be mainly attributed to the deficits of Transformer attention in handling image feature maps as key elements: (1) DETR has relatively low performance in detecting small objects. Modern object detectors use high-resolution feature maps to better detect small objects. However, high-resolution feature maps would lead to an unacceptable complexity for the self-attention module in the Transformer encoder of DETR, which has a quadratic complexity with the spatial size of input feature maps. (2) Compared with modern object detectors, DETR requires many more training epochs to converge. This is mainly because the attention modules processing image features are difficult to train. For example, at initialization, the cross-attention modules are almost of average attention on the whole feature maps. While, at the end of the training, the attention maps are learned to be very sparse, focusing only on the object extremities. It seems that DETR requires a long training schedule to learn such significant changes in the attention maps.
+
+![](images/6209356f3470f2dbb49a05da740dda03f5e4a9407234771d816fbe84313abc9b.jpg)  
+Figure 2: Illustration of the proposed deformable attention module.
+
+# 4 METHOD
+
+# 4.1 DEFORMABLE TRANSFORMERS FOR END-TO-END OBJECT DETECTION
+
+Deformable Attention Module. The core issue of applying Transformer attention on image feature maps is that it would look over all possible spatial locations. To address this, we present a deformable attention module. Inspired by deformable convolution (Dai et al., 2017; Zhu et al., 2019b), the deformable attention module only attends to a small set of key sampling points around a reference point, regardless of the spatial size of the feature maps, as shown in Fig. 2. By assigning only a small fixed number of keys for each query, the issues of convergence and feature spatial resolution can be mitigated.
+
+Given an input feature map $\pmb { x } \in \mathbb { R } ^ { C \times H \times W }$ , let $q$ index a query element with content feature $z _ { q }$ and a 2-d reference point $p _ { q }$ , the deformable attention feature is calculated by
+
+$$
+{ \mathrm { D e f o r m A t t n } } ( z _ { q } , p _ { q } , \mathbf { x } ) = \sum _ { m = 1 } ^ { M } W _ { m } { \big [ } \sum _ { k = 1 } ^ { K } A _ { m q k } \cdot W _ { m } ^ { \prime } { \mathbf { x } } { \big ( } p _ { q } + \Delta p _ { m q k } { \big ) } { \big ] } ,
+$$
+
+where $m$ indexes the attention head, $k$ indexes the sampled keys, and $K$ is the total sampled key number $( K \ll H W )$ . $\Delta { p } _ { m q k }$ and $A _ { m q k }$ denote the sampling offset and attention weight of the $k ^ { \mathrm { { t h } } }$ sampling point in the $m ^ { \mathrm { t h } }$ attention head, respectively. The scalar attention weight lies in the range unconstraine $[ 0 , 1 ]$ , normge. As $\begin{array} { r } { \sum _ { k = 1 } ^ { K } A _ { m q k } = 1 } \end{array}$ . bi $\Delta { p } _ { m q k } \in \mathbb { R } ^ { 2 }$ are of 2-d real numbers withtion is applied as in Dai et al. ${ \pmb p } _ { q } + \Delta { \pmb p } _ { m q k }$ (2017) in computing $\pmb { x } ( \pmb { p } _ { q } + \Delta \pmb { p } _ { m q k } )$ . Both $\Delta { { p } _ { m q k } }$ and $A _ { m q k }$ are obtained via linear projection over the query feature $z _ { q }$ . In implementation, the query feature $z _ { q }$ is fed to a linear projection operator of $3 M K$ channels, where the first $2 M K$ channels encode the sampling offsets $\Delta { p } _ { m q k }$ , and the remaining $M K$ channels are fed to a softmax operator to obtain the attention weights $A _ { m q k }$ .
+
+The deformable attention module is designed for processing convolutional feature maps as key elements. Let $N _ { q }$ be the number of query elements, when $M K$ is relatively small, the complexity of the deformable attention module is of $O ( 2 N _ { q } C ^ { 2 } + \operatorname* { m i n } ( H W C ^ { 2 } , N _ { q } K C ^ { 2 } ) )$ (See Appendix A.1 for details). When it is applied in DETR encoder, where $N _ { q } = H W$ , the complexity becomes $O ( H W C ^ { 2 } )$ , which is of linear complexity with the spatial size. When it is applied as the cross-attention modules in DETR decoder, where $N _ { q } = N$ $N$ is the number of object queries), the complexity becomes $O ( N K C ^ { 2 } )$ , which is irrelevant to the spatial size $H W$ .
+
+Multi-scale Deformable Attention Module. Most modern object detection frameworks benefit from multi-scale feature maps (Liu et al., 2020). Our proposed deformable attention module can be naturally extended for multi-scale feature maps.
+
+Let $\{ { \pmb x } ^ { l } \} _ { l = 1 } ^ { L }$ be the input multi-scale feature maps, where $\pmb { x } ^ { l } \in \mathbb { R } ^ { C \times H _ { l } \times W _ { l } }$ . Let $\hat { p } _ { q } \in [ 0 , 1 ] ^ { 2 }$ be the normalized coordinates of the reference point for each query element $q$ , then the multi-scale deformable attention module is applied as
+
+$$
+\mathrm { M S D e f o r m A t t n } ( z _ { q } , \hat { p } _ { q } , \{ x ^ { l } \} _ { l = 1 } ^ { L } ) = \sum _ { m = 1 } ^ { M } W _ { m } \big [ \sum _ { l = 1 } ^ { L } \sum _ { k = 1 } ^ { K } A _ { m l q k } \cdot W _ { m } ^ { \prime } x ^ { l } \big ( \phi _ { l } ( \hat { p } _ { q } ) + \Delta p _ { m l q k } \big ) \big ] ,
+$$
+
+where $m$ indexes the attention head, $l$ indexes the input feature level, and $k$ indexes the sampling point. $\Delta { { p } _ { m l q k } }$ and $A _ { m l q k }$ denote the sampling offset and attention weight of the $k ^ { \mathrm { { t h } } }$ sampling point in the $l ^ { \mathrm { t h } }$ feature level and the $m ^ { \mathrm { t h } }$ attention head, respectively. The scalar attention weight $A _ { m l q k }$ is normalized by $\begin{array} { r } { \sum _ { l = 1 } ^ { L } \sum _ { k = 1 } ^ { K } A _ { m l q k } = 1 } \end{array}$ . Here, we use normalized coordinates $\hat { p } _ { q } \in [ 0 , 1 ] ^ { 2 }$ for the clarity of scale formulation, in which the normalized coordinates $( 0 , 0 )$ and $( 1 , 1 )$ indicate the top-left and the bottom-right image corners, respectively. Function $\phi _ { l } ( \hat { \pmb { p } } _ { q } )$ in Equation 3 re-scales the normalized coordinates $\hat { p } _ { q }$ to the input feature map of the $l$ -th level. The multi-scale deformable attention is very similar to the previous single-scale version, except that it samples $L K$ points from multi-scale feature maps instead of $K$ points from single-scale feature maps.
+
+The proposed attention module will degenerate to deformable convolution (Dai et al., 2017), when $L = 1$ , $K = 1$ , and $W _ { m } ^ { \prime } \in \mathbb { R } ^ { C _ { v } \times C }$ is fixed as an identity matrix. Deformable convolution is designed for single-scale inputs, focusing only on one sampling point for each attention head. However, our multi-scale deformable attention looks over multiple sampling points from multi-scale inputs. The proposed (multi-scale) deformable attention module can also be perceived as an efficient variant of Transformer attention, where a pre-filtering mechanism is introduced by the deformable sampling locations. When the sampling points traverse all possible locations, the proposed attention module is equivalent to Transformer attention.
+
+Deformable Transformer Encoder. We replace the Transformer attention modules processing feature maps in DETR with the proposed multi-scale deformable attention module. Both the input and output of the encoder are of multi-scale feature maps with the same resolutions. In encoder, we extract multi-scale feature maps $\{ \pmb { x } ^ { l } \} _ { l = 1 } ^ { L - 1 }$ $ { \boldsymbol { L } } = 4 )$ from the output feature maps of stages $C _ { 3 }$ through $C _ { 5 }$ in ResNet (He et al., 2016) (transformed by a $1 \times 1$ convolution), where $C _ { l }$ is of resolution $2 ^ { l }$ lower than the input image. The lowest resolution feature map $\pmb { x } ^ { L }$ is obtained via a $3 \times 3$ stride 2 convolution on the final $C _ { 5 }$ stage, denoted as $C _ { 6 }$ . All the multi-scale feature maps are of $C = 2 5 6$ channels. Note that the top-down structure in FPN (Lin et al., 2017a) is not used, because our proposed multi-scale deformable attention in itself can exchange information among multi-scale feature maps. The constructing of multi-scale feature maps are also illustrated in Appendix A.2. Experiments in Section 5.2 show that adding FPN will not improve the performance.
+
+In application of the multi-scale deformable attention module in encoder, the output are of multiscale feature maps with the same resolutions as the input. Both the key and query elements are of pixels from the multi-scale feature maps. For each query pixel, the reference point is itself. To identify which feature level each query pixel lies in, we add a scale-level embedding, denoted as $e _ { l }$ , to the feature representation, in addition to the positional embedding. Different from the positional embedding with fixed encodings, the scale-level embedding $\{ e _ { l } \} _ { l = 1 } ^ { L ^ { - } }$ are randomly initialized and jointly trained with the network.
+
+Deformable Transformer Decoder. There are cross-attention and self-attention modules in the decoder. The query elements for both types of attention modules are of object queries. In the crossattention modules, object queries extract features from the feature maps, where the key elements are of the output feature maps from the encoder. In the self-attention modules, object queries interact with each other, where the key elements are of the object queries. Since our proposed deformable attention module is designed for processing convolutional feature maps as key elements, we only replace each cross-attention module to be the multi-scale deformable attention module, while leaving the self-attention modules unchanged. For each object query, the 2-d normalized coordinate of the reference point $\hat { p } _ { q }$ is predicted from its object query embedding via a learnable linear projection followed by a sigmoid function.
+
+Because the multi-scale deformable attention module extracts image features around the reference point, we let the detection head predict the bounding box as relative offsets w.r.t. the reference point to further reduce the optimization difficulty. The reference point is used as the initial guess of the box center. The detection head predicts the relative offsets w.r.t. the reference point. Check Appendix A.3 for the details. In this way, the learned decoder attention will have strong correlation with the predicted bounding boxes, which also accelerates the training convergence.
+
+By replacing Transformer attention modules with deformable attention modules in DETR, we establish an efficient and fast converging detection system, dubbed as Deformable DETR (see Fig. 1).
+
+# 4.2 ADDITIONAL IMPROVEMENTS AND VARIANTS FOR DEFORMABLE DETR
+
+Deformable DETR opens up possibilities for us to exploit various variants of end-to-end object detectors, thanks to its fast convergence, and computational and memory efficiency. Due to limited space, we only introduce the core ideas of these improvements and variants here. The implementation details are given in Appendix A.4.
+
+Iterative Bounding Box Refinement. This is inspired by the iterative refinement developed in optical flow estimation (Teed & Deng, 2020). We establish a simple and effective iterative bounding box refinement mechanism to improve detection performance. Here, each decoder layer refines the bounding boxes based on the predictions from the previous layer.
+
+Two-Stage Deformable DETR. In the original DETR, object queries in the decoder are irrelevant to the current image. Inspired by two-stage object detectors, we explore a variant of Deformable DETR for generating region proposals as the first stage. The generated region proposals will be fed into the decoder as object queries for further refinement, forming a two-stage Deformable DETR.
+
+In the first stage, to achieve high-recall proposals, each pixel in the multi-scale feature maps would serve as an object query. However, directly setting object queries as pixels will bring unacceptable computational and memory cost for the self-attention modules in the decoder, whose complexity grows quadratically with the number of queries. To avoid this problem, we remove the decoder and form an encoder-only Deformable DETR for region proposal generation. In it, each pixel is assigned as an object query, which directly predicts a bounding box. Top scoring bounding boxes are picked as region proposals. No NMS is applied before feeding the region proposals to the second stage.
+
+# 5 EXPERIMENT
+
+Dataset. We conduct experiments on COCO 2017 dataset (Lin et al., 2014). Our models are trained on the train set, and evaluated on the val set and test-dev set.
+
+Implementation Details. ImageNet (Deng et al., 2009) pre-trained ResNet-50 (He et al., 2016) is utilized as the backbone for ablations. Multi-scale feature maps are extracted without FPN (Lin et al., 2017a). $M = 8$ and $K = 4$ are set for deformable attentions by default. Parameters of the deformable Transformer encoder are shared among different feature levels. Other hyper-parameter setting and training strategy mainly follow DETR (Carion et al., 2020), except that Focal Loss (Lin et al., 2017b) with loss weight of 2 is used for bounding box classification, and the number of object queries is increased from 100 to 300. We also report the performance of DETR-DC5 with these modifications for a fair comparison, denoted as DETR- ${ \mathrm { . D C } } 5 ^ { + }$ . By default, models are trained for 50 epochs and the learning rate is decayed at the 40-th epoch by a factor of 0.1. Following DETR(Carion et al., 2020), we train our models using Adam optimizer (Kingma & Ba, 2015) with base learning rate of $2 \times 1 0 ^ { - 4 }$ , $\beta _ { 1 } = 0 . 9$ , $\beta _ { 2 } = 0 . 9 9 9$ , and weight decay of $1 0 ^ { - 4 }$ . Learning rates of the linear projections, used for predicting object query reference points and sampling offsets, are multiplied by a factor of 0.1. Run time is evaluated on NVIDIA Tesla V100 GPU.
+
+# 5.1 COMPARISON WITH DETR
+
+As shown in Table 1, compared with Faster $\mathrm { R - C N N + F P N }$ , DETR requires many more training epochs to converge, and delivers lower performance at detecting small objects. Compared with
+
+DETR, Deformable DETR achieves better performance (especially on small objects) with $1 0 \times$ less training epochs. Detailed convergence curves are shown in Fig. 3. With the aid of iterative bounding box refinement and two-stage paradigm, our method can further improve the detection accuracy.
+
+Our proposed Deformable DETR has on par FLOPs with Faster $\mathrm { R - C N N + F P N }$ and DETR-DC5. But the runtime speed is much faster $_ { ( 1 . 6 \times ) }$ than DETR-DC5, and is just $2 5 \%$ slower than Faster ${ \mathrm { R - C N N } } + { \mathrm { F P N } }$ . The speed issue of DETR-DC5 is mainly due to the large amount of memory access in Transformer attention. Our proposed deformable attention can mitigate this issue, at the cost of unordered memory access. Thus, it is still slightly slower than traditional convolution.
+
+Table 1: Comparision of Deformable DETR with DETR on COCO 2017 val set. DETR-DC5+ denotes DETR-DC5 with Focal Loss and 300 object queries.   
+
+<table><tr><td>Method</td><td>Epochs</td><td>AP</td><td>AP50 AP75 APsAPm APL</td><td></td><td></td><td></td><td></td><td>params FLOPs</td><td>Training GPU hours</td><td>Inference FPS</td></tr><tr><td>Faster R-CNN + FPN</td><td>109</td><td>42.0</td><td>62.1</td><td>45.5</td><td>26.6</td><td>45.4</td><td>53.4 42M</td><td>180G</td><td>380</td><td>26</td></tr><tr><td>DETR</td><td>500</td><td>42.0</td><td>62.4</td><td>44.2</td><td>20.5</td><td>45.8 61.1</td><td>41M</td><td>86G</td><td>2000</td><td>28</td></tr><tr><td>DETR-DC5</td><td>500</td><td>43.3</td><td>63.1</td><td>45.9</td><td>22.5</td><td>47.3 61.1</td><td>41M</td><td>187G</td><td>7000</td><td>12</td></tr><tr><td>DETR-DC5</td><td>50</td><td>35.3</td><td>55.7</td><td>36.8</td><td>15.2</td><td>37.5 53.6</td><td>41M</td><td>187G</td><td>700</td><td>12</td></tr><tr><td>DETR-DC5+</td><td>50</td><td>36.2</td><td>57.0</td><td>37.4</td><td>16.3</td><td>39.2 53.9</td><td>41M</td><td>187G</td><td>700</td><td>12</td></tr><tr><td>Deformable DETR</td><td>50</td><td>43.8</td><td>62.6</td><td>47.7</td><td>26.4</td><td>47.1</td><td>58.0 40M</td><td>173G</td><td>325</td><td>19</td></tr><tr><td>+ iterative bounding box refinement</td><td>50</td><td>45.4</td><td>64.7</td><td>49.0</td><td>26.8</td><td>48.3 61.7</td><td>40M</td><td>173G</td><td>325</td><td>19</td></tr><tr><td>++ two-stage Deformable DETR</td><td>50</td><td>46.2</td><td>65.2</td><td>50.0</td><td>28.8</td><td>49.2 61.7</td><td>40M</td><td>173G</td><td>340</td><td>19</td></tr></table>
+
+![](images/1415181d26f6e673cd3ac6c7579812e3267ed274df14fd0cace178f66918f9a8.jpg)  
+Figure 3: Convergence curves of Deformable DETR and DETR-DC5 on COCO 2017 val set. For Deformable DETR, we explore different training schedules by varying the epochs at which the learning rate is reduced (where the AP score leaps).
+
+# 5.2 ABLATION STUDY ON DEFORMABLE ATTENTION
+
+Table 2 presents ablations for various design choices of the proposed deformable attention module. Using multi-scale inputs instead of single-scale inputs can effectively improve detection accuracy with $\bar { 1 } . 7 \%$ AP, especially on small objects with $2 . 9 \%$ $\mathsf { A P } _ { \mathsf { S } }$ . Increasing the number of sampling points $K$ can further improve $0 . 9 \%$ AP. Using multi-scale deformable attention, which allows information exchange among different scale levels, can bring additional $1 . 5 \%$ improvement in AP. Because the cross-level feature exchange is already adopted, adding FPNs will not improve the performance. When multi-scale attention is not applied, and $K = 1$ , our (multi-scale) deformable attention module degenerates to deformable convolution, delivering noticeable lower accuracy.
+
+# 5.3 COMPARISON WITH STATE-OF-THE-ART METHODS
+
+Table 3 compares the proposed method with other state-of-the-art methods. Iterative bounding box refinement and two-stage mechanism are both utilized by our models in Table 3. With ResNet-101 and ResNeXt-101 (Xie et al., 2017), our method achieves 48.7 AP and 49.0 AP without bells and whistles, respectively. By using ResNeXt-101 with DCN (Zhu et al., 2019b), the accuracy rises to 50.1 AP. With additional test-time augmentations, the proposed method achieves 52.3 AP.
+
+Table 2: Ablations for deformable attention on COCO 2017 val set. “MS inputs” indicates using multi-scale inputs. “MS attention” indicates using multi-scale deformable attention. $K$ is the number of sampling points for each attention head on each feature level.   
+
+<table><tr><td></td><td>MS inputs MS attention K</td><td></td><td>FPNs</td><td>AP AP50</td><td>AP75</td><td>APs</td><td>APM</td><td>APL</td></tr><tr><td>√</td><td>1</td><td>4</td><td>FPN (Lin et al.,2017a)</td><td>43.8 62.6</td><td>47.8</td><td>26.5</td><td>47.3</td><td>58.1</td></tr><tr><td>√</td><td>√</td><td>4</td><td>BiFPN (Tan et al.,2020)</td><td>43.9 62.5</td><td>47.7</td><td>25.6</td><td>47.4</td><td>57.7</td></tr><tr><td></td><td></td><td>1</td><td></td><td>39.7 60.1</td><td>42.4</td><td>21.2</td><td>44.3</td><td>56.0</td></tr><tr><td>√</td><td></td><td>1</td><td>w/o</td><td>41.4 60.9</td><td>44.9</td><td>24.1</td><td>44.6</td><td>56.1</td></tr><tr><td>&lt;</td><td></td><td>4</td><td></td><td>42.3 61.4</td><td>46.0</td><td>24.8</td><td>45.1</td><td>56.3</td></tr><tr><td>√</td><td>√</td><td>4</td><td></td><td>43.8 62.6</td><td>47.7</td><td>26.4</td><td>47.1</td><td>58.0</td></tr></table>
+
+Table 3: Comparison of Deformable DETR with state-of-the-art methods on COCO 2017 test-dev set. “TTA” indicates test-time augmentations including horizontal flip and multi-scale testing.   
+
+<table><tr><td>Method</td><td>Backbone</td><td>TTA</td><td>AP</td><td>AP50</td><td>AP75</td><td>APs</td><td>APM APL</td></tr><tr><td>FCOS (Tian et al.,2019)</td><td>ResNeXt-101</td><td></td><td>44.7 64.1</td><td></td><td>48.4</td><td>27.6 47.5</td><td>55.6</td></tr><tr><td>ATSS (Zhang et al., 2020)</td><td>ResNeXt-101 +DCN</td><td>√ 50.7</td><td>68.9</td><td>56.3</td><td>33.2</td><td>52.9</td><td>62.4</td></tr><tr><td>TSD (Song et al.,2020)</td><td>SENet154 + DCN</td><td>√ 51.2</td><td>71.9</td><td>56.0</td><td>33.8</td><td>54.8</td><td>64.2</td></tr><tr><td>EfficientDet-D7 (Tan et al.,2020)</td><td>EfficientNet-B6</td><td>52.2</td><td>71.4</td><td>56.3</td><td>-</td><td>1</td><td>1</td></tr><tr><td>Deformable DETR</td><td>ResNet-50</td><td>46.9</td><td>66.4</td><td>50.8</td><td>27.7</td><td>49.7</td><td>59.9</td></tr><tr><td>Deformable DETR</td><td>ResNet-101</td><td>48.7</td><td>68.1</td><td>52.9</td><td>29.1</td><td>51.5</td><td>62.0</td></tr><tr><td>Deformable DETR</td><td>ResNeXt-101</td><td>49.0</td><td>68.5</td><td>53.2</td><td>29.7</td><td>51.7</td><td>62.8</td></tr><tr><td>Deformable DETR</td><td>ResNeXt-101+DCN</td><td>50.1</td><td>69.7</td><td>54.6</td><td>30.6</td><td>52.8</td><td>64.7</td></tr><tr><td>Deformable DETR</td><td>ResNeXt-101+DCN</td><td>52.3 厂</td><td>71.9</td><td>58.1</td><td></td><td>34.4 54.4</td><td>65.6</td></tr></table>
+
+# 6 CONCLUSION
+
+Deformable DETR is an end-to-end object detector, which is efficient and fast-converging. It enables us to explore more interesting and practical variants of end-to-end object detectors. At the core of Deformable DETR are the (multi-scale) deformable attention modules, which is an efficient attention mechanism in processing image feature maps. We hope our work opens up new possibilities in exploring end-to-end object detection.
+
+# ACKNOWLEDGMENTS
+
+The work is supported by the National Key R&D Program of China (2020AAA0105200), Beijing Academy of Artificial Intelligence, and the National Natural Science Foundation of China under grand No.U19B2044 and No.61836011.
+
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+
+# A APPENDIX
+
+# A.1 COMPLEXITY FOR DEFORMABLE ATTENTION
+
+Supposes the number of query elements is $N _ { q }$ , in the deformable attention module (see Equation 2), the complexity for calculating the sampling coordinate offsets $\Delta { p } _ { m q k }$ and attention weights $A _ { m q k }$ is of $O ( 3 N _ { q } C M K )$ . Given the sampling coordinate offsets and attention weights, the complexity of computing Equation 2 is $O ( N _ { q } C ^ { 2 } + N _ { q } K C ^ { 2 } + 5 N _ { q } K C )$ , where the factor of 5 in $5 N _ { q } K C$ is because of bilinear interpolation and the weighted sum in attention. On the other hand, we can also calculate $\pmb { W } _ { m } ^ { \prime } \pmb { x }$ before sampling, as it is independent to query, and the complexity of computing Equation 2 will become as $O ( \tilde { N _ { q } } C ^ { 2 ^ { - } } { + } H W C ^ { 2 } { + } \tilde { 5 } N _ { q } K C )$ . So the overall complexity of deformable attention is $O ( N _ { q } C ^ { 2 } + \operatorname * { m i n } ( H W C ^ { 2 } , N _ { q } K C ^ { 2 } ) + 5 N _ { q } K C + 3 N _ { q } C M K )$ . In our experiments, $M = 8 , K \le \dot { 4 }$ and $C \ = \ 2 5 6$ by default, thus $5 K + 3 M K < C$ and the complexity is of $O ( 2 N _ { q } C ^ { 2 } + \operatorname* { m i n } ( { H W C ^ { 2 } } , N _ { q } K C ^ { 2 } ) )$ ).
+
+# A.2 CONSTRUCTING MULT-SCALE FEATURE MAPS FOR DEFORMABLE DETR
+
+As discussed in Section 4.1 and illustrated in Figure 4, the input multi-scale feature maps of the encoder $\{ \pmb { x } ^ { l } \} _ { l = 1 } ^ { L - 1 }$ $( L = 4 )$ are extracted from the output feature maps of stages $C _ { 3 }$ through $C _ { 5 }$ in ResNet (He et al., 2016) (transformed by a $1 \times 1$ convolution). The lowest resolution feature map $\pmb { x } ^ { L }$ is obtained via a $3 \times 3$ stride 2 convolution on the final $C _ { 5 }$ stage. Note that FPN (Lin et al., 2017a) is not used, because our proposed multi-scale deformable attention in itself can exchange information among multi-scale feature maps.
+
+![](images/5ad43c71e284180418b84ede6789b3d619354a9c51df17febce271ec5faa561c.jpg)  
+Figure 4: Constructing mult-scale feature maps for Deformable DETR.
+
+# A.3 BOUNDING BOX PREDICTION IN DEFORMABLE DETR
+
+Since the multi-scale deformable attention module extracts image features around the reference point, we design the detection head to predict the bounding box as relative offsets w.r.t. the reference point to further reduce the optimization difficulty. The reference point is used as the initial guess of the box center. The detection head predicts the relative offsets w.r.t. the reference point $\hat { p } _ { q } =$ $( \hat { p } _ { q x } , \hat { p } _ { q y } )$ , i.e., $\hat { b } _ { q } = \{ \sigma \left( b _ { q x } + \sigma ^ { - 1 } ( \hat { p } _ { q x } ) \right) , \sigma \left( b _ { q y } + \sigma ^ { - 1 } ( \hat { p } _ { q y } ) \right) , \sigma ( b _ { q w } ) , \sigma ( b _ { q h } ) \}$ , where $b _ { q \{ x , y , w , h \} } \in$ $\mathbb { R }$ are predicted by the detection head. $\sigma$ and $\sigma ^ { - 1 }$ denote the sigmoid and the inverse sigmoid function, respectively. The usage of $\sigma$ and $\sigma ^ { - 1 }$ is to ensure $\hat { b }$ is of normalized coordinates, as $\hat { b } _ { q } \in [ 0 , 1 ] ^ { 4 }$ . In this way, the learned decoder attention will have strong correlation with the predicted bounding boxes, which also accelerates the training convergence.
+
+# A.4 MORE IMPLEMENTATION DETAILS
+
+Iterative Bounding Box Refinement. Here, each decoder layer refines the bounding boxes based on the predictions from the previous layer. Suppose there are $D$ number of decoder layers (e.g., $D = 6$ ), given a normalized bounding box $\hat { b } _ { q } ^ { d - 1 }$ predicted by the $( d - 1 )$ -th decoder layer, the $d$ -th
+
+decoder layer refines the box as
+
+ˆb $\begin{array} { r } { \ d _ { q } ^ { d } = \{ \sigma ( \Delta b _ { q x } ^ { d } + \sigma ^ { - 1 } ( \hat { b } _ { q x } ^ { d - 1 } ) ) , \sigma ( \Delta b _ { q y } ^ { d } + \sigma ^ { - 1 } ( \hat { b } _ { q y } ^ { d - 1 } ) ) , \sigma ( \Delta b _ { q w } ^ { d } + \sigma ^ { - 1 } ( \hat { b } _ { q w } ^ { d - 1 } ) ) , \sigma ( \Delta b _ { q h } ^ { d } + \sigma ^ { - 1 } ( \hat { b } _ { q h } ^ { d - 1 } ) ) \} , } \end{array}$ where $d \in \{ 1 , 2 , . . . , D \}$ , $\Delta b _ { q \{ x , y , w , h \} } ^ { d } \ \in \ \mathbb { R }$ are predicted at the $d$ -th decoder layer. Prediction heads for different decoder layers do not share parameters. The initial box is set as $\hat { b } _ { q x } ^ { 0 } = \hat { p } _ { q x }$ , $\hat { b } _ { q y } ^ { 0 } = \hat { p } _ { q y }$ , $\hat { b } _ { q w } ^ { 0 } = 0 . 1$ , and $\hat { b } _ { q h } ^ { 0 } = 0 . 1$ . The system is robust to the choice of $b _ { q w } ^ { 0 }$ and $b _ { q h } ^ { 0 }$ . We tried setting them as 0.05, 0.1, 0.2, 0.5, and achieved similar performance. To stabilize training, similar to Teed & Deng (2020), the gradients only back propagate through bdq{x,y,w,h}, and are blocked at $\sigma ^ { - 1 } ( \hat { b } _ { q \{ x , y , w , h \} } ^ { d - 1 } ) .$ .
+
+In iterative bounding box refinement, for the $d$ -th decoder layer, we sample key elements respective to the box $\hat { b } _ { q } ^ { d - 1 }$ predicted from the $( d - 1 )$ -th decoder layer. For Equation 3 in the cross-attention module of the $d$ -th decoder layer, $( \hat { b } _ { q x } ^ { d - 1 } , \hat { b } _ { q y } ^ { d - 1 } )$ serves as the new reference point. The sampling offset $\Delta { { p } _ { m l q k } }$ is also modulated by the box size, as $( \Delta p _ { m l q k x } \hat { b } _ { q w } ^ { d - 1 } , \Delta p _ { m l q k y } \hat { b } _ { q h } ^ { d - 1 } )$ . Such modifications make the sampling locations related to the center and size of previously predicted boxes.
+
+Two-Stage Deformable DETR. In the first stage, given the output feature maps of the encoder, a detection head is applied to each pixel. The detection head is of a 3-layer FFN for bounding box regression, and a linear projection for bounding box binary classification (i.e., foreground and background), respectively. Let $i$ index a pixel from feature level $l _ { i } \in \{ 1 , 2 , . . . , L \}$ with 2-d normalized coordinates $\bar { \pmb { p } } _ { i } = ( \hat { p _ { i x } } , \hat { p } _ { i y } ) \in [ 0 , 1 ] ^ { 2 }$ , its corresponding bounding box is predicted by
+
+$$
+\begin{array} { r } { \nu _ { i } = \{ \sigma ( \Delta b _ { i x } + \sigma ^ { - 1 } ( \hat { p } _ { i x } ) ) , \sigma ( \Delta b _ { i y } + \sigma ^ { - 1 } ( \hat { p } _ { i y } ) ) , \sigma ( \Delta b _ { i w } + \sigma ^ { - 1 } ( 2 ^ { l _ { i } - 1 } s ) ) , \sigma ( \Delta b _ { i h } + \sigma ^ { - 1 } ( 2 ^ { l _ { i } - 1 } s ) ) \} , } \end{array}
+$$
+
+where the base object scale $s$ is set as 0.05, $\Delta b _ { i \{ x , y , w , h \} } \in \mathbb { R }$ are predicted by the bounding box regression branch. The Hungarian loss in DETR is used for training the detection head.
+
+Given the predicted bounding boxes in the first stage, top scoring bounding boxes are picked as region proposals. In the second stage, these region proposals are fed into the decoder as initial boxes for the iterative bounding box refinement, where the positional embeddings of object queries are set as positional embeddings of region proposal coordinates.
+
+Initialization for Multi-scale Deformable Attention. In our experiments, the number of attention heads is set as $M \ = \ 8$ . In multi-scale deformable attention modules, $W _ { m } ^ { \prime } \ \in \ \mathbb { R } ^ { C _ { v } \times C }$ and $W _ { m } ~ \in ~ \mathbb { R } ^ { C \times C _ { v } }$ are randomly initialized. Weight parameters of the linear projection for predicting $A _ { m l q k }$ and $\Delta { { p } _ { m l q k } }$ are initialized to zero. Bias parameters of the linear projection are initialized to make $\begin{array} { r } { A _ { m l q k } = \frac { 1 } { L K } } \end{array}$ and $\{ \Delta \pmb { p } _ { 1 l q k } = ( - k , - k ) , \Delta \pmb { p } _ { 2 l q k } = ( - k , 0 ) , \Delta \pmb { p } _ { 3 l q k } =$ ( $\begin{array} { r } { - k , k ) , \Delta p _ { 4 l q k } = ( 0 , - k ) , \Delta p _ { 5 l q k } = ( 0 , k ) , \Delta p _ { 6 l q k } = ( k , - k ) , \Delta p _ { 7 l q k } = ( k , 0 ) , \Delta p _ { 8 l q k } = ( k , 0 ) , \Delta p _ { 9 l q k } = ( k , 0 ) , } \end{array}$ $( k , k ) \}$ $( k \in \{ \bar { 1 } , 2 , . . . K \} ,$ ) at initialization.
+
+For iterative bounding box refinement, the initialized bias parameters for $\Delta { { p } _ { m l q k } }$ prediction in the decoder are further multiplied with $\textstyle { \frac { 1 } { 2 K } }$ , so that all the sampling points at initialization are within the corresponding bounding boxes predicted from the previous decoder layer.
+
+# A.5 WHAT DEFORMABLE DETR LOOKS AT?
+
+For studying what Deformable DETR looks at to give final detection result, we draw the gradient norm of each item in final prediction (i.e., x/y coordinate of object center, width/height of object bounding box, category score of this object) with respect to each pixel in the image, as shown in Fig. 5. According to Taylor’s theorem, the gradient norm can reflect how much the output would be changed relative to the perturbation of the pixel, thus it could show us which pixels the model mainly relys on for predicting each item.
+
+The visualization indicates that Deformable DETR looks at extreme points of the object to determine its bounding box, which is similar to the observation in DETR (Carion et al., 2020). More concretely, Deformable DETR attends to left/right boundary of the object for x coordinate and width, and top/bottom boundary for y coordinate and height. Meanwhile, different to DETR (Carion et al., 2020), our Deformable DETR also looks at pixels inside the object for predicting its category.
+
+![](images/a9fe12c309c2d1336b9bf0f4799115b0dd2a918d29465d4a0d7f3661775e6f3e.jpg)  
+Figure 5: The gradient norm of each item (coordinate of object center $( x , y )$ , width/height of object bounding box $w / h$ , category score $c$ of this object) in final detection result with respect to each pixel in input image $I$ .
+
+# A.6 VISUALIZATION OF MULTI-SCALE DEFORMABLE ATTENTION
+
+For better understanding learned multi-scale deformable attention modules, we visualize sampling points and attention weights of the last layer in encoder and decoder, as shown in Fig. 6. For readibility, we combine the sampling points and attention weights from feature maps of different resolutions into one picture.
+
+Similar to DETR (Carion et al., 2020), the instances are already separated in the encoder of Deformable DETR. While in the decoder, our model is focused on the whole foreground instance instead of only extreme points as observed in DETR (Carion et al., 2020). Combined with the visualization of $\| \frac { \partial c } { \partial I } \|$ in Fig. 5, we can guess the reason is that our Deformable DETR needs not only extreme points but also interior points to detemine object category. The visualization also demonstrates that the proposed multi-scale deformable attention module can adapt its sampling points and attention weights according to different scales and shapes of the foreground object.
+
+![](images/92f45f16c4c4f54c269c75a44de5084118b752a87da461c186942903ac8cc2b2.jpg)  
+Figure 6: Visualization of multi-scale deformable attention. For readibility, we draw the sampling points and attention weights from feature maps of different resolutions in one picture. Each sampling point is marked as a filled circle whose color indicates its correspoinding attention weight. The reference point is shown as green cross marker, which is also equivalent to query point in encoder. In decoder, the predicted bounding box is shown as a green rectangle and the category and confidence score are texted just above it.
+
+# A.7 NOTATIONS
+
+Table 4: Lookup table for notations in the paper.   
+
+<table><tr><td>Notation</td><td>Description</td></tr><tr><td>m</td><td>indexforattentionhead</td></tr><tr><td>1</td><td>index for feature level of key element</td></tr><tr><td>q</td><td>index for query element</td></tr><tr><td>k</td><td>index for key element</td></tr><tr><td>Nq</td><td>number of query elements</td></tr><tr><td>Nk</td><td>number of key elements</td></tr><tr><td>M</td><td>number of attention heads</td></tr><tr><td>L</td><td>number of input feature levels</td></tr><tr><td>K</td><td>number of sampled keys in each feature level for each attention head</td></tr><tr><td>C</td><td>input feature dimension</td></tr><tr><td>C</td><td>feature dimension at each attention head</td></tr><tr><td>H</td><td>height of input feature map</td></tr><tr><td>W</td><td>width of input feature map</td></tr><tr><td>H</td><td>height of input feature map of lth feature level</td></tr><tr><td>Wl</td><td>width of input feature map of lth feature level</td></tr><tr><td>Amqk</td><td>attention weight of qth query to kth key at mth head</td></tr><tr><td>Amlqk</td><td> attention weight of qth query to kth key in lth feature level at mth head</td></tr><tr><td>2q</td><td>input feature of qth query</td></tr><tr><td>Pq</td><td>2-d coordinate of reference point for qth query</td></tr><tr><td>pq</td><td> normalized 2-d coordinate of reference point for qth query</td></tr><tr><td>C</td><td>input feature map (input feature of key elements)</td></tr><tr><td>Xk</td><td>input feature of kth key</td></tr><tr><td>xl</td><td>input feature map of lth feature level</td></tr><tr><td>△pmqk</td><td> sampling offset of qth query to kth key at mth head</td></tr><tr><td>△pmlqk</td><td> sampling offset of qth query to kth key in lth feature level at mth head</td></tr><tr><td>Wm</td><td>output projection matrix at mth head</td></tr><tr><td>Um</td><td>input query projection matrix at mth head</td></tr><tr><td>Vm</td><td>input key projection matrix at mth head</td></tr><tr><td>Wm</td><td>input value projection matrix at mth head</td></tr><tr><td>(p)</td><td>unnormalized 2-d coordinate of p in lth feature level</td></tr><tr><td>exp</td><td>exponential function</td></tr><tr><td>0</td><td>sigmoid function</td></tr><tr><td>9-1</td><td>inverse sigmoid function</td></tr></table>

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